TSTP Solution File: ALG045+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG045+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 18:02:06 EDT 2022
% Result : Unsatisfiable 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 49
% Syntax : Number of clauses : 155 ( 93 unt; 22 nHn; 155 RR)
% Number of literals : 255 ( 0 equ; 115 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(e1,e0),
file('ALG045+1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(e2,e0),
file('ALG045+1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(e3,e0),
file('ALG045+1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(e2,e1),
file('ALG045+1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(e3,e1),
file('ALG045+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(e3,e2),
file('ALG045+1.p',unknown),
[] ).
cnf(7,axiom,
equal(op(unit,e0),e0),
file('ALG045+1.p',unknown),
[] ).
cnf(8,axiom,
equal(op(e0,unit),e0),
file('ALG045+1.p',unknown),
[] ).
cnf(9,axiom,
equal(op(unit,e1),e1),
file('ALG045+1.p',unknown),
[] ).
cnf(10,axiom,
equal(op(e1,unit),e1),
file('ALG045+1.p',unknown),
[] ).
cnf(11,axiom,
equal(op(unit,e2),e2),
file('ALG045+1.p',unknown),
[] ).
cnf(12,axiom,
equal(op(e2,unit),e2),
file('ALG045+1.p',unknown),
[] ).
cnf(13,axiom,
equal(op(unit,e3),e3),
file('ALG045+1.p',unknown),
[] ).
cnf(14,axiom,
equal(op(e3,unit),e3),
file('ALG045+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ skC0
| equal(op(e1,e1),e0) ),
file('ALG045+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ skC0
| equal(op(e2,e2),e0) ),
file('ALG045+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ skC0
| equal(op(e3,e3),e0) ),
file('ALG045+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ skC1
| equal(op(e0,e0),e1) ),
file('ALG045+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ skC1
| equal(op(e2,e2),e1) ),
file('ALG045+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ skC1
| equal(op(e3,e3),e1) ),
file('ALG045+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ skC2
| equal(op(e0,e0),e2) ),
file('ALG045+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ skC2
| equal(op(e1,e1),e2) ),
file('ALG045+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ skC2
| equal(op(e3,e3),e2) ),
file('ALG045+1.p',unknown),
[] ).
cnf(30,axiom,
~ equal(op(e2,e0),op(e1,e0)),
file('ALG045+1.p',unknown),
[] ).
cnf(38,axiom,
~ equal(op(e3,e1),op(e2,e1)),
file('ALG045+1.p',unknown),
[] ).
cnf(41,axiom,
~ equal(op(e3,e2),op(e0,e2)),
file('ALG045+1.p',unknown),
[] ).
cnf(44,axiom,
~ equal(op(e3,e2),op(e2,e2)),
file('ALG045+1.p',unknown),
[] ).
cnf(46,axiom,
~ equal(op(e2,e3),op(e0,e3)),
file('ALG045+1.p',unknown),
[] ).
cnf(47,axiom,
~ equal(op(e3,e3),op(e0,e3)),
file('ALG045+1.p',unknown),
[] ).
cnf(49,axiom,
~ equal(op(e3,e3),op(e1,e3)),
file('ALG045+1.p',unknown),
[] ).
cnf(56,axiom,
~ equal(op(e0,e3),op(e0,e2)),
file('ALG045+1.p',unknown),
[] ).
cnf(63,axiom,
~ equal(op(e2,e1),op(e2,e0)),
file('ALG045+1.p',unknown),
[] ).
cnf(64,axiom,
~ equal(op(e2,e2),op(e2,e0)),
file('ALG045+1.p',unknown),
[] ).
cnf(66,axiom,
~ equal(op(e2,e2),op(e2,e1)),
file('ALG045+1.p',unknown),
[] ).
cnf(67,axiom,
~ equal(op(e2,e3),op(e2,e1)),
file('ALG045+1.p',unknown),
[] ).
cnf(70,axiom,
~ equal(op(e3,e2),op(e3,e0)),
file('ALG045+1.p',unknown),
[] ).
cnf(75,axiom,
( skC2
| skC1
| skC0
| equal(op(e0,e0),e3) ),
file('ALG045+1.p',unknown),
[] ).
cnf(76,axiom,
( skC2
| skC1
| skC0
| equal(op(e1,e1),e3) ),
file('ALG045+1.p',unknown),
[] ).
cnf(77,axiom,
( skC2
| skC1
| skC0
| equal(op(e2,e2),e3) ),
file('ALG045+1.p',unknown),
[] ).
cnf(78,axiom,
( skC2
| skC1
| skC0
| equal(op(e3,e3),e3) ),
file('ALG045+1.p',unknown),
[] ).
cnf(79,axiom,
( equal(e3,unit)
| equal(e2,unit)
| equal(e1,unit)
| equal(e0,unit) ),
file('ALG045+1.p',unknown),
[] ).
cnf(82,axiom,
( ~ equal(op(e2,e2),e0)
| ~ equal(op(e3,e2),e1) ),
file('ALG045+1.p',unknown),
[] ).
cnf(87,axiom,
( ~ equal(op(e0,e0),e1)
| ~ equal(op(e2,e0),e3) ),
file('ALG045+1.p',unknown),
[] ).
cnf(97,axiom,
( ~ equal(op(e3,e3),e2)
| ~ equal(op(e0,e3),e1) ),
file('ALG045+1.p',unknown),
[] ).
cnf(100,axiom,
( ~ equal(op(e1,e1),e3)
| ~ equal(op(e2,e1),e0) ),
file('ALG045+1.p',unknown),
[] ).
cnf(137,axiom,
( equal(op(e3,e2),e3)
| equal(op(e3,e2),e2)
| equal(op(e3,e2),e1)
| equal(op(e3,e2),e0) ),
file('ALG045+1.p',unknown),
[] ).
cnf(142,axiom,
( equal(op(e2,e1),e2)
| equal(op(e2,e1),e1)
| equal(op(e2,e1),e3)
| equal(op(e2,e1),e0) ),
file('ALG045+1.p',unknown),
[] ).
cnf(143,axiom,
( equal(op(e2,e0),e2)
| equal(op(e2,e0),e0)
| equal(op(e2,e0),e3)
| equal(op(e2,e0),e1) ),
file('ALG045+1.p',unknown),
[] ).
cnf(148,axiom,
( equal(op(e0,e3),e3)
| equal(op(e0,e3),e0)
| equal(op(e0,e3),e2)
| equal(op(e0,e3),e1) ),
file('ALG045+1.p',unknown),
[] ).
cnf(152,plain,
equal(e3,unit),
inference(spt,[spt(split,[position(s1)])],[79]),
[iquote('1:Spt:79.0')] ).
cnf(158,plain,
( ~ skC2
| equal(op(unit,unit),e2) ),
inference(rew,[status(thm),theory(equality)],[152,26]),
[iquote('1:Rew:152.0,26.1')] ).
cnf(163,plain,
( ~ skC1
| equal(op(unit,unit),e1) ),
inference(rew,[status(thm),theory(equality)],[152,22]),
[iquote('1:Rew:152.0,22.1')] ).
cnf(168,plain,
( ~ skC0
| equal(op(unit,unit),e0) ),
inference(rew,[status(thm),theory(equality)],[152,18]),
[iquote('1:Rew:152.0,18.1')] ).
cnf(177,plain,
( skC2
| skC1
| skC0
| equal(op(e2,e2),unit) ),
inference(rew,[status(thm),theory(equality)],[152,77]),
[iquote('1:Rew:152.0,77.3')] ).
cnf(181,plain,
( ~ equal(op(e1,e1),unit)
| ~ equal(op(e2,e1),e0) ),
inference(rew,[status(thm),theory(equality)],[152,100]),
[iquote('1:Rew:152.0,100.0')] ).
cnf(183,plain,
( skC2
| skC1
| skC0
| equal(op(e1,e1),unit) ),
inference(rew,[status(thm),theory(equality)],[152,76]),
[iquote('1:Rew:152.0,76.3')] ).
cnf(208,plain,
~ equal(op(e2,e1),op(unit,e1)),
inference(rew,[status(thm),theory(equality)],[152,38]),
[iquote('1:Rew:152.0,38.0')] ).
cnf(228,plain,
~ equal(op(e2,e1),op(e2,unit)),
inference(rew,[status(thm),theory(equality)],[152,67]),
[iquote('1:Rew:152.0,67.0')] ).
cnf(260,plain,
( equal(op(e2,e1),e2)
| equal(op(e2,e1),e1)
| equal(op(e2,e1),unit)
| equal(op(e2,e1),e0) ),
inference(rew,[status(thm),theory(equality)],[152,142]),
[iquote('1:Rew:152.0,142.2')] ).
cnf(262,plain,
~ equal(e2,unit),
inference(rew,[status(thm),theory(equality)],[152,6]),
[iquote('1:Rew:152.0,6.0')] ).
cnf(263,plain,
~ equal(e1,unit),
inference(rew,[status(thm),theory(equality)],[152,5]),
[iquote('1:Rew:152.0,5.0')] ).
cnf(264,plain,
~ equal(e0,unit),
inference(rew,[status(thm),theory(equality)],[152,3]),
[iquote('1:Rew:152.0,3.0')] ).
cnf(265,plain,
equal(op(unit,unit),unit),
inference(rew,[status(thm),theory(equality)],[152,14]),
[iquote('1:Rew:152.0,14.0')] ).
cnf(267,plain,
( ~ skC2
| equal(e2,unit) ),
inference(rew,[status(thm),theory(equality)],[265,158]),
[iquote('1:Rew:265.0,158.1')] ).
cnf(268,plain,
~ skC2,
inference(mrr,[status(thm)],[267,262]),
[iquote('1:MRR:267.1,262.0')] ).
cnf(269,plain,
( ~ skC1
| equal(e1,unit) ),
inference(rew,[status(thm),theory(equality)],[265,163]),
[iquote('1:Rew:265.0,163.1')] ).
cnf(270,plain,
~ skC1,
inference(mrr,[status(thm)],[269,263]),
[iquote('1:MRR:269.1,263.0')] ).
cnf(271,plain,
( ~ skC0
| equal(e0,unit) ),
inference(rew,[status(thm),theory(equality)],[265,168]),
[iquote('1:Rew:265.0,168.1')] ).
cnf(272,plain,
~ skC0,
inference(mrr,[status(thm)],[271,264]),
[iquote('1:MRR:271.1,264.0')] ).
cnf(273,plain,
equal(op(e2,e2),unit),
inference(mrr,[status(thm)],[177,268,270,272]),
[iquote('1:MRR:177.0,177.1,177.2,268.0,270.0,272.0')] ).
cnf(274,plain,
~ equal(op(e2,e1),unit),
inference(rew,[status(thm),theory(equality)],[273,66]),
[iquote('1:Rew:273.0,66.0')] ).
cnf(278,plain,
equal(op(e1,e1),unit),
inference(mrr,[status(thm)],[183,268,270,272]),
[iquote('1:MRR:183.0,183.1,183.2,268.0,270.0,272.0')] ).
cnf(294,plain,
~ equal(op(e2,e1),e1),
inference(rew,[status(thm),theory(equality)],[9,208]),
[iquote('1:Rew:9.0,208.0')] ).
cnf(304,plain,
~ equal(op(e2,e1),e2),
inference(rew,[status(thm),theory(equality)],[12,228]),
[iquote('1:Rew:12.0,228.0')] ).
cnf(328,plain,
( ~ equal(unit,unit)
| ~ equal(op(e2,e1),e0) ),
inference(rew,[status(thm),theory(equality)],[278,181]),
[iquote('1:Rew:278.0,181.0')] ).
cnf(329,plain,
~ equal(op(e2,e1),e0),
inference(obv,[status(thm),theory(equality)],[328]),
[iquote('1:Obv:328.0')] ).
cnf(384,plain,
$false,
inference(mrr,[status(thm)],[260,304,294,274,329]),
[iquote('1:MRR:260.0,260.1,260.2,260.3,304.0,294.0,274.0,329.0')] ).
cnf(385,plain,
~ equal(e3,unit),
inference(spt,[spt(split,[position(sa)])],[384,152]),
[iquote('1:Spt:384.0,79.0,152.0')] ).
cnf(386,plain,
( equal(e2,unit)
| equal(e1,unit)
| equal(e0,unit) ),
inference(spt,[spt(split,[position(s2)])],[79]),
[iquote('1:Spt:384.0,79.1,79.2,79.3')] ).
cnf(387,plain,
equal(e2,unit),
inference(spt,[spt(split,[position(s2s1)])],[386]),
[iquote('2:Spt:386.0')] ).
cnf(424,plain,
~ equal(op(e0,e3),op(e0,unit)),
inference(rew,[status(thm),theory(equality)],[387,56]),
[iquote('2:Rew:387.0,56.0')] ).
cnf(432,plain,
~ equal(e1,unit),
inference(rew,[status(thm),theory(equality)],[387,4]),
[iquote('2:Rew:387.0,4.0')] ).
cnf(433,plain,
~ equal(e0,unit),
inference(rew,[status(thm),theory(equality)],[387,2]),
[iquote('2:Rew:387.0,2.0')] ).
cnf(434,plain,
equal(op(unit,unit),unit),
inference(rew,[status(thm),theory(equality)],[387,12]),
[iquote('2:Rew:387.0,12.0')] ).
cnf(441,plain,
( ~ equal(op(e3,e3),unit)
| ~ equal(op(e0,e3),e1) ),
inference(rew,[status(thm),theory(equality)],[387,97]),
[iquote('2:Rew:387.0,97.0')] ).
cnf(442,plain,
( ~ skC2
| equal(op(e3,e3),unit) ),
inference(rew,[status(thm),theory(equality)],[387,26]),
[iquote('2:Rew:387.0,26.1')] ).
cnf(445,plain,
( ~ skC1
| equal(op(unit,unit),e1) ),
inference(rew,[status(thm),theory(equality)],[387,21]),
[iquote('2:Rew:387.0,21.1')] ).
cnf(447,plain,
( ~ skC0
| equal(op(unit,unit),e0) ),
inference(rew,[status(thm),theory(equality)],[387,17]),
[iquote('2:Rew:387.0,17.1')] ).
cnf(448,plain,
( skC2
| skC1
| skC0
| equal(op(unit,unit),e3) ),
inference(rew,[status(thm),theory(equality)],[387,77]),
[iquote('2:Rew:387.0,77.3')] ).
cnf(468,plain,
~ equal(op(e0,e3),op(unit,e3)),
inference(rew,[status(thm),theory(equality)],[387,46]),
[iquote('2:Rew:387.0,46.0')] ).
cnf(500,plain,
( equal(op(e0,e3),e3)
| equal(op(e0,e3),e0)
| equal(op(e0,e3),unit)
| equal(op(e0,e3),e1) ),
inference(rew,[status(thm),theory(equality)],[387,148]),
[iquote('2:Rew:387.0,148.2')] ).
cnf(502,plain,
( ~ skC1
| equal(e1,unit) ),
inference(rew,[status(thm),theory(equality)],[434,445]),
[iquote('2:Rew:434.0,445.1')] ).
cnf(503,plain,
~ skC1,
inference(mrr,[status(thm)],[502,432]),
[iquote('2:MRR:502.1,432.0')] ).
cnf(507,plain,
( ~ skC0
| equal(e0,unit) ),
inference(rew,[status(thm),theory(equality)],[434,447]),
[iquote('2:Rew:434.0,447.1')] ).
cnf(508,plain,
~ skC0,
inference(mrr,[status(thm)],[507,433]),
[iquote('2:MRR:507.1,433.0')] ).
cnf(524,plain,
~ equal(op(e0,e3),e0),
inference(rew,[status(thm),theory(equality)],[8,424]),
[iquote('2:Rew:8.0,424.0')] ).
cnf(526,plain,
( skC2
| skC1
| skC0
| equal(e3,unit) ),
inference(rew,[status(thm),theory(equality)],[434,448]),
[iquote('2:Rew:434.0,448.3')] ).
cnf(527,plain,
skC2,
inference(mrr,[status(thm)],[526,503,508,385]),
[iquote('2:MRR:526.1,526.2,526.3,503.0,508.0,385.0')] ).
cnf(528,plain,
equal(op(e3,e3),unit),
inference(mrr,[status(thm)],[442,527]),
[iquote('2:MRR:442.0,527.0')] ).
cnf(531,plain,
~ equal(op(e0,e3),unit),
inference(rew,[status(thm),theory(equality)],[528,47]),
[iquote('2:Rew:528.0,47.0')] ).
cnf(549,plain,
~ equal(op(e0,e3),e3),
inference(rew,[status(thm),theory(equality)],[13,468]),
[iquote('2:Rew:13.0,468.0')] ).
cnf(571,plain,
( ~ equal(unit,unit)
| ~ equal(op(e0,e3),e1) ),
inference(rew,[status(thm),theory(equality)],[528,441]),
[iquote('2:Rew:528.0,441.0')] ).
cnf(572,plain,
~ equal(op(e0,e3),e1),
inference(obv,[status(thm),theory(equality)],[571]),
[iquote('2:Obv:571.0')] ).
cnf(625,plain,
$false,
inference(mrr,[status(thm)],[500,549,524,531,572]),
[iquote('2:MRR:500.0,500.1,500.2,500.3,549.0,524.0,531.0,572.0')] ).
cnf(626,plain,
~ equal(e2,unit),
inference(spt,[spt(split,[position(s2sa)])],[625,387]),
[iquote('2:Spt:625.0,386.0,387.0')] ).
cnf(627,plain,
( equal(e1,unit)
| equal(e0,unit) ),
inference(spt,[spt(split,[position(s2s2)])],[386]),
[iquote('2:Spt:625.0,386.1,386.2')] ).
cnf(628,plain,
equal(e1,unit),
inference(spt,[spt(split,[position(s2s2s1)])],[627]),
[iquote('3:Spt:627.0')] ).
cnf(630,plain,
~ equal(op(e2,e0),op(unit,e0)),
inference(rew,[status(thm),theory(equality)],[628,30]),
[iquote('3:Rew:628.0,30.0')] ).
cnf(653,plain,
~ equal(e0,unit),
inference(rew,[status(thm),theory(equality)],[628,1]),
[iquote('3:Rew:628.0,1.0')] ).
cnf(654,plain,
equal(op(unit,unit),unit),
inference(rew,[status(thm),theory(equality)],[628,10]),
[iquote('3:Rew:628.0,10.0')] ).
cnf(660,plain,
~ equal(op(e3,e3),op(unit,e3)),
inference(rew,[status(thm),theory(equality)],[628,49]),
[iquote('3:Rew:628.0,49.0')] ).
cnf(679,plain,
( ~ skC2
| equal(op(unit,unit),e2) ),
inference(rew,[status(thm),theory(equality)],[628,24]),
[iquote('3:Rew:628.0,24.1')] ).
cnf(681,plain,
( ~ skC0
| equal(op(unit,unit),e0) ),
inference(rew,[status(thm),theory(equality)],[628,16]),
[iquote('3:Rew:628.0,16.1')] ).
cnf(693,plain,
( ~ skC1
| equal(op(e2,e2),unit) ),
inference(rew,[status(thm),theory(equality)],[628,21]),
[iquote('3:Rew:628.0,21.1')] ).
cnf(706,plain,
( ~ equal(op(e0,e0),unit)
| ~ equal(op(e2,e0),e3) ),
inference(rew,[status(thm),theory(equality)],[628,87]),
[iquote('3:Rew:628.0,87.0')] ).
cnf(708,plain,
( ~ skC1
| equal(op(e0,e0),unit) ),
inference(rew,[status(thm),theory(equality)],[628,19]),
[iquote('3:Rew:628.0,19.1')] ).
cnf(723,plain,
~ equal(op(e2,e0),op(e2,unit)),
inference(rew,[status(thm),theory(equality)],[628,63]),
[iquote('3:Rew:628.0,63.0')] ).
cnf(741,plain,
( equal(op(e2,e0),e2)
| equal(op(e2,e0),e0)
| equal(op(e2,e0),e3)
| equal(op(e2,e0),unit) ),
inference(rew,[status(thm),theory(equality)],[628,143]),
[iquote('3:Rew:628.0,143.3')] ).
cnf(743,plain,
( ~ skC2
| equal(e2,unit) ),
inference(rew,[status(thm),theory(equality)],[654,679]),
[iquote('3:Rew:654.0,679.1')] ).
cnf(744,plain,
~ skC2,
inference(mrr,[status(thm)],[743,626]),
[iquote('3:MRR:743.1,626.0')] ).
cnf(746,plain,
( skC1
| skC0
| equal(op(e3,e3),e3) ),
inference(mrr,[status(thm)],[78,744]),
[iquote('3:MRR:78.0,744.0')] ).
cnf(748,plain,
( ~ skC0
| equal(e0,unit) ),
inference(rew,[status(thm),theory(equality)],[654,681]),
[iquote('3:Rew:654.0,681.1')] ).
cnf(749,plain,
~ skC0,
inference(mrr,[status(thm)],[748,653]),
[iquote('3:MRR:748.1,653.0')] ).
cnf(751,plain,
( skC1
| equal(op(e3,e3),e3) ),
inference(mrr,[status(thm)],[746,749]),
[iquote('3:MRR:746.1,749.0')] ).
cnf(754,plain,
~ equal(op(e2,e0),e0),
inference(rew,[status(thm),theory(equality)],[7,630]),
[iquote('3:Rew:7.0,630.0')] ).
cnf(762,plain,
~ equal(op(e3,e3),e3),
inference(rew,[status(thm),theory(equality)],[13,660]),
[iquote('3:Rew:13.0,660.0')] ).
cnf(763,plain,
skC1,
inference(mrr,[status(thm)],[751,762]),
[iquote('3:MRR:751.1,762.0')] ).
cnf(764,plain,
equal(op(e2,e2),unit),
inference(mrr,[status(thm)],[693,763]),
[iquote('3:MRR:693.0,763.0')] ).
cnf(766,plain,
equal(op(e0,e0),unit),
inference(mrr,[status(thm)],[708,763]),
[iquote('3:MRR:708.0,763.0')] ).
cnf(769,plain,
~ equal(op(e2,e0),unit),
inference(rew,[status(thm),theory(equality)],[764,64]),
[iquote('3:Rew:764.0,64.0')] ).
cnf(797,plain,
~ equal(op(e2,e0),e2),
inference(rew,[status(thm),theory(equality)],[12,723]),
[iquote('3:Rew:12.0,723.0')] ).
cnf(819,plain,
( ~ equal(unit,unit)
| ~ equal(op(e2,e0),e3) ),
inference(rew,[status(thm),theory(equality)],[766,706]),
[iquote('3:Rew:766.0,706.0')] ).
cnf(820,plain,
~ equal(op(e2,e0),e3),
inference(obv,[status(thm),theory(equality)],[819]),
[iquote('3:Obv:819.0')] ).
cnf(865,plain,
$false,
inference(mrr,[status(thm)],[741,797,754,820,769]),
[iquote('3:MRR:741.0,741.1,741.2,741.3,797.0,754.0,820.0,769.0')] ).
cnf(866,plain,
~ equal(e1,unit),
inference(spt,[spt(split,[position(s2s2sa)])],[865,628]),
[iquote('3:Spt:865.0,627.0,628.0')] ).
cnf(867,plain,
equal(e0,unit),
inference(spt,[spt(split,[position(s2s2s2)])],[627]),
[iquote('3:Spt:865.0,627.1')] ).
cnf(868,plain,
equal(op(unit,unit),unit),
inference(rew,[status(thm),theory(equality)],[867,8]),
[iquote('3:Rew:867.0,8.0')] ).
cnf(872,plain,
~ equal(op(e3,e2),op(e3,unit)),
inference(rew,[status(thm),theory(equality)],[867,70]),
[iquote('3:Rew:867.0,70.0')] ).
cnf(874,plain,
~ equal(op(e3,e2),op(unit,e2)),
inference(rew,[status(thm),theory(equality)],[867,41]),
[iquote('3:Rew:867.0,41.0')] ).
cnf(878,plain,
~ equal(e1,unit),
inference(rew,[status(thm),theory(equality)],[867,1]),
[iquote('3:Rew:867.0,1.0')] ).
cnf(879,plain,
( ~ skC1
| equal(e1,unit) ),
inference(rew,[status(thm),theory(equality)],[868,19,867]),
[iquote('3:Rew:868.0,19.1,867.0,19.1')] ).
cnf(880,plain,
~ skC1,
inference(mrr,[status(thm)],[879,878]),
[iquote('3:MRR:879.1,878.0')] ).
cnf(882,plain,
( ~ skC2
| equal(e2,unit) ),
inference(rew,[status(thm),theory(equality)],[868,23,867]),
[iquote('3:Rew:868.0,23.1,867.0,23.1')] ).
cnf(883,plain,
~ skC2,
inference(mrr,[status(thm)],[882,626]),
[iquote('3:MRR:882.1,626.0')] ).
cnf(884,plain,
( ~ skC0
| equal(op(e2,e2),unit) ),
inference(rew,[status(thm),theory(equality)],[867,17]),
[iquote('3:Rew:867.0,17.1')] ).
cnf(904,plain,
( skC2
| skC1
| skC0
| equal(e3,unit) ),
inference(rew,[status(thm),theory(equality)],[868,75,867]),
[iquote('3:Rew:868.0,75.3,867.0,75.3')] ).
cnf(905,plain,
skC0,
inference(mrr,[status(thm)],[904,883,880,385]),
[iquote('3:MRR:904.0,904.1,904.3,883.0,880.0,385.0')] ).
cnf(907,plain,
equal(op(e2,e2),unit),
inference(mrr,[status(thm)],[884,905]),
[iquote('3:MRR:884.0,905.0')] ).
cnf(921,plain,
~ equal(op(e3,e2),unit),
inference(rew,[status(thm),theory(equality)],[907,44]),
[iquote('3:Rew:907.0,44.0')] ).
cnf(931,plain,
~ equal(op(e3,e2),e3),
inference(rew,[status(thm),theory(equality)],[14,872]),
[iquote('3:Rew:14.0,872.0')] ).
cnf(932,plain,
~ equal(op(e3,e2),e2),
inference(rew,[status(thm),theory(equality)],[11,874]),
[iquote('3:Rew:11.0,874.0')] ).
cnf(939,plain,
( ~ equal(unit,unit)
| ~ equal(op(e3,e2),e1) ),
inference(rew,[status(thm),theory(equality)],[907,82,867]),
[iquote('3:Rew:907.0,82.0,867.0,82.0')] ).
cnf(940,plain,
~ equal(op(e3,e2),e1),
inference(obv,[status(thm),theory(equality)],[939]),
[iquote('3:Obv:939.0')] ).
cnf(1027,plain,
( equal(op(e3,e2),e3)
| equal(op(e3,e2),e2)
| equal(op(e3,e2),e1)
| equal(op(e3,e2),unit) ),
inference(rew,[status(thm),theory(equality)],[867,137]),
[iquote('3:Rew:867.0,137.3')] ).
cnf(1028,plain,
$false,
inference(mrr,[status(thm)],[1027,931,932,940,921]),
[iquote('3:MRR:1027.0,1027.1,1027.2,1027.3,931.0,932.0,940.0,921.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG045+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n017.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 8 12:33:33 EDT 2022
% 0.12/0.34 % 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/sandbox2/benchmark/theBenchmark.p
% 0.19/0.48 SPASS derived 420 clauses, backtracked 411 clauses, performed 3 splits and kept 672 clauses.
% 0.19/0.48 SPASS allocated 85650 KBytes.
% 0.19/0.48 SPASS spent 0:00:00.13 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 3, length 155 :
% 0.19/0.48 % SZS output start Refutation
% See solution above
% 0.19/0.48 Formulae used in the proof : ax5 ax2 ax6 ax4 ax9 ax14 ax24 ax27 ax1
% 0.19/0.48
%------------------------------------------------------------------------------