TSTP Solution File: GRP229-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP229-1 : 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 2.33s 2.51s
% Output : Refutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 29
% Syntax : Number of clauses : 162 ( 41 unt; 90 nHn; 144 RR)
% Number of literals : 331 ( 330 equ; 109 neg)
% Maximal clause size : 11 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( inverse(A) != sk_c8
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c8,B) != sk_c7
| multiply(C,sk_c8) != B
| inverse(C) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(D) != sk_c8
| multiply(D,sk_c7) != sk_c8
| multiply(sk_c8,E) != sk_c7
| multiply(F,sk_c8) != E
| inverse(F) != sk_c8 ),
file('GRP229-1.p',unknown),
[] ).
cnf(2,plain,
( inverse(A) != sk_c8
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c8,B) != sk_c7
| multiply(C,sk_c8) != B
| inverse(C) != sk_c8
| inverse(sk_c8) != sk_c7 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[1])])])])])]),
[iquote('copy,1,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp')] ).
cnf(3,plain,
( inverse(A) != sk_c8
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c8,B) != sk_c7
| multiply(A,sk_c8) != B
| inverse(sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[2]),
[iquote('factor,2.1.5')] ).
cnf(4,axiom,
A = A,
file('GRP229-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(identity,A) = A,
file('GRP229-1.p',unknown),
[] ).
cnf(7,axiom,
multiply(inverse(A),A) = identity,
file('GRP229-1.p',unknown),
[] ).
cnf(9,axiom,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
file('GRP229-1.p',unknown),
[] ).
cnf(11,axiom,
( inverse(sk_c1) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('GRP229-1.p',unknown),
[] ).
cnf(12,axiom,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('GRP229-1.p',unknown),
[] ).
cnf(13,axiom,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('GRP229-1.p',unknown),
[] ).
cnf(14,axiom,
( inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('GRP229-1.p',unknown),
[] ).
cnf(15,axiom,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('GRP229-1.p',unknown),
[] ).
cnf(16,axiom,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('GRP229-1.p',unknown),
[] ).
cnf(17,axiom,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('GRP229-1.p',unknown),
[] ).
cnf(18,axiom,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('GRP229-1.p',unknown),
[] ).
cnf(19,axiom,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('GRP229-1.p',unknown),
[] ).
cnf(23,axiom,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('GRP229-1.p',unknown),
[] ).
cnf(24,axiom,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('GRP229-1.p',unknown),
[] ).
cnf(26,axiom,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('GRP229-1.p',unknown),
[] ).
cnf(27,axiom,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('GRP229-1.p',unknown),
[] ).
cnf(28,axiom,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c5) = sk_c8 ),
file('GRP229-1.p',unknown),
[] ).
cnf(29,axiom,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c8) = sk_c7 ),
file('GRP229-1.p',unknown),
[] ).
cnf(30,axiom,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c4) = sk_c8 ),
file('GRP229-1.p',unknown),
[] ).
cnf(32,axiom,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('GRP229-1.p',unknown),
[] ).
cnf(33,axiom,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('GRP229-1.p',unknown),
[] ).
cnf(34,axiom,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c5) = sk_c8 ),
file('GRP229-1.p',unknown),
[] ).
cnf(35,axiom,
( inverse(sk_c2) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('GRP229-1.p',unknown),
[] ).
cnf(36,axiom,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('GRP229-1.p',unknown),
[] ).
cnf(38,axiom,
( inverse(sk_c2) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('GRP229-1.p',unknown),
[] ).
cnf(39,axiom,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('GRP229-1.p',unknown),
[] ).
cnf(40,axiom,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('GRP229-1.p',unknown),
[] ).
cnf(41,plain,
( inverse(identity) != sk_c8
| sk_c8 != sk_c7
| multiply(sk_c8,A) != sk_c7
| sk_c8 != A
| inverse(sk_c8) != sk_c7 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[6,3]),6])]),
[iquote('para_from,5.1.1,3.4.1,demod,6,flip.2')] ).
cnf(45,plain,
( inverse(inverse(sk_c8)) != sk_c8
| multiply(inverse(sk_c8),sk_c7) != sk_c8
| multiply(sk_c8,A) != sk_c7
| identity != A
| inverse(sk_c8) != sk_c7 ),
inference(para_from,[status(thm),theory(equality)],[7,3]),
[iquote('para_from,7.1.1,3.4.1')] ).
cnf(64,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)],[9,7]),6])]),
[iquote('para_into,9.1.1.1,7.1.1,demod,6,flip.1')] ).
cnf(77,plain,
( multiply(sk_c8,sk_c2) = identity
| inverse(sk_c8) = sk_c7 ),
inference(para_from,[status(thm),theory(equality)],[35,7]),
[iquote('para_from,35.1.1,7.1.1.1')] ).
cnf(85,plain,
( multiply(sk_c8,sk_c2) = identity
| inverse(sk_c4) = sk_c8 ),
inference(para_from,[status(thm),theory(equality)],[36,7]),
[iquote('para_from,36.1.1,7.1.1.1')] ).
cnf(93,plain,
( multiply(sk_c8,sk_c2) = identity
| inverse(sk_c5) = sk_c8 ),
inference(para_from,[status(thm),theory(equality)],[40,7]),
[iquote('para_from,40.1.1,7.1.1.1')] ).
cnf(121,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(para_into,[status(thm),theory(equality)],[64,64]),
[iquote('para_into,64.1.1.2,64.1.1')] ).
cnf(123,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))) = C,
inference(para_into,[status(thm),theory(equality)],[64,9]),
[iquote('para_into,64.1.1.2,9.1.1')] ).
cnf(126,plain,
multiply(A,identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[64,7]),121]),
[iquote('para_into,64.1.1.2,7.1.1,demod,121')] ).
cnf(130,plain,
inverse(identity) = identity,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[126,7])]),
[iquote('para_into,125.1.1,7.1.1,flip.1')] ).
cnf(134,plain,
( sk_c8 != identity
| sk_c8 != sk_c7
| multiply(sk_c8,A) != sk_c7
| sk_c8 != A
| inverse(sk_c8) != sk_c7 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[41]),130])]),
[iquote('back_demod,41,demod,130,flip.1')] ).
cnf(136,plain,
( sk_c8 != identity
| sk_c8 != sk_c7
| inverse(sk_c8) != sk_c7 ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(factor,[status(thm)],[134]),126])]),
[iquote('factor,134.1.4,demod,126,factor_simp')] ).
cnf(137,plain,
( inverse(A) != sk_c8
| multiply(A,sk_c7) != sk_c8
| sk_c8 != sk_c7
| multiply(A,sk_c8) != identity
| inverse(sk_c8) != sk_c7 ),
inference(para_from,[status(thm),theory(equality)],[126,3]),
[iquote('para_from,125.1.1,3.3.1')] ).
cnf(150,plain,
inverse(sk_c1) = sk_c8,
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[15,2,12,13,14,16,11])])])])])]),
[iquote('hyper,15,2,12,13,14,16,11,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp')] ).
cnf(154,plain,
multiply(sk_c8,sk_c1) = identity,
inference(para_from,[status(thm),theory(equality)],[150,7]),
[iquote('para_from,149.1.1,7.1.1.1')] ).
cnf(157,plain,
( multiply(sk_c1,sk_c7) != sk_c8
| multiply(sk_c8,A) != sk_c7
| multiply(B,sk_c8) != A
| inverse(B) != sk_c8
| inverse(sk_c8) != sk_c7 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[150,2]),4]),
[iquote('para_from,149.1.1,2.1.1,unit_del,4')] ).
cnf(159,plain,
inverse(sk_c8) = sk_c1,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[154,64]),126]),
[iquote('para_from,154.1.1,64.1.1.2,demod,126')] ).
cnf(162,plain,
( multiply(sk_c1,sk_c7) != sk_c8
| multiply(sk_c8,A) != sk_c7
| multiply(B,sk_c8) != A
| inverse(B) != sk_c8
| sk_c7 != sk_c1 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[157]),159])]),
[iquote('back_demod,157,demod,159,flip.5')] ).
cnf(166,plain,
( inverse(A) != sk_c8
| multiply(A,sk_c7) != sk_c8
| sk_c8 != sk_c7
| multiply(A,sk_c8) != identity
| sk_c7 != sk_c1 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[137]),159])]),
[iquote('back_demod,137,demod,159,flip.5')] ).
cnf(167,plain,
( sk_c8 != identity
| sk_c8 != sk_c7
| sk_c7 != sk_c1 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[136]),159])]),
[iquote('back_demod,136,demod,159,flip.3')] ).
cnf(185,plain,
( multiply(sk_c8,sk_c2) = identity
| sk_c7 = sk_c1 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[77]),159])]),
[iquote('back_demod,77,demod,159,flip.2')] ).
cnf(192,plain,
( multiply(sk_c1,sk_c7) != sk_c8
| multiply(sk_c8,A) != sk_c7
| identity != A
| sk_c7 != sk_c1 ),
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[45]),159,150,159,159]),4])]),
[iquote('back_demod,45,demod,159,150,159,159,unit_del,4,flip.4')] ).
cnf(194,plain,
( multiply(sk_c2,sk_c8) = sk_c3
| sk_c7 = sk_c1 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[29]),159])]),
[iquote('back_demod,29,demod,159,flip.2')] ).
cnf(195,plain,
( multiply(sk_c8,sk_c3) = sk_c7
| sk_c7 = sk_c1 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[23]),159])]),
[iquote('back_demod,23,demod,159,flip.2')] ).
cnf(196,plain,
( multiply(sk_c1,sk_c7) = sk_c8
| sk_c7 = sk_c1 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[17]),159])]),
[iquote('back_demod,17,demod,159,flip.2')] ).
cnf(199,plain,
multiply(sk_c1,multiply(sk_c8,A)) = A,
inference(para_from,[status(thm),theory(equality)],[159,64]),
[iquote('para_from,158.1.1,64.1.1.1')] ).
cnf(202,plain,
multiply(sk_c1,sk_c8) = identity,
inference(para_from,[status(thm),theory(equality)],[159,7]),
[iquote('para_from,158.1.1,7.1.1.1')] ).
cnf(203,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[18,64]),150]),
[iquote('para_from,18.1.1,64.1.1.2,demod,150')] ).
cnf(207,plain,
( sk_c2 = sk_c1
| sk_c7 = sk_c1 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[185,199]),126])]),
[iquote('para_from,185.1.1,199.1.1.2,demod,126,flip.1')] ).
cnf(218,plain,
( sk_c3 = identity
| sk_c7 = sk_c1 ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[194,207]),202])]),
[iquote('para_into,194.1.1.1,207.1.1,demod,202,factor_simp')] ).
cnf(225,plain,
( sk_c8 = sk_c7
| sk_c7 = sk_c1 ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[195,218]),126])]),
[iquote('para_into,195.1.1.2,218.1.1,demod,126,factor_simp')] ).
cnf(226,plain,
( multiply(sk_c1,sk_c7) = sk_c3
| sk_c7 = sk_c1 ),
inference(para_from,[status(thm),theory(equality)],[195,199]),
[iquote('para_from,195.1.1,199.1.1.2')] ).
cnf(254,plain,
( multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c4,sk_c1) = sk_c8 ),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[196,19])]),
[iquote('para_from,196.2.1,19.2.1.2,factor_simp')] ).
cnf(255,plain,
( sk_c8 = sk_c3
| sk_c7 = sk_c1 ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[226,196])]),
[iquote('para_into,226.1.1,196.1.1,factor_simp')] ).
cnf(275,plain,
( inverse(sk_c3) = sk_c1
| sk_c7 = sk_c1 ),
inference(para_from,[status(thm),theory(equality)],[255,159]),
[iquote('para_from,255.1.1,158.1.1.1')] ).
cnf(289,plain,
( sk_c1 = identity
| sk_c7 = sk_c1 ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[275,218]),130])]),
[iquote('para_into,275.1.1.1,218.1.1,demod,130,factor_simp')] ).
cnf(294,plain,
( sk_c8 = identity
| sk_c7 = sk_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[289,202]),6]),
[iquote('para_from,289.1.1,201.1.1.1,demod,6')] ).
cnf(313,plain,
( sk_c7 = identity
| sk_c7 = sk_c1 ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[294,225])]),
[iquote('para_into,294.1.1,225.1.1,factor_simp')] ).
cnf(323,plain,
( sk_c8 = sk_c1
| sk_c7 = sk_c1 ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[313,196]),126])]),
[iquote('para_from,313.1.1,196.1.1.2,demod,126,factor_simp')] ).
cnf(344,plain,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(para_from,[status(thm),theory(equality)],[24,7]),
[iquote('para_from,24.2.1,7.1.1.1')] ).
cnf(351,plain,
sk_c7 = sk_c1,
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[323,225])])]),
[iquote('para_into,323.1.1,225.1.1,factor_simp,factor_simp')] ).
cnf(354,plain,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c8,sk_c3) = sk_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[344]),351]),
[iquote('back_demod,344,demod,351')] ).
cnf(384,plain,
( multiply(sk_c1,sk_c1) = sk_c8
| multiply(sk_c4,sk_c1) = sk_c8 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[254]),351]),
[iquote('back_demod,254,demod,351')] ).
cnf(401,plain,
( multiply(sk_c8,sk_c8) = sk_c1
| inverse(sk_c4) = sk_c8 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[203]),351]),
[iquote('back_demod,203,demod,351')] ).
cnf(404,plain,
( multiply(sk_c1,sk_c1) != sk_c8
| multiply(sk_c8,A) != sk_c1
| identity != A ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[192]),351,351,351]),4]),
[iquote('back_demod,192,demod,351,351,351,unit_del,4')] ).
cnf(425,plain,
( sk_c8 != identity
| sk_c8 != sk_c1 ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[167]),351,351]),4]),
[iquote('back_demod,167,demod,351,351,unit_del,4')] ).
cnf(426,plain,
( inverse(A) != sk_c8
| multiply(A,sk_c1) != sk_c8
| sk_c8 != sk_c1
| multiply(A,sk_c8) != identity ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[166]),351,351,351]),4]),
[iquote('back_demod,166,demod,351,351,351,unit_del,4')] ).
cnf(428,plain,
( multiply(sk_c1,sk_c1) != sk_c8
| multiply(sk_c8,A) != sk_c1
| multiply(B,sk_c8) != A
| inverse(B) != sk_c8 ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[162]),351,351,351]),4]),
[iquote('back_demod,162,demod,351,351,351,unit_del,4')] ).
cnf(431,plain,
( inverse(sk_c2) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[38]),351]),
[iquote('back_demod,38,demod,351')] ).
cnf(433,plain,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c8,sk_c6) = sk_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[32]),351]),
[iquote('back_demod,32,demod,351')] ).
cnf(435,plain,
( multiply(sk_c8,sk_c3) = sk_c1
| inverse(sk_c5) = sk_c8 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[28]),351]),
[iquote('back_demod,28,demod,351')] ).
cnf(436,plain,
( multiply(sk_c8,sk_c3) = sk_c1
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[27]),351]),
[iquote('back_demod,27,demod,351')] ).
cnf(437,plain,
( multiply(sk_c8,sk_c3) = sk_c1
| multiply(sk_c8,sk_c6) = sk_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[26]),351,351]),
[iquote('back_demod,26,demod,351,351')] ).
cnf(456,plain,
( sk_c2 = sk_c1
| inverse(sk_c4) = sk_c8 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[85,199]),126])]),
[iquote('para_from,85.1.1,199.1.1.2,demod,126,flip.1')] ).
cnf(460,plain,
( sk_c3 = identity
| inverse(sk_c4) = sk_c8 ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[456,30]),202])]),
[iquote('para_from,456.1.1,30.1.1.1,demod,202,factor_simp')] ).
cnf(468,plain,
( multiply(sk_c8,sk_c4) = identity
| sk_c3 = identity ),
inference(para_from,[status(thm),theory(equality)],[460,7]),
[iquote('para_from,460.2.1,7.1.1.1')] ).
cnf(477,plain,
( sk_c2 = sk_c1
| inverse(sk_c5) = sk_c8 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[93,199]),126])]),
[iquote('para_from,93.1.1,199.1.1.2,demod,126,flip.1')] ).
cnf(482,plain,
( sk_c3 = identity
| inverse(sk_c5) = sk_c8 ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[477,34]),202])]),
[iquote('para_from,477.1.1,34.1.1.1,demod,202,factor_simp')] ).
cnf(484,plain,
( multiply(sk_c8,sk_c5) = identity
| sk_c2 = sk_c1 ),
inference(para_from,[status(thm),theory(equality)],[477,7]),
[iquote('para_from,477.2.1,7.1.1.1')] ).
cnf(489,plain,
( multiply(sk_c8,sk_c5) = identity
| sk_c3 = identity ),
inference(para_from,[status(thm),theory(equality)],[482,7]),
[iquote('para_from,482.2.1,7.1.1.1')] ).
cnf(495,plain,
( sk_c5 = sk_c1
| sk_c2 = sk_c1 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[484,199]),126])]),
[iquote('para_from,484.1.1,199.1.1.2,demod,126,flip.1')] ).
cnf(498,plain,
( sk_c5 = sk_c1
| sk_c3 = identity ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[489,199]),126])]),
[iquote('para_from,489.1.1,199.1.1.2,demod,126,flip.1')] ).
cnf(522,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[121,126]),126]),
[iquote('para_into,120.1.1,125.1.1,demod,126')] ).
cnf(524,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[121,64])]),
[iquote('para_into,120.1.1,64.1.1,flip.1')] ).
cnf(526,plain,
multiply(A,inverse(A)) = identity,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[121,7])]),
[iquote('para_into,120.1.1,7.1.1,flip.1')] ).
cnf(529,plain,
( sk_c2 = sk_c1
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[522,39]),159])]),
[iquote('para_into,522.1.1.1,39.1.1,demod,159,flip.1')] ).
cnf(530,plain,
( sk_c5 = sk_c1
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[522,34]),159])]),
[iquote('para_into,522.1.1.1,34.2.1,demod,159,flip.1')] ).
cnf(556,plain,
( multiply(sk_c5,multiply(sk_c8,A)) = A
| sk_c3 = identity ),
inference(para_into,[status(thm),theory(equality)],[524,482]),
[iquote('para_into,524.1.1.2.1,482.2.1')] ).
cnf(581,plain,
( sk_c3 = identity
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[529,33]),202])]),
[iquote('para_from,529.1.1,33.1.1.1,demod,202,factor_simp')] ).
cnf(590,plain,
( multiply(inverse(sk_c2),sk_c3) = sk_c8
| sk_c5 = sk_c1 ),
inference(para_from,[status(thm),theory(equality)],[530,64]),
[iquote('para_from,530.2.1,64.1.1.2')] ).
cnf(613,plain,
multiply(inverse(multiply(A,B)),A) = inverse(B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[123,526]),126]),
[iquote('para_into,123.1.1.2.2,526.1.1,demod,126')] ).
cnf(627,plain,
( multiply(sk_c8,sk_c4) = identity
| sk_c8 = sk_c1 ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[354,468]),126])]),
[iquote('para_into,354.2.1.2,468.2.1,demod,126,factor_simp')] ).
cnf(632,plain,
( multiply(inverse(sk_c5),sk_c6) = sk_c8
| sk_c3 = identity ),
inference(para_from,[status(thm),theory(equality)],[581,64]),
[iquote('para_from,581.2.1,64.1.1.2')] ).
cnf(649,plain,
( sk_c4 = sk_c1
| sk_c8 = sk_c1 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[627,199]),126])]),
[iquote('para_from,627.1.1,199.1.1.2,demod,126,flip.1')] ).
cnf(679,plain,
( sk_c8 != identity
| sk_c4 = sk_c1 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[649,425]),4]),
[iquote('para_from,649.2.1,425.2.1,unit_del,4')] ).
cnf(686,plain,
( sk_c1 != identity
| sk_c4 = sk_c1 ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[679,649])]),
[iquote('para_into,679.1.1,649.2.1,factor_simp')] ).
cnf(821,plain,
( sk_c4 = sk_c1
| multiply(sk_c8,sk_c8) = sk_c1 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[401,522]),159])]),
[iquote('para_from,401.2.1,522.1.1.1,demod,159,flip.1')] ).
cnf(852,plain,
( sk_c4 = sk_c1
| sk_c1 = identity ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[821,649]),202])]),
[iquote('para_into,821.2.1.1,649.2.1,demod,202,factor_simp')] ).
cnf(859,plain,
sk_c4 = sk_c1,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[852,686])]),
[iquote('hyper,852,686,factor_simp')] ).
cnf(866,plain,
multiply(sk_c1,sk_c1) = sk_c8,
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[384]),859])]),
[iquote('back_demod,384,demod,859,factor_simp')] ).
cnf(867,plain,
( multiply(sk_c8,A) != sk_c1
| multiply(B,sk_c8) != A
| inverse(B) != sk_c8 ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[428]),866]),4]),
[iquote('back_demod,428,demod,866,unit_del,4')] ).
cnf(868,plain,
( multiply(sk_c8,A) != sk_c1
| identity != A ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[404]),866]),4]),
[iquote('back_demod,404,demod,866,unit_del,4')] ).
cnf(872,plain,
multiply(sk_c8,A) = multiply(sk_c1,multiply(sk_c1,A)),
inference(para_from,[status(thm),theory(equality)],[866,9]),
[iquote('para_from,865.1.1,9.1.1.1')] ).
cnf(874,plain,
( multiply(sk_c1,multiply(sk_c1,A)) != sk_c1
| identity != A ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[868]),872]),
[iquote('back_demod,868,demod,872')] ).
cnf(875,plain,
( multiply(sk_c1,multiply(sk_c1,A)) != sk_c1
| multiply(B,sk_c8) != A
| inverse(B) != sk_c8 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[867]),872]),
[iquote('back_demod,867,demod,872')] ).
cnf(903,plain,
( multiply(sk_c5,multiply(sk_c1,multiply(sk_c1,A))) = A
| sk_c3 = identity ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[556]),872]),
[iquote('back_demod,556,demod,872')] ).
cnf(935,plain,
( multiply(sk_c1,multiply(sk_c1,sk_c3)) = sk_c1
| multiply(sk_c1,multiply(sk_c1,sk_c6)) = sk_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[437]),872,872]),
[iquote('back_demod,437,demod,872,872')] ).
cnf(936,plain,
( multiply(sk_c1,multiply(sk_c1,sk_c3)) = sk_c1
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[436]),872]),
[iquote('back_demod,436,demod,872')] ).
cnf(937,plain,
( multiply(sk_c1,multiply(sk_c1,sk_c3)) = sk_c1
| inverse(sk_c5) = sk_c8 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[435]),872]),
[iquote('back_demod,435,demod,872')] ).
cnf(938,plain,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c1,multiply(sk_c1,sk_c6)) = sk_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[433]),872]),
[iquote('back_demod,433,demod,872')] ).
cnf(939,plain,
( inverse(sk_c2) = sk_c8
| multiply(sk_c1,multiply(sk_c1,sk_c6)) = sk_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[431]),872]),
[iquote('back_demod,431,demod,872')] ).
cnf(947,plain,
multiply(sk_c1,multiply(sk_c1,multiply(sk_c1,A))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[199]),872]),
[iquote('back_demod,199,demod,872')] ).
cnf(956,plain,
sk_c8 != sk_c1,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[426,150]),866,202]),4,4,4]),
[iquote('para_into,426.1.1,149.1.1,demod,866,202,unit_del,4,4,4')] ).
cnf(986,plain,
( multiply(sk_c1,multiply(sk_c1,sk_c3)) = sk_c8
| sk_c5 = sk_c1 ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[590,495]),150,872])]),
[iquote('para_into,590.1.1.1.1,495.2.1,demod,150,872,factor_simp')] ).
cnf(999,plain,
inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[613,64])]),
[iquote('para_into,613.1.1.1.1,64.1.1,flip.1')] ).
cnf(1011,plain,
( multiply(sk_c1,multiply(sk_c1,sk_c6)) = sk_c8
| sk_c3 = identity ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[632,498]),150,872])]),
[iquote('para_into,632.1.1.1.1,498.1.1,demod,150,872,factor_simp')] ).
cnf(1112,plain,
( A != sk_c1
| multiply(sk_c1,A) != identity ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[874,947])]),
[iquote('para_into,874.1.1,947.1.1,flip.2')] ).
cnf(1127,plain,
( multiply(sk_c1,multiply(sk_c1,A)) != sk_c1
| A != identity ),
inference(para_into,[status(thm),theory(equality)],[1112,947]),
[iquote('para_into,1112.2.1,947.1.1')] ).
cnf(1152,plain,
( multiply(A,sk_c8) != sk_c8
| inverse(A) != sk_c8 ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[875,526]),126,150]),4]),
[iquote('para_into,875.1.1.2,526.1.1,demod,126,150,unit_del,4')] ).
cnf(1238,plain,
( multiply(sk_c2,sk_c8) != sk_c8
| inverse(sk_c5) = sk_c8 ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[1152,40]),4]),
[iquote('para_into,1152.2.1,40.1.1,unit_del,4')] ).
cnf(1325,plain,
( sk_c8 != sk_c3
| inverse(sk_c5) = sk_c8 ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[1238,34])]),
[iquote('para_into,1238.1.1,34.1.1,factor_simp')] ).
cnf(1365,plain,
( multiply(sk_c1,multiply(sk_c1,sk_c5)) = identity
| sk_c8 != sk_c3 ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1325,7]),872]),
[iquote('para_from,1325.2.1,7.1.1.1,demod,872')] ).
cnf(1872,plain,
( multiply(sk_c1,sk_c6) = sk_c1
| sk_c3 = identity ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1011,947]),202,126])]),
[iquote('para_from,1011.1.1,947.1.1.2.2,demod,202,126,flip.1')] ).
cnf(1891,plain,
( multiply(inverse(sk_c6),sk_c8) = sk_c8
| sk_c3 = identity ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1872,999]),150,150])]),
[iquote('para_from,1872.1.1,998.1.1.1,demod,150,150,flip.1')] ).
cnf(1894,plain,
( multiply(sk_c6,sk_c8) = sk_c8
| sk_c3 = identity ),
inference(para_from,[status(thm),theory(equality)],[1891,524]),
[iquote('para_from,1891.1.1,524.1.1.2')] ).
cnf(1897,plain,
( multiply(sk_c1,inverse(sk_c6)) = sk_c1
| sk_c3 = identity ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1894,999]),159,159])]),
[iquote('para_from,1894.1.1,998.1.1.1,demod,159,159,flip.1')] ).
cnf(2064,plain,
( inverse(sk_c6) = multiply(sk_c5,sk_c8)
| sk_c3 = identity ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[903,1897]),866])]),
[iquote('para_into,903.1.1.2.2,1897.1.1,demod,866,factor_simp')] ).
cnf(2123,plain,
( multiply(sk_c1,inverse(sk_c5)) = sk_c6
| sk_c3 = identity ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[2064,522]),999,159]),
[iquote('para_from,2064.1.1,522.1.1.1,demod,999,159')] ).
cnf(2725,plain,
( multiply(sk_c1,sk_c5) != sk_c1
| sk_c8 != sk_c3 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1365,1112]),4]),
[iquote('para_from,1365.1.1,1112.2.1,unit_del,4')] ).
cnf(3003,plain,
( multiply(sk_c1,multiply(sk_c1,sk_c6)) = sk_c1
| multiply(sk_c1,inverse(sk_c5)) = sk_c6 ),
inference(hyper,[status(thm)],[935,1127,2123]),
[iquote('hyper,935,1127,2123')] ).
cnf(3088,plain,
( sk_c8 = sk_c3
| multiply(sk_c1,multiply(sk_c1,sk_c6)) = sk_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[935,947]),866]),
[iquote('para_from,935.1.1,947.1.1.2,demod,866')] ).
cnf(3095,plain,
( multiply(sk_c1,sk_c3) = identity
| multiply(sk_c1,multiply(sk_c1,sk_c6)) = sk_c1 ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[935,947]),866,202])]),
[iquote('para_from,935.1.1,947.1.1.2.2,demod,866,202,flip.1')] ).
cnf(3166,plain,
multiply(sk_c5,sk_c8) = sk_c6,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[936,1127,581])]),
[iquote('hyper,936,1127,581,factor_simp')] ).
cnf(3232,plain,
multiply(inverse(sk_c5),sk_c6) = sk_c8,
inference(para_from,[status(thm),theory(equality)],[3166,64]),
[iquote('para_from,3166.1.1,64.1.1.2')] ).
cnf(3236,plain,
( sk_c8 != sk_c6
| inverse(sk_c5) != sk_c8 ),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[3166,1152])]),
[iquote('para_from,3166.1.1,1152.1.1,flip.1')] ).
cnf(3350,plain,
inverse(sk_c5) = sk_c8,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[937,1127,482])]),
[iquote('hyper,937,1127,482,factor_simp')] ).
cnf(3352,plain,
multiply(sk_c1,multiply(sk_c1,sk_c3)) = sk_c1,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[937,875,935,3166])]),
[iquote('hyper,937,875,935,3166,factor_simp')] ).
cnf(3355,plain,
sk_c8 != sk_c6,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3236]),3350]),4]),
[iquote('back_demod,3236,demod,3350,unit_del,4')] ).
cnf(3357,plain,
multiply(sk_c1,multiply(sk_c1,sk_c6)) = sk_c8,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3232]),3350,872]),
[iquote('back_demod,3232,demod,3350,872')] ).
cnf(3364,plain,
sk_c6 = identity,
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3003]),3357,3350,202]),956])]),
[iquote('back_demod,3003,demod,3357,3350,202,unit_del,956,flip.1')] ).
cnf(3374,plain,
sk_c5 = sk_c1,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[986]),3352]),956]),
[iquote('back_demod,986,demod,3352,unit_del,956')] ).
cnf(3384,plain,
multiply(sk_c1,sk_c3) = identity,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3095]),3364,126,866]),956]),
[iquote('back_demod,3095,demod,3364,126,866,unit_del,956')] ).
cnf(3391,plain,
sk_c8 = sk_c3,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3088]),3364,126,866]),956]),
[iquote('back_demod,3088,demod,3364,126,866,unit_del,956')] ).
cnf(3393,plain,
( inverse(sk_c2) = sk_c3
| sk_c3 = sk_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[939]),3391,3364,126,866,3391]),
[iquote('back_demod,939,demod,3391,3364,126,866,3391')] ).
cnf(3394,plain,
( multiply(sk_c2,sk_c3) = sk_c3
| sk_c3 = sk_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[938]),3391,3364,126,866,3391]),
[iquote('back_demod,938,demod,3391,3364,126,866,3391')] ).
cnf(3398,plain,
sk_c3 != identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3355]),3391,3364]),
[iquote('back_demod,3355,demod,3391,3364')] ).
cnf(3413,plain,
sk_c3 != sk_c1,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2725]),3374,866,3391,3391]),4]),
[iquote('back_demod,2725,demod,3374,866,3391,3391,unit_del,4')] ).
cnf(3427,plain,
inverse(sk_c3) = sk_c1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[159]),3391]),
[iquote('back_demod,158,demod,3391')] ).
cnf(3430,plain,
inverse(sk_c2) = sk_c3,
inference(hyper,[status(thm)],[3393,3413]),
[iquote('hyper,3393,3413')] ).
cnf(3437,plain,
sk_c2 = sk_c1,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[3430,522]),3427])]),
[iquote('para_from,3430.1.1,522.1.1.1,demod,3427,flip.1')] ).
cnf(3438,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3394]),3437,3384]),3398,3413]),
[iquote('back_demod,3394,demod,3437,3384,unit_del,3398,3413')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP229-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n022.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 05:28:05 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.77/1.97 ----- Otter 3.3f, August 2004 -----
% 1.77/1.97 The process was started by sandbox2 on n022.cluster.edu,
% 1.77/1.97 Wed Jul 27 05:28:05 2022
% 1.77/1.97 The command was "./otter". The process ID is 519.
% 1.77/1.97
% 1.77/1.97 set(prolog_style_variables).
% 1.77/1.97 set(auto).
% 1.77/1.97 dependent: set(auto1).
% 1.77/1.97 dependent: set(process_input).
% 1.77/1.97 dependent: clear(print_kept).
% 1.77/1.97 dependent: clear(print_new_demod).
% 1.77/1.97 dependent: clear(print_back_demod).
% 1.77/1.97 dependent: clear(print_back_sub).
% 1.77/1.97 dependent: set(control_memory).
% 1.77/1.97 dependent: assign(max_mem, 12000).
% 1.77/1.97 dependent: assign(pick_given_ratio, 4).
% 1.77/1.97 dependent: assign(stats_level, 1).
% 1.77/1.97 dependent: assign(max_seconds, 10800).
% 1.77/1.97 clear(print_given).
% 1.77/1.97
% 1.77/1.97 list(usable).
% 1.77/1.97 0 [] A=A.
% 1.77/1.97 0 [] multiply(identity,X)=X.
% 1.77/1.97 0 [] multiply(inverse(X),X)=identity.
% 1.77/1.97 0 [] multiply(multiply(X,Y),Z)=multiply(X,multiply(Y,Z)).
% 1.77/1.97 0 [] inverse(sk_c1)=sk_c8|inverse(sk_c8)=sk_c7.
% 1.77/1.97 0 [] inverse(sk_c1)=sk_c8|inverse(sk_c4)=sk_c8.
% 1.77/1.97 0 [] inverse(sk_c1)=sk_c8|multiply(sk_c4,sk_c7)=sk_c8.
% 1.77/1.97 0 [] inverse(sk_c1)=sk_c8|multiply(sk_c8,sk_c6)=sk_c7.
% 1.77/1.97 0 [] inverse(sk_c1)=sk_c8|multiply(sk_c5,sk_c8)=sk_c6.
% 1.77/1.97 0 [] inverse(sk_c1)=sk_c8|inverse(sk_c5)=sk_c8.
% 1.77/1.97 0 [] multiply(sk_c1,sk_c7)=sk_c8|inverse(sk_c8)=sk_c7.
% 1.77/1.97 0 [] multiply(sk_c1,sk_c7)=sk_c8|inverse(sk_c4)=sk_c8.
% 1.77/1.97 0 [] multiply(sk_c1,sk_c7)=sk_c8|multiply(sk_c4,sk_c7)=sk_c8.
% 1.77/1.97 0 [] multiply(sk_c1,sk_c7)=sk_c8|multiply(sk_c8,sk_c6)=sk_c7.
% 1.77/1.97 0 [] multiply(sk_c1,sk_c7)=sk_c8|multiply(sk_c5,sk_c8)=sk_c6.
% 1.77/1.97 0 [] multiply(sk_c1,sk_c7)=sk_c8|inverse(sk_c5)=sk_c8.
% 1.77/1.97 0 [] multiply(sk_c8,sk_c3)=sk_c7|inverse(sk_c8)=sk_c7.
% 1.77/1.97 0 [] multiply(sk_c8,sk_c3)=sk_c7|inverse(sk_c4)=sk_c8.
% 1.77/1.97 0 [] multiply(sk_c8,sk_c3)=sk_c7|multiply(sk_c4,sk_c7)=sk_c8.
% 1.77/1.97 0 [] multiply(sk_c8,sk_c3)=sk_c7|multiply(sk_c8,sk_c6)=sk_c7.
% 1.77/1.97 0 [] multiply(sk_c8,sk_c3)=sk_c7|multiply(sk_c5,sk_c8)=sk_c6.
% 1.77/1.97 0 [] multiply(sk_c8,sk_c3)=sk_c7|inverse(sk_c5)=sk_c8.
% 1.77/1.97 0 [] multiply(sk_c2,sk_c8)=sk_c3|inverse(sk_c8)=sk_c7.
% 1.77/1.97 0 [] multiply(sk_c2,sk_c8)=sk_c3|inverse(sk_c4)=sk_c8.
% 1.77/1.97 0 [] multiply(sk_c2,sk_c8)=sk_c3|multiply(sk_c4,sk_c7)=sk_c8.
% 1.77/1.97 0 [] multiply(sk_c2,sk_c8)=sk_c3|multiply(sk_c8,sk_c6)=sk_c7.
% 1.77/1.97 0 [] multiply(sk_c2,sk_c8)=sk_c3|multiply(sk_c5,sk_c8)=sk_c6.
% 1.77/1.97 0 [] multiply(sk_c2,sk_c8)=sk_c3|inverse(sk_c5)=sk_c8.
% 1.77/1.97 0 [] inverse(sk_c2)=sk_c8|inverse(sk_c8)=sk_c7.
% 1.77/1.97 0 [] inverse(sk_c2)=sk_c8|inverse(sk_c4)=sk_c8.
% 1.77/1.97 0 [] inverse(sk_c2)=sk_c8|multiply(sk_c4,sk_c7)=sk_c8.
% 1.77/1.97 0 [] inverse(sk_c2)=sk_c8|multiply(sk_c8,sk_c6)=sk_c7.
% 1.77/1.97 0 [] inverse(sk_c2)=sk_c8|multiply(sk_c5,sk_c8)=sk_c6.
% 1.77/1.97 0 [] inverse(sk_c2)=sk_c8|inverse(sk_c5)=sk_c8.
% 1.77/1.97 0 [] inverse(X4)!=sk_c8|multiply(X4,sk_c7)!=sk_c8|multiply(sk_c8,X5)!=sk_c7|multiply(X6,sk_c8)!=X5|inverse(X6)!=sk_c8|inverse(sk_c8)!=sk_c7|inverse(X1)!=sk_c8|multiply(X1,sk_c7)!=sk_c8|multiply(sk_c8,X2)!=sk_c7|multiply(X3,sk_c8)!=X2|inverse(X3)!=sk_c8.
% 1.77/1.97 end_of_list.
% 1.77/1.97
% 1.77/1.97 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=11.
% 1.77/1.97
% 1.77/1.97 This ia a non-Horn set with equality. The strategy will be
% 1.77/1.97 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.77/1.97 deletion, with positive clauses in sos and nonpositive
% 1.77/1.97 clauses in usable.
% 1.77/1.97
% 1.77/1.97 dependent: set(knuth_bendix).
% 1.77/1.97 dependent: set(anl_eq).
% 1.77/1.97 dependent: set(para_from).
% 1.77/1.97 dependent: set(para_into).
% 1.77/1.97 dependent: clear(para_from_right).
% 1.77/1.97 dependent: clear(para_into_right).
% 1.77/1.97 dependent: set(para_from_vars).
% 1.77/1.97 dependent: set(eq_units_both_ways).
% 1.77/1.97 dependent: set(dynamic_demod_all).
% 1.77/1.97 dependent: set(dynamic_demod).
% 1.77/1.97 dependent: set(order_eq).
% 1.77/1.97 dependent: set(back_demod).
% 1.77/1.97 dependent: set(lrpo).
% 1.77/1.97 dependent: set(hyper_res).
% 1.77/1.97 dependent: set(unit_deletion).
% 1.77/1.97 dependent: set(factor).
% 1.77/1.97
% 1.77/1.97 ------------> process usable:
% 1.77/1.97 ** KEPT (pick-wt=27): 2 [copy,1,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] inverse(A)!=sk_c8|multiply(A,sk_c7)!=sk_c8|multiply(sk_c8,B)!=sk_c7|multiply(C,sk_c8)!=B|inverse(C)!=sk_c8|inverse(sk_c8)!=sk_c7.
% 1.77/1.97
% 1.77/1.97 ------------> process sos:
% 1.77/1.97 ** KEPT (pick-wt=3): 4 [] A=A.
% 1.77/1.97 ** KEPT (pick-wt=5): 5 [] multiply(identity,A)=A.
% 1.77/1.97 ---> New Demodulator: 6 [new_demod,5] multiply(identity,A)=A.
% 1.77/1.97 ** KEPT (pick-wt=6): 7 [] multiply(inverse(A),A)=identity.
% 1.77/1.97 ---> New Demodulator: 8 [new_demod,7] multiply(inverse(A),A)=identity.
% 1.77/1.97 ** KEPT (pick-wt=11): 9 [] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 2.33/2.51 ---> New Demodulator: 10 [new_demod,9] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 2.33/2.51 ** KEPT (pick-wt=8): 11 [] inverse(sk_c1)=sk_c8|inverse(sk_c8)=sk_c7.
% 2.33/2.51 ** KEPT (pick-wt=8): 12 [] inverse(sk_c1)=sk_c8|inverse(sk_c4)=sk_c8.
% 2.33/2.51 ** KEPT (pick-wt=9): 13 [] inverse(sk_c1)=sk_c8|multiply(sk_c4,sk_c7)=sk_c8.
% 2.33/2.51 ** KEPT (pick-wt=9): 14 [] inverse(sk_c1)=sk_c8|multiply(sk_c8,sk_c6)=sk_c7.
% 2.33/2.51 ** KEPT (pick-wt=9): 15 [] inverse(sk_c1)=sk_c8|multiply(sk_c5,sk_c8)=sk_c6.
% 2.33/2.51 ** KEPT (pick-wt=8): 16 [] inverse(sk_c1)=sk_c8|inverse(sk_c5)=sk_c8.
% 2.33/2.51 ** KEPT (pick-wt=9): 17 [] multiply(sk_c1,sk_c7)=sk_c8|inverse(sk_c8)=sk_c7.
% 2.33/2.51 ** KEPT (pick-wt=9): 18 [] multiply(sk_c1,sk_c7)=sk_c8|inverse(sk_c4)=sk_c8.
% 2.33/2.51 ** KEPT (pick-wt=10): 19 [] multiply(sk_c1,sk_c7)=sk_c8|multiply(sk_c4,sk_c7)=sk_c8.
% 2.33/2.51 ** KEPT (pick-wt=10): 20 [] multiply(sk_c1,sk_c7)=sk_c8|multiply(sk_c8,sk_c6)=sk_c7.
% 2.33/2.51 ** KEPT (pick-wt=10): 21 [] multiply(sk_c1,sk_c7)=sk_c8|multiply(sk_c5,sk_c8)=sk_c6.
% 2.33/2.51 ** KEPT (pick-wt=9): 22 [] multiply(sk_c1,sk_c7)=sk_c8|inverse(sk_c5)=sk_c8.
% 2.33/2.51 ** KEPT (pick-wt=9): 23 [] multiply(sk_c8,sk_c3)=sk_c7|inverse(sk_c8)=sk_c7.
% 2.33/2.51 ** KEPT (pick-wt=9): 24 [] multiply(sk_c8,sk_c3)=sk_c7|inverse(sk_c4)=sk_c8.
% 2.33/2.51 ** KEPT (pick-wt=10): 25 [] multiply(sk_c8,sk_c3)=sk_c7|multiply(sk_c4,sk_c7)=sk_c8.
% 2.33/2.51 ** KEPT (pick-wt=10): 26 [] multiply(sk_c8,sk_c3)=sk_c7|multiply(sk_c8,sk_c6)=sk_c7.
% 2.33/2.51 ** KEPT (pick-wt=10): 27 [] multiply(sk_c8,sk_c3)=sk_c7|multiply(sk_c5,sk_c8)=sk_c6.
% 2.33/2.51 ** KEPT (pick-wt=9): 28 [] multiply(sk_c8,sk_c3)=sk_c7|inverse(sk_c5)=sk_c8.
% 2.33/2.51 ** KEPT (pick-wt=9): 29 [] multiply(sk_c2,sk_c8)=sk_c3|inverse(sk_c8)=sk_c7.
% 2.33/2.51 ** KEPT (pick-wt=9): 30 [] multiply(sk_c2,sk_c8)=sk_c3|inverse(sk_c4)=sk_c8.
% 2.33/2.51 ** KEPT (pick-wt=10): 31 [] multiply(sk_c2,sk_c8)=sk_c3|multiply(sk_c4,sk_c7)=sk_c8.
% 2.33/2.51 ** KEPT (pick-wt=10): 32 [] multiply(sk_c2,sk_c8)=sk_c3|multiply(sk_c8,sk_c6)=sk_c7.
% 2.33/2.51 ** KEPT (pick-wt=10): 33 [] multiply(sk_c2,sk_c8)=sk_c3|multiply(sk_c5,sk_c8)=sk_c6.
% 2.33/2.51 ** KEPT (pick-wt=9): 34 [] multiply(sk_c2,sk_c8)=sk_c3|inverse(sk_c5)=sk_c8.
% 2.33/2.51 ** KEPT (pick-wt=8): 35 [] inverse(sk_c2)=sk_c8|inverse(sk_c8)=sk_c7.
% 2.33/2.51 ** KEPT (pick-wt=8): 36 [] inverse(sk_c2)=sk_c8|inverse(sk_c4)=sk_c8.
% 2.33/2.51 ** KEPT (pick-wt=9): 37 [] inverse(sk_c2)=sk_c8|multiply(sk_c4,sk_c7)=sk_c8.
% 2.33/2.51 ** KEPT (pick-wt=9): 38 [] inverse(sk_c2)=sk_c8|multiply(sk_c8,sk_c6)=sk_c7.
% 2.33/2.51 ** KEPT (pick-wt=9): 39 [] inverse(sk_c2)=sk_c8|multiply(sk_c5,sk_c8)=sk_c6.
% 2.33/2.51 ** KEPT (pick-wt=8): 40 [] inverse(sk_c2)=sk_c8|inverse(sk_c5)=sk_c8.
% 2.33/2.51 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 2.33/2.51 >>>> Starting back demodulation with 6.
% 2.33/2.51 >>>> Starting back demodulation with 8.
% 2.33/2.51 >>>> Starting back demodulation with 10.
% 2.33/2.51
% 2.33/2.51 ======= end of input processing =======
% 2.33/2.51
% 2.33/2.51 =========== start of search ===========
% 2.33/2.51
% 2.33/2.51 -------- PROOF --------
% 2.33/2.51
% 2.33/2.51 -----> EMPTY CLAUSE at 0.54 sec ----> 3438 [back_demod,3394,demod,3437,3384,unit_del,3398,3413] $F.
% 2.33/2.51
% 2.33/2.51 Length of proof is 132. Level of proof is 34.
% 2.33/2.51
% 2.33/2.51 ---------------- PROOF ----------------
% 2.33/2.51 % SZS status Unsatisfiable
% 2.33/2.51 % SZS output start Refutation
% See solution above
% 2.33/2.51 ------------ end of proof -------------
% 2.33/2.51
% 2.33/2.51
% 2.33/2.51 Search stopped by max_proofs option.
% 2.33/2.51
% 2.33/2.51
% 2.33/2.51 Search stopped by max_proofs option.
% 2.33/2.51
% 2.33/2.51 ============ end of search ============
% 2.33/2.51
% 2.33/2.51 -------------- statistics -------------
% 2.33/2.51 clauses given 492
% 2.33/2.51 clauses generated 54109
% 2.33/2.51 clauses kept 3377
% 2.33/2.51 clauses forward subsumed 52992
% 2.33/2.51 clauses back subsumed 1102
% 2.33/2.51 Kbytes malloced 3906
% 2.33/2.51
% 2.33/2.51 ----------- times (seconds) -----------
% 2.33/2.51 user CPU time 0.54 (0 hr, 0 min, 0 sec)
% 2.33/2.51 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.33/2.51 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.33/2.51
% 2.33/2.51 That finishes the proof of the theorem.
% 2.33/2.51
% 2.33/2.51 Process 519 finished Wed Jul 27 05:28:07 2022
% 2.33/2.51 Otter interrupted
% 2.33/2.51 PROOF FOUND
%------------------------------------------------------------------------------