TSTP Solution File: TOP051-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : TOP051-1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 : 600s
% DateTime : Thu Jul 21 21:35:04 EDT 2022
% Result : Unsatisfiable 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 14
% Syntax : Number of clauses : 139 ( 139 unt; 0 nHn; 139 RR)
% Number of literals : 139 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 14 con; 0-10 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(product(u,u),u),
file('TOP051-1.p',unknown),
[] ).
cnf(2,axiom,
equal(product(product(u,v),v),u),
file('TOP051-1.p',unknown),
[] ).
cnf(3,axiom,
equal(product(product(u,v),product(w,v)),product(product(u,w),v)),
file('TOP051-1.p',unknown),
[] ).
cnf(4,axiom,
equal(product(a1,a6),a2),
file('TOP051-1.p',unknown),
[] ).
cnf(5,axiom,
equal(product(a2,a7),a3),
file('TOP051-1.p',unknown),
[] ).
cnf(6,axiom,
equal(product(a3,a1),a4),
file('TOP051-1.p',unknown),
[] ).
cnf(7,axiom,
equal(product(a4,a10),a5),
file('TOP051-1.p',unknown),
[] ).
cnf(8,axiom,
equal(product(a5,a9),a6),
file('TOP051-1.p',unknown),
[] ).
cnf(9,axiom,
equal(product(a6,a2),a7),
file('TOP051-1.p',unknown),
[] ).
cnf(10,axiom,
equal(product(a7,a3),a8),
file('TOP051-1.p',unknown),
[] ).
cnf(11,axiom,
equal(product(a8,a6),a9),
file('TOP051-1.p',unknown),
[] ).
cnf(12,axiom,
equal(product(a9,a4),a10),
file('TOP051-1.p',unknown),
[] ).
cnf(13,axiom,
equal(product(a10,a5),a11),
file('TOP051-1.p',unknown),
[] ).
cnf(14,axiom,
~ equal(tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9),tuple(a1,a6,a5,a2,a7,a3,a4,a9,a10,a8)),
file('TOP051-1.p',unknown),
[] ).
cnf(29,plain,
equal(product(a10,a4),a9),
inference(spr,[status(thm),theory(equality)],[12,2]),
[iquote('0:SpR:12.0,2.0')] ).
cnf(30,plain,
equal(product(a9,a6),a8),
inference(spr,[status(thm),theory(equality)],[11,2]),
[iquote('0:SpR:11.0,2.0')] ).
cnf(31,plain,
equal(product(a2,a6),a1),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(33,plain,
equal(product(a7,a2),a6),
inference(spr,[status(thm),theory(equality)],[9,2]),
[iquote('0:SpR:9.0,2.0')] ).
cnf(34,plain,
equal(product(a6,a9),a5),
inference(spr,[status(thm),theory(equality)],[8,2]),
[iquote('0:SpR:8.0,2.0')] ).
cnf(35,plain,
equal(product(a5,a10),a4),
inference(spr,[status(thm),theory(equality)],[7,2]),
[iquote('0:SpR:7.0,2.0')] ).
cnf(50,plain,
equal(product(product(u,a9),a4),product(product(u,a4),a10)),
inference(spr,[status(thm),theory(equality)],[12,3]),
[iquote('0:SpR:12.0,3.0')] ).
cnf(51,plain,
equal(product(product(u,a10),a4),product(product(u,a4),a9)),
inference(spr,[status(thm),theory(equality)],[29,3]),
[iquote('0:SpR:29.0,3.0')] ).
cnf(52,plain,
equal(product(product(u,a8),a6),product(product(u,a6),a9)),
inference(spr,[status(thm),theory(equality)],[11,3]),
[iquote('0:SpR:11.0,3.0')] ).
cnf(53,plain,
equal(product(product(u,a6),a2),product(product(u,a1),a6)),
inference(spr,[status(thm),theory(equality)],[4,3]),
[iquote('0:SpR:4.0,3.0')] ).
cnf(55,plain,
equal(product(product(u,a2),a7),product(product(u,a6),a2)),
inference(spr,[status(thm),theory(equality)],[9,3]),
[iquote('0:SpR:9.0,3.0')] ).
cnf(57,plain,
equal(product(product(u,a10),a5),product(product(u,a4),a10)),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.0,3.0')] ).
cnf(58,plain,
equal(product(product(u,a3),a1),product(product(u,a1),a4)),
inference(spr,[status(thm),theory(equality)],[6,3]),
[iquote('0:SpR:6.0,3.0')] ).
cnf(59,plain,
equal(product(product(u,a7),a3),product(product(u,a2),a7)),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(64,plain,
equal(product(product(a9,u),a4),product(a10,product(u,a4))),
inference(spr,[status(thm),theory(equality)],[12,3]),
[iquote('0:SpR:12.0,3.0')] ).
cnf(65,plain,
equal(product(product(a10,u),a4),product(a9,product(u,a4))),
inference(spr,[status(thm),theory(equality)],[29,3]),
[iquote('0:SpR:29.0,3.0')] ).
cnf(66,plain,
equal(product(product(a8,u),a6),product(a9,product(u,a6))),
inference(spr,[status(thm),theory(equality)],[11,3]),
[iquote('0:SpR:11.0,3.0')] ).
cnf(74,plain,
equal(product(product(u,v),u),product(u,product(v,u))),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(77,plain,
equal(product(product(u,a2),a7),product(product(u,a1),a6)),
inference(rew,[status(thm),theory(equality)],[53,55]),
[iquote('0:Rew:53.0,55.0')] ).
cnf(79,plain,
equal(product(product(u,a7),a3),product(product(u,a1),a6)),
inference(rew,[status(thm),theory(equality)],[77,59]),
[iquote('0:Rew:77.0,59.0')] ).
cnf(90,plain,
equal(product(product(a2,u),a6),product(a1,product(u,a6))),
inference(spr,[status(thm),theory(equality)],[31,3]),
[iquote('0:SpR:31.0,3.0')] ).
cnf(104,plain,
equal(product(product(u,a9),a5),product(product(u,a6),a9)),
inference(spr,[status(thm),theory(equality)],[34,3]),
[iquote('0:SpR:34.0,3.0')] ).
cnf(107,plain,
equal(product(product(a5,u),a10),product(a4,product(u,a10))),
inference(spr,[status(thm),theory(equality)],[35,3]),
[iquote('0:SpR:35.0,3.0')] ).
cnf(125,plain,
equal(product(product(a5,a4),a10),product(a6,a4)),
inference(spr,[status(thm),theory(equality)],[8,50]),
[iquote('0:SpR:8.0,50.0')] ).
cnf(129,plain,
equal(product(a4,product(a4,a10)),product(a6,a4)),
inference(rew,[status(thm),theory(equality)],[107,125]),
[iquote('0:Rew:107.0,125.0')] ).
cnf(130,plain,
equal(product(a4,a5),product(a6,a4)),
inference(rew,[status(thm),theory(equality)],[7,129]),
[iquote('0:Rew:7.0,129.0')] ).
cnf(136,plain,
equal(product(product(a6,a4),a5),a4),
inference(spr,[status(thm),theory(equality)],[130,2]),
[iquote('0:SpR:130.0,2.0')] ).
cnf(138,plain,
equal(product(product(u,a5),product(a6,a4)),product(product(u,a4),a5)),
inference(spr,[status(thm),theory(equality)],[130,3]),
[iquote('0:SpR:130.0,3.0')] ).
cnf(153,plain,
equal(product(product(a4,a4),a9),product(a5,a4)),
inference(spr,[status(thm),theory(equality)],[7,51]),
[iquote('0:SpR:7.0,51.0')] ).
cnf(158,plain,
equal(product(a5,a4),product(a4,a9)),
inference(rew,[status(thm),theory(equality)],[1,153]),
[iquote('0:Rew:1.0,153.0')] ).
cnf(227,plain,
equal(product(product(a7,a1),a6),product(a6,a7)),
inference(spr,[status(thm),theory(equality)],[33,77]),
[iquote('0:SpR:33.0,77.0')] ).
cnf(229,plain,
equal(product(product(a2,a1),a6),product(a2,a7)),
inference(spr,[status(thm),theory(equality)],[1,77]),
[iquote('0:SpR:1.0,77.0')] ).
cnf(234,plain,
equal(product(product(a2,a1),a6),a3),
inference(rew,[status(thm),theory(equality)],[5,229]),
[iquote('0:Rew:5.0,229.0')] ).
cnf(235,plain,
equal(product(a1,product(a1,a6)),a3),
inference(rew,[status(thm),theory(equality)],[90,234]),
[iquote('0:Rew:90.0,234.0')] ).
cnf(236,plain,
equal(product(a1,a2),a3),
inference(rew,[status(thm),theory(equality)],[4,235]),
[iquote('0:Rew:4.0,235.0')] ).
cnf(240,plain,
equal(product(a3,a2),a1),
inference(spr,[status(thm),theory(equality)],[236,2]),
[iquote('0:SpR:236.0,2.0')] ).
cnf(248,plain,
equal(product(product(a3,a1),a6),product(a1,a7)),
inference(spr,[status(thm),theory(equality)],[240,77]),
[iquote('0:SpR:240.0,77.0')] ).
cnf(250,plain,
equal(product(a4,a6),product(a1,a7)),
inference(rew,[status(thm),theory(equality)],[6,248]),
[iquote('0:Rew:6.0,248.0')] ).
cnf(267,plain,
equal(product(product(a10,a4),a10),product(a10,a5)),
inference(spr,[status(thm),theory(equality)],[1,57]),
[iquote('0:SpR:1.0,57.0')] ).
cnf(272,plain,
equal(product(a9,a10),a11),
inference(rew,[status(thm),theory(equality)],[29,267,13]),
[iquote('0:Rew:29.0,267.0,13.0,267.0')] ).
cnf(287,plain,
equal(product(a11,a10),a9),
inference(spr,[status(thm),theory(equality)],[272,2]),
[iquote('0:SpR:272.0,2.0')] ).
cnf(289,plain,
equal(product(product(a9,a4),a9),product(a11,a4)),
inference(spr,[status(thm),theory(equality)],[272,51]),
[iquote('0:SpR:272.0,51.0')] ).
cnf(292,plain,
equal(product(a11,a4),product(a10,a9)),
inference(rew,[status(thm),theory(equality)],[12,289]),
[iquote('0:Rew:12.0,289.0')] ).
cnf(299,plain,
equal(product(product(a11,a4),a10),product(a9,a5)),
inference(spr,[status(thm),theory(equality)],[287,57]),
[iquote('0:SpR:287.0,57.0')] ).
cnf(303,plain,
equal(product(a10,product(a9,a10)),product(a9,a5)),
inference(rew,[status(thm),theory(equality)],[74,299,292]),
[iquote('0:Rew:74.0,299.0,292.0,299.0')] ).
cnf(304,plain,
equal(product(a9,a5),product(a10,a11)),
inference(rew,[status(thm),theory(equality)],[272,303]),
[iquote('0:Rew:272.0,303.0')] ).
cnf(318,plain,
equal(product(product(a7,a1),a4),product(a8,a1)),
inference(spr,[status(thm),theory(equality)],[10,58]),
[iquote('0:SpR:10.0,58.0')] ).
cnf(339,plain,
equal(product(product(u,a5),product(a10,a11)),product(product(u,a9),a5)),
inference(spr,[status(thm),theory(equality)],[304,3]),
[iquote('0:SpR:304.0,3.0')] ).
cnf(342,plain,
equal(product(product(u,a5),product(a10,a11)),product(product(u,a6),a9)),
inference(rew,[status(thm),theory(equality)],[104,339]),
[iquote('0:Rew:104.0,339.0')] ).
cnf(355,plain,
equal(product(product(a7,a1),a6),product(a7,a3)),
inference(spr,[status(thm),theory(equality)],[1,79]),
[iquote('0:SpR:1.0,79.0')] ).
cnf(361,plain,
equal(product(product(a7,a1),a6),a8),
inference(rew,[status(thm),theory(equality)],[10,355]),
[iquote('0:Rew:10.0,355.0')] ).
cnf(362,plain,
equal(product(a6,a7),a8),
inference(rew,[status(thm),theory(equality)],[227,361]),
[iquote('0:Rew:227.0,361.0')] ).
cnf(363,plain,
equal(product(product(a7,a1),a6),a8),
inference(rew,[status(thm),theory(equality)],[362,227]),
[iquote('0:Rew:362.0,227.0')] ).
cnf(367,plain,
equal(product(a8,a7),a6),
inference(spr,[status(thm),theory(equality)],[362,2]),
[iquote('0:SpR:362.0,2.0')] ).
cnf(390,plain,
equal(product(a8,a6),product(a7,a1)),
inference(spr,[status(thm),theory(equality)],[363,2]),
[iquote('0:SpR:363.0,2.0')] ).
cnf(392,plain,
equal(product(product(product(a7,a1),a1),a6),product(a8,a2)),
inference(spr,[status(thm),theory(equality)],[363,53]),
[iquote('0:SpR:363.0,53.0')] ).
cnf(394,plain,
equal(product(a7,a1),a9),
inference(rew,[status(thm),theory(equality)],[11,390]),
[iquote('0:Rew:11.0,390.0')] ).
cnf(396,plain,
equal(product(a8,a1),product(a9,a4)),
inference(rew,[status(thm),theory(equality)],[394,318]),
[iquote('0:Rew:394.0,318.0')] ).
cnf(399,plain,
equal(product(a8,a1),a10),
inference(rew,[status(thm),theory(equality)],[12,396]),
[iquote('0:Rew:12.0,396.0')] ).
cnf(401,plain,
equal(product(a8,a2),product(a7,a6)),
inference(rew,[status(thm),theory(equality)],[2,392]),
[iquote('0:Rew:2.0,392.0')] ).
cnf(421,plain,
equal(product(a9,a1),a7),
inference(spr,[status(thm),theory(equality)],[394,2]),
[iquote('0:SpR:394.0,2.0')] ).
cnf(449,plain,
equal(product(product(a10,a11),a4),product(a10,product(a5,a4))),
inference(spr,[status(thm),theory(equality)],[304,64]),
[iquote('0:SpR:304.0,64.0')] ).
cnf(463,plain,
equal(product(product(a10,a11),a4),product(a10,product(a4,a9))),
inference(rew,[status(thm),theory(equality)],[158,449]),
[iquote('0:Rew:158.0,449.0')] ).
cnf(464,plain,
equal(product(a9,product(a11,a4)),product(a10,product(a4,a9))),
inference(rew,[status(thm),theory(equality)],[65,463]),
[iquote('0:Rew:65.0,463.0')] ).
cnf(465,plain,
equal(product(a9,product(a10,a9)),product(a10,product(a4,a9))),
inference(rew,[status(thm),theory(equality)],[292,464]),
[iquote('0:Rew:292.0,464.0')] ).
cnf(480,plain,
equal(product(product(a8,a1),a6),product(product(a7,a6),a7)),
inference(spr,[status(thm),theory(equality)],[401,77]),
[iquote('0:SpR:401.0,77.0')] ).
cnf(483,plain,
equal(product(product(a7,a6),a7),product(a10,a6)),
inference(rew,[status(thm),theory(equality)],[399,480]),
[iquote('0:Rew:399.0,480.0')] ).
cnf(484,plain,
equal(product(a7,product(a6,a7)),product(a10,a6)),
inference(rew,[status(thm),theory(equality)],[74,483]),
[iquote('0:Rew:74.0,483.0')] ).
cnf(485,plain,
equal(product(a10,a6),product(a7,a8)),
inference(rew,[status(thm),theory(equality)],[362,484]),
[iquote('0:Rew:362.0,484.0')] ).
cnf(488,plain,
equal(product(product(a7,a8),a6),a10),
inference(spr,[status(thm),theory(equality)],[485,2]),
[iquote('0:SpR:485.0,2.0')] ).
cnf(493,plain,
equal(product(product(a7,a6),a9),a10),
inference(rew,[status(thm),theory(equality)],[52,488]),
[iquote('0:Rew:52.0,488.0')] ).
cnf(498,plain,
equal(product(a10,a9),product(a7,a6)),
inference(spr,[status(thm),theory(equality)],[493,2]),
[iquote('0:SpR:493.0,2.0')] ).
cnf(505,plain,
equal(product(a9,product(a7,a6)),product(a10,product(a4,a9))),
inference(rew,[status(thm),theory(equality)],[498,465]),
[iquote('0:Rew:498.0,465.0')] ).
cnf(520,plain,
equal(product(a9,product(a7,a6)),product(a6,a6)),
inference(spr,[status(thm),theory(equality)],[367,66]),
[iquote('0:SpR:367.0,66.0')] ).
cnf(529,plain,
equal(product(a9,product(a7,a6)),a6),
inference(rew,[status(thm),theory(equality)],[1,520]),
[iquote('0:Rew:1.0,520.0')] ).
cnf(530,plain,
equal(product(a10,product(a4,a9)),a6),
inference(rew,[status(thm),theory(equality)],[505,529]),
[iquote('0:Rew:505.0,529.0')] ).
cnf(531,plain,
equal(product(a9,product(a7,a6)),a6),
inference(rew,[status(thm),theory(equality)],[530,505]),
[iquote('0:Rew:530.0,505.0')] ).
cnf(550,plain,
equal(product(product(a10,a4),a10),product(product(a7,a6),a4)),
inference(spr,[status(thm),theory(equality)],[498,50]),
[iquote('0:SpR:498.0,50.0')] ).
cnf(553,plain,
equal(product(product(a7,a6),a4),a11),
inference(rew,[status(thm),theory(equality)],[272,550,29]),
[iquote('0:Rew:272.0,550.0,29.0,550.0')] ).
cnf(601,plain,
equal(product(a6,product(a4,a9)),a10),
inference(spr,[status(thm),theory(equality)],[530,2]),
[iquote('0:SpR:530.0,2.0')] ).
cnf(613,plain,
equal(product(a10,product(product(a7,a6),a4)),product(a6,a4)),
inference(spr,[status(thm),theory(equality)],[531,64]),
[iquote('0:SpR:531.0,64.0')] ).
cnf(614,plain,
equal(product(a10,a11),product(a6,a4)),
inference(rew,[status(thm),theory(equality)],[553,613]),
[iquote('0:Rew:553.0,613.0')] ).
cnf(617,plain,
equal(product(product(u,a5),product(a6,a4)),product(product(u,a6),a9)),
inference(rew,[status(thm),theory(equality)],[614,342]),
[iquote('0:Rew:614.0,342.0')] ).
cnf(622,plain,
equal(product(product(u,a4),a5),product(product(u,a6),a9)),
inference(rew,[status(thm),theory(equality)],[138,617]),
[iquote('0:Rew:138.0,617.0')] ).
cnf(623,plain,
equal(product(product(a6,a6),a9),a4),
inference(rew,[status(thm),theory(equality)],[622,136]),
[iquote('0:Rew:622.0,136.0')] ).
cnf(625,plain,
equal(a5,a4),
inference(rew,[status(thm),theory(equality)],[34,623,1]),
[iquote('0:Rew:34.0,623.0,1.0,623.0')] ).
cnf(626,plain,
equal(product(a10,a4),a11),
inference(rew,[status(thm),theory(equality)],[625,13]),
[iquote('0:Rew:625.0,13.0')] ).
cnf(627,plain,
equal(product(a4,a9),a6),
inference(rew,[status(thm),theory(equality)],[625,8]),
[iquote('0:Rew:625.0,8.0')] ).
cnf(628,plain,
equal(product(a4,a10),a4),
inference(rew,[status(thm),theory(equality)],[625,7]),
[iquote('0:Rew:625.0,7.0')] ).
cnf(630,plain,
~ equal(tuple(a2,a7,a6,a3,a8,a4,a4,a10,a11,a9),tuple(a1,a6,a4,a2,a7,a3,a4,a9,a10,a8)),
inference(rew,[status(thm),theory(equality)],[625,14]),
[iquote('0:Rew:625.0,14.0')] ).
cnf(631,plain,
equal(product(a6,a9),a4),
inference(rew,[status(thm),theory(equality)],[625,34]),
[iquote('0:Rew:625.0,34.0')] ).
cnf(668,plain,
equal(a11,a9),
inference(rew,[status(thm),theory(equality)],[29,626]),
[iquote('0:Rew:29.0,626.0')] ).
cnf(669,plain,
equal(product(a9,a10),a9),
inference(rew,[status(thm),theory(equality)],[668,272]),
[iquote('0:Rew:668.0,272.0')] ).
cnf(688,plain,
equal(product(a6,a6),a10),
inference(rew,[status(thm),theory(equality)],[627,601]),
[iquote('0:Rew:627.0,601.0')] ).
cnf(703,plain,
equal(a10,a6),
inference(rew,[status(thm),theory(equality)],[1,688]),
[iquote('0:Rew:1.0,688.0')] ).
cnf(708,plain,
equal(product(a8,a1),a6),
inference(rew,[status(thm),theory(equality)],[703,399]),
[iquote('0:Rew:703.0,399.0')] ).
cnf(735,plain,
equal(product(a4,a6),a4),
inference(rew,[status(thm),theory(equality)],[703,628]),
[iquote('0:Rew:703.0,628.0')] ).
cnf(736,plain,
equal(product(a9,a6),a9),
inference(rew,[status(thm),theory(equality)],[703,669]),
[iquote('0:Rew:703.0,669.0')] ).
cnf(738,plain,
equal(product(a1,a7),a4),
inference(rew,[status(thm),theory(equality)],[250,735]),
[iquote('0:Rew:250.0,735.0')] ).
cnf(745,plain,
equal(a8,a9),
inference(rew,[status(thm),theory(equality)],[30,736]),
[iquote('0:Rew:30.0,736.0')] ).
cnf(751,plain,
equal(product(a6,a7),a9),
inference(rew,[status(thm),theory(equality)],[745,362]),
[iquote('0:Rew:745.0,362.0')] ).
cnf(774,plain,
equal(product(a9,a1),a6),
inference(rew,[status(thm),theory(equality)],[745,708]),
[iquote('0:Rew:745.0,708.0')] ).
cnf(776,plain,
equal(a7,a6),
inference(rew,[status(thm),theory(equality)],[421,774]),
[iquote('0:Rew:421.0,774.0')] ).
cnf(778,plain,
equal(product(a2,a6),a3),
inference(rew,[status(thm),theory(equality)],[776,5]),
[iquote('0:Rew:776.0,5.0')] ).
cnf(811,plain,
equal(product(a1,a6),a4),
inference(rew,[status(thm),theory(equality)],[776,738]),
[iquote('0:Rew:776.0,738.0')] ).
cnf(814,plain,
equal(product(a6,a6),a9),
inference(rew,[status(thm),theory(equality)],[776,751]),
[iquote('0:Rew:776.0,751.0')] ).
cnf(817,plain,
equal(a3,a1),
inference(rew,[status(thm),theory(equality)],[31,778]),
[iquote('0:Rew:31.0,778.0')] ).
cnf(818,plain,
equal(product(a1,a1),a4),
inference(rew,[status(thm),theory(equality)],[817,6]),
[iquote('0:Rew:817.0,6.0')] ).
cnf(836,plain,
equal(a4,a2),
inference(rew,[status(thm),theory(equality)],[4,811]),
[iquote('0:Rew:4.0,811.0')] ).
cnf(840,plain,
equal(product(a6,a9),a2),
inference(rew,[status(thm),theory(equality)],[836,631]),
[iquote('0:Rew:836.0,631.0')] ).
cnf(846,plain,
equal(a9,a6),
inference(rew,[status(thm),theory(equality)],[1,814]),
[iquote('0:Rew:1.0,814.0')] ).
cnf(847,plain,
equal(a11,a6),
inference(rew,[status(thm),theory(equality)],[846,668]),
[iquote('0:Rew:846.0,668.0')] ).
cnf(849,plain,
equal(a8,a6),
inference(rew,[status(thm),theory(equality)],[846,745]),
[iquote('0:Rew:846.0,745.0')] ).
cnf(855,plain,
equal(a4,a1),
inference(rew,[status(thm),theory(equality)],[1,818]),
[iquote('0:Rew:1.0,818.0')] ).
cnf(856,plain,
equal(a2,a1),
inference(rew,[status(thm),theory(equality)],[836,855]),
[iquote('0:Rew:836.0,855.0')] ).
cnf(868,plain,
equal(a4,a1),
inference(rew,[status(thm),theory(equality)],[856,836]),
[iquote('0:Rew:856.0,836.0')] ).
cnf(875,plain,
equal(product(a6,a6),a1),
inference(rew,[status(thm),theory(equality)],[846,840,856]),
[iquote('0:Rew:846.0,840.0,856.0,840.0')] ).
cnf(876,plain,
equal(a6,a1),
inference(rew,[status(thm),theory(equality)],[1,875]),
[iquote('0:Rew:1.0,875.0')] ).
cnf(877,plain,
equal(a10,a1),
inference(rew,[status(thm),theory(equality)],[876,703]),
[iquote('0:Rew:876.0,703.0')] ).
cnf(878,plain,
equal(a7,a1),
inference(rew,[status(thm),theory(equality)],[876,776]),
[iquote('0:Rew:876.0,776.0')] ).
cnf(879,plain,
equal(a9,a1),
inference(rew,[status(thm),theory(equality)],[876,846]),
[iquote('0:Rew:876.0,846.0')] ).
cnf(880,plain,
equal(a11,a1),
inference(rew,[status(thm),theory(equality)],[876,847]),
[iquote('0:Rew:876.0,847.0')] ).
cnf(881,plain,
equal(a8,a1),
inference(rew,[status(thm),theory(equality)],[876,849]),
[iquote('0:Rew:876.0,849.0')] ).
cnf(1121,plain,
~ equal(tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1,a1),tuple(a1,a1,a1,a1,a1,a1,a1,a1,a1,a1)),
inference(rew,[status(thm),theory(equality)],[880,630,876,856,878,817,868,879,877,881]),
[iquote('0:Rew:880.0,630.0,876.0,630.0,856.0,630.0,878.0,630.0,817.0,630.0,868.0,630.0,879.0,630.0,877.0,630.0,881.0,630.0')] ).
cnf(1122,plain,
$false,
inference(obv,[status(thm),theory(equality)],[1121]),
[iquote('0:Obv:1121.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : TOP051-1 : TPTP v8.1.0. Released v8.1.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.32 % Computer : n029.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sun May 29 14:29:58 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.17/0.47
% 0.17/0.47 SPASS V 3.9
% 0.17/0.47 SPASS beiseite: Proof found.
% 0.17/0.47 % SZS status Theorem
% 0.17/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.47 SPASS derived 662 clauses, backtracked 0 clauses, performed 0 splits and kept 301 clauses.
% 0.17/0.47 SPASS allocated 63941 KBytes.
% 0.17/0.47 SPASS spent 0:00:00.14 on the problem.
% 0.17/0.47 0:00:00.04 for the input.
% 0.17/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.17/0.47 0:00:00.01 for inferences.
% 0.17/0.47 0:00:00.00 for the backtracking.
% 0.17/0.47 0:00:00.07 for the reduction.
% 0.17/0.47
% 0.17/0.47
% 0.17/0.47 Here is a proof with depth 7, length 139 :
% 0.17/0.47 % SZS output start Refutation
% See solution above
% 0.17/0.48 Formulae used in the proof : involutory_quandle involutory_quandle_01 involutory_quandle_02 knot knot_03 knot_04 knot_05 knot_06 knot_07 knot_08 knot_09 knot_10 knot_11 goal
% 0.17/0.48
%------------------------------------------------------------------------------