TSTP Solution File: ALG066+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG066+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 18:02:12 EDT 2022
% Result : Theorem 0.36s 0.54s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 114
% Syntax : Number of clauses : 405 ( 207 unt; 126 nHn; 405 RR)
% Number of literals : 861 ( 0 equ; 275 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 5 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('ALG066+1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(e2,e0),
file('ALG066+1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(e3,e0),
file('ALG066+1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(e4,e0),
file('ALG066+1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(e2,e1),
file('ALG066+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(e3,e1),
file('ALG066+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(e4,e1),
file('ALG066+1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(e3,e2),
file('ALG066+1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(e4,e2),
file('ALG066+1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(e4,e3),
file('ALG066+1.p',unknown),
[] ).
cnf(11,axiom,
equal(op(unit,e0),e0),
file('ALG066+1.p',unknown),
[] ).
cnf(12,axiom,
equal(op(e0,unit),e0),
file('ALG066+1.p',unknown),
[] ).
cnf(13,axiom,
equal(op(unit,e1),e1),
file('ALG066+1.p',unknown),
[] ).
cnf(14,axiom,
equal(op(e1,unit),e1),
file('ALG066+1.p',unknown),
[] ).
cnf(15,axiom,
equal(op(unit,e2),e2),
file('ALG066+1.p',unknown),
[] ).
cnf(16,axiom,
equal(op(e2,unit),e2),
file('ALG066+1.p',unknown),
[] ).
cnf(17,axiom,
equal(op(unit,e3),e3),
file('ALG066+1.p',unknown),
[] ).
cnf(18,axiom,
equal(op(e3,unit),e3),
file('ALG066+1.p',unknown),
[] ).
cnf(19,axiom,
equal(op(unit,e4),e4),
file('ALG066+1.p',unknown),
[] ).
cnf(20,axiom,
equal(op(e4,unit),e4),
file('ALG066+1.p',unknown),
[] ).
cnf(21,axiom,
equal(op(e4,e2),e1),
file('ALG066+1.p',unknown),
[] ).
cnf(22,axiom,
equal(op(e2,e4),e3),
file('ALG066+1.p',unknown),
[] ).
cnf(25,axiom,
~ equal(op(e3,e0),op(e0,e0)),
file('ALG066+1.p',unknown),
[] ).
cnf(27,axiom,
~ equal(op(e2,e0),op(e1,e0)),
file('ALG066+1.p',unknown),
[] ).
cnf(28,axiom,
~ equal(op(e3,e0),op(e1,e0)),
file('ALG066+1.p',unknown),
[] ).
cnf(31,axiom,
~ equal(op(e4,e0),op(e2,e0)),
file('ALG066+1.p',unknown),
[] ).
cnf(34,axiom,
~ equal(op(e2,e1),op(e0,e1)),
file('ALG066+1.p',unknown),
[] ).
cnf(37,axiom,
~ equal(op(e2,e1),op(e1,e1)),
file('ALG066+1.p',unknown),
[] ).
cnf(40,axiom,
~ equal(op(e3,e1),op(e2,e1)),
file('ALG066+1.p',unknown),
[] ).
cnf(41,axiom,
~ equal(op(e4,e1),op(e2,e1)),
file('ALG066+1.p',unknown),
[] ).
cnf(50,axiom,
~ equal(op(e3,e2),op(e2,e2)),
file('ALG066+1.p',unknown),
[] ).
cnf(51,axiom,
~ equal(op(e4,e2),op(e2,e2)),
file('ALG066+1.p',unknown),
[] ).
cnf(52,axiom,
~ equal(op(e4,e2),op(e3,e2)),
file('ALG066+1.p',unknown),
[] ).
cnf(53,axiom,
~ equal(op(e1,e3),op(e0,e3)),
file('ALG066+1.p',unknown),
[] ).
cnf(54,axiom,
~ equal(op(e2,e3),op(e0,e3)),
file('ALG066+1.p',unknown),
[] ).
cnf(56,axiom,
~ equal(op(e4,e3),op(e0,e3)),
file('ALG066+1.p',unknown),
[] ).
cnf(58,axiom,
~ equal(op(e3,e3),op(e1,e3)),
file('ALG066+1.p',unknown),
[] ).
cnf(59,axiom,
~ equal(op(e4,e3),op(e1,e3)),
file('ALG066+1.p',unknown),
[] ).
cnf(60,axiom,
~ equal(op(e3,e3),op(e2,e3)),
file('ALG066+1.p',unknown),
[] ).
cnf(61,axiom,
~ equal(op(e4,e3),op(e2,e3)),
file('ALG066+1.p',unknown),
[] ).
cnf(62,axiom,
~ equal(op(e4,e3),op(e3,e3)),
file('ALG066+1.p',unknown),
[] ).
cnf(63,axiom,
~ equal(op(e1,e4),op(e0,e4)),
file('ALG066+1.p',unknown),
[] ).
cnf(67,axiom,
~ equal(op(e2,e4),op(e1,e4)),
file('ALG066+1.p',unknown),
[] ).
cnf(70,axiom,
~ equal(op(e3,e4),op(e2,e4)),
file('ALG066+1.p',unknown),
[] ).
cnf(71,axiom,
~ equal(op(e4,e4),op(e2,e4)),
file('ALG066+1.p',unknown),
[] ).
cnf(73,axiom,
~ equal(op(e0,e1),op(e0,e0)),
file('ALG066+1.p',unknown),
[] ).
cnf(75,axiom,
~ equal(op(e0,e3),op(e0,e0)),
file('ALG066+1.p',unknown),
[] ).
cnf(77,axiom,
~ equal(op(e0,e2),op(e0,e1)),
file('ALG066+1.p',unknown),
[] ).
cnf(79,axiom,
~ equal(op(e0,e4),op(e0,e1)),
file('ALG066+1.p',unknown),
[] ).
cnf(81,axiom,
~ equal(op(e0,e4),op(e0,e2)),
file('ALG066+1.p',unknown),
[] ).
cnf(82,axiom,
~ equal(op(e0,e4),op(e0,e3)),
file('ALG066+1.p',unknown),
[] ).
cnf(86,axiom,
~ equal(op(e1,e4),op(e1,e0)),
file('ALG066+1.p',unknown),
[] ).
cnf(89,axiom,
~ equal(op(e1,e4),op(e1,e1)),
file('ALG066+1.p',unknown),
[] ).
cnf(93,axiom,
~ equal(op(e2,e1),op(e2,e0)),
file('ALG066+1.p',unknown),
[] ).
cnf(94,axiom,
~ equal(op(e2,e2),op(e2,e0)),
file('ALG066+1.p',unknown),
[] ).
cnf(95,axiom,
~ equal(op(e2,e3),op(e2,e0)),
file('ALG066+1.p',unknown),
[] ).
cnf(96,axiom,
~ equal(op(e2,e4),op(e2,e0)),
file('ALG066+1.p',unknown),
[] ).
cnf(98,axiom,
~ equal(op(e2,e3),op(e2,e1)),
file('ALG066+1.p',unknown),
[] ).
cnf(99,axiom,
~ equal(op(e2,e4),op(e2,e1)),
file('ALG066+1.p',unknown),
[] ).
cnf(101,axiom,
~ equal(op(e2,e4),op(e2,e2)),
file('ALG066+1.p',unknown),
[] ).
cnf(103,axiom,
~ equal(op(e3,e1),op(e3,e0)),
file('ALG066+1.p',unknown),
[] ).
cnf(107,axiom,
~ equal(op(e3,e2),op(e3,e1)),
file('ALG066+1.p',unknown),
[] ).
cnf(109,axiom,
~ equal(op(e3,e4),op(e3,e1)),
file('ALG066+1.p',unknown),
[] ).
cnf(121,axiom,
~ equal(op(e4,e4),op(e4,e2)),
file('ALG066+1.p',unknown),
[] ).
cnf(123,axiom,
equal(op(op(e4,e2),op(e4,e2)),e0),
file('ALG066+1.p',unknown),
[] ).
cnf(128,axiom,
( ~ equal(op(e1,e1),e0)
| equal(op(e1,e0),e1) ),
file('ALG066+1.p',unknown),
[] ).
cnf(132,axiom,
( ~ equal(op(e2,e2),e0)
| equal(op(e2,e0),e2) ),
file('ALG066+1.p',unknown),
[] ).
cnf(135,axiom,
( ~ equal(op(e2,e2),e4)
| equal(op(e2,e4),e2) ),
file('ALG066+1.p',unknown),
[] ).
cnf(136,axiom,
( ~ equal(op(e3,e3),e0)
| equal(op(e3,e0),e3) ),
file('ALG066+1.p',unknown),
[] ).
cnf(137,axiom,
( ~ equal(op(e3,e3),e1)
| equal(op(e3,e1),e3) ),
file('ALG066+1.p',unknown),
[] ).
cnf(138,axiom,
( ~ equal(op(e3,e3),e2)
| equal(op(e3,e2),e3) ),
file('ALG066+1.p',unknown),
[] ).
cnf(139,axiom,
( ~ equal(op(e3,e3),e4)
| equal(op(e3,e4),e3) ),
file('ALG066+1.p',unknown),
[] ).
cnf(140,axiom,
( ~ equal(op(e4,e4),e0)
| equal(op(e4,e0),e4) ),
file('ALG066+1.p',unknown),
[] ).
cnf(142,axiom,
( ~ equal(op(e4,e4),e2)
| equal(op(e4,e2),e4) ),
file('ALG066+1.p',unknown),
[] ).
cnf(150,axiom,
( ~ equal(e0,unit)
| ~ equal(op(e1,e1),e0)
| ~ skC0 ),
file('ALG066+1.p',unknown),
[] ).
cnf(206,axiom,
( ~ skC2
| ~ equal(e2,unit)
| ~ equal(op(e2,e2),e2) ),
file('ALG066+1.p',unknown),
[] ).
cnf(233,axiom,
( ~ equal(e3,unit)
| ~ equal(op(e2,e4),e3)
| ~ skC3 ),
file('ALG066+1.p',unknown),
[] ).
cnf(245,axiom,
( ~ skC0
| ~ equal(op(e0,e2),e0)
| equal(op(e0,e0),e2) ),
file('ALG066+1.p',unknown),
[] ).
cnf(246,axiom,
( ~ skC0
| ~ equal(op(e0,e3),e0)
| equal(op(e0,e0),e3) ),
file('ALG066+1.p',unknown),
[] ).
cnf(247,axiom,
( ~ skC0
| ~ equal(op(e0,e4),e0)
| equal(op(e0,e0),e4) ),
file('ALG066+1.p',unknown),
[] ).
cnf(262,axiom,
( ~ skC1
| ~ equal(op(e0,e4),e1)
| equal(op(e0,e1),e4) ),
file('ALG066+1.p',unknown),
[] ).
cnf(268,axiom,
( ~ equal(op(e2,e3),e1)
| ~ skC1
| equal(op(e2,e1),e3) ),
file('ALG066+1.p',unknown),
[] ).
cnf(274,axiom,
( ~ equal(op(e4,e2),e1)
| ~ skC1
| equal(op(e4,e1),e2) ),
file('ALG066+1.p',unknown),
[] ).
cnf(281,axiom,
( ~ skC2
| ~ equal(op(e1,e4),e2)
| equal(op(e1,e2),e4) ),
file('ALG066+1.p',unknown),
[] ).
cnf(284,axiom,
( ~ equal(op(e2,e3),e2)
| ~ skC2
| equal(op(e2,e2),e3) ),
file('ALG066+1.p',unknown),
[] ).
cnf(287,axiom,
( ~ equal(op(e3,e1),e2)
| ~ skC2
| equal(op(e3,e2),e1) ),
file('ALG066+1.p',unknown),
[] ).
cnf(300,axiom,
( ~ equal(op(e2,e4),e3)
| ~ skC3
| equal(op(e2,e3),e4) ),
file('ALG066+1.p',unknown),
[] ).
cnf(332,axiom,
( ~ equal(e4,unit)
| ~ equal(op(e4,e4),e4)
| skC3
| skC2
| skC1
| skC0 ),
file('ALG066+1.p',unknown),
[] ).
cnf(338,axiom,
( ~ equal(op(e1,e3),e4)
| equal(op(e1,e4),e3)
| skC0
| skC1
| skC2
| skC3 ),
file('ALG066+1.p',unknown),
[] ).
cnf(348,axiom,
( ~ equal(op(e4,e3),e4)
| equal(op(e4,e4),e3)
| skC0
| skC1
| skC2
| skC3 ),
file('ALG066+1.p',unknown),
[] ).
cnf(349,axiom,
( equal(e4,unit)
| equal(e3,unit)
| equal(e2,unit)
| equal(e1,unit)
| equal(e0,unit) ),
file('ALG066+1.p',unknown),
[] ).
cnf(350,axiom,
( equal(op(e0,e4),e4)
| equal(op(e1,e4),e4)
| equal(op(e2,e4),e4)
| equal(op(e3,e4),e4)
| equal(op(e4,e4),e4) ),
file('ALG066+1.p',unknown),
[] ).
cnf(353,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('ALG066+1.p',unknown),
[] ).
cnf(355,axiom,
( equal(op(e4,e0),e2)
| equal(op(e4,e1),e2)
| equal(op(e4,e2),e2)
| equal(op(e4,e3),e2)
| equal(op(e4,e4),e2) ),
file('ALG066+1.p',unknown),
[] ).
cnf(356,axiom,
( equal(op(e0,e4),e1)
| equal(op(e1,e4),e1)
| equal(op(e2,e4),e1)
| equal(op(e3,e4),e1)
| equal(op(e4,e4),e1) ),
file('ALG066+1.p',unknown),
[] ).
cnf(358,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('ALG066+1.p',unknown),
[] ).
cnf(360,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('ALG066+1.p',unknown),
[] ).
cnf(365,axiom,
( equal(op(e3,e3),e2)
| equal(op(e3,e2),e2)
| equal(op(e3,e4),e2)
| equal(op(e3,e1),e2)
| equal(op(e3,e0),e2) ),
file('ALG066+1.p',unknown),
[] ).
cnf(367,axiom,
( equal(op(e3,e0),e1)
| equal(op(e3,e1),e1)
| equal(op(e3,e2),e1)
| equal(op(e3,e3),e1)
| equal(op(e3,e4),e1) ),
file('ALG066+1.p',unknown),
[] ).
cnf(370,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('ALG066+1.p',unknown),
[] ).
cnf(371,axiom,
( equal(op(e2,e0),e4)
| equal(op(e2,e1),e4)
| equal(op(e2,e2),e4)
| equal(op(e2,e3),e4)
| equal(op(e2,e4),e4) ),
file('ALG066+1.p',unknown),
[] ).
cnf(377,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('ALG066+1.p',unknown),
[] ).
cnf(379,axiom,
( equal(op(e2,e0),e0)
| equal(op(e2,e1),e0)
| equal(op(e2,e2),e0)
| equal(op(e2,e3),e0)
| equal(op(e2,e4),e0) ),
file('ALG066+1.p',unknown),
[] ).
cnf(380,axiom,
( equal(op(e0,e1),e4)
| equal(op(e1,e1),e4)
| equal(op(e2,e1),e4)
| equal(op(e3,e1),e4)
| equal(op(e4,e1),e4) ),
file('ALG066+1.p',unknown),
[] ).
cnf(381,axiom,
( equal(op(e1,e0),e4)
| equal(op(e1,e1),e4)
| equal(op(e1,e2),e4)
| equal(op(e1,e3),e4)
| equal(op(e1,e4),e4) ),
file('ALG066+1.p',unknown),
[] ).
cnf(382,axiom,
( equal(op(e0,e1),e3)
| equal(op(e1,e1),e3)
| equal(op(e2,e1),e3)
| equal(op(e3,e1),e3)
| equal(op(e4,e1),e3) ),
file('ALG066+1.p',unknown),
[] ).
cnf(383,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('ALG066+1.p',unknown),
[] ).
cnf(384,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('ALG066+1.p',unknown),
[] ).
cnf(385,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('ALG066+1.p',unknown),
[] ).
cnf(406,axiom,
( equal(op(e3,e3),e0)
| equal(op(e3,e3),e1)
| equal(op(e3,e3),e2)
| equal(op(e3,e3),e3)
| equal(op(e3,e3),e4) ),
file('ALG066+1.p',unknown),
[] ).
cnf(412,axiom,
( equal(op(e2,e2),e0)
| equal(op(e2,e2),e1)
| equal(op(e2,e2),e2)
| equal(op(e2,e2),e3)
| equal(op(e2,e2),e4) ),
file('ALG066+1.p',unknown),
[] ).
cnf(414,axiom,
( equal(op(e2,e0),e0)
| equal(op(e2,e0),e1)
| equal(op(e2,e0),e2)
| equal(op(e2,e0),e3)
| equal(op(e2,e0),e4) ),
file('ALG066+1.p',unknown),
[] ).
cnf(415,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('ALG066+1.p',unknown),
[] ).
cnf(421,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('ALG066+1.p',unknown),
[] ).
cnf(425,plain,
~ equal(op(e4,e4),e1),
inference(rew,[status(thm),theory(equality)],[21,121]),
[iquote('0:Rew:21.0,121.0')] ).
cnf(430,plain,
~ equal(op(e2,e2),e3),
inference(rew,[status(thm),theory(equality)],[22,101]),
[iquote('0:Rew:22.0,101.0')] ).
cnf(431,plain,
~ equal(op(e2,e1),e3),
inference(rew,[status(thm),theory(equality)],[22,99]),
[iquote('0:Rew:22.0,99.0')] ).
cnf(432,plain,
~ equal(op(e2,e0),e3),
inference(rew,[status(thm),theory(equality)],[22,96]),
[iquote('0:Rew:22.0,96.0')] ).
cnf(433,plain,
~ equal(op(e4,e4),e3),
inference(rew,[status(thm),theory(equality)],[22,71]),
[iquote('0:Rew:22.0,71.0')] ).
cnf(434,plain,
~ equal(op(e3,e4),e3),
inference(rew,[status(thm),theory(equality)],[22,70]),
[iquote('0:Rew:22.0,70.0')] ).
cnf(435,plain,
~ equal(op(e1,e4),e3),
inference(rew,[status(thm),theory(equality)],[22,67]),
[iquote('0:Rew:22.0,67.0')] ).
cnf(437,plain,
~ equal(op(e3,e2),e1),
inference(rew,[status(thm),theory(equality)],[21,52]),
[iquote('0:Rew:21.0,52.0')] ).
cnf(438,plain,
~ equal(op(e2,e2),e1),
inference(rew,[status(thm),theory(equality)],[21,51]),
[iquote('0:Rew:21.0,51.0')] ).
cnf(441,plain,
equal(op(e1,e1),e0),
inference(rew,[status(thm),theory(equality)],[21,123]),
[iquote('0:Rew:21.0,123.0')] ).
cnf(442,plain,
~ equal(op(e1,e4),e0),
inference(rew,[status(thm),theory(equality)],[441,89]),
[iquote('0:Rew:441.0,89.0')] ).
cnf(448,plain,
~ equal(op(e2,e1),e0),
inference(rew,[status(thm),theory(equality)],[441,37]),
[iquote('0:Rew:441.0,37.0')] ).
cnf(450,plain,
( ~ equal(op(e4,e4),e2)
| equal(e4,e1) ),
inference(rew,[status(thm),theory(equality)],[21,142]),
[iquote('0:Rew:21.0,142.1')] ).
cnf(451,plain,
~ equal(op(e4,e4),e2),
inference(mrr,[status(thm)],[450,7]),
[iquote('0:MRR:450.1,7.0')] ).
cnf(452,plain,
~ equal(op(e3,e3),e4),
inference(mrr,[status(thm)],[139,434]),
[iquote('0:MRR:139.1,434.0')] ).
cnf(453,plain,
( ~ equal(op(e2,e2),e4)
| equal(e3,e2) ),
inference(rew,[status(thm),theory(equality)],[22,135]),
[iquote('0:Rew:22.0,135.1')] ).
cnf(454,plain,
~ equal(op(e2,e2),e4),
inference(mrr,[status(thm)],[453,8]),
[iquote('0:MRR:453.1,8.0')] ).
cnf(458,plain,
( ~ equal(e0,e0)
| equal(op(e1,e0),e1) ),
inference(rew,[status(thm),theory(equality)],[441,128]),
[iquote('0:Rew:441.0,128.0')] ).
cnf(459,plain,
equal(op(e1,e0),e1),
inference(obv,[status(thm),theory(equality)],[458]),
[iquote('0:Obv:458.0')] ).
cnf(460,plain,
~ equal(op(e1,e4),e1),
inference(rew,[status(thm),theory(equality)],[459,86]),
[iquote('0:Rew:459.0,86.0')] ).
cnf(464,plain,
~ equal(op(e3,e0),e1),
inference(rew,[status(thm),theory(equality)],[459,28]),
[iquote('0:Rew:459.0,28.0')] ).
cnf(465,plain,
~ equal(op(e2,e0),e1),
inference(rew,[status(thm),theory(equality)],[459,27]),
[iquote('0:Rew:459.0,27.0')] ).
cnf(469,plain,
( ~ equal(e3,unit)
| ~ equal(e3,e3)
| ~ skC3 ),
inference(rew,[status(thm),theory(equality)],[22,233]),
[iquote('0:Rew:22.0,233.1')] ).
cnf(470,plain,
( ~ skC3
| ~ equal(e3,unit) ),
inference(obv,[status(thm),theory(equality)],[469]),
[iquote('0:Obv:469.1')] ).
cnf(479,plain,
( ~ equal(e0,unit)
| ~ equal(e0,e0)
| ~ skC0 ),
inference(rew,[status(thm),theory(equality)],[441,150]),
[iquote('0:Rew:441.0,150.1')] ).
cnf(480,plain,
( ~ skC0
| ~ equal(e0,unit) ),
inference(obv,[status(thm),theory(equality)],[479]),
[iquote('0:Obv:479.1')] ).
cnf(483,plain,
( ~ equal(e3,e3)
| ~ skC3
| equal(op(e2,e3),e4) ),
inference(rew,[status(thm),theory(equality)],[22,300]),
[iquote('0:Rew:22.0,300.0')] ).
cnf(484,plain,
( ~ skC3
| equal(op(e2,e3),e4) ),
inference(obv,[status(thm),theory(equality)],[483]),
[iquote('0:Obv:483.0')] ).
cnf(490,plain,
( ~ skC2
| ~ equal(op(e3,e1),e2) ),
inference(mrr,[status(thm)],[287,437]),
[iquote('0:MRR:287.2,437.0')] ).
cnf(492,plain,
( ~ skC2
| ~ equal(op(e2,e3),e2) ),
inference(mrr,[status(thm)],[284,430]),
[iquote('0:MRR:284.2,430.0')] ).
cnf(496,plain,
( ~ equal(e1,e1)
| ~ skC1
| equal(op(e4,e1),e2) ),
inference(rew,[status(thm),theory(equality)],[21,274]),
[iquote('0:Rew:21.0,274.0')] ).
cnf(497,plain,
( ~ skC1
| equal(op(e4,e1),e2) ),
inference(obv,[status(thm),theory(equality)],[496]),
[iquote('0:Obv:496.0')] ).
cnf(499,plain,
( ~ skC1
| ~ equal(op(e2,e3),e1) ),
inference(mrr,[status(thm)],[268,431]),
[iquote('0:MRR:268.2,431.0')] ).
cnf(507,plain,
( ~ equal(op(e4,e3),e4)
| skC3
| skC2
| skC1
| skC0 ),
inference(mrr,[status(thm)],[348,433]),
[iquote('0:MRR:348.1,433.0')] ).
cnf(514,plain,
( ~ equal(op(e1,e3),e4)
| skC3
| skC2
| skC1
| skC0 ),
inference(mrr,[status(thm)],[338,435]),
[iquote('0:MRR:338.1,435.0')] ).
cnf(517,plain,
( equal(op(e0,e4),e4)
| equal(op(e1,e4),e4)
| equal(e4,e3)
| equal(op(e3,e4),e4)
| equal(op(e4,e4),e4) ),
inference(rew,[status(thm),theory(equality)],[22,350]),
[iquote('0:Rew:22.0,350.2')] ).
cnf(518,plain,
( equal(op(e4,e4),e4)
| equal(op(e3,e4),e4)
| equal(op(e1,e4),e4)
| equal(op(e0,e4),e4) ),
inference(mrr,[status(thm)],[517,10]),
[iquote('0:MRR:517.2,10.0')] ).
cnf(521,plain,
( equal(op(e4,e0),e3)
| equal(op(e4,e1),e3)
| equal(e3,e1)
| equal(op(e4,e3),e3)
| equal(op(e4,e4),e3) ),
inference(rew,[status(thm),theory(equality)],[21,353]),
[iquote('0:Rew:21.0,353.2')] ).
cnf(522,plain,
( equal(op(e4,e3),e3)
| equal(op(e4,e1),e3)
| equal(op(e4,e0),e3) ),
inference(mrr,[status(thm)],[521,6,433]),
[iquote('0:MRR:521.2,521.4,6.0,433.0')] ).
cnf(525,plain,
( equal(op(e4,e0),e2)
| equal(op(e4,e1),e2)
| equal(e2,e1)
| equal(op(e4,e3),e2)
| equal(op(e4,e4),e2) ),
inference(rew,[status(thm),theory(equality)],[21,355]),
[iquote('0:Rew:21.0,355.2')] ).
cnf(526,plain,
( equal(op(e4,e3),e2)
| equal(op(e4,e1),e2)
| equal(op(e4,e0),e2) ),
inference(mrr,[status(thm)],[525,5,451]),
[iquote('0:MRR:525.2,525.4,5.0,451.0')] ).
cnf(527,plain,
( equal(op(e0,e4),e1)
| equal(op(e1,e4),e1)
| equal(e3,e1)
| equal(op(e3,e4),e1)
| equal(op(e4,e4),e1) ),
inference(rew,[status(thm),theory(equality)],[22,356]),
[iquote('0:Rew:22.0,356.2')] ).
cnf(528,plain,
( equal(op(e3,e4),e1)
| equal(op(e0,e4),e1) ),
inference(mrr,[status(thm)],[527,460,6,425]),
[iquote('0:MRR:527.1,527.2,527.4,460.0,6.0,425.0')] ).
cnf(529,plain,
( equal(op(e0,e4),e0)
| equal(op(e1,e4),e0)
| equal(e3,e0)
| equal(op(e3,e4),e0)
| equal(op(e4,e4),e0) ),
inference(rew,[status(thm),theory(equality)],[22,358]),
[iquote('0:Rew:22.0,358.2')] ).
cnf(530,plain,
( equal(op(e4,e4),e0)
| equal(op(e0,e4),e0)
| equal(op(e3,e4),e0) ),
inference(mrr,[status(thm)],[529,442,3]),
[iquote('0:MRR:529.1,529.2,442.0,3.0')] ).
cnf(533,plain,
( equal(op(e4,e3),e4)
| equal(op(e2,e3),e4)
| equal(op(e1,e3),e4)
| equal(op(e0,e3),e4) ),
inference(mrr,[status(thm)],[360,452]),
[iquote('0:MRR:360.3,452.0')] ).
cnf(538,plain,
( equal(op(e3,e3),e1)
| equal(op(e3,e1),e1)
| equal(op(e3,e4),e1) ),
inference(mrr,[status(thm)],[367,464,437]),
[iquote('0:MRR:367.0,367.2,464.0,437.0')] ).
cnf(541,plain,
( equal(op(e0,e2),e4)
| equal(op(e1,e2),e4)
| equal(op(e2,e2),e4)
| equal(op(e3,e2),e4)
| equal(e4,e1) ),
inference(rew,[status(thm),theory(equality)],[21,370]),
[iquote('0:Rew:21.0,370.4')] ).
cnf(542,plain,
( equal(op(e3,e2),e4)
| equal(op(e1,e2),e4)
| equal(op(e0,e2),e4) ),
inference(mrr,[status(thm)],[541,454,7]),
[iquote('0:MRR:541.2,541.4,454.0,7.0')] ).
cnf(543,plain,
( equal(op(e2,e0),e4)
| equal(op(e2,e1),e4)
| equal(op(e2,e2),e4)
| equal(op(e2,e3),e4)
| equal(e4,e3) ),
inference(rew,[status(thm),theory(equality)],[22,371]),
[iquote('0:Rew:22.0,371.4')] ).
cnf(544,plain,
( equal(op(e2,e3),e4)
| equal(op(e2,e1),e4)
| equal(op(e2,e0),e4) ),
inference(mrr,[status(thm)],[543,454,10]),
[iquote('0:MRR:543.2,543.4,454.0,10.0')] ).
cnf(551,plain,
( equal(op(e2,e0),e1)
| equal(op(e2,e1),e1)
| equal(op(e2,e2),e1)
| equal(op(e2,e3),e1)
| equal(e3,e1) ),
inference(rew,[status(thm),theory(equality)],[22,377]),
[iquote('0:Rew:22.0,377.4')] ).
cnf(552,plain,
( equal(op(e2,e1),e1)
| equal(op(e2,e3),e1) ),
inference(mrr,[status(thm)],[551,465,438,6]),
[iquote('0:MRR:551.0,551.2,551.4,465.0,438.0,6.0')] ).
cnf(555,plain,
( equal(op(e2,e0),e0)
| equal(op(e2,e1),e0)
| equal(op(e2,e2),e0)
| equal(op(e2,e3),e0)
| equal(e3,e0) ),
inference(rew,[status(thm),theory(equality)],[22,379]),
[iquote('0:Rew:22.0,379.4')] ).
cnf(556,plain,
( equal(op(e2,e2),e0)
| equal(op(e2,e0),e0)
| equal(op(e2,e3),e0) ),
inference(mrr,[status(thm)],[555,448,3]),
[iquote('0:MRR:555.1,555.4,448.0,3.0')] ).
cnf(557,plain,
( equal(op(e0,e1),e4)
| equal(e4,e0)
| equal(op(e2,e1),e4)
| equal(op(e3,e1),e4)
| equal(op(e4,e1),e4) ),
inference(rew,[status(thm),theory(equality)],[441,380]),
[iquote('0:Rew:441.0,380.1')] ).
cnf(558,plain,
( equal(op(e4,e1),e4)
| equal(op(e3,e1),e4)
| equal(op(e2,e1),e4)
| equal(op(e0,e1),e4) ),
inference(mrr,[status(thm)],[557,4]),
[iquote('0:MRR:557.1,4.0')] ).
cnf(559,plain,
( equal(e4,e1)
| equal(e4,e0)
| equal(op(e1,e2),e4)
| equal(op(e1,e3),e4)
| equal(op(e1,e4),e4) ),
inference(rew,[status(thm),theory(equality)],[441,381,459]),
[iquote('0:Rew:441.0,381.1,459.0,381.0')] ).
cnf(560,plain,
( equal(op(e1,e4),e4)
| equal(op(e1,e3),e4)
| equal(op(e1,e2),e4) ),
inference(mrr,[status(thm)],[559,7,4]),
[iquote('0:MRR:559.0,559.1,7.0,4.0')] ).
cnf(561,plain,
( equal(op(e0,e1),e3)
| equal(e3,e0)
| equal(op(e2,e1),e3)
| equal(op(e3,e1),e3)
| equal(op(e4,e1),e3) ),
inference(rew,[status(thm),theory(equality)],[441,382]),
[iquote('0:Rew:441.0,382.1')] ).
cnf(562,plain,
( equal(op(e3,e1),e3)
| equal(op(e4,e1),e3)
| equal(op(e0,e1),e3) ),
inference(mrr,[status(thm)],[561,3,431]),
[iquote('0:MRR:561.1,561.2,3.0,431.0')] ).
cnf(563,plain,
( equal(e3,e1)
| equal(e3,e0)
| equal(op(e1,e2),e3)
| equal(op(e1,e3),e3)
| equal(op(e1,e4),e3) ),
inference(rew,[status(thm),theory(equality)],[441,383,459]),
[iquote('0:Rew:441.0,383.1,459.0,383.0')] ).
cnf(564,plain,
( equal(op(e1,e3),e3)
| equal(op(e1,e2),e3) ),
inference(mrr,[status(thm)],[563,6,3,435]),
[iquote('0:MRR:563.0,563.1,563.4,6.0,3.0,435.0')] ).
cnf(566,plain,
( equal(op(e0,e1),e2)
| equal(e2,e0)
| equal(op(e2,e1),e2)
| equal(op(e3,e1),e2)
| equal(op(e4,e1),e2) ),
inference(rew,[status(thm),theory(equality)],[441,384]),
[iquote('0:Rew:441.0,384.1')] ).
cnf(567,plain,
( equal(op(e2,e1),e2)
| equal(op(e4,e1),e2)
| equal(op(e3,e1),e2)
| equal(op(e0,e1),e2) ),
inference(mrr,[status(thm)],[566,2]),
[iquote('0:MRR:566.1,2.0')] ).
cnf(568,plain,
( equal(e2,e1)
| equal(e2,e0)
| equal(op(e1,e2),e2)
| equal(op(e1,e3),e2)
| equal(op(e1,e4),e2) ),
inference(rew,[status(thm),theory(equality)],[441,385,459]),
[iquote('0:Rew:441.0,385.1,459.0,385.0')] ).
cnf(569,plain,
( equal(op(e1,e2),e2)
| equal(op(e1,e4),e2)
| equal(op(e1,e3),e2) ),
inference(mrr,[status(thm)],[568,5,2]),
[iquote('0:MRR:568.0,568.1,5.0,2.0')] ).
cnf(588,plain,
( equal(op(e3,e3),e3)
| equal(op(e3,e3),e2)
| equal(op(e3,e3),e1)
| equal(op(e3,e3),e0) ),
inference(mrr,[status(thm)],[406,452]),
[iquote('0:MRR:406.4,452.0')] ).
cnf(593,plain,
( equal(op(e2,e2),e2)
| equal(op(e2,e2),e0) ),
inference(mrr,[status(thm)],[412,438,430,454]),
[iquote('0:MRR:412.1,412.3,412.4,438.0,430.0,454.0')] ).
cnf(595,plain,
( equal(op(e2,e0),e2)
| equal(op(e2,e0),e0)
| equal(op(e2,e0),e4) ),
inference(mrr,[status(thm)],[414,465,432]),
[iquote('0:MRR:414.1,414.3,465.0,432.0')] ).
cnf(596,plain,
( equal(op(e1,e4),e4)
| equal(op(e1,e4),e2) ),
inference(mrr,[status(thm)],[415,442,460,435]),
[iquote('0:MRR:415.0,415.1,415.3,442.0,460.0,435.0')] ).
cnf(603,plain,
equal(e3,unit),
inference(spt,[spt(split,[position(s1)])],[349]),
[iquote('1:Spt:349.1')] ).
cnf(614,plain,
( ~ equal(op(e4,unit),e4)
| skC3
| skC2
| skC1
| skC0 ),
inference(rew,[status(thm),theory(equality)],[603,507]),
[iquote('1:Rew:603.0,507.0')] ).
cnf(640,plain,
( equal(op(unit,e4),e1)
| equal(op(e0,e4),e1) ),
inference(rew,[status(thm),theory(equality)],[603,528]),
[iquote('1:Rew:603.0,528.0')] ).
cnf(654,plain,
( equal(op(unit,e2),e4)
| equal(op(e1,e2),e4)
| equal(op(e0,e2),e4) ),
inference(rew,[status(thm),theory(equality)],[603,542]),
[iquote('1:Rew:603.0,542.0')] ).
cnf(662,plain,
~ equal(op(e2,e2),op(unit,e2)),
inference(rew,[status(thm),theory(equality)],[603,50]),
[iquote('1:Rew:603.0,50.0')] ).
cnf(665,plain,
( equal(op(e2,e1),e2)
| equal(op(e4,e1),e2)
| equal(op(unit,e1),e2)
| equal(op(e0,e1),e2) ),
inference(rew,[status(thm),theory(equality)],[603,567]),
[iquote('1:Rew:603.0,567.2')] ).
cnf(668,plain,
( equal(op(e4,e1),e4)
| equal(op(unit,e1),e4)
| equal(op(e2,e1),e4)
| equal(op(e0,e1),e4) ),
inference(rew,[status(thm),theory(equality)],[603,558]),
[iquote('1:Rew:603.0,558.1')] ).
cnf(697,plain,
( ~ skC2
| ~ equal(op(e2,unit),e2) ),
inference(rew,[status(thm),theory(equality)],[603,492]),
[iquote('1:Rew:603.0,492.1')] ).
cnf(703,plain,
~ equal(op(e2,e1),op(e2,unit)),
inference(rew,[status(thm),theory(equality)],[603,98]),
[iquote('1:Rew:603.0,98.0')] ).
cnf(704,plain,
~ equal(op(e2,e0),op(e2,unit)),
inference(rew,[status(thm),theory(equality)],[603,95]),
[iquote('1:Rew:603.0,95.0')] ).
cnf(722,plain,
( ~ skC0
| ~ equal(op(e0,unit),e0)
| equal(op(e0,e0),e3) ),
inference(rew,[status(thm),theory(equality)],[603,246]),
[iquote('1:Rew:603.0,246.1')] ).
cnf(743,plain,
( equal(op(unit,e1),unit)
| equal(op(e4,e1),e3)
| equal(op(e0,e1),e3) ),
inference(rew,[status(thm),theory(equality)],[603,562]),
[iquote('1:Rew:603.0,562.0')] ).
cnf(747,plain,
( ~ skC3
| ~ equal(unit,unit) ),
inference(rew,[status(thm),theory(equality)],[603,470]),
[iquote('1:Rew:603.0,470.1')] ).
cnf(753,plain,
( equal(op(e1,e3),e3)
| equal(op(e1,e2),unit) ),
inference(rew,[status(thm),theory(equality)],[603,564]),
[iquote('1:Rew:603.0,564.1')] ).
cnf(757,plain,
~ equal(e4,unit),
inference(rew,[status(thm),theory(equality)],[603,10]),
[iquote('1:Rew:603.0,10.0')] ).
cnf(758,plain,
~ equal(e2,unit),
inference(rew,[status(thm),theory(equality)],[603,8]),
[iquote('1:Rew:603.0,8.0')] ).
cnf(759,plain,
~ equal(e1,unit),
inference(rew,[status(thm),theory(equality)],[603,6]),
[iquote('1:Rew:603.0,6.0')] ).
cnf(780,plain,
~ skC3,
inference(obv,[status(thm),theory(equality)],[747]),
[iquote('1:Obv:747.1')] ).
cnf(821,plain,
~ equal(op(e2,e2),e2),
inference(rew,[status(thm),theory(equality)],[15,662]),
[iquote('1:Rew:15.0,662.0')] ).
cnf(822,plain,
equal(op(e2,e2),e0),
inference(mrr,[status(thm)],[593,821]),
[iquote('1:MRR:593.0,821.0')] ).
cnf(827,plain,
~ equal(op(e2,e0),e0),
inference(rew,[status(thm),theory(equality)],[822,94]),
[iquote('1:Rew:822.0,94.0')] ).
cnf(832,plain,
( equal(op(e2,e0),e2)
| equal(op(e2,e0),e4) ),
inference(mrr,[status(thm)],[595,827]),
[iquote('1:MRR:595.1,827.0')] ).
cnf(851,plain,
( ~ skC2
| ~ equal(e2,e2) ),
inference(rew,[status(thm),theory(equality)],[16,697]),
[iquote('1:Rew:16.0,697.1')] ).
cnf(852,plain,
~ skC2,
inference(obv,[status(thm),theory(equality)],[851]),
[iquote('1:Obv:851.1')] ).
cnf(856,plain,
~ equal(op(e2,e1),e2),
inference(rew,[status(thm),theory(equality)],[16,703]),
[iquote('1:Rew:16.0,703.0')] ).
cnf(857,plain,
~ equal(op(e2,e0),e2),
inference(rew,[status(thm),theory(equality)],[16,704]),
[iquote('1:Rew:16.0,704.0')] ).
cnf(879,plain,
( ~ equal(e4,e4)
| skC3
| skC2
| skC1
| skC0 ),
inference(rew,[status(thm),theory(equality)],[20,614]),
[iquote('1:Rew:20.0,614.0')] ).
cnf(880,plain,
( skC3
| skC2
| skC1
| skC0 ),
inference(obv,[status(thm),theory(equality)],[879]),
[iquote('1:Obv:879.0')] ).
cnf(881,plain,
( skC1
| skC0 ),
inference(mrr,[status(thm)],[880,780,852]),
[iquote('1:MRR:880.0,880.1,780.0,852.0')] ).
cnf(882,plain,
( equal(e4,e1)
| equal(op(e0,e4),e1) ),
inference(rew,[status(thm),theory(equality)],[19,640]),
[iquote('1:Rew:19.0,640.0')] ).
cnf(883,plain,
equal(op(e0,e4),e1),
inference(mrr,[status(thm)],[882,7]),
[iquote('1:MRR:882.0,7.0')] ).
cnf(884,plain,
( ~ skC1
| ~ equal(e1,e1)
| equal(op(e0,e1),e4) ),
inference(rew,[status(thm),theory(equality)],[883,262]),
[iquote('1:Rew:883.0,262.1')] ).
cnf(894,plain,
( equal(e1,unit)
| equal(op(e1,e2),unit) ),
inference(rew,[status(thm),theory(equality)],[14,753,603]),
[iquote('1:Rew:14.0,753.0,603.0,753.0')] ).
cnf(895,plain,
equal(op(e1,e2),unit),
inference(mrr,[status(thm)],[894,759]),
[iquote('1:MRR:894.0,759.0')] ).
cnf(900,plain,
equal(op(e2,e0),e4),
inference(mrr,[status(thm)],[832,857]),
[iquote('1:MRR:832.0,857.0')] ).
cnf(902,plain,
~ equal(op(e2,e1),e4),
inference(rew,[status(thm),theory(equality)],[900,93]),
[iquote('1:Rew:900.0,93.0')] ).
cnf(913,plain,
( ~ skC1
| equal(op(e0,e1),e4) ),
inference(obv,[status(thm),theory(equality)],[884]),
[iquote('1:Obv:884.1')] ).
cnf(918,plain,
( ~ skC0
| ~ equal(e0,e0)
| equal(op(e0,e0),unit) ),
inference(rew,[status(thm),theory(equality)],[603,722,12]),
[iquote('1:Rew:603.0,722.2,12.0,722.1')] ).
cnf(919,plain,
( ~ skC0
| equal(op(e0,e0),unit) ),
inference(obv,[status(thm),theory(equality)],[918]),
[iquote('1:Obv:918.1')] ).
cnf(926,plain,
( equal(e4,e2)
| equal(e4,unit)
| equal(op(e0,e2),e4) ),
inference(rew,[status(thm),theory(equality)],[895,654,15]),
[iquote('1:Rew:895.0,654.1,15.0,654.0')] ).
cnf(927,plain,
equal(op(e0,e2),e4),
inference(mrr,[status(thm)],[926,9,757]),
[iquote('1:MRR:926.0,926.1,9.0,757.0')] ).
cnf(929,plain,
~ equal(op(e0,e1),e4),
inference(rew,[status(thm),theory(equality)],[927,77]),
[iquote('1:Rew:927.0,77.0')] ).
cnf(934,plain,
~ skC1,
inference(mrr,[status(thm)],[913,929]),
[iquote('1:MRR:913.1,929.0')] ).
cnf(935,plain,
skC0,
inference(mrr,[status(thm)],[881,934]),
[iquote('1:MRR:881.0,934.0')] ).
cnf(936,plain,
equal(op(e0,e0),unit),
inference(mrr,[status(thm)],[919,935]),
[iquote('1:MRR:919.0,935.0')] ).
cnf(938,plain,
~ equal(op(e0,e1),unit),
inference(rew,[status(thm),theory(equality)],[936,73]),
[iquote('1:Rew:936.0,73.0')] ).
cnf(949,plain,
( equal(e1,unit)
| equal(op(e4,e1),unit)
| equal(op(e0,e1),unit) ),
inference(rew,[status(thm),theory(equality)],[603,743,13]),
[iquote('1:Rew:603.0,743.2,603.0,743.1,13.0,743.0')] ).
cnf(950,plain,
equal(op(e4,e1),unit),
inference(mrr,[status(thm)],[949,759,938]),
[iquote('1:MRR:949.0,949.2,759.0,938.0')] ).
cnf(969,plain,
( equal(op(e2,e1),e2)
| equal(e2,unit)
| equal(e2,e1)
| equal(op(e0,e1),e2) ),
inference(rew,[status(thm),theory(equality)],[13,665,950]),
[iquote('1:Rew:13.0,665.2,950.0,665.1')] ).
cnf(970,plain,
equal(op(e0,e1),e2),
inference(mrr,[status(thm)],[969,856,758,5]),
[iquote('1:MRR:969.0,969.1,969.2,856.0,758.0,5.0')] ).
cnf(977,plain,
( equal(e4,unit)
| equal(e4,e1)
| equal(op(e2,e1),e4)
| equal(e4,e2) ),
inference(rew,[status(thm),theory(equality)],[970,668,13,950]),
[iquote('1:Rew:970.0,668.3,13.0,668.1,950.0,668.0')] ).
cnf(978,plain,
$false,
inference(mrr,[status(thm)],[977,757,7,902,9]),
[iquote('1:MRR:977.0,977.1,977.2,977.3,757.0,7.0,902.0,9.0')] ).
cnf(985,plain,
~ equal(e3,unit),
inference(spt,[spt(split,[position(sa)])],[978,603]),
[iquote('1:Spt:978.0,349.1,603.0')] ).
cnf(986,plain,
( equal(e4,unit)
| equal(e2,unit)
| equal(e1,unit)
| equal(e0,unit) ),
inference(spt,[spt(split,[position(s2)])],[349]),
[iquote('1:Spt:978.0,349.0,349.2,349.3,349.4')] ).
cnf(987,plain,
equal(e4,unit),
inference(spt,[spt(split,[position(s2s1)])],[986]),
[iquote('2:Spt:986.0')] ).
cnf(988,plain,
~ equal(e2,unit),
inference(rew,[status(thm),theory(equality)],[987,9]),
[iquote('2:Rew:987.0,9.0')] ).
cnf(989,plain,
~ equal(e1,unit),
inference(rew,[status(thm),theory(equality)],[987,7]),
[iquote('2:Rew:987.0,7.0')] ).
cnf(992,plain,
equal(op(unit,unit),unit),
inference(rew,[status(thm),theory(equality)],[987,20]),
[iquote('2:Rew:987.0,20.0')] ).
cnf(997,plain,
~ equal(op(e0,e3),op(e0,unit)),
inference(rew,[status(thm),theory(equality)],[987,82]),
[iquote('2:Rew:987.0,82.0')] ).
cnf(1008,plain,
( ~ skC0
| ~ equal(op(e0,unit),e0)
| equal(op(e0,e0),e4) ),
inference(rew,[status(thm),theory(equality)],[987,247]),
[iquote('2:Rew:987.0,247.1')] ).
cnf(1022,plain,
( equal(op(e1,e2),e2)
| equal(op(e1,unit),e2)
| equal(op(e1,e3),e2) ),
inference(rew,[status(thm),theory(equality)],[987,569]),
[iquote('2:Rew:987.0,569.1')] ).
cnf(1028,plain,
~ equal(op(e3,e1),op(e3,unit)),
inference(rew,[status(thm),theory(equality)],[987,109]),
[iquote('2:Rew:987.0,109.0')] ).
cnf(1056,plain,
~ equal(op(e0,e3),op(unit,e3)),
inference(rew,[status(thm),theory(equality)],[987,56]),
[iquote('2:Rew:987.0,56.0')] ).
cnf(1057,plain,
~ equal(op(e1,e3),op(unit,e3)),
inference(rew,[status(thm),theory(equality)],[987,59]),
[iquote('2:Rew:987.0,59.0')] ).
cnf(1073,plain,
( equal(op(e2,e1),e2)
| equal(op(unit,e1),e2)
| equal(op(e3,e1),e2)
| equal(op(e0,e1),e2) ),
inference(rew,[status(thm),theory(equality)],[987,567]),
[iquote('2:Rew:987.0,567.1')] ).
cnf(1076,plain,
( ~ skC1
| equal(op(unit,e1),e2) ),
inference(rew,[status(thm),theory(equality)],[987,497]),
[iquote('2:Rew:987.0,497.1')] ).
cnf(1077,plain,
( equal(op(e3,e1),e3)
| equal(op(unit,e1),e3)
| equal(op(e0,e1),e3) ),
inference(rew,[status(thm),theory(equality)],[987,562]),
[iquote('2:Rew:987.0,562.1')] ).
cnf(1083,plain,
~ equal(op(e2,e1),op(unit,e1)),
inference(rew,[status(thm),theory(equality)],[987,41]),
[iquote('2:Rew:987.0,41.0')] ).
cnf(1091,plain,
~ equal(op(e2,e0),op(unit,e0)),
inference(rew,[status(thm),theory(equality)],[987,31]),
[iquote('2:Rew:987.0,31.0')] ).
cnf(1098,plain,
( equal(op(e2,e3),unit)
| equal(op(e2,e1),e4)
| equal(op(e2,e0),e4) ),
inference(rew,[status(thm),theory(equality)],[987,544]),
[iquote('2:Rew:987.0,544.0')] ).
cnf(1100,plain,
( ~ skC3
| equal(op(e2,e3),unit) ),
inference(rew,[status(thm),theory(equality)],[987,484]),
[iquote('2:Rew:987.0,484.1')] ).
cnf(1102,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)],[987,421]),
[iquote('2:Rew:987.0,421.2')] ).
cnf(1117,plain,
( ~ equal(e4,unit)
| ~ equal(op(unit,unit),unit)
| skC3
| skC2
| skC1
| skC0 ),
inference(rew,[status(thm),theory(equality)],[987,332]),
[iquote('2:Rew:987.0,332.1')] ).
cnf(1157,plain,
( ~ skC1
| equal(e2,e1) ),
inference(rew,[status(thm),theory(equality)],[13,1076]),
[iquote('2:Rew:13.0,1076.1')] ).
cnf(1158,plain,
~ skC1,
inference(mrr,[status(thm)],[1157,5]),
[iquote('2:MRR:1157.1,5.0')] ).
cnf(1159,plain,
~ equal(op(e0,e3),e0),
inference(rew,[status(thm),theory(equality)],[12,997]),
[iquote('2:Rew:12.0,997.0')] ).
cnf(1174,plain,
~ equal(op(e3,e1),e3),
inference(rew,[status(thm),theory(equality)],[18,1028]),
[iquote('2:Rew:18.0,1028.0')] ).
cnf(1186,plain,
~ equal(op(e0,e3),e3),
inference(rew,[status(thm),theory(equality)],[17,1056]),
[iquote('2:Rew:17.0,1056.0')] ).
cnf(1187,plain,
~ equal(op(e1,e3),e3),
inference(rew,[status(thm),theory(equality)],[17,1057]),
[iquote('2:Rew:17.0,1057.0')] ).
cnf(1188,plain,
equal(op(e1,e2),e3),
inference(mrr,[status(thm)],[564,1187]),
[iquote('2:MRR:564.0,1187.0')] ).
cnf(1208,plain,
~ equal(op(e2,e1),e1),
inference(rew,[status(thm),theory(equality)],[13,1083]),
[iquote('2:Rew:13.0,1083.0')] ).
cnf(1209,plain,
equal(op(e2,e3),e1),
inference(mrr,[status(thm)],[552,1208]),
[iquote('2:MRR:552.0,1208.0')] ).
cnf(1211,plain,
~ equal(op(e0,e3),e1),
inference(rew,[status(thm),theory(equality)],[1209,54]),
[iquote('2:Rew:1209.0,54.0')] ).
cnf(1217,plain,
( equal(op(e2,e2),e0)
| equal(op(e2,e0),e0)
| equal(e1,e0) ),
inference(rew,[status(thm),theory(equality)],[1209,556]),
[iquote('2:Rew:1209.0,556.2')] ).
cnf(1221,plain,
( ~ skC3
| equal(e1,unit) ),
inference(rew,[status(thm),theory(equality)],[1209,1100]),
[iquote('2:Rew:1209.0,1100.1')] ).
cnf(1222,plain,
~ skC3,
inference(mrr,[status(thm)],[1221,989]),
[iquote('2:MRR:1221.1,989.0')] ).
cnf(1227,plain,
~ equal(op(e2,e0),e0),
inference(rew,[status(thm),theory(equality)],[11,1091]),
[iquote('2:Rew:11.0,1091.0')] ).
cnf(1244,plain,
( ~ skC0
| ~ equal(e0,e0)
| equal(op(e0,e0),unit) ),
inference(rew,[status(thm),theory(equality)],[987,1008,12]),
[iquote('2:Rew:987.0,1008.2,12.0,1008.1')] ).
cnf(1245,plain,
( ~ skC0
| equal(op(e0,e0),unit) ),
inference(obv,[status(thm),theory(equality)],[1244]),
[iquote('2:Obv:1244.1')] ).
cnf(1251,plain,
equal(op(e2,e2),e0),
inference(mrr,[status(thm)],[1217,1227,1]),
[iquote('2:MRR:1217.1,1217.2,1227.0,1.0')] ).
cnf(1258,plain,
( ~ equal(e0,e0)
| equal(op(e2,e0),e2) ),
inference(rew,[status(thm),theory(equality)],[1251,132]),
[iquote('2:Rew:1251.0,132.0')] ).
cnf(1261,plain,
equal(op(e2,e0),e2),
inference(obv,[status(thm),theory(equality)],[1258]),
[iquote('2:Obv:1258.0')] ).
cnf(1271,plain,
( ~ equal(unit,unit)
| ~ equal(unit,unit)
| skC3
| skC2
| skC1
| skC0 ),
inference(rew,[status(thm),theory(equality)],[992,1117,987]),
[iquote('2:Rew:992.0,1117.1,987.0,1117.0')] ).
cnf(1272,plain,
( skC3
| skC2
| skC1
| skC0 ),
inference(obv,[status(thm),theory(equality)],[1271]),
[iquote('2:Obv:1271.1')] ).
cnf(1273,plain,
( skC2
| skC0 ),
inference(mrr,[status(thm)],[1272,1222,1158]),
[iquote('2:MRR:1272.0,1272.2,1222.0,1158.0')] ).
cnf(1286,plain,
( equal(e3,e2)
| equal(e2,e1)
| equal(op(e1,e3),e2) ),
inference(rew,[status(thm),theory(equality)],[14,1022,1188]),
[iquote('2:Rew:14.0,1022.1,1188.0,1022.0')] ).
cnf(1287,plain,
equal(op(e1,e3),e2),
inference(mrr,[status(thm)],[1286,8,5]),
[iquote('2:MRR:1286.0,1286.1,8.0,5.0')] ).
cnf(1290,plain,
~ equal(op(e0,e3),e2),
inference(rew,[status(thm),theory(equality)],[1287,53]),
[iquote('2:Rew:1287.0,53.0')] ).
cnf(1300,plain,
( equal(op(e3,e1),e3)
| equal(e3,e1)
| equal(op(e0,e1),e3) ),
inference(rew,[status(thm),theory(equality)],[13,1077]),
[iquote('2:Rew:13.0,1077.1')] ).
cnf(1301,plain,
equal(op(e0,e1),e3),
inference(mrr,[status(thm)],[1300,1174,6]),
[iquote('2:MRR:1300.0,1300.1,1174.0,6.0')] ).
cnf(1312,plain,
( equal(e1,unit)
| equal(op(e2,e1),unit)
| equal(e2,unit) ),
inference(rew,[status(thm),theory(equality)],[1261,1098,987,1209]),
[iquote('2:Rew:1261.0,1098.2,987.0,1098.2,987.0,1098.1,1209.0,1098.0')] ).
cnf(1313,plain,
equal(op(e2,e1),unit),
inference(mrr,[status(thm)],[1312,989,988]),
[iquote('2:MRR:1312.0,1312.2,989.0,988.0')] ).
cnf(1335,plain,
( equal(e2,unit)
| equal(e2,e1)
| equal(op(e3,e1),e2)
| equal(e3,e2) ),
inference(rew,[status(thm),theory(equality)],[1301,1073,13,1313]),
[iquote('2:Rew:1301.0,1073.3,13.0,1073.1,1313.0,1073.0')] ).
cnf(1336,plain,
equal(op(e3,e1),e2),
inference(mrr,[status(thm)],[1335,988,5,8]),
[iquote('2:MRR:1335.0,1335.1,1335.3,988.0,5.0,8.0')] ).
cnf(1341,plain,
( ~ skC2
| ~ equal(e2,e2) ),
inference(rew,[status(thm),theory(equality)],[1336,490]),
[iquote('2:Rew:1336.0,490.1')] ).
cnf(1353,plain,
~ skC2,
inference(obv,[status(thm),theory(equality)],[1341]),
[iquote('2:Obv:1341.1')] ).
cnf(1354,plain,
skC0,
inference(mrr,[status(thm)],[1273,1353]),
[iquote('2:MRR:1273.0,1353.0')] ).
cnf(1355,plain,
equal(op(e0,e0),unit),
inference(mrr,[status(thm)],[1245,1354]),
[iquote('2:MRR:1245.0,1354.0')] ).
cnf(1357,plain,
~ equal(op(e0,e3),unit),
inference(rew,[status(thm),theory(equality)],[1355,75]),
[iquote('2:Rew:1355.0,75.0')] ).
cnf(1378,plain,
$false,
inference(mrr,[status(thm)],[1102,1186,1159,1357,1290,1211]),
[iquote('2:MRR:1102.0,1102.1,1102.2,1102.3,1102.4,1186.0,1159.0,1357.0,1290.0,1211.0')] ).
cnf(1379,plain,
~ equal(e4,unit),
inference(spt,[spt(split,[position(s2sa)])],[1378,987]),
[iquote('2:Spt:1378.0,986.0,987.0')] ).
cnf(1380,plain,
( equal(e2,unit)
| equal(e1,unit)
| equal(e0,unit) ),
inference(spt,[spt(split,[position(s2s2)])],[986]),
[iquote('2:Spt:1378.0,986.1,986.2,986.3')] ).
cnf(1381,plain,
equal(e2,unit),
inference(spt,[spt(split,[position(s2s2s1)])],[1380]),
[iquote('3:Spt:1380.0')] ).
cnf(1382,plain,
~ equal(e1,unit),
inference(rew,[status(thm),theory(equality)],[1381,5]),
[iquote('3:Rew:1381.0,5.0')] ).
cnf(1384,plain,
equal(op(unit,unit),unit),
inference(rew,[status(thm),theory(equality)],[1381,16]),
[iquote('3:Rew:1381.0,16.0')] ).
cnf(1409,plain,
( equal(op(e1,e4),e4)
| equal(op(e1,e3),e4)
| equal(op(e1,unit),e4) ),
inference(rew,[status(thm),theory(equality)],[1381,560]),
[iquote('3:Rew:1381.0,560.2')] ).
cnf(1416,plain,
( ~ skC3
| equal(op(unit,e3),e4) ),
inference(rew,[status(thm),theory(equality)],[1381,484]),
[iquote('3:Rew:1381.0,484.1')] ).
cnf(1417,plain,
~ equal(op(e4,e3),op(unit,e3)),
inference(rew,[status(thm),theory(equality)],[1381,61]),
[iquote('3:Rew:1381.0,61.0')] ).
cnf(1445,plain,
~ equal(op(e3,e1),op(unit,e1)),
inference(rew,[status(thm),theory(equality)],[1381,40]),
[iquote('3:Rew:1381.0,40.0')] ).
cnf(1446,plain,
( equal(op(e4,e1),e4)
| equal(op(e3,e1),e4)
| equal(op(unit,e1),e4)
| equal(op(e0,e1),e4) ),
inference(rew,[status(thm),theory(equality)],[1381,558]),
[iquote('3:Rew:1381.0,558.2')] ).
cnf(1451,plain,
~ equal(op(e0,e4),op(e0,unit)),
inference(rew,[status(thm),theory(equality)],[1381,81]),
[iquote('3:Rew:1381.0,81.0')] ).
cnf(1459,plain,
( ~ skC0
| ~ equal(op(e0,unit),e0)
| equal(op(e0,e0),e2) ),
inference(rew,[status(thm),theory(equality)],[1381,245]),
[iquote('3:Rew:1381.0,245.1')] ).
cnf(1471,plain,
~ equal(op(e3,e1),op(e3,unit)),
inference(rew,[status(thm),theory(equality)],[1381,107]),
[iquote('3:Rew:1381.0,107.0')] ).
cnf(1486,plain,
( equal(op(e4,e3),e2)
| equal(op(e4,e1),unit)
| equal(op(e4,e0),e2) ),
inference(rew,[status(thm),theory(equality)],[1381,526]),
[iquote('3:Rew:1381.0,526.1')] ).
cnf(1489,plain,
( ~ skC1
| equal(op(e4,e1),unit) ),
inference(rew,[status(thm),theory(equality)],[1381,497]),
[iquote('3:Rew:1381.0,497.1')] ).
cnf(1502,plain,
( equal(op(e3,e3),e2)
| equal(op(e3,e2),e2)
| equal(op(e3,e4),e2)
| equal(op(e3,e1),unit)
| equal(op(e3,e0),e2) ),
inference(rew,[status(thm),theory(equality)],[1381,365]),
[iquote('3:Rew:1381.0,365.3')] ).
cnf(1509,plain,
( ~ skC2
| ~ equal(unit,unit)
| ~ equal(op(e2,e2),e2) ),
inference(rew,[status(thm),theory(equality)],[1381,206]),
[iquote('3:Rew:1381.0,206.1')] ).
cnf(1519,plain,
( equal(op(e1,e2),e2)
| equal(op(e1,e4),unit)
| equal(op(e1,e3),e2) ),
inference(rew,[status(thm),theory(equality)],[1381,569]),
[iquote('3:Rew:1381.0,569.1')] ).
cnf(1547,plain,
( ~ skC3
| equal(e4,e3) ),
inference(rew,[status(thm),theory(equality)],[17,1416]),
[iquote('3:Rew:17.0,1416.1')] ).
cnf(1548,plain,
~ skC3,
inference(mrr,[status(thm)],[1547,10]),
[iquote('3:MRR:1547.1,10.0')] ).
cnf(1551,plain,
( ~ equal(op(e1,e3),e4)
| skC2
| skC1
| skC0 ),
inference(mrr,[status(thm)],[514,1548]),
[iquote('3:MRR:514.1,1548.0')] ).
cnf(1560,plain,
~ equal(op(e4,e3),e3),
inference(rew,[status(thm),theory(equality)],[17,1417]),
[iquote('3:Rew:17.0,1417.0')] ).
cnf(1561,plain,
( equal(op(e4,e1),e3)
| equal(op(e4,e0),e3) ),
inference(mrr,[status(thm)],[522,1560]),
[iquote('3:MRR:522.0,1560.0')] ).
cnf(1581,plain,
~ equal(op(e3,e1),e1),
inference(rew,[status(thm),theory(equality)],[13,1445]),
[iquote('3:Rew:13.0,1445.0')] ).
cnf(1582,plain,
( equal(op(e3,e3),e1)
| equal(op(e3,e4),e1) ),
inference(mrr,[status(thm)],[538,1581]),
[iquote('3:MRR:538.1,1581.0')] ).
cnf(1583,plain,
~ equal(op(e0,e4),e0),
inference(rew,[status(thm),theory(equality)],[12,1451]),
[iquote('3:Rew:12.0,1451.0')] ).
cnf(1585,plain,
( equal(op(e4,e4),e0)
| equal(op(e3,e4),e0) ),
inference(mrr,[status(thm)],[530,1583]),
[iquote('3:MRR:530.1,1583.0')] ).
cnf(1596,plain,
~ equal(op(e3,e1),e3),
inference(rew,[status(thm),theory(equality)],[18,1471]),
[iquote('3:Rew:18.0,1471.0')] ).
cnf(1597,plain,
~ equal(op(e3,e3),e1),
inference(mrr,[status(thm)],[137,1596]),
[iquote('3:MRR:137.1,1596.0')] ).
cnf(1611,plain,
equal(op(e3,e4),e1),
inference(mrr,[status(thm)],[1582,1597]),
[iquote('3:MRR:1582.0,1597.0')] ).
cnf(1621,plain,
( equal(op(e4,e4),e4)
| equal(e4,e1)
| equal(op(e1,e4),e4)
| equal(op(e0,e4),e4) ),
inference(rew,[status(thm),theory(equality)],[1611,518]),
[iquote('3:Rew:1611.0,518.1')] ).
cnf(1633,plain,
( equal(op(e4,e4),e0)
| equal(e1,e0) ),
inference(rew,[status(thm),theory(equality)],[1611,1585]),
[iquote('3:Rew:1611.0,1585.1')] ).
cnf(1634,plain,
equal(op(e4,e4),e0),
inference(mrr,[status(thm)],[1633,1]),
[iquote('3:MRR:1633.1,1.0')] ).
cnf(1643,plain,
( ~ equal(e0,e0)
| equal(op(e4,e0),e4) ),
inference(rew,[status(thm),theory(equality)],[1634,140]),
[iquote('3:Rew:1634.0,140.0')] ).
cnf(1645,plain,
equal(op(e4,e0),e4),
inference(obv,[status(thm),theory(equality)],[1643]),
[iquote('3:Obv:1643.0')] ).
cnf(1651,plain,
( equal(op(e4,e1),e3)
| equal(e4,e3) ),
inference(rew,[status(thm),theory(equality)],[1645,1561]),
[iquote('3:Rew:1645.0,1561.1')] ).
cnf(1654,plain,
equal(op(e4,e1),e3),
inference(mrr,[status(thm)],[1651,10]),
[iquote('3:MRR:1651.1,10.0')] ).
cnf(1660,plain,
( ~ skC1
| equal(e3,unit) ),
inference(rew,[status(thm),theory(equality)],[1654,1489]),
[iquote('3:Rew:1654.0,1489.1')] ).
cnf(1662,plain,
~ skC1,
inference(mrr,[status(thm)],[1660,985]),
[iquote('3:MRR:1660.1,985.0')] ).
cnf(1663,plain,
( ~ equal(op(e1,e3),e4)
| skC2
| skC0 ),
inference(mrr,[status(thm)],[1551,1662]),
[iquote('3:MRR:1551.2,1662.0')] ).
cnf(1679,plain,
( ~ skC2
| ~ equal(op(e2,e2),e2) ),
inference(obv,[status(thm),theory(equality)],[1509]),
[iquote('3:Obv:1509.1')] ).
cnf(1680,plain,
( ~ skC2
| ~ equal(unit,unit) ),
inference(rew,[status(thm),theory(equality)],[1384,1679,1381]),
[iquote('3:Rew:1384.0,1679.1,1381.0,1679.1')] ).
cnf(1681,plain,
~ skC2,
inference(obv,[status(thm),theory(equality)],[1680]),
[iquote('3:Obv:1680.1')] ).
cnf(1682,plain,
( ~ equal(op(e1,e3),e4)
| skC0 ),
inference(mrr,[status(thm)],[1663,1681]),
[iquote('3:MRR:1663.1,1681.0')] ).
cnf(1691,plain,
( ~ skC0
| ~ equal(e0,e0)
| equal(op(e0,e0),unit) ),
inference(rew,[status(thm),theory(equality)],[1381,1459,12]),
[iquote('3:Rew:1381.0,1459.2,12.0,1459.1')] ).
cnf(1692,plain,
( ~ skC0
| equal(op(e0,e0),unit) ),
inference(obv,[status(thm),theory(equality)],[1691]),
[iquote('3:Obv:1691.1')] ).
cnf(1701,plain,
( equal(op(e1,e4),e4)
| equal(op(e1,e3),e4)
| equal(e4,e1) ),
inference(rew,[status(thm),theory(equality)],[14,1409]),
[iquote('3:Rew:14.0,1409.2')] ).
cnf(1702,plain,
( equal(op(e1,e4),e4)
| equal(op(e1,e3),e4) ),
inference(mrr,[status(thm)],[1701,7]),
[iquote('3:MRR:1701.2,7.0')] ).
cnf(1711,plain,
( equal(op(e4,e3),unit)
| equal(e3,unit)
| equal(e4,unit) ),
inference(rew,[status(thm),theory(equality)],[1645,1486,1381,1654]),
[iquote('3:Rew:1645.0,1486.2,1381.0,1486.2,1654.0,1486.1,1381.0,1486.0')] ).
cnf(1712,plain,
equal(op(e4,e3),unit),
inference(mrr,[status(thm)],[1711,985,1379]),
[iquote('3:MRR:1711.1,1711.2,985.0,1379.0')] ).
cnf(1714,plain,
~ equal(op(e3,e3),unit),
inference(rew,[status(thm),theory(equality)],[1712,62]),
[iquote('3:Rew:1712.0,62.0')] ).
cnf(1715,plain,
~ equal(op(e1,e3),unit),
inference(rew,[status(thm),theory(equality)],[1712,59]),
[iquote('3:Rew:1712.0,59.0')] ).
cnf(1721,plain,
( equal(e1,unit)
| equal(op(e1,e4),unit)
| equal(op(e1,e3),unit) ),
inference(rew,[status(thm),theory(equality)],[1381,1519,14]),
[iquote('3:Rew:1381.0,1519.2,14.0,1519.0,1381.0,1519.0')] ).
cnf(1722,plain,
equal(op(e1,e4),unit),
inference(mrr,[status(thm)],[1721,1382,1715]),
[iquote('3:MRR:1721.0,1721.2,1382.0,1715.0')] ).
cnf(1728,plain,
( equal(e4,unit)
| equal(op(e1,e3),e4) ),
inference(rew,[status(thm),theory(equality)],[1722,1702]),
[iquote('3:Rew:1722.0,1702.0')] ).
cnf(1729,plain,
equal(op(e1,e3),e4),
inference(mrr,[status(thm)],[1728,1379]),
[iquote('3:MRR:1728.0,1379.0')] ).
cnf(1734,plain,
( ~ equal(e4,e4)
| skC0 ),
inference(rew,[status(thm),theory(equality)],[1729,1682]),
[iquote('3:Rew:1729.0,1682.0')] ).
cnf(1736,plain,
skC0,
inference(obv,[status(thm),theory(equality)],[1734]),
[iquote('3:Obv:1734.0')] ).
cnf(1737,plain,
equal(op(e0,e0),unit),
inference(mrr,[status(thm)],[1692,1736]),
[iquote('3:MRR:1692.0,1736.0')] ).
cnf(1741,plain,
~ equal(op(e3,e0),unit),
inference(rew,[status(thm),theory(equality)],[1737,25]),
[iquote('3:Rew:1737.0,25.0')] ).
cnf(1747,plain,
( equal(e4,e0)
| equal(e4,e1)
| equal(e4,unit)
| equal(op(e0,e4),e4) ),
inference(rew,[status(thm),theory(equality)],[1722,1621,1634]),
[iquote('3:Rew:1722.0,1621.2,1634.0,1621.0')] ).
cnf(1748,plain,
equal(op(e0,e4),e4),
inference(mrr,[status(thm)],[1747,4,7,1379]),
[iquote('3:MRR:1747.0,1747.1,1747.2,4.0,7.0,1379.0')] ).
cnf(1750,plain,
~ equal(op(e0,e1),e4),
inference(rew,[status(thm),theory(equality)],[1748,79]),
[iquote('3:Rew:1748.0,79.0')] ).
cnf(1758,plain,
( equal(e4,e3)
| equal(op(e3,e1),e4)
| equal(e4,e1)
| equal(op(e0,e1),e4) ),
inference(rew,[status(thm),theory(equality)],[13,1446,1654]),
[iquote('3:Rew:13.0,1446.2,1654.0,1446.0')] ).
cnf(1759,plain,
equal(op(e3,e1),e4),
inference(mrr,[status(thm)],[1758,10,7,1750]),
[iquote('3:MRR:1758.0,1758.2,1758.3,10.0,7.0,1750.0')] ).
cnf(1778,plain,
( equal(op(e3,e3),unit)
| equal(e3,unit)
| equal(e1,unit)
| equal(e4,unit)
| equal(op(e3,e0),unit) ),
inference(rew,[status(thm),theory(equality)],[1381,1502,1759,1611,18]),
[iquote('3:Rew:1381.0,1502.4,1759.0,1502.3,1611.0,1502.2,1381.0,1502.2,18.0,1502.1,1381.0,1502.1,1381.0,1502.0')] ).
cnf(1779,plain,
$false,
inference(mrr,[status(thm)],[1778,1714,985,1382,1379,1741]),
[iquote('3:MRR:1778.0,1778.1,1778.2,1778.3,1778.4,1714.0,985.0,1382.0,1379.0,1741.0')] ).
cnf(1780,plain,
~ equal(e2,unit),
inference(spt,[spt(split,[position(s2s2sa)])],[1779,1381]),
[iquote('3:Spt:1779.0,1380.0,1381.0')] ).
cnf(1781,plain,
( equal(e1,unit)
| equal(e0,unit) ),
inference(spt,[spt(split,[position(s2s2s2)])],[1380]),
[iquote('3:Spt:1779.0,1380.1,1380.2')] ).
cnf(1782,plain,
equal(e1,unit),
inference(spt,[spt(split,[position(s2s2s2s1)])],[1781]),
[iquote('4:Spt:1781.0')] ).
cnf(1874,plain,
~ equal(op(e3,e3),op(unit,e3)),
inference(rew,[status(thm),theory(equality)],[1782,58]),
[iquote('4:Rew:1782.0,58.0')] ).
cnf(1886,plain,
~ equal(op(e3,e2),op(e3,unit)),
inference(rew,[status(thm),theory(equality)],[1782,107]),
[iquote('4:Rew:1782.0,107.0')] ).
cnf(1890,plain,
~ equal(op(e3,e0),op(e3,unit)),
inference(rew,[status(thm),theory(equality)],[1782,103]),
[iquote('4:Rew:1782.0,103.0')] ).
cnf(1901,plain,
( equal(op(e2,e1),e1)
| equal(op(e2,e3),unit) ),
inference(rew,[status(thm),theory(equality)],[1782,552]),
[iquote('4:Rew:1782.0,552.1')] ).
cnf(1909,plain,
( equal(op(e3,e3),e3)
| equal(op(e3,e3),e2)
| equal(op(e3,e3),unit)
| equal(op(e3,e3),e0) ),
inference(rew,[status(thm),theory(equality)],[1782,588]),
[iquote('4:Rew:1782.0,588.2')] ).
cnf(2008,plain,
~ equal(op(e3,e3),e3),
inference(rew,[status(thm),theory(equality)],[17,1874]),
[iquote('4:Rew:17.0,1874.0')] ).
cnf(2009,plain,
~ equal(op(e3,e2),e3),
inference(rew,[status(thm),theory(equality)],[18,1886]),
[iquote('4:Rew:18.0,1886.0')] ).
cnf(2010,plain,
~ equal(op(e3,e3),e2),
inference(mrr,[status(thm)],[138,2009]),
[iquote('4:MRR:138.1,2009.0')] ).
cnf(2014,plain,
~ equal(op(e3,e0),e3),
inference(rew,[status(thm),theory(equality)],[18,1890]),
[iquote('4:Rew:18.0,1890.0')] ).
cnf(2015,plain,
~ equal(op(e3,e3),e0),
inference(mrr,[status(thm)],[136,2014]),
[iquote('4:MRR:136.1,2014.0')] ).
cnf(2028,plain,
( equal(e2,unit)
| equal(op(e2,e3),unit) ),
inference(rew,[status(thm),theory(equality)],[16,1901,1782]),
[iquote('4:Rew:16.0,1901.0,1782.0,1901.0')] ).
cnf(2029,plain,
equal(op(e2,e3),unit),
inference(mrr,[status(thm)],[2028,1780]),
[iquote('4:MRR:2028.0,1780.0')] ).
cnf(2034,plain,
~ equal(op(e3,e3),unit),
inference(rew,[status(thm),theory(equality)],[2029,60]),
[iquote('4:Rew:2029.0,60.0')] ).
cnf(2139,plain,
$false,
inference(mrr,[status(thm)],[1909,2008,2010,2034,2015]),
[iquote('4:MRR:1909.0,1909.1,1909.2,1909.3,2008.0,2010.0,2034.0,2015.0')] ).
cnf(2140,plain,
~ equal(e1,unit),
inference(spt,[spt(split,[position(s2s2s2sa)])],[2139,1782]),
[iquote('4:Spt:2139.0,1781.0,1782.0')] ).
cnf(2141,plain,
equal(e0,unit),
inference(spt,[spt(split,[position(s2s2s2s2)])],[1781]),
[iquote('4:Spt:2139.0,1781.1')] ).
cnf(2162,plain,
( ~ skC0
| ~ equal(unit,unit) ),
inference(rew,[status(thm),theory(equality)],[2141,480]),
[iquote('4:Rew:2141.0,480.1')] ).
cnf(2163,plain,
~ skC0,
inference(obv,[status(thm),theory(equality)],[2162]),
[iquote('4:Obv:2162.1')] ).
cnf(2168,plain,
~ equal(op(e1,e3),e3),
inference(rew,[status(thm),theory(equality)],[17,53,2141]),
[iquote('4:Rew:17.0,53.0,2141.0,53.0')] ).
cnf(2169,plain,
~ equal(op(e1,e4),e4),
inference(rew,[status(thm),theory(equality)],[19,63,2141]),
[iquote('4:Rew:19.0,63.0,2141.0,63.0')] ).
cnf(2174,plain,
~ equal(op(e2,e1),e1),
inference(rew,[status(thm),theory(equality)],[13,34,2141]),
[iquote('4:Rew:13.0,34.0,2141.0,34.0')] ).
cnf(2201,plain,
~ equal(op(e4,e3),e3),
inference(rew,[status(thm),theory(equality)],[17,56,2141]),
[iquote('4:Rew:17.0,56.0,2141.0,56.0')] ).
cnf(2216,plain,
equal(op(e2,e3),e1),
inference(mrr,[status(thm)],[552,2174]),
[iquote('4:MRR:552.0,2174.0')] ).
cnf(2218,plain,
( ~ skC3
| equal(e4,e1) ),
inference(rew,[status(thm),theory(equality)],[2216,484]),
[iquote('4:Rew:2216.0,484.1')] ).
cnf(2219,plain,
( ~ skC1
| ~ equal(e1,e1) ),
inference(rew,[status(thm),theory(equality)],[2216,499]),
[iquote('4:Rew:2216.0,499.1')] ).
cnf(2226,plain,
~ skC3,
inference(mrr,[status(thm)],[2218,7]),
[iquote('4:MRR:2218.1,7.0')] ).
cnf(2227,plain,
~ skC1,
inference(obv,[status(thm),theory(equality)],[2219]),
[iquote('4:Obv:2219.1')] ).
cnf(2228,plain,
( ~ equal(op(e1,e3),e4)
| skC2 ),
inference(mrr,[status(thm)],[514,2226,2227,2163]),
[iquote('4:MRR:514.1,514.3,514.4,2226.0,2227.0,2163.0')] ).
cnf(2229,plain,
equal(op(e1,e4),e2),
inference(mrr,[status(thm)],[596,2169]),
[iquote('4:MRR:596.0,2169.0')] ).
cnf(2237,plain,
equal(op(e1,e2),e3),
inference(mrr,[status(thm)],[564,2168]),
[iquote('4:MRR:564.0,2168.0')] ).
cnf(2270,plain,
( ~ skC2
| ~ equal(e2,e2)
| equal(e4,e3) ),
inference(rew,[status(thm),theory(equality)],[2237,281,2229]),
[iquote('4:Rew:2237.0,281.2,2229.0,281.1')] ).
cnf(2271,plain,
( ~ skC2
| equal(e4,e3) ),
inference(obv,[status(thm),theory(equality)],[2270]),
[iquote('4:Obv:2270.1')] ).
cnf(2272,plain,
~ skC2,
inference(mrr,[status(thm)],[2271,10]),
[iquote('4:MRR:2271.1,10.0')] ).
cnf(2273,plain,
~ equal(op(e1,e3),e4),
inference(mrr,[status(thm)],[2228,2272]),
[iquote('4:MRR:2228.1,2272.0')] ).
cnf(2278,plain,
( equal(op(e4,e3),e3)
| equal(op(e4,e1),e3)
| equal(e4,e3) ),
inference(rew,[status(thm),theory(equality)],[20,522,2141]),
[iquote('4:Rew:20.0,522.2,2141.0,522.2')] ).
cnf(2279,plain,
equal(op(e4,e1),e3),
inference(mrr,[status(thm)],[2278,2201,10]),
[iquote('4:MRR:2278.0,2278.2,2201.0,10.0')] ).
cnf(2286,plain,
( equal(op(e4,e3),e2)
| equal(e3,e2)
| equal(e4,e2) ),
inference(rew,[status(thm),theory(equality)],[20,526,2141,2279]),
[iquote('4:Rew:20.0,526.2,2141.0,526.2,2279.0,526.1')] ).
cnf(2287,plain,
equal(op(e4,e3),e2),
inference(mrr,[status(thm)],[2286,8,9]),
[iquote('4:MRR:2286.1,2286.2,8.0,9.0')] ).
cnf(2353,plain,
( equal(e4,e2)
| equal(e4,e1)
| equal(op(e1,e3),e4)
| equal(e4,e3) ),
inference(rew,[status(thm),theory(equality)],[17,533,2141,2216,2287]),
[iquote('4:Rew:17.0,533.3,2141.0,533.3,2216.0,533.1,2287.0,533.0')] ).
cnf(2354,plain,
$false,
inference(mrr,[status(thm)],[2353,9,7,2273,10]),
[iquote('4:MRR:2353.0,2353.1,2353.2,2353.3,9.0,7.0,2273.0,10.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : ALG066+1 : TPTP v8.1.0. Released v2.7.0.
% 0.00/0.08 % Command : run_spass %d %s
% 0.08/0.28 % Computer : n026.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Tue Jun 7 23:55:31 EDT 2022
% 0.08/0.28 % CPUTime :
% 0.36/0.54
% 0.36/0.54 SPASS V 3.9
% 0.36/0.54 SPASS beiseite: Proof found.
% 0.36/0.54 % SZS status Theorem
% 0.36/0.54 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.36/0.54 SPASS derived 1100 clauses, backtracked 976 clauses, performed 4 splits and kept 1481 clauses.
% 0.36/0.54 SPASS allocated 86456 KBytes.
% 0.36/0.54 SPASS spent 0:00:00.25 on the problem.
% 0.36/0.54 0:00:00.03 for the input.
% 0.36/0.54 0:00:00.06 for the FLOTTER CNF translation.
% 0.36/0.54 0:00:00.00 for inferences.
% 0.36/0.54 0:00:00.00 for the backtracking.
% 0.36/0.54 0:00:00.12 for the reduction.
% 0.36/0.54
% 0.36/0.54
% 0.36/0.54 Here is a proof with depth 4, length 405 :
% 0.36/0.54 % SZS output start Refutation
% See solution above
% 0.36/0.55 Formulae used in the proof : ax5 ax2 ax6 ax4 co1 ax3 ax1
% 0.36/0.55
%------------------------------------------------------------------------------