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
%------------------------------------------------------------------------------