TSTP Solution File: BOO026-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO026-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n013.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 12:47:37 EDT 2022
% Result : Unsatisfiable 2.27s 2.43s
% Output : Refutation 2.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 11
% Syntax : Number of clauses : 118 ( 118 unt; 0 nHn; 34 RR)
% Number of literals : 118 ( 117 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 140 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(add(a,b),b) != b,
file('BOO026-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('BOO026-1.p',unknown),
[] ).
cnf(3,axiom,
multiply(A,add(B,C)) = add(multiply(B,A),multiply(C,A)),
file('BOO026-1.p',unknown),
[] ).
cnf(5,axiom,
add(A,inverse(A)) = n1,
file('BOO026-1.p',unknown),
[] ).
cnf(6,axiom,
add(A,multiply(B,C)) = multiply(add(B,A),add(C,A)),
file('BOO026-1.p',unknown),
[] ).
cnf(8,plain,
multiply(add(A,B),add(C,B)) = add(B,multiply(A,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(10,axiom,
multiply(A,inverse(A)) = n0,
file('BOO026-1.p',unknown),
[] ).
cnf(11,axiom,
add(multiply(A,inverse(A)),add(multiply(A,B),multiply(inverse(A),B))) = B,
file('BOO026-1.p',unknown),
[] ).
cnf(12,plain,
add(n0,add(multiply(A,B),multiply(inverse(A),B))) = B,
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11]),10]),
[iquote('copy,11,demod,10')] ).
cnf(14,axiom,
add(multiply(A,inverse(B)),add(multiply(A,B),multiply(inverse(B),B))) = A,
file('BOO026-1.p',unknown),
[] ).
cnf(16,axiom,
add(multiply(A,inverse(B)),add(multiply(A,A),multiply(inverse(B),A))) = A,
file('BOO026-1.p',unknown),
[] ).
cnf(18,axiom,
multiply(add(A,inverse(A)),multiply(add(A,B),add(inverse(A),B))) = B,
file('BOO026-1.p',unknown),
[] ).
cnf(20,plain,
multiply(n1,add(A,n0)) = A,
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[18]),5,8,10]),
[iquote('copy,18,demod,5,8,10')] ).
cnf(21,axiom,
multiply(add(A,inverse(B)),multiply(add(A,B),add(inverse(B),B))) = A,
file('BOO026-1.p',unknown),
[] ).
cnf(22,plain,
multiply(add(A,inverse(B)),add(B,multiply(A,inverse(B)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[21]),8]),
[iquote('copy,21,demod,8')] ).
cnf(27,plain,
add(multiply(A,B),multiply(C,B)) = multiply(B,add(A,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3])]),
[iquote('copy,3,flip.1')] ).
cnf(35,plain,
multiply(A,n1) = add(multiply(B,A),multiply(inverse(B),A)),
inference(para_into,[status(thm),theory(equality)],[3,5]),
[iquote('para_into,3.1.1.2,4.1.1')] ).
cnf(37,plain,
add(multiply(A,n1),multiply(n0,n1)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[3,20])]),
[iquote('para_into,3.1.1,19.1.1,flip.1')] ).
cnf(39,plain,
add(multiply(A,B),multiply(inverse(A),B)) = multiply(B,n1),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[35])]),
[iquote('copy,35,flip.1')] ).
cnf(78,plain,
add(n0,multiply(A,n1)) = A,
inference(para_from,[status(thm),theory(equality)],[39,12]),
[iquote('para_from,39.1.1,12.1.1.2')] ).
cnf(83,plain,
add(multiply(n0,n1),multiply(multiply(A,n1),B)) = multiply(A,add(B,multiply(n0,n1))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,37])]),
[iquote('para_into,7.1.1.1,36.1.1,flip.1')] ).
cnf(85,plain,
multiply(n1,add(A,inverse(B))) = add(inverse(B),multiply(B,A)),
inference(para_into,[status(thm),theory(equality)],[8,5]),
[iquote('para_into,7.1.1.1,4.1.1')] ).
cnf(88,plain,
multiply(add(A,multiply(n0,n1)),B) = add(multiply(n0,n1),multiply(A,multiply(B,n1))),
inference(para_into,[status(thm),theory(equality)],[8,37]),
[iquote('para_into,7.1.1.2,36.1.1')] ).
cnf(92,plain,
multiply(add(A,inverse(B)),n1) = add(inverse(B),multiply(A,B)),
inference(para_into,[status(thm),theory(equality)],[8,5]),
[iquote('para_into,7.1.1.2,4.1.1')] ).
cnf(93,plain,
add(multiply(A,add(B,C)),multiply(C,add(B,C))) = add(C,multiply(B,A)),
inference(para_into,[status(thm),theory(equality)],[8,3]),
[iquote('para_into,7.1.1,3.1.1')] ).
cnf(96,plain,
add(inverse(A),multiply(A,B)) = multiply(n1,add(B,inverse(A))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[85])]),
[iquote('copy,85,flip.1')] ).
cnf(97,plain,
add(multiply(n0,n1),multiply(A,multiply(B,n1))) = multiply(add(A,multiply(n0,n1)),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[88])]),
[iquote('copy,88,flip.1')] ).
cnf(98,plain,
add(A,multiply(B,C)) = add(multiply(C,add(B,A)),multiply(A,add(B,A))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[93])]),
[iquote('copy,93,flip.1')] ).
cnf(99,plain,
add(add(A,multiply(B,C)),multiply(inverse(add(B,A)),add(C,A))) = multiply(add(C,A),n1),
inference(para_from,[status(thm),theory(equality)],[8,39]),
[iquote('para_from,7.1.1,39.1.1.1')] ).
cnf(104,plain,
multiply(add(A,multiply(B,n1)),B) = add(multiply(B,n1),multiply(A,n0)),
inference(para_from,[status(thm),theory(equality)],[78,8]),
[iquote('para_from,77.1.1,7.1.1.2')] ).
cnf(106,plain,
multiply(A,B) = add(multiply(n0,A),multiply(multiply(B,n1),A)),
inference(para_from,[status(thm),theory(equality)],[78,3]),
[iquote('para_from,77.1.1,3.1.1.2')] ).
cnf(108,plain,
add(multiply(n0,A),multiply(multiply(B,n1),A)) = multiply(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[106])]),
[iquote('copy,106,flip.1')] ).
cnf(115,plain,
add(multiply(A,add(B,inverse(A))),multiply(multiply(B,inverse(A)),add(B,inverse(A)))) = B,
inference(para_into,[status(thm),theory(equality)],[22,3]),
[iquote('para_into,22.1.1,3.1.1')] ).
cnf(150,plain,
add(A,multiply(B,add(A,n0))) = multiply(add(A,n0),add(n1,B)),
inference(para_into,[status(thm),theory(equality)],[27,20]),
[iquote('para_into,27.1.1.1,19.1.1')] ).
cnf(151,plain,
add(n0,multiply(A,inverse(B))) = multiply(inverse(B),add(B,A)),
inference(para_into,[status(thm),theory(equality)],[27,10]),
[iquote('para_into,27.1.1.1,9.1.1')] ).
cnf(156,plain,
add(multiply(A,add(B,multiply(C,inverse(B)))),C) = multiply(add(B,multiply(C,inverse(B))),add(A,add(C,inverse(B)))),
inference(para_into,[status(thm),theory(equality)],[27,22]),
[iquote('para_into,27.1.1.2,22.1.1')] ).
cnf(170,plain,
multiply(add(A,multiply(B,inverse(A))),add(C,add(B,inverse(A)))) = add(multiply(C,add(A,multiply(B,inverse(A)))),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[156])]),
[iquote('copy,156,flip.1')] ).
cnf(177,plain,
add(multiply(A,inverse(B)),multiply(B,add(A,inverse(B)))) = A,
inference(para_from,[status(thm),theory(equality)],[27,14]),
[iquote('para_from,27.1.1,14.1.1.2')] ).
cnf(180,plain,
multiply(multiply(A,add(B,C)),add(D,multiply(C,A))) = add(multiply(C,A),multiply(multiply(B,A),D)),
inference(para_from,[status(thm),theory(equality)],[27,8]),
[iquote('para_from,27.1.1,7.1.1.1')] ).
cnf(183,plain,
add(multiply(A,B),multiply(multiply(C,B),D)) = multiply(multiply(B,add(C,A)),add(D,multiply(A,B))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[180])]),
[iquote('copy,180,flip.1')] ).
cnf(205,plain,
add(inverse(A),multiply(A,A)) = multiply(n1,n1),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[85,5])]),
[iquote('para_into,85.1.1.2,4.1.1,flip.1')] ).
cnf(229,plain,
add(multiply(inverse(inverse(A)),inverse(A)),add(multiply(inverse(inverse(A)),inverse(inverse(A))),n0)) = inverse(inverse(A)),
inference(para_into,[status(thm),theory(equality)],[16,10]),
[iquote('para_into,16.1.1.2.2,9.1.1')] ).
cnf(243,plain,
add(inverse(add(A,B)),add(B,multiply(A,A))) = multiply(n1,n1),
inference(para_into,[status(thm),theory(equality)],[205,8]),
[iquote('para_into,205.1.1.2,7.1.1')] ).
cnf(249,plain,
add(multiply(A,A),multiply(inverse(A),B)) = multiply(multiply(n1,n1),add(B,multiply(A,A))),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[205,8])]),
[iquote('para_from,205.1.1,7.1.1.1,flip.1')] ).
cnf(282,plain,
add(inverse(A),add(multiply(B,A),multiply(C,A))) = multiply(n1,add(add(B,C),inverse(A))),
inference(para_into,[status(thm),theory(equality)],[96,3]),
[iquote('para_into,96.1.1.2,3.1.1')] ).
cnf(287,plain,
multiply(add(A,inverse(inverse(A))),multiply(n1,add(inverse(inverse(A)),inverse(A)))) = A,
inference(para_from,[status(thm),theory(equality)],[96,22]),
[iquote('para_from,96.1.1,22.1.1.2')] ).
cnf(332,plain,
multiply(add(A,n0),add(n1,multiply(n0,n1))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[106,20]),83])]),
[iquote('para_into,106.1.1,19.1.1,demod,83,flip.1')] ).
cnf(337,plain,
add(multiply(n0,A),multiply(multiply(add(B,C),n1),A)) = add(multiply(B,A),multiply(C,A)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[106,3])]),
[iquote('para_into,106.1.1,3.1.1,flip.1')] ).
cnf(401,plain,
add(multiply(n0,add(a,b)),multiply(multiply(b,n1),add(a,b))) != b,
inference(para_from,[status(thm),theory(equality)],[106,1]),
[iquote('para_from,106.1.1,1.1.1')] ).
cnf(505,plain,
multiply(inverse(A),add(A,A)) = add(n0,n0),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[151,10])]),
[iquote('para_into,151.1.1.2,9.1.1,flip.1')] ).
cnf(513,plain,
multiply(inverse(multiply(A,B)),multiply(B,add(A,A))) = add(n0,n0),
inference(para_into,[status(thm),theory(equality)],[505,27]),
[iquote('para_into,505.1.1.2,27.1.1')] ).
cnf(559,plain,
add(inverse(A),add(multiply(A,n1),multiply(n0,n0))) = multiply(n1,n1),
inference(para_into,[status(thm),theory(equality)],[243,78]),
[iquote('para_into,243.1.1.1.1,77.1.1')] ).
cnf(579,plain,
multiply(n1,A) = multiply(A,add(n1,multiply(n0,n1))),
inference(para_into,[status(thm),theory(equality)],[83,108]),
[iquote('para_into,82.1.1,108.1.1')] ).
cnf(580,plain,
multiply(A,add(n1,multiply(n0,n1))) = multiply(n1,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[579])]),
[iquote('copy,579,flip.1')] ).
cnf(592,plain,
add(multiply(n0,n1),multiply(n1,n1)) = multiply(n1,n1),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[580,579]),8]),
[iquote('para_into,580.1.1,579.1.1,demod,8')] ).
cnf(594,plain,
add(multiply(n1,A),multiply(multiply(n0,n1),A)) = multiply(n1,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[580,106]),337]),
[iquote('para_into,580.1.1,106.1.1,demod,337')] ).
cnf(596,plain,
multiply(n1,add(n0,n1)) = multiply(n1,n1),
inference(para_into,[status(thm),theory(equality)],[592,27]),
[iquote('para_into,591.1.1,27.1.1')] ).
cnf(603,plain,
multiply(inverse(multiply(n1,n1)),add(n1,multiply(n0,n1))) = add(n0,n0),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[596,513]),8]),
[iquote('para_from,595.1.1,513.1.1.1.1,demod,8')] ).
cnf(613,plain,
add(multiply(n1,n1),multiply(n1,n1)) = add(n1,multiply(n0,n1)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[93,596]),596]),
[iquote('para_into,93.1.1.1,595.1.1,demod,596')] ).
cnf(632,plain,
multiply(n1,add(n1,n1)) = add(n1,multiply(n0,n1)),
inference(para_into,[status(thm),theory(equality)],[613,27]),
[iquote('para_into,613.1.1,27.1.1')] ).
cnf(635,plain,
add(multiply(n1,A),multiply(multiply(A,n1),A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[98,37]),78,78])]),
[iquote('para_into,98.1.1,36.1.1,demod,78,78,flip.1')] ).
cnf(640,plain,
multiply(n1,n0) = n0,
inference(para_into,[status(thm),theory(equality)],[635,594]),
[iquote('para_into,635.1.1,593.1.1')] ).
cnf(642,plain,
multiply(A,add(n1,multiply(A,n1))) = A,
inference(para_into,[status(thm),theory(equality)],[635,27]),
[iquote('para_into,635.1.1,27.1.1')] ).
cnf(655,plain,
add(multiply(A,n0),n0) = multiply(n0,add(A,n1)),
inference(para_from,[status(thm),theory(equality)],[640,27]),
[iquote('para_from,639.1.1,27.1.1.2')] ).
cnf(658,plain,
multiply(n1,add(n0,inverse(n1))) = add(inverse(n1),n0),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[640,96])]),
[iquote('para_from,639.1.1,96.1.1.2,flip.1')] ).
cnf(660,plain,
add(n0,multiply(A,n0)) = multiply(n0,add(n1,A)),
inference(para_from,[status(thm),theory(equality)],[640,27]),
[iquote('para_from,639.1.1,27.1.1.1')] ).
cnf(671,plain,
add(n1,multiply(multiply(n0,n1),add(n1,multiply(n1,n1)))) = n1,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[642,594]),642]),
[iquote('para_from,641.1.1,593.1.1.1,demod,642')] ).
cnf(676,plain,
multiply(n0,add(n1,n1)) = add(n0,n0),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[655,640])]),
[iquote('para_into,655.1.1.1,639.1.1,flip.1')] ).
cnf(679,plain,
add(multiply(n0,n1),multiply(inverse(n1),n1)) = add(inverse(n1),n0),
inference(para_into,[status(thm),theory(equality)],[658,3]),
[iquote('para_into,658.1.1,3.1.1')] ).
cnf(691,plain,
multiply(A,A) = add(multiply(A,n1),multiply(n0,n0)),
inference(para_into,[status(thm),theory(equality)],[104,78]),
[iquote('para_into,103.1.1.1,77.1.1')] ).
cnf(692,plain,
add(multiply(A,n1),multiply(n0,n0)) = multiply(A,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[691])]),
[iquote('copy,691,flip.1')] ).
cnf(703,plain,
multiply(multiply(n1,n1),add(A,multiply(A,A))) = multiply(A,n1),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[692,99]),78,78,249,78]),
[iquote('para_from,692.1.1,99.1.1.1,demod,78,78,249,78')] ).
cnf(709,plain,
multiply(n1,add(inverse(n1),multiply(n0,n1))) = add(inverse(n1),n0),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[679,98]),594]),
[iquote('para_into,679.1.1,98.1.1,demod,594')] ).
cnf(723,plain,
multiply(multiply(n1,n1),multiply(n0,add(n1,n0))) = multiply(n0,n1),
inference(para_into,[status(thm),theory(equality)],[703,660]),
[iquote('para_into,703.1.1.2,660.1.1')] ).
cnf(725,plain,
multiply(multiply(n1,n1),multiply(n0,n0)) = multiply(multiply(n0,n1),n1),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[703,97]),37]),
[iquote('para_into,703.1.1.2,97.1.1,demod,37')] ).
cnf(735,plain,
multiply(n1,add(multiply(n0,n0),multiply(n0,n1))) = n0,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[725,83]),83,642])]),
[iquote('para_from,725.1.1,82.1.1.2,demod,83,642,flip.1')] ).
cnf(737,plain,
add(multiply(n0,n1),multiply(multiply(n0,n0),n1)) = n0,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[735,579]),8]),
[iquote('para_into,735.1.1,579.1.1,demod,8')] ).
cnf(741,plain,
multiply(n1,add(n0,multiply(n0,n0))) = n0,
inference(para_into,[status(thm),theory(equality)],[737,27]),
[iquote('para_into,737.1.1,27.1.1')] ).
cnf(748,plain,
multiply(n1,multiply(n0,add(n1,n0))) = n0,
inference(para_into,[status(thm),theory(equality)],[741,660]),
[iquote('para_into,741.1.1.2,660.1.1')] ).
cnf(771,plain,
multiply(n1,inverse(multiply(n1,n1))) = add(n0,n0),
inference(para_into,[status(thm),theory(equality)],[603,580]),
[iquote('para_into,603.1.1,580.1.1')] ).
cnf(773,plain,
multiply(add(A,n0),add(n1,n1)) = add(A,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[150,579]),332])]),
[iquote('para_into,150.1.1.2,579.1.1,demod,332,flip.1')] ).
cnf(793,plain,
multiply(add(n1,multiply(n0,n1)),add(n1,multiply(n1,n1))) = n1,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[183,635]),632])]),
[iquote('para_into,183.1.1,635.1.1,demod,632,flip.1')] ).
cnf(800,plain,
multiply(n1,n1) = n1,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[793,88]),104,640,20,592]),
[iquote('para_into,793.1.1,88.1.1,demod,104,640,20,592')] ).
cnf(808,plain,
add(n0,n0) = n0,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[771]),800,10])]),
[iquote('back_demod,771,demod,800,10,flip.1')] ).
cnf(812,plain,
multiply(n0,n1) = n0,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[723]),800,748])]),
[iquote('back_demod,723,demod,800,748,flip.1')] ).
cnf(824,plain,
add(n1,n0) = n1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[671]),812,800,676,808]),
[iquote('back_demod,671,demod,812,800,676,808')] ).
cnf(830,plain,
add(n1,n1) = n1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[613]),800,800,812,824]),
[iquote('back_demod,613,demod,800,800,812,824')] ).
cnf(836,plain,
multiply(inverse(n1),n1) = n0,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[603]),800,812,824,808]),
[iquote('back_demod,603,demod,800,812,824,808')] ).
cnf(846,plain,
add(n0,n1) = n1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[592]),812,800,800]),
[iquote('back_demod,591,demod,812,800,800')] ).
cnf(853,plain,
add(inverse(A),add(multiply(A,n1),multiply(n0,n0))) = n1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[559]),800]),
[iquote('back_demod,559,demod,800')] ).
cnf(876,plain,
multiply(n1,A) = multiply(A,n1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[579]),812,824]),
[iquote('back_demod,579,demod,812,824')] ).
cnf(884,plain,
multiply(add(A,n0),n1) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[332]),812,824]),
[iquote('back_demod,331,demod,812,824')] ).
cnf(895,plain,
multiply(inverse(A),add(A,A)) = n0,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[505]),808]),
[iquote('back_demod,505,demod,808')] ).
cnf(904,plain,
multiply(n0,n0) = n0,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[737]),812,78]),
[iquote('back_demod,737,demod,812,78')] ).
cnf(906,plain,
add(inverse(n1),n0) = inverse(n1),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[709]),812,20])]),
[iquote('back_demod,709,demod,812,20,flip.1')] ).
cnf(910,plain,
inverse(n1) = n0,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[679]),812,836,808,906])]),
[iquote('back_demod,679,demod,812,836,808,906,flip.1')] ).
cnf(926,plain,
add(n0,multiply(multiply(A,n1),B)) = multiply(A,add(B,n0)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[83]),812,812]),
[iquote('back_demod,82,demod,812,812')] ).
cnf(931,plain,
add(multiply(A,n1),n0) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[37]),812]),
[iquote('back_demod,36,demod,812')] ).
cnf(937,plain,
add(A,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[773]),830,884])]),
[iquote('back_demod,773,demod,830,884,flip.1')] ).
cnf(945,plain,
add(inverse(A),A) = n1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[853]),904,931]),
[iquote('back_demod,853,demod,904,931')] ).
cnf(947,plain,
multiply(A,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[692]),904,931])]),
[iquote('back_demod,692,demod,904,931,flip.1')] ).
cnf(966,plain,
multiply(inverse(A),A) = n0,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[895]),937]),
[iquote('back_demod,895,demod,937')] ).
cnf(975,plain,
add(inverse(inverse(A)),n0) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[287]),945,947,92,10]),
[iquote('back_demod,287,demod,945,947,92,10')] ).
cnf(981,plain,
inverse(inverse(A)) = add(n0,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[229]),966,947,975])]),
[iquote('back_demod,229,demod,966,947,975,flip.1')] ).
cnf(1006,plain,
add(add(n0,A),n0) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[975]),981]),
[iquote('back_demod,974,demod,981')] ).
cnf(1083,plain,
multiply(n1,A) = add(n0,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[812,282]),910,78,910,1006])]),
[iquote('para_from,811.1.1,282.1.1.2.1,demod,910,78,910,1006,flip.1')] ).
cnf(1116,plain,
multiply(A,n1) = add(n0,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[876]),1083])]),
[iquote('back_demod,876,demod,1083,flip.1')] ).
cnf(1160,plain,
add(n0,multiply(add(n0,A),B)) = multiply(A,add(B,n0)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[926]),1116]),
[iquote('back_demod,926,demod,1116')] ).
cnf(1167,plain,
add(multiply(n0,add(a,b)),add(b,multiply(n0,a))) != b,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[401]),1116,8]),
[iquote('back_demod,401,demod,1116,8')] ).
cnf(1190,plain,
add(add(n0,A),inverse(B)) = add(n0,add(A,inverse(B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[937,170]),947,5,1083,947,5,1116])]),
[iquote('para_from,936.1.1,170.1.1.2.2,demod,947,5,1083,947,5,1116,flip.1')] ).
cnf(1201,plain,
add(inverse(A),n0) = inverse(A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[937,177]),947,10]),
[iquote('para_from,936.1.1,177.1.1.2.2,demod,947,10')] ).
cnf(1233,plain,
add(n0,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[945,115]),981,1190,5,846,1116,981,1116,1160,1201,10,1006,981])]),
[iquote('para_from,944.1.1,115.1.1.2.2,demod,981,1190,5,846,1116,981,1116,1160,1201,10,1006,981,flip.1')] ).
cnf(1235,plain,
add(A,n0) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[945,115]),1116,1233,981,1233,10,981,1233,5,1116,937,981,1233]),
[iquote('para_from,944.1.1,115.1.1.1.2,demod,1116,1233,981,1233,10,981,1233,5,1116,937,981,1233')] ).
cnf(1290,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[981]),1233]),
[iquote('back_demod,980,demod,1233')] ).
cnf(1316,plain,
multiply(n0,inverse(A)) = n0,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1233,177]),10,1235]),
[iquote('para_from,1232.1.1,177.1.1.2.2,demod,10,1235')] ).
cnf(1331,plain,
multiply(n0,A) = n0,
inference(para_into,[status(thm),theory(equality)],[1316,1290]),
[iquote('para_into,1316.1.1.2,1290.1.1')] ).
cnf(1332,plain,
b != b,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1167]),1331,1331,1235,1233]),
[iquote('back_demod,1167,demod,1331,1331,1235,1233')] ).
cnf(1333,plain,
$false,
inference(binary,[status(thm)],[1332,2]),
[iquote('binary,1332.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : BOO026-1 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n013.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 02:28:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.92/2.11 ----- Otter 3.3f, August 2004 -----
% 1.92/2.11 The process was started by sandbox2 on n013.cluster.edu,
% 1.92/2.11 Wed Jul 27 02:28:00 2022
% 1.92/2.11 The command was "./otter". The process ID is 31085.
% 1.92/2.11
% 1.92/2.11 set(prolog_style_variables).
% 1.92/2.11 set(auto).
% 1.92/2.11 dependent: set(auto1).
% 1.92/2.11 dependent: set(process_input).
% 1.92/2.11 dependent: clear(print_kept).
% 1.92/2.11 dependent: clear(print_new_demod).
% 1.92/2.11 dependent: clear(print_back_demod).
% 1.92/2.11 dependent: clear(print_back_sub).
% 1.92/2.11 dependent: set(control_memory).
% 1.92/2.11 dependent: assign(max_mem, 12000).
% 1.92/2.11 dependent: assign(pick_given_ratio, 4).
% 1.92/2.11 dependent: assign(stats_level, 1).
% 1.92/2.11 dependent: assign(max_seconds, 10800).
% 1.92/2.11 clear(print_given).
% 1.92/2.11
% 1.92/2.11 list(usable).
% 1.92/2.11 0 [] A=A.
% 1.92/2.11 0 [] multiply(X,add(Y,Z))=add(multiply(Y,X),multiply(Z,X)).
% 1.92/2.11 0 [] add(X,inverse(X))=n1.
% 1.92/2.11 0 [] add(X,multiply(Y,Z))=multiply(add(Y,X),add(Z,X)).
% 1.92/2.11 0 [] multiply(X,inverse(X))=n0.
% 1.92/2.11 0 [] add(multiply(X,inverse(X)),add(multiply(X,Y),multiply(inverse(X),Y)))=Y.
% 1.92/2.11 0 [] add(multiply(X,inverse(Y)),add(multiply(X,Y),multiply(inverse(Y),Y)))=X.
% 1.92/2.11 0 [] add(multiply(X,inverse(Y)),add(multiply(X,X),multiply(inverse(Y),X)))=X.
% 1.92/2.11 0 [] multiply(add(X,inverse(X)),multiply(add(X,Y),add(inverse(X),Y)))=Y.
% 1.92/2.11 0 [] multiply(add(X,inverse(Y)),multiply(add(X,Y),add(inverse(Y),Y)))=X.
% 1.92/2.11 0 [] multiply(add(X,inverse(Y)),multiply(add(X,X),add(inverse(Y),X)))=X.
% 1.92/2.11 0 [] multiply(add(a,b),b)!=b.
% 1.92/2.11 end_of_list.
% 1.92/2.11
% 1.92/2.11 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.92/2.11
% 1.92/2.11 All clauses are units, and equality is present; the
% 1.92/2.11 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.92/2.11
% 1.92/2.11 dependent: set(knuth_bendix).
% 1.92/2.11 dependent: set(anl_eq).
% 1.92/2.11 dependent: set(para_from).
% 1.92/2.11 dependent: set(para_into).
% 1.92/2.11 dependent: clear(para_from_right).
% 1.92/2.11 dependent: clear(para_into_right).
% 1.92/2.11 dependent: set(para_from_vars).
% 1.92/2.11 dependent: set(eq_units_both_ways).
% 1.92/2.11 dependent: set(dynamic_demod_all).
% 1.92/2.11 dependent: set(dynamic_demod).
% 1.92/2.11 dependent: set(order_eq).
% 1.92/2.11 dependent: set(back_demod).
% 1.92/2.11 dependent: set(lrpo).
% 1.92/2.11
% 1.92/2.11 ------------> process usable:
% 1.92/2.11 ** KEPT (pick-wt=7): 1 [] multiply(add(a,b),b)!=b.
% 1.92/2.11
% 1.92/2.11 ------------> process sos:
% 1.92/2.11 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.92/2.11 ** KEPT (pick-wt=13): 3 [] multiply(A,add(B,C))=add(multiply(B,A),multiply(C,A)).
% 1.92/2.11 ** KEPT (pick-wt=6): 4 [] add(A,inverse(A))=n1.
% 1.92/2.11 ---> New Demodulator: 5 [new_demod,4] add(A,inverse(A))=n1.
% 1.92/2.11 ** KEPT (pick-wt=13): 7 [copy,6,flip.1] multiply(add(A,B),add(C,B))=add(B,multiply(A,C)).
% 1.92/2.11 ---> New Demodulator: 8 [new_demod,7] multiply(add(A,B),add(C,B))=add(B,multiply(A,C)).
% 1.92/2.11 ** KEPT (pick-wt=6): 9 [] multiply(A,inverse(A))=n0.
% 1.92/2.11 ---> New Demodulator: 10 [new_demod,9] multiply(A,inverse(A))=n0.
% 1.92/2.11 ** KEPT (pick-wt=12): 12 [copy,11,demod,10] add(n0,add(multiply(A,B),multiply(inverse(A),B)))=B.
% 1.92/2.11 ---> New Demodulator: 13 [new_demod,12] add(n0,add(multiply(A,B),multiply(inverse(A),B)))=B.
% 1.92/2.11 ** KEPT (pick-wt=15): 14 [] add(multiply(A,inverse(B)),add(multiply(A,B),multiply(inverse(B),B)))=A.
% 1.92/2.11 ---> New Demodulator: 15 [new_demod,14] add(multiply(A,inverse(B)),add(multiply(A,B),multiply(inverse(B),B)))=A.
% 1.92/2.11 ** KEPT (pick-wt=15): 16 [] add(multiply(A,inverse(B)),add(multiply(A,A),multiply(inverse(B),A)))=A.
% 1.92/2.11 ---> New Demodulator: 17 [new_demod,16] add(multiply(A,inverse(B)),add(multiply(A,A),multiply(inverse(B),A)))=A.
% 1.92/2.11 ** KEPT (pick-wt=7): 19 [copy,18,demod,5,8,10] multiply(n1,add(A,n0))=A.
% 1.92/2.11 ---> New Demodulator: 20 [new_demod,19] multiply(n1,add(A,n0))=A.
% 1.92/2.11 ** KEPT (pick-wt=13): 22 [copy,21,demod,8] multiply(add(A,inverse(B)),add(B,multiply(A,inverse(B))))=A.
% 1.92/2.11 ---> New Demodulator: 23 [new_demod,22] multiply(add(A,inverse(B)),add(B,multiply(A,inverse(B))))=A.
% 1.92/2.11 ** KEPT (pick-wt=13): 25 [copy,24,demod,8] multiply(add(A,inverse(B)),add(A,multiply(A,inverse(B))))=A.
% 1.92/2.11 ---> New Demodulator: 26 [new_demod,25] multiply(add(A,inverse(B)),add(A,multiply(A,inverse(B))))=A.
% 1.92/2.11 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.92/2.11 ** KEPT (pick-wt=13): 27 [copy,3,flip.1] add(multiply(A,B),multiply(C,B))=multiply(B,add(A,C)).
% 1.92/2.11 >>>> Starting back demodulation with 5.
% 1.92/2.11 >>>> Starting back demodulation with 8.
% 1.92/2.11 >>>> Starting back demodulation with 10.
% 1.92/2.11 >>>> Starting back demodulation with 13.
% 1.92/2.11 >>>> Starting back demodulation with 15.
% 2.27/2.43 >>>> Starting back demodulation with 17.
% 2.27/2.43 >>>> Starting back demodulation with 20.
% 2.27/2.43 >>>> Starting back demodulation with 23.
% 2.27/2.43 >>>> Starting back demodulation with 26.
% 2.27/2.43 Following clause subsumed by 3 during input processing: 0 [copy,27,flip.1] multiply(A,add(B,C))=add(multiply(B,A),multiply(C,A)).
% 2.27/2.43
% 2.27/2.43 ======= end of input processing =======
% 2.27/2.43
% 2.27/2.43 =========== start of search ===========
% 2.27/2.43
% 2.27/2.43
% 2.27/2.43 Resetting weight limit to 14.
% 2.27/2.43
% 2.27/2.43
% 2.27/2.43 Resetting weight limit to 14.
% 2.27/2.43
% 2.27/2.43 sos_size=249
% 2.27/2.43
% 2.27/2.43
% 2.27/2.43 Resetting weight limit to 13.
% 2.27/2.43
% 2.27/2.43
% 2.27/2.43 Resetting weight limit to 13.
% 2.27/2.43
% 2.27/2.43 sos_size=236
% 2.27/2.43
% 2.27/2.43
% 2.27/2.43 Resetting weight limit to 6.
% 2.27/2.43
% 2.27/2.43
% 2.27/2.43 Resetting weight limit to 6.
% 2.27/2.43
% 2.27/2.43 sos_size=88
% 2.27/2.43
% 2.27/2.43 -------- PROOF --------
% 2.27/2.43
% 2.27/2.43 ----> UNIT CONFLICT at 0.31 sec ----> 1333 [binary,1332.1,2.1] $F.
% 2.27/2.43
% 2.27/2.43 Length of proof is 106. Level of proof is 28.
% 2.27/2.43
% 2.27/2.43 ---------------- PROOF ----------------
% 2.27/2.43 % SZS status Unsatisfiable
% 2.27/2.43 % SZS output start Refutation
% See solution above
% 2.27/2.43 ------------ end of proof -------------
% 2.27/2.43
% 2.27/2.43
% 2.27/2.43 Search stopped by max_proofs option.
% 2.27/2.43
% 2.27/2.43
% 2.27/2.43 Search stopped by max_proofs option.
% 2.27/2.43
% 2.27/2.43 ============ end of search ============
% 2.27/2.43
% 2.27/2.43 -------------- statistics -------------
% 2.27/2.43 clauses given 362
% 2.27/2.43 clauses generated 34622
% 2.27/2.43 clauses kept 809
% 2.27/2.43 clauses forward subsumed 2917
% 2.27/2.43 clauses back subsumed 20
% 2.27/2.43 Kbytes malloced 8789
% 2.27/2.43
% 2.27/2.43 ----------- times (seconds) -----------
% 2.27/2.43 user CPU time 0.31 (0 hr, 0 min, 0 sec)
% 2.27/2.43 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.27/2.43 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.27/2.43
% 2.27/2.43 That finishes the proof of the theorem.
% 2.27/2.43
% 2.27/2.43 Process 31085 finished Wed Jul 27 02:28:02 2022
% 2.27/2.43 Otter interrupted
% 2.27/2.43 PROOF FOUND
%------------------------------------------------------------------------------