TSTP Solution File: NUM854+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM854+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:10:06 EDT 2022
% Result : Theorem 1.83s 1.99s
% Output : Refutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 5 ( 4 unt; 0 nHn; 3 RR)
% Number of literals : 6 ( 0 equ; 2 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 4 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ greater(vmul(vd508,vd511),vmul(vd509,vd511)),
file('NUM854+2.p',unknown),
[] ).
cnf(7,axiom,
( ~ greater(A,B)
| greater(vmul(A,C),vmul(B,C)) ),
file('NUM854+2.p',unknown),
[] ).
cnf(25,axiom,
greater(vd508,vd509),
file('NUM854+2.p',unknown),
[] ).
cnf(54,plain,
greater(vmul(vd508,A),vmul(vd509,A)),
inference(hyper,[status(thm)],[25,7]),
[iquote('hyper,25,7')] ).
cnf(55,plain,
$false,
inference(binary,[status(thm)],[54,1]),
[iquote('binary,54.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM854+2 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 09:44:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.78/1.99 ----- Otter 3.3f, August 2004 -----
% 1.78/1.99 The process was started by sandbox on n021.cluster.edu,
% 1.78/1.99 Wed Jul 27 09:44:53 2022
% 1.78/1.99 The command was "./otter". The process ID is 15195.
% 1.78/1.99
% 1.78/1.99 set(prolog_style_variables).
% 1.78/1.99 set(auto).
% 1.78/1.99 dependent: set(auto1).
% 1.78/1.99 dependent: set(process_input).
% 1.78/1.99 dependent: clear(print_kept).
% 1.78/1.99 dependent: clear(print_new_demod).
% 1.78/1.99 dependent: clear(print_back_demod).
% 1.78/1.99 dependent: clear(print_back_sub).
% 1.78/1.99 dependent: set(control_memory).
% 1.78/1.99 dependent: assign(max_mem, 12000).
% 1.78/1.99 dependent: assign(pick_given_ratio, 4).
% 1.78/1.99 dependent: assign(stats_level, 1).
% 1.78/1.99 dependent: assign(max_seconds, 10800).
% 1.78/1.99 clear(print_given).
% 1.78/1.99
% 1.78/1.99 formula_list(usable).
% 1.78/1.99 all A (A=A).
% 1.78/1.99 -greater(vmul(vd508,vd511),vmul(vd509,vd511)).
% 1.78/1.99 greater(vd511,vd512).
% 1.78/1.99 greater(vd508,vd509).
% 1.78/1.99 all Vd496 Vd497 Vd498 (less(vmul(Vd496,Vd497),vmul(Vd498,Vd497))->less(Vd496,Vd498)).
% 1.78/1.99 all Vd491 Vd492 Vd493 (vmul(Vd491,Vd492)=vmul(Vd493,Vd492)->Vd491=Vd493).
% 1.78/1.99 all Vd486 Vd487 Vd488 (greater(vmul(Vd486,Vd487),vmul(Vd488,Vd487))->greater(Vd486,Vd488)).
% 1.78/1.99 all Vd456 Vd465 Vd466 (less(Vd465,Vd466)->less(vmul(Vd465,Vd456),vmul(Vd466,Vd456))).
% 1.78/1.99 all Vd456 Vd461 Vd462 (Vd461=Vd462->vmul(Vd461,Vd456)=vmul(Vd462,Vd456)).
% 1.78/1.99 all Vd456 Vd457 Vd458 (greater(Vd457,Vd458)->greater(vmul(Vd457,Vd456),vmul(Vd458,Vd456))).
% 1.78/1.99 all Vd444 Vd445 Vd446 (vmul(vmul(Vd444,Vd445),Vd446)=vmul(Vd444,vmul(Vd445,Vd446))).
% 1.78/1.99 all Vd432 Vd433 Vd434 (vmul(Vd432,vplus(Vd433,Vd434))=vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434))).
% 1.78/1.99 all Vd418 Vd419 (vmul(Vd418,Vd419)=vmul(Vd419,Vd418)).
% 1.78/1.99 all Vd408 Vd409 (vmul(vsucc(Vd408),Vd409)=vplus(vmul(Vd408,Vd409),Vd409)).
% 1.78/1.99 all Vd400 (vmul(v1,Vd400)=Vd400).
% 1.78/1.99 all Vd396 Vd397 (vmul(Vd396,vsucc(Vd397))=vplus(vmul(Vd396,Vd397),Vd396)&vmul(Vd396,v1)=Vd396).
% 1.78/1.99 all Vd226 Vd227 (less(Vd226,Vd227)->greater(Vd227,Vd226)).
% 1.78/1.99 all Vd208 Vd209 (greater(Vd208,Vd209)->less(Vd209,Vd208)).
% 1.78/1.99 all Vd203 Vd204 (Vd203=Vd204|greater(Vd203,Vd204)|less(Vd203,Vd204)).
% 1.78/1.99 all Vd203 Vd204 (Vd203!=Vd204| -less(Vd203,Vd204)).
% 1.78/1.99 all Vd203 Vd204 (-greater(Vd203,Vd204)| -less(Vd203,Vd204)).
% 1.78/1.99 all Vd203 Vd204 (Vd203!=Vd204| -greater(Vd203,Vd204)).
% 1.78/1.99 all Vd198 Vd199 (less(Vd199,Vd198)<-> (exists Vd201 (Vd198=vplus(Vd199,Vd201)))).
% 1.78/1.99 all Vd193 Vd194 (greater(Vd194,Vd193)<-> (exists Vd196 (Vd194=vplus(Vd193,Vd196)))).
% 1.78/1.99 all Vd120 Vd121 (Vd120=Vd121| (exists Vd123 (Vd120=vplus(Vd121,Vd123)))| (exists Vd125 (Vd121=vplus(Vd120,Vd125)))).
% 1.78/1.99 all Vd120 Vd121 (Vd120!=Vd121| -(exists Vd125 (Vd121=vplus(Vd120,Vd125)))).
% 1.78/1.99 all Vd120 Vd121 (-(exists Vd123 (Vd120=vplus(Vd121,Vd123)))| -(exists Vd125 (Vd121=vplus(Vd120,Vd125)))).
% 1.78/1.99 all Vd120 Vd121 (Vd120!=Vd121| -(exists Vd123 (Vd120=vplus(Vd121,Vd123)))).
% 1.78/1.99 end_of_list.
% 1.78/1.99
% 1.78/1.99 -------> usable clausifies to:
% 1.78/1.99
% 1.78/1.99 list(usable).
% 1.78/1.99 0 [] A=A.
% 1.78/1.99 0 [] -greater(vmul(vd508,vd511),vmul(vd509,vd511)).
% 1.78/1.99 0 [] greater(vd511,vd512).
% 1.78/1.99 0 [] greater(vd508,vd509).
% 1.78/1.99 0 [] -less(vmul(Vd496,Vd497),vmul(Vd498,Vd497))|less(Vd496,Vd498).
% 1.78/1.99 0 [] vmul(Vd491,Vd492)!=vmul(Vd493,Vd492)|Vd491=Vd493.
% 1.78/1.99 0 [] -greater(vmul(Vd486,Vd487),vmul(Vd488,Vd487))|greater(Vd486,Vd488).
% 1.78/1.99 0 [] -less(Vd465,Vd466)|less(vmul(Vd465,Vd456),vmul(Vd466,Vd456)).
% 1.78/1.99 0 [] Vd461!=Vd462|vmul(Vd461,Vd456)=vmul(Vd462,Vd456).
% 1.78/1.99 0 [] -greater(Vd457,Vd458)|greater(vmul(Vd457,Vd456),vmul(Vd458,Vd456)).
% 1.78/1.99 0 [] vmul(vmul(Vd444,Vd445),Vd446)=vmul(Vd444,vmul(Vd445,Vd446)).
% 1.78/1.99 0 [] vmul(Vd432,vplus(Vd433,Vd434))=vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)).
% 1.78/1.99 0 [] vmul(Vd418,Vd419)=vmul(Vd419,Vd418).
% 1.78/1.99 0 [] vmul(vsucc(Vd408),Vd409)=vplus(vmul(Vd408,Vd409),Vd409).
% 1.78/1.99 0 [] vmul(v1,Vd400)=Vd400.
% 1.78/1.99 0 [] vmul(Vd396,vsucc(Vd397))=vplus(vmul(Vd396,Vd397),Vd396).
% 1.78/1.99 0 [] vmul(Vd396,v1)=Vd396.
% 1.78/1.99 0 [] -less(Vd226,Vd227)|greater(Vd227,Vd226).
% 1.78/1.99 0 [] -greater(Vd208,Vd209)|less(Vd209,Vd208).
% 1.78/1.99 0 [] Vd203=Vd204|greater(Vd203,Vd204)|less(Vd203,Vd204).
% 1.78/1.99 0 [] Vd203!=Vd204| -less(Vd203,Vd204).
% 1.78/1.99 0 [] -greater(Vd203,Vd204)| -less(Vd203,Vd204).
% 1.78/1.99 0 [] Vd203!=Vd204| -greater(Vd203,Vd204).
% 1.78/1.99 0 [] -less(Vd199,Vd198)|Vd198=vplus(Vd199,$f1(Vd198,Vd199)).
% 1.78/1.99 0 [] less(Vd199,Vd198)|Vd198!=vplus(Vd199,Vd201).
% 1.78/1.99 0 [] -greater(Vd194,Vd193)|Vd194=vplus(Vd193,$f2(Vd193,Vd194)).
% 1.78/1.99 0 [] greater(Vd194,Vd193)|Vd194!=vplus(Vd193,Vd196).
% 1.78/1.99 0 [] Vd120=Vd121|Vd120=vplus(Vd121,$f3(Vd120,Vd121))|Vd121=vplus(Vd120,$f4(Vd120,Vd121)).
% 1.78/1.99 0 [] Vd120!=Vd121|Vd121!=vplus(Vd120,Vd125).
% 1.78/1.99 0 [] Vd120!=vplus(Vd121,Vd123)|Vd121!=vplus(Vd120,Vd125).
% 1.78/1.99 0 [] Vd120!=Vd121|Vd120!=vplus(Vd121,Vd123).
% 1.78/1.99 end_of_list.
% 1.78/1.99
% 1.78/1.99 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.78/1.99
% 1.78/1.99 This ia a non-Horn set with equality. The strategy will be
% 1.78/1.99 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.78/1.99 deletion, with positive clauses in sos and nonpositive
% 1.78/1.99 clauses in usable.
% 1.78/1.99
% 1.78/1.99 dependent: set(knuth_bendix).
% 1.78/1.99 dependent: set(anl_eq).
% 1.78/1.99 dependent: set(para_from).
% 1.78/1.99 dependent: set(para_into).
% 1.78/1.99 dependent: clear(para_from_right).
% 1.78/1.99 dependent: clear(para_into_right).
% 1.78/1.99 dependent: set(para_from_vars).
% 1.78/1.99 dependent: set(eq_units_both_ways).
% 1.78/1.99 dependent: set(dynamic_demod_all).
% 1.78/1.99 dependent: set(dynamic_demod).
% 1.78/1.99 dependent: set(order_eq).
% 1.78/1.99 dependent: set(back_demod).
% 1.78/1.99 dependent: set(lrpo).
% 1.78/1.99 dependent: set(hyper_res).
% 1.78/1.99 dependent: set(unit_deletion).
% 1.78/1.99 dependent: set(factor).
% 1.78/1.99
% 1.78/1.99 ------------> process usable:
% 1.78/1.99 ** KEPT (pick-wt=7): 1 [] -greater(vmul(vd508,vd511),vmul(vd509,vd511)).
% 1.78/1.99 ** KEPT (pick-wt=10): 2 [] -less(vmul(A,B),vmul(C,B))|less(A,C).
% 1.78/1.99 ** KEPT (pick-wt=10): 3 [] vmul(A,B)!=vmul(C,B)|A=C.
% 1.78/1.99 ** KEPT (pick-wt=10): 4 [] -greater(vmul(A,B),vmul(C,B))|greater(A,C).
% 1.78/1.99 ** KEPT (pick-wt=10): 5 [] -less(A,B)|less(vmul(A,C),vmul(B,C)).
% 1.78/1.99 ** KEPT (pick-wt=10): 6 [] A!=B|vmul(A,C)=vmul(B,C).
% 1.78/1.99 ** KEPT (pick-wt=10): 7 [] -greater(A,B)|greater(vmul(A,C),vmul(B,C)).
% 1.78/1.99 ** KEPT (pick-wt=6): 8 [] -less(A,B)|greater(B,A).
% 1.78/1.99 ** KEPT (pick-wt=6): 9 [] -greater(A,B)|less(B,A).
% 1.78/1.99 ** KEPT (pick-wt=6): 10 [] A!=B| -less(A,B).
% 1.78/1.99 ** KEPT (pick-wt=6): 11 [] -greater(A,B)| -less(A,B).
% 1.78/1.99 ** KEPT (pick-wt=6): 12 [] A!=B| -greater(A,B).
% 1.78/1.99 ** KEPT (pick-wt=10): 14 [copy,13,flip.2] -less(A,B)|vplus(A,$f1(B,A))=B.
% 1.78/1.99 ** KEPT (pick-wt=8): 15 [] less(A,B)|B!=vplus(A,C).
% 1.78/1.99 ** KEPT (pick-wt=10): 17 [copy,16,flip.2] -greater(A,B)|vplus(B,$f2(B,A))=A.
% 1.78/1.99 ** KEPT (pick-wt=8): 18 [] greater(A,B)|A!=vplus(B,C).
% 1.78/1.99 ** KEPT (pick-wt=8): 19 [] A!=B|B!=vplus(A,C).
% 1.78/1.99 ** KEPT (pick-wt=10): 20 [] A!=vplus(B,C)|B!=vplus(A,D).
% 1.83/1.99 ** KEPT (pick-wt=8): 21 [] A!=B|A!=vplus(B,C).
% 1.83/1.99
% 1.83/1.99 ------------> process sos:
% 1.83/1.99 ** KEPT (pick-wt=3): 23 [] A=A.
% 1.83/1.99 ** KEPT (pick-wt=3): 24 [] greater(vd511,vd512).
% 1.83/1.99 ** KEPT (pick-wt=3): 25 [] greater(vd508,vd509).
% 1.83/1.99 ** KEPT (pick-wt=11): 26 [] vmul(vmul(A,B),C)=vmul(A,vmul(B,C)).
% 1.83/1.99 ---> New Demodulator: 27 [new_demod,26] vmul(vmul(A,B),C)=vmul(A,vmul(B,C)).
% 1.83/1.99 ** KEPT (pick-wt=13): 29 [copy,28,flip.1] vplus(vmul(A,B),vmul(A,C))=vmul(A,vplus(B,C)).
% 1.83/1.99 ---> New Demodulator: 30 [new_demod,29] vplus(vmul(A,B),vmul(A,C))=vmul(A,vplus(B,C)).
% 1.83/1.99 ** KEPT (pick-wt=7): 31 [] vmul(A,B)=vmul(B,A).
% 1.83/1.99 ** KEPT (pick-wt=10): 32 [] vmul(vsucc(A),B)=vplus(vmul(A,B),B).
% 1.83/1.99 ** KEPT (pick-wt=5): 33 [] vmul(v1,A)=A.
% 1.83/1.99 ---> New Demodulator: 34 [new_demod,33] vmul(v1,A)=A.
% 1.83/1.99 ** KEPT (pick-wt=10): 35 [] vmul(A,vsucc(B))=vplus(vmul(A,B),A).
% 1.83/1.99 ** KEPT (pick-wt=5): 36 [] vmul(A,v1)=A.
% 1.83/1.99 ---> New Demodulator: 37 [new_demod,36] vmul(A,v1)=A.
% 1.83/1.99 ** KEPT (pick-wt=9): 38 [] A=B|greater(A,B)|less(A,B).
% 1.83/1.99 ** KEPT (pick-wt=17): 40 [copy,39,flip.2,flip.3] A=B|vplus(B,$f3(A,B))=A|vplus(A,$f4(A,B))=B.
% 1.83/1.99 Following clause subsumed by 23 during input processing: 0 [copy,23,flip.1] A=A.
% 1.83/1.99 >>>> Starting back demodulation with 27.
% 1.83/1.99 >>>> Starting back demodulation with 30.
% 1.83/1.99 Following clause subsumed by 31 during input processing: 0 [copy,31,flip.1] vmul(A,B)=vmul(B,A).
% 1.83/1.99 ** KEPT (pick-wt=10): 41 [copy,32,flip.1] vplus(vmul(A,B),B)=vmul(vsucc(A),B).
% 1.83/1.99 >>>> Starting back demodulation with 34.
% 1.83/1.99 ** KEPT (pick-wt=10): 42 [copy,35,flip.1] vplus(vmul(A,B),A)=vmul(A,vsucc(B)).
% 1.83/1.99 >>>> Starting back demodulation with 37.
% 1.83/1.99 Following clause subsumed by 32 during input processing: 0 [copy,41,flip.1] vmul(vsucc(A),B)=vplus(vmul(A,B),B).
% 1.83/1.99 Following clause subsumed by 35 during input processing: 0 [copy,42,flip.1] vmul(A,vsucc(B))=vplus(vmul(A,B),A).
% 1.83/1.99
% 1.83/1.99 ======= end of input processing =======
% 1.83/1.99
% 1.83/1.99 =========== start of search ===========
% 1.83/1.99
% 1.83/1.99 -------- PROOF --------
% 1.83/1.99
% 1.83/1.99 ----> UNIT CONFLICT at 0.00 sec ----> 55 [binary,54.1,1.1] $F.
% 1.83/1.99
% 1.83/1.99 Length of proof is 1. Level of proof is 1.
% 1.83/1.99
% 1.83/1.99 ---------------- PROOF ----------------
% 1.83/1.99 % SZS status Theorem
% 1.83/1.99 % SZS output start Refutation
% See solution above
% 1.83/1.99 ------------ end of proof -------------
% 1.83/1.99
% 1.83/1.99
% 1.83/1.99 Search stopped by max_proofs option.
% 1.83/1.99
% 1.83/1.99
% 1.83/1.99 Search stopped by max_proofs option.
% 1.83/1.99
% 1.83/1.99 ============ end of search ============
% 1.83/1.99
% 1.83/1.99 -------------- statistics -------------
% 1.83/1.99 clauses given 3
% 1.83/1.99 clauses generated 13
% 1.83/1.99 clauses kept 44
% 1.83/1.99 clauses forward subsumed 6
% 1.83/1.99 clauses back subsumed 0
% 1.83/1.99 Kbytes malloced 976
% 1.83/1.99
% 1.83/1.99 ----------- times (seconds) -----------
% 1.83/1.99 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.83/1.99 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.83/1.99 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.83/1.99
% 1.83/1.99 That finishes the proof of the theorem.
% 1.83/1.99
% 1.83/1.99 Process 15195 finished Wed Jul 27 09:44:54 2022
% 1.83/1.99 Otter interrupted
% 1.83/1.99 PROOF FOUND
%------------------------------------------------------------------------------