TSTP Solution File: NUM848+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM848+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 13:10:05 EDT 2022
% Result : Theorem 1.96s 2.13s
% Output : Refutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 10 RR)
% Number of literals : 15 ( 14 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 7 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
file('NUM848+1.p',unknown),
[] ).
cnf(2,plain,
vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))) != vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(50,axiom,
A = A,
file('NUM848+1.p',unknown),
[] ).
cnf(52,axiom,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
file('NUM848+1.p',unknown),
[] ).
cnf(53,axiom,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436),
file('NUM848+1.p',unknown),
[] ).
cnf(55,plain,
vplus(vmul(vd436,vplus(vd437,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[53]),52]),
[iquote('copy,53,demod,52')] ).
cnf(56,axiom,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vplus(vd437,vd439)),vd436),
file('NUM848+1.p',unknown),
[] ).
cnf(57,plain,
vmul(vd436,vsucc(vplus(vd437,vd439))) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[56]),55]),
[iquote('copy,56,demod,55')] ).
cnf(77,axiom,
vmul(A,vsucc(B)) = vplus(vmul(A,B),A),
file('NUM848+1.p',unknown),
[] ).
cnf(89,axiom,
vplus(v1,A) = vsucc(A),
file('NUM848+1.p',unknown),
[] ).
cnf(91,plain,
vsucc(A) = vplus(v1,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[89])]),
[iquote('copy,89,flip.1')] ).
cnf(103,plain,
vplus(vmul(A,B),A) = vmul(A,vplus(v1,B)),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[77])]),91]),
[iquote('copy,77,flip.1,demod,91')] ).
cnf(105,plain,
vplus(vmul(vd436,vd437),vmul(vd436,vplus(v1,vd439))) = vmul(vd436,vplus(v1,vplus(vd437,vd439))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[57]),91,103])]),
[iquote('back_demod,57,demod,91,103,flip.1')] ).
cnf(108,plain,
vmul(vd436,vplus(v1,vplus(vd437,vd439))) != vmul(vd436,vplus(v1,vplus(vd437,vd439))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),91,105,103,105]),
[iquote('back_demod,2,demod,91,105,103,105')] ).
cnf(109,plain,
$false,
inference(binary,[status(thm)],[108,50]),
[iquote('binary,108.1,50.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM848+1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n022.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 09:54:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.96/2.12 ----- Otter 3.3f, August 2004 -----
% 1.96/2.12 The process was started by sandbox on n022.cluster.edu,
% 1.96/2.12 Wed Jul 27 09:54:50 2022
% 1.96/2.12 The command was "./otter". The process ID is 18962.
% 1.96/2.12
% 1.96/2.12 set(prolog_style_variables).
% 1.96/2.12 set(auto).
% 1.96/2.12 dependent: set(auto1).
% 1.96/2.12 dependent: set(process_input).
% 1.96/2.12 dependent: clear(print_kept).
% 1.96/2.12 dependent: clear(print_new_demod).
% 1.96/2.12 dependent: clear(print_back_demod).
% 1.96/2.12 dependent: clear(print_back_sub).
% 1.96/2.12 dependent: set(control_memory).
% 1.96/2.12 dependent: assign(max_mem, 12000).
% 1.96/2.12 dependent: assign(pick_given_ratio, 4).
% 1.96/2.12 dependent: assign(stats_level, 1).
% 1.96/2.12 dependent: assign(max_seconds, 10800).
% 1.96/2.12 clear(print_given).
% 1.96/2.12
% 1.96/2.12 formula_list(usable).
% 1.96/2.12 all A (A=A).
% 1.96/2.12 vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))!=vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))).
% 1.96/2.12 vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 1.96/2.12 vplus(vmul(vd436,vplus(vd437,vd439)),vd436)=vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436).
% 1.96/2.12 vmul(vd436,vsucc(vplus(vd437,vd439)))=vplus(vmul(vd436,vplus(vd437,vd439)),vd436).
% 1.96/2.13 vmul(vd436,vplus(vd437,vsucc(vd439)))=vmul(vd436,vsucc(vplus(vd437,vd439))).
% 1.96/2.13 vmul(vd436,vplus(vd437,vd439))=vplus(vmul(vd436,vd437),vmul(vd436,vd439)).
% 1.96/2.13 vplus(vmul(vd436,vd437),vd436)=vplus(vmul(vd436,vd437),vmul(vd436,v1)).
% 1.96/2.13 vmul(vd436,vsucc(vd437))=vplus(vmul(vd436,vd437),vd436).
% 1.96/2.13 vmul(vd436,vplus(vd437,v1))=vmul(vd436,vsucc(vd437)).
% 1.96/2.13 all Vd418 Vd419 (vmul(Vd418,Vd419)=vmul(Vd419,Vd418)).
% 1.96/2.13 all Vd408 Vd409 (vmul(vsucc(Vd408),Vd409)=vplus(vmul(Vd408,Vd409),Vd409)).
% 1.96/2.13 all Vd400 (vmul(v1,Vd400)=Vd400).
% 1.96/2.13 all Vd396 Vd397 (vmul(Vd396,vsucc(Vd397))=vplus(vmul(Vd396,Vd397),Vd396)&vmul(Vd396,v1)=Vd396).
% 1.96/2.13 all Vd386 Vd387 (less(Vd386,vplus(Vd387,v1))->le_q(Vd386,Vd387)).
% 1.96/2.13 all Vd375 Vd376 (greater(Vd375,Vd376)->ge_q(Vd375,vplus(Vd376,v1))).
% 1.96/2.13 all Vd369 ge_q(Vd369,v1).
% 1.96/2.13 all Vd362 Vd363 Vd365 Vd366 (ge_q(Vd365,Vd366)&ge_q(Vd362,Vd363)->ge_q(vplus(Vd362,Vd365),vplus(Vd363,Vd366))).
% 1.96/2.13 all Vd353 Vd354 Vd355 Vd356 (greater(Vd355,Vd356)&ge_q(Vd353,Vd354)|ge_q(Vd355,Vd356)&greater(Vd353,Vd354)->greater(vplus(Vd353,Vd355),vplus(Vd354,Vd356))).
% 1.96/2.13 all Vd337 Vd338 Vd340 Vd341 (greater(Vd340,Vd341)&greater(Vd337,Vd338)->greater(vplus(Vd337,Vd340),vplus(Vd338,Vd341))).
% 1.96/2.13 all Vd328 Vd329 Vd330 (less(vplus(Vd328,Vd330),vplus(Vd329,Vd330))->less(Vd328,Vd329)).
% 1.96/2.13 all Vd328 Vd329 Vd330 (vplus(Vd328,Vd330)=vplus(Vd329,Vd330)->Vd328=Vd329).
% 1.96/2.13 all Vd328 Vd329 Vd330 (greater(vplus(Vd328,Vd330),vplus(Vd329,Vd330))->greater(Vd328,Vd329)).
% 1.96/2.13 all Vd301 Vd302 Vd303 (less(Vd301,Vd302)->less(vplus(Vd301,Vd303),vplus(Vd302,Vd303))).
% 1.96/2.13 all Vd301 Vd302 Vd303 (Vd301=Vd302->vplus(Vd301,Vd303)=vplus(Vd302,Vd303)).
% 1.96/2.13 all Vd301 Vd302 Vd303 (greater(Vd301,Vd302)->greater(vplus(Vd301,Vd303),vplus(Vd302,Vd303))).
% 1.96/2.13 all Vd295 Vd296 greater(vplus(Vd295,Vd296),Vd295).
% 1.96/2.13 all Vd289 Vd290 Vd292 (le_q(Vd290,Vd292)&le_q(Vd289,Vd290)->le_q(Vd289,Vd292)).
% 1.96/2.13 all Vd281 Vd282 Vd283 (less(Vd282,Vd283)&le_q(Vd281,Vd282)|le_q(Vd282,Vd283)&less(Vd281,Vd282)->less(Vd281,Vd283)).
% 1.96/2.13 all Vd262 Vd263 Vd265 (less(Vd263,Vd265)&less(Vd262,Vd263)->less(Vd262,Vd265)).
% 1.96/2.13 all Vd258 Vd259 (le_q(Vd258,Vd259)->ge_q(Vd259,Vd258)).
% 1.96/2.13 all Vd254 Vd255 (ge_q(Vd254,Vd255)->le_q(Vd255,Vd254)).
% 1.96/2.13 all Vd249 Vd250 (le_q(Vd250,Vd249)<->less(Vd250,Vd249)|Vd250=Vd249).
% 1.96/2.13 all Vd244 Vd245 (ge_q(Vd245,Vd244)<->greater(Vd245,Vd244)|Vd245=Vd244).
% 1.96/2.13 all Vd226 Vd227 (less(Vd226,Vd227)->greater(Vd227,Vd226)).
% 1.96/2.13 all Vd208 Vd209 (greater(Vd208,Vd209)->less(Vd209,Vd208)).
% 1.96/2.13 all Vd203 Vd204 (Vd203=Vd204|greater(Vd203,Vd204)|less(Vd203,Vd204)).
% 1.96/2.13 all Vd203 Vd204 (Vd203!=Vd204| -less(Vd203,Vd204)).
% 1.96/2.13 all Vd203 Vd204 (-greater(Vd203,Vd204)| -less(Vd203,Vd204)).
% 1.96/2.13 all Vd203 Vd204 (Vd203!=Vd204| -greater(Vd203,Vd204)).
% 1.96/2.13 all Vd198 Vd199 (less(Vd199,Vd198)<-> (exists Vd201 (Vd198=vplus(Vd199,Vd201)))).
% 1.96/2.13 all Vd193 Vd194 (greater(Vd194,Vd193)<-> (exists Vd196 (Vd194=vplus(Vd193,Vd196)))).
% 1.96/2.13 all Vd120 Vd121 (Vd120=Vd121| (exists Vd123 (Vd120=vplus(Vd121,Vd123)))| (exists Vd125 (Vd121=vplus(Vd120,Vd125)))).
% 1.96/2.13 all Vd120 Vd121 (Vd120!=Vd121| -(exists Vd125 (Vd121=vplus(Vd120,Vd125)))).
% 1.96/2.13 all Vd120 Vd121 (-(exists Vd123 (Vd120=vplus(Vd121,Vd123)))| -(exists Vd125 (Vd121=vplus(Vd120,Vd125)))).
% 1.96/2.13 all Vd120 Vd121 (Vd120!=Vd121| -(exists Vd123 (Vd120=vplus(Vd121,Vd123)))).
% 1.96/2.13 all Vd104 Vd105 (Vd104!=Vd105-> (all Vd107 (vplus(Vd107,Vd104)!=vplus(Vd107,Vd105)))).
% 1.96/2.13 all Vd92 Vd93 (Vd93!=vplus(Vd92,Vd93)).
% 1.96/2.13 all Vd78 Vd79 (vplus(Vd79,Vd78)=vplus(Vd78,Vd79)).
% 1.96/2.13 all Vd68 Vd69 (vplus(vsucc(Vd68),Vd69)=vsucc(vplus(Vd68,Vd69))).
% 1.96/2.13 all Vd59 (vplus(v1,Vd59)=vsucc(Vd59)).
% 1.96/2.13 all Vd46 Vd47 Vd48 (vplus(vplus(Vd46,Vd47),Vd48)=vplus(Vd46,vplus(Vd47,Vd48))).
% 1.96/2.13 all Vd42 Vd43 (vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43))&vplus(Vd42,v1)=vsucc(Vd42)).
% 1.96/2.13 all Vd24 (Vd24!=v1->Vd24=vsucc(vskolem2(Vd24))).
% 1.96/2.13 all Vd16 (vsucc(Vd16)!=Vd16).
% 1.96/2.13 all Vd7 Vd8 (Vd7!=Vd8->vsucc(Vd7)!=vsucc(Vd8)).
% 1.96/2.13 all Vd3 Vd4 (vsucc(Vd3)=vsucc(Vd4)->Vd3=Vd4).
% 1.96/2.13 all Vd1 (vsucc(Vd1)!=v1).
% 1.96/2.13 end_of_list.
% 1.96/2.13
% 1.96/2.13 -------> usable clausifies to:
% 1.96/2.13
% 1.96/2.13 list(usable).
% 1.96/2.13 0 [] A=A.
% 1.96/2.13 0 [] vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436))!=vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))).
% 1.96/2.13 0 [] vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 1.96/2.13 0 [] vplus(vmul(vd436,vplus(vd437,vd439)),vd436)=vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436).
% 1.96/2.13 0 [] vmul(vd436,vsucc(vplus(vd437,vd439)))=vplus(vmul(vd436,vplus(vd437,vd439)),vd436).
% 1.96/2.13 0 [] vmul(vd436,vplus(vd437,vsucc(vd439)))=vmul(vd436,vsucc(vplus(vd437,vd439))).
% 1.96/2.13 0 [] vmul(vd436,vplus(vd437,vd439))=vplus(vmul(vd436,vd437),vmul(vd436,vd439)).
% 1.96/2.13 0 [] vplus(vmul(vd436,vd437),vd436)=vplus(vmul(vd436,vd437),vmul(vd436,v1)).
% 1.96/2.13 0 [] vmul(vd436,vsucc(vd437))=vplus(vmul(vd436,vd437),vd436).
% 1.96/2.13 0 [] vmul(vd436,vplus(vd437,v1))=vmul(vd436,vsucc(vd437)).
% 1.96/2.13 0 [] vmul(Vd418,Vd419)=vmul(Vd419,Vd418).
% 1.96/2.13 0 [] vmul(vsucc(Vd408),Vd409)=vplus(vmul(Vd408,Vd409),Vd409).
% 1.96/2.13 0 [] vmul(v1,Vd400)=Vd400.
% 1.96/2.13 0 [] vmul(Vd396,vsucc(Vd397))=vplus(vmul(Vd396,Vd397),Vd396).
% 1.96/2.13 0 [] vmul(Vd396,v1)=Vd396.
% 1.96/2.13 0 [] -less(Vd386,vplus(Vd387,v1))|le_q(Vd386,Vd387).
% 1.96/2.13 0 [] -greater(Vd375,Vd376)|ge_q(Vd375,vplus(Vd376,v1)).
% 1.96/2.13 0 [] ge_q(Vd369,v1).
% 1.96/2.13 0 [] -ge_q(Vd365,Vd366)| -ge_q(Vd362,Vd363)|ge_q(vplus(Vd362,Vd365),vplus(Vd363,Vd366)).
% 1.96/2.13 0 [] -greater(Vd355,Vd356)| -ge_q(Vd353,Vd354)|greater(vplus(Vd353,Vd355),vplus(Vd354,Vd356)).
% 1.96/2.13 0 [] -ge_q(Vd355,Vd356)| -greater(Vd353,Vd354)|greater(vplus(Vd353,Vd355),vplus(Vd354,Vd356)).
% 1.96/2.13 0 [] -greater(Vd340,Vd341)| -greater(Vd337,Vd338)|greater(vplus(Vd337,Vd340),vplus(Vd338,Vd341)).
% 1.96/2.13 0 [] -less(vplus(Vd328,Vd330),vplus(Vd329,Vd330))|less(Vd328,Vd329).
% 1.96/2.13 0 [] vplus(Vd328,Vd330)!=vplus(Vd329,Vd330)|Vd328=Vd329.
% 1.96/2.13 0 [] -greater(vplus(Vd328,Vd330),vplus(Vd329,Vd330))|greater(Vd328,Vd329).
% 1.96/2.13 0 [] -less(Vd301,Vd302)|less(vplus(Vd301,Vd303),vplus(Vd302,Vd303)).
% 1.96/2.13 0 [] Vd301!=Vd302|vplus(Vd301,Vd303)=vplus(Vd302,Vd303).
% 1.96/2.13 0 [] -greater(Vd301,Vd302)|greater(vplus(Vd301,Vd303),vplus(Vd302,Vd303)).
% 1.96/2.13 0 [] greater(vplus(Vd295,Vd296),Vd295).
% 1.96/2.13 0 [] -le_q(Vd290,Vd292)| -le_q(Vd289,Vd290)|le_q(Vd289,Vd292).
% 1.96/2.13 0 [] -less(Vd282,Vd283)| -le_q(Vd281,Vd282)|less(Vd281,Vd283).
% 1.96/2.13 0 [] -le_q(Vd282,Vd283)| -less(Vd281,Vd282)|less(Vd281,Vd283).
% 1.96/2.13 0 [] -less(Vd263,Vd265)| -less(Vd262,Vd263)|less(Vd262,Vd265).
% 1.96/2.13 0 [] -le_q(Vd258,Vd259)|ge_q(Vd259,Vd258).
% 1.96/2.13 0 [] -ge_q(Vd254,Vd255)|le_q(Vd255,Vd254).
% 1.96/2.13 0 [] -le_q(Vd250,Vd249)|less(Vd250,Vd249)|Vd250=Vd249.
% 1.96/2.13 0 [] le_q(Vd250,Vd249)| -less(Vd250,Vd249).
% 1.96/2.13 0 [] le_q(Vd250,Vd249)|Vd250!=Vd249.
% 1.96/2.13 0 [] -ge_q(Vd245,Vd244)|greater(Vd245,Vd244)|Vd245=Vd244.
% 1.96/2.13 0 [] ge_q(Vd245,Vd244)| -greater(Vd245,Vd244).
% 1.96/2.13 0 [] ge_q(Vd245,Vd244)|Vd245!=Vd244.
% 1.96/2.13 0 [] -less(Vd226,Vd227)|greater(Vd227,Vd226).
% 1.96/2.13 0 [] -greater(Vd208,Vd209)|less(Vd209,Vd208).
% 1.96/2.13 0 [] Vd203=Vd204|greater(Vd203,Vd204)|less(Vd203,Vd204).
% 1.96/2.13 0 [] Vd203!=Vd204| -less(Vd203,Vd204).
% 1.96/2.13 0 [] -greater(Vd203,Vd204)| -less(Vd203,Vd204).
% 1.96/2.13 0 [] Vd203!=Vd204| -greater(Vd203,Vd204).
% 1.96/2.13 0 [] -less(Vd199,Vd198)|Vd198=vplus(Vd199,$f1(Vd198,Vd199)).
% 1.96/2.13 0 [] less(Vd199,Vd198)|Vd198!=vplus(Vd199,Vd201).
% 1.96/2.13 0 [] -greater(Vd194,Vd193)|Vd194=vplus(Vd193,$f2(Vd193,Vd194)).
% 1.96/2.13 0 [] greater(Vd194,Vd193)|Vd194!=vplus(Vd193,Vd196).
% 1.96/2.13 0 [] Vd120=Vd121|Vd120=vplus(Vd121,$f3(Vd120,Vd121))|Vd121=vplus(Vd120,$f4(Vd120,Vd121)).
% 1.96/2.13 0 [] Vd120!=Vd121|Vd121!=vplus(Vd120,Vd125).
% 1.96/2.13 0 [] Vd120!=vplus(Vd121,Vd123)|Vd121!=vplus(Vd120,Vd125).
% 1.96/2.13 0 [] Vd120!=Vd121|Vd120!=vplus(Vd121,Vd123).
% 1.96/2.13 0 [] Vd104=Vd105|vplus(Vd107,Vd104)!=vplus(Vd107,Vd105).
% 1.96/2.13 0 [] Vd93!=vplus(Vd92,Vd93).
% 1.96/2.13 0 [] vplus(Vd79,Vd78)=vplus(Vd78,Vd79).
% 1.96/2.13 0 [] vplus(vsucc(Vd68),Vd69)=vsucc(vplus(Vd68,Vd69)).
% 1.96/2.13 0 [] vplus(v1,Vd59)=vsucc(Vd59).
% 1.96/2.13 0 [] vplus(vplus(Vd46,Vd47),Vd48)=vplus(Vd46,vplus(Vd47,Vd48)).
% 1.96/2.13 0 [] vplus(Vd42,vsucc(Vd43))=vsucc(vplus(Vd42,Vd43)).
% 1.96/2.13 0 [] vplus(Vd42,v1)=vsucc(Vd42).
% 1.96/2.13 0 [] Vd24=v1|Vd24=vsucc(vskolem2(Vd24)).
% 1.96/2.13 0 [] vsucc(Vd16)!=Vd16.
% 1.96/2.13 0 [] Vd7=Vd8|vsucc(Vd7)!=vsucc(Vd8).
% 1.96/2.13 0 [] vsucc(Vd3)!=vsucc(Vd4)|Vd3=Vd4.
% 1.96/2.13 0 [] vsucc(Vd1)!=v1.
% 1.96/2.13 end_of_list.
% 1.96/2.13
% 1.96/2.13 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.96/2.13
% 1.96/2.13 This ia a non-Horn set with equality. The strategy will be
% 1.96/2.13 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.96/2.13 deletion, with positive clauses in sos and nonpositive
% 1.96/2.13 clauses in usable.
% 1.96/2.13
% 1.96/2.13 dependent: set(knuth_bendix).
% 1.96/2.13 dependent: set(anl_eq).
% 1.96/2.13 dependent: set(para_from).
% 1.96/2.13 dependent: set(para_into).
% 1.96/2.13 dependent: clear(para_from_right).
% 1.96/2.13 dependent: clear(para_into_right).
% 1.96/2.13 dependent: set(para_from_vars).
% 1.96/2.13 dependent: set(eq_units_both_ways).
% 1.96/2.13 dependent: set(dynamic_demod_all).
% 1.96/2.13 dependent: set(dynamic_demod).
% 1.96/2.13 dependent: set(order_eq).
% 1.96/2.13 dependent: set(back_demod).
% 1.96/2.13 dependent: set(lrpo).
% 1.96/2.13 dependent: set(hyper_res).
% 1.96/2.13 dependent: set(unit_deletion).
% 1.96/2.13 dependent: set(factor).
% 1.96/2.13
% 1.96/2.13 ------------> process usable:
% 1.96/2.13 ** KEPT (pick-wt=18): 2 [copy,1,flip.1] vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439)))!=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 1.96/2.13 ** KEPT (pick-wt=8): 3 [] -less(A,vplus(B,v1))|le_q(A,B).
% 1.96/2.13 ** KEPT (pick-wt=8): 4 [] -greater(A,B)|ge_q(A,vplus(B,v1)).
% 1.96/2.13 ** KEPT (pick-wt=13): 5 [] -ge_q(A,B)| -ge_q(C,D)|ge_q(vplus(C,A),vplus(D,B)).
% 1.96/2.13 ** KEPT (pick-wt=13): 6 [] -greater(A,B)| -ge_q(C,D)|greater(vplus(C,A),vplus(D,B)).
% 1.96/2.13 ** KEPT (pick-wt=13): 7 [] -ge_q(A,B)| -greater(C,D)|greater(vplus(C,A),vplus(D,B)).
% 1.96/2.13 ** KEPT (pick-wt=13): 8 [] -greater(A,B)| -greater(C,D)|greater(vplus(C,A),vplus(D,B)).
% 1.96/2.13 ** KEPT (pick-wt=10): 9 [] -less(vplus(A,B),vplus(C,B))|less(A,C).
% 1.96/2.13 ** KEPT (pick-wt=10): 10 [] vplus(A,B)!=vplus(C,B)|A=C.
% 1.96/2.13 ** KEPT (pick-wt=10): 11 [] -greater(vplus(A,B),vplus(C,B))|greater(A,C).
% 1.96/2.13 ** KEPT (pick-wt=10): 12 [] -less(A,B)|less(vplus(A,C),vplus(B,C)).
% 1.96/2.13 ** KEPT (pick-wt=10): 13 [] A!=B|vplus(A,C)=vplus(B,C).
% 1.96/2.13 ** KEPT (pick-wt=10): 14 [] -greater(A,B)|greater(vplus(A,C),vplus(B,C)).
% 1.96/2.13 ** KEPT (pick-wt=9): 15 [] -le_q(A,B)| -le_q(C,A)|le_q(C,B).
% 1.96/2.13 ** KEPT (pick-wt=9): 16 [] -less(A,B)| -le_q(C,A)|less(C,B).
% 1.96/2.13 ** KEPT (pick-wt=9): 17 [] -le_q(A,B)| -less(C,A)|less(C,B).
% 1.96/2.13 ** KEPT (pick-wt=9): 18 [] -less(A,B)| -less(C,A)|less(C,B).
% 1.96/2.13 ** KEPT (pick-wt=6): 19 [] -le_q(A,B)|ge_q(B,A).
% 1.96/2.13 ** KEPT (pick-wt=6): 20 [] -ge_q(A,B)|le_q(B,A).
% 1.96/2.13 ** KEPT (pick-wt=9): 21 [] -le_q(A,B)|less(A,B)|A=B.
% 1.96/2.13 ** KEPT (pick-wt=6): 22 [] le_q(A,B)| -less(A,B).
% 1.96/2.13 ** KEPT (pick-wt=6): 23 [] le_q(A,B)|A!=B.
% 1.96/2.13 ** KEPT (pick-wt=9): 24 [] -ge_q(A,B)|greater(A,B)|A=B.
% 1.96/2.13 ** KEPT (pick-wt=6): 25 [] ge_q(A,B)| -greater(A,B).
% 1.96/2.13 ** KEPT (pick-wt=6): 26 [] ge_q(A,B)|A!=B.
% 1.96/2.13 ** KEPT (pick-wt=6): 27 [] -less(A,B)|greater(B,A).
% 1.96/2.13 ** KEPT (pick-wt=6): 28 [] -greater(A,B)|less(B,A).
% 1.96/2.13 ** KEPT (pick-wt=6): 29 [] A!=B| -less(A,B).
% 1.96/2.13 ** KEPT (pick-wt=6): 30 [] -greater(A,B)| -less(A,B).
% 1.96/2.13 ** KEPT (pick-wt=6): 31 [] A!=B| -greater(A,B).
% 1.96/2.13 ** KEPT (pick-wt=10): 33 [copy,32,flip.2] -less(A,B)|vplus(A,$f1(B,A))=B.
% 1.96/2.13 ** KEPT (pick-wt=8): 34 [] less(A,B)|B!=vplus(A,C).
% 1.96/2.13 ** KEPT (pick-wt=10): 36 [copy,35,flip.2] -greater(A,B)|vplus(B,$f2(B,A))=A.
% 1.96/2.13 ** KEPT (pick-wt=8): 37 [] greater(A,B)|A!=vplus(B,C).
% 1.96/2.13 ** KEPT (pick-wt=8): 38 [] A!=B|B!=vplus(A,C).
% 1.96/2.13 ** KEPT (pick-wt=10): 39 [] A!=vplus(B,C)|B!=vplus(A,D).
% 1.96/2.13 ** KEPT (pick-wt=8): 40 [] A!=B|A!=vplus(B,C).
% 1.96/2.13 ** KEPT (pick-wt=10): 41 [] A=B|vplus(C,A)!=vplus(C,B).
% 1.96/2.13 ** KEPT (pick-wt=5): 43 [copy,42,flip.1] vplus(A,B)!=B.
% 1.96/2.13 ** KEPT (pick-wt=4): 44 [] vsucc(A)!=A.
% 1.96/2.13 ** KEPT (pick-wt=8): 45 [] A=B|vsucc(A)!=vsucc(B).
% 1.96/2.13 Following clause subsumed by 45 during input processing: 0 [] vsucc(A)!=vsucc(B)|A=B.
% 1.96/2.13 ** KEPT (pick-wt=4): 46 [] vsucc(A)!=v1.
% 1.96/2.13
% 1.96/2.13 ------------> process sos:
% 1.96/2.13 ** KEPT (pick-wt=3): 50 [] A=A.
% 1.96/2.13 ** KEPT (pick-wt=19): 51 [] vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 1.96/2.13 ---> New Demodulator: 52 [new_demod,51] vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436)=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 1.96/2.13 ** KEPT (pick-wt=17): 54 [copy,53,demod,52] vplus(vmul(vd436,vplus(vd437,vd439)),vd436)=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 1.96/2.13 ---> New Demodulator: 55 [new_demod,54] vplus(vmul(vd436,vplus(vd437,vd439)),vd436)=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 1.96/2.13 ** KEPT (pick-wt=16): 57 [copy,56,demod,55] vmul(vd436,vsucc(vplus(vd437,vd439)))=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 1.96/2.13 ---> New Demodulator: 58 [new_demod,57] vmul(vd436,vsucc(vplus(vd437,vd439)))=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 1.96/2.13 ** KEPT (pick-wt=16): 60 [copy,59,demod,58] vmul(vd436,vplus(vd437,vsucc(vd439)))=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 1.96/2.13 ---> New Demodulator: 61 [new_demod,60] vmul(vd436,vplus(vd437,vsucc(vd439)))=vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)).
% 1.96/2.13 ** KEPT (pick-wt=13): 63 [copy,62,flip.1] vplus(vmul(vd436,vd437),vmul(vd436,vd439))=vmul(vd436,vplus(vd437,vd439)).
% 1.96/2.13 ---> New Demodulator: 64 [new_demod,63] vplus(vmul(vd436,vd437),vmul(vd436,vd439))=vmul(vd436,vplus(vd437,vd439)).
% 1.96/2.13 ** KEPT (pick-wt=13): 66 [copy,65,flip.1] vplus(vmul(vd436,vd437),vmul(vd436,v1))=vplus(vmul(vd436,vd437),vd436).
% 1.96/2.13 ---> New Demodulator: 67 [new_demod,66] vplus(vmul(vd436,vd437),vmul(vd436,v1))=vplus(vmul(vd436,vd437),vd436).
% 1.96/2.13 ** KEPT (pick-wt=10): 68 [] vmul(vd436,vsucc(vd437))=vplus(vmul(vd436,vd437),vd436).
% 1.96/2.13 ---> New Demodulator: 69 [new_demod,68] vmul(vd436,vsucc(vd437))=vplus(vmul(vd436,vd437),vd436).
% 1.96/2.13 ** KEPT (pick-wt=11): 71 [copy,70,demod,69,flip.1] vplus(vmul(vd436,vd437),vd436)=vmul(vd436,vplus(vd437,v1)).
% 1.96/2.13 ---> New Demodulator: 72 [new_demod,71] vplus(vmul(vd436,vd437),vd436)=vmul(vd436,vplus(vd437,v1)).
% 1.96/2.13 ** KEPT (pick-wt=7): 73 [] vmul(A,B)=vmul(B,A).
% 1.96/2.13 ** KEPT (pick-wt=10): 74 [] vmul(vsucc(A),B)=vplus(vmul(A,B),B).
% 1.96/2.13 ** KEPT (pick-wt=5): 75 [] vmul(v1,A)=A.
% 1.96/2.13 ---> New Demodulator: 76 [new_demod,75] vmul(v1,A)=A.
% 1.96/2.13 ** KEPT (pick-wt=10): 77 [] vmul(A,vsucc(B))=vplus(vmul(A,B),A).
% 1.96/2.13 ** KEPT (pick-wt=5): 78 [] vmul(A,v1)=A.
% 1.96/2.13 ---> New Demodulator: 79 [new_demod,78] vmul(A,v1)=A.
% 1.96/2.13 ** KEPT (pick-wt=3): 80 [] ge_q(A,v1).
% 1.96/2.13 ** KEPT (pick-wt=5): 81 [] greater(vplus(A,B),A).
% 1.96/2.13 ** KEPT (pick-wt=9): 82 [] A=B|greater(A,B)|less(A,B).
% 1.96/2.13 ** KEPT (pick-wt=17): 84 [copy,83,flip.2,flip.3] A=B|vplus(B,$f3(A,B))=A|vplus(A,$f4(A,B))=B.
% 1.96/2.13 ** KEPT (pick-wt=7): 85 [] vplus(A,B)=vplus(B,A).
% 1.96/2.13 ** KEPT (pick-wt=9): 87 [copy,86,flip.1] vsucc(vplus(A,B))=vplus(vsucc(A),B).
% 1.96/2.13 ---> New Demodulator: 88 [new_demod,87] vsucc(vplus(A,B))=vplus(vsucc(A),B).
% 1.96/2.13 ** KEPT (pick-wt=6): 90 [copy,89,flip.1] vsucc(A)=vplus(v1,A).
% 1.96/2.13 ---> New Demodulator: 91 [new_demod,90] vsucc(A)=vplus(v1,A).
% 1.96/2.13 ** KEPT (pick-wt=11): 92 [] vplus(vplus(A,B),C)=vplus(A,vplus(B,C)).
% 1.96/2.13 ---> New Demodulator: 93 [new_demod,92] vplus(vplus(A,B),C)=vplus(A,vplus(B,C)).
% 1.96/2.13 ** KEPT (pick-wt=11): 95 [copy,94,demod,91,91] vplus(A,vplus(v1,B))=vplus(v1,vplus(A,B)).
% 1.96/2.13 Following clause subsumed by 85 during input processing: 0 [demod,91] vplus(A,v1)=vplus(v1,A).
% 1.96/2.13 ** KEPT (pick-wt=9): 97 [copy,96,demod,91,flip.2] A=v1|vplus(v1,vskolem2(A))=A.
% 1.96/2.13 Following clause subsumed by 50 during input processing: 0 [copy,50,flip.1] A=A.
% 1.96/2.13 >>>> Starting back demodulation with 52.
% 1.96/2.13 >>>> Starting back demodulation with 55.
% 1.96/2.13 >>>> Starting back demodulation with 58.
% 1.96/2.13 >>>> Starting back demodulation with 61.
% 1.96/2.13 >>>> Starting back demodulation with 64.
% 1.96/2.13 >> back demodulating 51 with 64.
% 1.96/2.13 >>>> Starting back demodulation with 67.
% 1.96/2.13 >>>> Starting back demodulation with 69.
% 1.96/2.13 >>>> Starting back demodulation with 72.
% 1.96/2.13 >> back demodulating 68 with 72.
% 1.96/2.13 >> back demodulating 66 with 72.
% 1.96/2.13 Following clause subsumed by 73 during input processing: 0 [copy,73,flip.1] vmul(A,B)=vmul(B,A).
% 1.96/2.13 ** KEPT (pick-wt=11): 100 [copy,74,flip.1,demod,91] vplus(vmul(A,B),B)=vmul(vplus(v1,A),B).
% 1.96/2.13 ---> New Demodulator: 101 [new_demod,100] vplus(vmul(A,B
% 1.96/2.13 -------- PROOF --------
% 1.96/2.13 ),B)=vmul(vplus(v1,A),B).
% 1.96/2.13 >>>> Starting back demodulation with 76.
% 1.96/2.13 ** KEPT (pick-wt=11): 102 [copy,77,flip.1,demod,91] vplus(vmul(A,B),A)=vmul(A,vplus(v1,B)).
% 1.96/2.13 ---> New Demodulator: 103 [new_demod,102] vplus(vmul(A,B),A)=vmul(A,vplus(v1,B)).
% 1.96/2.13 >>>> Starting back demodulation with 79.
% 1.96/2.13 Following clause subsumed by 85 during input processing: 0 [copy,85,flip.1] vplus(A,B)=vplus(B,A).
% 1.96/2.13 >>>> Starting back demodulation with 88.
% 1.96/2.13 >> back demodulating 57 with 88.
% 1.96/2.13 >>>> Starting back demodulation with 91.
% 1.96/2.13 >> back demodulating 87 with 91.
% 1.96/2.13 >> back demodulating 77 with 91.
% 1.96/2.13 >> back demodulating 74 with 91.
% 1.96/2.13 >> back demodulating 60 with 91.
% 1.96/2.13 >> back demodulating 46 with 91.
% 1.96/2.13 >> back demodulating 45 with 91.
% 1.96/2.13 >> back demodulating 44 with 91.
% 1.96/2.13 >> back demodulating 2 with 91.
% 1.96/2.13
% 1.96/2.13 ----> UNIT CONFLICT at 0.01 sec ----> 109 [binary,108.1,50.1] $F.
% 1.96/2.13
% 1.96/2.13 Length of proof is 7. Level of proof is 4.
% 1.96/2.13
% 1.96/2.13 ---------------- PROOF ----------------
% 1.96/2.13 % SZS status Theorem
% 1.96/2.13 % SZS output start Refutation
% See solution above
% 1.96/2.13 ------------ end of proof -------------
% 1.96/2.13
% 1.96/2.13
% 1.96/2.13 Search stopped by max_proofs option.
% 1.96/2.13
% 1.96/2.13
% 1.96/2.13 Search stopped by max_proofs option.
% 1.96/2.13
% 1.96/2.13 ============ end of search ============
% 1.96/2.13
% 1.96/2.13 -------------- statistics -------------
% 1.96/2.13 clauses given 0
% 1.96/2.13 clauses generated 5
% 1.96/2.13 clauses kept 75
% 1.96/2.13 clauses forward subsumed 13
% 1.96/2.13 clauses back subsumed 0
% 1.96/2.13 Kbytes malloced 976
% 1.96/2.13
% 1.96/2.13 ----------- times (seconds) -----------
% 1.96/2.13 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.96/2.13 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.96/2.13 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.96/2.13
% 1.96/2.13 That finishes the proof of the theorem.
% 1.96/2.13
% 1.96/2.13 Process 18962 finished Wed Jul 27 09:54:52 2022
% 1.96/2.13 Otter interrupted
% 1.96/2.13 PROOF FOUND
%------------------------------------------------------------------------------