TSTP Solution File: ALG077+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG077+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 56
% Syntax : Number of clauses : 180 ( 172 unt; 8 nHn; 180 RR)
% Number of literals : 200 ( 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(1,axiom,
~ equal(e11,e10),
file('ALG077+1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(e14,e10),
file('ALG077+1.p',unknown),
[] ).
cnf(11,axiom,
~ equal(e21,e20),
file('ALG077+1.p',unknown),
[] ).
cnf(13,axiom,
~ equal(e23,e20),
file('ALG077+1.p',unknown),
[] ).
cnf(19,axiom,
~ equal(e24,e22),
file('ALG077+1.p',unknown),
[] ).
cnf(20,axiom,
~ equal(e24,e23),
file('ALG077+1.p',unknown),
[] ).
cnf(46,axiom,
equal(h(j(e20)),e20),
file('ALG077+1.p',unknown),
[] ).
cnf(49,axiom,
equal(h(j(e23)),e23),
file('ALG077+1.p',unknown),
[] ).
cnf(50,axiom,
equal(h(j(e24)),e24),
file('ALG077+1.p',unknown),
[] ).
cnf(51,axiom,
equal(j(h(e10)),e10),
file('ALG077+1.p',unknown),
[] ).
cnf(52,axiom,
equal(j(h(e11)),e11),
file('ALG077+1.p',unknown),
[] ).
cnf(53,axiom,
equal(j(h(e12)),e12),
file('ALG077+1.p',unknown),
[] ).
cnf(54,axiom,
equal(j(h(e13)),e13),
file('ALG077+1.p',unknown),
[] ).
cnf(55,axiom,
equal(j(h(e14)),e14),
file('ALG077+1.p',unknown),
[] ).
cnf(56,axiom,
equal(op1(e10,e10),e10),
file('ALG077+1.p',unknown),
[] ).
cnf(62,axiom,
equal(op1(e11,e11),e14),
file('ALG077+1.p',unknown),
[] ).
cnf(63,axiom,
equal(op1(e11,e12),e13),
file('ALG077+1.p',unknown),
[] ).
cnf(65,axiom,
equal(op1(e11,e14),e12),
file('ALG077+1.p',unknown),
[] ).
cnf(66,axiom,
equal(op1(e12,e10),e12),
file('ALG077+1.p',unknown),
[] ).
cnf(67,axiom,
equal(op1(e12,e11),e10),
file('ALG077+1.p',unknown),
[] ).
cnf(73,axiom,
equal(op1(e13,e12),e10),
file('ALG077+1.p',unknown),
[] ).
cnf(76,axiom,
equal(op1(e14,e10),e14),
file('ALG077+1.p',unknown),
[] ).
cnf(78,axiom,
equal(op1(e14,e12),e11),
file('ALG077+1.p',unknown),
[] ).
cnf(80,axiom,
equal(op1(e14,e14),e10),
file('ALG077+1.p',unknown),
[] ).
cnf(87,axiom,
equal(op2(e21,e21),e22),
file('ALG077+1.p',unknown),
[] ).
cnf(88,axiom,
equal(op2(e21,e22),e23),
file('ALG077+1.p',unknown),
[] ).
cnf(89,axiom,
equal(op2(e21,e23),e24),
file('ALG077+1.p',unknown),
[] ).
cnf(90,axiom,
equal(op2(e21,e24),e20),
file('ALG077+1.p',unknown),
[] ).
cnf(92,axiom,
equal(op2(e22,e21),e24),
file('ALG077+1.p',unknown),
[] ).
cnf(93,axiom,
equal(op2(e22,e22),e21),
file('ALG077+1.p',unknown),
[] ).
cnf(97,axiom,
equal(op2(e23,e21),e20),
file('ALG077+1.p',unknown),
[] ).
cnf(98,axiom,
equal(op2(e23,e22),e24),
file('ALG077+1.p',unknown),
[] ).
cnf(99,axiom,
equal(op2(e23,e23),e21),
file('ALG077+1.p',unknown),
[] ).
cnf(102,axiom,
equal(op2(e24,e21),e23),
file('ALG077+1.p',unknown),
[] ).
cnf(104,axiom,
equal(op2(e24,e23),e22),
file('ALG077+1.p',unknown),
[] ).
cnf(105,axiom,
equal(op2(e24,e24),e21),
file('ALG077+1.p',unknown),
[] ).
cnf(112,axiom,
equal(op2(h(e11),h(e11)),h(op1(e11,e11))),
file('ALG077+1.p',unknown),
[] ).
cnf(113,axiom,
equal(op2(h(e11),h(e12)),h(op1(e11,e12))),
file('ALG077+1.p',unknown),
[] ).
cnf(115,axiom,
equal(op2(h(e11),h(e14)),h(op1(e11,e14))),
file('ALG077+1.p',unknown),
[] ).
cnf(116,axiom,
equal(op2(h(e12),h(e10)),h(op1(e12,e10))),
file('ALG077+1.p',unknown),
[] ).
cnf(117,axiom,
equal(op2(h(e12),h(e11)),h(op1(e12,e11))),
file('ALG077+1.p',unknown),
[] ).
cnf(126,axiom,
equal(op2(h(e14),h(e10)),h(op1(e14,e10))),
file('ALG077+1.p',unknown),
[] ).
cnf(128,axiom,
equal(op2(h(e14),h(e12)),h(op1(e14,e12))),
file('ALG077+1.p',unknown),
[] ).
cnf(137,axiom,
equal(op1(j(e21),j(e21)),j(op2(e21,e21))),
file('ALG077+1.p',unknown),
[] ).
cnf(138,axiom,
equal(op1(j(e21),j(e22)),j(op2(e21,e22))),
file('ALG077+1.p',unknown),
[] ).
cnf(140,axiom,
equal(op1(j(e21),j(e24)),j(op2(e21,e24))),
file('ALG077+1.p',unknown),
[] ).
cnf(142,axiom,
equal(op1(j(e22),j(e21)),j(op2(e22,e21))),
file('ALG077+1.p',unknown),
[] ).
cnf(143,axiom,
equal(op1(j(e22),j(e22)),j(op2(e22,e22))),
file('ALG077+1.p',unknown),
[] ).
cnf(147,axiom,
equal(op1(j(e23),j(e21)),j(op2(e23,e21))),
file('ALG077+1.p',unknown),
[] ).
cnf(148,axiom,
equal(op1(j(e23),j(e22)),j(op2(e23,e22))),
file('ALG077+1.p',unknown),
[] ).
cnf(149,axiom,
equal(op1(j(e23),j(e23)),j(op2(e23,e23))),
file('ALG077+1.p',unknown),
[] ).
cnf(152,axiom,
equal(op1(j(e24),j(e21)),j(op2(e24,e21))),
file('ALG077+1.p',unknown),
[] ).
cnf(154,axiom,
equal(op1(j(e24),j(e23)),j(op2(e24,e23))),
file('ALG077+1.p',unknown),
[] ).
cnf(155,axiom,
equal(op1(j(e24),j(e24)),j(op2(e24,e24))),
file('ALG077+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('ALG077+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('ALG077+1.p',unknown),
[] ).
cnf(166,plain,
equal(op1(j(e24),j(e24)),j(e21)),
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(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(172,plain,
equal(op1(j(e23),j(e23)),j(e21)),
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(e20)),
inference(rew,[status(thm),theory(equality)],[97,147]),
[iquote('0:Rew:97.0,147.0')] ).
cnf(178,plain,
equal(op1(j(e22),j(e22)),j(e21)),
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(181,plain,
equal(op1(j(e21),j(e24)),j(e20)),
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(e22)),
inference(rew,[status(thm),theory(equality)],[87,137]),
[iquote('0:Rew:87.0,137.0')] ).
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(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(e21)),
inference(rew,[status(thm),theory(equality)],[217,166]),
[iquote('1:Rew:217.0,166.0')] ).
cnf(235,plain,
equal(op1(e10,j(e21)),j(e23)),
inference(rew,[status(thm),theory(equality)],[217,169]),
[iquote('1:Rew:217.0,169.0')] ).
cnf(246,plain,
equal(j(e21),e10),
inference(rew,[status(thm),theory(equality)],[56,232]),
[iquote('1:Rew:56.0,232.0')] ).
cnf(274,plain,
equal(j(e23),e10),
inference(rew,[status(thm),theory(equality)],[56,235,246]),
[iquote('1:Rew:56.0,235.0,246.0,235.0')] ).
cnf(275,plain,
equal(h(e10),e23),
inference(rew,[status(thm),theory(equality)],[274,49]),
[iquote('1:Rew:274.0,49.0')] ).
cnf(277,plain,
equal(e24,e23),
inference(rew,[status(thm),theory(equality)],[216,275]),
[iquote('1:Rew:216.0,275.0')] ).
cnf(278,plain,
$false,
inference(mrr,[status(thm)],[277,20]),
[iquote('1:MRR:277.0,20.0')] ).
cnf(292,plain,
~ equal(h(e10),e24),
inference(spt,[spt(split,[position(sa)])],[278,216]),
[iquote('1:Spt:278.0,165.0,216.0')] ).
cnf(293,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:278.0,165.1,165.2,165.3,165.4')] ).
cnf(294,plain,
equal(h(e10),e23),
inference(spt,[spt(split,[position(s2s1)])],[293]),
[iquote('2:Spt:293.0')] ).
cnf(295,plain,
equal(j(e23),e10),
inference(rew,[status(thm),theory(equality)],[294,51]),
[iquote('2:Rew:294.0,51.0')] ).
cnf(318,plain,
equal(op1(e10,j(e21)),j(e20)),
inference(rew,[status(thm),theory(equality)],[295,174]),
[iquote('2:Rew:295.0,174.0')] ).
cnf(319,plain,
equal(op1(e10,e10),j(e21)),
inference(rew,[status(thm),theory(equality)],[295,172]),
[iquote('2:Rew:295.0,172.0')] ).
cnf(325,plain,
equal(j(e21),e10),
inference(rew,[status(thm),theory(equality)],[56,319]),
[iquote('2:Rew:56.0,319.0')] ).
cnf(355,plain,
equal(j(e20),e10),
inference(rew,[status(thm),theory(equality)],[56,318,325]),
[iquote('2:Rew:56.0,318.0,325.0,318.0')] ).
cnf(356,plain,
equal(h(e10),e20),
inference(rew,[status(thm),theory(equality)],[355,46]),
[iquote('2:Rew:355.0,46.0')] ).
cnf(360,plain,
equal(e23,e20),
inference(rew,[status(thm),theory(equality)],[294,356]),
[iquote('2:Rew:294.0,356.0')] ).
cnf(361,plain,
$false,
inference(mrr,[status(thm)],[360,13]),
[iquote('2:MRR:360.0,13.0')] ).
cnf(368,plain,
~ equal(h(e10),e23),
inference(spt,[spt(split,[position(s2sa)])],[361,294]),
[iquote('2:Spt:361.0,293.0,294.0')] ).
cnf(369,plain,
( equal(h(e10),e22)
| equal(h(e10),e21)
| equal(h(e10),e20) ),
inference(spt,[spt(split,[position(s2s2)])],[293]),
[iquote('2:Spt:361.0,293.1,293.2,293.3')] ).
cnf(370,plain,
equal(h(e10),e22),
inference(spt,[spt(split,[position(s2s2s1)])],[369]),
[iquote('3:Spt:369.0')] ).
cnf(372,plain,
equal(j(e22),e10),
inference(rew,[status(thm),theory(equality)],[370,51]),
[iquote('3:Rew:370.0,51.0')] ).
cnf(389,plain,
equal(op1(j(e21),e10),j(e23)),
inference(rew,[status(thm),theory(equality)],[372,183]),
[iquote('3:Rew:372.0,183.0')] ).
cnf(392,plain,
equal(op1(j(e23),e10),j(e24)),
inference(rew,[status(thm),theory(equality)],[372,173]),
[iquote('3:Rew:372.0,173.0')] ).
cnf(394,plain,
equal(op1(e10,e10),j(e21)),
inference(rew,[status(thm),theory(equality)],[372,178]),
[iquote('3:Rew:372.0,178.0')] ).
cnf(402,plain,
equal(j(e21),e10),
inference(rew,[status(thm),theory(equality)],[56,394]),
[iquote('3:Rew:56.0,394.0')] ).
cnf(414,plain,
equal(j(e23),e10),
inference(rew,[status(thm),theory(equality)],[56,389,402]),
[iquote('3:Rew:56.0,389.0,402.0,389.0')] ).
cnf(432,plain,
equal(j(e24),e10),
inference(rew,[status(thm),theory(equality)],[56,392,414]),
[iquote('3:Rew:56.0,392.0,414.0,392.0')] ).
cnf(433,plain,
equal(h(e10),e24),
inference(rew,[status(thm),theory(equality)],[432,50]),
[iquote('3:Rew:432.0,50.0')] ).
cnf(436,plain,
equal(e24,e22),
inference(rew,[status(thm),theory(equality)],[370,433]),
[iquote('3:Rew:370.0,433.0')] ).
cnf(437,plain,
$false,
inference(mrr,[status(thm)],[436,19]),
[iquote('3:MRR:436.0,19.0')] ).
cnf(450,plain,
~ equal(h(e10),e22),
inference(spt,[spt(split,[position(s2s2sa)])],[437,370]),
[iquote('3:Spt:437.0,369.0,370.0')] ).
cnf(451,plain,
( equal(h(e10),e21)
| equal(h(e10),e20) ),
inference(spt,[spt(split,[position(s2s2s2)])],[369]),
[iquote('3:Spt:437.0,369.1,369.2')] ).
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(j(e22),e10),j(e24)),
inference(rew,[status(thm),theory(equality)],[454,179]),
[iquote('4:Rew:454.0,179.0')] ).
cnf(472,plain,
equal(op1(e10,e10),j(e22)),
inference(rew,[status(thm),theory(equality)],[454,184]),
[iquote('4:Rew:454.0,184.0')] ).
cnf(475,plain,
equal(op1(e10,j(e24)),j(e20)),
inference(rew,[status(thm),theory(equality)],[454,181]),
[iquote('4:Rew:454.0,181.0')] ).
cnf(485,plain,
equal(j(e22),e10),
inference(rew,[status(thm),theory(equality)],[56,472]),
[iquote('4:Rew:56.0,472.0')] ).
cnf(497,plain,
equal(j(e24),e10),
inference(rew,[status(thm),theory(equality)],[56,471,485]),
[iquote('4:Rew:56.0,471.0,485.0,471.0')] ).
cnf(510,plain,
equal(j(e20),e10),
inference(rew,[status(thm),theory(equality)],[56,475,497]),
[iquote('4:Rew:56.0,475.0,497.0,475.0')] ).
cnf(511,plain,
equal(h(e10),e20),
inference(rew,[status(thm),theory(equality)],[510,46]),
[iquote('4:Rew:510.0,46.0')] ).
cnf(515,plain,
equal(e21,e20),
inference(rew,[status(thm),theory(equality)],[452,511]),
[iquote('4:Rew:452.0,511.0')] ).
cnf(516,plain,
$false,
inference(mrr,[status(thm)],[515,11]),
[iquote('4:MRR:515.0,11.0')] ).
cnf(528,plain,
~ equal(h(e10),e21),
inference(spt,[spt(split,[position(s2s2s2sa)])],[516,452]),
[iquote('4:Spt:516.0,451.0,452.0')] ).
cnf(529,plain,
equal(h(e10),e20),
inference(spt,[spt(split,[position(s2s2s2s2)])],[451]),
[iquote('4:Spt:516.0,451.1')] ).
cnf(532,plain,
equal(j(e20),e10),
inference(rew,[status(thm),theory(equality)],[529,51]),
[iquote('4:Rew:529.0,51.0')] ).
cnf(537,plain,
equal(op2(h(e14),e20),h(e14)),
inference(rew,[status(thm),theory(equality)],[529,195]),
[iquote('4:Rew:529.0,195.0')] ).
cnf(540,plain,
equal(op2(h(e12),h(e11)),e20),
inference(rew,[status(thm),theory(equality)],[529,204]),
[iquote('4:Rew:529.0,204.0')] ).
cnf(541,plain,
equal(op2(h(e12),e20),h(e12)),
inference(rew,[status(thm),theory(equality)],[529,205]),
[iquote('4:Rew:529.0,205.0')] ).
cnf(563,plain,
equal(h(e11),e24),
inference(spt,[spt(split,[position(s2s2s2s2s1)])],[164]),
[iquote('5:Spt:164.0')] ).
cnf(572,plain,
equal(op2(e24,e24),h(e14)),
inference(rew,[status(thm),theory(equality)],[563,209]),
[iquote('5:Rew:563.0,209.0')] ).
cnf(590,plain,
equal(h(e14),e21),
inference(rew,[status(thm),theory(equality)],[105,572]),
[iquote('5:Rew:105.0,572.0')] ).
cnf(591,plain,
equal(j(e21),e14),
inference(rew,[status(thm),theory(equality)],[590,55]),
[iquote('5:Rew:590.0,55.0')] ).
cnf(605,plain,
equal(op1(j(e22),j(e22)),e14),
inference(rew,[status(thm),theory(equality)],[591,178]),
[iquote('5:Rew:591.0,178.0')] ).
cnf(606,plain,
equal(op1(e14,e14),j(e22)),
inference(rew,[status(thm),theory(equality)],[591,184]),
[iquote('5:Rew:591.0,184.0')] ).
cnf(612,plain,
equal(j(e22),e10),
inference(rew,[status(thm),theory(equality)],[80,606]),
[iquote('5:Rew:80.0,606.0')] ).
cnf(690,plain,
equal(e14,e10),
inference(rew,[status(thm),theory(equality)],[56,605,612]),
[iquote('5:Rew:56.0,605.0,612.0,605.0')] ).
cnf(691,plain,
$false,
inference(mrr,[status(thm)],[690,4]),
[iquote('5:MRR:690.0,4.0')] ).
cnf(692,plain,
~ equal(h(e11),e24),
inference(spt,[spt(split,[position(s2s2s2s2sa)])],[691,563]),
[iquote('5:Spt:691.0,164.0,563.0')] ).
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:691.0,164.1,164.2,164.3,164.4')] ).
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(722,plain,
equal(h(e14),e21),
inference(rew,[status(thm),theory(equality)],[99,701]),
[iquote('6:Rew:99.0,701.0')] ).
cnf(723,plain,
equal(j(e21),e14),
inference(rew,[status(thm),theory(equality)],[722,55]),
[iquote('6:Rew:722.0,55.0')] ).
cnf(737,plain,
equal(op1(e14,e14),j(e22)),
inference(rew,[status(thm),theory(equality)],[723,184]),
[iquote('6:Rew:723.0,184.0')] ).
cnf(738,plain,
equal(op1(j(e22),j(e22)),e14),
inference(rew,[status(thm),theory(equality)],[723,178]),
[iquote('6:Rew:723.0,178.0')] ).
cnf(744,plain,
equal(j(e22),e10),
inference(rew,[status(thm),theory(equality)],[80,737]),
[iquote('6:Rew:80.0,737.0')] ).
cnf(821,plain,
equal(e14,e10),
inference(rew,[status(thm),theory(equality)],[56,738,744]),
[iquote('6:Rew:56.0,738.0,744.0,738.0')] ).
cnf(822,plain,
$false,
inference(mrr,[status(thm)],[821,4]),
[iquote('6:MRR:821.0,4.0')] ).
cnf(823,plain,
~ equal(h(e11),e23),
inference(spt,[spt(split,[position(s2s2s2s2s2sa)])],[822,694]),
[iquote('6:Spt:822.0,693.0,694.0')] ).
cnf(824,plain,
( equal(h(e11),e22)
| equal(h(e11),e21)
| equal(h(e11),e20) ),
inference(spt,[spt(split,[position(s2s2s2s2s2s2)])],[693]),
[iquote('6:Spt:822.0,693.1,693.2,693.3')] ).
cnf(825,plain,
equal(h(e11),e22),
inference(spt,[spt(split,[position(s2s2s2s2s2s2s1)])],[824]),
[iquote('7:Spt:824.0')] ).
cnf(827,plain,
equal(j(e22),e11),
inference(rew,[status(thm),theory(equality)],[825,52]),
[iquote('7:Rew:825.0,52.0')] ).
cnf(840,plain,
equal(op2(e22,e22),h(e14)),
inference(rew,[status(thm),theory(equality)],[825,209]),
[iquote('7:Rew:825.0,209.0')] ).
cnf(852,plain,
equal(op1(j(e21),j(e21)),e11),
inference(rew,[status(thm),theory(equality)],[827,184]),
[iquote('7:Rew:827.0,184.0')] ).
cnf(854,plain,
equal(h(e14),e21),
inference(rew,[status(thm),theory(equality)],[93,840]),
[iquote('7:Rew:93.0,840.0')] ).
cnf(855,plain,
equal(j(e21),e14),
inference(rew,[status(thm),theory(equality)],[854,55]),
[iquote('7:Rew:854.0,55.0')] ).
cnf(918,plain,
equal(e11,e10),
inference(rew,[status(thm),theory(equality)],[80,852,855]),
[iquote('7:Rew:80.0,852.0,855.0,852.0')] ).
cnf(919,plain,
$false,
inference(mrr,[status(thm)],[918,1]),
[iquote('7:MRR:918.0,1.0')] ).
cnf(929,plain,
~ equal(h(e11),e22),
inference(spt,[spt(split,[position(s2s2s2s2s2s2sa)])],[919,825]),
[iquote('7:Spt:919.0,824.0,825.0')] ).
cnf(930,plain,
( equal(h(e11),e21)
| equal(h(e11),e20) ),
inference(spt,[spt(split,[position(s2s2s2s2s2s2s2)])],[824]),
[iquote('7:Spt:919.0,824.1,824.2')] ).
cnf(931,plain,
equal(h(e11),e21),
inference(spt,[spt(split,[position(s2s2s2s2s2s2s2s1)])],[930]),
[iquote('8:Spt:930.0')] ).
cnf(940,plain,
equal(op2(e21,e21),h(e14)),
inference(rew,[status(thm),theory(equality)],[931,209]),
[iquote('8:Rew:931.0,209.0')] ).
cnf(941,plain,
equal(op2(e21,h(e12)),h(e13)),
inference(rew,[status(thm),theory(equality)],[931,208]),
[iquote('8:Rew:931.0,208.0')] ).
cnf(942,plain,
equal(op2(e21,h(e14)),h(e12)),
inference(rew,[status(thm),theory(equality)],[931,206]),
[iquote('8:Rew:931.0,206.0')] ).
cnf(961,plain,
equal(h(e14),e22),
inference(rew,[status(thm),theory(equality)],[87,940]),
[iquote('8:Rew:87.0,940.0')] ).
cnf(962,plain,
equal(j(e22),e14),
inference(rew,[status(thm),theory(equality)],[961,55]),
[iquote('8:Rew:961.0,55.0')] ).
cnf(978,plain,
equal(op1(j(e24),j(e23)),e14),
inference(rew,[status(thm),theory(equality)],[962,167]),
[iquote('8:Rew:962.0,167.0')] ).
cnf(982,plain,
equal(h(e12),e23),
inference(rew,[status(thm),theory(equality)],[88,942,961]),
[iquote('8:Rew:88.0,942.0,961.0,942.0')] ).
cnf(983,plain,
equal(j(e23),e12),
inference(rew,[status(thm),theory(equality)],[982,53]),
[iquote('8:Rew:982.0,53.0')] ).
cnf(988,plain,
equal(op2(e21,e23),h(e13)),
inference(rew,[status(thm),theory(equality)],[982,941]),
[iquote('8:Rew:982.0,941.0')] ).
cnf(996,plain,
equal(h(e13),e24),
inference(rew,[status(thm),theory(equality)],[89,988]),
[iquote('8:Rew:89.0,988.0')] ).
cnf(997,plain,
equal(j(e24),e13),
inference(rew,[status(thm),theory(equality)],[996,54]),
[iquote('8:Rew:996.0,54.0')] ).
cnf(1039,plain,
equal(e14,e10),
inference(rew,[status(thm),theory(equality)],[73,978,997,983]),
[iquote('8:Rew:73.0,978.0,997.0,978.0,983.0,978.0')] ).
cnf(1040,plain,
$false,
inference(mrr,[status(thm)],[1039,4]),
[iquote('8:MRR:1039.0,4.0')] ).
cnf(1041,plain,
~ equal(h(e11),e21),
inference(spt,[spt(split,[position(s2s2s2s2s2s2s2sa)])],[1040,931]),
[iquote('8:Spt:1040.0,930.0,931.0')] ).
cnf(1042,plain,
equal(h(e11),e20),
inference(spt,[spt(split,[position(s2s2s2s2s2s2s2s2)])],[930]),
[iquote('8:Spt:1040.0,930.1')] ).
cnf(1049,plain,
equal(op2(h(e12),e20),e20),
inference(rew,[status(thm),theory(equality)],[1042,540]),
[iquote('8:Rew:1042.0,540.0')] ).
cnf(1053,plain,
equal(h(e12),e20),
inference(rew,[status(thm),theory(equality)],[1049,541]),
[iquote('8:Rew:1049.0,541.0')] ).
cnf(1067,plain,
equal(h(e14),e20),
inference(rew,[status(thm),theory(equality)],[537,193,1053,1042]),
[iquote('8:Rew:537.0,193.0,1053.0,193.0,1042.0,193.0')] ).
cnf(1068,plain,
equal(j(e20),e14),
inference(rew,[status(thm),theory(equality)],[1067,55]),
[iquote('8:Rew:1067.0,55.0')] ).
cnf(1072,plain,
equal(e14,e10),
inference(rew,[status(thm),theory(equality)],[532,1068]),
[iquote('8:Rew:532.0,1068.0')] ).
cnf(1073,plain,
$false,
inference(mrr,[status(thm)],[1072,4]),
[iquote('8:MRR:1072.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG077+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.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 00:03:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.48
% 0.19/0.48 SPASS V 3.9
% 0.19/0.48 SPASS beiseite: Proof found.
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.48 SPASS derived 468 clauses, backtracked 476 clauses, performed 8 splits and kept 858 clauses.
% 0.19/0.48 SPASS allocated 85611 KBytes.
% 0.19/0.48 SPASS spent 0:00:00.14 on the problem.
% 0.19/0.48 0:00:00.04 for the input.
% 0.19/0.48 0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.48 0:00:00.00 for inferences.
% 0.19/0.48 0:00:00.00 for the backtracking.
% 0.19/0.48 0:00:00.04 for the reduction.
% 0.19/0.48
% 0.19/0.48
% 0.19/0.48 Here is a proof with depth 4, length 180 :
% 0.19/0.48 % SZS output start Refutation
% See solution above
% 0.19/0.48 Formulae used in the proof : ax1 ax2 co1 ax4 ax5
% 0.19/0.48
%------------------------------------------------------------------------------