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  
%------------------------------------------------------------------------------