TSTP Solution File: ALG078+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ALG078+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n017.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 14 18:02:14 EDT 2022

% Result   : Theorem 0.18s 0.47s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   66
% Syntax   : Number of clauses     :  213 ( 205 unt;   8 nHn; 213 RR)
%            Number of literals    :  233 (   0 equ;  15 neg)
%            Maximal clause size   :    5 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;  10 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(4,axiom,
    ~ equal(e14,e10),
    file('ALG078+1.p',unknown),
    [] ).

cnf(9,axiom,
    ~ equal(e14,e12),
    file('ALG078+1.p',unknown),
    [] ).

cnf(11,axiom,
    ~ equal(e21,e20),
    file('ALG078+1.p',unknown),
    [] ).

cnf(13,axiom,
    ~ equal(e23,e20),
    file('ALG078+1.p',unknown),
    [] ).

cnf(14,axiom,
    ~ equal(e24,e20),
    file('ALG078+1.p',unknown),
    [] ).

cnf(17,axiom,
    ~ equal(e24,e21),
    file('ALG078+1.p',unknown),
    [] ).

cnf(19,axiom,
    ~ equal(e24,e22),
    file('ALG078+1.p',unknown),
    [] ).

cnf(46,axiom,
    equal(h(j(e20)),e20),
    file('ALG078+1.p',unknown),
    [] ).

cnf(47,axiom,
    equal(h(j(e21)),e21),
    file('ALG078+1.p',unknown),
    [] ).

cnf(50,axiom,
    equal(h(j(e24)),e24),
    file('ALG078+1.p',unknown),
    [] ).

cnf(51,axiom,
    equal(j(h(e10)),e10),
    file('ALG078+1.p',unknown),
    [] ).

cnf(52,axiom,
    equal(j(h(e11)),e11),
    file('ALG078+1.p',unknown),
    [] ).

cnf(53,axiom,
    equal(j(h(e12)),e12),
    file('ALG078+1.p',unknown),
    [] ).

cnf(55,axiom,
    equal(j(h(e14)),e14),
    file('ALG078+1.p',unknown),
    [] ).

cnf(56,axiom,
    equal(op1(e10,e10),e10),
    file('ALG078+1.p',unknown),
    [] ).

cnf(58,axiom,
    equal(op1(e10,e12),e12),
    file('ALG078+1.p',unknown),
    [] ).

cnf(62,axiom,
    equal(op1(e11,e11),e14),
    file('ALG078+1.p',unknown),
    [] ).

cnf(63,axiom,
    equal(op1(e11,e12),e13),
    file('ALG078+1.p',unknown),
    [] ).

cnf(65,axiom,
    equal(op1(e11,e14),e12),
    file('ALG078+1.p',unknown),
    [] ).

cnf(66,axiom,
    equal(op1(e12,e10),e12),
    file('ALG078+1.p',unknown),
    [] ).

cnf(67,axiom,
    equal(op1(e12,e11),e10),
    file('ALG078+1.p',unknown),
    [] ).

cnf(76,axiom,
    equal(op1(e14,e10),e14),
    file('ALG078+1.p',unknown),
    [] ).

cnf(77,axiom,
    equal(op1(e14,e11),e13),
    file('ALG078+1.p',unknown),
    [] ).

cnf(78,axiom,
    equal(op1(e14,e12),e11),
    file('ALG078+1.p',unknown),
    [] ).

cnf(80,axiom,
    equal(op1(e14,e14),e10),
    file('ALG078+1.p',unknown),
    [] ).

cnf(85,axiom,
    equal(op2(e20,e24),e24),
    file('ALG078+1.p',unknown),
    [] ).

cnf(87,axiom,
    equal(op2(e21,e21),e22),
    file('ALG078+1.p',unknown),
    [] ).

cnf(88,axiom,
    equal(op2(e21,e22),e24),
    file('ALG078+1.p',unknown),
    [] ).

cnf(89,axiom,
    equal(op2(e21,e23),e20),
    file('ALG078+1.p',unknown),
    [] ).

cnf(90,axiom,
    equal(op2(e21,e24),e23),
    file('ALG078+1.p',unknown),
    [] ).

cnf(91,axiom,
    equal(op2(e22,e20),e22),
    file('ALG078+1.p',unknown),
    [] ).

cnf(93,axiom,
    equal(op2(e22,e22),e23),
    file('ALG078+1.p',unknown),
    [] ).

cnf(94,axiom,
    equal(op2(e22,e23),e24),
    file('ALG078+1.p',unknown),
    [] ).

cnf(95,axiom,
    equal(op2(e22,e24),e21),
    file('ALG078+1.p',unknown),
    [] ).

cnf(96,axiom,
    equal(op2(e23,e20),e23),
    file('ALG078+1.p',unknown),
    [] ).

cnf(97,axiom,
    equal(op2(e23,e21),e24),
    file('ALG078+1.p',unknown),
    [] ).

cnf(99,axiom,
    equal(op2(e23,e23),e21),
    file('ALG078+1.p',unknown),
    [] ).

cnf(100,axiom,
    equal(op2(e23,e24),e22),
    file('ALG078+1.p',unknown),
    [] ).

cnf(103,axiom,
    equal(op2(e24,e22),e21),
    file('ALG078+1.p',unknown),
    [] ).

cnf(104,axiom,
    equal(op2(e24,e23),e22),
    file('ALG078+1.p',unknown),
    [] ).

cnf(105,axiom,
    equal(op2(e24,e24),e20),
    file('ALG078+1.p',unknown),
    [] ).

cnf(108,axiom,
    equal(op2(h(e10),h(e12)),h(op1(e10,e12))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(112,axiom,
    equal(op2(h(e11),h(e11)),h(op1(e11,e11))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(113,axiom,
    equal(op2(h(e11),h(e12)),h(op1(e11,e12))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(115,axiom,
    equal(op2(h(e11),h(e14)),h(op1(e11,e14))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(116,axiom,
    equal(op2(h(e12),h(e10)),h(op1(e12,e10))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(117,axiom,
    equal(op2(h(e12),h(e11)),h(op1(e12,e11))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(126,axiom,
    equal(op2(h(e14),h(e10)),h(op1(e14,e10))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(127,axiom,
    equal(op2(h(e14),h(e11)),h(op1(e14,e11))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(128,axiom,
    equal(op2(h(e14),h(e12)),h(op1(e14,e12))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(137,axiom,
    equal(op1(j(e21),j(e21)),j(op2(e21,e21))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(138,axiom,
    equal(op1(j(e21),j(e22)),j(op2(e21,e22))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(139,axiom,
    equal(op1(j(e21),j(e23)),j(op2(e21,e23))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(140,axiom,
    equal(op1(j(e21),j(e24)),j(op2(e21,e24))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(141,axiom,
    equal(op1(j(e22),j(e20)),j(op2(e22,e20))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(143,axiom,
    equal(op1(j(e22),j(e22)),j(op2(e22,e22))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(144,axiom,
    equal(op1(j(e22),j(e23)),j(op2(e22,e23))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(145,axiom,
    equal(op1(j(e22),j(e24)),j(op2(e22,e24))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(146,axiom,
    equal(op1(j(e23),j(e20)),j(op2(e23,e20))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(149,axiom,
    equal(op1(j(e23),j(e23)),j(op2(e23,e23))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(150,axiom,
    equal(op1(j(e23),j(e24)),j(op2(e23,e24))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(153,axiom,
    equal(op1(j(e24),j(e22)),j(op2(e24,e22))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(154,axiom,
    equal(op1(j(e24),j(e23)),j(op2(e24,e23))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(155,axiom,
    equal(op1(j(e24),j(e24)),j(op2(e24,e24))),
    file('ALG078+1.p',unknown),
    [] ).

cnf(164,axiom,
    ( equal(h(e11),e24)
    | equal(h(e11),e23)
    | equal(h(e11),e22)
    | equal(h(e11),e21)
    | equal(h(e11),e20) ),
    file('ALG078+1.p',unknown),
    [] ).

cnf(165,axiom,
    ( equal(h(e10),e24)
    | equal(h(e10),e23)
    | equal(h(e10),e22)
    | equal(h(e10),e21)
    | equal(h(e10),e20) ),
    file('ALG078+1.p',unknown),
    [] ).

cnf(166,plain,
    equal(op1(j(e24),j(e24)),j(e20)),
    inference(rew,[status(thm),theory(equality)],[105,155]),
    [iquote('0:Rew:105.0,155.0')] ).

cnf(167,plain,
    equal(op1(j(e24),j(e23)),j(e22)),
    inference(rew,[status(thm),theory(equality)],[104,154]),
    [iquote('0:Rew:104.0,154.0')] ).

cnf(168,plain,
    equal(op1(j(e24),j(e22)),j(e21)),
    inference(rew,[status(thm),theory(equality)],[103,153]),
    [iquote('0:Rew:103.0,153.0')] ).

cnf(171,plain,
    equal(op1(j(e23),j(e24)),j(e22)),
    inference(rew,[status(thm),theory(equality)],[100,150]),
    [iquote('0:Rew:100.0,150.0')] ).

cnf(172,plain,
    equal(op1(j(e23),j(e23)),j(e21)),
    inference(rew,[status(thm),theory(equality)],[99,149]),
    [iquote('0:Rew:99.0,149.0')] ).

cnf(175,plain,
    equal(op1(j(e23),j(e20)),j(e23)),
    inference(rew,[status(thm),theory(equality)],[96,146]),
    [iquote('0:Rew:96.0,146.0')] ).

cnf(176,plain,
    equal(op1(j(e22),j(e24)),j(e21)),
    inference(rew,[status(thm),theory(equality)],[95,145]),
    [iquote('0:Rew:95.0,145.0')] ).

cnf(177,plain,
    equal(op1(j(e22),j(e23)),j(e24)),
    inference(rew,[status(thm),theory(equality)],[94,144]),
    [iquote('0:Rew:94.0,144.0')] ).

cnf(178,plain,
    equal(op1(j(e22),j(e22)),j(e23)),
    inference(rew,[status(thm),theory(equality)],[93,143]),
    [iquote('0:Rew:93.0,143.0')] ).

cnf(180,plain,
    equal(op1(j(e22),j(e20)),j(e22)),
    inference(rew,[status(thm),theory(equality)],[91,141]),
    [iquote('0:Rew:91.0,141.0')] ).

cnf(181,plain,
    equal(op1(j(e21),j(e24)),j(e23)),
    inference(rew,[status(thm),theory(equality)],[90,140]),
    [iquote('0:Rew:90.0,140.0')] ).

cnf(182,plain,
    equal(op1(j(e21),j(e23)),j(e20)),
    inference(rew,[status(thm),theory(equality)],[89,139]),
    [iquote('0:Rew:89.0,139.0')] ).

cnf(183,plain,
    equal(op1(j(e21),j(e22)),j(e24)),
    inference(rew,[status(thm),theory(equality)],[88,138]),
    [iquote('0:Rew:88.0,138.0')] ).

cnf(184,plain,
    equal(op1(j(e21),j(e21)),j(e22)),
    inference(rew,[status(thm),theory(equality)],[87,137]),
    [iquote('0:Rew:87.0,137.0')] ).

cnf(193,plain,
    equal(op2(h(e14),h(e12)),h(e11)),
    inference(rew,[status(thm),theory(equality)],[78,128]),
    [iquote('0:Rew:78.0,128.0')] ).

cnf(194,plain,
    equal(op2(h(e14),h(e11)),h(e13)),
    inference(rew,[status(thm),theory(equality)],[77,127]),
    [iquote('0:Rew:77.0,127.0')] ).

cnf(195,plain,
    equal(op2(h(e14),h(e10)),h(e14)),
    inference(rew,[status(thm),theory(equality)],[76,126]),
    [iquote('0:Rew:76.0,126.0')] ).

cnf(204,plain,
    equal(op2(h(e12),h(e11)),h(e10)),
    inference(rew,[status(thm),theory(equality)],[67,117]),
    [iquote('0:Rew:67.0,117.0')] ).

cnf(205,plain,
    equal(op2(h(e12),h(e10)),h(e12)),
    inference(rew,[status(thm),theory(equality)],[66,116]),
    [iquote('0:Rew:66.0,116.0')] ).

cnf(206,plain,
    equal(op2(h(e11),h(e14)),h(e12)),
    inference(rew,[status(thm),theory(equality)],[65,115]),
    [iquote('0:Rew:65.0,115.0')] ).

cnf(208,plain,
    equal(op2(h(e11),h(e12)),h(e13)),
    inference(rew,[status(thm),theory(equality)],[63,113]),
    [iquote('0:Rew:63.0,113.0')] ).

cnf(209,plain,
    equal(op2(h(e11),h(e11)),h(e14)),
    inference(rew,[status(thm),theory(equality)],[62,112]),
    [iquote('0:Rew:62.0,112.0')] ).

cnf(213,plain,
    equal(op2(h(e10),h(e12)),h(e12)),
    inference(rew,[status(thm),theory(equality)],[58,108]),
    [iquote('0:Rew:58.0,108.0')] ).

cnf(216,plain,
    equal(h(e10),e24),
    inference(spt,[spt(split,[position(s1)])],[165]),
    [iquote('1:Spt:165.0')] ).

cnf(217,plain,
    equal(j(e24),e10),
    inference(rew,[status(thm),theory(equality)],[216,51]),
    [iquote('1:Rew:216.0,51.0')] ).

cnf(232,plain,
    equal(op1(e10,e10),j(e20)),
    inference(rew,[status(thm),theory(equality)],[217,166]),
    [iquote('1:Rew:217.0,166.0')] ).

cnf(237,plain,
    equal(op1(j(e23),e10),j(e22)),
    inference(rew,[status(thm),theory(equality)],[217,171]),
    [iquote('1:Rew:217.0,171.0')] ).

cnf(239,plain,
    equal(op1(j(e22),e10),j(e21)),
    inference(rew,[status(thm),theory(equality)],[217,176]),
    [iquote('1:Rew:217.0,176.0')] ).

cnf(246,plain,
    equal(j(e20),e10),
    inference(rew,[status(thm),theory(equality)],[56,232]),
    [iquote('1:Rew:56.0,232.0')] ).

cnf(249,plain,
    equal(op1(j(e23),e10),j(e23)),
    inference(rew,[status(thm),theory(equality)],[246,175]),
    [iquote('1:Rew:246.0,175.0')] ).

cnf(251,plain,
    equal(op1(j(e22),e10),j(e22)),
    inference(rew,[status(thm),theory(equality)],[246,180]),
    [iquote('1:Rew:246.0,180.0')] ).

cnf(252,plain,
    equal(op1(j(e21),j(e23)),e10),
    inference(rew,[status(thm),theory(equality)],[246,182]),
    [iquote('1:Rew:246.0,182.0')] ).

cnf(262,plain,
    equal(j(e23),j(e22)),
    inference(rew,[status(thm),theory(equality)],[237,249]),
    [iquote('1:Rew:237.0,249.0')] ).

cnf(264,plain,
    equal(op1(j(e22),j(e22)),j(e21)),
    inference(rew,[status(thm),theory(equality)],[262,172]),
    [iquote('1:Rew:262.0,172.0')] ).

cnf(276,plain,
    equal(j(e22),j(e21)),
    inference(rew,[status(thm),theory(equality)],[239,251]),
    [iquote('1:Rew:239.0,251.0')] ).

cnf(283,plain,
    equal(j(e23),j(e21)),
    inference(rew,[status(thm),theory(equality)],[276,262]),
    [iquote('1:Rew:276.0,262.0')] ).

cnf(287,plain,
    equal(op1(j(e21),j(e21)),e10),
    inference(rew,[status(thm),theory(equality)],[283,252]),
    [iquote('1:Rew:283.0,252.0')] ).

cnf(297,plain,
    equal(j(e21),e10),
    inference(rew,[status(thm),theory(equality)],[287,264,276]),
    [iquote('1:Rew:287.0,264.0,276.0,264.0')] ).

cnf(298,plain,
    equal(h(e10),e21),
    inference(rew,[status(thm),theory(equality)],[297,47]),
    [iquote('1:Rew:297.0,47.0')] ).

cnf(304,plain,
    equal(e24,e21),
    inference(rew,[status(thm),theory(equality)],[216,298]),
    [iquote('1:Rew:216.0,298.0')] ).

cnf(305,plain,
    $false,
    inference(mrr,[status(thm)],[304,17]),
    [iquote('1:MRR:304.0,17.0')] ).

cnf(308,plain,
    ~ equal(h(e10),e24),
    inference(spt,[spt(split,[position(sa)])],[305,216]),
    [iquote('1:Spt:305.0,165.0,216.0')] ).

cnf(309,plain,
    ( equal(h(e10),e23)
    | equal(h(e10),e22)
    | equal(h(e10),e21)
    | equal(h(e10),e20) ),
    inference(spt,[spt(split,[position(s2)])],[165]),
    [iquote('1:Spt:305.0,165.1,165.2,165.3,165.4')] ).

cnf(310,plain,
    equal(h(e10),e23),
    inference(spt,[spt(split,[position(s2s1)])],[309]),
    [iquote('2:Spt:309.0')] ).

cnf(311,plain,
    equal(j(e23),e10),
    inference(rew,[status(thm),theory(equality)],[310,51]),
    [iquote('2:Rew:310.0,51.0')] ).

cnf(328,plain,
    equal(op1(j(e22),e10),j(e24)),
    inference(rew,[status(thm),theory(equality)],[311,177]),
    [iquote('2:Rew:311.0,177.0')] ).

cnf(338,plain,
    equal(op1(e10,e10),j(e21)),
    inference(rew,[status(thm),theory(equality)],[311,172]),
    [iquote('2:Rew:311.0,172.0')] ).

cnf(341,plain,
    equal(j(e21),e10),
    inference(rew,[status(thm),theory(equality)],[56,338]),
    [iquote('2:Rew:56.0,338.0')] ).

cnf(349,plain,
    equal(op1(e10,e10),j(e22)),
    inference(rew,[status(thm),theory(equality)],[341,184]),
    [iquote('2:Rew:341.0,184.0')] ).

cnf(352,plain,
    equal(j(e22),e10),
    inference(rew,[status(thm),theory(equality)],[56,349]),
    [iquote('2:Rew:56.0,349.0')] ).

cnf(359,plain,
    equal(j(e24),e10),
    inference(rew,[status(thm),theory(equality)],[56,328,352]),
    [iquote('2:Rew:56.0,328.0,352.0,328.0')] ).

cnf(363,plain,
    equal(op1(e10,e10),j(e20)),
    inference(rew,[status(thm),theory(equality)],[359,166]),
    [iquote('2:Rew:359.0,166.0')] ).

cnf(367,plain,
    equal(j(e20),e10),
    inference(rew,[status(thm),theory(equality)],[56,363]),
    [iquote('2:Rew:56.0,363.0')] ).

cnf(368,plain,
    equal(h(e10),e20),
    inference(rew,[status(thm),theory(equality)],[367,46]),
    [iquote('2:Rew:367.0,46.0')] ).

cnf(372,plain,
    equal(e23,e20),
    inference(rew,[status(thm),theory(equality)],[310,368]),
    [iquote('2:Rew:310.0,368.0')] ).

cnf(373,plain,
    $false,
    inference(mrr,[status(thm)],[372,13]),
    [iquote('2:MRR:372.0,13.0')] ).

cnf(385,plain,
    ~ equal(h(e10),e23),
    inference(spt,[spt(split,[position(s2sa)])],[373,310]),
    [iquote('2:Spt:373.0,309.0,310.0')] ).

cnf(386,plain,
    ( equal(h(e10),e22)
    | equal(h(e10),e21)
    | equal(h(e10),e20) ),
    inference(spt,[spt(split,[position(s2s2)])],[309]),
    [iquote('2:Spt:373.0,309.1,309.2,309.3')] ).

cnf(387,plain,
    equal(h(e10),e22),
    inference(spt,[spt(split,[position(s2s2s1)])],[386]),
    [iquote('3:Spt:386.0')] ).

cnf(389,plain,
    equal(j(e22),e10),
    inference(rew,[status(thm),theory(equality)],[387,51]),
    [iquote('3:Rew:387.0,51.0')] ).

cnf(405,plain,
    equal(op1(e10,e10),j(e23)),
    inference(rew,[status(thm),theory(equality)],[389,178]),
    [iquote('3:Rew:389.0,178.0')] ).

cnf(409,plain,
    equal(op1(e10,j(e23)),j(e24)),
    inference(rew,[status(thm),theory(equality)],[389,177]),
    [iquote('3:Rew:389.0,177.0')] ).

cnf(419,plain,
    equal(j(e23),e10),
    inference(rew,[status(thm),theory(equality)],[56,405]),
    [iquote('3:Rew:56.0,405.0')] ).

cnf(448,plain,
    equal(j(e24),e10),
    inference(rew,[status(thm),theory(equality)],[56,409,419]),
    [iquote('3:Rew:56.0,409.0,419.0,409.0')] ).

cnf(449,plain,
    equal(h(e10),e24),
    inference(rew,[status(thm),theory(equality)],[448,50]),
    [iquote('3:Rew:448.0,50.0')] ).

cnf(452,plain,
    equal(e24,e22),
    inference(rew,[status(thm),theory(equality)],[387,449]),
    [iquote('3:Rew:387.0,449.0')] ).

cnf(453,plain,
    $false,
    inference(mrr,[status(thm)],[452,19]),
    [iquote('3:MRR:452.0,19.0')] ).

cnf(466,plain,
    ~ equal(h(e10),e22),
    inference(spt,[spt(split,[position(s2s2sa)])],[453,387]),
    [iquote('3:Spt:453.0,386.0,387.0')] ).

cnf(467,plain,
    ( equal(h(e10),e21)
    | equal(h(e10),e20) ),
    inference(spt,[spt(split,[position(s2s2s2)])],[386]),
    [iquote('3:Spt:453.0,386.1,386.2')] ).

cnf(468,plain,
    equal(h(e10),e21),
    inference(spt,[spt(split,[position(s2s2s2s1)])],[467]),
    [iquote('4:Spt:467.0')] ).

cnf(470,plain,
    equal(j(e21),e10),
    inference(rew,[status(thm),theory(equality)],[468,51]),
    [iquote('4:Rew:468.0,51.0')] ).

cnf(487,plain,
    equal(op1(e10,j(e22)),j(e24)),
    inference(rew,[status(thm),theory(equality)],[470,183]),
    [iquote('4:Rew:470.0,183.0')] ).

cnf(491,plain,
    equal(op1(e10,e10),j(e22)),
    inference(rew,[status(thm),theory(equality)],[470,184]),
    [iquote('4:Rew:470.0,184.0')] ).

cnf(501,plain,
    equal(j(e22),e10),
    inference(rew,[status(thm),theory(equality)],[56,491]),
    [iquote('4:Rew:56.0,491.0')] ).

cnf(518,plain,
    equal(j(e24),e10),
    inference(rew,[status(thm),theory(equality)],[56,487,501]),
    [iquote('4:Rew:56.0,487.0,501.0,487.0')] ).

cnf(522,plain,
    equal(op1(e10,e10),j(e20)),
    inference(rew,[status(thm),theory(equality)],[518,166]),
    [iquote('4:Rew:518.0,166.0')] ).

cnf(525,plain,
    equal(j(e20),e10),
    inference(rew,[status(thm),theory(equality)],[56,522]),
    [iquote('4:Rew:56.0,522.0')] ).

cnf(526,plain,
    equal(h(e10),e20),
    inference(rew,[status(thm),theory(equality)],[525,46]),
    [iquote('4:Rew:525.0,46.0')] ).

cnf(530,plain,
    equal(e21,e20),
    inference(rew,[status(thm),theory(equality)],[468,526]),
    [iquote('4:Rew:468.0,526.0')] ).

cnf(531,plain,
    $false,
    inference(mrr,[status(thm)],[530,11]),
    [iquote('4:MRR:530.0,11.0')] ).

cnf(544,plain,
    ~ equal(h(e10),e21),
    inference(spt,[spt(split,[position(s2s2s2sa)])],[531,468]),
    [iquote('4:Spt:531.0,467.0,468.0')] ).

cnf(545,plain,
    equal(h(e10),e20),
    inference(spt,[spt(split,[position(s2s2s2s2)])],[467]),
    [iquote('4:Spt:531.0,467.1')] ).

cnf(548,plain,
    equal(j(e20),e10),
    inference(rew,[status(thm),theory(equality)],[545,51]),
    [iquote('4:Rew:545.0,51.0')] ).

cnf(553,plain,
    equal(op2(h(e14),e20),h(e14)),
    inference(rew,[status(thm),theory(equality)],[545,195]),
    [iquote('4:Rew:545.0,195.0')] ).

cnf(556,plain,
    equal(op2(h(e12),h(e11)),e20),
    inference(rew,[status(thm),theory(equality)],[545,204]),
    [iquote('4:Rew:545.0,204.0')] ).

cnf(557,plain,
    equal(op2(h(e12),e20),h(e12)),
    inference(rew,[status(thm),theory(equality)],[545,205]),
    [iquote('4:Rew:545.0,205.0')] ).

cnf(562,plain,
    equal(op2(e20,h(e12)),h(e12)),
    inference(rew,[status(thm),theory(equality)],[545,213]),
    [iquote('4:Rew:545.0,213.0')] ).

cnf(579,plain,
    equal(h(e11),e24),
    inference(spt,[spt(split,[position(s2s2s2s2s1)])],[164]),
    [iquote('5:Spt:164.0')] ).

cnf(581,plain,
    equal(op2(h(e14),h(e12)),e24),
    inference(rew,[status(thm),theory(equality)],[579,193]),
    [iquote('5:Rew:579.0,193.0')] ).

cnf(582,plain,
    equal(op2(h(e14),e24),h(e13)),
    inference(rew,[status(thm),theory(equality)],[579,194]),
    [iquote('5:Rew:579.0,194.0')] ).

cnf(587,plain,
    equal(op2(e24,h(e12)),h(e13)),
    inference(rew,[status(thm),theory(equality)],[579,208]),
    [iquote('5:Rew:579.0,208.0')] ).

cnf(588,plain,
    equal(op2(e24,e24),h(e14)),
    inference(rew,[status(thm),theory(equality)],[579,209]),
    [iquote('5:Rew:579.0,209.0')] ).

cnf(608,plain,
    equal(h(e14),e20),
    inference(rew,[status(thm),theory(equality)],[105,588]),
    [iquote('5:Rew:105.0,588.0')] ).

cnf(619,plain,
    equal(h(e12),e24),
    inference(rew,[status(thm),theory(equality)],[562,581,608]),
    [iquote('5:Rew:562.0,581.0,608.0,581.0')] ).

cnf(627,plain,
    equal(h(e13),e24),
    inference(rew,[status(thm),theory(equality)],[85,582,608]),
    [iquote('5:Rew:85.0,582.0,608.0,582.0')] ).

cnf(641,plain,
    equal(e24,e20),
    inference(rew,[status(thm),theory(equality)],[105,587,619,627]),
    [iquote('5:Rew:105.0,587.0,619.0,587.0,627.0,587.0')] ).

cnf(642,plain,
    $false,
    inference(mrr,[status(thm)],[641,14]),
    [iquote('5:MRR:641.0,14.0')] ).

cnf(647,plain,
    ~ equal(h(e11),e24),
    inference(spt,[spt(split,[position(s2s2s2s2sa)])],[642,579]),
    [iquote('5:Spt:642.0,164.0,579.0')] ).

cnf(648,plain,
    ( equal(h(e11),e23)
    | equal(h(e11),e22)
    | equal(h(e11),e21)
    | equal(h(e11),e20) ),
    inference(spt,[spt(split,[position(s2s2s2s2s2)])],[164]),
    [iquote('5:Spt:642.0,164.1,164.2,164.3,164.4')] ).

cnf(649,plain,
    equal(h(e11),e23),
    inference(spt,[spt(split,[position(s2s2s2s2s2s1)])],[648]),
    [iquote('6:Spt:648.0')] ).

cnf(656,plain,
    equal(op2(e23,e23),h(e14)),
    inference(rew,[status(thm),theory(equality)],[649,209]),
    [iquote('6:Rew:649.0,209.0')] ).

cnf(658,plain,
    equal(op2(e23,h(e14)),h(e12)),
    inference(rew,[status(thm),theory(equality)],[649,206]),
    [iquote('6:Rew:649.0,206.0')] ).

cnf(677,plain,
    equal(h(e14),e21),
    inference(rew,[status(thm),theory(equality)],[99,656]),
    [iquote('6:Rew:99.0,656.0')] ).

cnf(678,plain,
    equal(j(e21),e14),
    inference(rew,[status(thm),theory(equality)],[677,55]),
    [iquote('6:Rew:677.0,55.0')] ).

cnf(689,plain,
    equal(op1(e14,e14),j(e22)),
    inference(rew,[status(thm),theory(equality)],[678,184]),
    [iquote('6:Rew:678.0,184.0')] ).

cnf(693,plain,
    equal(op1(j(e24),j(e22)),e14),
    inference(rew,[status(thm),theory(equality)],[678,168]),
    [iquote('6:Rew:678.0,168.0')] ).

cnf(699,plain,
    equal(j(e22),e10),
    inference(rew,[status(thm),theory(equality)],[80,689]),
    [iquote('6:Rew:80.0,689.0')] ).

cnf(710,plain,
    equal(h(e12),e24),
    inference(rew,[status(thm),theory(equality)],[97,658,677]),
    [iquote('6:Rew:97.0,658.0,677.0,658.0')] ).

cnf(711,plain,
    equal(j(e24),e12),
    inference(rew,[status(thm),theory(equality)],[710,53]),
    [iquote('6:Rew:710.0,53.0')] ).

cnf(765,plain,
    equal(e14,e12),
    inference(rew,[status(thm),theory(equality)],[66,693,711,699]),
    [iquote('6:Rew:66.0,693.0,711.0,693.0,699.0,693.0')] ).

cnf(766,plain,
    $false,
    inference(mrr,[status(thm)],[765,9]),
    [iquote('6:MRR:765.0,9.0')] ).

cnf(767,plain,
    ~ equal(h(e11),e23),
    inference(spt,[spt(split,[position(s2s2s2s2s2sa)])],[766,649]),
    [iquote('6:Spt:766.0,648.0,649.0')] ).

cnf(768,plain,
    ( equal(h(e11),e22)
    | equal(h(e11),e21)
    | equal(h(e11),e20) ),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2)])],[648]),
    [iquote('6:Spt:766.0,648.1,648.2,648.3')] ).

cnf(769,plain,
    equal(h(e11),e22),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2s1)])],[768]),
    [iquote('7:Spt:768.0')] ).

cnf(771,plain,
    equal(j(e22),e11),
    inference(rew,[status(thm),theory(equality)],[769,52]),
    [iquote('7:Rew:769.0,52.0')] ).

cnf(784,plain,
    equal(op2(e22,e22),h(e14)),
    inference(rew,[status(thm),theory(equality)],[769,209]),
    [iquote('7:Rew:769.0,209.0')] ).

cnf(792,plain,
    equal(op1(e11,j(e23)),j(e24)),
    inference(rew,[status(thm),theory(equality)],[771,177]),
    [iquote('7:Rew:771.0,177.0')] ).

cnf(798,plain,
    equal(h(e14),e23),
    inference(rew,[status(thm),theory(equality)],[93,784]),
    [iquote('7:Rew:93.0,784.0')] ).

cnf(799,plain,
    equal(j(e23),e14),
    inference(rew,[status(thm),theory(equality)],[798,55]),
    [iquote('7:Rew:798.0,55.0')] ).

cnf(813,plain,
    equal(op1(j(e21),j(e24)),e14),
    inference(rew,[status(thm),theory(equality)],[799,181]),
    [iquote('7:Rew:799.0,181.0')] ).

cnf(814,plain,
    equal(op1(e14,e14),j(e21)),
    inference(rew,[status(thm),theory(equality)],[799,172]),
    [iquote('7:Rew:799.0,172.0')] ).

cnf(820,plain,
    equal(j(e21),e10),
    inference(rew,[status(thm),theory(equality)],[80,814]),
    [iquote('7:Rew:80.0,814.0')] ).

cnf(867,plain,
    equal(j(e24),e12),
    inference(rew,[status(thm),theory(equality)],[65,792,799]),
    [iquote('7:Rew:65.0,792.0,799.0,792.0')] ).

cnf(899,plain,
    equal(e14,e12),
    inference(rew,[status(thm),theory(equality)],[58,813,820,867]),
    [iquote('7:Rew:58.0,813.0,820.0,813.0,867.0,813.0')] ).

cnf(900,plain,
    $false,
    inference(mrr,[status(thm)],[899,9]),
    [iquote('7:MRR:899.0,9.0')] ).

cnf(901,plain,
    ~ equal(h(e11),e22),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2sa)])],[900,769]),
    [iquote('7:Spt:900.0,768.0,769.0')] ).

cnf(902,plain,
    ( equal(h(e11),e21)
    | equal(h(e11),e20) ),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2s2)])],[768]),
    [iquote('7:Spt:900.0,768.1,768.2')] ).

cnf(903,plain,
    equal(h(e11),e21),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2s2s1)])],[902]),
    [iquote('8:Spt:902.0')] ).

cnf(912,plain,
    equal(op2(e21,e21),h(e14)),
    inference(rew,[status(thm),theory(equality)],[903,209]),
    [iquote('8:Rew:903.0,209.0')] ).

cnf(914,plain,
    equal(op2(e21,h(e14)),h(e12)),
    inference(rew,[status(thm),theory(equality)],[903,206]),
    [iquote('8:Rew:903.0,206.0')] ).

cnf(933,plain,
    equal(h(e14),e22),
    inference(rew,[status(thm),theory(equality)],[87,912]),
    [iquote('8:Rew:87.0,912.0')] ).

cnf(934,plain,
    equal(j(e22),e14),
    inference(rew,[status(thm),theory(equality)],[933,55]),
    [iquote('8:Rew:933.0,55.0')] ).

cnf(946,plain,
    equal(op1(e14,e14),j(e23)),
    inference(rew,[status(thm),theory(equality)],[934,178]),
    [iquote('8:Rew:934.0,178.0')] ).

cnf(949,plain,
    equal(op1(j(e24),j(e23)),e14),
    inference(rew,[status(thm),theory(equality)],[934,167]),
    [iquote('8:Rew:934.0,167.0')] ).

cnf(955,plain,
    equal(j(e23),e10),
    inference(rew,[status(thm),theory(equality)],[80,946]),
    [iquote('8:Rew:80.0,946.0')] ).

cnf(967,plain,
    equal(h(e12),e24),
    inference(rew,[status(thm),theory(equality)],[88,914,933]),
    [iquote('8:Rew:88.0,914.0,933.0,914.0')] ).

cnf(968,plain,
    equal(j(e24),e12),
    inference(rew,[status(thm),theory(equality)],[967,53]),
    [iquote('8:Rew:967.0,53.0')] ).

cnf(1022,plain,
    equal(e14,e12),
    inference(rew,[status(thm),theory(equality)],[66,949,968,955]),
    [iquote('8:Rew:66.0,949.0,968.0,949.0,955.0,949.0')] ).

cnf(1023,plain,
    $false,
    inference(mrr,[status(thm)],[1022,9]),
    [iquote('8:MRR:1022.0,9.0')] ).

cnf(1024,plain,
    ~ equal(h(e11),e21),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2s2sa)])],[1023,903]),
    [iquote('8:Spt:1023.0,902.0,903.0')] ).

cnf(1025,plain,
    equal(h(e11),e20),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2s2s2)])],[902]),
    [iquote('8:Spt:1023.0,902.1')] ).

cnf(1032,plain,
    equal(op2(h(e12),e20),e20),
    inference(rew,[status(thm),theory(equality)],[1025,556]),
    [iquote('8:Rew:1025.0,556.0')] ).

cnf(1036,plain,
    equal(h(e12),e20),
    inference(rew,[status(thm),theory(equality)],[1032,557]),
    [iquote('8:Rew:1032.0,557.0')] ).

cnf(1050,plain,
    equal(h(e14),e20),
    inference(rew,[status(thm),theory(equality)],[553,193,1036,1025]),
    [iquote('8:Rew:553.0,193.0,1036.0,193.0,1025.0,193.0')] ).

cnf(1051,plain,
    equal(j(e20),e14),
    inference(rew,[status(thm),theory(equality)],[1050,55]),
    [iquote('8:Rew:1050.0,55.0')] ).

cnf(1055,plain,
    equal(e14,e10),
    inference(rew,[status(thm),theory(equality)],[548,1051]),
    [iquote('8:Rew:548.0,1051.0')] ).

cnf(1056,plain,
    $false,
    inference(mrr,[status(thm)],[1055,4]),
    [iquote('8:MRR:1055.0,4.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : ALG078+1 : TPTP v8.1.0. Released v2.7.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n017.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  : 600
% 0.12/0.33  % DateTime : Tue Jun  7 21:37:32 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.47  
% 0.18/0.47  SPASS V 3.9 
% 0.18/0.47  SPASS beiseite: Proof found.
% 0.18/0.47  % SZS status Theorem
% 0.18/0.47  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.47  SPASS derived 464 clauses, backtracked 458 clauses, performed 8 splits and kept 852 clauses.
% 0.18/0.47  SPASS allocated 85611 KBytes.
% 0.18/0.47  SPASS spent	0:00:00.14 on the problem.
% 0.18/0.47  		0:00:00.03 for the input.
% 0.18/0.47  		0:00:00.03 for the FLOTTER CNF translation.
% 0.18/0.47  		0:00:00.00 for inferences.
% 0.18/0.47  		0:00:00.00 for the backtracking.
% 0.18/0.47  		0:00:00.04 for the reduction.
% 0.18/0.47  
% 0.18/0.47  
% 0.18/0.47  Here is a proof with depth 4, length 213 :
% 0.18/0.47  % SZS output start Refutation
% See solution above
% 0.18/0.48  Formulae used in the proof : ax1 ax2 co1 ax4 ax5
% 0.18/0.48  
%------------------------------------------------------------------------------