TSTP Solution File: NUM852+2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM852+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 1.65s 1.82s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 13 ( 8 unt; 0 nHn; 11 RR)
% Number of literals : 18 ( 8 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
file('NUM852+2.p',unknown),
[] ).
cnf(4,axiom,
( ~ greater(A,B)
| vmul(vplus(B,vskolem9(A,B)),vd469) = vplus(vmul(B,vd469),vmul(vskolem9(A,B),vd469)) ),
file('NUM852+2.p',unknown),
[] ).
cnf(5,plain,
( ~ greater(A,B)
| vplus(vmul(B,vd469),vmul(vskolem9(A,B),vd469)) = vmul(vplus(B,vskolem9(A,B)),vd469) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.2')] ).
cnf(8,axiom,
( ~ greater(A,B)
| A = vplus(B,vskolem9(A,B)) ),
file('NUM852+2.p',unknown),
[] ).
cnf(9,plain,
( ~ greater(A,B)
| vplus(B,vskolem9(A,B)) = A ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[8])]),
[iquote('copy,8,flip.2')] ).
cnf(20,axiom,
( greater(A,B)
| A != vplus(B,C) ),
file('NUM852+2.p',unknown),
[] ).
cnf(21,axiom,
A = A,
file('NUM852+2.p',unknown),
[] ).
cnf(22,axiom,
greater(vd481,vd480),
file('NUM852+2.p',unknown),
[] ).
cnf(33,plain,
greater(vplus(A,B),A),
inference(hyper,[status(thm)],[21,20]),
[iquote('hyper,21,20')] ).
cnf(38,plain,
vplus(vd480,vskolem9(vd481,vd480)) = vd481,
inference(hyper,[status(thm)],[22,9]),
[iquote('hyper,22,9')] ).
cnf(39,plain,
vplus(vmul(vd480,vd469),vmul(vskolem9(vd481,vd480),vd469)) = vmul(vd481,vd469),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[22,5]),38]),
[iquote('hyper,22,5,demod,38')] ).
cnf(298,plain,
greater(vmul(vd481,vd469),vmul(vd480,vd469)),
inference(para_from,[status(thm),theory(equality)],[39,33]),
[iquote('para_from,39.1.1,33.1.1')] ).
cnf(299,plain,
$false,
inference(binary,[status(thm)],[298,1]),
[iquote('binary,298.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM852+2 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 09:37:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.65/1.81 ----- Otter 3.3f, August 2004 -----
% 1.65/1.81 The process was started by sandbox2 on n009.cluster.edu,
% 1.65/1.81 Wed Jul 27 09:37:51 2022
% 1.65/1.81 The command was "./otter". The process ID is 1285.
% 1.65/1.81
% 1.65/1.81 set(prolog_style_variables).
% 1.65/1.81 set(auto).
% 1.65/1.81 dependent: set(auto1).
% 1.65/1.81 dependent: set(process_input).
% 1.65/1.81 dependent: clear(print_kept).
% 1.65/1.81 dependent: clear(print_new_demod).
% 1.65/1.81 dependent: clear(print_back_demod).
% 1.65/1.81 dependent: clear(print_back_sub).
% 1.65/1.81 dependent: set(control_memory).
% 1.65/1.81 dependent: assign(max_mem, 12000).
% 1.65/1.81 dependent: assign(pick_given_ratio, 4).
% 1.65/1.81 dependent: assign(stats_level, 1).
% 1.65/1.81 dependent: assign(max_seconds, 10800).
% 1.65/1.81 clear(print_given).
% 1.65/1.81
% 1.65/1.81 formula_list(usable).
% 1.65/1.81 all A (A=A).
% 1.65/1.81 -greater(vmul(vd481,vd469),vmul(vd480,vd469)).
% 1.65/1.81 greater(vd481,vd480).
% 1.65/1.81 less(vd480,vd481).
% 1.65/1.81 all Vd476 Vd477 (Vd476=Vd477->vmul(Vd476,vd469)=vmul(Vd477,vd469)).
% 1.65/1.81 all Vd470 Vd471 (greater(Vd470,Vd471)->greater(vplus(vmul(Vd471,vd469),vmul(vskolem9(Vd470,Vd471),vd469)),vmul(Vd471,vd469))).
% 1.65/1.81 all Vd470 Vd471 (greater(Vd470,Vd471)->vmul(vplus(Vd471,vskolem9(Vd470,Vd471)),vd469)=vplus(vmul(Vd471,vd469),vmul(vskolem9(Vd470,Vd471),vd469))).
% 1.65/1.82 all Vd470 Vd471 (greater(Vd470,Vd471)->vmul(Vd470,vd469)=vmul(vplus(Vd471,vskolem9(Vd470,Vd471)),vd469)).
% 1.65/1.82 all Vd470 Vd471 (greater(Vd470,Vd471)->Vd470=vplus(Vd471,vskolem9(Vd470,Vd471))).
% 1.65/1.82 all Vd444 Vd445 Vd446 (vmul(vmul(Vd444,Vd445),Vd446)=vmul(Vd444,vmul(Vd445,Vd446))).
% 1.65/1.82 all Vd432 Vd433 Vd434 (vmul(Vd432,vplus(Vd433,Vd434))=vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434))).
% 1.65/1.82 all Vd418 Vd419 (vmul(Vd418,Vd419)=vmul(Vd419,Vd418)).
% 1.65/1.82 all Vd408 Vd409 (vmul(vsucc(Vd408),Vd409)=vplus(vmul(Vd408,Vd409),Vd409)).
% 1.65/1.82 all Vd226 Vd227 (less(Vd226,Vd227)->greater(Vd227,Vd226)).
% 1.65/1.82 all Vd208 Vd209 (greater(Vd208,Vd209)->less(Vd209,Vd208)).
% 1.65/1.82 all Vd203 Vd204 (Vd203=Vd204|greater(Vd203,Vd204)|less(Vd203,Vd204)).
% 1.65/1.82 all Vd203 Vd204 (Vd203!=Vd204| -less(Vd203,Vd204)).
% 1.65/1.82 all Vd203 Vd204 (-greater(Vd203,Vd204)| -less(Vd203,Vd204)).
% 1.65/1.82 all Vd203 Vd204 (Vd203!=Vd204| -greater(Vd203,Vd204)).
% 1.65/1.82 all Vd198 Vd199 (less(Vd199,Vd198)<-> (exists Vd201 (Vd198=vplus(Vd199,Vd201)))).
% 1.65/1.82 all Vd193 Vd194 (greater(Vd194,Vd193)<-> (exists Vd196 (Vd194=vplus(Vd193,Vd196)))).
% 1.65/1.82 end_of_list.
% 1.65/1.82
% 1.65/1.82 -------> usable clausifies to:
% 1.65/1.82
% 1.65/1.82 list(usable).
% 1.65/1.82 0 [] A=A.
% 1.65/1.82 0 [] -greater(vmul(vd481,vd469),vmul(vd480,vd469)).
% 1.65/1.82 0 [] greater(vd481,vd480).
% 1.65/1.82 0 [] less(vd480,vd481).
% 1.65/1.82 0 [] Vd476!=Vd477|vmul(Vd476,vd469)=vmul(Vd477,vd469).
% 1.65/1.82 0 [] -greater(Vd470,Vd471)|greater(vplus(vmul(Vd471,vd469),vmul(vskolem9(Vd470,Vd471),vd469)),vmul(Vd471,vd469)).
% 1.65/1.82 0 [] -greater(Vd470,Vd471)|vmul(vplus(Vd471,vskolem9(Vd470,Vd471)),vd469)=vplus(vmul(Vd471,vd469),vmul(vskolem9(Vd470,Vd471),vd469)).
% 1.65/1.82 0 [] -greater(Vd470,Vd471)|vmul(Vd470,vd469)=vmul(vplus(Vd471,vskolem9(Vd470,Vd471)),vd469).
% 1.65/1.82 0 [] -greater(Vd470,Vd471)|Vd470=vplus(Vd471,vskolem9(Vd470,Vd471)).
% 1.65/1.82 0 [] vmul(vmul(Vd444,Vd445),Vd446)=vmul(Vd444,vmul(Vd445,Vd446)).
% 1.65/1.82 0 [] vmul(Vd432,vplus(Vd433,Vd434))=vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)).
% 1.65/1.82 0 [] vmul(Vd418,Vd419)=vmul(Vd419,Vd418).
% 1.65/1.82 0 [] vmul(vsucc(Vd408),Vd409)=vplus(vmul(Vd408,Vd409),Vd409).
% 1.65/1.82 0 [] -less(Vd226,Vd227)|greater(Vd227,Vd226).
% 1.65/1.82 0 [] -greater(Vd208,Vd209)|less(Vd209,Vd208).
% 1.65/1.82 0 [] Vd203=Vd204|greater(Vd203,Vd204)|less(Vd203,Vd204).
% 1.65/1.82 0 [] Vd203!=Vd204| -less(Vd203,Vd204).
% 1.65/1.82 0 [] -greater(Vd203,Vd204)| -less(Vd203,Vd204).
% 1.65/1.82 0 [] Vd203!=Vd204| -greater(Vd203,Vd204).
% 1.65/1.82 0 [] -less(Vd199,Vd198)|Vd198=vplus(Vd199,$f1(Vd198,Vd199)).
% 1.65/1.82 0 [] less(Vd199,Vd198)|Vd198!=vplus(Vd199,Vd201).
% 1.65/1.82 0 [] -greater(Vd194,Vd193)|Vd194=vplus(Vd193,$f2(Vd193,Vd194)).
% 1.65/1.82 0 [] greater(Vd194,Vd193)|Vd194!=vplus(Vd193,Vd196).
% 1.65/1.82 end_of_list.
% 1.65/1.82
% 1.65/1.82 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.65/1.82
% 1.65/1.82 This ia a non-Horn set with equality. The strategy will be
% 1.65/1.82 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.65/1.82 deletion, with positive clauses in sos and nonpositive
% 1.65/1.82 clauses in usable.
% 1.65/1.82
% 1.65/1.82 dependent: set(knuth_bendix).
% 1.65/1.82 dependent: set(anl_eq).
% 1.65/1.82 dependent: set(para_from).
% 1.65/1.82 dependent: set(para_into).
% 1.65/1.82 dependent: clear(para_from_right).
% 1.65/1.82 dependent: clear(para_into_right).
% 1.65/1.82 dependent: set(para_from_vars).
% 1.65/1.82 dependent: set(eq_units_both_ways).
% 1.65/1.82 dependent: set(dynamic_demod_all).
% 1.65/1.82 dependent: set(dynamic_demod).
% 1.65/1.82 dependent: set(order_eq).
% 1.65/1.82 dependent: set(back_demod).
% 1.65/1.82 dependent: set(lrpo).
% 1.65/1.82 dependent: set(hyper_res).
% 1.65/1.82 dependent: set(unit_deletion).
% 1.65/1.82 dependent: set(factor).
% 1.65/1.82
% 1.65/1.82 ------------> process usable:
% 1.65/1.82 ** KEPT (pick-wt=7): 1 [] -greater(vmul(vd481,vd469),vmul(vd480,vd469)).
% 1.65/1.82 ** KEPT (pick-wt=10): 2 [] A!=B|vmul(A,vd469)=vmul(B,vd469).
% 1.65/1.82 ** KEPT (pick-wt=16): 3 [] -greater(A,B)|greater(vplus(vmul(B,vd469),vmul(vskolem9(A,B),vd469)),vmul(B,vd469)).
% 1.65/1.82 ** KEPT (pick-wt=20): 5 [copy,4,flip.2] -greater(A,B)|vplus(vmul(B,vd469),vmul(vskolem9(A,B),vd469))=vmul(vplus(B,vskolem9(A,B)),vd469).
% 1.65/1.82 ** KEPT (pick-wt=14): 7 [copy,6,flip.2] -greater(A,B)|vmul(vplus(B,vskolem9(A,B)),vd469)=vmul(A,vd469).
% 1.65/1.82 ** KEPT (pick-wt=10): 9 [copy,8,flip.2] -greater(A,B)|vplus(B,vskolem9(A,B))=A.
% 1.65/1.82 ** KEPT (pick-wt=6): 10 [] -less(A,B)|greater(B,A).
% 1.65/1.82 ** KEPT (pick-wt=6): 11 [] -greater(A,B)|less(B,A).
% 1.65/1.82 ** KEPT (pick-wt=6): 12 [] A!=B| -less(A,B).
% 1.65/1.82 ** KEPT (pick-wt=6): 13 [] -greater(A,B)| -less(A,B).
% 1.65/1.82 ** KEPT (pick-wt=6): 14 [] A!=B| -greater(A,B).
% 1.65/1.82 ** KEPT (pick-wt=10): 16 [copy,15,flip.2] -less(A,B)|vplus(A,$f1(B,A))=B.
% 1.65/1.82 ** KEPT (pick-wt=8): 17 [] less(A,B)|B!=vplus(A,C).
% 1.65/1.82 ** KEPT (pick-wt=10): 19 [copy,18,flip.2] -greater(A,B)|vplus(B,$f2(B,A))=A.
% 1.65/1.82 ** KEPT (pick-wt=8): 20 [] greater(A,B)|A!=vplus(B,C).
% 1.65/1.82
% 1.65/1.82 ------------> process sos:
% 1.65/1.82 ** KEPT (pick-wt=3): 21 [] A=A.
% 1.65/1.82 ** KEPT (pick-wt=3): 22 [] greater(vd481,vd480).
% 1.65/1.82 ** KEPT (pick-wt=3): 23 [] less(vd480,vd481).
% 1.65/1.82 ** KEPT (pick-wt=11): 24 [] vmul(vmul(A,B),C)=vmul(A,vmul(B,C)).
% 1.65/1.82 ---> New Demodulator: 25 [new_demod,24] vmul(vmul(A,B),C)=vmul(A,vmul(B,C)).
% 1.65/1.82 ** KEPT (pick-wt=13): 27 [copy,26,flip.1] vplus(vmul(A,B),vmul(A,C))=vmul(A,vplus(B,C)).
% 1.65/1.82 ---> New Demodulator: 28 [new_demod,27] vplus(vmul(A,B),vmul(A,C))=vmul(A,vplus(B,C)).
% 1.65/1.82 ** KEPT (pick-wt=7): 29 [] vmul(A,B)=vmul(B,A).
% 1.65/1.82 ** KEPT (pick-wt=10): 30 [] vmul(vsucc(A),B)=vplus(vmul(A,B),B).
% 1.65/1.82 ** KEPT (pick-wt=9): 31 [] A=B|greater(A,B)|less(A,B).
% 1.65/1.82 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] A=A.
% 1.65/1.82 >>>> Starting back demodulation with 25.
% 1.65/1.82 >>>> Starting back demodulation with 28.
% 1.65/1.82 Following clause subsumed by 29 during input processing: 0 [copy,29,flip.1] vmul(A,B)=vmul(B,A).
% 1.65/1.82 ** KEPT (pick-wt=10): 32 [copy,30,flip.1] vplus(vmul(A,B),B)=vmul(vsucc(A),B).
% 1.65/1.82 Following clause subsumed by 30 during input processing: 0 [copy,32,flip.1] vmul(vsucc(A),B)=vplus(vmul(A,B),B).
% 1.65/1.82
% 1.65/1.82 ======= end of input processing =======
% 1.65/1.82
% 1.65/1.82 =========== start of search ===========
% 1.65/1.82
% 1.65/1.82 -------- PROOF --------
% 1.65/1.82
% 1.65/1.82 ----> UNIT CONFLICT at 0.01 sec ----> 299 [binary,298.1,1.1] $F.
% 1.65/1.82
% 1.65/1.82 Length of proof is 6. Level of proof is 4.
% 1.65/1.82
% 1.65/1.82 ---------------- PROOF ----------------
% 1.65/1.82 % SZS status Theorem
% 1.65/1.82 % SZS output start Refutation
% See solution above
% 1.65/1.82 ------------ end of proof -------------
% 1.65/1.82
% 1.65/1.82
% 1.65/1.82 Search stopped by max_proofs option.
% 1.65/1.82
% 1.65/1.82
% 1.65/1.82 Search stopped by max_proofs option.
% 1.65/1.82
% 1.65/1.82 ============ end of search ============
% 1.65/1.82
% 1.65/1.82 -------------- statistics -------------
% 1.65/1.82 clauses given 26
% 1.65/1.82 clauses generated 344
% 1.65/1.82 clauses kept 262
% 1.65/1.82 clauses forward subsumed 126
% 1.65/1.82 clauses back subsumed 4
% 1.65/1.82 Kbytes malloced 2929
% 1.65/1.82
% 1.65/1.82 ----------- times (seconds) -----------
% 1.65/1.82 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.65/1.82 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.82 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.65/1.82
% 1.65/1.82 That finishes the proof of the theorem.
% 1.65/1.82
% 1.65/1.82 Process 1285 finished Wed Jul 27 09:37:52 2022
% 1.65/1.83 Otter interrupted
% 1.65/1.83 PROOF FOUND
%------------------------------------------------------------------------------