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