TSTP Solution File: GRP226-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP226-1 : TPTP v8.1.0. Released v2.5.0.
% 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 12:56:45 EDT 2022
% Result : Unsatisfiable 243.42s 243.61s
% Output : Refutation 243.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 17
% Syntax : Number of clauses : 101 ( 37 unt; 44 nHn; 89 RR)
% Number of literals : 218 ( 217 equ; 95 neg)
% Maximal clause size : 9 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( inverse(A) != sk_c7
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c7,B) != sk_c6
| multiply(C,sk_c7) != B
| inverse(C) != sk_c7
| inverse(D) != sk_c7
| multiply(D,sk_c6) != sk_c7
| multiply(E,sk_c6) != sk_c7
| inverse(E) != sk_c6 ),
file('GRP226-1.p',unknown),
[] ).
cnf(2,plain,
( inverse(A) != sk_c7
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c7,B) != sk_c6
| multiply(C,sk_c7) != B
| inverse(C) != sk_c7
| multiply(D,sk_c6) != sk_c7
| inverse(D) != sk_c6 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[1])])]),
[iquote('copy,1,factor_simp,factor_simp')] ).
cnf(3,plain,
( inverse(A) != sk_c7
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c7,B) != sk_c6
| multiply(A,sk_c7) != B
| multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c6 ),
inference(factor,[status(thm)],[2]),
[iquote('factor,2.1.5')] ).
cnf(5,plain,
( inverse(A) != sk_c7
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c7,B) != sk_c6
| multiply(A,sk_c7) != B
| inverse(A) != sk_c6 ),
inference(factor,[status(thm)],[3]),
[iquote('factor,3.2.5')] ).
cnf(6,axiom,
A = A,
file('GRP226-1.p',unknown),
[] ).
cnf(8,axiom,
multiply(identity,A) = A,
file('GRP226-1.p',unknown),
[] ).
cnf(9,axiom,
multiply(inverse(A),A) = identity,
file('GRP226-1.p',unknown),
[] ).
cnf(11,axiom,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
file('GRP226-1.p',unknown),
[] ).
cnf(13,axiom,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('GRP226-1.p',unknown),
[] ).
cnf(14,axiom,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('GRP226-1.p',unknown),
[] ).
cnf(15,axiom,
( inverse(sk_c1) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('GRP226-1.p',unknown),
[] ).
cnf(16,axiom,
( inverse(sk_c1) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('GRP226-1.p',unknown),
[] ).
cnf(17,axiom,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('GRP226-1.p',unknown),
[] ).
cnf(18,axiom,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('GRP226-1.p',unknown),
[] ).
cnf(23,axiom,
( multiply(sk_c7,sk_c3) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('GRP226-1.p',unknown),
[] ).
cnf(24,axiom,
( multiply(sk_c7,sk_c3) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('GRP226-1.p',unknown),
[] ).
cnf(27,axiom,
( multiply(sk_c2,sk_c7) = sk_c3
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('GRP226-1.p',unknown),
[] ).
cnf(28,axiom,
( multiply(sk_c2,sk_c7) = sk_c3
| inverse(sk_c5) = sk_c6 ),
file('GRP226-1.p',unknown),
[] ).
cnf(31,axiom,
( inverse(sk_c2) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('GRP226-1.p',unknown),
[] ).
cnf(32,axiom,
( inverse(sk_c2) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('GRP226-1.p',unknown),
[] ).
cnf(43,plain,
( inverse(A) != sk_c7
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c7,B) != sk_c6
| multiply(A,sk_c7) != B
| sk_c7 != identity
| inverse(inverse(sk_c6)) != sk_c6 ),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[9,3])]),
[iquote('para_from,9.1.1,3.5.1,flip.5')] ).
cnf(44,plain,
( inverse(inverse(sk_c7)) != sk_c7
| multiply(inverse(sk_c7),sk_c6) != sk_c7
| multiply(sk_c7,A) != sk_c6
| identity != A
| inverse(inverse(sk_c7)) != sk_c6 ),
inference(para_from,[status(thm),theory(equality)],[9,5]),
[iquote('para_from,9.1.1,5.4.1')] ).
cnf(68,plain,
( multiply(sk_c7,sk_c4) = identity
| inverse(sk_c1) = sk_c7 ),
inference(para_from,[status(thm),theory(equality)],[13,9]),
[iquote('para_from,13.2.1,9.1.1.1')] ).
cnf(79,plain,
( multiply(sk_c7,sk_c1) = identity
| inverse(sk_c5) = sk_c6 ),
inference(para_from,[status(thm),theory(equality)],[16,9]),
[iquote('para_from,16.1.1,9.1.1.1')] ).
cnf(90,plain,
( multiply(sk_c6,sk_c5) = identity
| inverse(sk_c1) = sk_c7 ),
inference(para_from,[status(thm),theory(equality)],[16,9]),
[iquote('para_from,16.2.1,9.1.1.1')] ).
cnf(97,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[11,9]),8])]),
[iquote('para_into,11.1.1.1,9.1.1,demod,8,flip.1')] ).
cnf(99,plain,
( inverse(A) != sk_c7
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c7,B) != sk_c6
| multiply(A,sk_c7) != B
| multiply(C,multiply(D,sk_c6)) != sk_c7
| inverse(multiply(C,D)) != sk_c6 ),
inference(para_from,[status(thm),theory(equality)],[11,3]),
[iquote('para_from,11.1.1,3.5.1')] ).
cnf(133,plain,
( multiply(sk_c7,sk_c2) = identity
| inverse(sk_c5) = sk_c6 ),
inference(para_from,[status(thm),theory(equality)],[32,9]),
[iquote('para_from,32.1.1,9.1.1.1')] ).
cnf(160,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(para_into,[status(thm),theory(equality)],[97,97]),
[iquote('para_into,97.1.1.2,97.1.1')] ).
cnf(164,plain,
multiply(A,identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[97,9]),160]),
[iquote('para_into,97.1.1.2,9.1.1,demod,160')] ).
cnf(168,plain,
inverse(identity) = identity,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[164,9])]),
[iquote('para_into,163.1.1,9.1.1,flip.1')] ).
cnf(466,plain,
( inverse(sk_c7) = sk_c4
| inverse(sk_c1) = sk_c7 ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[68,97]),164]),
[iquote('para_from,68.1.1,97.1.1.2,demod,164')] ).
cnf(487,plain,
( multiply(sk_c4,sk_c7) = identity
| inverse(sk_c1) = sk_c7 ),
inference(para_from,[status(thm),theory(equality)],[466,9]),
[iquote('para_from,466.1.1,9.1.1.1')] ).
cnf(506,plain,
( inverse(sk_c7) = sk_c1
| inverse(sk_c5) = sk_c6 ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[79,97]),164]),
[iquote('para_from,79.1.1,97.1.1.2,demod,164')] ).
cnf(547,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c3
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(para_from,[status(thm),theory(equality)],[23,97]),
[iquote('para_from,23.1.1,97.1.1.2')] ).
cnf(561,plain,
( inverse(sk_c6) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[90,97]),164]),
[iquote('para_from,90.1.1,97.1.1.2,demod,164')] ).
cnf(578,plain,
( multiply(sk_c5,sk_c6) = identity
| inverse(sk_c1) = sk_c7 ),
inference(para_from,[status(thm),theory(equality)],[561,9]),
[iquote('para_from,561.1.1,9.1.1.1')] ).
cnf(700,plain,
( multiply(inverse(sk_c2),sk_c3) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(para_from,[status(thm),theory(equality)],[27,97]),
[iquote('para_from,27.1.1,97.1.1.2')] ).
cnf(754,plain,
( inverse(sk_c7) = sk_c2
| inverse(sk_c5) = sk_c6 ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[133,97]),164]),
[iquote('para_from,133.1.1,97.1.1.2,demod,164')] ).
cnf(772,plain,
( sk_c2 = sk_c1
| inverse(sk_c5) = sk_c6 ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[754,506])]),
[iquote('para_into,754.1.1,506.1.1,factor_simp')] ).
cnf(813,plain,
( sk_c7 != identity
| sk_c7 != sk_c6
| multiply(sk_c7,A) != sk_c6
| sk_c7 != A
| inverse(inverse(sk_c6)) != sk_c6 ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[43,168]),8,8])]),
[iquote('para_into,43.1.1,167.1.1,demod,8,8,factor_simp')] ).
cnf(872,plain,
( sk_c7 != identity
| sk_c7 != sk_c6
| inverse(inverse(sk_c6)) != sk_c6 ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(factor,[status(thm)],[813]),164])]),
[iquote('factor,813.1.4,demod,164,factor_simp')] ).
cnf(873,plain,
( multiply(sk_c1,sk_c7) = sk_c3
| inverse(sk_c5) = sk_c6 ),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[772,28])]),
[iquote('para_from,772.1.1,28.1.1.1,factor_simp')] ).
cnf(933,plain,
( inverse(inverse(sk_c7)) != sk_c7
| multiply(inverse(sk_c7),sk_c6) != sk_c7
| sk_c7 != sk_c6
| inverse(inverse(sk_c7)) != sk_c6 ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[44,164]),6]),
[iquote('para_into,44.3.1,163.1.1,unit_del,6')] ).
cnf(1037,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[160,164]),164]),
[iquote('para_into,159.1.1,163.1.1,demod,164')] ).
cnf(1040,plain,
multiply(A,inverse(A)) = identity,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[160,9])]),
[iquote('para_into,159.1.1,9.1.1,flip.1')] ).
cnf(1062,plain,
( multiply(inverse(sk_c7),sk_c6) != sk_c7
| sk_c7 != sk_c6 ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[933]),1037,1037]),6])]),
[iquote('back_demod,933,demod,1037,1037,unit_del,6,factor_simp')] ).
cnf(1072,plain,
( sk_c7 != identity
| sk_c7 != sk_c6 ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[872]),1037]),6]),
[iquote('back_demod,872,demod,1037,unit_del,6')] ).
cnf(1146,plain,
( inverse(sk_c7) = sk_c2
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(para_into,[status(thm),theory(equality)],[1037,31]),
[iquote('para_into,1036.1.1.1,31.1.1')] ).
cnf(1153,plain,
( inverse(sk_c7) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(para_into,[status(thm),theory(equality)],[1037,17]),
[iquote('para_into,1036.1.1.1,17.2.1')] ).
cnf(1628,plain,
( sk_c7 = identity
| inverse(sk_c1) = sk_c7 ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[578,15])]),
[iquote('para_into,578.1.1,15.2.1,factor_simp')] ).
cnf(1644,plain,
( sk_c7 != sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1628,1072]),6]),
[iquote('para_from,1628.1.1,1072.1.1,unit_del,6')] ).
cnf(1648,plain,
( sk_c4 = identity
| inverse(sk_c1) = sk_c7 ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1628,487]),164])]),
[iquote('para_from,1628.1.1,487.1.1.2,demod,164,factor_simp')] ).
cnf(1753,plain,
( inverse(sk_c1) = sk_c7
| sk_c7 = sk_c6 ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1648,14]),8])]),
[iquote('para_from,1648.1.1,14.2.1.1,demod,8,factor_simp')] ).
cnf(1864,plain,
inverse(sk_c1) = sk_c7,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[1753,1644])]),
[iquote('hyper,1753,1644,factor_simp')] ).
cnf(1917,plain,
multiply(sk_c1,sk_c7) = identity,
inference(para_from,[status(thm),theory(equality)],[1864,1040]),
[iquote('para_from,1864.1.1,1040.1.1.2')] ).
cnf(1921,plain,
inverse(sk_c7) = sk_c1,
inference(para_from,[status(thm),theory(equality)],[1864,1037]),
[iquote('para_from,1864.1.1,1036.1.1.1')] ).
cnf(1922,plain,
multiply(sk_c7,multiply(sk_c1,A)) = A,
inference(para_from,[status(thm),theory(equality)],[1864,97]),
[iquote('para_from,1864.1.1,97.1.1.1')] ).
cnf(1924,plain,
multiply(sk_c7,sk_c1) = identity,
inference(para_from,[status(thm),theory(equality)],[1864,9]),
[iquote('para_from,1864.1.1,9.1.1.1')] ).
cnf(1989,plain,
( sk_c3 = identity
| inverse(sk_c5) = sk_c6 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[873]),1917])]),
[iquote('back_demod,873,demod,1917,flip.1')] ).
cnf(2052,plain,
( sk_c4 = sk_c1
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1153]),1921])]),
[iquote('back_demod,1153,demod,1921,flip.1')] ).
cnf(2056,plain,
( sk_c2 = sk_c1
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1146]),1921])]),
[iquote('back_demod,1146,demod,1921,flip.1')] ).
cnf(2060,plain,
( multiply(sk_c1,sk_c6) != sk_c7
| sk_c7 != sk_c6 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1062]),1921]),
[iquote('back_demod,1062,demod,1921')] ).
cnf(2102,plain,
( multiply(sk_c1,sk_c6) = sk_c3
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[547]),1921]),
[iquote('back_demod,547,demod,1921')] ).
cnf(2118,plain,
( sk_c7 != sk_c1
| multiply(sk_c7,sk_c6) != sk_c7
| multiply(sk_c7,A) != sk_c6
| multiply(sk_c7,sk_c7) != A
| multiply(B,multiply(C,sk_c6)) != sk_c7
| inverse(multiply(B,C)) != sk_c6 ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[99,1921])]),
[iquote('para_into,99.1.1,1920.1.1,flip.1')] ).
cnf(2334,plain,
( sk_c7 = sk_c6
| inverse(sk_c5) = sk_c6 ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1989,24]),164])]),
[iquote('para_from,1989.1.1,24.1.1.2,demod,164,factor_simp')] ).
cnf(2526,plain,
( inverse(sk_c6) = sk_c5
| sk_c7 = sk_c6 ),
inference(para_from,[status(thm),theory(equality)],[2334,1037]),
[iquote('para_from,2334.2.1,1036.1.1.1')] ).
cnf(3287,plain,
multiply(sk_c1,sk_c6) = sk_c7,
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[2052,18])])]),
[iquote('para_from,2052.1.1,18.2.1.1,factor_simp,factor_simp')] ).
cnf(3332,plain,
( sk_c7 = sk_c3
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2102]),3287]),
[iquote('back_demod,2102,demod,3287')] ).
cnf(3337,plain,
sk_c7 != sk_c6,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2060]),3287]),6]),
[iquote('back_demod,2060,demod,3287,unit_del,6')] ).
cnf(3383,plain,
inverse(sk_c6) = sk_c5,
inference(hyper,[status(thm)],[3337,2526]),
[iquote('hyper,3337,2526')] ).
cnf(3490,plain,
multiply(sk_c5,sk_c6) = identity,
inference(para_from,[status(thm),theory(equality)],[3383,9]),
[iquote('para_from,3383.1.1,9.1.1.1')] ).
cnf(3509,plain,
( sk_c7 = sk_c3
| sk_c7 = identity ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3332]),3490])]),
[iquote('back_demod,3332,demod,3490,flip.2')] ).
cnf(3544,plain,
( sk_c2 = sk_c1
| sk_c7 = identity ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2056]),3490])]),
[iquote('back_demod,2056,demod,3490,flip.2')] ).
cnf(3553,plain,
( multiply(inverse(sk_c2),sk_c3) = sk_c7
| sk_c7 = identity ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[700]),3490])]),
[iquote('back_demod,700,demod,3490,flip.2')] ).
cnf(3590,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(para_from,[status(thm),theory(equality)],[3287,1922]),
[iquote('para_from,3286.1.1,1922.1.1.2')] ).
cnf(3594,plain,
multiply(sk_c7,A) = multiply(sk_c1,multiply(sk_c6,A)),
inference(para_from,[status(thm),theory(equality)],[3287,11]),
[iquote('para_from,3286.1.1,11.1.1.1')] ).
cnf(3630,plain,
( sk_c7 != sk_c1
| multiply(sk_c1,multiply(sk_c6,sk_c6)) != sk_c7
| multiply(sk_c1,multiply(sk_c6,A)) != sk_c6
| multiply(sk_c1,multiply(sk_c6,sk_c7)) != A
| multiply(B,multiply(C,sk_c6)) != sk_c7
| inverse(multiply(B,C)) != sk_c6 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2118]),3594,3594,3594]),
[iquote('back_demod,2118,demod,3594,3594,3594')] ).
cnf(3638,plain,
multiply(sk_c1,multiply(sk_c6,sk_c7)) = sk_c6,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3590]),3594]),
[iquote('back_demod,3590,demod,3594')] ).
cnf(3799,plain,
multiply(sk_c1,multiply(sk_c6,sk_c1)) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1924]),3594]),
[iquote('back_demod,1924,demod,3594')] ).
cnf(3837,plain,
( sk_c7 != sk_c1
| multiply(sk_c1,multiply(sk_c6,sk_c6)) != sk_c7
| multiply(sk_c1,multiply(sk_c6,A)) != sk_c6
| sk_c6 != A
| sk_c6 != sk_c1 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(factor,[status(thm)],[3630]),3638,3287,1921])]),
[iquote('factor,3630.2.5,demod,3638,3287,1921,flip.5')] ).
cnf(3858,plain,
( sk_c7 != sk_c1
| multiply(sk_c1,multiply(sk_c6,sk_c6)) != sk_c7
| sk_c6 != identity
| sk_c6 != sk_c1 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(factor,[status(thm)],[3837]),3799])]),
[iquote('factor,3837.4.5,demod,3799,flip.3')] ).
cnf(3866,plain,
( sk_c1 = identity
| sk_c7 = sk_c3 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[3509,1921]),168])]),
[iquote('para_from,3509.2.1,1920.1.1.1,demod,168,flip.1')] ).
cnf(3874,plain,
( sk_c1 = identity
| sk_c2 = sk_c1 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[3544,1921]),168])]),
[iquote('para_from,3544.2.1,1920.1.1.1,demod,168,flip.1')] ).
cnf(3880,plain,
sk_c7 = sk_c3,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[3866,3287]),8]),3337]),
[iquote('para_from,3866.1.1,3286.1.1.1,demod,8,unit_del,3337')] ).
cnf(3889,plain,
( sk_c3 != sk_c1
| multiply(sk_c1,multiply(sk_c6,sk_c6)) != sk_c3
| sk_c6 != identity
| sk_c6 != sk_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3858]),3880,3880]),
[iquote('back_demod,3858,demod,3880,3880')] ).
cnf(4068,plain,
multiply(sk_c1,multiply(sk_c6,sk_c3)) = sk_c6,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3638]),3880]),
[iquote('back_demod,3637,demod,3880')] ).
cnf(4071,plain,
multiply(sk_c1,multiply(sk_c6,A)) = multiply(sk_c3,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3594]),3880])]),
[iquote('back_demod,3593,demod,3880,flip.1')] ).
cnf(4082,plain,
( multiply(inverse(sk_c2),sk_c3) = sk_c3
| sk_c3 = identity ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3553]),3880,3880]),
[iquote('back_demod,3553,demod,3880,3880')] ).
cnf(4095,plain,
sk_c6 != sk_c3,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3337]),3880])]),
[iquote('back_demod,3337,demod,3880,flip.1')] ).
cnf(4096,plain,
multiply(sk_c1,sk_c6) = sk_c3,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3287]),3880]),
[iquote('back_demod,3286,demod,3880')] ).
cnf(4133,plain,
inverse(sk_c1) = sk_c3,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1864]),3880]),
[iquote('back_demod,1864,demod,3880')] ).
cnf(4248,plain,
multiply(sk_c3,sk_c3) = sk_c6,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4068]),4071]),
[iquote('back_demod,4068,demod,4071')] ).
cnf(4324,plain,
( sk_c3 != sk_c1
| multiply(sk_c3,sk_c6) != sk_c3
| sk_c6 != identity
| sk_c6 != sk_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3889]),4071]),
[iquote('back_demod,3889,demod,4071')] ).
cnf(4330,plain,
multiply(sk_c3,sk_c1) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3799]),4071]),
[iquote('back_demod,3798,demod,4071')] ).
cnf(4349,plain,
sk_c2 = sk_c1,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[3874,4096]),8]),4095]),
[iquote('para_from,3874.1.1,4096.1.1.1,demod,8,unit_del,4095')] ).
cnf(4351,plain,
sk_c3 = identity,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4082]),4349,4133,4248]),4095]),
[iquote('back_demod,4082,demod,4349,4133,4248,unit_del,4095')] ).
cnf(4353,plain,
sk_c1 = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4330]),4351,8]),
[iquote('back_demod,4330,demod,4351,8')] ).
cnf(4354,plain,
sk_c6 != identity,
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4324]),4351,4353,4351,8,4351,4353]),6])])]),
[iquote('back_demod,4324,demod,4351,4353,4351,8,4351,4353,unit_del,6,factor_simp,factor_simp')] ).
cnf(4356,plain,
sk_c6 = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4248]),4351,4351,164])]),
[iquote('back_demod,4247,demod,4351,4351,164,flip.1')] ).
cnf(4358,plain,
$false,
inference(binary,[status(thm)],[4356,4354]),
[iquote('binary,4356.1,4354.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP226-1 : TPTP v8.1.0. Released v2.5.0.
% 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 05:32:35 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.75/1.95 ----- Otter 3.3f, August 2004 -----
% 1.75/1.95 The process was started by sandbox on n022.cluster.edu,
% 1.75/1.95 Wed Jul 27 05:32:35 2022
% 1.75/1.95 The command was "./otter". The process ID is 4232.
% 1.75/1.95
% 1.75/1.95 set(prolog_style_variables).
% 1.75/1.95 set(auto).
% 1.75/1.95 dependent: set(auto1).
% 1.75/1.95 dependent: set(process_input).
% 1.75/1.95 dependent: clear(print_kept).
% 1.75/1.95 dependent: clear(print_new_demod).
% 1.75/1.95 dependent: clear(print_back_demod).
% 1.75/1.95 dependent: clear(print_back_sub).
% 1.75/1.95 dependent: set(control_memory).
% 1.75/1.95 dependent: assign(max_mem, 12000).
% 1.75/1.95 dependent: assign(pick_given_ratio, 4).
% 1.75/1.95 dependent: assign(stats_level, 1).
% 1.75/1.95 dependent: assign(max_seconds, 10800).
% 1.75/1.95 clear(print_given).
% 1.75/1.95
% 1.75/1.95 list(usable).
% 1.75/1.95 0 [] A=A.
% 1.75/1.95 0 [] multiply(identity,X)=X.
% 1.75/1.95 0 [] multiply(inverse(X),X)=identity.
% 1.75/1.95 0 [] multiply(multiply(X,Y),Z)=multiply(X,multiply(Y,Z)).
% 1.75/1.95 0 [] inverse(sk_c1)=sk_c7|inverse(sk_c4)=sk_c7.
% 1.75/1.95 0 [] inverse(sk_c1)=sk_c7|multiply(sk_c4,sk_c6)=sk_c7.
% 1.75/1.95 0 [] inverse(sk_c1)=sk_c7|multiply(sk_c5,sk_c6)=sk_c7.
% 1.75/1.95 0 [] inverse(sk_c1)=sk_c7|inverse(sk_c5)=sk_c6.
% 1.75/1.95 0 [] multiply(sk_c1,sk_c6)=sk_c7|inverse(sk_c4)=sk_c7.
% 1.75/1.95 0 [] multiply(sk_c1,sk_c6)=sk_c7|multiply(sk_c4,sk_c6)=sk_c7.
% 1.75/1.95 0 [] multiply(sk_c1,sk_c6)=sk_c7|multiply(sk_c5,sk_c6)=sk_c7.
% 1.75/1.95 0 [] multiply(sk_c1,sk_c6)=sk_c7|inverse(sk_c5)=sk_c6.
% 1.75/1.95 0 [] multiply(sk_c7,sk_c3)=sk_c6|inverse(sk_c4)=sk_c7.
% 1.75/1.95 0 [] multiply(sk_c7,sk_c3)=sk_c6|multiply(sk_c4,sk_c6)=sk_c7.
% 1.75/1.95 0 [] multiply(sk_c7,sk_c3)=sk_c6|multiply(sk_c5,sk_c6)=sk_c7.
% 1.75/1.95 0 [] multiply(sk_c7,sk_c3)=sk_c6|inverse(sk_c5)=sk_c6.
% 1.75/1.95 0 [] multiply(sk_c2,sk_c7)=sk_c3|inverse(sk_c4)=sk_c7.
% 1.75/1.95 0 [] multiply(sk_c2,sk_c7)=sk_c3|multiply(sk_c4,sk_c6)=sk_c7.
% 1.75/1.95 0 [] multiply(sk_c2,sk_c7)=sk_c3|multiply(sk_c5,sk_c6)=sk_c7.
% 1.75/1.95 0 [] multiply(sk_c2,sk_c7)=sk_c3|inverse(sk_c5)=sk_c6.
% 1.75/1.95 0 [] inverse(sk_c2)=sk_c7|inverse(sk_c4)=sk_c7.
% 1.75/1.95 0 [] inverse(sk_c2)=sk_c7|multiply(sk_c4,sk_c6)=sk_c7.
% 1.75/1.95 0 [] inverse(sk_c2)=sk_c7|multiply(sk_c5,sk_c6)=sk_c7.
% 1.75/1.95 0 [] inverse(sk_c2)=sk_c7|inverse(sk_c5)=sk_c6.
% 1.75/1.95 0 [] inverse(X3)!=sk_c7|multiply(X3,sk_c6)!=sk_c7|multiply(sk_c7,X4)!=sk_c6|multiply(X5,sk_c7)!=X4|inverse(X5)!=sk_c7|inverse(X1)!=sk_c7|multiply(X1,sk_c6)!=sk_c7|multiply(X2,sk_c6)!=sk_c7|inverse(X2)!=sk_c6.
% 1.75/1.95 end_of_list.
% 1.75/1.95
% 1.75/1.95 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=9.
% 1.75/1.95
% 1.75/1.95 This ia a non-Horn set with equality. The strategy will be
% 1.75/1.95 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.75/1.95 deletion, with positive clauses in sos and nonpositive
% 1.75/1.95 clauses in usable.
% 1.75/1.95
% 1.75/1.95 dependent: set(knuth_bendix).
% 1.75/1.95 dependent: set(anl_eq).
% 1.75/1.95 dependent: set(para_from).
% 1.75/1.95 dependent: set(para_into).
% 1.75/1.95 dependent: clear(para_from_right).
% 1.75/1.95 dependent: clear(para_into_right).
% 1.75/1.95 dependent: set(para_from_vars).
% 1.75/1.95 dependent: set(eq_units_both_ways).
% 1.75/1.95 dependent: set(dynamic_demod_all).
% 1.75/1.95 dependent: set(dynamic_demod).
% 1.75/1.95 dependent: set(order_eq).
% 1.75/1.95 dependent: set(back_demod).
% 1.75/1.95 dependent: set(lrpo).
% 1.75/1.95 dependent: set(hyper_res).
% 1.75/1.95 dependent: set(unit_deletion).
% 1.75/1.95 dependent: set(factor).
% 1.75/1.95
% 1.75/1.95 ------------> process usable:
% 1.75/1.95 ** KEPT (pick-wt=32): 2 [copy,1,factor_simp,factor_simp] inverse(A)!=sk_c7|multiply(A,sk_c6)!=sk_c7|multiply(sk_c7,B)!=sk_c6|multiply(C,sk_c7)!=B|inverse(C)!=sk_c7|multiply(D,sk_c6)!=sk_c7|inverse(D)!=sk_c6.
% 1.75/1.95
% 1.75/1.95 ------------> process sos:
% 1.75/1.95 ** KEPT (pick-wt=3): 6 [] A=A.
% 1.75/1.95 ** KEPT (pick-wt=5): 7 [] multiply(identity,A)=A.
% 1.75/1.95 ---> New Demodulator: 8 [new_demod,7] multiply(identity,A)=A.
% 1.75/1.95 ** KEPT (pick-wt=6): 9 [] multiply(inverse(A),A)=identity.
% 1.75/1.95 ---> New Demodulator: 10 [new_demod,9] multiply(inverse(A),A)=identity.
% 1.75/1.95 ** KEPT (pick-wt=11): 11 [] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.75/1.95 ---> New Demodulator: 12 [new_demod,11] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.75/1.95 ** KEPT (pick-wt=8): 13 [] inverse(sk_c1)=sk_c7|inverse(sk_c4)=sk_c7.
% 1.75/1.95 ** KEPT (pick-wt=9): 14 [] inverse(sk_c1)=sk_c7|multiply(sk_c4,sk_c6)=sk_c7.
% 1.75/1.95 ** KEPT (pick-wt=9): 15 [] inverse(sk_c1)=sk_c7|multiply(sk_c5,sk_c6)=sk_c7.
% 1.75/1.95 ** KEPT (pick-wt=8): 16 [] inverse(sk_c1)=sk_c7|inverse(sk_c5)=sk_c6.
% 1.75/1.95 ** KEPT (pick-wt=9): 17 [] multiply(sk_c1,sk_c6)=sk_c7|inverse(sk_c4)=sk_c7.
% 1.75/1.95 ** KEPT (pick-wt=10): 18 [] multiply(sk_c1,sk_c6)=sk_c7|multiply(sk_c4,sk_c6)=sk_c7.
% 1.75/1.95 ** KEPT (pick-wt=10): 19 [] multiply(sk_c1,sk_c6)=sk_c7|multiply(sk_c5,sk_c6)=sk_c7.
% 243.42/243.61 ** KEPT (pick-wt=9): 20 [] multiply(sk_c1,sk_c6)=sk_c7|inverse(sk_c5)=sk_c6.
% 243.42/243.61 ** KEPT (pick-wt=9): 21 [] multiply(sk_c7,sk_c3)=sk_c6|inverse(sk_c4)=sk_c7.
% 243.42/243.61 ** KEPT (pick-wt=10): 22 [] multiply(sk_c7,sk_c3)=sk_c6|multiply(sk_c4,sk_c6)=sk_c7.
% 243.42/243.61 ** KEPT (pick-wt=10): 23 [] multiply(sk_c7,sk_c3)=sk_c6|multiply(sk_c5,sk_c6)=sk_c7.
% 243.42/243.61 ** KEPT (pick-wt=9): 24 [] multiply(sk_c7,sk_c3)=sk_c6|inverse(sk_c5)=sk_c6.
% 243.42/243.61 ** KEPT (pick-wt=9): 25 [] multiply(sk_c2,sk_c7)=sk_c3|inverse(sk_c4)=sk_c7.
% 243.42/243.61 ** KEPT (pick-wt=10): 26 [] multiply(sk_c2,sk_c7)=sk_c3|multiply(sk_c4,sk_c6)=sk_c7.
% 243.42/243.61 ** KEPT (pick-wt=10): 27 [] multiply(sk_c2,sk_c7)=sk_c3|multiply(sk_c5,sk_c6)=sk_c7.
% 243.42/243.61 ** KEPT (pick-wt=9): 28 [] multiply(sk_c2,sk_c7)=sk_c3|inverse(sk_c5)=sk_c6.
% 243.42/243.61 ** KEPT (pick-wt=8): 29 [] inverse(sk_c2)=sk_c7|inverse(sk_c4)=sk_c7.
% 243.42/243.61 ** KEPT (pick-wt=9): 30 [] inverse(sk_c2)=sk_c7|multiply(sk_c4,sk_c6)=sk_c7.
% 243.42/243.61 ** KEPT (pick-wt=9): 31 [] inverse(sk_c2)=sk_c7|multiply(sk_c5,sk_c6)=sk_c7.
% 243.42/243.61 ** KEPT (pick-wt=8): 32 [] inverse(sk_c2)=sk_c7|inverse(sk_c5)=sk_c6.
% 243.42/243.61 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 243.42/243.61 >>>> Starting back demodulation with 8.
% 243.42/243.61 >>>> Starting back demodulation with 10.
% 243.42/243.61 >>>> Starting back demodulation with 12.
% 243.42/243.61
% 243.42/243.61 ======= end of input processing =======
% 243.42/243.61
% 243.42/243.61 =========== start of search ===========
% 243.42/243.61
% 243.42/243.61
% 243.42/243.61 Resetting weight limit to 7.
% 243.42/243.61
% 243.42/243.61
% 243.42/243.61 Resetting weight limit to 7.
% 243.42/243.61
% 243.42/243.61 sos_size=254
% 243.42/243.61
% 243.42/243.61 -- HEY sandbox, WE HAVE A PROOF!! --
% 243.42/243.61
% 243.42/243.61 ----> UNIT CONFLICT at 241.65 sec ----> 4358 [binary,4356.1,4354.1] $F.
% 243.42/243.61
% 243.42/243.61 Length of proof is 83. Level of proof is 23.
% 243.42/243.61
% 243.42/243.61 ---------------- PROOF ----------------
% 243.42/243.61 % SZS status Unsatisfiable
% 243.42/243.61 % SZS output start Refutation
% See solution above
% 243.42/243.61 ------------ end of proof -------------
% 243.42/243.61
% 243.42/243.61
% 243.42/243.61 Search stopped by max_proofs option.
% 243.42/243.61
% 243.42/243.61
% 243.42/243.61 Search stopped by max_proofs option.
% 243.42/243.61
% 243.42/243.61 ============ end of search ============
% 243.42/243.61
% 243.42/243.61 -------------- statistics -------------
% 243.42/243.61 clauses given 143
% 243.42/243.61 clauses generated 876828
% 243.42/243.61 clauses kept 4297
% 243.42/243.61 clauses forward subsumed 875230
% 243.42/243.61 clauses back subsumed 1266
% 243.42/243.61 Kbytes malloced 4882
% 243.42/243.61
% 243.42/243.61 ----------- times (seconds) -----------
% 243.42/243.61 user CPU time 241.65 (0 hr, 4 min, 1 sec)
% 243.42/243.61 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 243.42/243.61 wall-clock time 243 (0 hr, 4 min, 3 sec)
% 243.42/243.61
% 243.42/243.61 That finishes the proof of the theorem.
% 243.42/243.61
% 243.42/243.61 Process 4232 finished Wed Jul 27 05:36:38 2022
% 243.42/243.62 Otter interrupted
% 243.42/243.62 PROOF FOUND
%------------------------------------------------------------------------------