TSTP Solution File: ALG061+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG061+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 18:02:10 EDT 2022
% Result : Theorem 0.18s 0.56s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 103
% Syntax : Number of clauses : 322 ( 195 unt; 105 nHn; 322 RR)
% Number of literals : 622 ( 0 equ; 165 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(e1,e0),
file('ALG061+1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(e2,e0),
file('ALG061+1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(e3,e0),
file('ALG061+1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(e4,e0),
file('ALG061+1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(e2,e1),
file('ALG061+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(e3,e1),
file('ALG061+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(e4,e1),
file('ALG061+1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(e3,e2),
file('ALG061+1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(e4,e2),
file('ALG061+1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(e4,e3),
file('ALG061+1.p',unknown),
[] ).
cnf(11,axiom,
equal(op(unit,e0),e0),
file('ALG061+1.p',unknown),
[] ).
cnf(12,axiom,
equal(op(e0,unit),e0),
file('ALG061+1.p',unknown),
[] ).
cnf(13,axiom,
equal(op(unit,e1),e1),
file('ALG061+1.p',unknown),
[] ).
cnf(14,axiom,
equal(op(e1,unit),e1),
file('ALG061+1.p',unknown),
[] ).
cnf(15,axiom,
equal(op(unit,e2),e2),
file('ALG061+1.p',unknown),
[] ).
cnf(16,axiom,
equal(op(e2,unit),e2),
file('ALG061+1.p',unknown),
[] ).
cnf(17,axiom,
equal(op(unit,e3),e3),
file('ALG061+1.p',unknown),
[] ).
cnf(18,axiom,
equal(op(e3,unit),e3),
file('ALG061+1.p',unknown),
[] ).
cnf(19,axiom,
equal(op(unit,e4),e4),
file('ALG061+1.p',unknown),
[] ).
cnf(20,axiom,
equal(op(e4,unit),e4),
file('ALG061+1.p',unknown),
[] ).
cnf(21,axiom,
equal(op(e1,e1),e4),
file('ALG061+1.p',unknown),
[] ).
cnf(22,axiom,
~ equal(op(e1,e0),op(e0,e0)),
file('ALG061+1.p',unknown),
[] ).
cnf(23,axiom,
~ equal(op(e2,e0),op(e0,e0)),
file('ALG061+1.p',unknown),
[] ).
cnf(28,axiom,
~ equal(op(e4,e0),op(e1,e0)),
file('ALG061+1.p',unknown),
[] ).
cnf(30,axiom,
~ equal(op(e4,e0),op(e2,e0)),
file('ALG061+1.p',unknown),
[] ).
cnf(33,axiom,
~ equal(op(e2,e1),op(e0,e1)),
file('ALG061+1.p',unknown),
[] ).
cnf(36,axiom,
~ equal(op(e2,e1),op(e1,e1)),
file('ALG061+1.p',unknown),
[] ).
cnf(45,axiom,
~ equal(op(e4,e2),op(e0,e2)),
file('ALG061+1.p',unknown),
[] ).
cnf(48,axiom,
~ equal(op(e4,e2),op(e1,e2)),
file('ALG061+1.p',unknown),
[] ).
cnf(50,axiom,
~ equal(op(e4,e2),op(e2,e2)),
file('ALG061+1.p',unknown),
[] ).
cnf(54,axiom,
~ equal(op(e3,e3),op(e0,e3)),
file('ALG061+1.p',unknown),
[] ).
cnf(55,axiom,
~ equal(op(e4,e3),op(e0,e3)),
file('ALG061+1.p',unknown),
[] ).
cnf(56,axiom,
~ equal(op(e2,e3),op(e1,e3)),
file('ALG061+1.p',unknown),
[] ).
cnf(60,axiom,
~ equal(op(e4,e3),op(e2,e3)),
file('ALG061+1.p',unknown),
[] ).
cnf(61,axiom,
~ equal(op(e4,e3),op(e3,e3)),
file('ALG061+1.p',unknown),
[] ).
cnf(62,axiom,
~ equal(op(e1,e4),op(e0,e4)),
file('ALG061+1.p',unknown),
[] ).
cnf(63,axiom,
~ equal(op(e2,e4),op(e0,e4)),
file('ALG061+1.p',unknown),
[] ).
cnf(64,axiom,
~ equal(op(e3,e4),op(e0,e4)),
file('ALG061+1.p',unknown),
[] ).
cnf(65,axiom,
~ equal(op(e4,e4),op(e0,e4)),
file('ALG061+1.p',unknown),
[] ).
cnf(68,axiom,
~ equal(op(e4,e4),op(e1,e4)),
file('ALG061+1.p',unknown),
[] ).
cnf(70,axiom,
~ equal(op(e4,e4),op(e2,e4)),
file('ALG061+1.p',unknown),
[] ).
cnf(72,axiom,
~ equal(op(e0,e1),op(e0,e0)),
file('ALG061+1.p',unknown),
[] ).
cnf(74,axiom,
~ equal(op(e0,e3),op(e0,e0)),
file('ALG061+1.p',unknown),
[] ).
cnf(75,axiom,
~ equal(op(e0,e4),op(e0,e0)),
file('ALG061+1.p',unknown),
[] ).
cnf(77,axiom,
~ equal(op(e0,e3),op(e0,e1)),
file('ALG061+1.p',unknown),
[] ).
cnf(78,axiom,
~ equal(op(e0,e4),op(e0,e1)),
file('ALG061+1.p',unknown),
[] ).
cnf(79,axiom,
~ equal(op(e0,e3),op(e0,e2)),
file('ALG061+1.p',unknown),
[] ).
cnf(81,axiom,
~ equal(op(e0,e4),op(e0,e3)),
file('ALG061+1.p',unknown),
[] ).
cnf(82,axiom,
~ equal(op(e1,e1),op(e1,e0)),
file('ALG061+1.p',unknown),
[] ).
cnf(85,axiom,
~ equal(op(e1,e4),op(e1,e0)),
file('ALG061+1.p',unknown),
[] ).
cnf(87,axiom,
~ equal(op(e1,e3),op(e1,e1)),
file('ALG061+1.p',unknown),
[] ).
cnf(88,axiom,
~ equal(op(e1,e4),op(e1,e1)),
file('ALG061+1.p',unknown),
[] ).
cnf(90,axiom,
~ equal(op(e1,e4),op(e1,e2)),
file('ALG061+1.p',unknown),
[] ).
cnf(91,axiom,
~ equal(op(e1,e4),op(e1,e3)),
file('ALG061+1.p',unknown),
[] ).
cnf(92,axiom,
~ equal(op(e2,e1),op(e2,e0)),
file('ALG061+1.p',unknown),
[] ).
cnf(96,axiom,
~ equal(op(e2,e2),op(e2,e1)),
file('ALG061+1.p',unknown),
[] ).
cnf(98,axiom,
~ equal(op(e2,e4),op(e2,e1)),
file('ALG061+1.p',unknown),
[] ).
cnf(100,axiom,
~ equal(op(e2,e4),op(e2,e2)),
file('ALG061+1.p',unknown),
[] ).
cnf(106,axiom,
~ equal(op(e3,e2),op(e3,e1)),
file('ALG061+1.p',unknown),
[] ).
cnf(111,axiom,
~ equal(op(e3,e4),op(e3,e3)),
file('ALG061+1.p',unknown),
[] ).
cnf(113,axiom,
~ equal(op(e4,e2),op(e4,e0)),
file('ALG061+1.p',unknown),
[] ).
cnf(117,axiom,
~ equal(op(e4,e3),op(e4,e1)),
file('ALG061+1.p',unknown),
[] ).
cnf(118,axiom,
~ equal(op(e4,e4),op(e4,e1)),
file('ALG061+1.p',unknown),
[] ).
cnf(119,axiom,
~ equal(op(e4,e3),op(e4,e2)),
file('ALG061+1.p',unknown),
[] ).
cnf(120,axiom,
~ equal(op(e4,e4),op(e4,e2)),
file('ALG061+1.p',unknown),
[] ).
cnf(121,axiom,
~ equal(op(e4,e4),op(e4,e3)),
file('ALG061+1.p',unknown),
[] ).
cnf(122,axiom,
( ~ skC0
| equal(op(e0,op(e0,e0)),e0) ),
file('ALG061+1.p',unknown),
[] ).
cnf(123,axiom,
( ~ skC1
| equal(op(e0,op(e1,e0)),e1) ),
file('ALG061+1.p',unknown),
[] ).
cnf(124,axiom,
( ~ skC2
| equal(op(e0,op(e2,e0)),e2) ),
file('ALG061+1.p',unknown),
[] ).
cnf(125,axiom,
( ~ skC3
| equal(op(e0,op(e3,e0)),e3) ),
file('ALG061+1.p',unknown),
[] ).
cnf(138,axiom,
( ~ skC16
| equal(op(e4,op(e0,e4)),e0) ),
file('ALG061+1.p',unknown),
[] ).
cnf(139,axiom,
( ~ skC17
| equal(op(e4,op(e1,e4)),e1) ),
file('ALG061+1.p',unknown),
[] ).
cnf(140,axiom,
( ~ skC18
| equal(op(e4,op(e2,e4)),e2) ),
file('ALG061+1.p',unknown),
[] ).
cnf(141,axiom,
( ~ skC19
| equal(op(e4,op(e3,e4)),e3) ),
file('ALG061+1.p',unknown),
[] ).
cnf(142,axiom,
equal(op(op(e1,e1),op(e1,e1)),e2),
file('ALG061+1.p',unknown),
[] ).
cnf(143,axiom,
( ~ equal(op(e0,op(e0,e0)),e0)
| ~ skC0 ),
file('ALG061+1.p',unknown),
[] ).
cnf(163,axiom,
( equal(op(e0,op(e4,e0)),e4)
| skC0
| skC1
| skC2
| skC3 ),
file('ALG061+1.p',unknown),
[] ).
cnf(167,axiom,
( equal(op(e4,op(e4,e4)),e4)
| skC16
| skC17
| skC18
| skC19 ),
file('ALG061+1.p',unknown),
[] ).
cnf(168,axiom,
equal(op(e1,op(op(e1,e1),op(e1,e1))),e0),
file('ALG061+1.p',unknown),
[] ).
cnf(173,axiom,
( ~ equal(op(e4,op(e4,e4)),e4)
| skC16
| skC17
| skC18
| skC19 ),
file('ALG061+1.p',unknown),
[] ).
cnf(174,axiom,
( equal(e4,unit)
| equal(e3,unit)
| equal(e2,unit)
| equal(e1,unit)
| equal(e0,unit) ),
file('ALG061+1.p',unknown),
[] ).
cnf(175,axiom,
equal(op(op(op(e1,e1),op(e1,e1)),op(op(e1,e1),op(e1,e1))),e3),
file('ALG061+1.p',unknown),
[] ).
cnf(179,axiom,
( equal(op(e4,e0),e3)
| equal(op(e4,e1),e3)
| equal(op(e4,e2),e3)
| equal(op(e4,e3),e3)
| equal(op(e4,e4),e3) ),
file('ALG061+1.p',unknown),
[] ).
cnf(184,axiom,
( equal(op(e0,e4),e0)
| equal(op(e1,e4),e0)
| equal(op(e2,e4),e0)
| equal(op(e3,e4),e0)
| equal(op(e4,e4),e0) ),
file('ALG061+1.p',unknown),
[] ).
cnf(185,axiom,
( equal(op(e4,e0),e0)
| equal(op(e4,e1),e0)
| equal(op(e4,e2),e0)
| equal(op(e4,e3),e0)
| equal(op(e4,e4),e0) ),
file('ALG061+1.p',unknown),
[] ).
cnf(186,axiom,
( equal(op(e0,e3),e4)
| equal(op(e1,e3),e4)
| equal(op(e2,e3),e4)
| equal(op(e3,e3),e4)
| equal(op(e4,e3),e4) ),
file('ALG061+1.p',unknown),
[] ).
cnf(190,axiom,
( equal(op(e0,e3),e2)
| equal(op(e1,e3),e2)
| equal(op(e2,e3),e2)
| equal(op(e3,e3),e2)
| equal(op(e4,e3),e2) ),
file('ALG061+1.p',unknown),
[] ).
cnf(196,axiom,
( equal(op(e0,e2),e4)
| equal(op(e1,e2),e4)
| equal(op(e2,e2),e4)
| equal(op(e3,e2),e4)
| equal(op(e4,e2),e4) ),
file('ALG061+1.p',unknown),
[] ).
cnf(200,axiom,
( equal(op(e0,e2),e2)
| equal(op(e1,e2),e2)
| equal(op(e2,e2),e2)
| equal(op(e3,e2),e2)
| equal(op(e4,e2),e2) ),
file('ALG061+1.p',unknown),
[] ).
cnf(203,axiom,
( equal(op(e2,e0),e1)
| equal(op(e2,e1),e1)
| equal(op(e2,e2),e1)
| equal(op(e2,e3),e1)
| equal(op(e2,e4),e1) ),
file('ALG061+1.p',unknown),
[] ).
cnf(209,axiom,
( equal(op(e1,e0),e3)
| equal(op(e1,e1),e3)
| equal(op(e1,e2),e3)
| equal(op(e1,e3),e3)
| equal(op(e1,e4),e3) ),
file('ALG061+1.p',unknown),
[] ).
cnf(210,axiom,
( equal(op(e0,e1),e2)
| equal(op(e1,e1),e2)
| equal(op(e2,e1),e2)
| equal(op(e3,e1),e2)
| equal(op(e4,e1),e2) ),
file('ALG061+1.p',unknown),
[] ).
cnf(211,axiom,
( equal(op(e1,e0),e2)
| equal(op(e1,e1),e2)
| equal(op(e1,e2),e2)
| equal(op(e1,e3),e2)
| equal(op(e1,e4),e2) ),
file('ALG061+1.p',unknown),
[] ).
cnf(213,axiom,
( equal(op(e1,e0),e1)
| equal(op(e1,e1),e1)
| equal(op(e1,e2),e1)
| equal(op(e1,e3),e1)
| equal(op(e1,e4),e1) ),
file('ALG061+1.p',unknown),
[] ).
cnf(216,axiom,
( equal(op(e0,e0),e4)
| equal(op(e1,e0),e4)
| equal(op(e2,e0),e4)
| equal(op(e3,e0),e4)
| equal(op(e4,e0),e4) ),
file('ALG061+1.p',unknown),
[] ).
cnf(228,axiom,
( equal(op(e4,e2),e0)
| equal(op(e4,e2),e1)
| equal(op(e4,e2),e2)
| equal(op(e4,e2),e3)
| equal(op(e4,e2),e4) ),
file('ALG061+1.p',unknown),
[] ).
cnf(236,axiom,
( equal(op(e2,e4),e0)
| equal(op(e2,e4),e1)
| equal(op(e2,e4),e2)
| equal(op(e2,e4),e3)
| equal(op(e2,e4),e4) ),
file('ALG061+1.p',unknown),
[] ).
cnf(239,axiom,
( equal(op(e2,e1),e0)
| equal(op(e2,e1),e1)
| equal(op(e2,e1),e2)
| equal(op(e2,e1),e3)
| equal(op(e2,e1),e4) ),
file('ALG061+1.p',unknown),
[] ).
cnf(241,axiom,
( equal(op(e1,e4),e0)
| equal(op(e1,e4),e1)
| equal(op(e1,e4),e2)
| equal(op(e1,e4),e3)
| equal(op(e1,e4),e4) ),
file('ALG061+1.p',unknown),
[] ).
cnf(246,axiom,
( equal(op(e0,e4),e0)
| equal(op(e0,e4),e1)
| equal(op(e0,e4),e2)
| equal(op(e0,e4),e3)
| equal(op(e0,e4),e4) ),
file('ALG061+1.p',unknown),
[] ).
cnf(247,axiom,
( equal(op(e0,e3),e3)
| equal(op(e0,e3),e0)
| equal(op(e0,e3),e4)
| equal(op(e0,e3),e2)
| equal(op(e0,e3),e1) ),
file('ALG061+1.p',unknown),
[] ).
cnf(254,axiom,
( equal(op(e0,e0),e1)
| equal(op(e1,e1),e1)
| equal(op(e2,e2),e1)
| equal(op(e3,e3),e1)
| equal(op(e4,e4),e1) ),
file('ALG061+1.p',unknown),
[] ).
cnf(255,axiom,
( equal(op(e0,e0),e0)
| equal(op(e1,e1),e0)
| equal(op(e2,e2),e0)
| equal(op(e3,e3),e0)
| equal(op(e4,e4),e0) ),
file('ALG061+1.p',unknown),
[] ).
cnf(256,plain,
~ equal(op(e1,e4),e4),
inference(rew,[status(thm),theory(equality)],[21,88]),
[iquote('0:Rew:21.0,88.0')] ).
cnf(257,plain,
~ equal(op(e1,e3),e4),
inference(rew,[status(thm),theory(equality)],[21,87]),
[iquote('0:Rew:21.0,87.0')] ).
cnf(259,plain,
~ equal(op(e1,e0),e4),
inference(rew,[status(thm),theory(equality)],[21,82]),
[iquote('0:Rew:21.0,82.0')] ).
cnf(262,plain,
~ equal(op(e2,e1),e4),
inference(rew,[status(thm),theory(equality)],[21,36]),
[iquote('0:Rew:21.0,36.0')] ).
cnf(264,plain,
equal(op(e4,e4),e2),
inference(rew,[status(thm),theory(equality)],[21,142]),
[iquote('0:Rew:21.0,142.0')] ).
cnf(265,plain,
~ equal(op(e4,e3),e2),
inference(rew,[status(thm),theory(equality)],[264,121]),
[iquote('0:Rew:264.0,121.0')] ).
cnf(266,plain,
~ equal(op(e4,e2),e2),
inference(rew,[status(thm),theory(equality)],[264,120]),
[iquote('0:Rew:264.0,120.0')] ).
cnf(267,plain,
~ equal(op(e4,e1),e2),
inference(rew,[status(thm),theory(equality)],[264,118]),
[iquote('0:Rew:264.0,118.0')] ).
cnf(270,plain,
~ equal(op(e2,e4),e2),
inference(rew,[status(thm),theory(equality)],[264,70]),
[iquote('0:Rew:264.0,70.0')] ).
cnf(271,plain,
~ equal(op(e1,e4),e2),
inference(rew,[status(thm),theory(equality)],[264,68]),
[iquote('0:Rew:264.0,68.0')] ).
cnf(272,plain,
~ equal(op(e0,e4),e2),
inference(rew,[status(thm),theory(equality)],[264,65]),
[iquote('0:Rew:264.0,65.0')] ).
cnf(280,plain,
( ~ equal(e0,e0)
| ~ skC0 ),
inference(rew,[status(thm),theory(equality)],[122,143]),
[iquote('0:Rew:122.1,143.0')] ).
cnf(281,plain,
~ skC0,
inference(obv,[status(thm),theory(equality)],[280]),
[iquote('0:Obv:280.0')] ).
cnf(282,plain,
equal(op(e1,e2),e0),
inference(rew,[status(thm),theory(equality)],[264,168,21]),
[iquote('0:Rew:264.0,168.0,21.0,168.0')] ).
cnf(283,plain,
~ equal(op(e1,e4),e0),
inference(rew,[status(thm),theory(equality)],[282,90]),
[iquote('0:Rew:282.0,90.0')] ).
cnf(287,plain,
~ equal(op(e4,e2),e0),
inference(rew,[status(thm),theory(equality)],[282,48]),
[iquote('0:Rew:282.0,48.0')] ).
cnf(293,plain,
( equal(op(e4,e2),e4)
| skC16
| skC17
| skC18
| skC19 ),
inference(rew,[status(thm),theory(equality)],[264,167]),
[iquote('0:Rew:264.0,167.0')] ).
cnf(297,plain,
( skC3
| skC2
| skC1
| equal(op(e0,op(e4,e0)),e4) ),
inference(mrr,[status(thm)],[163,281]),
[iquote('0:MRR:163.1,281.0')] ).
cnf(298,plain,
( ~ equal(e4,e4)
| skC16
| skC17
| skC18
| skC19 ),
inference(rew,[status(thm),theory(equality)],[293,173,264]),
[iquote('0:Rew:293.0,173.0,264.0,173.0')] ).
cnf(299,plain,
( skC19
| skC18
| skC17
| skC16 ),
inference(obv,[status(thm),theory(equality)],[298]),
[iquote('0:Obv:298.0')] ).
cnf(304,plain,
equal(op(e2,e2),e3),
inference(rew,[status(thm),theory(equality)],[264,175,21]),
[iquote('0:Rew:264.0,175.0,21.0,175.0')] ).
cnf(305,plain,
~ equal(op(e2,e4),e3),
inference(rew,[status(thm),theory(equality)],[304,100]),
[iquote('0:Rew:304.0,100.0')] ).
cnf(307,plain,
~ equal(op(e2,e1),e3),
inference(rew,[status(thm),theory(equality)],[304,96]),
[iquote('0:Rew:304.0,96.0')] ).
cnf(309,plain,
~ equal(op(e4,e2),e3),
inference(rew,[status(thm),theory(equality)],[304,50]),
[iquote('0:Rew:304.0,50.0')] ).
cnf(319,plain,
( equal(op(e4,e0),e3)
| equal(op(e4,e1),e3)
| equal(op(e4,e2),e3)
| equal(op(e4,e3),e3)
| equal(e3,e2) ),
inference(rew,[status(thm),theory(equality)],[264,179]),
[iquote('0:Rew:264.0,179.4')] ).
cnf(320,plain,
( equal(op(e4,e3),e3)
| equal(op(e4,e1),e3)
| equal(op(e4,e0),e3) ),
inference(mrr,[status(thm)],[319,309,8]),
[iquote('0:MRR:319.2,319.4,309.0,8.0')] ).
cnf(325,plain,
( equal(op(e0,e4),e0)
| equal(op(e1,e4),e0)
| equal(op(e2,e4),e0)
| equal(op(e3,e4),e0)
| equal(e2,e0) ),
inference(rew,[status(thm),theory(equality)],[264,184]),
[iquote('0:Rew:264.0,184.4')] ).
cnf(326,plain,
( equal(op(e0,e4),e0)
| equal(op(e3,e4),e0)
| equal(op(e2,e4),e0) ),
inference(mrr,[status(thm)],[325,283,2]),
[iquote('0:MRR:325.1,325.4,283.0,2.0')] ).
cnf(327,plain,
( equal(op(e4,e0),e0)
| equal(op(e4,e1),e0)
| equal(op(e4,e2),e0)
| equal(op(e4,e3),e0)
| equal(e2,e0) ),
inference(rew,[status(thm),theory(equality)],[264,185]),
[iquote('0:Rew:264.0,185.4')] ).
cnf(328,plain,
( equal(op(e4,e0),e0)
| equal(op(e4,e3),e0)
| equal(op(e4,e1),e0) ),
inference(mrr,[status(thm)],[327,287,2]),
[iquote('0:MRR:327.2,327.4,287.0,2.0')] ).
cnf(329,plain,
( equal(op(e4,e3),e4)
| equal(op(e3,e3),e4)
| equal(op(e2,e3),e4)
| equal(op(e0,e3),e4) ),
inference(mrr,[status(thm)],[186,257]),
[iquote('0:MRR:186.1,257.0')] ).
cnf(333,plain,
( equal(op(e3,e3),e2)
| equal(op(e2,e3),e2)
| equal(op(e1,e3),e2)
| equal(op(e0,e3),e2) ),
inference(mrr,[status(thm)],[190,265]),
[iquote('0:MRR:190.4,265.0')] ).
cnf(337,plain,
( equal(op(e0,e2),e4)
| equal(e4,e0)
| equal(e4,e3)
| equal(op(e3,e2),e4)
| equal(op(e4,e2),e4) ),
inference(rew,[status(thm),theory(equality)],[304,196,282]),
[iquote('0:Rew:304.0,196.2,282.0,196.1')] ).
cnf(338,plain,
( equal(op(e4,e2),e4)
| equal(op(e3,e2),e4)
| equal(op(e0,e2),e4) ),
inference(mrr,[status(thm)],[337,4,10]),
[iquote('0:MRR:337.1,337.2,4.0,10.0')] ).
cnf(341,plain,
( equal(op(e0,e2),e2)
| equal(e2,e0)
| equal(e3,e2)
| equal(op(e3,e2),e2)
| equal(op(e4,e2),e2) ),
inference(rew,[status(thm),theory(equality)],[304,200,282]),
[iquote('0:Rew:304.0,200.2,282.0,200.1')] ).
cnf(342,plain,
( equal(op(e3,e2),e2)
| equal(op(e0,e2),e2) ),
inference(mrr,[status(thm)],[341,2,8,266]),
[iquote('0:MRR:341.1,341.2,341.4,2.0,8.0,266.0')] ).
cnf(347,plain,
( equal(op(e2,e0),e1)
| equal(op(e2,e1),e1)
| equal(e3,e1)
| equal(op(e2,e3),e1)
| equal(op(e2,e4),e1) ),
inference(rew,[status(thm),theory(equality)],[304,203]),
[iquote('0:Rew:304.0,203.2')] ).
cnf(348,plain,
( equal(op(e2,e1),e1)
| equal(op(e2,e4),e1)
| equal(op(e2,e3),e1)
| equal(op(e2,e0),e1) ),
inference(mrr,[status(thm)],[347,6]),
[iquote('0:MRR:347.2,6.0')] ).
cnf(353,plain,
( equal(op(e1,e0),e3)
| equal(e4,e3)
| equal(e3,e0)
| equal(op(e1,e3),e3)
| equal(op(e1,e4),e3) ),
inference(rew,[status(thm),theory(equality)],[282,209,21]),
[iquote('0:Rew:282.0,209.2,21.0,209.1')] ).
cnf(354,plain,
( equal(op(e1,e3),e3)
| equal(op(e1,e4),e3)
| equal(op(e1,e0),e3) ),
inference(mrr,[status(thm)],[353,10,3]),
[iquote('0:MRR:353.1,353.2,10.0,3.0')] ).
cnf(355,plain,
( equal(op(e0,e1),e2)
| equal(e4,e2)
| equal(op(e2,e1),e2)
| equal(op(e3,e1),e2)
| equal(op(e4,e1),e2) ),
inference(rew,[status(thm),theory(equality)],[21,210]),
[iquote('0:Rew:21.0,210.1')] ).
cnf(356,plain,
( equal(op(e2,e1),e2)
| equal(op(e3,e1),e2)
| equal(op(e0,e1),e2) ),
inference(mrr,[status(thm)],[355,9,267]),
[iquote('0:MRR:355.1,355.4,9.0,267.0')] ).
cnf(357,plain,
( equal(op(e1,e0),e2)
| equal(e4,e2)
| equal(e2,e0)
| equal(op(e1,e3),e2)
| equal(op(e1,e4),e2) ),
inference(rew,[status(thm),theory(equality)],[282,211,21]),
[iquote('0:Rew:282.0,211.2,21.0,211.1')] ).
cnf(358,plain,
( equal(op(e1,e3),e2)
| equal(op(e1,e0),e2) ),
inference(mrr,[status(thm)],[357,9,2,271]),
[iquote('0:MRR:357.1,357.2,357.4,9.0,2.0,271.0')] ).
cnf(361,plain,
( equal(op(e1,e0),e1)
| equal(e4,e1)
| equal(e1,e0)
| equal(op(e1,e3),e1)
| equal(op(e1,e4),e1) ),
inference(rew,[status(thm),theory(equality)],[282,213,21]),
[iquote('0:Rew:282.0,213.2,21.0,213.1')] ).
cnf(362,plain,
( equal(op(e1,e4),e1)
| equal(op(e1,e3),e1)
| equal(op(e1,e0),e1) ),
inference(mrr,[status(thm)],[361,7,1]),
[iquote('0:MRR:361.1,361.2,7.0,1.0')] ).
cnf(365,plain,
( equal(op(e4,e0),e4)
| equal(op(e0,e0),e4)
| equal(op(e3,e0),e4)
| equal(op(e2,e0),e4) ),
inference(mrr,[status(thm)],[216,259]),
[iquote('0:MRR:216.1,259.0')] ).
cnf(374,plain,
( equal(op(e4,e2),e4)
| equal(op(e4,e2),e1) ),
inference(mrr,[status(thm)],[228,287,266,309]),
[iquote('0:MRR:228.0,228.2,228.3,287.0,266.0,309.0')] ).
cnf(380,plain,
( equal(op(e2,e4),e4)
| equal(op(e2,e4),e1)
| equal(op(e2,e4),e0) ),
inference(mrr,[status(thm)],[236,270,305]),
[iquote('0:MRR:236.2,236.3,270.0,305.0')] ).
cnf(382,plain,
( equal(op(e2,e1),e2)
| equal(op(e2,e1),e1)
| equal(op(e2,e1),e0) ),
inference(mrr,[status(thm)],[239,307,262]),
[iquote('0:MRR:239.3,239.4,307.0,262.0')] ).
cnf(384,plain,
( equal(op(e1,e4),e1)
| equal(op(e1,e4),e3) ),
inference(mrr,[status(thm)],[241,283,271,256]),
[iquote('0:MRR:241.0,241.2,241.4,283.0,271.0,256.0')] ).
cnf(387,plain,
( equal(op(e0,e4),e4)
| equal(op(e0,e4),e0)
| equal(op(e0,e4),e3)
| equal(op(e0,e4),e1) ),
inference(mrr,[status(thm)],[246,272]),
[iquote('0:MRR:246.2,272.0')] ).
cnf(390,plain,
( equal(op(e0,e0),e1)
| equal(e4,e1)
| equal(e3,e1)
| equal(op(e3,e3),e1)
| equal(e2,e1) ),
inference(rew,[status(thm),theory(equality)],[264,254,304,21]),
[iquote('0:Rew:264.0,254.4,304.0,254.2,21.0,254.1')] ).
cnf(391,plain,
( equal(op(e3,e3),e1)
| equal(op(e0,e0),e1) ),
inference(mrr,[status(thm)],[390,7,6,5]),
[iquote('0:MRR:390.1,390.2,390.4,7.0,6.0,5.0')] ).
cnf(392,plain,
( equal(op(e0,e0),e0)
| equal(e4,e0)
| equal(e3,e0)
| equal(op(e3,e3),e0)
| equal(e2,e0) ),
inference(rew,[status(thm),theory(equality)],[264,255,304,21]),
[iquote('0:Rew:264.0,255.4,304.0,255.2,21.0,255.1')] ).
cnf(393,plain,
( equal(op(e0,e0),e0)
| equal(op(e3,e3),e0) ),
inference(mrr,[status(thm)],[392,4,3,2]),
[iquote('0:MRR:392.1,392.2,392.4,4.0,3.0,2.0')] ).
cnf(394,plain,
equal(e0,unit),
inference(spt,[spt(split,[position(s1)])],[174]),
[iquote('1:Spt:174.4')] ).
cnf(399,plain,
( equal(op(e4,e3),e3)
| equal(op(e4,e1),e3)
| equal(op(e4,unit),e3) ),
inference(rew,[status(thm),theory(equality)],[394,320]),
[iquote('1:Rew:394.0,320.2')] ).
cnf(404,plain,
~ equal(op(e4,e2),op(e4,unit)),
inference(rew,[status(thm),theory(equality)],[394,113]),
[iquote('1:Rew:394.0,113.0')] ).
cnf(425,plain,
~ equal(op(e2,e1),op(e2,unit)),
inference(rew,[status(thm),theory(equality)],[394,92]),
[iquote('1:Rew:394.0,92.0')] ).
cnf(434,plain,
~ equal(op(e1,e4),op(e1,unit)),
inference(rew,[status(thm),theory(equality)],[394,85]),
[iquote('1:Rew:394.0,85.0')] ).
cnf(448,plain,
~ equal(op(e4,e3),op(unit,e3)),
inference(rew,[status(thm),theory(equality)],[394,55]),
[iquote('1:Rew:394.0,55.0')] ).
cnf(459,plain,
~ equal(op(e2,e4),op(unit,e4)),
inference(rew,[status(thm),theory(equality)],[394,63]),
[iquote('1:Rew:394.0,63.0')] ).
cnf(480,plain,
~ equal(op(e2,e1),op(unit,e1)),
inference(rew,[status(thm),theory(equality)],[394,33]),
[iquote('1:Rew:394.0,33.0')] ).
cnf(492,plain,
( equal(op(unit,e4),unit)
| equal(op(e3,e4),e0)
| equal(op(e2,e4),e0) ),
inference(rew,[status(thm),theory(equality)],[394,326]),
[iquote('1:Rew:394.0,326.0')] ).
cnf(494,plain,
( equal(op(e2,e4),e4)
| equal(op(e2,e4),e1)
| equal(op(e2,e4),unit) ),
inference(rew,[status(thm),theory(equality)],[394,380]),
[iquote('1:Rew:394.0,380.2')] ).
cnf(507,plain,
( equal(op(e2,e1),e2)
| equal(op(e2,e1),e1)
| equal(op(e2,e1),unit) ),
inference(rew,[status(thm),theory(equality)],[394,382]),
[iquote('1:Rew:394.0,382.2')] ).
cnf(508,plain,
~ equal(e4,unit),
inference(rew,[status(thm),theory(equality)],[394,4]),
[iquote('1:Rew:394.0,4.0')] ).
cnf(510,plain,
~ equal(e2,unit),
inference(rew,[status(thm),theory(equality)],[394,2]),
[iquote('1:Rew:394.0,2.0')] ).
cnf(521,plain,
( ~ skC16
| equal(op(e4,op(unit,e4)),unit) ),
inference(rew,[status(thm),theory(equality)],[394,138]),
[iquote('1:Rew:394.0,138.1')] ).
cnf(550,plain,
~ equal(op(e4,e2),e4),
inference(rew,[status(thm),theory(equality)],[20,404]),
[iquote('1:Rew:20.0,404.0')] ).
cnf(551,plain,
equal(op(e4,e2),e1),
inference(mrr,[status(thm)],[374,550]),
[iquote('1:MRR:374.0,550.0')] ).
cnf(554,plain,
~ equal(op(e4,e3),e1),
inference(rew,[status(thm),theory(equality)],[551,119]),
[iquote('1:Rew:551.0,119.0')] ).
cnf(568,plain,
~ equal(op(e2,e1),e2),
inference(rew,[status(thm),theory(equality)],[16,425]),
[iquote('1:Rew:16.0,425.0')] ).
cnf(571,plain,
~ equal(op(e1,e4),e1),
inference(rew,[status(thm),theory(equality)],[14,434]),
[iquote('1:Rew:14.0,434.0')] ).
cnf(572,plain,
equal(op(e1,e4),e3),
inference(mrr,[status(thm)],[384,571]),
[iquote('1:MRR:384.0,571.0')] ).
cnf(578,plain,
( ~ skC17
| equal(op(e4,e3),e1) ),
inference(rew,[status(thm),theory(equality)],[572,139]),
[iquote('1:Rew:572.0,139.1')] ).
cnf(583,plain,
~ skC17,
inference(mrr,[status(thm)],[578,554]),
[iquote('1:MRR:578.1,554.0')] ).
cnf(584,plain,
( skC19
| skC18
| skC16 ),
inference(mrr,[status(thm)],[299,583]),
[iquote('1:MRR:299.2,583.0')] ).
cnf(589,plain,
~ equal(op(e4,e3),e3),
inference(rew,[status(thm),theory(equality)],[17,448]),
[iquote('1:Rew:17.0,448.0')] ).
cnf(595,plain,
~ equal(op(e2,e4),e4),
inference(rew,[status(thm),theory(equality)],[19,459]),
[iquote('1:Rew:19.0,459.0')] ).
cnf(606,plain,
~ equal(op(e2,e1),e1),
inference(rew,[status(thm),theory(equality)],[13,480]),
[iquote('1:Rew:13.0,480.0')] ).
cnf(615,plain,
( ~ skC16
| equal(e2,unit) ),
inference(rew,[status(thm),theory(equality)],[264,521,19]),
[iquote('1:Rew:264.0,521.1,19.0,521.1')] ).
cnf(616,plain,
~ skC16,
inference(mrr,[status(thm)],[615,510]),
[iquote('1:MRR:615.1,510.0')] ).
cnf(617,plain,
( skC19
| skC18 ),
inference(mrr,[status(thm)],[584,616]),
[iquote('1:MRR:584.2,616.0')] ).
cnf(675,plain,
( equal(op(e4,e3),e3)
| equal(op(e4,e1),e3)
| equal(e4,e3) ),
inference(rew,[status(thm),theory(equality)],[20,399]),
[iquote('1:Rew:20.0,399.2')] ).
cnf(676,plain,
equal(op(e4,e1),e3),
inference(mrr,[status(thm)],[675,589,10]),
[iquote('1:MRR:675.0,675.2,589.0,10.0')] ).
cnf(716,plain,
( equal(e4,unit)
| equal(op(e3,e4),unit)
| equal(op(e2,e4),unit) ),
inference(rew,[status(thm),theory(equality)],[394,492,19]),
[iquote('1:Rew:394.0,492.2,394.0,492.1,19.0,492.0')] ).
cnf(717,plain,
( equal(op(e3,e4),unit)
| equal(op(e2,e4),unit) ),
inference(mrr,[status(thm)],[716,508]),
[iquote('1:MRR:716.0,508.0')] ).
cnf(718,plain,
( equal(op(e2,e4),e1)
| equal(op(e2,e4),unit) ),
inference(mrr,[status(thm)],[494,595]),
[iquote('1:MRR:494.0,595.0')] ).
cnf(730,plain,
equal(op(e2,e1),unit),
inference(mrr,[status(thm)],[507,568,606]),
[iquote('1:MRR:507.0,507.1,568.0,606.0')] ).
cnf(733,plain,
~ equal(op(e2,e4),unit),
inference(rew,[status(thm),theory(equality)],[730,98]),
[iquote('1:Rew:730.0,98.0')] ).
cnf(740,plain,
equal(op(e3,e4),unit),
inference(mrr,[status(thm)],[717,733]),
[iquote('1:MRR:717.1,733.0')] ).
cnf(741,plain,
equal(op(e2,e4),e1),
inference(mrr,[status(thm)],[718,733]),
[iquote('1:MRR:718.1,733.0')] ).
cnf(744,plain,
( ~ skC19
| equal(op(e4,unit),e3) ),
inference(rew,[status(thm),theory(equality)],[740,141]),
[iquote('1:Rew:740.0,141.1')] ).
cnf(751,plain,
( ~ skC18
| equal(op(e4,e1),e2) ),
inference(rew,[status(thm),theory(equality)],[741,140]),
[iquote('1:Rew:741.0,140.1')] ).
cnf(757,plain,
( ~ skC19
| equal(e4,e3) ),
inference(rew,[status(thm),theory(equality)],[20,744]),
[iquote('1:Rew:20.0,744.1')] ).
cnf(758,plain,
~ skC19,
inference(mrr,[status(thm)],[757,10]),
[iquote('1:MRR:757.1,10.0')] ).
cnf(759,plain,
skC18,
inference(mrr,[status(thm)],[617,758]),
[iquote('1:MRR:617.0,758.0')] ).
cnf(760,plain,
( ~ skC18
| equal(e3,e2) ),
inference(rew,[status(thm),theory(equality)],[676,751]),
[iquote('1:Rew:676.0,751.1')] ).
cnf(761,plain,
$false,
inference(mrr,[status(thm)],[760,759,8]),
[iquote('1:MRR:760.0,760.1,759.0,8.0')] ).
cnf(778,plain,
~ equal(e0,unit),
inference(spt,[spt(split,[position(sa)])],[761,394]),
[iquote('1:Spt:761.0,174.4,394.0')] ).
cnf(779,plain,
( equal(e4,unit)
| equal(e3,unit)
| equal(e2,unit)
| equal(e1,unit) ),
inference(spt,[spt(split,[position(s2)])],[174]),
[iquote('1:Spt:761.0,174.0,174.1,174.2,174.3')] ).
cnf(780,plain,
equal(e4,unit),
inference(spt,[spt(split,[position(s2s1)])],[779]),
[iquote('2:Spt:779.0')] ).
cnf(782,plain,
~ equal(e2,unit),
inference(rew,[status(thm),theory(equality)],[780,9]),
[iquote('2:Rew:780.0,9.0')] ).
cnf(792,plain,
~ equal(op(e0,e2),op(unit,e2)),
inference(rew,[status(thm),theory(equality)],[780,45]),
[iquote('2:Rew:780.0,45.0')] ).
cnf(808,plain,
~ equal(op(e0,e0),op(e0,unit)),
inference(rew,[status(thm),theory(equality)],[780,75]),
[iquote('2:Rew:780.0,75.0')] ).
cnf(846,plain,
~ equal(op(e0,e3),op(unit,e3)),
inference(rew,[status(thm),theory(equality)],[780,55]),
[iquote('2:Rew:780.0,55.0')] ).
cnf(875,plain,
~ equal(op(e2,e1),op(e2,unit)),
inference(rew,[status(thm),theory(equality)],[780,98]),
[iquote('2:Rew:780.0,98.0')] ).
cnf(888,plain,
( equal(op(unit,e2),unit)
| equal(op(e3,e2),e4)
| equal(op(e0,e2),e4) ),
inference(rew,[status(thm),theory(equality)],[780,338]),
[iquote('2:Rew:780.0,338.0')] ).
cnf(911,plain,
( equal(op(e0,e3),e3)
| equal(op(e0,e3),e0)
| equal(op(e0,e3),unit)
| equal(op(e0,e3),e2)
| equal(op(e0,e3),e1) ),
inference(rew,[status(thm),theory(equality)],[780,247]),
[iquote('2:Rew:780.0,247.2')] ).
cnf(930,plain,
~ equal(op(e0,e2),e2),
inference(rew,[status(thm),theory(equality)],[15,792]),
[iquote('2:Rew:15.0,792.0')] ).
cnf(931,plain,
equal(op(e3,e2),e2),
inference(mrr,[status(thm)],[342,930]),
[iquote('2:MRR:342.1,930.0')] ).
cnf(938,plain,
~ equal(op(e3,e1),e2),
inference(rew,[status(thm),theory(equality)],[931,106]),
[iquote('2:Rew:931.0,106.0')] ).
cnf(943,plain,
( equal(op(e2,e1),e2)
| equal(op(e0,e1),e2) ),
inference(mrr,[status(thm)],[356,938]),
[iquote('2:MRR:356.1,938.0')] ).
cnf(951,plain,
~ equal(op(e0,e0),e0),
inference(rew,[status(thm),theory(equality)],[12,808]),
[iquote('2:Rew:12.0,808.0')] ).
cnf(952,plain,
equal(op(e3,e3),e0),
inference(mrr,[status(thm)],[393,951]),
[iquote('2:MRR:393.0,951.0')] ).
cnf(953,plain,
~ equal(op(e0,e3),e0),
inference(rew,[status(thm),theory(equality)],[952,54]),
[iquote('2:Rew:952.0,54.0')] ).
cnf(958,plain,
( equal(e1,e0)
| equal(op(e0,e0),e1) ),
inference(rew,[status(thm),theory(equality)],[952,391]),
[iquote('2:Rew:952.0,391.0')] ).
cnf(976,plain,
~ equal(op(e0,e3),e3),
inference(rew,[status(thm),theory(equality)],[17,846]),
[iquote('2:Rew:17.0,846.0')] ).
cnf(994,plain,
~ equal(op(e2,e1),e2),
inference(rew,[status(thm),theory(equality)],[16,875]),
[iquote('2:Rew:16.0,875.0')] ).
cnf(998,plain,
equal(op(e0,e0),e1),
inference(mrr,[status(thm)],[958,1]),
[iquote('2:MRR:958.0,1.0')] ).
cnf(1004,plain,
~ equal(op(e0,e3),e1),
inference(rew,[status(thm),theory(equality)],[998,74]),
[iquote('2:Rew:998.0,74.0')] ).
cnf(1028,plain,
equal(op(e0,e1),e2),
inference(mrr,[status(thm)],[943,994]),
[iquote('2:MRR:943.0,994.0')] ).
cnf(1032,plain,
~ equal(op(e0,e3),e2),
inference(rew,[status(thm),theory(equality)],[1028,77]),
[iquote('2:Rew:1028.0,77.0')] ).
cnf(1090,plain,
( equal(e2,unit)
| equal(e2,unit)
| equal(op(e0,e2),unit) ),
inference(rew,[status(thm),theory(equality)],[780,888,931,15]),
[iquote('2:Rew:780.0,888.2,931.0,888.1,780.0,888.1,15.0,888.0')] ).
cnf(1091,plain,
( equal(e2,unit)
| equal(op(e0,e2),unit) ),
inference(obv,[status(thm),theory(equality)],[1090]),
[iquote('2:Obv:1090.0')] ).
cnf(1092,plain,
equal(op(e0,e2),unit),
inference(mrr,[status(thm)],[1091,782]),
[iquote('2:MRR:1091.0,782.0')] ).
cnf(1095,plain,
~ equal(op(e0,e3),unit),
inference(rew,[status(thm),theory(equality)],[1092,79]),
[iquote('2:Rew:1092.0,79.0')] ).
cnf(1149,plain,
$false,
inference(mrr,[status(thm)],[911,976,953,1095,1032,1004]),
[iquote('2:MRR:911.0,911.1,911.2,911.3,911.4,976.0,953.0,1095.0,1032.0,1004.0')] ).
cnf(1150,plain,
~ equal(e4,unit),
inference(spt,[spt(split,[position(s2sa)])],[1149,780]),
[iquote('2:Spt:1149.0,779.0,780.0')] ).
cnf(1151,plain,
( equal(e3,unit)
| equal(e2,unit)
| equal(e1,unit) ),
inference(spt,[spt(split,[position(s2s2)])],[779]),
[iquote('2:Spt:1149.0,779.1,779.2,779.3')] ).
cnf(1152,plain,
equal(e3,unit),
inference(spt,[spt(split,[position(s2s2s1)])],[1151]),
[iquote('3:Spt:1151.0')] ).
cnf(1154,plain,
~ equal(e1,unit),
inference(rew,[status(thm),theory(equality)],[1152,6]),
[iquote('3:Rew:1152.0,6.0')] ).
cnf(1155,plain,
equal(op(unit,unit),unit),
inference(rew,[status(thm),theory(equality)],[1152,18]),
[iquote('3:Rew:1152.0,18.0')] ).
cnf(1190,plain,
~ equal(op(e0,e4),op(unit,e4)),
inference(rew,[status(thm),theory(equality)],[1152,64]),
[iquote('3:Rew:1152.0,64.0')] ).
cnf(1209,plain,
~ equal(op(e1,e4),op(e1,unit)),
inference(rew,[status(thm),theory(equality)],[1152,91]),
[iquote('3:Rew:1152.0,91.0')] ).
cnf(1250,plain,
( equal(op(unit,unit),e1)
| equal(op(e0,e0),e1) ),
inference(rew,[status(thm),theory(equality)],[1152,391]),
[iquote('3:Rew:1152.0,391.0')] ).
cnf(1252,plain,
~ equal(op(e0,e4),op(e0,unit)),
inference(rew,[status(thm),theory(equality)],[1152,81]),
[iquote('3:Rew:1152.0,81.0')] ).
cnf(1274,plain,
( equal(op(e1,e4),e1)
| equal(op(e1,e4),unit) ),
inference(rew,[status(thm),theory(equality)],[1152,384]),
[iquote('3:Rew:1152.0,384.1')] ).
cnf(1290,plain,
( equal(op(e0,e4),e4)
| equal(op(e0,e4),e0)
| equal(op(e0,e4),unit)
| equal(op(e0,e4),e1) ),
inference(rew,[status(thm),theory(equality)],[1152,387]),
[iquote('3:Rew:1152.0,387.2')] ).
cnf(1316,plain,
~ equal(op(e0,e4),e4),
inference(rew,[status(thm),theory(equality)],[19,1190]),
[iquote('3:Rew:19.0,1190.0')] ).
cnf(1332,plain,
~ equal(op(e1,e4),e1),
inference(rew,[status(thm),theory(equality)],[14,1209]),
[iquote('3:Rew:14.0,1209.0')] ).
cnf(1352,plain,
~ equal(op(e0,e4),e0),
inference(rew,[status(thm),theory(equality)],[12,1252]),
[iquote('3:Rew:12.0,1252.0')] ).
cnf(1391,plain,
( equal(e1,unit)
| equal(op(e0,e0),e1) ),
inference(rew,[status(thm),theory(equality)],[1155,1250]),
[iquote('3:Rew:1155.0,1250.0')] ).
cnf(1392,plain,
equal(op(e0,e0),e1),
inference(mrr,[status(thm)],[1391,1154]),
[iquote('3:MRR:1391.0,1154.0')] ).
cnf(1394,plain,
~ equal(op(e0,e4),e1),
inference(rew,[status(thm),theory(equality)],[1392,75]),
[iquote('3:Rew:1392.0,75.0')] ).
cnf(1404,plain,
equal(op(e1,e4),unit),
inference(mrr,[status(thm)],[1274,1332]),
[iquote('3:MRR:1274.0,1332.0')] ).
cnf(1409,plain,
~ equal(op(e0,e4),unit),
inference(rew,[status(thm),theory(equality)],[1404,62]),
[iquote('3:Rew:1404.0,62.0')] ).
cnf(1514,plain,
$false,
inference(mrr,[status(thm)],[1290,1316,1352,1409,1394]),
[iquote('3:MRR:1290.0,1290.1,1290.2,1290.3,1316.0,1352.0,1409.0,1394.0')] ).
cnf(1519,plain,
~ equal(e3,unit),
inference(spt,[spt(split,[position(s2s2sa)])],[1514,1152]),
[iquote('3:Spt:1514.0,1151.0,1152.0')] ).
cnf(1520,plain,
( equal(e2,unit)
| equal(e1,unit) ),
inference(spt,[spt(split,[position(s2s2s2)])],[1151]),
[iquote('3:Spt:1514.0,1151.1,1151.2')] ).
cnf(1521,plain,
equal(e2,unit),
inference(spt,[spt(split,[position(s2s2s2s1)])],[1520]),
[iquote('4:Spt:1520.0')] ).
cnf(1522,plain,
~ equal(e1,unit),
inference(rew,[status(thm),theory(equality)],[1521,5]),
[iquote('4:Rew:1521.0,5.0')] ).
cnf(1540,plain,
~ equal(op(e0,e0),op(unit,e0)),
inference(rew,[status(thm),theory(equality)],[1521,23]),
[iquote('4:Rew:1521.0,23.0')] ).
cnf(1541,plain,
~ equal(op(e4,e0),op(unit,e0)),
inference(rew,[status(thm),theory(equality)],[1521,30]),
[iquote('4:Rew:1521.0,30.0')] ).
cnf(1542,plain,
( equal(op(e4,e0),e4)
| equal(op(e0,e0),e4)
| equal(op(e3,e0),e4)
| equal(op(unit,e0),e4) ),
inference(rew,[status(thm),theory(equality)],[1521,365]),
[iquote('4:Rew:1521.0,365.3')] ).
cnf(1550,plain,
~ equal(op(e1,e3),op(unit,e3)),
inference(rew,[status(thm),theory(equality)],[1521,56]),
[iquote('4:Rew:1521.0,56.0')] ).
cnf(1551,plain,
~ equal(op(e4,e3),op(unit,e3)),
inference(rew,[status(thm),theory(equality)],[1521,60]),
[iquote('4:Rew:1521.0,60.0')] ).
cnf(1616,plain,
( equal(op(e1,e3),e2)
| equal(op(e1,e0),unit) ),
inference(rew,[status(thm),theory(equality)],[1521,358]),
[iquote('4:Rew:1521.0,358.1')] ).
cnf(1623,plain,
( ~ skC2
| equal(op(e0,op(unit,e0)),unit) ),
inference(rew,[status(thm),theory(equality)],[1521,124]),
[iquote('4:Rew:1521.0,124.1')] ).
cnf(1629,plain,
( equal(op(e3,e3),e2)
| equal(op(e2,e3),e2)
| equal(op(e1,e3),unit)
| equal(op(e0,e3),e2) ),
inference(rew,[status(thm),theory(equality)],[1521,333]),
[iquote('4:Rew:1521.0,333.2')] ).
cnf(1670,plain,
~ equal(op(e0,e0),e0),
inference(rew,[status(thm),theory(equality)],[11,1540]),
[iquote('4:Rew:11.0,1540.0')] ).
cnf(1671,plain,
equal(op(e3,e3),e0),
inference(mrr,[status(thm)],[393,1670]),
[iquote('4:MRR:393.0,1670.0')] ).
cnf(1677,plain,
~ equal(op(e4,e3),e0),
inference(rew,[status(thm),theory(equality)],[1671,61]),
[iquote('4:Rew:1671.0,61.0')] ).
cnf(1679,plain,
( equal(e1,e0)
| equal(op(e0,e0),e1) ),
inference(rew,[status(thm),theory(equality)],[1671,391]),
[iquote('4:Rew:1671.0,391.0')] ).
cnf(1682,plain,
( equal(op(e4,e0),e0)
| equal(op(e4,e1),e0) ),
inference(mrr,[status(thm)],[328,1677]),
[iquote('4:MRR:328.1,1677.0')] ).
cnf(1685,plain,
~ equal(op(e4,e0),e0),
inference(rew,[status(thm),theory(equality)],[11,1541]),
[iquote('4:Rew:11.0,1541.0')] ).
cnf(1691,plain,
~ equal(op(e1,e3),e3),
inference(rew,[status(thm),theory(equality)],[17,1550]),
[iquote('4:Rew:17.0,1550.0')] ).
cnf(1692,plain,
( equal(op(e1,e4),e3)
| equal(op(e1,e0),e3) ),
inference(mrr,[status(thm)],[354,1691]),
[iquote('4:MRR:354.0,1691.0')] ).
cnf(1693,plain,
~ equal(op(e4,e3),e3),
inference(rew,[status(thm),theory(equality)],[17,1551]),
[iquote('4:Rew:17.0,1551.0')] ).
cnf(1694,plain,
( equal(op(e4,e1),e3)
| equal(op(e4,e0),e3) ),
inference(mrr,[status(thm)],[320,1693]),
[iquote('4:MRR:320.0,1693.0')] ).
cnf(1725,plain,
equal(op(e0,e0),e1),
inference(mrr,[status(thm)],[1679,1]),
[iquote('4:MRR:1679.0,1.0')] ).
cnf(1728,plain,
~ equal(op(e1,e0),e1),
inference(rew,[status(thm),theory(equality)],[1725,22]),
[iquote('4:Rew:1725.0,22.0')] ).
cnf(1733,plain,
( equal(op(e1,e4),e1)
| equal(op(e1,e3),e1) ),
inference(mrr,[status(thm)],[362,1728]),
[iquote('4:MRR:362.2,1728.0')] ).
cnf(1745,plain,
( ~ skC2
| equal(e1,unit) ),
inference(rew,[status(thm),theory(equality)],[1725,1623,11]),
[iquote('4:Rew:1725.0,1623.1,11.0,1623.1')] ).
cnf(1746,plain,
~ skC2,
inference(mrr,[status(thm)],[1745,1522]),
[iquote('4:MRR:1745.1,1522.0')] ).
cnf(1747,plain,
( skC3
| skC1
| equal(op(e0,op(e4,e0)),e4) ),
inference(mrr,[status(thm)],[297,1746]),
[iquote('4:MRR:297.1,1746.0')] ).
cnf(1749,plain,
( equal(op(e1,e3),unit)
| equal(op(e1,e0),unit) ),
inference(rew,[status(thm),theory(equality)],[1521,1616]),
[iquote('4:Rew:1521.0,1616.0')] ).
cnf(1758,plain,
equal(op(e4,e1),e0),
inference(mrr,[status(thm)],[1682,1685]),
[iquote('4:MRR:1682.0,1685.0')] ).
cnf(1768,plain,
( equal(e3,e0)
| equal(op(e4,e0),e3) ),
inference(rew,[status(thm),theory(equality)],[1758,1694]),
[iquote('4:Rew:1758.0,1694.0')] ).
cnf(1769,plain,
equal(op(e4,e0),e3),
inference(mrr,[status(thm)],[1768,3]),
[iquote('4:MRR:1768.0,3.0')] ).
cnf(1772,plain,
~ equal(op(e1,e0),e3),
inference(rew,[status(thm),theory(equality)],[1769,28]),
[iquote('4:Rew:1769.0,28.0')] ).
cnf(1777,plain,
( skC3
| skC1
| equal(op(e0,e3),e4) ),
inference(rew,[status(thm),theory(equality)],[1769,1747]),
[iquote('4:Rew:1769.0,1747.2')] ).
cnf(1778,plain,
equal(op(e1,e4),e3),
inference(mrr,[status(thm)],[1692,1772]),
[iquote('4:MRR:1692.1,1772.0')] ).
cnf(1784,plain,
~ equal(op(e0,e4),e3),
inference(rew,[status(thm),theory(equality)],[1778,62]),
[iquote('4:Rew:1778.0,62.0')] ).
cnf(1802,plain,
( equal(e3,e1)
| equal(op(e1,e3),e1) ),
inference(rew,[status(thm),theory(equality)],[1778,1733]),
[iquote('4:Rew:1778.0,1733.0')] ).
cnf(1803,plain,
equal(op(e1,e3),e1),
inference(mrr,[status(thm)],[1802,6]),
[iquote('4:MRR:1802.0,6.0')] ).
cnf(1812,plain,
( equal(e1,unit)
| equal(op(e1,e0),unit) ),
inference(rew,[status(thm),theory(equality)],[1803,1749]),
[iquote('4:Rew:1803.0,1749.0')] ).
cnf(1817,plain,
equal(op(e1,e0),unit),
inference(mrr,[status(thm)],[1812,1522]),
[iquote('4:MRR:1812.0,1522.0')] ).
cnf(1821,plain,
( ~ skC1
| equal(op(e0,unit),e1) ),
inference(rew,[status(thm),theory(equality)],[1817,123]),
[iquote('4:Rew:1817.0,123.1')] ).
cnf(1825,plain,
( ~ skC1
| equal(e1,e0) ),
inference(rew,[status(thm),theory(equality)],[12,1821]),
[iquote('4:Rew:12.0,1821.1')] ).
cnf(1826,plain,
~ skC1,
inference(mrr,[status(thm)],[1825,1]),
[iquote('4:MRR:1825.1,1.0')] ).
cnf(1827,plain,
( skC3
| equal(op(e0,e3),e4) ),
inference(mrr,[status(thm)],[1777,1826]),
[iquote('4:MRR:1777.1,1826.0')] ).
cnf(1882,plain,
( equal(e4,e3)
| equal(e4,e1)
| equal(op(e3,e0),e4)
| equal(e4,e0) ),
inference(rew,[status(thm),theory(equality)],[11,1542,1725,1769]),
[iquote('4:Rew:11.0,1542.3,1725.0,1542.1,1769.0,1542.0')] ).
cnf(1883,plain,
equal(op(e3,e0),e4),
inference(mrr,[status(thm)],[1882,10,7,4]),
[iquote('4:MRR:1882.0,1882.1,1882.3,10.0,7.0,4.0')] ).
cnf(1884,plain,
( ~ skC3
| equal(op(e0,e4),e3) ),
inference(rew,[status(thm),theory(equality)],[1883,125]),
[iquote('4:Rew:1883.0,125.1')] ).
cnf(1890,plain,
~ skC3,
inference(mrr,[status(thm)],[1884,1784]),
[iquote('4:MRR:1884.1,1784.0')] ).
cnf(1891,plain,
equal(op(e0,e3),e4),
inference(mrr,[status(thm)],[1827,1890]),
[iquote('4:MRR:1827.0,1890.0')] ).
cnf(1910,plain,
( equal(e0,unit)
| equal(e3,unit)
| equal(e1,unit)
| equal(e4,unit) ),
inference(rew,[status(thm),theory(equality)],[1891,1629,1521,1803,17,1671]),
[iquote('4:Rew:1891.0,1629.3,1521.0,1629.3,1803.0,1629.2,17.0,1629.1,1521.0,1629.1,1671.0,1629.0,1521.0,1629.0')] ).
cnf(1911,plain,
$false,
inference(mrr,[status(thm)],[1910,778,1519,1522,1150]),
[iquote('4:MRR:1910.0,1910.1,1910.2,1910.3,778.0,1519.0,1522.0,1150.0')] ).
cnf(1912,plain,
~ equal(e2,unit),
inference(spt,[spt(split,[position(s2s2s2sa)])],[1911,1521]),
[iquote('4:Spt:1911.0,1520.0,1521.0')] ).
cnf(1913,plain,
equal(e1,unit),
inference(spt,[spt(split,[position(s2s2s2s2)])],[1520]),
[iquote('4:Spt:1911.0,1520.1')] ).
cnf(1920,plain,
~ equal(e2,unit),
inference(rew,[status(thm),theory(equality)],[1913,5]),
[iquote('4:Rew:1913.0,5.0')] ).
cnf(1958,plain,
~ equal(op(e0,e0),e0),
inference(rew,[status(thm),theory(equality)],[12,72,1913]),
[iquote('4:Rew:12.0,72.0,1913.0,72.0')] ).
cnf(1963,plain,
~ equal(op(e4,e3),e4),
inference(rew,[status(thm),theory(equality)],[20,117,1913]),
[iquote('4:Rew:20.0,117.0,1913.0,117.0')] ).
cnf(1969,plain,
~ equal(op(e0,e4),e0),
inference(rew,[status(thm),theory(equality)],[12,78,1913]),
[iquote('4:Rew:12.0,78.0,1913.0,78.0')] ).
cnf(2002,plain,
equal(op(e3,e3),e0),
inference(mrr,[status(thm)],[393,1958]),
[iquote('4:MRR:393.0,1958.0')] ).
cnf(2005,plain,
~ equal(op(e3,e4),e0),
inference(rew,[status(thm),theory(equality)],[2002,111]),
[iquote('4:Rew:2002.0,111.0')] ).
cnf(2012,plain,
( equal(e0,unit)
| equal(op(e0,e0),unit) ),
inference(rew,[status(thm),theory(equality)],[1913,391,2002]),
[iquote('4:Rew:1913.0,391.1,2002.0,391.0,1913.0,391.0')] ).
cnf(2013,plain,
equal(op(e0,e0),unit),
inference(mrr,[status(thm)],[2012,778]),
[iquote('4:MRR:2012.0,778.0')] ).
cnf(2015,plain,
~ equal(op(e2,e0),unit),
inference(rew,[status(thm),theory(equality)],[2013,23]),
[iquote('4:Rew:2013.0,23.0')] ).
cnf(2041,plain,
equal(op(e2,e4),e0),
inference(mrr,[status(thm)],[326,1969,2005]),
[iquote('4:MRR:326.0,326.1,1969.0,2005.0')] ).
cnf(2119,plain,
( equal(e2,unit)
| equal(e0,unit)
| equal(op(e2,e3),unit)
| equal(op(e2,e0),unit) ),
inference(rew,[status(thm),theory(equality)],[1913,348,2041,16]),
[iquote('4:Rew:1913.0,348.3,1913.0,348.2,2041.0,348.1,1913.0,348.1,16.0,348.0,1913.0,348.0')] ).
cnf(2120,plain,
equal(op(e2,e3),unit),
inference(mrr,[status(thm)],[2119,1920,778,2015]),
[iquote('4:MRR:2119.0,2119.1,2119.3,1920.0,778.0,2015.0')] ).
cnf(2148,plain,
( equal(op(e4,e3),e4)
| equal(e4,e0)
| equal(e4,unit)
| equal(op(e0,e3),e4) ),
inference(rew,[status(thm),theory(equality)],[2120,329,2002]),
[iquote('4:Rew:2120.0,329.2,2002.0,329.1')] ).
cnf(2149,plain,
equal(op(e0,e3),e4),
inference(mrr,[status(thm)],[2148,1963,4,1150]),
[iquote('4:MRR:2148.0,2148.1,2148.2,1963.0,4.0,1150.0')] ).
cnf(2201,plain,
( equal(e2,e0)
| equal(e2,unit)
| equal(e3,e2)
| equal(e4,e2) ),
inference(rew,[status(thm),theory(equality)],[2149,333,17,1913,2120,2002]),
[iquote('4:Rew:2149.0,333.3,17.0,333.2,1913.0,333.2,2120.0,333.1,2002.0,333.0')] ).
cnf(2202,plain,
$false,
inference(mrr,[status(thm)],[2201,2,1920,8,9]),
[iquote('4:MRR:2201.0,2201.1,2201.2,2201.3,2.0,1920.0,8.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ALG061+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.12 % 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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 09:59:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.56
% 0.18/0.56 SPASS V 3.9
% 0.18/0.56 SPASS beiseite: Proof found.
% 0.18/0.56 % SZS status Theorem
% 0.18/0.56 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.56 SPASS derived 1141 clauses, backtracked 850 clauses, performed 4 splits and kept 1453 clauses.
% 0.18/0.56 SPASS allocated 86192 KBytes.
% 0.18/0.56 SPASS spent 0:00:00.22 on the problem.
% 0.18/0.56 0:00:00.04 for the input.
% 0.18/0.56 0:00:00.05 for the FLOTTER CNF translation.
% 0.18/0.56 0:00:00.00 for inferences.
% 0.18/0.56 0:00:00.00 for the backtracking.
% 0.18/0.56 0:00:00.10 for the reduction.
% 0.18/0.56
% 0.18/0.56
% 0.18/0.56 Here is a proof with depth 4, length 322 :
% 0.18/0.56 % SZS output start Refutation
% See solution above
% 0.18/0.57 Formulae used in the proof : ax5 ax2 ax6 ax4 co1 ax3 ax1
% 0.18/0.57
%------------------------------------------------------------------------------