TSTP Solution File: TOP051-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : TOP051-1 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n023.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 21:34:38 EDT 2022

% Result   : Unsatisfiable 0.49s 0.67s
% Output   : Refutation 0.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :   14
% Syntax   : Number of clauses     :  128 ( 128 unt;   0 nHn; 101 RR)
%            Number of literals    :  128 ( 127 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;  11 con; 0-10 aty)
%            Number of variables   :   30 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(involutory_quandle,axiom,
    product(X,X) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle) ).

cnf(involutory_quandle_01,axiom,
    product(product(X,Y),Y) = X,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle_01) ).

cnf(involutory_quandle_02,axiom,
    product(product(X,Y),Z) = product(product(X,Z),product(Y,Z)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutory_quandle_02) ).

cnf(knot,axiom,
    product(a1,a6) = a2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot) ).

cnf(knot_03,axiom,
    product(a2,a7) = a3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_03) ).

cnf(knot_04,axiom,
    product(a3,a1) = a4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_04) ).

cnf(knot_05,axiom,
    product(a4,a10) = a5,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_05) ).

cnf(knot_06,axiom,
    product(a5,a9) = a6,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_06) ).

cnf(knot_07,axiom,
    product(a6,a2) = a7,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_07) ).

cnf(knot_08,axiom,
    product(a7,a3) = a8,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_08) ).

cnf(knot_09,axiom,
    product(a8,a6) = a9,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_09) ).

cnf(knot_10,axiom,
    product(a9,a4) = a10,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_10) ).

cnf(knot_11,axiom,
    product(a10,a5) = a11,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',knot_11) ).

cnf(goal,negated_conjecture,
    tuple(a1,a6,a5,a2,a7,a3,a4,a9,a10,a8) != tuple(a2,a7,a6,a3,a8,a4,a5,a10,a11,a9),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).

cnf(17,plain,
    product(a5,a10) = a4,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_05,theory(equality)]) ).

cnf(18,plain,
    product(a10,a4) = a9,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_10,theory(equality)]) ).

cnf(21,plain,
    product(a7,a2) = a6,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_07,theory(equality)]) ).

cnf(22,plain,
    product(a2,a6) = a1,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot,theory(equality)]) ).

cnf(23,plain,
    product(a9,a6) = a8,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_09,theory(equality)]) ).

cnf(24,plain,
    product(a4,a1) = a3,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,knot_04,theory(equality)]) ).

cnf(25,plain,
    product(a6,X) = product(product(a5,X),product(a9,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_06,theory(equality)]) ).

cnf(26,plain,
    product(a11,X) = product(product(a10,X),product(a5,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_11,theory(equality)]) ).

cnf(27,plain,
    product(a5,X) = product(product(a4,X),product(a10,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_05,theory(equality)]) ).

cnf(28,plain,
    product(a10,X) = product(product(a9,X),product(a4,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_10,theory(equality)]) ).

cnf(29,plain,
    product(a8,X) = product(product(a7,X),product(a3,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_08,theory(equality)]) ).

cnf(30,plain,
    product(a3,X) = product(product(a2,X),product(a7,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_03,theory(equality)]) ).

cnf(31,plain,
    product(a7,X) = product(product(a6,X),product(a2,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_07,theory(equality)]) ).

cnf(32,plain,
    product(a2,X) = product(product(a1,X),product(a6,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot,theory(equality)]) ).

cnf(33,plain,
    product(a9,X) = product(product(a8,X),product(a6,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_09,theory(equality)]) ).

cnf(34,plain,
    product(a4,X) = product(product(a3,X),product(a1,X)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_04,theory(equality)]) ).

cnf(35,plain,
    product(product(a5,X),a9) = product(a6,product(X,a9)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_06,theory(equality)]) ).

cnf(39,plain,
    product(product(a7,X),a3) = product(a8,product(X,a3)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_08,theory(equality)]) ).

cnf(50,plain,
    product(product(X,a7),a3) = product(product(X,a3),a8),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_08,theory(equality)]) ).

cnf(51,plain,
    product(product(X,a2),a7) = product(product(X,a3),a8),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_03,theory(equality)]),50,theory(equality)]) ).

cnf(53,plain,
    product(product(X,a6),a2) = product(product(X,a2),a7),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot_07,theory(equality)]) ).

cnf(54,plain,
    product(product(X,a1),a6) = product(product(X,a2),a7),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,knot,theory(equality)]),53,theory(equality)]) ).

cnf(55,plain,
    product(product(X,a1),a6) = product(product(X,a3),a8),
    inference('REWRITE',[status(thm)],[51,54,theory(equality)]) ).

cnf(76,plain,
    product(product(a5,X),a10) = product(a4,product(X,a10)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,17,theory(equality)]) ).

cnf(80,plain,
    product(product(a10,X),a4) = product(a9,product(X,a4)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,18,theory(equality)]) ).

cnf(102,plain,
    product(a6,a10) = product(a4,product(a9,a10)),
    inference('PARAMODULATE',[status(thm)],[25,17,theory(equality)]) ).

cnf(104,plain,
    product(a6,a4) = product(a4,a5),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[25,knot_10,theory(equality)]),knot_05,76,theory(equality)]) ).

cnf(108,plain,
    product(product(a4,a5),a4) = a6,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,104,theory(equality)]) ).

cnf(112,plain,
    a6 = product(a4,product(a5,a4)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,108,theory(equality)]),involutory_quandle,theory(equality)]) ).

cnf(121,plain,
    product(product(X,a4),product(a5,a4)) = product(product(X,product(a5,a4)),a6),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,112,theory(equality)]) ).

cnf(122,plain,
    product(a11,a10) = a9,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[26,involutory_quandle,theory(equality)]),18,17,theory(equality)]) ).

cnf(127,plain,
    product(a9,a10) = a11,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,122,theory(equality)]) ).

cnf(128,plain,
    product(a6,a10) = product(a4,a11),
    inference('REWRITE',[status(thm)],[102,127,theory(equality)]) ).

cnf(138,plain,
    product(a5,a1) = product(a3,product(a10,a1)),
    inference('PARAMODULATE',[status(thm)],[27,24,theory(equality)]) ).

cnf(139,plain,
    product(a5,a4) = product(a4,a9),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[27,involutory_quandle,theory(equality)]),18,theory(equality)]) ).

cnf(150,plain,
    product(a10,a6) = product(a8,product(a4,a6)),
    inference('PARAMODULATE',[status(thm)],[28,23,theory(equality)]) ).

cnf(151,plain,
    product(a10,a9) = product(a11,a4),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[28,involutory_quandle,theory(equality)]),knot_11,80,139,theory(equality)]) ).

cnf(153,plain,
    product(a10,product(a5,a4)) = product(product(a11,a4),a6),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[28,112,theory(equality)]),knot_11,80,theory(equality)]) ).

cnf(157,plain,
    a6 = product(product(a5,a11),a4),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[27,151,theory(equality)]),involutory_quandle_02,139,knot_06,theory(equality)]) ).

cnf(158,plain,
    product(a11,a9) = product(product(a11,a4),a6),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[26,151,theory(equality)]),knot_06,theory(equality)]) ).

cnf(159,plain,
    product(a10,product(a5,a4)) = product(a11,a9),
    inference('REWRITE',[status(thm)],[153,158,theory(equality)]) ).

cnf(161,plain,
    product(product(a10,X),a9) = product(product(a11,a4),product(X,a9)),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,151,theory(equality)]) ).

cnf(163,plain,
    product(a4,a5) = product(a5,a11),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,157,theory(equality)]),104,theory(equality)]) ).

cnf(164,plain,
    product(a6,a4) = product(a5,a11),
    inference('REWRITE',[status(thm)],[104,163,theory(equality)]) ).

cnf(184,plain,
    product(a8,a1) = product(product(a7,a1),a4),
    inference('PARAMODULATE',[status(thm)],[29,knot_04,theory(equality)]) ).

cnf(202,plain,
    product(a3,a2) = a1,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[30,involutory_quandle,theory(equality)]),22,21,theory(equality)]) ).

cnf(205,plain,
    a3 = product(product(a2,a1),a6),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[30,knot_08,theory(equality)]),55,involutory_quandle,theory(equality)]) ).

cnf(210,plain,
    product(a1,a2) = a3,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,202,theory(equality)]) ).

cnf(220,plain,
    product(a3,a6) = product(a2,a1),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,205,theory(equality)]) ).

cnf(223,plain,
    product(product(X,product(a2,a1)),a6) = product(product(X,a6),a3),
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,205,theory(equality)]) ).

cnf(228,plain,
    product(a7,a6) = product(a6,a1),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[31,involutory_quandle,theory(equality)]),22,theory(equality)]) ).

cnf(236,plain,
    a9 = product(a7,a1),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[29,228,theory(equality)]),31,220,knot_09,theory(equality)]) ).

cnf(237,plain,
    product(a8,a1) = a10,
    inference('REWRITE',[status(thm)],[184,knot_10,236,theory(equality)]) ).

cnf(242,plain,
    product(a10,a1) = a8,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,237,theory(equality)]) ).

cnf(243,plain,
    product(a5,a1) = product(a3,a8),
    inference('REWRITE',[status(thm)],[138,242,theory(equality)]) ).

cnf(252,plain,
    a4 = product(product(a2,a1),a9),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[30,236,theory(equality)]),knot_04,theory(equality)]) ).

cnf(264,plain,
    product(product(a5,a1),a8) = a3,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,243,theory(equality)]) ).

cnf(271,plain,
    product(a5,a4) = product(a2,a1),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,252,theory(equality)]),139,theory(equality)]) ).

cnf(272,plain,
    a6 = product(a4,product(a2,a1)),
    inference('REWRITE',[status(thm)],[112,271,theory(equality)]) ).

cnf(276,plain,
    product(product(X,a4),product(a2,a1)) = product(product(X,a6),a3),
    inference('REWRITE',[status(thm)],[121,223,271,theory(equality)]) ).

cnf(278,plain,
    product(a2,a1) = product(a4,a9),
    inference('REWRITE',[status(thm)],[139,271,theory(equality)]) ).

cnf(282,plain,
    product(a10,product(a2,a1)) = product(a11,a9),
    inference('REWRITE',[status(thm)],[159,271,theory(equality)]) ).

cnf(286,plain,
    product(a11,a4) = product(a9,product(a2,a1)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[28,278,theory(equality)]),involutory_quandle,151,theory(equality)]) ).

cnf(287,plain,
    a6 = product(product(a2,a1),product(a11,a4)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[27,278,theory(equality)]),151,knot_06,theory(equality)]) ).

cnf(288,plain,
    product(product(a2,a1),a4) = a5,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,271,theory(equality)]) ).

cnf(289,plain,
    product(a5,a11) = product(product(a2,a1),a10),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[25,271,theory(equality)]),knot_10,164,theory(equality)]) ).

cnf(293,plain,
    product(a5,product(a2,a1)) = product(product(a5,a11),a9),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[27,272,theory(equality)]),35,282,theory(equality)]) ).

cnf(295,plain,
    product(a2,a4) = product(product(a1,a4),product(a5,a11)),
    inference('PARAMODULATE',[status(thm)],[32,164,theory(equality)]) ).

cnf(307,plain,
    a11 = product(product(a8,a10),product(a4,a11)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[33,128,theory(equality)]),127,theory(equality)]) ).

cnf(348,plain,
    product(a4,a6) = product(product(a2,a1),a2),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[34,knot,theory(equality)]),220,theory(equality)]) ).

cnf(349,plain,
    product(a4,a2) = product(a1,a3),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[34,202,theory(equality)]),210,theory(equality)]) ).

cnf(353,plain,
    product(a10,a2) = product(product(a9,a2),product(a1,a3)),
    inference('PARAMODULATE',[status(thm)],[28,349,theory(equality)]) ).

cnf(364,plain,
    product(a4,a6) = product(a2,a3),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,348,theory(equality)]),210,involutory_quandle,theory(equality)]) ).

cnf(365,plain,
    product(a10,a6) = product(a8,product(a2,a3)),
    inference('REWRITE',[status(thm)],[150,364,theory(equality)]) ).

cnf(370,plain,
    product(product(a2,a3),a6) = a4,
    inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,364,theory(equality)]) ).

cnf(379,plain,
    a4 = product(a1,product(a2,a1)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_02,370,theory(equality)]),220,22,theory(equality)]) ).

cnf(425,plain,
    product(a6,a3) = product(a10,a6),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[39,21,theory(equality)]),365,theory(equality)]) ).

cnf(435,plain,
    product(a11,a4) = a6,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[involutory_quandle_01,425,theory(equality)]),286,18,276,theory(equality)]) ).

cnf(440,plain,
    product(product(a10,X),a9) = product(product(a5,X),a9),
    inference('REWRITE',[status(thm)],[161,35,435,theory(equality)]) ).

cnf(446,plain,
    product(a5,product(a2,a1)) = product(product(a10,a11),a9),
    inference('REWRITE',[status(thm)],[293,440,theory(equality)]) ).

cnf(455,plain,
    a6 = a3,
    inference('REWRITE',[status(thm)],[287,205,435,theory(equality)]) ).

cnf(456,plain,
    product(a1,a3) = a2,
    inference('REWRITE',[status(thm)],[knot,455,theory(equality)]) ).

cnf(459,plain,
    product(a10,a2) = a9,
    inference('REWRITE',[status(thm)],[353,involutory_quandle_01,456,theory(equality)]) ).

cnf(469,plain,
    a1 = a7,
    inference('REWRITE',[status(thm)],[knot_07,202,455,theory(equality)]) ).

cnf(470,plain,
    product(a2,a1) = a3,
    inference('REWRITE',[status(thm)],[knot_03,469,theory(equality)]) ).

cnf(473,plain,
    a3 = product(a4,a9),
    inference('REWRITE',[status(thm)],[278,470,theory(equality)]) ).

cnf(480,plain,
    product(a3,a4) = a5,
    inference('REWRITE',[status(thm)],[288,470,theory(equality)]) ).

cnf(481,plain,
    product(a5,a11) = product(a3,a10),
    inference('REWRITE',[status(thm)],[289,470,theory(equality)]) ).

cnf(486,plain,
    product(a2,a4) = product(product(a1,a4),product(a3,a10)),
    inference('REWRITE',[status(thm)],[295,481,theory(equality)]) ).

cnf(498,plain,
    a4 = a2,
    inference('REWRITE',[status(thm)],[379,456,470,theory(equality)]) ).

cnf(528,plain,
    a11 = product(product(a8,a10),product(a2,a11)),
    inference('REWRITE',[status(thm)],[307,498,theory(equality)]) ).

cnf(542,plain,
    a3 = product(a2,a9),
    inference('REWRITE',[status(thm)],[473,498,theory(equality)]) ).

cnf(548,plain,
    a1 = a5,
    inference('REWRITE',[status(thm)],[480,202,498,theory(equality)]) ).

cnf(549,plain,
    a8 = a11,
    inference('REWRITE',[status(thm)],[knot_11,242,548,theory(equality)]) ).

cnf(550,plain,
    product(a11,a1) = a10,
    inference('REWRITE',[status(thm)],[237,549,theory(equality)]) ).

cnf(551,plain,
    product(a10,a1) = a11,
    inference('REWRITE',[status(thm)],[242,549,theory(equality)]) ).

cnf(559,plain,
    a11 = product(a9,product(a2,a11)),
    inference('REWRITE',[status(thm)],[528,122,549,theory(equality)]) ).

cnf(566,plain,
    product(a1,a11) = a3,
    inference('REWRITE',[status(thm)],[264,549,involutory_quandle,548,theory(equality)]) ).

cnf(579,plain,
    a3 = product(a3,a10),
    inference('REWRITE',[status(thm)],[481,566,548,theory(equality)]) ).

cnf(606,plain,
    a2 = a3,
    inference('REWRITE',[status(thm)],[486,579,210,involutory_quandle,498,theory(equality)]) ).

cnf(607,plain,
    a2 = a1,
    inference('REWRITE',[status(thm)],[202,involutory_quandle,606,theory(equality)]) ).

cnf(608,plain,
    a11 = a9,
    inference('REWRITE',[status(thm)],[459,551,607,theory(equality)]) ).

cnf(616,plain,
    a4 = a1,
    inference('REWRITE',[status(thm)],[498,607,theory(equality)]) ).

cnf(622,plain,
    a11 = product(a11,product(a1,a11)),
    inference('REWRITE',[status(thm)],[559,608,607,theory(equality)]) ).

cnf(636,plain,
    a1 = a3,
    inference('REWRITE',[status(thm)],[606,607,theory(equality)]) ).

cnf(638,plain,
    a1 = product(a1,a11),
    inference('REWRITE',[status(thm)],[542,608,607,606,theory(equality)]) ).

cnf(639,plain,
    a11 = a10,
    inference('REWRITE',[status(thm)],[622,550,638,theory(equality)]) ).

cnf(640,plain,
    a8 = a10,
    inference('REWRITE',[status(thm)],[549,639,theory(equality)]) ).

cnf(647,plain,
    a10 = a9,
    inference('REWRITE',[status(thm)],[608,639,theory(equality)]) ).

cnf(654,plain,
    a1 = a10,
    inference('REWRITE',[status(thm)],[446,647,639,involutory_quandle,636,548,470,theory(equality)]) ).

cnf(655,plain,
    a11 = a1,
    inference('REWRITE',[status(thm)],[639,654,theory(equality)]) ).

cnf(656,plain,
    a8 = a1,
    inference('REWRITE',[status(thm)],[640,654,theory(equality)]) ).

cnf(658,plain,
    a1 = a9,
    inference('REWRITE',[status(thm)],[647,654,theory(equality)]) ).

cnf(662,plain,
    $false,
    inference('REWRITE',[status(thm)],[goal,655,656,654,658,616,469,607,548,636,455,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : TOP051-1 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.13  % Command  : run-snark %s %d
% 0.12/0.34  % Computer : n023.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun May 29 14:42:57 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.45  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46  * 
% 0.19/0.46  * 
% 0.19/0.47  #<PACKAGE "SNARK-USER">
% 0.19/0.47  * 
% 0.19/0.47  SNARK-TPTP-OPTIONS
% 0.19/0.47  * 
% 0.19/0.47  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.47   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.47   (USE-FACTORING :POS)
% 0.19/0.47   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.47   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.47   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.47   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.47   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.47   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.47   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.47   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.47   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.47   (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.47  * 
% 0.19/0.47  "."
% 0.19/0.47  * 
% 0.19/0.47  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-29T14:42:57
% 0.19/0.47  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n023.cluster.edu at 2022-05-29T14:42:57
% 0.49/0.67  
% 0.49/0.67  
% 0.49/0.67  #||
% 0.49/0.67  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.49/0.67  % SZS output start Refutation
% See solution above
% 0.49/0.69  ||#
% 0.49/0.69  
% 0.49/0.69  ; Summary of computation:
% 0.49/0.69  ;      1333 formulas have been input or derived (from 95 formulas).
% 0.49/0.69  ;       662 (50%) were retained.  Of these,
% 0.49/0.69  ;          634 (96%) were simplified or subsumed later,
% 0.49/0.69  ;           28 ( 4%) are still being kept.
% 0.49/0.69  ; 
% 0.49/0.69  ; Run time in seconds excluding printing time:
% 0.49/0.69  ;     0.002   1%   Read assertion file          (1 call)
% 0.49/0.69  ;     0.000   0%   Assert                       (14 calls)
% 0.49/0.69  ;     0.052  25%   Process new row              (1,154 calls)
% 0.49/0.69  ;     0.003   1%   Resolution                   (188 calls)
% 0.49/0.69  ;     0.012   6%   Paramodulation               (94 calls)
% 0.49/0.69  ;     0.050  24%   Forward simplification       (1,150 calls)
% 0.49/0.69  ;     0.026  13%   Backward simplification      (662 calls)
% 0.49/0.69  ;     0.029  14%   Ordering                     (3,813 calls)
% 0.49/0.69  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.49/0.69  ;     0.000   0%   Purity testing               (1 call)
% 0.49/0.69  ;     0.032  16%   Other
% 0.49/0.69  ;     0.206        Total
% 0.49/0.69  ;     0.222        Real time
% 0.49/0.69  ; 
% 0.49/0.69  ; Term-hash-array has 1,596 terms in all.
% 0.49/0.69  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.49/0.69  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.49/0.69  ; Path-index has 98 entries (1,028 at peak, 1,849 added, 1,751 deleted).
% 0.49/0.69  ; Path-index has 139 nodes (427 at peak, 633 added, 494 deleted).
% 0.49/0.69  ; Trie-index has 98 entries (1,028 at peak, 1,849 added, 1,751 deleted).
% 0.49/0.69  ; Trie-index has 285 nodes (3,854 at peak, 7,020 added, 6,735 deleted).
% 0.49/0.69  ; Retrieved 9,187 generalization terms in 5,928 calls.
% 0.49/0.69  ; Retrieved 784 instance terms in 697 calls.
% 0.49/0.69  ; Retrieved 2,025 unifiable terms in 647 calls.
% 0.49/0.69  ; 
% 0.49/0.69  ; The agenda of backward simplifiable rows to process has 164 entries:
% 0.49/0.69  ;   164 with value 0
% 0.49/0.69  ; The agenda of rows to process has 6 entries:
% 0.49/0.69  ;     3 with value 17              3 with value 19
% 0.49/0.69  ; The agenda of input rows to give has 2 entries:
% 0.49/0.69  ;     2 with value 4
% 0.49/0.69  ; The agenda of rows to give has 22 entries:
% 0.49/0.69  ;     1 with value (4 6)           1 with value (4 10)           4 with value (4 23)
% 0.49/0.69  ;     3 with value (4 7)           1 with value (4 15)           4 with value (4 24)
% 0.49/0.69  ;     1 with value (4 8)           3 with value (4 18)           2 with value (4 26)
% 0.49/0.69  ;     2 with value (4 9)
% 0.49/0.69  Evaluation took:
% 0.49/0.69    0.222 seconds of real time
% 0.49/0.69    0.201 seconds of user run time
% 0.49/0.69    0.021102 seconds of system run time
% 0.49/0.69    [Run times include 0.007 seconds GC run time.]
% 0.49/0.69    0 calls to %EVAL
% 0.49/0.69    0 page faults and
% 0.49/0.69    21,507,920 bytes consed.
% 0.49/0.69  :PROOF-FOUND
% 0.49/0.69  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-05-29T14:42:57
% 0.49/0.69  :PROOF-FOUND
% 0.49/0.69  * 
%------------------------------------------------------------------------------