TSTP Solution File: ALG082+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ALG082+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% 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 14 18:02:15 EDT 2022

% Result   : Theorem 0.19s 0.49s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   66
% Syntax   : Number of clauses     :  214 ( 206 unt;   8 nHn; 214 RR)
%            Number of literals    :  234 (   0 equ;  14 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('ALG082+1.p',unknown),
    [] ).

cnf(10,axiom,
    ~ equal(e14,e13),
    file('ALG082+1.p',unknown),
    [] ).

cnf(14,axiom,
    ~ equal(e24,e20),
    file('ALG082+1.p',unknown),
    [] ).

cnf(16,axiom,
    ~ equal(e23,e21),
    file('ALG082+1.p',unknown),
    [] ).

cnf(17,axiom,
    ~ equal(e24,e21),
    file('ALG082+1.p',unknown),
    [] ).

cnf(18,axiom,
    ~ equal(e23,e22),
    file('ALG082+1.p',unknown),
    [] ).

cnf(47,axiom,
    equal(h(j(e21)),e21),
    file('ALG082+1.p',unknown),
    [] ).

cnf(48,axiom,
    equal(h(j(e22)),e22),
    file('ALG082+1.p',unknown),
    [] ).

cnf(49,axiom,
    equal(h(j(e23)),e23),
    file('ALG082+1.p',unknown),
    [] ).

cnf(51,axiom,
    equal(j(h(e10)),e10),
    file('ALG082+1.p',unknown),
    [] ).

cnf(52,axiom,
    equal(j(h(e11)),e11),
    file('ALG082+1.p',unknown),
    [] ).

cnf(54,axiom,
    equal(j(h(e13)),e13),
    file('ALG082+1.p',unknown),
    [] ).

cnf(55,axiom,
    equal(j(h(e14)),e14),
    file('ALG082+1.p',unknown),
    [] ).

cnf(56,axiom,
    equal(op1(e10,e10),e10),
    file('ALG082+1.p',unknown),
    [] ).

cnf(59,axiom,
    equal(op1(e10,e13),e13),
    file('ALG082+1.p',unknown),
    [] ).

cnf(62,axiom,
    equal(op1(e11,e11),e14),
    file('ALG082+1.p',unknown),
    [] ).

cnf(64,axiom,
    equal(op1(e11,e13),e12),
    file('ALG082+1.p',unknown),
    [] ).

cnf(65,axiom,
    equal(op1(e11,e14),e13),
    file('ALG082+1.p',unknown),
    [] ).

cnf(66,axiom,
    equal(op1(e12,e10),e12),
    file('ALG082+1.p',unknown),
    [] ).

cnf(67,axiom,
    equal(op1(e12,e11),e10),
    file('ALG082+1.p',unknown),
    [] ).

cnf(68,axiom,
    equal(op1(e12,e12),e13),
    file('ALG082+1.p',unknown),
    [] ).

cnf(72,axiom,
    equal(op1(e13,e11),e12),
    file('ALG082+1.p',unknown),
    [] ).

cnf(76,axiom,
    equal(op1(e14,e10),e14),
    file('ALG082+1.p',unknown),
    [] ).

cnf(77,axiom,
    equal(op1(e14,e11),e13),
    file('ALG082+1.p',unknown),
    [] ).

cnf(78,axiom,
    equal(op1(e14,e12),e11),
    file('ALG082+1.p',unknown),
    [] ).

cnf(79,axiom,
    equal(op1(e14,e13),e10),
    file('ALG082+1.p',unknown),
    [] ).

cnf(80,axiom,
    equal(op1(e14,e14),e12),
    file('ALG082+1.p',unknown),
    [] ).

cnf(81,axiom,
    equal(op2(e20,e20),e20),
    file('ALG082+1.p',unknown),
    [] ).

cnf(86,axiom,
    equal(op2(e21,e20),e21),
    file('ALG082+1.p',unknown),
    [] ).

cnf(87,axiom,
    equal(op2(e21,e21),e24),
    file('ALG082+1.p',unknown),
    [] ).

cnf(88,axiom,
    equal(op2(e21,e22),e23),
    file('ALG082+1.p',unknown),
    [] ).

cnf(90,axiom,
    equal(op2(e21,e24),e22),
    file('ALG082+1.p',unknown),
    [] ).

cnf(93,axiom,
    equal(op2(e22,e22),e24),
    file('ALG082+1.p',unknown),
    [] ).

cnf(94,axiom,
    equal(op2(e22,e23),e21),
    file('ALG082+1.p',unknown),
    [] ).

cnf(95,axiom,
    equal(op2(e22,e24),e23),
    file('ALG082+1.p',unknown),
    [] ).

cnf(96,axiom,
    equal(op2(e23,e20),e23),
    file('ALG082+1.p',unknown),
    [] ).

cnf(97,axiom,
    equal(op2(e23,e21),e22),
    file('ALG082+1.p',unknown),
    [] ).

cnf(99,axiom,
    equal(op2(e23,e23),e24),
    file('ALG082+1.p',unknown),
    [] ).

cnf(100,axiom,
    equal(op2(e23,e24),e21),
    file('ALG082+1.p',unknown),
    [] ).

cnf(101,axiom,
    equal(op2(e24,e20),e24),
    file('ALG082+1.p',unknown),
    [] ).

cnf(104,axiom,
    equal(op2(e24,e23),e22),
    file('ALG082+1.p',unknown),
    [] ).

cnf(105,axiom,
    equal(op2(e24,e24),e20),
    file('ALG082+1.p',unknown),
    [] ).

cnf(109,axiom,
    equal(op2(h(e10),h(e13)),h(op1(e10,e13))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(112,axiom,
    equal(op2(h(e11),h(e11)),h(op1(e11,e11))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(114,axiom,
    equal(op2(h(e11),h(e13)),h(op1(e11,e13))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(116,axiom,
    equal(op2(h(e12),h(e10)),h(op1(e12,e10))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(117,axiom,
    equal(op2(h(e12),h(e11)),h(op1(e12,e11))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(126,axiom,
    equal(op2(h(e14),h(e10)),h(op1(e14,e10))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(128,axiom,
    equal(op2(h(e14),h(e12)),h(op1(e14,e12))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(129,axiom,
    equal(op2(h(e14),h(e13)),h(op1(e14,e13))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(130,axiom,
    equal(op2(h(e14),h(e14)),h(op1(e14,e14))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(136,axiom,
    equal(op1(j(e21),j(e20)),j(op2(e21,e20))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(137,axiom,
    equal(op1(j(e21),j(e21)),j(op2(e21,e21))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(138,axiom,
    equal(op1(j(e21),j(e22)),j(op2(e21,e22))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(140,axiom,
    equal(op1(j(e21),j(e24)),j(op2(e21,e24))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(143,axiom,
    equal(op1(j(e22),j(e22)),j(op2(e22,e22))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(144,axiom,
    equal(op1(j(e22),j(e23)),j(op2(e22,e23))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(145,axiom,
    equal(op1(j(e22),j(e24)),j(op2(e22,e24))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(146,axiom,
    equal(op1(j(e23),j(e20)),j(op2(e23,e20))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(147,axiom,
    equal(op1(j(e23),j(e21)),j(op2(e23,e21))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(149,axiom,
    equal(op1(j(e23),j(e23)),j(op2(e23,e23))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(150,axiom,
    equal(op1(j(e23),j(e24)),j(op2(e23,e24))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(154,axiom,
    equal(op1(j(e24),j(e23)),j(op2(e24,e23))),
    file('ALG082+1.p',unknown),
    [] ).

cnf(155,axiom,
    equal(op1(j(e24),j(e24)),j(op2(e24,e24))),
    file('ALG082+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('ALG082+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('ALG082+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(171,plain,
    equal(op1(j(e23),j(e24)),j(e21)),
    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(e24)),
    inference(rew,[status(thm),theory(equality)],[99,149]),
    [iquote('0:Rew:99.0,149.0')] ).

cnf(174,plain,
    equal(op1(j(e23),j(e21)),j(e22)),
    inference(rew,[status(thm),theory(equality)],[97,147]),
    [iquote('0:Rew:97.0,147.0')] ).

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(e23)),
    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(e21)),
    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(e24)),
    inference(rew,[status(thm),theory(equality)],[93,143]),
    [iquote('0:Rew:93.0,143.0')] ).

cnf(181,plain,
    equal(op1(j(e21),j(e24)),j(e22)),
    inference(rew,[status(thm),theory(equality)],[90,140]),
    [iquote('0:Rew:90.0,140.0')] ).

cnf(183,plain,
    equal(op1(j(e21),j(e22)),j(e23)),
    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(e24)),
    inference(rew,[status(thm),theory(equality)],[87,137]),
    [iquote('0:Rew:87.0,137.0')] ).

cnf(185,plain,
    equal(op1(j(e21),j(e20)),j(e21)),
    inference(rew,[status(thm),theory(equality)],[86,136]),
    [iquote('0:Rew:86.0,136.0')] ).

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(207,plain,
    equal(op2(h(e11),h(e13)),h(e12)),
    inference(rew,[status(thm),theory(equality)],[64,114]),
    [iquote('0:Rew:64.0,114.0')] ).

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(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(e21)),
    inference(rew,[status(thm),theory(equality)],[217,171]),
    [iquote('1:Rew:217.0,171.0')] ).

cnf(241,plain,
    equal(op1(j(e21),e10),j(e22)),
    inference(rew,[status(thm),theory(equality)],[217,181]),
    [iquote('1:Rew:217.0,181.0')] ).

cnf(242,plain,
    equal(op1(j(e21),j(e21)),e10),
    inference(rew,[status(thm),theory(equality)],[217,184]),
    [iquote('1:Rew:217.0,184.0')] ).

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(253,plain,
    equal(op1(j(e21),e10),j(e21)),
    inference(rew,[status(thm),theory(equality)],[246,185]),
    [iquote('1:Rew:246.0,185.0')] ).

cnf(262,plain,
    equal(j(e23),j(e21)),
    inference(rew,[status(thm),theory(equality)],[237,249]),
    [iquote('1:Rew:237.0,249.0')] ).

cnf(264,plain,
    equal(op1(j(e21),j(e21)),j(e22)),
    inference(rew,[status(thm),theory(equality)],[262,174]),
    [iquote('1:Rew:262.0,174.0')] ).

cnf(277,plain,
    equal(j(e22),j(e21)),
    inference(rew,[status(thm),theory(equality)],[241,253]),
    [iquote('1:Rew:241.0,253.0')] ).

cnf(292,plain,
    equal(j(e21),e10),
    inference(rew,[status(thm),theory(equality)],[242,264,277]),
    [iquote('1:Rew:242.0,264.0,277.0,264.0')] ).

cnf(293,plain,
    equal(h(e10),e21),
    inference(rew,[status(thm),theory(equality)],[292,47]),
    [iquote('1:Rew:292.0,47.0')] ).

cnf(299,plain,
    equal(e24,e21),
    inference(rew,[status(thm),theory(equality)],[216,293]),
    [iquote('1:Rew:216.0,293.0')] ).

cnf(300,plain,
    $false,
    inference(mrr,[status(thm)],[299,17]),
    [iquote('1:MRR:299.0,17.0')] ).

cnf(303,plain,
    ~ equal(h(e10),e24),
    inference(spt,[spt(split,[position(sa)])],[300,216]),
    [iquote('1:Spt:300.0,165.0,216.0')] ).

cnf(304,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:300.0,165.1,165.2,165.3,165.4')] ).

cnf(305,plain,
    equal(h(e10),e23),
    inference(spt,[spt(split,[position(s2s1)])],[304]),
    [iquote('2:Spt:304.0')] ).

cnf(306,plain,
    equal(j(e23),e10),
    inference(rew,[status(thm),theory(equality)],[305,51]),
    [iquote('2:Rew:305.0,51.0')] ).

cnf(323,plain,
    equal(op1(e10,e10),j(e24)),
    inference(rew,[status(thm),theory(equality)],[306,172]),
    [iquote('2:Rew:306.0,172.0')] ).

cnf(326,plain,
    equal(op1(j(e24),e10),j(e22)),
    inference(rew,[status(thm),theory(equality)],[306,167]),
    [iquote('2:Rew:306.0,167.0')] ).

cnf(336,plain,
    equal(j(e24),e10),
    inference(rew,[status(thm),theory(equality)],[56,323]),
    [iquote('2:Rew:56.0,323.0')] ).

cnf(365,plain,
    equal(j(e22),e10),
    inference(rew,[status(thm),theory(equality)],[56,326,336]),
    [iquote('2:Rew:56.0,326.0,336.0,326.0')] ).

cnf(366,plain,
    equal(h(e10),e22),
    inference(rew,[status(thm),theory(equality)],[365,48]),
    [iquote('2:Rew:365.0,48.0')] ).

cnf(368,plain,
    equal(e23,e22),
    inference(rew,[status(thm),theory(equality)],[305,366]),
    [iquote('2:Rew:305.0,366.0')] ).

cnf(369,plain,
    $false,
    inference(mrr,[status(thm)],[368,18]),
    [iquote('2:MRR:368.0,18.0')] ).

cnf(384,plain,
    ~ equal(h(e10),e23),
    inference(spt,[spt(split,[position(s2sa)])],[369,305]),
    [iquote('2:Spt:369.0,304.0,305.0')] ).

cnf(385,plain,
    ( equal(h(e10),e22)
    | equal(h(e10),e21)
    | equal(h(e10),e20) ),
    inference(spt,[spt(split,[position(s2s2)])],[304]),
    [iquote('2:Spt:369.0,304.1,304.2,304.3')] ).

cnf(386,plain,
    equal(h(e10),e22),
    inference(spt,[spt(split,[position(s2s2s1)])],[385]),
    [iquote('3:Spt:385.0')] ).

cnf(388,plain,
    equal(j(e22),e10),
    inference(rew,[status(thm),theory(equality)],[386,51]),
    [iquote('3:Rew:386.0,51.0')] ).

cnf(405,plain,
    equal(op1(e10,j(e23)),j(e21)),
    inference(rew,[status(thm),theory(equality)],[388,177]),
    [iquote('3:Rew:388.0,177.0')] ).

cnf(406,plain,
    equal(op1(j(e21),e10),j(e23)),
    inference(rew,[status(thm),theory(equality)],[388,183]),
    [iquote('3:Rew:388.0,183.0')] ).

cnf(408,plain,
    equal(op1(j(e24),j(e23)),e10),
    inference(rew,[status(thm),theory(equality)],[388,167]),
    [iquote('3:Rew:388.0,167.0')] ).

cnf(411,plain,
    equal(op1(e10,e10),j(e24)),
    inference(rew,[status(thm),theory(equality)],[388,178]),
    [iquote('3:Rew:388.0,178.0')] ).

cnf(418,plain,
    equal(j(e24),e10),
    inference(rew,[status(thm),theory(equality)],[56,411]),
    [iquote('3:Rew:56.0,411.0')] ).

cnf(444,plain,
    equal(j(e21),e10),
    inference(rew,[status(thm),theory(equality)],[405,408,418]),
    [iquote('3:Rew:405.0,408.0,418.0,408.0')] ).

cnf(448,plain,
    equal(op1(e10,e10),j(e23)),
    inference(rew,[status(thm),theory(equality)],[444,406]),
    [iquote('3:Rew:444.0,406.0')] ).

cnf(451,plain,
    equal(j(e23),e10),
    inference(rew,[status(thm),theory(equality)],[56,448]),
    [iquote('3:Rew:56.0,448.0')] ).

cnf(452,plain,
    equal(h(e10),e23),
    inference(rew,[status(thm),theory(equality)],[451,49]),
    [iquote('3:Rew:451.0,49.0')] ).

cnf(455,plain,
    equal(e23,e22),
    inference(rew,[status(thm),theory(equality)],[386,452]),
    [iquote('3:Rew:386.0,452.0')] ).

cnf(456,plain,
    $false,
    inference(mrr,[status(thm)],[455,18]),
    [iquote('3:MRR:455.0,18.0')] ).

cnf(470,plain,
    ~ equal(h(e10),e22),
    inference(spt,[spt(split,[position(s2s2sa)])],[456,386]),
    [iquote('3:Spt:456.0,385.0,386.0')] ).

cnf(471,plain,
    ( equal(h(e10),e21)
    | equal(h(e10),e20) ),
    inference(spt,[spt(split,[position(s2s2s2)])],[385]),
    [iquote('3:Spt:456.0,385.1,385.2')] ).

cnf(472,plain,
    equal(h(e10),e21),
    inference(spt,[spt(split,[position(s2s2s2s1)])],[471]),
    [iquote('4:Spt:471.0')] ).

cnf(474,plain,
    equal(j(e21),e10),
    inference(rew,[status(thm),theory(equality)],[472,51]),
    [iquote('4:Rew:472.0,51.0')] ).

cnf(492,plain,
    equal(op1(e10,j(e24)),j(e22)),
    inference(rew,[status(thm),theory(equality)],[474,181]),
    [iquote('4:Rew:474.0,181.0')] ).

cnf(494,plain,
    equal(op1(e10,j(e22)),j(e23)),
    inference(rew,[status(thm),theory(equality)],[474,183]),
    [iquote('4:Rew:474.0,183.0')] ).

cnf(497,plain,
    equal(op1(e10,e10),j(e24)),
    inference(rew,[status(thm),theory(equality)],[474,184]),
    [iquote('4:Rew:474.0,184.0')] ).

cnf(505,plain,
    equal(j(e24),e10),
    inference(rew,[status(thm),theory(equality)],[56,497]),
    [iquote('4:Rew:56.0,497.0')] ).

cnf(529,plain,
    equal(j(e22),e10),
    inference(rew,[status(thm),theory(equality)],[56,492,505]),
    [iquote('4:Rew:56.0,492.0,505.0,492.0')] ).

cnf(535,plain,
    equal(j(e23),e10),
    inference(rew,[status(thm),theory(equality)],[56,494,529]),
    [iquote('4:Rew:56.0,494.0,529.0,494.0')] ).

cnf(536,plain,
    equal(h(e10),e23),
    inference(rew,[status(thm),theory(equality)],[535,49]),
    [iquote('4:Rew:535.0,49.0')] ).

cnf(537,plain,
    equal(e23,e21),
    inference(rew,[status(thm),theory(equality)],[472,536]),
    [iquote('4:Rew:472.0,536.0')] ).

cnf(538,plain,
    $false,
    inference(mrr,[status(thm)],[537,16]),
    [iquote('4:MRR:537.0,16.0')] ).

cnf(553,plain,
    ~ equal(h(e10),e21),
    inference(spt,[spt(split,[position(s2s2s2sa)])],[538,472]),
    [iquote('4:Spt:538.0,471.0,472.0')] ).

cnf(554,plain,
    equal(h(e10),e20),
    inference(spt,[spt(split,[position(s2s2s2s2)])],[471]),
    [iquote('4:Spt:538.0,471.1')] ).

cnf(557,plain,
    equal(j(e20),e10),
    inference(rew,[status(thm),theory(equality)],[554,51]),
    [iquote('4:Rew:554.0,51.0')] ).

cnf(561,plain,
    equal(op2(h(e14),h(e13)),e20),
    inference(rew,[status(thm),theory(equality)],[554,192]),
    [iquote('4:Rew:554.0,192.0')] ).

cnf(562,plain,
    equal(op2(h(e14),e20),h(e14)),
    inference(rew,[status(thm),theory(equality)],[554,195]),
    [iquote('4:Rew:554.0,195.0')] ).

cnf(565,plain,
    equal(op2(h(e12),h(e11)),e20),
    inference(rew,[status(thm),theory(equality)],[554,204]),
    [iquote('4:Rew:554.0,204.0')] ).

cnf(566,plain,
    equal(op2(h(e12),e20),h(e12)),
    inference(rew,[status(thm),theory(equality)],[554,205]),
    [iquote('4:Rew:554.0,205.0')] ).

cnf(570,plain,
    equal(op2(e20,h(e13)),h(e13)),
    inference(rew,[status(thm),theory(equality)],[554,212]),
    [iquote('4:Rew:554.0,212.0')] ).

cnf(588,plain,
    equal(h(e11),e24),
    inference(spt,[spt(split,[position(s2s2s2s2s1)])],[164]),
    [iquote('5:Spt:164.0')] ).

cnf(596,plain,
    equal(op2(e24,h(e13)),h(e12)),
    inference(rew,[status(thm),theory(equality)],[588,207]),
    [iquote('5:Rew:588.0,207.0')] ).

cnf(597,plain,
    equal(op2(e24,e24),h(e14)),
    inference(rew,[status(thm),theory(equality)],[588,209]),
    [iquote('5:Rew:588.0,209.0')] ).

cnf(617,plain,
    equal(h(e14),e20),
    inference(rew,[status(thm),theory(equality)],[105,597]),
    [iquote('5:Rew:105.0,597.0')] ).

cnf(619,plain,
    equal(op2(e20,e20),h(e12)),
    inference(rew,[status(thm),theory(equality)],[617,191]),
    [iquote('5:Rew:617.0,191.0')] ).

cnf(622,plain,
    equal(op2(e20,h(e13)),e20),
    inference(rew,[status(thm),theory(equality)],[617,561]),
    [iquote('5:Rew:617.0,561.0')] ).

cnf(628,plain,
    equal(h(e12),e20),
    inference(rew,[status(thm),theory(equality)],[81,619]),
    [iquote('5:Rew:81.0,619.0')] ).

cnf(641,plain,
    equal(h(e13),e20),
    inference(rew,[status(thm),theory(equality)],[570,622]),
    [iquote('5:Rew:570.0,622.0')] ).

cnf(661,plain,
    equal(e24,e20),
    inference(rew,[status(thm),theory(equality)],[101,596,641,628]),
    [iquote('5:Rew:101.0,596.0,641.0,596.0,628.0,596.0')] ).

cnf(662,plain,
    $false,
    inference(mrr,[status(thm)],[661,14]),
    [iquote('5:MRR:661.0,14.0')] ).

cnf(665,plain,
    ~ equal(h(e11),e24),
    inference(spt,[spt(split,[position(s2s2s2s2sa)])],[662,588]),
    [iquote('5:Spt:662.0,164.0,588.0')] ).

cnf(666,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:662.0,164.1,164.2,164.3,164.4')] ).

cnf(667,plain,
    equal(h(e11),e23),
    inference(spt,[spt(split,[position(s2s2s2s2s2s1)])],[666]),
    [iquote('6:Spt:666.0')] ).

cnf(668,plain,
    equal(j(e23),e11),
    inference(rew,[status(thm),theory(equality)],[667,52]),
    [iquote('6:Rew:667.0,52.0')] ).

cnf(674,plain,
    equal(op2(e23,e23),h(e14)),
    inference(rew,[status(thm),theory(equality)],[667,209]),
    [iquote('6:Rew:667.0,209.0')] ).

cnf(685,plain,
    equal(op1(j(e22),e11),j(e21)),
    inference(rew,[status(thm),theory(equality)],[668,177]),
    [iquote('6:Rew:668.0,177.0')] ).

cnf(691,plain,
    equal(op1(j(e24),e11),j(e22)),
    inference(rew,[status(thm),theory(equality)],[668,167]),
    [iquote('6:Rew:668.0,167.0')] ).

cnf(695,plain,
    equal(h(e14),e24),
    inference(rew,[status(thm),theory(equality)],[99,674]),
    [iquote('6:Rew:99.0,674.0')] ).

cnf(696,plain,
    equal(j(e24),e14),
    inference(rew,[status(thm),theory(equality)],[695,55]),
    [iquote('6:Rew:695.0,55.0')] ).

cnf(711,plain,
    equal(op1(j(e21),j(e21)),e14),
    inference(rew,[status(thm),theory(equality)],[696,184]),
    [iquote('6:Rew:696.0,184.0')] ).

cnf(755,plain,
    equal(j(e22),e13),
    inference(rew,[status(thm),theory(equality)],[77,691,696]),
    [iquote('6:Rew:77.0,691.0,696.0,691.0')] ).

cnf(762,plain,
    equal(op1(e13,e11),j(e21)),
    inference(rew,[status(thm),theory(equality)],[755,685]),
    [iquote('6:Rew:755.0,685.0')] ).

cnf(771,plain,
    equal(j(e21),e12),
    inference(rew,[status(thm),theory(equality)],[72,762]),
    [iquote('6:Rew:72.0,762.0')] ).

cnf(799,plain,
    equal(e14,e13),
    inference(rew,[status(thm),theory(equality)],[68,711,771]),
    [iquote('6:Rew:68.0,711.0,771.0,711.0')] ).

cnf(800,plain,
    $false,
    inference(mrr,[status(thm)],[799,10]),
    [iquote('6:MRR:799.0,10.0')] ).

cnf(801,plain,
    ~ equal(h(e11),e23),
    inference(spt,[spt(split,[position(s2s2s2s2s2sa)])],[800,667]),
    [iquote('6:Spt:800.0,666.0,667.0')] ).

cnf(802,plain,
    ( equal(h(e11),e22)
    | equal(h(e11),e21)
    | equal(h(e11),e20) ),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2)])],[666]),
    [iquote('6:Spt:800.0,666.1,666.2,666.3')] ).

cnf(803,plain,
    equal(h(e11),e22),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2s1)])],[802]),
    [iquote('7:Spt:802.0')] ).

cnf(805,plain,
    equal(j(e22),e11),
    inference(rew,[status(thm),theory(equality)],[803,52]),
    [iquote('7:Rew:803.0,52.0')] ).

cnf(818,plain,
    equal(op2(e22,e22),h(e14)),
    inference(rew,[status(thm),theory(equality)],[803,209]),
    [iquote('7:Rew:803.0,209.0')] ).

cnf(825,plain,
    equal(op1(e11,j(e24)),j(e23)),
    inference(rew,[status(thm),theory(equality)],[805,176]),
    [iquote('7:Rew:805.0,176.0')] ).

cnf(827,plain,
    equal(op1(e11,j(e23)),j(e21)),
    inference(rew,[status(thm),theory(equality)],[805,177]),
    [iquote('7:Rew:805.0,177.0')] ).

cnf(832,plain,
    equal(h(e14),e24),
    inference(rew,[status(thm),theory(equality)],[93,818]),
    [iquote('7:Rew:93.0,818.0')] ).

cnf(833,plain,
    equal(j(e24),e14),
    inference(rew,[status(thm),theory(equality)],[832,55]),
    [iquote('7:Rew:832.0,55.0')] ).

cnf(848,plain,
    equal(op1(j(e21),j(e21)),e14),
    inference(rew,[status(thm),theory(equality)],[833,184]),
    [iquote('7:Rew:833.0,184.0')] ).

cnf(892,plain,
    equal(j(e23),e13),
    inference(rew,[status(thm),theory(equality)],[65,825,833]),
    [iquote('7:Rew:65.0,825.0,833.0,825.0')] ).

cnf(906,plain,
    equal(j(e21),e12),
    inference(rew,[status(thm),theory(equality)],[64,827,892]),
    [iquote('7:Rew:64.0,827.0,892.0,827.0')] ).

cnf(934,plain,
    equal(e14,e13),
    inference(rew,[status(thm),theory(equality)],[68,848,906]),
    [iquote('7:Rew:68.0,848.0,906.0,848.0')] ).

cnf(935,plain,
    $false,
    inference(mrr,[status(thm)],[934,10]),
    [iquote('7:MRR:934.0,10.0')] ).

cnf(936,plain,
    ~ equal(h(e11),e22),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2sa)])],[935,803]),
    [iquote('7:Spt:935.0,802.0,803.0')] ).

cnf(937,plain,
    ( equal(h(e11),e21)
    | equal(h(e11),e20) ),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2s2)])],[802]),
    [iquote('7:Spt:935.0,802.1,802.2')] ).

cnf(938,plain,
    equal(h(e11),e21),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2s2s1)])],[937]),
    [iquote('8:Spt:937.0')] ).

cnf(940,plain,
    equal(j(e21),e11),
    inference(rew,[status(thm),theory(equality)],[938,52]),
    [iquote('8:Rew:938.0,52.0')] ).

cnf(947,plain,
    equal(op2(e21,e21),h(e14)),
    inference(rew,[status(thm),theory(equality)],[938,209]),
    [iquote('8:Rew:938.0,209.0')] ).

cnf(960,plain,
    equal(op1(e11,j(e24)),j(e22)),
    inference(rew,[status(thm),theory(equality)],[940,181]),
    [iquote('8:Rew:940.0,181.0')] ).

cnf(964,plain,
    equal(op1(e11,j(e22)),j(e23)),
    inference(rew,[status(thm),theory(equality)],[940,183]),
    [iquote('8:Rew:940.0,183.0')] ).

cnf(968,plain,
    equal(h(e14),e24),
    inference(rew,[status(thm),theory(equality)],[87,947]),
    [iquote('8:Rew:87.0,947.0')] ).

cnf(969,plain,
    equal(j(e24),e14),
    inference(rew,[status(thm),theory(equality)],[968,55]),
    [iquote('8:Rew:968.0,55.0')] ).

cnf(984,plain,
    equal(op1(j(e23),j(e23)),e14),
    inference(rew,[status(thm),theory(equality)],[969,172]),
    [iquote('8:Rew:969.0,172.0')] ).

cnf(1027,plain,
    equal(j(e22),e13),
    inference(rew,[status(thm),theory(equality)],[65,960,969]),
    [iquote('8:Rew:65.0,960.0,969.0,960.0')] ).

cnf(1041,plain,
    equal(j(e23),e12),
    inference(rew,[status(thm),theory(equality)],[64,964,1027]),
    [iquote('8:Rew:64.0,964.0,1027.0,964.0')] ).

cnf(1070,plain,
    equal(e14,e13),
    inference(rew,[status(thm),theory(equality)],[68,984,1041]),
    [iquote('8:Rew:68.0,984.0,1041.0,984.0')] ).

cnf(1071,plain,
    $false,
    inference(mrr,[status(thm)],[1070,10]),
    [iquote('8:MRR:1070.0,10.0')] ).

cnf(1072,plain,
    ~ equal(h(e11),e21),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2s2sa)])],[1071,938]),
    [iquote('8:Spt:1071.0,937.0,938.0')] ).

cnf(1073,plain,
    equal(h(e11),e20),
    inference(spt,[spt(split,[position(s2s2s2s2s2s2s2s2)])],[937]),
    [iquote('8:Spt:1071.0,937.1')] ).

cnf(1080,plain,
    equal(op2(h(e12),e20),e20),
    inference(rew,[status(thm),theory(equality)],[1073,565]),
    [iquote('8:Rew:1073.0,565.0')] ).

cnf(1084,plain,
    equal(h(e12),e20),
    inference(rew,[status(thm),theory(equality)],[1080,566]),
    [iquote('8:Rew:1080.0,566.0')] ).

cnf(1091,plain,
    equal(h(e14),e20),
    inference(rew,[status(thm),theory(equality)],[562,193,1084,1073]),
    [iquote('8:Rew:562.0,193.0,1084.0,193.0,1073.0,193.0')] ).

cnf(1093,plain,
    equal(op2(e20,h(e13)),e20),
    inference(rew,[status(thm),theory(equality)],[1091,561]),
    [iquote('8:Rew:1091.0,561.0')] ).

cnf(1099,plain,
    equal(h(e13),e20),
    inference(rew,[status(thm),theory(equality)],[570,1093]),
    [iquote('8:Rew:570.0,1093.0')] ).

cnf(1100,plain,
    equal(j(e20),e13),
    inference(rew,[status(thm),theory(equality)],[1099,54]),
    [iquote('8:Rew:1099.0,54.0')] ).

cnf(1103,plain,
    equal(e13,e10),
    inference(rew,[status(thm),theory(equality)],[557,1100]),
    [iquote('8:Rew:557.0,1100.0')] ).

cnf(1104,plain,
    $false,
    inference(mrr,[status(thm)],[1103,3]),
    [iquote('8:MRR:1103.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : ALG082+1 : TPTP v8.1.0. Released v2.7.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n023.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 : Thu Jun  9 01:39:08 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.49  
% 0.19/0.49  SPASS V 3.9 
% 0.19/0.49  SPASS beiseite: Proof found.
% 0.19/0.49  % SZS status Theorem
% 0.19/0.49  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.49  SPASS derived 480 clauses, backtracked 458 clauses, performed 8 splits and kept 886 clauses.
% 0.19/0.49  SPASS allocated 85615 KBytes.
% 0.19/0.49  SPASS spent	0:00:00.15 on the problem.
% 0.19/0.49  		0:00:00.03 for the input.
% 0.19/0.49  		0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.49  		0:00:00.00 for inferences.
% 0.19/0.49  		0:00:00.00 for the backtracking.
% 0.19/0.49  		0:00:00.05 for the reduction.
% 0.19/0.49  
% 0.19/0.49  
% 0.19/0.49  Here is a proof with depth 4, length 214 :
% 0.19/0.49  % SZS output start Refutation
% See solution above
% 0.19/0.49  Formulae used in the proof : ax1 ax2 co1 ax4 ax5
% 0.19/0.49  
%------------------------------------------------------------------------------