%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM853+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 3.82s 3.98s
% Output : Refutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 20
% Syntax : Number of clauses : 45 ( 23 unt; 4 nHn; 28 RR)
% Number of literals : 72 ( 40 equ; 28 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 73 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ greater(vd486,vd488),
file('NUM853+2.p',unknown),
[] ).
cnf(2,axiom,
( ~ less(A,B)
| less(vmul(A,C),vmul(B,C)) ),
file('NUM853+2.p',unknown),
[] ).
cnf(3,axiom,
( A != B
| vmul(A,C) = vmul(B,C) ),
file('NUM853+2.p',unknown),
[] ).
cnf(4,axiom,
( ~ greater(A,B)
| greater(vmul(A,C),vmul(B,C)) ),
file('NUM853+2.p',unknown),
[] ).
cnf(8,axiom,
( ~ less(A,B)
| greater(B,A) ),
file('NUM853+2.p',unknown),
[] ).
cnf(9,axiom,
( ~ greater(A,B)
| less(B,A) ),
file('NUM853+2.p',unknown),
[] ).
cnf(11,axiom,
( ~ greater(A,B)
| ~ less(A,B) ),
file('NUM853+2.p',unknown),
[] ).
cnf(13,axiom,
( ~ less(A,B)
| B = vplus(A,dollar_f1(B,A)) ),
file('NUM853+2.p',unknown),
[] ).
cnf(14,plain,
( ~ less(A,B)
| vplus(A,dollar_f1(B,A)) = B ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.2')] ).
cnf(15,axiom,
( less(A,B)
| B != vplus(A,C) ),
file('NUM853+2.p',unknown),
[] ).
cnf(16,axiom,
( ~ greater(A,B)
| A = vplus(B,dollar_f2(B,A)) ),
file('NUM853+2.p',unknown),
[] ).
cnf(17,plain,
( ~ greater(A,B)
| vplus(B,dollar_f2(B,A)) = A ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[16])]),
[iquote('copy,16,flip.2')] ).
cnf(20,axiom,
( A != vplus(B,C)
| B != vplus(A,D) ),
file('NUM853+2.p',unknown),
[] ).
cnf(22,axiom,
( A = B
| vplus(C,A) != vplus(C,B) ),
file('NUM853+2.p',unknown),
[] ).
cnf(28,plain,
vplus(A,B) != A,
inference(flip,[status(thm),theory(equality)],[inference(factor,[status(thm)],[20])]),
[iquote('factor,20.1.2,flip.1')] ).
cnf(29,axiom,
A = A,
file('NUM853+2.p',unknown),
[] ).
cnf(30,axiom,
greater(vmul(vd486,vd487),vmul(vd488,vd487)),
file('NUM853+2.p',unknown),
[] ).
cnf(32,axiom,
vmul(vmul(A,B),C) = vmul(A,vmul(B,C)),
file('NUM853+2.p',unknown),
[] ).
cnf(36,axiom,
vmul(A,B) = vmul(B,A),
file('NUM853+2.p',unknown),
[] ).
cnf(39,axiom,
vmul(v1,A) = A,
file('NUM853+2.p',unknown),
[] ).
cnf(42,axiom,
vmul(A,v1) = A,
file('NUM853+2.p',unknown),
[] ).
cnf(44,axiom,
( A = B
| greater(A,B)
| less(A,B) ),
file('NUM853+2.p',unknown),
[] ).
cnf(47,axiom,
vplus(A,B) = vplus(B,A),
file('NUM853+2.p',unknown),
[] ).
cnf(66,plain,
less(A,vplus(A,B)),
inference(hyper,[status(thm)],[29,15]),
[iquote('hyper,29,15')] ).
cnf(71,plain,
( A = B
| vplus(C,B) != vplus(C,A) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[39,22]),39]),
[iquote('para_into,38.1.1,22.1.1,demod,39')] ).
cnf(78,plain,
( A = B
| B != A ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[42,3]),42]),
[iquote('para_into,41.1.1,3.2.1,demod,42')] ).
cnf(84,plain,
vplus(vmul(vd488,vd487),dollar_f2(vmul(vd488,vd487),vmul(vd486,vd487))) = vmul(vd486,vd487),
inference(hyper,[status(thm)],[30,17]),
[iquote('hyper,30,17')] ).
cnf(88,plain,
greater(vmul(vd486,vmul(vd487,A)),vmul(vd488,vmul(vd487,A))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[30,4]),32,32]),
[iquote('hyper,30,4,demod,32,32')] ).
cnf(97,plain,
vplus(A,dollar_f1(vplus(A,B),A)) = vplus(A,B),
inference(hyper,[status(thm)],[66,14]),
[iquote('hyper,66,14')] ).
cnf(112,plain,
( ~ less(A,B)
| vplus(A,C) = B
| C != dollar_f1(B,A) ),
inference(para_from,[status(thm),theory(equality)],[78,14]),
[iquote('para_from,78.1.1,14.2.1.2')] ).
cnf(131,plain,
( ~ greater(A,vd488)
| A != vd486 ),
inference(para_from,[status(thm),theory(equality)],[78,1]),
[iquote('para_from,78.1.1,1.1.1')] ).
cnf(144,plain,
( ~ greater(A,B)
| A != vd486
| vplus(C,vd488) != vplus(C,B) ),
inference(para_into,[status(thm),theory(equality)],[131,22]),
[iquote('para_into,131.1.2,22.1.1')] ).
cnf(214,plain,
( A = B
| greater(A,B)
| greater(B,A) ),
inference(hyper,[status(thm)],[44,8]),
[iquote('hyper,44,8')] ).
cnf(216,plain,
( A = B
| greater(A,B)
| less(vmul(A,C),vmul(B,C)) ),
inference(hyper,[status(thm)],[44,2]),
[iquote('hyper,44,2')] ).
cnf(1112,plain,
vmul(vd488,vd487) != vmul(vd486,vd487),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[84,28])]),
[iquote('para_from,84.1.1,28.1.1,flip.1')] ).
cnf(1132,plain,
vmul(vd487,vd488) != vmul(vd486,vd487),
inference(para_into,[status(thm),theory(equality)],[1112,36]),
[iquote('para_into,1112.1.1,36.1.1')] ).
cnf(1210,plain,
dollar_f1(vplus(A,B),A) = B,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[97,71])]),
[iquote('hyper,97,71,flip.1')] ).
cnf(1214,plain,
dollar_f1(vplus(A,B),B) = A,
inference(para_into,[status(thm),theory(equality)],[1210,47]),
[iquote('para_into,1210.1.1.1,47.1.1')] ).
cnf(1888,plain,
( vd488 = vd486
| greater(vd488,vd486) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[214,144,1214,47]),1214,1214])]),
[iquote('hyper,214,144,1213,47,demod,1214,1214,flip.1')] ).
cnf(1893,plain,
greater(vd488,vd486),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1888,1132]),36]),
[iquote('para_from,1888.1.1,1132.1.1.2,unit_del,36')] ).
cnf(1906,plain,
less(vd486,vd488),
inference(hyper,[status(thm)],[1893,9]),
[iquote('hyper,1893,9')] ).
cnf(1918,plain,
vplus(vd486,dollar_f1(vd488,vd486)) = vd488,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1906,112,1214]),1214]),
[iquote('hyper,1906,112,1213,demod,1214')] ).
cnf(1930,plain,
vd488 = vd486,
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[216,11,88]),1])]),
[iquote('hyper,216,11,88,unit_del,1,flip.1')] ).
cnf(1940,plain,
vplus(vd486,dollar_f1(vd486,vd486)) = vd486,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1918]),1930,1930]),
[iquote('back_demod,1918,demod,1930,1930')] ).
cnf(1942,plain,
$false,
inference(binary,[status(thm)],[1940,28]),
[iquote('binary,1940.1,28.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM853+2 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 10:05:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.10/2.28 ----- Otter 3.3f, August 2004 -----
% 2.10/2.28 The process was started by sandbox on n025.cluster.edu,
% 2.10/2.28 Wed Jul 27 10:05:00 2022
% 2.10/2.28 The command was "./otter". The process ID is 8388.
% 2.10/2.28
% 2.10/2.28 set(prolog_style_variables).
% 2.10/2.28 set(auto).
% 2.10/2.28 dependent: set(auto1).
% 2.10/2.28 dependent: set(process_input).
% 2.10/2.28 dependent: clear(print_kept).
% 2.10/2.28 dependent: clear(print_new_demod).
% 2.10/2.28 dependent: clear(print_back_demod).
% 2.10/2.28 dependent: clear(print_back_sub).
% 2.10/2.28 dependent: set(control_memory).
% 2.10/2.28 dependent: assign(max_mem, 12000).
% 2.10/2.28 dependent: assign(pick_given_ratio, 4).
% 2.10/2.28 dependent: assign(stats_level, 1).
% 2.10/2.28 dependent: assign(max_seconds, 10800).
% 2.10/2.28 clear(print_given).
% 2.10/2.28
% 2.10/2.28 formula_list(usable).
% 2.10/2.28 all A (A=A).
% 2.10/2.28 -greater(vd486,vd488).
% 2.10/2.28 greater(vmul(vd486,vd487),vmul(vd488,vd487)).
% 2.10/2.28 all Vd456 Vd465 Vd466 (less(Vd465,Vd466)->less(vmul(Vd465,Vd456),vmul(Vd466,Vd456))).
% 2.10/2.28 all Vd456 Vd461 Vd462 (Vd461=Vd462->vmul(Vd461,Vd456)=vmul(Vd462,Vd456)).
% 2.10/2.28 all Vd456 Vd457 Vd458 (greater(Vd457,Vd458)->greater(vmul(Vd457,Vd456),vmul(Vd458,Vd456))).
% 2.10/2.28 all Vd444 Vd445 Vd446 (vmul(vmul(Vd444,Vd445),Vd446)=vmul(Vd444,vmul(Vd445,Vd446))).
% 2.10/2.28 all Vd432 Vd433 Vd434 (vmul(Vd432,vplus(Vd433,Vd434))=vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434))).
% 2.10/2.28 all Vd418 Vd419 (vmul(Vd418,Vd419)=vmul(Vd419,Vd418)).
% 2.10/2.28 all Vd408 Vd409 (vmul(vsucc(Vd408),Vd409)=vplus(vmul(Vd408,Vd409),Vd409)).
% 2.10/2.28 all Vd400 (vmul(v1,Vd400)=Vd400).
% 2.10/2.28 all Vd396 Vd397 (vmul(Vd396,vsucc(Vd397))=vplus(vmul(Vd396,Vd397),Vd396)&vmul(Vd396,v1)=Vd396).
% 2.10/2.28 all Vd386 Vd387 (less(Vd386,vplus(Vd387,v1))->le_q(Vd386,Vd387)).
% 2.10/2.28 all Vd375 Vd376 (greater(Vd375,Vd376)->ge_q(Vd375,vplus(Vd376,v1))).
% 2.10/2.28 all Vd369 ge_q(Vd369,v1).
% 2.10/2.28 all Vd362 Vd363 Vd365 Vd366 (ge_q(Vd365,Vd366)&ge_q(Vd362,Vd363)->ge_q(vplus(Vd362,Vd365),vplus(Vd363,Vd366))).
% 2.10/2.28 all Vd226 Vd227 (less(Vd226,Vd227)->greater(Vd227,Vd226)).
% 2.10/2.28 all Vd208 Vd209 (greater(Vd208,Vd209)->less(Vd209,Vd208)).
% 2.10/2.28 all Vd203 Vd204 (Vd203=Vd204|greater(Vd203,Vd204)|less(Vd203,Vd204)).
% 2.10/2.28 all Vd203 Vd204 (Vd203!=Vd204| -less(Vd203,Vd204)).
% 2.10/2.28 all Vd203 Vd204 (-greater(Vd203,Vd204)| -less(Vd203,Vd204)).
% 2.10/2.28 all Vd203 Vd204 (Vd203!=Vd204| -greater(Vd203,Vd204)).
% 2.10/2.28 all Vd198 Vd199 (less(Vd199,Vd198)<-> (exists Vd201 (Vd198=vplus(Vd199,Vd201)))).
% 2.10/2.28 all Vd193 Vd194 (greater(Vd194,Vd193)<-> (exists Vd196 (Vd194=vplus(Vd193,Vd196)))).
% 2.10/2.28 all Vd120 Vd121 (Vd120=Vd121| (exists Vd123 (Vd120=vplus(Vd121,Vd123)))| (exists Vd125 (Vd121=vplus(Vd120,Vd125)))).
% 2.10/2.28 all Vd120 Vd121 (Vd120!=Vd121| -(exists Vd125 (Vd121=vplus(Vd120,Vd125)))).
% 2.10/2.28 all Vd120 Vd121 (-(exists Vd123 (Vd120=vplus(Vd121,Vd123)))| -(exists Vd125 (Vd121=vplus(Vd120,Vd125)))).
% 2.10/2.28 all Vd120 Vd121 (Vd120!=Vd121| -(exists Vd123 (Vd120=vplus(Vd121,Vd123)))).
% 2.10/2.28 all Vd104 Vd105 (Vd104!=Vd105-> (all Vd107 (vplus(Vd107,Vd104)!=vplus(Vd107,Vd105)))).
% 2.10/2.28 all Vd92 Vd93 (Vd93!=vplus(Vd92,Vd93)).
% 2.10/2.28 all Vd78 Vd79 (vplus(Vd79,Vd78)=vplus(Vd78,Vd79)).
% 2.10/2.28 all Vd68 Vd69 (vplus(vsucc(Vd68),Vd69)=vsucc(vplus(Vd68,Vd69))).
% 2.10/2.28 all Vd59 (vplus(v1,Vd59)=vsucc(Vd59)).
% 2.10/2.28 all Vd46 Vd47 Vd48 (vplus(vplus(Vd46,Vd47),Vd48)=vplus(Vd46,vplus(Vd47,Vd48))).
% 2.10/2.28 all Vd42 Vd43 (vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43))&vplus(Vd42,v1)=vsucc(Vd42)).
% 2.10/2.28 all Vd24 (Vd24!=v1->Vd24=vsucc(vskolem2(Vd24))).
% 2.10/2.28 all Vd16 (vsucc(Vd16)!=Vd16).
% 2.10/2.28 all Vd7 Vd8 (Vd7!=Vd8->vsucc(Vd7)!=vsucc(Vd8)).
% 2.10/2.28 end_of_list.
% 2.10/2.28
% 2.10/2.28 -------> usable clausifies to:
% 2.10/2.28
% 2.10/2.28 list(usable).
% 2.10/2.28 0 [] A=A.
% 2.10/2.28 0 [] -greater(vd486,vd488).
% 2.10/2.28 0 [] greater(vmul(vd486,vd487),vmul(vd488,vd487)).
% 2.10/2.28 0 [] -less(Vd465,Vd466)|less(vmul(Vd465,Vd456),vmul(Vd466,Vd456)).
% 2.10/2.28 0 [] Vd461!=Vd462|vmul(Vd461,Vd456)=vmul(Vd462,Vd456).
% 2.10/2.28 0 [] -greater(Vd457,Vd458)|greater(vmul(Vd457,Vd456),vmul(Vd458,Vd456)).
% 2.10/2.28 0 [] vmul(vmul(Vd444,Vd445),Vd446)=vmul(Vd444,vmul(Vd445,Vd446)).
% 2.10/2.28 0 [] vmul(Vd432,vplus(Vd433,Vd434))=vplus(vmul(Vd432,Vd433),vmul(Vd432,Vd434)).
% 2.10/2.28 0 [] vmul(Vd418,Vd419)=vmul(Vd419,Vd418).
% 2.10/2.28 0 [] vmul(vsucc(Vd408),Vd409)=vplus(vmul(Vd408,Vd409),Vd409).
% 2.10/2.28 0 [] vmul(v1,Vd400)=Vd400.
% 2.10/2.28 0 [] vmul(Vd396,vsucc(Vd397))=vplus(vmul(Vd396,Vd397),Vd396).
% 2.10/2.28 0 [] vmul(Vd396,v1)=Vd396.
% 2.10/2.28 0 [] -less(Vd386,vplus(Vd387,v1))|le_q(Vd386,Vd387).
% 2.10/2.28 0 [] -greater(Vd375,Vd376)|ge_q(Vd375,vplus(Vd376,v1)).
% 2.10/2.28 0 [] ge_q(Vd369,v1).
% 2.10/2.28 0 [] -ge_q(Vd365,Vd366)| -ge_q(Vd362,Vd363)|ge_q(vplus(Vd362,Vd365),vplus(Vd363,Vd366)).
% 2.10/2.28 0 [] -less(Vd226,Vd227)|greater(Vd227,Vd226).
% 2.10/2.28 0 [] -greater(Vd208,Vd209)|less(Vd209,Vd208).
% 2.10/2.28 0 [] Vd203=Vd204|greater(Vd203,Vd204)|less(Vd203,Vd204).
% 2.10/2.28 0 [] Vd203!=Vd204| -less(Vd203,Vd204).
% 2.10/2.28 0 [] -greater(Vd203,Vd204)| -less(Vd203,Vd204).
% 2.10/2.28 0 [] Vd203!=Vd204| -greater(Vd203,Vd204).
% 2.10/2.28 0 [] -less(Vd199,Vd198)|Vd198=vplus(Vd199,$f1(Vd198,Vd199)).
% 2.10/2.28 0 [] less(Vd199,Vd198)|Vd198!=vplus(Vd199,Vd201).
% 2.10/2.28 0 [] -greater(Vd194,Vd193)|Vd194=vplus(Vd193,$f2(Vd193,Vd194)).
% 2.10/2.28 0 [] greater(Vd194,Vd193)|Vd194!=vplus(Vd193,Vd196).
% 2.10/2.28 0 [] Vd120=Vd121|Vd120=vplus(Vd121,$f3(Vd120,Vd121))|Vd121=vplus(Vd120,$f4(Vd120,Vd121)).
% 2.10/2.28 0 [] Vd120!=Vd121|Vd121!=vplus(Vd120,Vd125).
% 2.10/2.28 0 [] Vd120!=vplus(Vd121,Vd123)|Vd121!=vplus(Vd120,Vd125).
% 2.10/2.28 0 [] Vd120!=Vd121|Vd120!=vplus(Vd121,Vd123).
% 2.10/2.28 0 [] Vd104=Vd105|vplus(Vd107,Vd104)!=vplus(Vd107,Vd105).
% 2.10/2.28 0 [] Vd93!=vplus(Vd92,Vd93).
% 2.10/2.28 0 [] vplus(Vd79,Vd78)=vplus(Vd78,Vd79).
% 2.10/2.28 0 [] vplus(vsucc(Vd68),Vd69)=vsucc(vplus(Vd68,Vd69)).
% 2.10/2.28 0 [] vplus(v1,Vd59)=vsucc(Vd59).
% 2.10/2.28 0 [] vplus(vplus(Vd46,Vd47),Vd48)=vplus(Vd46,vplus(Vd47,Vd48)).
% 2.10/2.28 0 [] vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43)).
% 2.10/2.28 0 [] vplus(Vd42,v1)=vsucc(Vd42).
% 2.10/2.28 0 [] Vd24=v1|Vd24=vsucc(vskolem2(Vd24)).
% 2.10/2.28 0 [] vsucc(Vd16)!=Vd16.
% 2.10/2.28 0 [] Vd7=Vd8|vsucc(Vd7)!=vsucc(Vd8).
% 2.10/2.28 end_of_list.
% 2.10/2.28
% 2.10/2.28 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 2.10/2.28
% 2.10/2.28 This ia a non-Horn set with equality. The strategy will be
% 2.10/2.28 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.10/2.28 deletion, with positive clauses in sos and nonpositive
% 2.10/2.28 clauses in usable.
% 2.10/2.28
% 2.10/2.28 dependent: set(knuth_bendix).
% 2.10/2.28 dependent: set(anl_eq).
% 2.10/2.28 dependent: set(para_from).
% 2.10/2.28 dependent: set(para_into).
% 2.10/2.28 dependent: clear(para_from_right).
% 2.10/2.28 dependent: clear(para_into_right).
% 2.10/2.28 dependent: set(para_from_vars).
% 2.10/2.28 dependent: set(eq_units_both_ways).
% 2.10/2.28 dependent: set(dynamic_demod_all).
% 2.10/2.28 dependent: set(dynamic_demod).
% 2.10/2.28 dependent: set(order_eq).
% 2.10/2.28 dependent: set(back_demod).
% 2.10/2.28 dependent: set(lrpo).
% 2.10/2.28 dependent: set(hyper_res).
% 2.10/2.28 dependent: set(unit_deletion).
% 2.10/2.28 dependent: set(factor).
% 2.10/2.28
% 2.10/2.28 ------------> process usable:
% 2.10/2.28 ** KEPT (pick-wt=3): 1 [] -greater(vd486,vd488).
% 2.10/2.28 ** KEPT (pick-wt=10): 2 [] -less(A,B)|less(vmul(A,C),vmul(B,C)).
% 2.10/2.28 ** KEPT (pick-wt=10): 3 [] A!=B|vmul(A,C)=vmul(B,C).
% 2.10/2.28 ** KEPT (pick-wt=10): 4 [] -greater(A,B)|greater(vmul(A,C),vmul(B,C)).
% 2.10/2.28 ** KEPT (pick-wt=8): 5 [] -less(A,vplus(B,v1))|le_q(A,B).
% 2.10/2.28 ** KEPT (pick-wt=8): 6 [] -greater(A,B)|ge_q(A,vplus(B,v1)).
% 2.10/2.28 ** KEPT (pick-wt=13): 7 [] -ge_q(A,B)| -ge_q(C,D)|ge_q(vplus(C,A),vplus(D,B)).
% 2.10/2.28 ** KEPT (pick-wt=6): 8 [] -less(A,B)|greater(B,A).
% 2.10/2.28 ** KEPT (pick-wt=6): 9 [] -greater(A,B)|less(B,A).
% 2.10/2.28 ** KEPT (pick-wt=6): 10 [] A!=B| -less(A,B).
% 2.10/2.28 ** KEPT (pick-wt=6): 11 [] -greater(A,B)| -less(A,B).
% 2.10/2.28 ** KEPT (pick-wt=6): 12 [] A!=B| -greater(A,B).
% 2.10/2.28 ** KEPT (pick-wt=10): 14 [copy,13,flip.2] -less(A,B)|vplus(A,$f1(B,A))=B.
% 2.10/2.28 ** KEPT (pick-wt=8): 15 [] less(A,B)|B!=vplus(A,C).
% 2.10/2.28 ** KEPT (pick-wt=10): 17 [copy,16,flip.2] -greater(A,B)|vplus(B,$f2(B,A))=A.
% 2.10/2.28 ** KEPT (pick-wt=8): 18 [] greater(A,B)|A!=vplus(B,C).
% 2.10/2.28 ** KEPT (pick-wt=8): 19 [] A!=B|B!=vplus(A,C).
% 2.10/2.28 ** KEPT (pick-wt=10): 20 [] A!=vplus(B,C)|B!=vplus(A,D).
% 2.10/2.28 ** KEPT (pick-wt=8): 21 [] A!=B|A!=vplus(B,C).
% 2.10/2.28 ** KEPT (pick-wt=10): 22 [] A=B|vplus(C,A)!=vplus(C,B).
% 2.10/2.28 ** KEPT (pick-wt=5): 24 [copy,23,flip.1] vplus(A,B)!=B.
% 2.10/2.28 ** KEPT (pick-wt=4): 25 [] vsucc(A)!=A.
% 2.10/2.28 ** KEPT (pick-wt=8): 26 [] A=B|vsucc(A)!=vsucc(B).
% 2.10/2.28
% 2.10/2.28 ------------> process sos:
% 2.10/2.28 ** KEPT (pick-wt=3): 29 [] A=A.
% 2.10/2.28 ** KEPT (pick-wt=7): 30 [] greater(vmul(vd486,vd487),vmul(vd488,vd487)).
% 2.10/2.28 ** KEPT (pick-wt=11): 31 [] vmul(vmul(A,B),C)=vmul(A,vmul(B,C)).
% 2.10/2.28 ---> New Demodulator: 32 [new_demod,31] vmul(vmul(A,B),C)=vmul(A,vmul(B,C)).
% 2.10/2.28 ** KEPT (pick-wt=13): 34 [copy,33,flip.1] vplus(vmul(A,B),vmul(A,C))=vmul(A,vplus(B,C)).
% 2.10/2.28 ---> New Demodulator: 35 [new_demod,34] vplus(vmul(A,B),vmul(A,C))=vmul(A,vplus(B,C)).
% 2.10/2.28 ** KEPT (pick-wt=7): 36 [] vmul(A,B)=vmul(B,A).
% 2.10/2.28 ** KEPT (pick-wt=10): 37 [] vmul(vsucc(A),B)=vplus(vmul(A,B),B).
% 2.10/2.28 ** KEPT (pick-wt=5): 38 [] vmul(v1,A)=A.
% 2.10/2.28 ---> New Demodulator: 39 [new_demod,38] vmul(v1,A)=A.
% 2.10/2.28 ** KEPT (pick-wt=10): 40 [] vmul(A,vsucc(B))=vplus(vmul(A,B),A).
% 2.10/2.28 ** KEPT (pick-wt=5): 41 [] vmul(A,v1)=A.
% 3.82/3.98 ---> New Demodulator: 42 [new_demod,41] vmul(A,v1)=A.
% 3.82/3.98 ** KEPT (pick-wt=3): 43 [] ge_q(A,v1).
% 3.82/3.98 ** KEPT (pick-wt=9): 44 [] A=B|greater(A,B)|less(A,B).
% 3.82/3.98 ** KEPT (pick-wt=17): 46 [copy,45,flip.2,flip.3] A=B|vplus(B,$f3(A,B))=A|vplus(A,$f4(A,B))=B.
% 3.82/3.98 ** KEPT (pick-wt=7): 47 [] vplus(A,B)=vplus(B,A).
% 3.82/3.98 ** KEPT (pick-wt=9): 49 [copy,48,flip.1] vsucc(vplus(A,B))=vplus(vsucc(A),B).
% 3.82/3.98 ---> New Demodulator: 50 [new_demod,49] vsucc(vplus(A,B))=vplus(vsucc(A),B).
% 3.82/3.98 ** KEPT (pick-wt=6): 52 [copy,51,flip.1] vsucc(A)=vplus(v1,A).
% 3.82/3.98 ---> New Demodulator: 53 [new_demod,52] vsucc(A)=vplus(v1,A).
% 3.82/3.98 ** KEPT (pick-wt=11): 54 [] vplus(vplus(A,B),C)=vplus(A,vplus(B,C)).
% 3.82/3.98 ---> New Demodulator: 55 [new_demod,54] vplus(vplus(A,B),C)=vplus(A,vplus(B,C)).
% 3.82/3.98 ** KEPT (pick-wt=11): 57 [copy,56,demod,53,53] vplus(A,vplus(v1,B))=vplus(v1,vplus(A,B)).
% 3.82/3.98 Following clause subsumed by 47 during input processing: 0 [demod,53] vplus(A,v1)=vplus(v1,A).
% 3.82/3.98 ** KEPT (pick-wt=9): 59 [copy,58,demod,53,flip.2] A=v1|vplus(v1,vskolem2(A))=A.
% 3.82/3.98 Following clause subsumed by 29 during input processing: 0 [copy,29,flip.1] A=A.
% 3.82/3.98 >>>> Starting back demodulation with 32.
% 3.82/3.98 >>>> Starting back demodulation with 35.
% 3.82/3.98 Following clause subsumed by 36 during input processing: 0 [copy,36,flip.1] vmul(A,B)=vmul(B,A).
% 3.82/3.98 ** KEPT (pick-wt=11): 60 [copy,37,flip.1,demod,53] vplus(vmul(A,B),B)=vmul(vplus(v1,A),B).
% 3.82/3.98 ---> New Demodulator: 61 [new_demod,60] vplus(vmul(A,B),B)=vmul(vplus(v1,A),B).
% 3.82/3.98 >>>> Starting back demodulation with 39.
% 3.82/3.98 ** KEPT (pick-wt=11): 62 [copy,40,flip.1,demod,53] vplus(vmul(A,B),A)=vmul(A,vplus(v1,B)).
% 3.82/3.98 ---> New Demodulator: 63 [new_demod,62] vplus(vmul(A,B),A)=vmul(A,vplus(v1,B)).
% 3.82/3.98 >>>> Starting back demodulation with 42.
% 3.82/3.98 Following clause subsumed by 47 during input processing: 0 [copy,47,flip.1] vplus(A,B)=vplus(B,A).
% 3.82/3.98 >>>> Starting back demodulation with 50.
% 3.82/3.98 >>>> Starting back demodulation with 53.
% 3.82/3.98 >> back demodulating 49 with 53.
% 3.82/3.98 >> back demodulating 40 with 53.
% 3.82/3.98 >> back demodulating 37 with 53.
% 3.82/3.98 >> back demodulating 26 with 53.
% 3.82/3.98 >> back demodulating 25 with 53.
% 3.82/3.98 >>>> Starting back demodulation with 55.
% 3.82/3.98 ** KEPT (pick-wt=11): 64 [copy,57,flip.1] vplus(v1,vplus(A,B))=vplus(A,vplus(v1,B)).
% 3.82/3.98 >>>> Starting back demodulation with 61.
% 3.82/3.98 >>>> Starting back demodulation with 63.
% 3.82/3.98 Following clause subsumed by 57 during input processing: 0 [copy,64,flip.1] vplus(A,vplus(v1,B))=vplus(v1,vplus(A,B)).
% 3.82/3.98
% 3.82/3.98 ======= end of input processing =======
% 3.82/3.98
% 3.82/3.98 =========== start of search ===========
% 3.82/3.98
% 3.82/3.98
% 3.82/3.98 Resetting weight limit to 9.
% 3.82/3.98
% 3.82/3.98
% 3.82/3.98 Resetting weight limit to 9.
% 3.82/3.98
% 3.82/3.98 sos_size=701
% 3.82/3.98
% 3.82/3.98
% 3.82/3.98 Resetting weight limit to 8.
% 3.82/3.98
% 3.82/3.98
% 3.82/3.98 Resetting weight limit to 8.
% 3.82/3.98
% 3.82/3.98 sos_size=863
% 3.82/3.98
% 3.82/3.98
% 3.82/3.98 Resetting weight limit to 7.
% 3.82/3.98
% 3.82/3.98
% 3.82/3.98 Resetting weight limit to 7.
% 3.82/3.98
% 3.82/3.98 sos_size=1049
% 3.82/3.98
% 3.82/3.98 -------- PROOF --------
% 3.82/3.98
% 3.82/3.98 ----> UNIT CONFLICT at 1.70 sec ----> 1942 [binary,1940.1,28.1] $F.
% 3.82/3.98
% 3.82/3.98 Length of proof is 24. Level of proof is 9.
% 3.82/3.98
% 3.82/3.98 ---------------- PROOF ----------------
% 3.82/3.98 % SZS status Theorem
% 3.82/3.98 % SZS output start Refutation
% See solution above
% 3.82/3.98 ------------ end of proof -------------
% 3.82/3.98
% 3.82/3.98
% 3.82/3.98 Search stopped by max_proofs option.
% 3.82/3.98
% 3.82/3.98
% 3.82/3.98 Search stopped by max_proofs option.
% 3.82/3.98
% 3.82/3.98 ============ end of search ============
% 3.82/3.98
% 3.82/3.98 -------------- statistics -------------
% 3.82/3.98 clauses given 606
% 3.82/3.98 clauses generated 257699
% 3.82/3.98 clauses kept 1856
% 3.82/3.98 clauses forward subsumed 11211
% 3.82/3.98 clauses back subsumed 217
% 3.82/3.98 Kbytes malloced 6835
% 3.82/3.98
% 3.82/3.98 ----------- times (seconds) -----------
% 3.82/3.98 user CPU time 1.70 (0 hr, 0 min, 1 sec)
% 3.82/3.98 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 3.82/3.98 wall-clock time 4 (0 hr, 0 min, 4 sec)
% 3.82/3.98
% 3.82/3.98 That finishes the proof of the theorem.
% 3.82/3.98
% 3.82/3.98 Process 8388 finished Wed Jul 27 10:05:04 2022
% 3.82/3.98 Otter interrupted
% 3.82/3.98 PROOF FOUND
%------------------------------------------------------------------------------