TSTP Solution File: ALG083+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ALG083+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 18:02:16 EDT 2022

% Result   : Theorem 0.20s 0.50s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   62
% Syntax   : Number of clauses     :  206 ( 198 unt;   8 nHn; 206 RR)
%            Number of literals    :  226 (   0 equ;  16 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(3,axiom,
    ~ equal(e13,e10),
    file('ALG083+1.p',unknown),
    [] ).

cnf(6,axiom,
    ~ equal(e13,e11),
    file('ALG083+1.p',unknown),
    [] ).

cnf(9,axiom,
    ~ equal(e14,e12),
    file('ALG083+1.p',unknown),
    [] ).

cnf(11,axiom,
    ~ equal(e21,e20),
    file('ALG083+1.p',unknown),
    [] ).

cnf(12,axiom,
    ~ equal(e22,e20),
    file('ALG083+1.p',unknown),
    [] ).

cnf(14,axiom,
    ~ equal(e24,e20),
    file('ALG083+1.p',unknown),
    [] ).

cnf(15,axiom,
    ~ equal(e22,e21),
    file('ALG083+1.p',unknown),
    [] ).

cnf(16,axiom,
    ~ equal(e23,e21),
    file('ALG083+1.p',unknown),
    [] ).

cnf(46,axiom,
    equal(h(j(e20)),e20),
    file('ALG083+1.p',unknown),
    [] ).

cnf(47,axiom,
    equal(h(j(e21)),e21),
    file('ALG083+1.p',unknown),
    [] ).

cnf(48,axiom,
    equal(h(j(e22)),e22),
    file('ALG083+1.p',unknown),
    [] ).

cnf(51,axiom,
    equal(j(h(e10)),e10),
    file('ALG083+1.p',unknown),
    [] ).

cnf(52,axiom,
    equal(j(h(e11)),e11),
    file('ALG083+1.p',unknown),
    [] ).

cnf(53,axiom,
    equal(j(h(e12)),e12),
    file('ALG083+1.p',unknown),
    [] ).

cnf(54,axiom,
    equal(j(h(e13)),e13),
    file('ALG083+1.p',unknown),
    [] ).

cnf(55,axiom,
    equal(j(h(e14)),e14),
    file('ALG083+1.p',unknown),
    [] ).

cnf(56,axiom,
    equal(op1(e10,e10),e10),
    file('ALG083+1.p',unknown),
    [] ).

cnf(58,axiom,
    equal(op1(e10,e12),e12),
    file('ALG083+1.p',unknown),
    [] ).

cnf(59,axiom,
    equal(op1(e10,e13),e13),
    file('ALG083+1.p',unknown),
    [] ).

cnf(62,axiom,
    equal(op1(e11,e11),e14),
    file('ALG083+1.p',unknown),
    [] ).

cnf(63,axiom,
    equal(op1(e11,e12),e10),
    file('ALG083+1.p',unknown),
    [] ).

cnf(66,axiom,
    equal(op1(e12,e10),e12),
    file('ALG083+1.p',unknown),
    [] ).

cnf(67,axiom,
    equal(op1(e12,e11),e10),
    file('ALG083+1.p',unknown),
    [] ).

cnf(70,axiom,
    equal(op1(e12,e14),e11),
    file('ALG083+1.p',unknown),
    [] ).

cnf(76,axiom,
    equal(op1(e14,e10),e14),
    file('ALG083+1.p',unknown),
    [] ).

cnf(77,axiom,
    equal(op1(e14,e11),e13),
    file('ALG083+1.p',unknown),
    [] ).

cnf(78,axiom,
    equal(op1(e14,e12),e11),
    file('ALG083+1.p',unknown),
    [] ).

cnf(79,axiom,
    equal(op1(e14,e13),e10),
    file('ALG083+1.p',unknown),
    [] ).

cnf(80,axiom,
    equal(op1(e14,e14),e12),
    file('ALG083+1.p',unknown),
    [] ).

cnf(81,axiom,
    equal(op2(e20,e20),e20),
    file('ALG083+1.p',unknown),
    [] ).

cnf(83,axiom,
    equal(op2(e20,e22),e22),
    file('ALG083+1.p',unknown),
    [] ).

cnf(87,axiom,
    equal(op2(e21,e21),e20),
    file('ALG083+1.p',unknown),
    [] ).

cnf(88,axiom,
    equal(op2(e21,e22),e24),
    file('ALG083+1.p',unknown),
    [] ).

cnf(89,axiom,
    equal(op2(e21,e23),e22),
    file('ALG083+1.p',unknown),
    [] ).

cnf(93,axiom,
    equal(op2(e22,e22),e23),
    file('ALG083+1.p',unknown),
    [] ).

cnf(95,axiom,
    equal(op2(e22,e24),e21),
    file('ALG083+1.p',unknown),
    [] ).

cnf(98,axiom,
    equal(op2(e23,e22),e21),
    file('ALG083+1.p',unknown),
    [] ).

cnf(99,axiom,
    equal(op2(e23,e23),e24),
    file('ALG083+1.p',unknown),
    [] ).

cnf(103,axiom,
    equal(op2(e24,e22),e20),
    file('ALG083+1.p',unknown),
    [] ).

cnf(104,axiom,
    equal(op2(e24,e23),e21),
    file('ALG083+1.p',unknown),
    [] ).

cnf(105,axiom,
    equal(op2(e24,e24),e22),
    file('ALG083+1.p',unknown),
    [] ).

cnf(109,axiom,
    equal(op2(h(e10),h(e13)),h(op1(e10,e13))),
    file('ALG083+1.p',unknown),
    [] ).

cnf(112,axiom,
    equal(op2(h(e11),h(e11)),h(op1(e11,e11))),
    file('ALG083+1.p',unknown),
    [] ).

cnf(116,axiom,
    equal(op2(h(e12),h(e10)),h(op1(e12,e10))),
    file('ALG083+1.p',unknown),
    [] ).

cnf(117,axiom,
    equal(op2(h(e12),h(e11)),h(op1(e12,e11))),
    file('ALG083+1.p',unknown),
    [] ).

cnf(126,axiom,
    equal(op2(h(e14),h(e10)),h(op1(e14,e10))),
    file('ALG083+1.p',unknown),
    [] ).

cnf(128,axiom,
    equal(op2(h(e14),h(e12)),h(op1(e14,e12))),
    file('ALG083+1.p',unknown),
    [] ).

cnf(129,axiom,
    equal(op2(h(e14),h(e13)),h(op1(e14,e13))),
    file('ALG083+1.p',unknown),
    [] ).

cnf(130,axiom,
    equal(op2(h(e14),h(e14)),h(op1(e14,e14))),
    file('ALG083+1.p',unknown),
    [] ).

cnf(133,axiom,
    equal(op1(j(e20),j(e22)),j(op2(e20,e22))),
    file('ALG083+1.p',unknown),
    [] ).

cnf(137,axiom,
    equal(op1(j(e21),j(e21)),j(op2(e21,e21))),
    file('ALG083+1.p',unknown),
    [] ).

cnf(138,axiom,
    equal(op1(j(e21),j(e22)),j(op2(e21,e22))),
    file('ALG083+1.p',unknown),
    [] ).

cnf(139,axiom,
    equal(op1(j(e21),j(e23)),j(op2(e21,e23))),
    file('ALG083+1.p',unknown),
    [] ).

cnf(143,axiom,
    equal(op1(j(e22),j(e22)),j(op2(e22,e22))),
    file('ALG083+1.p',unknown),
    [] ).

cnf(145,axiom,
    equal(op1(j(e22),j(e24)),j(op2(e22,e24))),
    file('ALG083+1.p',unknown),
    [] ).

cnf(148,axiom,
    equal(op1(j(e23),j(e22)),j(op2(e23,e22))),
    file('ALG083+1.p',unknown),
    [] ).

cnf(149,axiom,
    equal(op1(j(e23),j(e23)),j(op2(e23,e23))),
    file('ALG083+1.p',unknown),
    [] ).

cnf(153,axiom,
    equal(op1(j(e24),j(e22)),j(op2(e24,e22))),
    file('ALG083+1.p',unknown),
    [] ).

cnf(154,axiom,
    equal(op1(j(e24),j(e23)),j(op2(e24,e23))),
    file('ALG083+1.p',unknown),
    [] ).

cnf(155,axiom,
    equal(op1(j(e24),j(e24)),j(op2(e24,e24))),
    file('ALG083+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('ALG083+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('ALG083+1.p',unknown),
    [] ).

cnf(166,plain,
    equal(op1(j(e24),j(e24)),j(e22)),
    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(e21)),
    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(e20)),
    inference(rew,[status(thm),theory(equality)],[103,153]),
    [iquote('0:Rew:103.0,153.0')] ).

cnf(172,plain,
    equal(op1(j(e23),j(e23)),j(e24)),
    inference(rew,[status(thm),theory(equality)],[99,149]),
    [iquote('0:Rew:99.0,149.0')] ).

cnf(173,plain,
    equal(op1(j(e23),j(e22)),j(e21)),
    inference(rew,[status(thm),theory(equality)],[98,148]),
    [iquote('0:Rew:98.0,148.0')] ).

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(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(182,plain,
    equal(op1(j(e21),j(e23)),j(e22)),
    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(e20)),
    inference(rew,[status(thm),theory(equality)],[87,137]),
    [iquote('0:Rew:87.0,137.0')] ).

cnf(188,plain,
    equal(op1(j(e20),j(e22)),j(e22)),
    inference(rew,[status(thm),theory(equality)],[83,133]),
    [iquote('0:Rew:83.0,133.0')] ).

cnf(191,plain,
    equal(op2(h(e14),h(e14)),h(e12)),
    inference(rew,[status(thm),theory(equality)],[80,130]),
    [iquote('0:Rew:80.0,130.0')] ).

cnf(192,plain,
    equal(op2(h(e14),h(e13)),h(e10)),
    inference(rew,[status(thm),theory(equality)],[79,129]),
    [iquote('0:Rew:79.0,129.0')] ).

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(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(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(212,plain,
    equal(op2(h(e10),h(e13)),h(e13)),
    inference(rew,[status(thm),theory(equality)],[59,109]),
    [iquote('0:Rew:59.0,109.0')] ).

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(e22)),
    inference(rew,[status(thm),theory(equality)],[217,166]),
    [iquote('1:Rew:217.0,166.0')] ).

cnf(233,plain,
    equal(op1(e10,j(e23)),j(e21)),
    inference(rew,[status(thm),theory(equality)],[217,167]),
    [iquote('1:Rew:217.0,167.0')] ).

cnf(246,plain,
    equal(j(e22),e10),
    inference(rew,[status(thm),theory(equality)],[56,232]),
    [iquote('1:Rew:56.0,232.0')] ).

cnf(251,plain,
    equal(op1(e10,e10),j(e23)),
    inference(rew,[status(thm),theory(equality)],[246,178]),
    [iquote('1:Rew:246.0,178.0')] ).

cnf(257,plain,
    equal(j(e23),e10),
    inference(rew,[status(thm),theory(equality)],[56,251]),
    [iquote('1:Rew:56.0,251.0')] ).

cnf(263,plain,
    equal(j(e21),e10),
    inference(rew,[status(thm),theory(equality)],[56,233,257]),
    [iquote('1:Rew:56.0,233.0,257.0,233.0')] ).

cnf(265,plain,
    equal(op1(e10,e10),j(e20)),
    inference(rew,[status(thm),theory(equality)],[263,184]),
    [iquote('1:Rew:263.0,184.0')] ).

cnf(270,plain,
    equal(j(e20),e10),
    inference(rew,[status(thm),theory(equality)],[56,265]),
    [iquote('1:Rew:56.0,265.0')] ).

cnf(271,plain,
    equal(h(e10),e20),
    inference(rew,[status(thm),theory(equality)],[270,46]),
    [iquote('1:Rew:270.0,46.0')] ).

cnf(275,plain,
    equal(e24,e20),
    inference(rew,[status(thm),theory(equality)],[216,271]),
    [iquote('1:Rew:216.0,271.0')] ).

cnf(276,plain,
    $false,
    inference(mrr,[status(thm)],[275,14]),
    [iquote('1:MRR:275.0,14.0')] ).

cnf(291,plain,
    ~ equal(h(e10),e24),
    inference(spt,[spt(split,[position(sa)])],[276,216]),
    [iquote('1:Spt:276.0,165.0,216.0')] ).

cnf(292,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:276.0,165.1,165.2,165.3,165.4')] ).

cnf(293,plain,
    equal(h(e10),e23),
    inference(spt,[spt(split,[position(s2s1)])],[292]),
    [iquote('2:Spt:292.0')] ).

cnf(294,plain,
    equal(j(e23),e10),
    inference(rew,[status(thm),theory(equality)],[293,51]),
    [iquote('2:Rew:293.0,51.0')] ).

cnf(311,plain,
    equal(op1(e10,e10),j(e24)),
    inference(rew,[status(thm),theory(equality)],[294,172]),
    [iquote('2:Rew:294.0,172.0')] ).

cnf(314,plain,
    equal(op1(j(e24),e10),j(e21)),
    inference(rew,[status(thm),theory(equality)],[294,167]),
    [iquote('2:Rew:294.0,167.0')] ).

cnf(324,plain,
    equal(j(e24),e10),
    inference(rew,[status(thm),theory(equality)],[56,311]),
    [iquote('2:Rew:56.0,311.0')] ).

cnf(353,plain,
    equal(j(e21),e10),
    inference(rew,[status(thm),theory(equality)],[56,314,324]),
    [iquote('2:Rew:56.0,314.0,324.0,314.0')] ).

cnf(354,plain,
    equal(h(e10),e21),
    inference(rew,[status(thm),theory(equality)],[353,47]),
    [iquote('2:Rew:353.0,47.0')] ).

cnf(357,plain,
    equal(e23,e21),
    inference(rew,[status(thm),theory(equality)],[293,354]),
    [iquote('2:Rew:293.0,354.0')] ).

cnf(358,plain,
    $false,
    inference(mrr,[status(thm)],[357,16]),
    [iquote('2:MRR:357.0,16.0')] ).

cnf(371,plain,
    ~ equal(h(e10),e23),
    inference(spt,[spt(split,[position(s2sa)])],[358,293]),
    [iquote('2:Spt:358.0,292.0,293.0')] ).

cnf(372,plain,
    ( equal(h(e10),e22)
    | equal(h(e10),e21)
    | equal(h(e10),e20) ),
    inference(spt,[spt(split,[position(s2s2)])],[292]),
    [iquote('2:Spt:358.0,292.1,292.2,292.3')] ).

cnf(373,plain,
    equal(h(e10),e22),
    inference(spt,[spt(split,[position(s2s2s1)])],[372]),
    [iquote('3:Spt:372.0')] ).

cnf(375,plain,
    equal(j(e22),e10),
    inference(rew,[status(thm),theory(equality)],[373,51]),
    [iquote('3:Rew:373.0,51.0')] ).

cnf(391,plain,
    equal(op1(j(e23),e10),j(e21)),
    inference(rew,[status(thm),theory(equality)],[375,173]),
    [iquote('3:Rew:375.0,173.0')] ).

cnf(394,plain,
    equal(op1(e10,e10),j(e23)),
    inference(rew,[status(thm),theory(equality)],[375,178]),
    [iquote('3:Rew:375.0,178.0')] ).

cnf(405,plain,
    equal(j(e23),e10),
    inference(rew,[status(thm),theory(equality)],[56,394]),
    [iquote('3:Rew:56.0,394.0')] ).

cnf(422,plain,
    equal(j(e21),e10),
    inference(rew,[status(thm),theory(equality)],[56,391,405]),
    [iquote('3:Rew:56.0,391.0,405.0,391.0')] ).

cnf(424,plain,
    equal(op1(e10,e10),j(e20)),
    inference(rew,[status(thm),theory(equality)],[422,184]),
    [iquote('3:Rew:422.0,184.0')] ).

cnf(429,plain,
    equal(j(e20),e10),
    inference(rew,[status(thm),theory(equality)],[56,424]),
    [iquote('3:Rew:56.0,424.0')] ).

cnf(430,plain,
    equal(h(e10),e20),
    inference(rew,[status(thm),theory(equality)],[429,46]),
    [iquote('3:Rew:429.0,46.0')] ).

cnf(434,plain,
    equal(e22,e20),
    inference(rew,[status(thm),theory(equality)],[373,430]),
    [iquote('3:Rew:373.0,430.0')] ).

cnf(435,plain,
    $false,
    inference(mrr,[status(thm)],[434,12]),
    [iquote('3:MRR:434.0,12.0')] ).

cnf(450,plain,
    ~ equal(h(e10),e22),
    inference(spt,[spt(split,[position(s2s2sa)])],[435,373]),
    [iquote('3:Spt:435.0,372.0,373.0')] ).

cnf(451,plain,
    ( equal(h(e10),e21)
    | equal(h(e10),e20) ),
    inference(spt,[spt(split,[position(s2s2s2)])],[372]),
    [iquote('3:Spt:435.0,372.1,372.2')] ).

cnf(452,plain,
    equal(h(e10),e21),
    inference(spt,[spt(split,[position(s2s2s2s1)])],[451]),
    [iquote('4:Spt:451.0')] ).

cnf(454,plain,
    equal(j(e21),e10),
    inference(rew,[status(thm),theory(equality)],[452,51]),
    [iquote('4:Rew:452.0,51.0')] ).

cnf(471,plain,
    equal(op1(e10,j(e22)),j(e24)),
    inference(rew,[status(thm),theory(equality)],[454,183]),
    [iquote('4:Rew:454.0,183.0')] ).

cnf(474,plain,
    equal(op1(e10,j(e23)),j(e22)),
    inference(rew,[status(thm),theory(equality)],[454,182]),
    [iquote('4:Rew:454.0,182.0')] ).

cnf(482,plain,
    equal(op1(e10,e10),j(e20)),
    inference(rew,[status(thm),theory(equality)],[454,184]),
    [iquote('4:Rew:454.0,184.0')] ).

cnf(485,plain,
    equal(j(e20),e10),
    inference(rew,[status(thm),theory(equality)],[56,482]),
    [iquote('4:Rew:56.0,482.0')] ).

cnf(487,plain,
    equal(op1(e10,j(e22)),j(e22)),
    inference(rew,[status(thm),theory(equality)],[485,188]),
    [iquote('4:Rew:485.0,188.0')] ).

cnf(489,plain,
    equal(op1(j(e24),j(e22)),e10),
    inference(rew,[status(thm),theory(equality)],[485,168]),
    [iquote('4:Rew:485.0,168.0')] ).

cnf(501,plain,
    equal(j(e24),j(e22)),
    inference(rew,[status(thm),theory(equality)],[471,487]),
    [iquote('4:Rew:471.0,487.0')] ).

cnf(514,plain,
    equal(j(e23),e10),
    inference(rew,[status(thm),theory(equality)],[178,489,501]),
    [iquote('4:Rew:178.0,489.0,501.0,489.0')] ).

cnf(517,plain,
    equal(op1(e10,e10),j(e22)),
    inference(rew,[status(thm),theory(equality)],[514,474]),
    [iquote('4:Rew:514.0,474.0')] ).

cnf(522,plain,
    equal(j(e22),e10),
    inference(rew,[status(thm),theory(equality)],[56,517]),
    [iquote('4:Rew:56.0,517.0')] ).

cnf(523,plain,
    equal(h(e10),e22),
    inference(rew,[status(thm),theory(equality)],[522,48]),
    [iquote('4:Rew:522.0,48.0')] ).

cnf(526,plain,
    equal(e22,e21),
    inference(rew,[status(thm),theory(equality)],[452,523]),
    [iquote('4:Rew:452.0,523.0')] ).

cnf(527,plain,
    $false,
    inference(mrr,[status(thm)],[526,15]),
    [iquote('4:MRR:526.0,15.0')] ).

cnf(545,plain,
    ~ equal(h(e10),e21),
    inference(spt,[spt(split,[position(s2s2s2sa)])],[527,452]),
    [iquote('4:Spt:527.0,451.0,452.0')] ).

cnf(546,plain,
    equal(h(e10),e20),
    inference(spt,[spt(split,[position(s2s2s2s2)])],[451]),
    [iquote('4:Spt:527.0,451.1')] ).

cnf(549,plain,
    equal(j(e20),e10),
    inference(rew,[status(thm),theory(equality)],[546,51]),
    [iquote('4:Rew:546.0,51.0')] ).

cnf(553,plain,
    equal(op2(h(e14),h(e13)),e20),
    inference(rew,[status(thm),theory(equality)],[546,192]),
    [iquote('4:Rew:546.0,192.0')] ).

cnf(554,plain,
    equal(op2(h(e14),e20),h(e14)),
    inference(rew,[status(thm),theory(equality)],[546,195]),
    [iquote('4:Rew:546.0,195.0')] ).

cnf(557,plain,
    equal(op2(h(e12),h(e11)),e20),
    inference(rew,[status(thm),theory(equality)],[546,204]),
    [iquote('4:Rew:546.0,204.0')] ).

cnf(558,plain,
    equal(op2(h(e12),e20),h(e12)),
    inference(rew,[status(thm),theory(equality)],[546,205]),
    [iquote('4:Rew:546.0,205.0')] ).

cnf(562,plain,
    equal(op2(e20,h(e13)),h(e13)),
    inference(rew,[status(thm),theory(equality)],[546,212]),
    [iquote('4:Rew:546.0,212.0')] ).

cnf(580,plain,
    equal(h(e11),e24),
    inference(spt,[spt(split,[position(s2s2s2s2s1)])],[164]),
    [iquote('5:Spt:164.0')] ).

cnf(581,plain,
    equal(j(e24),e11),
    inference(rew,[status(thm),theory(equality)],[580,52]),
    [iquote('5:Rew:580.0,52.0')] ).

cnf(589,plain,
    equal(op2(e24,e24),h(e14)),
    inference(rew,[status(thm),theory(equality)],[580,209]),
    [iquote('5:Rew:580.0,209.0')] ).

cnf(595,plain,
    equal(op1(e11,j(e23)),j(e21)),
    inference(rew,[status(thm),theory(equality)],[581,167]),
    [iquote('5:Rew:581.0,167.0')] ).

cnf(607,plain,
    equal(h(e14),e22),
    inference(rew,[status(thm),theory(equality)],[105,589]),
    [iquote('5:Rew:105.0,589.0')] ).

cnf(608,plain,
    equal(j(e22),e14),
    inference(rew,[status(thm),theory(equality)],[607,55]),
    [iquote('5:Rew:607.0,55.0')] ).

cnf(609,plain,
    equal(op2(e22,e22),h(e12)),
    inference(rew,[status(thm),theory(equality)],[607,191]),
    [iquote('5:Rew:607.0,191.0')] ).

cnf(619,plain,
    equal(op1(j(e21),j(e23)),e14),
    inference(rew,[status(thm),theory(equality)],[608,182]),
    [iquote('5:Rew:608.0,182.0')] ).

cnf(627,plain,
    equal(h(e12),e23),
    inference(rew,[status(thm),theory(equality)],[93,609]),
    [iquote('5:Rew:93.0,609.0')] ).

cnf(628,plain,
    equal(j(e23),e12),
    inference(rew,[status(thm),theory(equality)],[627,53]),
    [iquote('5:Rew:627.0,53.0')] ).

cnf(667,plain,
    equal(j(e21),e10),
    inference(rew,[status(thm),theory(equality)],[63,595,628]),
    [iquote('5:Rew:63.0,595.0,628.0,595.0')] ).

cnf(694,plain,
    equal(e14,e12),
    inference(rew,[status(thm),theory(equality)],[58,619,667,628]),
    [iquote('5:Rew:58.0,619.0,667.0,619.0,628.0,619.0')] ).

cnf(695,plain,
    $false,
    inference(mrr,[status(thm)],[694,9]),
    [iquote('5:MRR:694.0,9.0')] ).

cnf(696,plain,
    ~ equal(h(e11),e24),
    inference(spt,[spt(split,[position(s2s2s2s2sa)])],[695,580]),
    [iquote('5:Spt:695.0,164.0,580.0')] ).

cnf(697,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:695.0,164.1,164.2,164.3,164.4')] ).

cnf(698,plain,
    equal(h(e11),e23),
    inference(spt,[spt(split,[position(s2s2s2s2s2s1)])],[697]),
    [iquote('6:Spt:697.0')] ).

cnf(699,plain,
    equal(j(e23),e11),
    inference(rew,[status(thm),theory(equality)],[698,52]),
    [iquote('6:Rew:698.0,52.0')] ).

cnf(705,plain,
    equal(op2(e23,e23),h(e14)),
    inference(rew,[status(thm),theory(equality)],[698,209]),
    [iquote('6:Rew:698.0,209.0')] ).

cnf(721,plain,
    equal(op1(j(e24),e11),j(e21)),
    inference(rew,[status(thm),theory(equality)],[699,167]),
    [iquote('6:Rew:699.0,167.0')] ).

cnf(726,plain,
    equal(h(e14),e24),
    inference(rew,[status(thm),theory(equality)],[99,705]),
    [iquote('6:Rew:99.0,705.0')] ).

cnf(727,plain,
    equal(j(e24),e14),
    inference(rew,[status(thm),theory(equality)],[726,55]),
    [iquote('6:Rew:726.0,55.0')] ).

cnf(734,plain,
    equal(op2(e24,e24),h(e12)),
    inference(rew,[status(thm),theory(equality)],[726,191]),
    [iquote('6:Rew:726.0,191.0')] ).

cnf(742,plain,
    equal(op1(j(e22),e14),j(e21)),
    inference(rew,[status(thm),theory(equality)],[727,176]),
    [iquote('6:Rew:727.0,176.0')] ).

cnf(746,plain,
    equal(h(e12),e22),
    inference(rew,[status(thm),theory(equality)],[105,734]),
    [iquote('6:Rew:105.0,734.0')] ).

cnf(747,plain,
    equal(j(e22),e12),
    inference(rew,[status(thm),theory(equality)],[746,53]),
    [iquote('6:Rew:746.0,53.0')] ).

cnf(788,plain,
    equal(j(e21),e13),
    inference(rew,[status(thm),theory(equality)],[77,721,727]),
    [iquote('6:Rew:77.0,721.0,727.0,721.0')] ).

cnf(815,plain,
    equal(e13,e11),
    inference(rew,[status(thm),theory(equality)],[70,742,747,788]),
    [iquote('6:Rew:70.0,742.0,747.0,742.0,788.0,742.0')] ).

cnf(816,plain,
    $false,
    inference(mrr,[status(thm)],[815,6]),
    [iquote('6:MRR:815.0,6.0')] ).

cnf(817,plain,
    ~ equal(h(e11),e23),
    inference(spt,[spt(split,[position(s2s2s2s2s2sa)])],[816,698]),
    [iquote('6:Spt:816.0,697.0,698.0')] ).

cnf(818,plain,
    ( equal(h(e11),e22)
    | equal(h(e11),e21)
    | equal(h(e11),e20) ),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2)])],[697]),
    [iquote('6:Spt:816.0,697.1,697.2,697.3')] ).

cnf(819,plain,
    equal(h(e11),e22),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2s1)])],[818]),
    [iquote('7:Spt:818.0')] ).

cnf(821,plain,
    equal(j(e22),e11),
    inference(rew,[status(thm),theory(equality)],[819,52]),
    [iquote('7:Rew:819.0,52.0')] ).

cnf(834,plain,
    equal(op2(e22,e22),h(e14)),
    inference(rew,[status(thm),theory(equality)],[819,209]),
    [iquote('7:Rew:819.0,209.0')] ).

cnf(840,plain,
    equal(op1(j(e23),e11),j(e21)),
    inference(rew,[status(thm),theory(equality)],[821,173]),
    [iquote('7:Rew:821.0,173.0')] ).

cnf(848,plain,
    equal(h(e14),e23),
    inference(rew,[status(thm),theory(equality)],[93,834]),
    [iquote('7:Rew:93.0,834.0')] ).

cnf(849,plain,
    equal(j(e23),e14),
    inference(rew,[status(thm),theory(equality)],[848,55]),
    [iquote('7:Rew:848.0,55.0')] ).

cnf(854,plain,
    equal(op2(e23,e23),h(e12)),
    inference(rew,[status(thm),theory(equality)],[848,191]),
    [iquote('7:Rew:848.0,191.0')] ).

cnf(861,plain,
    equal(op1(j(e24),e14),j(e21)),
    inference(rew,[status(thm),theory(equality)],[849,167]),
    [iquote('7:Rew:849.0,167.0')] ).

cnf(868,plain,
    equal(h(e12),e24),
    inference(rew,[status(thm),theory(equality)],[99,854]),
    [iquote('7:Rew:99.0,854.0')] ).

cnf(869,plain,
    equal(j(e24),e12),
    inference(rew,[status(thm),theory(equality)],[868,53]),
    [iquote('7:Rew:868.0,53.0')] ).

cnf(908,plain,
    equal(j(e21),e13),
    inference(rew,[status(thm),theory(equality)],[77,840,849]),
    [iquote('7:Rew:77.0,840.0,849.0,840.0')] ).

cnf(931,plain,
    equal(e13,e11),
    inference(rew,[status(thm),theory(equality)],[70,861,869,908]),
    [iquote('7:Rew:70.0,861.0,869.0,861.0,908.0,861.0')] ).

cnf(932,plain,
    $false,
    inference(mrr,[status(thm)],[931,6]),
    [iquote('7:MRR:931.0,6.0')] ).

cnf(935,plain,
    ~ equal(h(e11),e22),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2sa)])],[932,819]),
    [iquote('7:Spt:932.0,818.0,819.0')] ).

cnf(936,plain,
    ( equal(h(e11),e21)
    | equal(h(e11),e20) ),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2s2)])],[818]),
    [iquote('7:Spt:932.0,818.1,818.2')] ).

cnf(937,plain,
    equal(h(e11),e21),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2s2s1)])],[936]),
    [iquote('8:Spt:936.0')] ).

cnf(946,plain,
    equal(op2(e21,e21),h(e14)),
    inference(rew,[status(thm),theory(equality)],[937,209]),
    [iquote('8:Rew:937.0,209.0')] ).

cnf(953,plain,
    equal(op2(h(e14),h(e12)),e21),
    inference(rew,[status(thm),theory(equality)],[937,193]),
    [iquote('8:Rew:937.0,193.0')] ).

cnf(969,plain,
    equal(h(e14),e20),
    inference(rew,[status(thm),theory(equality)],[87,946]),
    [iquote('8:Rew:87.0,946.0')] ).

cnf(977,plain,
    equal(op2(e20,e20),h(e12)),
    inference(rew,[status(thm),theory(equality)],[969,191]),
    [iquote('8:Rew:969.0,191.0')] ).

cnf(988,plain,
    equal(h(e12),e20),
    inference(rew,[status(thm),theory(equality)],[81,977]),
    [iquote('8:Rew:81.0,977.0')] ).

cnf(1012,plain,
    equal(e21,e20),
    inference(rew,[status(thm),theory(equality)],[81,953,969,988]),
    [iquote('8:Rew:81.0,953.0,969.0,953.0,988.0,953.0')] ).

cnf(1013,plain,
    $false,
    inference(mrr,[status(thm)],[1012,11]),
    [iquote('8:MRR:1012.0,11.0')] ).

cnf(1017,plain,
    ~ equal(h(e11),e21),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2s2sa)])],[1013,937]),
    [iquote('8:Spt:1013.0,936.0,937.0')] ).

cnf(1018,plain,
    equal(h(e11),e20),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2s2s2)])],[936]),
    [iquote('8:Spt:1013.0,936.1')] ).

cnf(1025,plain,
    equal(op2(h(e12),e20),e20),
    inference(rew,[status(thm),theory(equality)],[1018,557]),
    [iquote('8:Rew:1018.0,557.0')] ).

cnf(1029,plain,
    equal(h(e12),e20),
    inference(rew,[status(thm),theory(equality)],[1025,558]),
    [iquote('8:Rew:1025.0,558.0')] ).

cnf(1036,plain,
    equal(h(e14),e20),
    inference(rew,[status(thm),theory(equality)],[554,193,1029,1018]),
    [iquote('8:Rew:554.0,193.0,1029.0,193.0,1018.0,193.0')] ).

cnf(1038,plain,
    equal(op2(e20,h(e13)),e20),
    inference(rew,[status(thm),theory(equality)],[1036,553]),
    [iquote('8:Rew:1036.0,553.0')] ).

cnf(1044,plain,
    equal(h(e13),e20),
    inference(rew,[status(thm),theory(equality)],[562,1038]),
    [iquote('8:Rew:562.0,1038.0')] ).

cnf(1045,plain,
    equal(j(e20),e13),
    inference(rew,[status(thm),theory(equality)],[1044,54]),
    [iquote('8:Rew:1044.0,54.0')] ).

cnf(1048,plain,
    equal(e13,e10),
    inference(rew,[status(thm),theory(equality)],[549,1045]),
    [iquote('8:Rew:549.0,1045.0')] ).

cnf(1049,plain,
    $false,
    inference(mrr,[status(thm)],[1048,3]),
    [iquote('8:MRR:1048.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ALG083+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Wed Jun  8 09:28:04 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.50  
% 0.20/0.50  SPASS V 3.9 
% 0.20/0.50  SPASS beiseite: Proof found.
% 0.20/0.50  % SZS status Theorem
% 0.20/0.50  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.50  SPASS derived 458 clauses, backtracked 458 clauses, performed 8 splits and kept 847 clauses.
% 0.20/0.50  SPASS allocated 85609 KBytes.
% 0.20/0.50  SPASS spent	0:00:00.15 on the problem.
% 0.20/0.50  		0:00:00.04 for the input.
% 0.20/0.50  		0:00:00.04 for the FLOTTER CNF translation.
% 0.20/0.50  		0:00:00.00 for inferences.
% 0.20/0.50  		0:00:00.00 for the backtracking.
% 0.20/0.50  		0:00:00.05 for the reduction.
% 0.20/0.50  
% 0.20/0.50  
% 0.20/0.50  Here is a proof with depth 4, length 206 :
% 0.20/0.50  % SZS output start Refutation
% See solution above
% 0.20/0.51  Formulae used in the proof : ax1 ax2 co1 ax4 ax5
% 0.20/0.51  
%------------------------------------------------------------------------------