TSTP Solution File: ALG075+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG075+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 75
% Syntax : Number of clauses : 235 ( 227 unt; 8 nHn; 235 RR)
% Number of literals : 255 ( 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('ALG075+1.p',unknown),
[] ).
cnf(11,axiom,
~ equal(e21,e20),
file('ALG075+1.p',unknown),
[] ).
cnf(12,axiom,
~ equal(e22,e20),
file('ALG075+1.p',unknown),
[] ).
cnf(13,axiom,
~ equal(e23,e20),
file('ALG075+1.p',unknown),
[] ).
cnf(14,axiom,
~ equal(e24,e20),
file('ALG075+1.p',unknown),
[] ).
cnf(15,axiom,
~ equal(e22,e21),
file('ALG075+1.p',unknown),
[] ).
cnf(16,axiom,
~ equal(e23,e21),
file('ALG075+1.p',unknown),
[] ).
cnf(17,axiom,
~ equal(e24,e21),
file('ALG075+1.p',unknown),
[] ).
cnf(47,axiom,
equal(h(j(e21)),e21),
file('ALG075+1.p',unknown),
[] ).
cnf(48,axiom,
equal(h(j(e22)),e22),
file('ALG075+1.p',unknown),
[] ).
cnf(51,axiom,
equal(j(h(e10)),e10),
file('ALG075+1.p',unknown),
[] ).
cnf(54,axiom,
equal(j(h(e13)),e13),
file('ALG075+1.p',unknown),
[] ).
cnf(56,axiom,
equal(op1(e10,e10),e10),
file('ALG075+1.p',unknown),
[] ).
cnf(59,axiom,
equal(op1(e10,e13),e13),
file('ALG075+1.p',unknown),
[] ).
cnf(62,axiom,
equal(op1(e11,e11),e14),
file('ALG075+1.p',unknown),
[] ).
cnf(64,axiom,
equal(op1(e11,e13),e12),
file('ALG075+1.p',unknown),
[] ).
cnf(66,axiom,
equal(op1(e12,e10),e12),
file('ALG075+1.p',unknown),
[] ).
cnf(67,axiom,
equal(op1(e12,e11),e10),
file('ALG075+1.p',unknown),
[] ).
cnf(76,axiom,
equal(op1(e14,e10),e14),
file('ALG075+1.p',unknown),
[] ).
cnf(78,axiom,
equal(op1(e14,e12),e11),
file('ALG075+1.p',unknown),
[] ).
cnf(79,axiom,
equal(op1(e14,e13),e10),
file('ALG075+1.p',unknown),
[] ).
cnf(80,axiom,
equal(op1(e14,e14),e12),
file('ALG075+1.p',unknown),
[] ).
cnf(81,axiom,
equal(op2(e20,e20),e20),
file('ALG075+1.p',unknown),
[] ).
cnf(82,axiom,
equal(op2(e20,e21),e21),
file('ALG075+1.p',unknown),
[] ).
cnf(83,axiom,
equal(op2(e20,e22),e22),
file('ALG075+1.p',unknown),
[] ).
cnf(84,axiom,
equal(op2(e20,e23),e23),
file('ALG075+1.p',unknown),
[] ).
cnf(85,axiom,
equal(op2(e20,e24),e24),
file('ALG075+1.p',unknown),
[] ).
cnf(86,axiom,
equal(op2(e21,e20),e21),
file('ALG075+1.p',unknown),
[] ).
cnf(87,axiom,
equal(op2(e21,e21),e20),
file('ALG075+1.p',unknown),
[] ).
cnf(88,axiom,
equal(op2(e21,e22),e23),
file('ALG075+1.p',unknown),
[] ).
cnf(90,axiom,
equal(op2(e21,e24),e22),
file('ALG075+1.p',unknown),
[] ).
cnf(91,axiom,
equal(op2(e22,e20),e22),
file('ALG075+1.p',unknown),
[] ).
cnf(92,axiom,
equal(op2(e22,e21),e24),
file('ALG075+1.p',unknown),
[] ).
cnf(93,axiom,
equal(op2(e22,e22),e20),
file('ALG075+1.p',unknown),
[] ).
cnf(94,axiom,
equal(op2(e22,e23),e21),
file('ALG075+1.p',unknown),
[] ).
cnf(95,axiom,
equal(op2(e22,e24),e23),
file('ALG075+1.p',unknown),
[] ).
cnf(96,axiom,
equal(op2(e23,e20),e23),
file('ALG075+1.p',unknown),
[] ).
cnf(97,axiom,
equal(op2(e23,e21),e22),
file('ALG075+1.p',unknown),
[] ).
cnf(98,axiom,
equal(op2(e23,e22),e24),
file('ALG075+1.p',unknown),
[] ).
cnf(99,axiom,
equal(op2(e23,e23),e20),
file('ALG075+1.p',unknown),
[] ).
cnf(100,axiom,
equal(op2(e23,e24),e21),
file('ALG075+1.p',unknown),
[] ).
cnf(101,axiom,
equal(op2(e24,e20),e24),
file('ALG075+1.p',unknown),
[] ).
cnf(102,axiom,
equal(op2(e24,e21),e23),
file('ALG075+1.p',unknown),
[] ).
cnf(105,axiom,
equal(op2(e24,e24),e20),
file('ALG075+1.p',unknown),
[] ).
cnf(109,axiom,
equal(op2(h(e10),h(e13)),h(op1(e10,e13))),
file('ALG075+1.p',unknown),
[] ).
cnf(112,axiom,
equal(op2(h(e11),h(e11)),h(op1(e11,e11))),
file('ALG075+1.p',unknown),
[] ).
cnf(114,axiom,
equal(op2(h(e11),h(e13)),h(op1(e11,e13))),
file('ALG075+1.p',unknown),
[] ).
cnf(116,axiom,
equal(op2(h(e12),h(e10)),h(op1(e12,e10))),
file('ALG075+1.p',unknown),
[] ).
cnf(117,axiom,
equal(op2(h(e12),h(e11)),h(op1(e12,e11))),
file('ALG075+1.p',unknown),
[] ).
cnf(126,axiom,
equal(op2(h(e14),h(e10)),h(op1(e14,e10))),
file('ALG075+1.p',unknown),
[] ).
cnf(128,axiom,
equal(op2(h(e14),h(e12)),h(op1(e14,e12))),
file('ALG075+1.p',unknown),
[] ).
cnf(129,axiom,
equal(op2(h(e14),h(e13)),h(op1(e14,e13))),
file('ALG075+1.p',unknown),
[] ).
cnf(130,axiom,
equal(op2(h(e14),h(e14)),h(op1(e14,e14))),
file('ALG075+1.p',unknown),
[] ).
cnf(132,axiom,
equal(op1(j(e20),j(e21)),j(op2(e20,e21))),
file('ALG075+1.p',unknown),
[] ).
cnf(133,axiom,
equal(op1(j(e20),j(e22)),j(op2(e20,e22))),
file('ALG075+1.p',unknown),
[] ).
cnf(134,axiom,
equal(op1(j(e20),j(e23)),j(op2(e20,e23))),
file('ALG075+1.p',unknown),
[] ).
cnf(135,axiom,
equal(op1(j(e20),j(e24)),j(op2(e20,e24))),
file('ALG075+1.p',unknown),
[] ).
cnf(136,axiom,
equal(op1(j(e21),j(e20)),j(op2(e21,e20))),
file('ALG075+1.p',unknown),
[] ).
cnf(137,axiom,
equal(op1(j(e21),j(e21)),j(op2(e21,e21))),
file('ALG075+1.p',unknown),
[] ).
cnf(138,axiom,
equal(op1(j(e21),j(e22)),j(op2(e21,e22))),
file('ALG075+1.p',unknown),
[] ).
cnf(140,axiom,
equal(op1(j(e21),j(e24)),j(op2(e21,e24))),
file('ALG075+1.p',unknown),
[] ).
cnf(141,axiom,
equal(op1(j(e22),j(e20)),j(op2(e22,e20))),
file('ALG075+1.p',unknown),
[] ).
cnf(142,axiom,
equal(op1(j(e22),j(e21)),j(op2(e22,e21))),
file('ALG075+1.p',unknown),
[] ).
cnf(143,axiom,
equal(op1(j(e22),j(e22)),j(op2(e22,e22))),
file('ALG075+1.p',unknown),
[] ).
cnf(144,axiom,
equal(op1(j(e22),j(e23)),j(op2(e22,e23))),
file('ALG075+1.p',unknown),
[] ).
cnf(145,axiom,
equal(op1(j(e22),j(e24)),j(op2(e22,e24))),
file('ALG075+1.p',unknown),
[] ).
cnf(146,axiom,
equal(op1(j(e23),j(e20)),j(op2(e23,e20))),
file('ALG075+1.p',unknown),
[] ).
cnf(147,axiom,
equal(op1(j(e23),j(e21)),j(op2(e23,e21))),
file('ALG075+1.p',unknown),
[] ).
cnf(148,axiom,
equal(op1(j(e23),j(e22)),j(op2(e23,e22))),
file('ALG075+1.p',unknown),
[] ).
cnf(149,axiom,
equal(op1(j(e23),j(e23)),j(op2(e23,e23))),
file('ALG075+1.p',unknown),
[] ).
cnf(150,axiom,
equal(op1(j(e23),j(e24)),j(op2(e23,e24))),
file('ALG075+1.p',unknown),
[] ).
cnf(152,axiom,
equal(op1(j(e24),j(e21)),j(op2(e24,e21))),
file('ALG075+1.p',unknown),
[] ).
cnf(155,axiom,
equal(op1(j(e24),j(e24)),j(op2(e24,e24))),
file('ALG075+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('ALG075+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('ALG075+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(169,plain,
equal(op1(j(e24),j(e21)),j(e23)),
inference(rew,[status(thm),theory(equality)],[102,152]),
[iquote('0:Rew:102.0,152.0')] ).
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(e20)),
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(e24)),
inference(rew,[status(thm),theory(equality)],[98,148]),
[iquote('0:Rew:98.0,148.0')] ).
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(e20)),
inference(rew,[status(thm),theory(equality)],[93,143]),
[iquote('0:Rew:93.0,143.0')] ).
cnf(179,plain,
equal(op1(j(e22),j(e21)),j(e24)),
inference(rew,[status(thm),theory(equality)],[92,142]),
[iquote('0:Rew:92.0,142.0')] ).
cnf(180,plain,
equal(op1(j(e22),j(e20)),j(e22)),
inference(rew,[status(thm),theory(equality)],[91,141]),
[iquote('0:Rew:91.0,141.0')] ).
cnf(181,plain,
equal(op1(j(e21),j(e24)),j(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(e20)),
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(186,plain,
equal(op1(j(e20),j(e24)),j(e24)),
inference(rew,[status(thm),theory(equality)],[85,135]),
[iquote('0:Rew:85.0,135.0')] ).
cnf(187,plain,
equal(op1(j(e20),j(e23)),j(e23)),
inference(rew,[status(thm),theory(equality)],[84,134]),
[iquote('0:Rew:84.0,134.0')] ).
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(189,plain,
equal(op1(j(e20),j(e21)),j(e21)),
inference(rew,[status(thm),theory(equality)],[82,132]),
[iquote('0:Rew:82.0,132.0')] ).
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(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(252,plain,
equal(op1(j(e21),j(e21)),e10),
inference(rew,[status(thm),theory(equality)],[246,184]),
[iquote('1:Rew:246.0,184.0')] ).
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)],[252,264,277]),
[iquote('1:Rew:252.0,264.0,277.0,264.0')] ).
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(325,plain,
equal(op1(e10,j(e24)),j(e21)),
inference(rew,[status(thm),theory(equality)],[306,171]),
[iquote('2:Rew:306.0,171.0')] ).
cnf(330,plain,
equal(op1(e10,e10),j(e20)),
inference(rew,[status(thm),theory(equality)],[306,172]),
[iquote('2:Rew:306.0,172.0')] ).
cnf(333,plain,
equal(op1(e10,j(e21)),j(e22)),
inference(rew,[status(thm),theory(equality)],[306,174]),
[iquote('2:Rew:306.0,174.0')] ).
cnf(336,plain,
equal(j(e20),e10),
inference(rew,[status(thm),theory(equality)],[56,330]),
[iquote('2:Rew:56.0,330.0')] ).
cnf(338,plain,
equal(op1(e10,j(e24)),j(e24)),
inference(rew,[status(thm),theory(equality)],[336,186]),
[iquote('2:Rew:336.0,186.0')] ).
cnf(340,plain,
equal(op1(j(e24),j(e24)),e10),
inference(rew,[status(thm),theory(equality)],[336,166]),
[iquote('2:Rew:336.0,166.0')] ).
cnf(342,plain,
equal(op1(e10,j(e21)),j(e21)),
inference(rew,[status(thm),theory(equality)],[336,189]),
[iquote('2:Rew:336.0,189.0')] ).
cnf(352,plain,
equal(j(e24),j(e21)),
inference(rew,[status(thm),theory(equality)],[325,338]),
[iquote('2:Rew:325.0,338.0')] ).
cnf(354,plain,
equal(op1(j(e21),j(e21)),j(e22)),
inference(rew,[status(thm),theory(equality)],[352,181]),
[iquote('2:Rew:352.0,181.0')] ).
cnf(367,plain,
equal(op1(j(e21),j(e21)),e10),
inference(rew,[status(thm),theory(equality)],[352,340]),
[iquote('2:Rew:352.0,340.0')] ).
cnf(368,plain,
equal(j(e22),j(e21)),
inference(rew,[status(thm),theory(equality)],[333,342]),
[iquote('2:Rew:333.0,342.0')] ).
cnf(382,plain,
equal(j(e21),e10),
inference(rew,[status(thm),theory(equality)],[367,354,368]),
[iquote('2:Rew:367.0,354.0,368.0,354.0')] ).
cnf(383,plain,
equal(h(e10),e21),
inference(rew,[status(thm),theory(equality)],[382,47]),
[iquote('2:Rew:382.0,47.0')] ).
cnf(389,plain,
equal(e23,e21),
inference(rew,[status(thm),theory(equality)],[305,383]),
[iquote('2:Rew:305.0,383.0')] ).
cnf(390,plain,
$false,
inference(mrr,[status(thm)],[389,16]),
[iquote('2:MRR:389.0,16.0')] ).
cnf(393,plain,
~ equal(h(e10),e23),
inference(spt,[spt(split,[position(s2sa)])],[390,305]),
[iquote('2:Spt:390.0,304.0,305.0')] ).
cnf(394,plain,
( equal(h(e10),e22)
| equal(h(e10),e21)
| equal(h(e10),e20) ),
inference(spt,[spt(split,[position(s2s2)])],[304]),
[iquote('2:Spt:390.0,304.1,304.2,304.3')] ).
cnf(395,plain,
equal(h(e10),e22),
inference(spt,[spt(split,[position(s2s2s1)])],[394]),
[iquote('3:Spt:394.0')] ).
cnf(397,plain,
equal(j(e22),e10),
inference(rew,[status(thm),theory(equality)],[395,51]),
[iquote('3:Rew:395.0,51.0')] ).
cnf(414,plain,
equal(op1(e10,j(e23)),j(e21)),
inference(rew,[status(thm),theory(equality)],[397,177]),
[iquote('3:Rew:397.0,177.0')] ).
cnf(417,plain,
equal(op1(j(e23),e10),j(e24)),
inference(rew,[status(thm),theory(equality)],[397,173]),
[iquote('3:Rew:397.0,173.0')] ).
cnf(419,plain,
equal(op1(e10,e10),j(e20)),
inference(rew,[status(thm),theory(equality)],[397,178]),
[iquote('3:Rew:397.0,178.0')] ).
cnf(427,plain,
equal(j(e20),e10),
inference(rew,[status(thm),theory(equality)],[56,419]),
[iquote('3:Rew:56.0,419.0')] ).
cnf(430,plain,
equal(op1(j(e23),e10),j(e23)),
inference(rew,[status(thm),theory(equality)],[427,175]),
[iquote('3:Rew:427.0,175.0')] ).
cnf(431,plain,
equal(op1(e10,j(e23)),j(e23)),
inference(rew,[status(thm),theory(equality)],[427,187]),
[iquote('3:Rew:427.0,187.0')] ).
cnf(432,plain,
equal(op1(j(e21),j(e21)),e10),
inference(rew,[status(thm),theory(equality)],[427,184]),
[iquote('3:Rew:427.0,184.0')] ).
cnf(443,plain,
equal(j(e24),j(e23)),
inference(rew,[status(thm),theory(equality)],[417,430]),
[iquote('3:Rew:417.0,430.0')] ).
cnf(445,plain,
equal(op1(j(e23),j(e21)),j(e23)),
inference(rew,[status(thm),theory(equality)],[443,169]),
[iquote('3:Rew:443.0,169.0')] ).
cnf(457,plain,
equal(j(e23),j(e21)),
inference(rew,[status(thm),theory(equality)],[414,431]),
[iquote('3:Rew:414.0,431.0')] ).
cnf(476,plain,
equal(j(e21),e10),
inference(rew,[status(thm),theory(equality)],[432,445,457]),
[iquote('3:Rew:432.0,445.0,457.0,445.0')] ).
cnf(477,plain,
equal(h(e10),e21),
inference(rew,[status(thm),theory(equality)],[476,47]),
[iquote('3:Rew:476.0,47.0')] ).
cnf(483,plain,
equal(e22,e21),
inference(rew,[status(thm),theory(equality)],[395,477]),
[iquote('3:Rew:395.0,477.0')] ).
cnf(484,plain,
$false,
inference(mrr,[status(thm)],[483,15]),
[iquote('3:MRR:483.0,15.0')] ).
cnf(487,plain,
~ equal(h(e10),e22),
inference(spt,[spt(split,[position(s2s2sa)])],[484,395]),
[iquote('3:Spt:484.0,394.0,395.0')] ).
cnf(488,plain,
( equal(h(e10),e21)
| equal(h(e10),e20) ),
inference(spt,[spt(split,[position(s2s2s2)])],[394]),
[iquote('3:Spt:484.0,394.1,394.2')] ).
cnf(489,plain,
equal(h(e10),e21),
inference(spt,[spt(split,[position(s2s2s2s1)])],[488]),
[iquote('4:Spt:488.0')] ).
cnf(491,plain,
equal(j(e21),e10),
inference(rew,[status(thm),theory(equality)],[489,51]),
[iquote('4:Rew:489.0,51.0')] ).
cnf(509,plain,
equal(op1(j(e22),e10),j(e24)),
inference(rew,[status(thm),theory(equality)],[491,179]),
[iquote('4:Rew:491.0,179.0')] ).
cnf(511,plain,
equal(op1(e10,j(e22)),j(e23)),
inference(rew,[status(thm),theory(equality)],[491,183]),
[iquote('4:Rew:491.0,183.0')] ).
cnf(516,plain,
equal(op1(e10,e10),j(e20)),
inference(rew,[status(thm),theory(equality)],[491,184]),
[iquote('4:Rew:491.0,184.0')] ).
cnf(522,plain,
equal(j(e20),e10),
inference(rew,[status(thm),theory(equality)],[56,516]),
[iquote('4:Rew:56.0,516.0')] ).
cnf(524,plain,
equal(op1(e10,j(e22)),j(e22)),
inference(rew,[status(thm),theory(equality)],[522,188]),
[iquote('4:Rew:522.0,188.0')] ).
cnf(525,plain,
equal(op1(j(e22),e10),j(e22)),
inference(rew,[status(thm),theory(equality)],[522,180]),
[iquote('4:Rew:522.0,180.0')] ).
cnf(526,plain,
equal(op1(j(e22),j(e22)),e10),
inference(rew,[status(thm),theory(equality)],[522,178]),
[iquote('4:Rew:522.0,178.0')] ).
cnf(538,plain,
equal(j(e23),j(e22)),
inference(rew,[status(thm),theory(equality)],[511,524]),
[iquote('4:Rew:511.0,524.0')] ).
cnf(540,plain,
equal(op1(j(e22),j(e24)),j(e22)),
inference(rew,[status(thm),theory(equality)],[538,176]),
[iquote('4:Rew:538.0,176.0')] ).
cnf(552,plain,
equal(j(e24),j(e22)),
inference(rew,[status(thm),theory(equality)],[509,525]),
[iquote('4:Rew:509.0,525.0')] ).
cnf(569,plain,
equal(j(e22),e10),
inference(rew,[status(thm),theory(equality)],[526,540,552]),
[iquote('4:Rew:526.0,540.0,552.0,540.0')] ).
cnf(570,plain,
equal(h(e10),e22),
inference(rew,[status(thm),theory(equality)],[569,48]),
[iquote('4:Rew:569.0,48.0')] ).
cnf(576,plain,
equal(e22,e21),
inference(rew,[status(thm),theory(equality)],[489,570]),
[iquote('4:Rew:489.0,570.0')] ).
cnf(577,plain,
$false,
inference(mrr,[status(thm)],[576,15]),
[iquote('4:MRR:576.0,15.0')] ).
cnf(580,plain,
~ equal(h(e10),e21),
inference(spt,[spt(split,[position(s2s2s2sa)])],[577,489]),
[iquote('4:Spt:577.0,488.0,489.0')] ).
cnf(581,plain,
equal(h(e10),e20),
inference(spt,[spt(split,[position(s2s2s2s2)])],[488]),
[iquote('4:Spt:577.0,488.1')] ).
cnf(584,plain,
equal(j(e20),e10),
inference(rew,[status(thm),theory(equality)],[581,51]),
[iquote('4:Rew:581.0,51.0')] ).
cnf(588,plain,
equal(op2(h(e14),h(e13)),e20),
inference(rew,[status(thm),theory(equality)],[581,192]),
[iquote('4:Rew:581.0,192.0')] ).
cnf(589,plain,
equal(op2(h(e14),e20),h(e14)),
inference(rew,[status(thm),theory(equality)],[581,195]),
[iquote('4:Rew:581.0,195.0')] ).
cnf(592,plain,
equal(op2(h(e12),h(e11)),e20),
inference(rew,[status(thm),theory(equality)],[581,204]),
[iquote('4:Rew:581.0,204.0')] ).
cnf(593,plain,
equal(op2(h(e12),e20),h(e12)),
inference(rew,[status(thm),theory(equality)],[581,205]),
[iquote('4:Rew:581.0,205.0')] ).
cnf(597,plain,
equal(op2(e20,h(e13)),h(e13)),
inference(rew,[status(thm),theory(equality)],[581,212]),
[iquote('4:Rew:581.0,212.0')] ).
cnf(615,plain,
equal(h(e11),e24),
inference(spt,[spt(split,[position(s2s2s2s2s1)])],[164]),
[iquote('5:Spt:164.0')] ).
cnf(623,plain,
equal(op2(e24,h(e13)),h(e12)),
inference(rew,[status(thm),theory(equality)],[615,207]),
[iquote('5:Rew:615.0,207.0')] ).
cnf(624,plain,
equal(op2(e24,e24),h(e14)),
inference(rew,[status(thm),theory(equality)],[615,209]),
[iquote('5:Rew:615.0,209.0')] ).
cnf(644,plain,
equal(h(e14),e20),
inference(rew,[status(thm),theory(equality)],[105,624]),
[iquote('5:Rew:105.0,624.0')] ).
cnf(646,plain,
equal(op2(e20,e20),h(e12)),
inference(rew,[status(thm),theory(equality)],[644,191]),
[iquote('5:Rew:644.0,191.0')] ).
cnf(649,plain,
equal(op2(e20,h(e13)),e20),
inference(rew,[status(thm),theory(equality)],[644,588]),
[iquote('5:Rew:644.0,588.0')] ).
cnf(655,plain,
equal(h(e12),e20),
inference(rew,[status(thm),theory(equality)],[81,646]),
[iquote('5:Rew:81.0,646.0')] ).
cnf(668,plain,
equal(h(e13),e20),
inference(rew,[status(thm),theory(equality)],[597,649]),
[iquote('5:Rew:597.0,649.0')] ).
cnf(688,plain,
equal(e24,e20),
inference(rew,[status(thm),theory(equality)],[101,623,668,655]),
[iquote('5:Rew:101.0,623.0,668.0,623.0,655.0,623.0')] ).
cnf(689,plain,
$false,
inference(mrr,[status(thm)],[688,14]),
[iquote('5:MRR:688.0,14.0')] ).
cnf(692,plain,
~ equal(h(e11),e24),
inference(spt,[spt(split,[position(s2s2s2s2sa)])],[689,615]),
[iquote('5:Spt:689.0,164.0,615.0')] ).
cnf(693,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:689.0,164.1,164.2,164.3,164.4')] ).
cnf(694,plain,
equal(h(e11),e23),
inference(spt,[spt(split,[position(s2s2s2s2s2s1)])],[693]),
[iquote('6:Spt:693.0')] ).
cnf(701,plain,
equal(op2(e23,e23),h(e14)),
inference(rew,[status(thm),theory(equality)],[694,209]),
[iquote('6:Rew:694.0,209.0')] ).
cnf(708,plain,
equal(op2(h(e14),h(e12)),e23),
inference(rew,[status(thm),theory(equality)],[694,193]),
[iquote('6:Rew:694.0,193.0')] ).
cnf(724,plain,
equal(h(e14),e20),
inference(rew,[status(thm),theory(equality)],[99,701]),
[iquote('6:Rew:99.0,701.0')] ).
cnf(732,plain,
equal(op2(e20,e20),h(e12)),
inference(rew,[status(thm),theory(equality)],[724,191]),
[iquote('6:Rew:724.0,191.0')] ).
cnf(743,plain,
equal(h(e12),e20),
inference(rew,[status(thm),theory(equality)],[81,732]),
[iquote('6:Rew:81.0,732.0')] ).
cnf(767,plain,
equal(e23,e20),
inference(rew,[status(thm),theory(equality)],[81,708,724,743]),
[iquote('6:Rew:81.0,708.0,724.0,708.0,743.0,708.0')] ).
cnf(768,plain,
$false,
inference(mrr,[status(thm)],[767,13]),
[iquote('6:MRR:767.0,13.0')] ).
cnf(772,plain,
~ equal(h(e11),e23),
inference(spt,[spt(split,[position(s2s2s2s2s2sa)])],[768,694]),
[iquote('6:Spt:768.0,693.0,694.0')] ).
cnf(773,plain,
( equal(h(e11),e22)
| equal(h(e11),e21)
| equal(h(e11),e20) ),
inference(spt,[spt(split,[position(s2s2s2s2s2s2)])],[693]),
[iquote('6:Spt:768.0,693.1,693.2,693.3')] ).
cnf(774,plain,
equal(h(e11),e22),
inference(spt,[spt(split,[position(s2s2s2s2s2s2s1)])],[773]),
[iquote('7:Spt:773.0')] ).
cnf(788,plain,
equal(op2(e22,h(e13)),h(e12)),
inference(rew,[status(thm),theory(equality)],[774,207]),
[iquote('7:Rew:774.0,207.0')] ).
cnf(789,plain,
equal(op2(e22,e22),h(e14)),
inference(rew,[status(thm),theory(equality)],[774,209]),
[iquote('7:Rew:774.0,209.0')] ).
cnf(805,plain,
equal(h(e14),e20),
inference(rew,[status(thm),theory(equality)],[93,789]),
[iquote('7:Rew:93.0,789.0')] ).
cnf(807,plain,
equal(op2(e20,h(e13)),e20),
inference(rew,[status(thm),theory(equality)],[805,588]),
[iquote('7:Rew:805.0,588.0')] ).
cnf(811,plain,
equal(op2(e20,e20),h(e12)),
inference(rew,[status(thm),theory(equality)],[805,191]),
[iquote('7:Rew:805.0,191.0')] ).
cnf(816,plain,
equal(h(e13),e20),
inference(rew,[status(thm),theory(equality)],[597,807]),
[iquote('7:Rew:597.0,807.0')] ).
cnf(824,plain,
equal(h(e12),e20),
inference(rew,[status(thm),theory(equality)],[81,811]),
[iquote('7:Rew:81.0,811.0')] ).
cnf(848,plain,
equal(e22,e20),
inference(rew,[status(thm),theory(equality)],[91,788,816,824]),
[iquote('7:Rew:91.0,788.0,816.0,788.0,824.0,788.0')] ).
cnf(849,plain,
$false,
inference(mrr,[status(thm)],[848,12]),
[iquote('7:MRR:848.0,12.0')] ).
cnf(853,plain,
~ equal(h(e11),e22),
inference(spt,[spt(split,[position(s2s2s2s2s2s2sa)])],[849,774]),
[iquote('7:Spt:849.0,773.0,774.0')] ).
cnf(854,plain,
( equal(h(e11),e21)
| equal(h(e11),e20) ),
inference(spt,[spt(split,[position(s2s2s2s2s2s2s2)])],[773]),
[iquote('7:Spt:849.0,773.1,773.2')] ).
cnf(855,plain,
equal(h(e11),e21),
inference(spt,[spt(split,[position(s2s2s2s2s2s2s2s1)])],[854]),
[iquote('8:Spt:854.0')] ).
cnf(864,plain,
equal(op2(e21,e21),h(e14)),
inference(rew,[status(thm),theory(equality)],[855,209]),
[iquote('8:Rew:855.0,209.0')] ).
cnf(871,plain,
equal(op2(h(e14),h(e12)),e21),
inference(rew,[status(thm),theory(equality)],[855,193]),
[iquote('8:Rew:855.0,193.0')] ).
cnf(887,plain,
equal(h(e14),e20),
inference(rew,[status(thm),theory(equality)],[87,864]),
[iquote('8:Rew:87.0,864.0')] ).
cnf(895,plain,
equal(op2(e20,e20),h(e12)),
inference(rew,[status(thm),theory(equality)],[887,191]),
[iquote('8:Rew:887.0,191.0')] ).
cnf(906,plain,
equal(h(e12),e20),
inference(rew,[status(thm),theory(equality)],[81,895]),
[iquote('8:Rew:81.0,895.0')] ).
cnf(930,plain,
equal(e21,e20),
inference(rew,[status(thm),theory(equality)],[81,871,887,906]),
[iquote('8:Rew:81.0,871.0,887.0,871.0,906.0,871.0')] ).
cnf(931,plain,
$false,
inference(mrr,[status(thm)],[930,11]),
[iquote('8:MRR:930.0,11.0')] ).
cnf(935,plain,
~ equal(h(e11),e21),
inference(spt,[spt(split,[position(s2s2s2s2s2s2s2sa)])],[931,855]),
[iquote('8:Spt:931.0,854.0,855.0')] ).
cnf(936,plain,
equal(h(e11),e20),
inference(spt,[spt(split,[position(s2s2s2s2s2s2s2s2)])],[854]),
[iquote('8:Spt:931.0,854.1')] ).
cnf(943,plain,
equal(op2(h(e12),e20),e20),
inference(rew,[status(thm),theory(equality)],[936,592]),
[iquote('8:Rew:936.0,592.0')] ).
cnf(947,plain,
equal(h(e12),e20),
inference(rew,[status(thm),theory(equality)],[943,593]),
[iquote('8:Rew:943.0,593.0')] ).
cnf(954,plain,
equal(h(e14),e20),
inference(rew,[status(thm),theory(equality)],[589,193,947,936]),
[iquote('8:Rew:589.0,193.0,947.0,193.0,936.0,193.0')] ).
cnf(956,plain,
equal(op2(e20,h(e13)),e20),
inference(rew,[status(thm),theory(equality)],[954,588]),
[iquote('8:Rew:954.0,588.0')] ).
cnf(962,plain,
equal(h(e13),e20),
inference(rew,[status(thm),theory(equality)],[597,956]),
[iquote('8:Rew:597.0,956.0')] ).
cnf(963,plain,
equal(j(e20),e13),
inference(rew,[status(thm),theory(equality)],[962,54]),
[iquote('8:Rew:962.0,54.0')] ).
cnf(966,plain,
equal(e13,e10),
inference(rew,[status(thm),theory(equality)],[584,963]),
[iquote('8:Rew:584.0,963.0')] ).
cnf(967,plain,
$false,
inference(mrr,[status(thm)],[966,3]),
[iquote('8:MRR:966.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : ALG075+1 : TPTP v8.1.0. Released v2.7.0.
% 0.02/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n029.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 : Wed Jun 8 18:19:06 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/sandbox2/benchmark/theBenchmark.p
% 0.19/0.49 SPASS derived 453 clauses, backtracked 404 clauses, performed 8 splits and kept 817 clauses.
% 0.19/0.49 SPASS allocated 85581 KBytes.
% 0.19/0.49 SPASS spent 0:00:00.14 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 235 :
% 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
%------------------------------------------------------------------------------