----- Otter 3.3, August 2003 ----- The process was started by mccune on gyro.thornwood, Wed Aug 6 14:25:55 2003 The command was "../../bin/otter". The process ID is 5814. set(hyper_res). clear(back_sub). assign(pick_given_ratio,3). assign(max_proofs,3). assign(max_weight,16). clear(print_kept). set(order_history). assign(max_mem,1500). op(800,yfx,->). list(usable). 1 [] -P(x->y)| -P(x)|P(y). end_of_list. list(sos). 2 [] P(x->y-> (y->z-> (x->z))). 3 [] P(-x->x->x). 4 [] P(x-> (-x->y)). end_of_list. list(passive). 5 [] -P(a->a)|$Ans(CN_16). 6 [] -P(b-> (a->b))|$Ans(CN_18). 7 [] -P(a->b->c-> (b->c))|$Ans(CN_19). end_of_list. ======= end of input processing ======= =========== start of search =========== given clause #1: (wt=12) 2 [] P(x->y-> (y->z-> (x->z))). given clause #2: (wt=7) 3 [] P(-x->x->x). given clause #3: (wt=7) 4 [] P(x-> (-x->y)). given clause #4: (wt=10) 10 [hyper,1,4,4] P(-(x-> (-x->y))->z). given clause #5: (wt=16) 8 [hyper,1,2,2] P(x->y-> (z->y)->u-> (z->x->u)). given clause #6: (wt=10) 12 [hyper,1,4,3] P(-(-x->x->x)->y). given clause #7: (wt=11) 9 [hyper,1,2,3] P(x->y-> (-x->x->y)). given clause #8: (wt=10) 24 [hyper,1,9,4] P(-x->x-> (-x->y)). given clause #9: (wt=11) 11 [hyper,1,2,4] P(-x->y->z-> (x->z)). -------- PROOF -------- 35 [binary,34.1,5.1] $Ans(CN_16). ----> UNIT CONFLICT at 0.01 sec ----> 35 [binary,34.1,5.1] $Ans(CN_16). Length of proof is 2. Level of proof is 2. ---------------- PROOF ---------------- 1 [] -P(x->y)| -P(x)|P(y). 2 [] P(x->y-> (y->z-> (x->z))). 3 [] P(-x->x->x). 4 [] P(x-> (-x->y)). 5 [] -P(a->a)|$Ans(CN_16). 11 [hyper,1,2,4] P(-x->y->z-> (x->z)). 34 [hyper,1,11,3] P(x->x). 35 [binary,34.1,5.1] $Ans(CN_16). ------------ end of proof ------------- given clause #10: (wt=4) 34 [hyper,1,11,3] P(x->x). given clause #11: (wt=7) 37 [hyper,1,4,34] P(-(x->x)->y). given clause #12: (wt=10) 33 [hyper,1,11,4] P(x-> (-(-x->y)->z)). given clause #13: (wt=15) 13 [hyper,1,4,2] P(-(x->y-> (y->z-> (x->z)))->u). given clause #14: (wt=10) 39 [hyper,1,4,37] P(-(-(x->x)->y)->z). given clause #15: (wt=11) 29 [hyper,1,8,11] P(x-> -y-> (y-> (x->z))). given clause #16: (wt=9) 52 [hyper,1,11,29] P(x-> (y-> (-x->z))). given clause #17: (wt=13) 14 [hyper,1,4,10] P(-(-(x-> (-x->y))->z)->u). given clause #18: (wt=9) 56 [hyper,1,29,37] P(x-> (-(y->y)->z)). given clause #19: (wt=11) 32 [hyper,1,11,9] P(x-> (-(-x)-> -x->y)). given clause #20: (wt=11) 36 [hyper,1,11,2] P(x-> (y->z-> (-x->z))). given clause #21: (wt=14) 15 [hyper,1,2,10] P(x->y-> (-(z-> (-z->u))->y)). given clause #22: (wt=11) 40 [hyper,1,2,37] P(x->y-> (-(z->z)->y)). given clause #23: (wt=12) 55 [hyper,1,29,39] P(x-> (-(-(y->y)->z)->u)). given clause #24: (wt=12) 57 [hyper,1,29,12] P(x-> (-(-y->y->y)->z)). given clause #25: (wt=16) 16 [hyper,1,8,8] P(x-> (y->z)-> (u->y-> (x-> (u->z)))). given clause #26: (wt=12) 58 [hyper,1,29,10] P(x-> (-(y-> (-y->z))->u)). given clause #27: (wt=12) 61 [hyper,1,11,52] P(x-> (y-> (-(-x->z)->u))). given clause #28: (wt=12) 62 [hyper,1,9,52] P(-x->x-> (y-> (-x->z))). given clause #29: (wt=15) 17 [hyper,1,8,4] P(x->y-> (-(y->z-> (x->z))->u)). given clause #30: (wt=12) 63 [hyper,1,4,52] P(-(x-> (y-> (-x->z)))->u). given clause #31: (wt=12) 75 [hyper,1,4,56] P(-(x-> (-(y->y)->z))->u). given clause #32: (wt=13) 19 [hyper,1,4,12] P(-(-(-x->x->x)->y)->z). given clause #33: (wt=16) 18 [hyper,1,8,2] P(x->y-> (x->z->u-> (y->z->u))). given clause #34: (wt=13) 25 [hyper,1,9,3] P(-(-x->x)-> (-x->x)->x). given clause #35: (wt=13) 27 [hyper,1,4,24] P(-(-x->x-> (-x->y))->z). given clause #36: (wt=13) 38 [hyper,1,9,37] P(-(-(x->x))-> -(x->x)->y). given clause #37: (wt=14) 20 [hyper,1,2,12] P(x->y-> (-(-z->z->z)->y)). given clause #38: (wt=13) 42 [hyper,1,11,33] P(x-> (-(-(-x->y)->z)->u)). given clause #39: (wt=13) 43 [hyper,1,9,33] P(-x->x-> (-(-x->y)->z)). given clause #40: (wt=13) 44 [hyper,1,4,33] P(-(x-> (-(-x->y)->z))->u). given clause #41: (wt=16) 21 [hyper,1,9,9] P(-(x->y)-> (x->y)-> (-x->x->y)). given clause #42: (wt=13) 46 [hyper,1,33,37] P(-(-(-(x->x)->y)->z)->u). given clause #43: (wt=13) 64 [hyper,1,2,52] P(x-> (-y->z)->u-> (y->u)). given clause #44: (wt=12) 122 [hyper,1,64,4] P(x-> (-(y-> (-x->z))->u)). given clause #45: (wt=14) 22 [hyper,1,4,9] P(-(x->y-> (-x->x->y))->z). given clause #46: (wt=13) 76 [hyper,1,2,56] P(-(x->x)->y->z-> (u->z)). given clause #47: (wt=6) 132 [hyper,1,76,3] P(x-> (y->y)). given clause #48: (wt=9) 131 [hyper,1,76,21] P(x-> (-y->y->y)). given clause #49: (wt=15) 23 [hyper,1,2,9] P(-x->x->y->z-> (x->y->z)). given clause #50: (wt=9) 141 [hyper,1,4,132] P(-(x-> (y->y))->z). given clause #51: (wt=10) 140 [hyper,1,16,132] P(x->y-> (z-> (x->y))). given clause #52: (wt=8) 162 [hyper,1,140,132] P(x-> (y-> (z->z))). given clause #53: (wt=16) 26 [hyper,1,9,24] P(-(-x->x)-> (-x->x)-> (-x->y)). given clause #54: (wt=9) 181 [hyper,1,140,4] P(x-> (y-> (-y->z))). given clause #55: (wt=10) 142 [hyper,1,2,132] P(x->x->y-> (z->y)). given clause #56: (wt=10) 183 [hyper,1,140,162] P(x-> (y-> (z-> (u->u)))). given clause #57: (wt=14) 28 [hyper,1,2,24] P(-x->y->z-> (-x->x->z)). given clause #58: (wt=11) 129 [hyper,1,76,62] P(x-> (y-> (-(z->z)->u))). given clause #59: (wt=11) 135 [hyper,1,52,132] P(x-> (-(y-> (z->z))->u)). given clause #60: (wt=11) 154 [hyper,1,64,140] P(x-> (y-> (z-> (-x->u)))). given clause #61: (wt=14) 30 [hyper,1,4,11] P(-(-x->y->z-> (x->z))->u). given clause #62: (wt=11) 163 [hyper,1,140,131] P(x-> (y-> (-z->z->z))). given clause #63: (wt=11) 171 [hyper,1,140,52] P(x-> (y-> (z-> (-y->u)))). given clause #64: (wt=11) 190 [hyper,1,4,162] P(-(x-> (y-> (z->z)))->u). given clause #65: (wt=15) 31 [hyper,1,2,11] P(x->y->z-> (-x->u->y->z)). given clause #66: (wt=10) 249 [hyper,1,31,3] P(-(-x)->y->x->x). given clause #67: (wt=11) 192 [hyper,1,140,181] P(x-> (y-> (z-> (-z->u)))). given clause #68: (wt=12) 137 [hyper,1,33,132] P(-(-(x-> (y->y))->z)->u). given clause #69: (wt=16) 41 [hyper,1,33,33] P(-(-(x-> (-(-x->y)->z))->u)->v). given clause #70: (wt=12) 147 [hyper,1,4,131] P(-(x-> (-y->y->y))->z). given clause #71: (wt=12) 153 [hyper,1,140,140] P(x-> (y->z-> (u-> (y->z)))). given clause #72: (wt=12) 174 [hyper,1,140,33] P(x-> (y-> (-(-y->z)->u))). given clause #73: (wt=14) 45 [hyper,1,2,33] P(-(-x->y)->z->u-> (x->u)). given clause #74: (wt=12) 178 [hyper,1,140,24] P(x-> (-y->y-> (-y->z))). given clause #75: (wt=12) 191 [hyper,1,2,162] P(x-> (y->y)->z-> (u->z)). given clause #76: (wt=12) 197 [hyper,1,4,181] P(-(x-> (y-> (-y->z)))->u). given clause #77: (wt=16) 47 [hyper,1,33,24] P(-(-(-x->x-> (-x->y))->z)->u). given clause #78: (wt=12) 199 [hyper,1,140,142] P(x-> (y->y->z-> (u->z))). given clause #79: (wt=12) 202 [hyper,1,140,183] P(x-> (y-> (z-> (u-> (v->v))))). given clause #80: (wt=12) 251 [hyper,1,140,249] P(x-> (-(-y)->z->y->y)). given clause #81: (wt=16) 48 [hyper,1,33,12] P(-(-(-(-x->x->x)->y)->z)->u). given clause #82: (wt=12) 256 [hyper,1,8,249] P(x-> -(-(x->y))-> (x->y)). given clause #83: (wt=13) 87 [hyper,1,16,56] P(x-> -(y->y)-> (z-> (x->u))). given clause #84: (wt=13) 89 [hyper,1,16,52] P(x->y-> (z-> (x-> (-z->u)))). given clause #85: (wt=16) 49 [hyper,1,33,10] P(-(-(-(x-> (-x->y))->z)->u)->v). given clause #86: (wt=13) 121 [hyper,1,64,16] P(x-> (y-> -x-> (z-> (y->u)))). given clause #87: (wt=13) 123 [hyper,1,64,2] P(x-> (-x->y->z-> (u->z))). given clause #88: (wt=13) 139 [hyper,1,17,132] P(-(x->x->y-> (z->y))->u). given clause #89: (wt=16) 50 [hyper,1,33,39] P(-(-(-(-(x->x)->y)->z)->u)->v). given clause #90: (wt=13) 146 [hyper,1,16,131] P(x-> (-y->y)-> (z-> (x->y))). given clause #91: (wt=8) 308 [hyper,1,64,146] P(x-> (y-> (z->x))). given clause #92: (wt=8) 322 [hyper,1,146,308] P(x-> (y-> (z->y))). -------- PROOF -------- 361 [binary,360.1,6.1] $Ans(CN_18). ----> UNIT CONFLICT at 0.05 sec ----> 361 [binary,360.1,6.1] $Ans(CN_18). Length of proof is 17. Level of proof is 10. ---------------- PROOF ---------------- 1 [] -P(x->y)| -P(x)|P(y). 2 [] P(x->y-> (y->z-> (x->z))). 3 [] P(-x->x->x). 4 [] P(x-> (-x->y)). 6 [] -P(b-> (a->b))|$Ans(CN_18). 8 [hyper,1,2,2] P(x->y-> (z->y)->u-> (z->x->u)). 9 [hyper,1,2,3] P(x->y-> (-x->x->y)). 11 [hyper,1,2,4] P(-x->y->z-> (x->z)). 16 [hyper,1,8,8] P(x-> (y->z)-> (u->y-> (x-> (u->z)))). 21 [hyper,1,9,9] P(-(x->y)-> (x->y)-> (-x->x->y)). 29 [hyper,1,8,11] P(x-> -y-> (y-> (x->z))). 34 [hyper,1,11,3] P(x->x). 37 [hyper,1,4,34] P(-(x->x)->y). 52 [hyper,1,11,29] P(x-> (y-> (-x->z))). 56 [hyper,1,29,37] P(x-> (-(y->y)->z)). 64 [hyper,1,2,52] P(x-> (-y->z)->u-> (y->u)). 76 [hyper,1,2,56] P(-(x->x)->y->z-> (u->z)). 131 [hyper,1,76,21] P(x-> (-y->y->y)). 146 [hyper,1,16,131] P(x-> (-y->y)-> (z-> (x->y))). 308 [hyper,1,64,146] P(x-> (y-> (z->x))). 322 [hyper,1,146,308] P(x-> (y-> (z->y))). 360 [hyper,1,322,322] P(x-> (y->x)). 361 [binary,360.1,6.1] $Ans(CN_18). ------------ end of proof ------------- given clause #93: (wt=14) 51 [hyper,1,2,39] P(x->y-> (-(-(z->z)->u)->y)). given clause #94: (wt=6) 360 [hyper,1,322,322] P(x-> (y->x)). -------- PROOF -------- 387 [binary,386.1,7.1] $Ans(CN_19). ----> UNIT CONFLICT at 0.05 sec ----> 387 [binary,386.1,7.1] $Ans(CN_19). Length of proof is 18. Level of proof is 11. ---------------- PROOF ---------------- 1 [] -P(x->y)| -P(x)|P(y). 2 [] P(x->y-> (y->z-> (x->z))). 3 [] P(-x->x->x). 4 [] P(x-> (-x->y)). 7 [] -P(a->b->c-> (b->c))|$Ans(CN_19). 8 [hyper,1,2,2] P(x->y-> (z->y)->u-> (z->x->u)). 9 [hyper,1,2,3] P(x->y-> (-x->x->y)). 11 [hyper,1,2,4] P(-x->y->z-> (x->z)). 16 [hyper,1,8,8] P(x-> (y->z)-> (u->y-> (x-> (u->z)))). 21 [hyper,1,9,9] P(-(x->y)-> (x->y)-> (-x->x->y)). 29 [hyper,1,8,11] P(x-> -y-> (y-> (x->z))). 34 [hyper,1,11,3] P(x->x). 37 [hyper,1,4,34] P(-(x->x)->y). 52 [hyper,1,11,29] P(x-> (y-> (-x->z))). 56 [hyper,1,29,37] P(x-> (-(y->y)->z)). 64 [hyper,1,2,52] P(x-> (-y->z)->u-> (y->u)). 76 [hyper,1,2,56] P(-(x->x)->y->z-> (u->z)). 131 [hyper,1,76,21] P(x-> (-y->y->y)). 146 [hyper,1,16,131] P(x-> (-y->y)-> (z-> (x->y))). 308 [hyper,1,64,146] P(x-> (y-> (z->x))). 322 [hyper,1,146,308] P(x-> (y-> (z->y))). 360 [hyper,1,322,322] P(x-> (y->x)). 386 [hyper,1,2,360] P(x->y->z-> (y->z)). 387 [binary,386.1,7.1] $Ans(CN_19). ------------ end of proof ------------- Search stopped by max_proofs option. Search stopped by max_proofs option. ============ end of search ============ -------------- statistics ------------- clauses given 94 clauses generated 5345 hyper_res generated 5345 demod & eval rewrites 0 clauses wt,lit,sk delete 1477 tautologies deleted 0 clauses forward subsumed 3491 (subsumed by sos) 447 unit deletions 0 factor simplifications 0 clauses kept 377 new demodulators 0 empty clauses 3 clauses back demodulated 0 clauses back subsumed 0 usable size 95 sos size 286 demodulators size 0 passive size 3 hot size 0 Kbytes malloced 415 ----------- times (seconds) ----------- user CPU time 0.05 (0 hr, 0 min, 0 sec) system CPU time 0.06 (0 hr, 0 min, 0 sec) wall-clock time 0 (0 hr, 0 min, 0 sec) input time 0.00 clausify time 0.00 pick given time 0.00 hyper_res time 0.02 pre_process time 0.03 renumber time 0.00 demod time 0.00 order equalities 0.00 unit deleletion 0.00 factor simplify 0.00 weigh cl time 0.00 hints keep time 0.00 sort lits time 0.00 forward subsume 0.03 delete cl time 0.00 keep cl time 0.00 hints time 0.00 print_cl time 0.00 conflict time 0.00 new demod time 0.00 post_process time 0.00 back demod time 0.00 back subsume 0.00 factor time 0.00 unindex time 0.00 That finishes the proof of the theorem. Process 5814 finished Wed Aug 6 14:25:55 2003