%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG076+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 : 16
% Number of leaves : 64
% Syntax : Number of clauses : 206 ( 198 unt; 8 nHn; 206 RR)
% Number of literals : 226 ( 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('ALG076+1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(e14,e13),
file('ALG076+1.p',unknown),
[] ).
cnf(11,axiom,
~ equal(e21,e20),
file('ALG076+1.p',unknown),
[] ).
cnf(12,axiom,
~ equal(e22,e20),
file('ALG076+1.p',unknown),
[] ).
cnf(14,axiom,
~ equal(e24,e20),
file('ALG076+1.p',unknown),
[] ).
cnf(15,axiom,
~ equal(e22,e21),
file('ALG076+1.p',unknown),
[] ).
cnf(16,axiom,
~ equal(e23,e21),
file('ALG076+1.p',unknown),
[] ).
cnf(46,axiom,
equal(h(j(e20)),e20),
file('ALG076+1.p',unknown),
[] ).
cnf(47,axiom,
equal(h(j(e21)),e21),
file('ALG076+1.p',unknown),
[] ).
cnf(48,axiom,
equal(h(j(e22)),e22),
file('ALG076+1.p',unknown),
[] ).
cnf(51,axiom,
equal(j(h(e10)),e10),
file('ALG076+1.p',unknown),
[] ).
cnf(52,axiom,
equal(j(h(e11)),e11),
file('ALG076+1.p',unknown),
[] ).
cnf(54,axiom,
equal(j(h(e13)),e13),
file('ALG076+1.p',unknown),
[] ).
cnf(55,axiom,
equal(j(h(e14)),e14),
file('ALG076+1.p',unknown),
[] ).
cnf(56,axiom,
equal(op1(e10,e10),e10),
file('ALG076+1.p',unknown),
[] ).
cnf(60,axiom,
equal(op1(e10,e14),e14),
file('ALG076+1.p',unknown),
[] ).
cnf(62,axiom,
equal(op1(e11,e11),e14),
file('ALG076+1.p',unknown),
[] ).
cnf(63,axiom,
equal(op1(e11,e12),e13),
file('ALG076+1.p',unknown),
[] ).
cnf(65,axiom,
equal(op1(e11,e14),e12),
file('ALG076+1.p',unknown),
[] ).
cnf(66,axiom,
equal(op1(e12,e10),e12),
file('ALG076+1.p',unknown),
[] ).
cnf(67,axiom,
equal(op1(e12,e11),e10),
file('ALG076+1.p',unknown),
[] ).
cnf(71,axiom,
equal(op1(e13,e10),e13),
file('ALG076+1.p',unknown),
[] ).
cnf(76,axiom,
equal(op1(e14,e10),e14),
file('ALG076+1.p',unknown),
[] ).
cnf(77,axiom,
equal(op1(e14,e11),e13),
file('ALG076+1.p',unknown),
[] ).
cnf(78,axiom,
equal(op1(e14,e12),e11),
file('ALG076+1.p',unknown),
[] ).
cnf(79,axiom,
equal(op1(e14,e13),e12),
file('ALG076+1.p',unknown),
[] ).
cnf(80,axiom,
equal(op1(e14,e14),e10),
file('ALG076+1.p',unknown),
[] ).
cnf(81,axiom,
equal(op2(e20,e20),e20),
file('ALG076+1.p',unknown),
[] ).
cnf(83,axiom,
equal(op2(e20,e22),e22),
file('ALG076+1.p',unknown),
[] ).
cnf(86,axiom,
equal(op2(e21,e20),e21),
file('ALG076+1.p',unknown),
[] ).
cnf(87,axiom,
equal(op2(e21,e21),e20),
file('ALG076+1.p',unknown),
[] ).
cnf(88,axiom,
equal(op2(e21,e22),e24),
file('ALG076+1.p',unknown),
[] ).
cnf(89,axiom,
equal(op2(e21,e23),e22),
file('ALG076+1.p',unknown),
[] ).
cnf(90,axiom,
equal(op2(e21,e24),e23),
file('ALG076+1.p',unknown),
[] ).
cnf(93,axiom,
equal(op2(e22,e22),e23),
file('ALG076+1.p',unknown),
[] ).
cnf(95,axiom,
equal(op2(e22,e24),e21),
file('ALG076+1.p',unknown),
[] ).
cnf(98,axiom,
equal(op2(e23,e22),e21),
file('ALG076+1.p',unknown),
[] ).
cnf(99,axiom,
equal(op2(e23,e23),e24),
file('ALG076+1.p',unknown),
[] ).
cnf(103,axiom,
equal(op2(e24,e22),e20),
file('ALG076+1.p',unknown),
[] ).
cnf(104,axiom,
equal(op2(e24,e23),e21),
file('ALG076+1.p',unknown),
[] ).
cnf(105,axiom,
equal(op2(e24,e24),e22),
file('ALG076+1.p',unknown),
[] ).
cnf(112,axiom,
equal(op2(h(e11),h(e11)),h(op1(e11,e11))),
file('ALG076+1.p',unknown),
[] ).
cnf(113,axiom,
equal(op2(h(e11),h(e12)),h(op1(e11,e12))),
file('ALG076+1.p',unknown),
[] ).
cnf(115,axiom,
equal(op2(h(e11),h(e14)),h(op1(e11,e14))),
file('ALG076+1.p',unknown),
[] ).
cnf(116,axiom,
equal(op2(h(e12),h(e10)),h(op1(e12,e10))),
file('ALG076+1.p',unknown),
[] ).
cnf(117,axiom,
equal(op2(h(e12),h(e11)),h(op1(e12,e11))),
file('ALG076+1.p',unknown),
[] ).
cnf(126,axiom,
equal(op2(h(e14),h(e10)),h(op1(e14,e10))),
file('ALG076+1.p',unknown),
[] ).
cnf(127,axiom,
equal(op2(h(e14),h(e11)),h(op1(e14,e11))),
file('ALG076+1.p',unknown),
[] ).
cnf(128,axiom,
equal(op2(h(e14),h(e12)),h(op1(e14,e12))),
file('ALG076+1.p',unknown),
[] ).
cnf(129,axiom,
equal(op2(h(e14),h(e13)),h(op1(e14,e13))),
file('ALG076+1.p',unknown),
[] ).
cnf(133,axiom,
equal(op1(j(e20),j(e22)),j(op2(e20,e22))),
file('ALG076+1.p',unknown),
[] ).
cnf(137,axiom,
equal(op1(j(e21),j(e21)),j(op2(e21,e21))),
file('ALG076+1.p',unknown),
[] ).
cnf(138,axiom,
equal(op1(j(e21),j(e22)),j(op2(e21,e22))),
file('ALG076+1.p',unknown),
[] ).
cnf(139,axiom,
equal(op1(j(e21),j(e23)),j(op2(e21,e23))),
file('ALG076+1.p',unknown),
[] ).
cnf(140,axiom,
equal(op1(j(e21),j(e24)),j(op2(e21,e24))),
file('ALG076+1.p',unknown),
[] ).
cnf(143,axiom,
equal(op1(j(e22),j(e22)),j(op2(e22,e22))),
file('ALG076+1.p',unknown),
[] ).
cnf(145,axiom,
equal(op1(j(e22),j(e24)),j(op2(e22,e24))),
file('ALG076+1.p',unknown),
[] ).
cnf(148,axiom,
equal(op1(j(e23),j(e22)),j(op2(e23,e22))),
file('ALG076+1.p',unknown),
[] ).
cnf(149,axiom,
equal(op1(j(e23),j(e23)),j(op2(e23,e23))),
file('ALG076+1.p',unknown),
[] ).
cnf(153,axiom,
equal(op1(j(e24),j(e22)),j(op2(e24,e22))),
file('ALG076+1.p',unknown),
[] ).
cnf(154,axiom,
equal(op1(j(e24),j(e23)),j(op2(e24,e23))),
file('ALG076+1.p',unknown),
[] ).
cnf(155,axiom,
equal(op1(j(e24),j(e24)),j(op2(e24,e24))),
file('ALG076+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('ALG076+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('ALG076+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(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(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(192,plain,
equal(op2(h(e14),h(e13)),h(e12)),
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(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(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(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(580,plain,
equal(h(e11),e24),
inference(spt,[spt(split,[position(s2s2s2s2s1)])],[164]),
[iquote('5:Spt:164.0')] ).
cnf(583,plain,
equal(op2(h(e14),e24),h(e13)),
inference(rew,[status(thm),theory(equality)],[580,194]),
[iquote('5:Rew:580.0,194.0')] ).
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(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(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(623,plain,
equal(op1(e14,e14),j(e23)),
inference(rew,[status(thm),theory(equality)],[608,178]),
[iquote('5:Rew:608.0,178.0')] ).
cnf(629,plain,
equal(j(e23),e10),
inference(rew,[status(thm),theory(equality)],[80,623]),
[iquote('5:Rew:80.0,623.0')] ).
cnf(642,plain,
equal(h(e13),e21),
inference(rew,[status(thm),theory(equality)],[95,583,607]),
[iquote('5:Rew:95.0,583.0,607.0,583.0')] ).
cnf(643,plain,
equal(j(e21),e13),
inference(rew,[status(thm),theory(equality)],[642,54]),
[iquote('5:Rew:642.0,54.0')] ).
cnf(697,plain,
equal(e14,e13),
inference(rew,[status(thm),theory(equality)],[71,619,643,629]),
[iquote('5:Rew:71.0,619.0,643.0,619.0,629.0,619.0')] ).
cnf(698,plain,
$false,
inference(mrr,[status(thm)],[697,10]),
[iquote('5:MRR:697.0,10.0')] ).
cnf(699,plain,
~ equal(h(e11),e24),
inference(spt,[spt(split,[position(s2s2s2s2sa)])],[698,580]),
[iquote('5:Spt:698.0,164.0,580.0')] ).
cnf(700,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:698.0,164.1,164.2,164.3,164.4')] ).
cnf(701,plain,
equal(h(e11),e23),
inference(spt,[spt(split,[position(s2s2s2s2s2s1)])],[700]),
[iquote('6:Spt:700.0')] ).
cnf(702,plain,
equal(j(e23),e11),
inference(rew,[status(thm),theory(equality)],[701,52]),
[iquote('6:Rew:701.0,52.0')] ).
cnf(708,plain,
equal(op2(e23,e23),h(e14)),
inference(rew,[status(thm),theory(equality)],[701,209]),
[iquote('6:Rew:701.0,209.0')] ).
cnf(724,plain,
equal(op1(j(e24),e11),j(e21)),
inference(rew,[status(thm),theory(equality)],[702,167]),
[iquote('6:Rew:702.0,167.0')] ).
cnf(729,plain,
equal(h(e14),e24),
inference(rew,[status(thm),theory(equality)],[99,708]),
[iquote('6:Rew:99.0,708.0')] ).
cnf(730,plain,
equal(j(e24),e14),
inference(rew,[status(thm),theory(equality)],[729,55]),
[iquote('6:Rew:729.0,55.0')] ).
cnf(742,plain,
equal(op1(e14,e14),j(e22)),
inference(rew,[status(thm),theory(equality)],[730,166]),
[iquote('6:Rew:730.0,166.0')] ).
cnf(745,plain,
equal(op1(j(e22),e14),j(e21)),
inference(rew,[status(thm),theory(equality)],[730,176]),
[iquote('6:Rew:730.0,176.0')] ).
cnf(751,plain,
equal(j(e22),e10),
inference(rew,[status(thm),theory(equality)],[80,742]),
[iquote('6:Rew:80.0,742.0')] ).
cnf(797,plain,
equal(j(e21),e13),
inference(rew,[status(thm),theory(equality)],[77,724,730]),
[iquote('6:Rew:77.0,724.0,730.0,724.0')] ).
cnf(829,plain,
equal(e14,e13),
inference(rew,[status(thm),theory(equality)],[60,745,751,797]),
[iquote('6:Rew:60.0,745.0,751.0,745.0,797.0,745.0')] ).
cnf(830,plain,
$false,
inference(mrr,[status(thm)],[829,10]),
[iquote('6:MRR:829.0,10.0')] ).
cnf(831,plain,
~ equal(h(e11),e23),
inference(spt,[spt(split,[position(s2s2s2s2s2sa)])],[830,701]),
[iquote('6:Spt:830.0,700.0,701.0')] ).
cnf(832,plain,
( equal(h(e11),e22)
| equal(h(e11),e21)
| equal(h(e11),e20) ),
inference(spt,[spt(split,[position(s2s2s2s2s2s2)])],[700]),
[iquote('6:Spt:830.0,700.1,700.2,700.3')] ).
cnf(833,plain,
equal(h(e11),e22),
inference(spt,[spt(split,[position(s2s2s2s2s2s2s1)])],[832]),
[iquote('7:Spt:832.0')] ).
cnf(842,plain,
equal(op2(h(e14),e22),h(e13)),
inference(rew,[status(thm),theory(equality)],[833,194]),
[iquote('7:Rew:833.0,194.0')] ).
cnf(848,plain,
equal(op2(e22,e22),h(e14)),
inference(rew,[status(thm),theory(equality)],[833,209]),
[iquote('7:Rew:833.0,209.0')] ).
cnf(862,plain,
equal(h(e14),e23),
inference(rew,[status(thm),theory(equality)],[93,848]),
[iquote('7:Rew:93.0,848.0')] ).
cnf(863,plain,
equal(j(e23),e14),
inference(rew,[status(thm),theory(equality)],[862,55]),
[iquote('7:Rew:862.0,55.0')] ).
cnf(877,plain,
equal(op1(j(e21),j(e24)),e14),
inference(rew,[status(thm),theory(equality)],[863,181]),
[iquote('7:Rew:863.0,181.0')] ).
cnf(878,plain,
equal(op1(e14,e14),j(e24)),
inference(rew,[status(thm),theory(equality)],[863,172]),
[iquote('7:Rew:863.0,172.0')] ).
cnf(884,plain,
equal(j(e24),e10),
inference(rew,[status(thm),theory(equality)],[80,878]),
[iquote('7:Rew:80.0,878.0')] ).
cnf(897,plain,
equal(h(e13),e21),
inference(rew,[status(thm),theory(equality)],[98,842,862]),
[iquote('7:Rew:98.0,842.0,862.0,842.0')] ).
cnf(898,plain,
equal(j(e21),e13),
inference(rew,[status(thm),theory(equality)],[897,54]),
[iquote('7:Rew:897.0,54.0')] ).
cnf(952,plain,
equal(e14,e13),
inference(rew,[status(thm),theory(equality)],[71,877,898,884]),
[iquote('7:Rew:71.0,877.0,898.0,877.0,884.0,877.0')] ).
cnf(953,plain,
$false,
inference(mrr,[status(thm)],[952,10]),
[iquote('7:MRR:952.0,10.0')] ).
cnf(954,plain,
~ equal(h(e11),e22),
inference(spt,[spt(split,[position(s2s2s2s2s2s2sa)])],[953,833]),
[iquote('7:Spt:953.0,832.0,833.0')] ).
cnf(955,plain,
( equal(h(e11),e21)
| equal(h(e11),e20) ),
inference(spt,[spt(split,[position(s2s2s2s2s2s2s2)])],[832]),
[iquote('7:Spt:953.0,832.1,832.2')] ).
cnf(956,plain,
equal(h(e11),e21),
inference(spt,[spt(split,[position(s2s2s2s2s2s2s2s1)])],[955]),
[iquote('8:Spt:955.0')] ).
cnf(965,plain,
equal(op2(e21,e21),h(e14)),
inference(rew,[status(thm),theory(equality)],[956,209]),
[iquote('8:Rew:956.0,209.0')] ).
cnf(966,plain,
equal(op2(e21,h(e12)),h(e13)),
inference(rew,[status(thm),theory(equality)],[956,208]),
[iquote('8:Rew:956.0,208.0')] ).
cnf(967,plain,
equal(op2(e21,h(e14)),h(e12)),
inference(rew,[status(thm),theory(equality)],[956,206]),
[iquote('8:Rew:956.0,206.0')] ).
cnf(988,plain,
equal(h(e14),e20),
inference(rew,[status(thm),theory(equality)],[87,965]),
[iquote('8:Rew:87.0,965.0')] ).
cnf(996,plain,
equal(op2(e20,h(e13)),h(e12)),
inference(rew,[status(thm),theory(equality)],[988,192]),
[iquote('8:Rew:988.0,192.0')] ).
cnf(999,plain,
equal(h(e12),e21),
inference(rew,[status(thm),theory(equality)],[86,967,988]),
[iquote('8:Rew:86.0,967.0,988.0,967.0')] ).
cnf(1005,plain,
equal(op2(e21,e21),h(e13)),
inference(rew,[status(thm),theory(equality)],[999,966]),
[iquote('8:Rew:999.0,966.0')] ).
cnf(1008,plain,
equal(h(e13),e20),
inference(rew,[status(thm),theory(equality)],[87,1005]),
[iquote('8:Rew:87.0,1005.0')] ).
cnf(1031,plain,
equal(e21,e20),
inference(rew,[status(thm),theory(equality)],[81,996,1008,999]),
[iquote('8:Rew:81.0,996.0,1008.0,996.0,999.0,996.0')] ).
cnf(1032,plain,
$false,
inference(mrr,[status(thm)],[1031,11]),
[iquote('8:MRR:1031.0,11.0')] ).
cnf(1033,plain,
~ equal(h(e11),e21),
inference(spt,[spt(split,[position(s2s2s2s2s2s2s2sa)])],[1032,956]),
[iquote('8:Spt:1032.0,955.0,956.0')] ).
cnf(1034,plain,
equal(h(e11),e20),
inference(spt,[spt(split,[position(s2s2s2s2s2s2s2s2)])],[955]),
[iquote('8:Spt:1032.0,955.1')] ).
cnf(1041,plain,
equal(op2(h(e12),e20),e20),
inference(rew,[status(thm),theory(equality)],[1034,557]),
[iquote('8:Rew:1034.0,557.0')] ).
cnf(1045,plain,
equal(h(e12),e20),
inference(rew,[status(thm),theory(equality)],[1041,558]),
[iquote('8:Rew:1041.0,558.0')] ).
cnf(1059,plain,
equal(h(e14),e20),
inference(rew,[status(thm),theory(equality)],[554,193,1045,1034]),
[iquote('8:Rew:554.0,193.0,1045.0,193.0,1034.0,193.0')] ).
cnf(1060,plain,
equal(j(e20),e14),
inference(rew,[status(thm),theory(equality)],[1059,55]),
[iquote('8:Rew:1059.0,55.0')] ).
cnf(1064,plain,
equal(e14,e10),
inference(rew,[status(thm),theory(equality)],[549,1060]),
[iquote('8:Rew:549.0,1060.0')] ).
cnf(1065,plain,
$false,
inference(mrr,[status(thm)],[1064,4]),
[iquote('8:MRR:1064.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG076+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jun 8 04:19:21 EDT 2022
% 0.13/0.34 % 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/sandbox/benchmark/theBenchmark.p
% 0.18/0.47 SPASS derived 460 clauses, backtracked 458 clauses, performed 8 splits and kept 852 clauses.
% 0.18/0.47 SPASS allocated 85613 KBytes.
% 0.18/0.47 SPASS spent 0:00:00.13 on the problem.
% 0.18/0.47 0:00:00.04 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 0:00:00.03 for the reduction.
% 0.18/0.47
% 0.18/0.47
% 0.18/0.47 Here is a proof with depth 4, length 206 :
% 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
%------------------------------------------------------------------------------