TSTP Solution File: ALG063+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG063+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 18:02:11 EDT 2022
% Result : Theorem 0.37s 0.55s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 112
% Syntax : Number of clauses : 351 ( 205 unt; 89 nHn; 351 RR)
% Number of literals : 688 ( 0 equ; 215 neg)
% Maximal clause size : 25 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 26 ( 25 usr; 25 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('ALG063+1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(e2,e0),
file('ALG063+1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(e3,e0),
file('ALG063+1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(e4,e0),
file('ALG063+1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(e2,e1),
file('ALG063+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(e3,e1),
file('ALG063+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(e4,e1),
file('ALG063+1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(e3,e2),
file('ALG063+1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(e4,e2),
file('ALG063+1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(e4,e3),
file('ALG063+1.p',unknown),
[] ).
cnf(11,axiom,
equal(op(unit,e0),e0),
file('ALG063+1.p',unknown),
[] ).
cnf(12,axiom,
equal(op(e0,unit),e0),
file('ALG063+1.p',unknown),
[] ).
cnf(13,axiom,
equal(op(unit,e1),e1),
file('ALG063+1.p',unknown),
[] ).
cnf(15,axiom,
equal(op(unit,e2),e2),
file('ALG063+1.p',unknown),
[] ).
cnf(16,axiom,
equal(op(e2,unit),e2),
file('ALG063+1.p',unknown),
[] ).
cnf(17,axiom,
equal(op(unit,e3),e3),
file('ALG063+1.p',unknown),
[] ).
cnf(18,axiom,
equal(op(e3,unit),e3),
file('ALG063+1.p',unknown),
[] ).
cnf(19,axiom,
equal(op(unit,e4),e4),
file('ALG063+1.p',unknown),
[] ).
cnf(20,axiom,
equal(op(e4,unit),e4),
file('ALG063+1.p',unknown),
[] ).
cnf(21,axiom,
equal(op(e1,e1),e4),
file('ALG063+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ skC0
| equal(op(e0,e0),e0) ),
file('ALG063+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ skC1
| equal(op(e1,e1),e0) ),
file('ALG063+1.p',unknown),
[] ).
cnf(26,axiom,
( ~ skC2
| equal(op(e2,e2),e0) ),
file('ALG063+1.p',unknown),
[] ).
cnf(27,axiom,
( ~ skC3
| equal(op(e0,e0),e3) ),
file('ALG063+1.p',unknown),
[] ).
cnf(28,axiom,
( ~ skC3
| equal(op(e3,e3),e0) ),
file('ALG063+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ skC4
| equal(op(e4,e4),e0) ),
file('ALG063+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ skC5
| equal(op(e1,e1),e0) ),
file('ALG063+1.p',unknown),
[] ).
cnf(33,axiom,
( ~ skC6
| equal(op(e1,e1),e1) ),
file('ALG063+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ skC7
| equal(op(e1,e1),e2) ),
file('ALG063+1.p',unknown),
[] ).
cnf(36,axiom,
( ~ skC8
| equal(op(e1,e1),e3) ),
file('ALG063+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ skC9
| equal(op(e4,e4),e1) ),
file('ALG063+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ skC10
| equal(op(e2,e2),e0) ),
file('ALG063+1.p',unknown),
[] ).
cnf(43,axiom,
( ~ skC11
| equal(op(e1,e1),e2) ),
file('ALG063+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ skC12
| equal(op(e2,e2),e2) ),
file('ALG063+1.p',unknown),
[] ).
cnf(46,axiom,
( ~ skC13
| equal(op(e3,e3),e2) ),
file('ALG063+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ skC14
| equal(op(e2,e2),e4) ),
file('ALG063+1.p',unknown),
[] ).
cnf(50,axiom,
( ~ skC15
| equal(op(e0,e0),e3) ),
file('ALG063+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ skC16
| equal(op(e1,e1),e3) ),
file('ALG063+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ skC17
| equal(op(e3,e3),e2) ),
file('ALG063+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ skC18
| equal(op(e3,e3),e3) ),
file('ALG063+1.p',unknown),
[] ).
cnf(57,axiom,
( ~ skC19
| equal(op(e4,e4),e3) ),
file('ALG063+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ skC20
| equal(op(e4,e4),e0) ),
file('ALG063+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ skC21
| equal(op(e4,e4),e1) ),
file('ALG063+1.p',unknown),
[] ).
cnf(63,axiom,
( ~ skC22
| equal(op(e2,e2),e4) ),
file('ALG063+1.p',unknown),
[] ).
cnf(64,axiom,
( ~ skC23
| equal(op(e4,e4),e3) ),
file('ALG063+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ equal(op(e0,e0),e0)
| ~ skC0 ),
file('ALG063+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ equal(op(e2,e2),e2)
| ~ skC12 ),
file('ALG063+1.p',unknown),
[] ).
cnf(84,axiom,
( ~ equal(op(e3,e3),e3)
| ~ skC18 ),
file('ALG063+1.p',unknown),
[] ).
cnf(91,axiom,
~ equal(op(e2,e0),op(e0,e0)),
file('ALG063+1.p',unknown),
[] ).
cnf(92,axiom,
~ equal(op(e3,e0),op(e0,e0)),
file('ALG063+1.p',unknown),
[] ).
cnf(93,axiom,
~ equal(op(e4,e0),op(e0,e0)),
file('ALG063+1.p',unknown),
[] ).
cnf(97,axiom,
~ equal(op(e3,e0),op(e2,e0)),
file('ALG063+1.p',unknown),
[] ).
cnf(98,axiom,
~ equal(op(e4,e0),op(e2,e0)),
file('ALG063+1.p',unknown),
[] ).
cnf(99,axiom,
~ equal(op(e4,e0),op(e3,e0)),
file('ALG063+1.p',unknown),
[] ).
cnf(100,axiom,
~ equal(op(e1,e1),op(e0,e1)),
file('ALG063+1.p',unknown),
[] ).
cnf(104,axiom,
~ equal(op(e2,e1),op(e1,e1)),
file('ALG063+1.p',unknown),
[] ).
cnf(107,axiom,
~ equal(op(e3,e1),op(e2,e1)),
file('ALG063+1.p',unknown),
[] ).
cnf(108,axiom,
~ equal(op(e4,e1),op(e2,e1)),
file('ALG063+1.p',unknown),
[] ).
cnf(110,axiom,
~ equal(op(e1,e2),op(e0,e2)),
file('ALG063+1.p',unknown),
[] ).
cnf(111,axiom,
~ equal(op(e2,e2),op(e0,e2)),
file('ALG063+1.p',unknown),
[] ).
cnf(112,axiom,
~ equal(op(e3,e2),op(e0,e2)),
file('ALG063+1.p',unknown),
[] ).
cnf(113,axiom,
~ equal(op(e4,e2),op(e0,e2)),
file('ALG063+1.p',unknown),
[] ).
cnf(114,axiom,
~ equal(op(e2,e2),op(e1,e2)),
file('ALG063+1.p',unknown),
[] ).
cnf(116,axiom,
~ equal(op(e4,e2),op(e1,e2)),
file('ALG063+1.p',unknown),
[] ).
cnf(118,axiom,
~ equal(op(e4,e2),op(e2,e2)),
file('ALG063+1.p',unknown),
[] ).
cnf(119,axiom,
~ equal(op(e4,e2),op(e3,e2)),
file('ALG063+1.p',unknown),
[] ).
cnf(129,axiom,
~ equal(op(e4,e3),op(e3,e3)),
file('ALG063+1.p',unknown),
[] ).
cnf(131,axiom,
~ equal(op(e2,e4),op(e0,e4)),
file('ALG063+1.p',unknown),
[] ).
cnf(133,axiom,
~ equal(op(e4,e4),op(e0,e4)),
file('ALG063+1.p',unknown),
[] ).
cnf(137,axiom,
~ equal(op(e3,e4),op(e2,e4)),
file('ALG063+1.p',unknown),
[] ).
cnf(138,axiom,
~ equal(op(e4,e4),op(e2,e4)),
file('ALG063+1.p',unknown),
[] ).
cnf(140,axiom,
~ equal(op(e0,e1),op(e0,e0)),
file('ALG063+1.p',unknown),
[] ).
cnf(141,axiom,
~ equal(op(e0,e2),op(e0,e0)),
file('ALG063+1.p',unknown),
[] ).
cnf(144,axiom,
~ equal(op(e0,e2),op(e0,e1)),
file('ALG063+1.p',unknown),
[] ).
cnf(155,axiom,
~ equal(op(e1,e3),op(e1,e1)),
file('ALG063+1.p',unknown),
[] ).
cnf(164,axiom,
~ equal(op(e2,e2),op(e2,e1)),
file('ALG063+1.p',unknown),
[] ).
cnf(165,axiom,
~ equal(op(e2,e3),op(e2,e1)),
file('ALG063+1.p',unknown),
[] ).
cnf(166,axiom,
~ equal(op(e2,e4),op(e2,e1)),
file('ALG063+1.p',unknown),
[] ).
cnf(168,axiom,
~ equal(op(e2,e4),op(e2,e2)),
file('ALG063+1.p',unknown),
[] ).
cnf(170,axiom,
~ equal(op(e3,e1),op(e3,e0)),
file('ALG063+1.p',unknown),
[] ).
cnf(173,axiom,
~ equal(op(e3,e4),op(e3,e0)),
file('ALG063+1.p',unknown),
[] ).
cnf(174,axiom,
~ equal(op(e3,e2),op(e3,e1)),
file('ALG063+1.p',unknown),
[] ).
cnf(184,axiom,
~ equal(op(e4,e2),op(e4,e1)),
file('ALG063+1.p',unknown),
[] ).
cnf(185,axiom,
~ equal(op(e4,e3),op(e4,e1)),
file('ALG063+1.p',unknown),
[] ).
cnf(186,axiom,
~ equal(op(e4,e4),op(e4,e1)),
file('ALG063+1.p',unknown),
[] ).
cnf(187,axiom,
~ equal(op(e4,e3),op(e4,e2)),
file('ALG063+1.p',unknown),
[] ).
cnf(188,axiom,
~ equal(op(e4,e4),op(e4,e2)),
file('ALG063+1.p',unknown),
[] ).
cnf(189,axiom,
~ equal(op(e4,e4),op(e4,e3)),
file('ALG063+1.p',unknown),
[] ).
cnf(190,axiom,
equal(op(op(e1,e1),op(e1,e1)),e2),
file('ALG063+1.p',unknown),
[] ).
cnf(191,axiom,
equal(op(e1,op(op(e1,e1),op(e1,e1))),e0),
file('ALG063+1.p',unknown),
[] ).
cnf(192,axiom,
( equal(e4,unit)
| equal(e3,unit)
| equal(e2,unit)
| equal(e1,unit)
| equal(e0,unit) ),
file('ALG063+1.p',unknown),
[] ).
cnf(193,axiom,
equal(op(op(op(e1,e1),op(e1,e1)),op(op(e1,e1),op(e1,e1))),e3),
file('ALG063+1.p',unknown),
[] ).
cnf(203,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('ALG063+1.p',unknown),
[] ).
cnf(204,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('ALG063+1.p',unknown),
[] ).
cnf(208,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('ALG063+1.p',unknown),
[] ).
cnf(210,axiom,
( equal(op(e3,e3),e1)
| equal(op(e1,e3),e1)
| equal(op(e4,e3),e1)
| equal(op(e2,e3),e1)
| equal(op(e0,e3),e1) ),
file('ALG063+1.p',unknown),
[] ).
cnf(215,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('ALG063+1.p',unknown),
[] ).
cnf(218,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('ALG063+1.p',unknown),
[] ).
cnf(221,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('ALG063+1.p',unknown),
[] ).
cnf(226,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('ALG063+1.p',unknown),
[] ).
cnf(228,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('ALG063+1.p',unknown),
[] ).
cnf(235,axiom,
( equal(op(e0,e0),e4)
| equal(op(e0,e1),e4)
| equal(op(e0,e2),e4)
| equal(op(e0,e3),e4)
| equal(op(e0,e4),e4) ),
file('ALG063+1.p',unknown),
[] ).
cnf(239,axiom,
( equal(op(e0,e0),e2)
| equal(op(e0,e1),e2)
| equal(op(e0,e2),e2)
| equal(op(e0,e3),e2)
| equal(op(e0,e4),e2) ),
file('ALG063+1.p',unknown),
[] ).
cnf(241,axiom,
( equal(op(e0,e1),e1)
| equal(op(e0,e0),e1)
| equal(op(e0,e4),e1)
| equal(op(e0,e3),e1)
| equal(op(e0,e2),e1) ),
file('ALG063+1.p',unknown),
[] ).
cnf(246,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('ALG063+1.p',unknown),
[] ).
cnf(253,axiom,
( equal(op(e3,e0),e3)
| equal(op(e3,e0),e0)
| equal(op(e3,e0),e4)
| equal(op(e3,e0),e2)
| equal(op(e3,e0),e1) ),
file('ALG063+1.p',unknown),
[] ).
cnf(254,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('ALG063+1.p',unknown),
[] ).
cnf(257,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('ALG063+1.p',unknown),
[] ).
cnf(266,axiom,
( equal(op(e0,e2),e0)
| equal(op(e0,e2),e1)
| equal(op(e0,e2),e2)
| equal(op(e0,e2),e3)
| equal(op(e0,e2),e4) ),
file('ALG063+1.p',unknown),
[] ).
cnf(272,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('ALG063+1.p',unknown),
[] ).
cnf(273,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('ALG063+1.p',unknown),
[] ).
cnf(274,axiom,
( equal(op(e4,e4),e4)
| skC0
| skC1
| skC2
| skC3
| skC4
| skC5
| skC6
| skC7
| skC8
| skC9
| skC10
| skC11
| skC12
| skC13
| skC14
| skC15
| skC16
| skC17
| skC18
| skC19
| skC20
| skC21
| skC22
| skC23 ),
file('ALG063+1.p',unknown),
[] ).
cnf(276,plain,
( ~ skC16
| equal(e4,e3) ),
inference(rew,[status(thm),theory(equality)],[21,52]),
[iquote('0:Rew:21.0,52.1')] ).
cnf(277,plain,
~ skC16,
inference(mrr,[status(thm)],[276,10]),
[iquote('0:MRR:276.1,10.0')] ).
cnf(278,plain,
( ~ skC11
| equal(e4,e2) ),
inference(rew,[status(thm),theory(equality)],[21,43]),
[iquote('0:Rew:21.0,43.1')] ).
cnf(279,plain,
~ skC11,
inference(mrr,[status(thm)],[278,9]),
[iquote('0:MRR:278.1,9.0')] ).
cnf(280,plain,
( ~ skC8
| equal(e4,e3) ),
inference(rew,[status(thm),theory(equality)],[21,36]),
[iquote('0:Rew:21.0,36.1')] ).
cnf(281,plain,
~ skC8,
inference(mrr,[status(thm)],[280,10]),
[iquote('0:MRR:280.1,10.0')] ).
cnf(282,plain,
( ~ skC7
| equal(e4,e2) ),
inference(rew,[status(thm),theory(equality)],[21,34]),
[iquote('0:Rew:21.0,34.1')] ).
cnf(283,plain,
~ skC7,
inference(mrr,[status(thm)],[282,9]),
[iquote('0:MRR:282.1,9.0')] ).
cnf(284,plain,
( ~ skC6
| equal(e4,e1) ),
inference(rew,[status(thm),theory(equality)],[21,33]),
[iquote('0:Rew:21.0,33.1')] ).
cnf(285,plain,
~ skC6,
inference(mrr,[status(thm)],[284,7]),
[iquote('0:MRR:284.1,7.0')] ).
cnf(286,plain,
( ~ skC5
| equal(e4,e0) ),
inference(rew,[status(thm),theory(equality)],[21,31]),
[iquote('0:Rew:21.0,31.1')] ).
cnf(287,plain,
~ skC5,
inference(mrr,[status(thm)],[286,4]),
[iquote('0:MRR:286.1,4.0')] ).
cnf(288,plain,
( ~ skC1
| equal(e4,e0) ),
inference(rew,[status(thm),theory(equality)],[21,24]),
[iquote('0:Rew:21.0,24.1')] ).
cnf(289,plain,
~ skC1,
inference(mrr,[status(thm)],[288,4]),
[iquote('0:MRR:288.1,4.0')] ).
cnf(291,plain,
~ equal(op(e1,e3),e4),
inference(rew,[status(thm),theory(equality)],[21,155]),
[iquote('0:Rew:21.0,155.0')] ).
cnf(296,plain,
~ equal(op(e2,e1),e4),
inference(rew,[status(thm),theory(equality)],[21,104]),
[iquote('0:Rew:21.0,104.0')] ).
cnf(297,plain,
~ equal(op(e0,e1),e4),
inference(rew,[status(thm),theory(equality)],[21,100]),
[iquote('0:Rew:21.0,100.0')] ).
cnf(298,plain,
( ~ equal(e3,e3)
| ~ skC18 ),
inference(rew,[status(thm),theory(equality)],[55,84]),
[iquote('0:Rew:55.1,84.0')] ).
cnf(299,plain,
~ skC18,
inference(obv,[status(thm),theory(equality)],[298]),
[iquote('0:Obv:298.0')] ).
cnf(300,plain,
( ~ equal(e2,e2)
| ~ skC12 ),
inference(rew,[status(thm),theory(equality)],[44,78]),
[iquote('0:Rew:44.1,78.0')] ).
cnf(301,plain,
~ skC12,
inference(obv,[status(thm),theory(equality)],[300]),
[iquote('0:Obv:300.0')] ).
cnf(302,plain,
( ~ equal(e0,e0)
| ~ skC0 ),
inference(rew,[status(thm),theory(equality)],[22,66]),
[iquote('0:Rew:22.1,66.0')] ).
cnf(303,plain,
~ skC0,
inference(obv,[status(thm),theory(equality)],[302]),
[iquote('0:Obv:302.0')] ).
cnf(304,plain,
equal(op(e4,e4),e2),
inference(rew,[status(thm),theory(equality)],[21,190]),
[iquote('0:Rew:21.0,190.0')] ).
cnf(305,plain,
( ~ skC19
| equal(e3,e2) ),
inference(rew,[status(thm),theory(equality)],[304,57]),
[iquote('0:Rew:304.0,57.1')] ).
cnf(306,plain,
( ~ skC23
| equal(e3,e2) ),
inference(rew,[status(thm),theory(equality)],[304,64]),
[iquote('0:Rew:304.0,64.1')] ).
cnf(307,plain,
( ~ skC9
| equal(e2,e1) ),
inference(rew,[status(thm),theory(equality)],[304,39]),
[iquote('0:Rew:304.0,39.1')] ).
cnf(308,plain,
( ~ skC21
| equal(e2,e1) ),
inference(rew,[status(thm),theory(equality)],[304,60]),
[iquote('0:Rew:304.0,60.1')] ).
cnf(309,plain,
( ~ skC4
| equal(e2,e0) ),
inference(rew,[status(thm),theory(equality)],[304,30]),
[iquote('0:Rew:304.0,30.1')] ).
cnf(310,plain,
( ~ skC20
| equal(e2,e0) ),
inference(rew,[status(thm),theory(equality)],[304,58]),
[iquote('0:Rew:304.0,58.1')] ).
cnf(311,plain,
~ equal(op(e4,e3),e2),
inference(rew,[status(thm),theory(equality)],[304,189]),
[iquote('0:Rew:304.0,189.0')] ).
cnf(312,plain,
~ equal(op(e4,e2),e2),
inference(rew,[status(thm),theory(equality)],[304,188]),
[iquote('0:Rew:304.0,188.0')] ).
cnf(313,plain,
~ equal(op(e4,e1),e2),
inference(rew,[status(thm),theory(equality)],[304,186]),
[iquote('0:Rew:304.0,186.0')] ).
cnf(316,plain,
~ equal(op(e2,e4),e2),
inference(rew,[status(thm),theory(equality)],[304,138]),
[iquote('0:Rew:304.0,138.0')] ).
cnf(318,plain,
~ equal(op(e0,e4),e2),
inference(rew,[status(thm),theory(equality)],[304,133]),
[iquote('0:Rew:304.0,133.0')] ).
cnf(319,plain,
~ skC19,
inference(mrr,[status(thm)],[305,8]),
[iquote('0:MRR:305.1,8.0')] ).
cnf(320,plain,
~ skC23,
inference(mrr,[status(thm)],[306,8]),
[iquote('0:MRR:306.1,8.0')] ).
cnf(321,plain,
~ skC9,
inference(mrr,[status(thm)],[307,5]),
[iquote('0:MRR:307.1,5.0')] ).
cnf(322,plain,
~ skC21,
inference(mrr,[status(thm)],[308,5]),
[iquote('0:MRR:308.1,5.0')] ).
cnf(323,plain,
~ skC4,
inference(mrr,[status(thm)],[309,2]),
[iquote('0:MRR:309.1,2.0')] ).
cnf(324,plain,
~ skC20,
inference(mrr,[status(thm)],[310,2]),
[iquote('0:MRR:310.1,2.0')] ).
cnf(325,plain,
equal(op(e1,e2),e0),
inference(rew,[status(thm),theory(equality)],[304,191,21]),
[iquote('0:Rew:304.0,191.0,21.0,191.0')] ).
cnf(330,plain,
~ equal(op(e4,e2),e0),
inference(rew,[status(thm),theory(equality)],[325,116]),
[iquote('0:Rew:325.0,116.0')] ).
cnf(332,plain,
~ equal(op(e2,e2),e0),
inference(rew,[status(thm),theory(equality)],[325,114]),
[iquote('0:Rew:325.0,114.0')] ).
cnf(333,plain,
~ equal(op(e0,e2),e0),
inference(rew,[status(thm),theory(equality)],[325,110]),
[iquote('0:Rew:325.0,110.0')] ).
cnf(334,plain,
~ skC10,
inference(mrr,[status(thm)],[40,332]),
[iquote('0:MRR:40.1,332.0')] ).
cnf(335,plain,
~ skC2,
inference(mrr,[status(thm)],[26,332]),
[iquote('0:MRR:26.1,332.0')] ).
cnf(336,plain,
equal(op(e2,e2),e3),
inference(rew,[status(thm),theory(equality)],[304,193,21]),
[iquote('0:Rew:304.0,193.0,21.0,193.0')] ).
cnf(337,plain,
( ~ skC14
| equal(e4,e3) ),
inference(rew,[status(thm),theory(equality)],[336,47]),
[iquote('0:Rew:336.0,47.1')] ).
cnf(338,plain,
( ~ skC22
| equal(e4,e3) ),
inference(rew,[status(thm),theory(equality)],[336,63]),
[iquote('0:Rew:336.0,63.1')] ).
cnf(339,plain,
~ equal(op(e2,e4),e3),
inference(rew,[status(thm),theory(equality)],[336,168]),
[iquote('0:Rew:336.0,168.0')] ).
cnf(341,plain,
~ equal(op(e2,e1),e3),
inference(rew,[status(thm),theory(equality)],[336,164]),
[iquote('0:Rew:336.0,164.0')] ).
cnf(343,plain,
~ equal(op(e4,e2),e3),
inference(rew,[status(thm),theory(equality)],[336,118]),
[iquote('0:Rew:336.0,118.0')] ).
cnf(345,plain,
~ equal(op(e0,e2),e3),
inference(rew,[status(thm),theory(equality)],[336,111]),
[iquote('0:Rew:336.0,111.0')] ).
cnf(347,plain,
~ skC14,
inference(mrr,[status(thm)],[337,10]),
[iquote('0:MRR:337.1,10.0')] ).
cnf(348,plain,
~ skC22,
inference(mrr,[status(thm)],[338,10]),
[iquote('0:MRR:338.1,10.0')] ).
cnf(363,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)],[304,203]),
[iquote('0:Rew:304.0,203.4')] ).
cnf(364,plain,
( equal(op(e4,e0),e0)
| equal(op(e4,e3),e0)
| equal(op(e4,e1),e0) ),
inference(mrr,[status(thm)],[363,330,2]),
[iquote('0:MRR:363.2,363.4,330.0,2.0')] ).
cnf(365,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)],[204,291]),
[iquote('0:MRR:204.1,291.0')] ).
cnf(369,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)],[208,311]),
[iquote('0:MRR:208.4,311.0')] ).
cnf(375,plain,
( equal(op(e2,e0),e4)
| equal(op(e2,e1),e4)
| equal(e4,e3)
| equal(op(e2,e3),e4)
| equal(op(e2,e4),e4) ),
inference(rew,[status(thm),theory(equality)],[336,215]),
[iquote('0:Rew:336.0,215.2')] ).
cnf(376,plain,
( equal(op(e2,e4),e4)
| equal(op(e2,e3),e4)
| equal(op(e2,e0),e4) ),
inference(mrr,[status(thm)],[375,296,10]),
[iquote('0:MRR:375.1,375.2,296.0,10.0')] ).
cnf(377,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)],[336,218,325]),
[iquote('0:Rew:336.0,218.2,325.0,218.1')] ).
cnf(378,plain,
( equal(op(e3,e2),e2)
| equal(op(e0,e2),e2) ),
inference(mrr,[status(thm)],[377,2,8,312]),
[iquote('0:MRR:377.1,377.2,377.4,2.0,8.0,312.0')] ).
cnf(383,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)],[336,221]),
[iquote('0:Rew:336.0,221.2')] ).
cnf(384,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)],[383,6]),
[iquote('0:MRR:383.2,6.0')] ).
cnf(387,plain,
( equal(op(e0,e1),e3)
| equal(e4,e3)
| equal(op(e2,e1),e3)
| equal(op(e3,e1),e3)
| equal(op(e4,e1),e3) ),
inference(rew,[status(thm),theory(equality)],[21,226]),
[iquote('0:Rew:21.0,226.1')] ).
cnf(388,plain,
( equal(op(e3,e1),e3)
| equal(op(e4,e1),e3)
| equal(op(e0,e1),e3) ),
inference(mrr,[status(thm)],[387,10,341]),
[iquote('0:MRR:387.1,387.2,10.0,341.0')] ).
cnf(391,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)],[21,228]),
[iquote('0:Rew:21.0,228.1')] ).
cnf(392,plain,
( equal(op(e2,e1),e2)
| equal(op(e3,e1),e2)
| equal(op(e0,e1),e2) ),
inference(mrr,[status(thm)],[391,9,313]),
[iquote('0:MRR:391.1,391.4,9.0,313.0')] ).
cnf(402,plain,
( equal(op(e0,e4),e4)
| equal(op(e0,e0),e4)
| equal(op(e0,e3),e4)
| equal(op(e0,e2),e4) ),
inference(mrr,[status(thm)],[235,297]),
[iquote('0:MRR:235.1,297.0')] ).
cnf(406,plain,
( equal(op(e0,e2),e2)
| equal(op(e0,e0),e2)
| equal(op(e0,e3),e2)
| equal(op(e0,e1),e2) ),
inference(mrr,[status(thm)],[239,318]),
[iquote('0:MRR:239.4,318.0')] ).
cnf(410,plain,
( equal(op(e4,e2),e4)
| equal(op(e4,e2),e1) ),
inference(mrr,[status(thm)],[246,330,312,343]),
[iquote('0:MRR:246.0,246.2,246.3,330.0,312.0,343.0')] ).
cnf(416,plain,
( equal(op(e2,e4),e4)
| equal(op(e2,e4),e1)
| equal(op(e2,e4),e0) ),
inference(mrr,[status(thm)],[254,316,339]),
[iquote('0:MRR:254.2,254.3,316.0,339.0')] ).
cnf(418,plain,
( equal(op(e2,e1),e2)
| equal(op(e2,e1),e1)
| equal(op(e2,e1),e0) ),
inference(mrr,[status(thm)],[257,341,296]),
[iquote('0:MRR:257.3,257.4,341.0,296.0')] ).
cnf(424,plain,
( equal(op(e0,e2),e2)
| equal(op(e0,e2),e4)
| equal(op(e0,e2),e1) ),
inference(mrr,[status(thm)],[266,333,345]),
[iquote('0:MRR:266.0,266.3,333.0,345.0')] ).
cnf(426,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)],[304,272,336,21]),
[iquote('0:Rew:304.0,272.4,336.0,272.2,21.0,272.1')] ).
cnf(427,plain,
( equal(op(e3,e3),e1)
| equal(op(e0,e0),e1) ),
inference(mrr,[status(thm)],[426,7,6,5]),
[iquote('0:MRR:426.1,426.2,426.4,7.0,6.0,5.0')] ).
cnf(428,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)],[304,273,336,21]),
[iquote('0:Rew:304.0,273.4,336.0,273.2,21.0,273.1')] ).
cnf(429,plain,
( equal(op(e0,e0),e0)
| equal(op(e3,e3),e0) ),
inference(mrr,[status(thm)],[428,4,3,2]),
[iquote('0:MRR:428.1,428.2,428.4,4.0,3.0,2.0')] ).
cnf(430,plain,
( equal(e4,e2)
| skC0
| skC1
| skC2
| skC3
| skC4
| skC5
| skC6
| skC7
| skC8
| skC9
| skC10
| skC11
| skC12
| skC13
| skC14
| skC15
| skC16
| skC17
| skC18
| skC19
| skC20
| skC21
| skC22
| skC23 ),
inference(rew,[status(thm),theory(equality)],[304,274]),
[iquote('0:Rew:304.0,274.0')] ).
cnf(431,plain,
( skC17
| skC15
| skC13
| skC3 ),
inference(mrr,[status(thm)],[430,9,303,289,335,323,287,285,283,281,321,334,279,301,347,277,299,319,324,322,348,320]),
[iquote('0:MRR:430.0,430.1,430.2,430.3,430.5,430.6,430.7,430.8,430.9,430.10,430.11,430.12,430.13,430.15,430.17,430.19,430.20,430.21,430.22,430.23,430.24,9.0,303.0,289.0,335.0,323.0,287.0,285.0,283.0,281.0,321.0,334.0,279.0,301.0,347.0,277.0,299.0,319.0,324.0,322.0,348.0,320.0')] ).
cnf(432,plain,
equal(e3,unit),
inference(spt,[spt(split,[position(s1)])],[192]),
[iquote('1:Spt:192.1')] ).
cnf(436,plain,
( ~ skC13
| equal(op(unit,unit),e2) ),
inference(rew,[status(thm),theory(equality)],[432,46]),
[iquote('1:Rew:432.0,46.1')] ).
cnf(437,plain,
( ~ skC17
| equal(op(unit,unit),e2) ),
inference(rew,[status(thm),theory(equality)],[432,53]),
[iquote('1:Rew:432.0,53.1')] ).
cnf(441,plain,
( ~ skC3
| equal(op(unit,unit),e0) ),
inference(rew,[status(thm),theory(equality)],[432,28]),
[iquote('1:Rew:432.0,28.1')] ).
cnf(452,plain,
( ~ skC15
| equal(op(e0,e0),unit) ),
inference(rew,[status(thm),theory(equality)],[432,50]),
[iquote('1:Rew:432.0,50.1')] ).
cnf(458,plain,
~ equal(op(e4,e2),op(e4,unit)),
inference(rew,[status(thm),theory(equality)],[432,187]),
[iquote('1:Rew:432.0,187.0')] ).
cnf(468,plain,
~ equal(op(e2,e4),op(unit,e4)),
inference(rew,[status(thm),theory(equality)],[432,137]),
[iquote('1:Rew:432.0,137.0')] ).
cnf(479,plain,
~ equal(op(e0,e2),op(unit,e2)),
inference(rew,[status(thm),theory(equality)],[432,112]),
[iquote('1:Rew:432.0,112.0')] ).
cnf(481,plain,
( equal(op(e2,e1),e2)
| equal(op(unit,e1),e2)
| equal(op(e0,e1),e2) ),
inference(rew,[status(thm),theory(equality)],[432,392]),
[iquote('1:Rew:432.0,392.1')] ).
cnf(489,plain,
~ equal(op(e2,e1),op(unit,e1)),
inference(rew,[status(thm),theory(equality)],[432,107]),
[iquote('1:Rew:432.0,107.0')] ).
cnf(511,plain,
~ equal(op(e2,e1),op(e2,unit)),
inference(rew,[status(thm),theory(equality)],[432,165]),
[iquote('1:Rew:432.0,165.0')] ).
cnf(530,plain,
( equal(op(e0,e1),e1)
| equal(op(e0,e0),e1)
| equal(op(e0,e4),e1)
| equal(op(e0,unit),e1)
| equal(op(e0,e2),e1) ),
inference(rew,[status(thm),theory(equality)],[432,241]),
[iquote('1:Rew:432.0,241.3')] ).
cnf(553,plain,
~ equal(e2,unit),
inference(rew,[status(thm),theory(equality)],[432,8]),
[iquote('1:Rew:432.0,8.0')] ).
cnf(554,plain,
~ equal(e1,unit),
inference(rew,[status(thm),theory(equality)],[432,6]),
[iquote('1:Rew:432.0,6.0')] ).
cnf(555,plain,
~ equal(e0,unit),
inference(rew,[status(thm),theory(equality)],[432,3]),
[iquote('1:Rew:432.0,3.0')] ).
cnf(556,plain,
equal(op(unit,unit),unit),
inference(rew,[status(thm),theory(equality)],[432,18]),
[iquote('1:Rew:432.0,18.0')] ).
cnf(574,plain,
( ~ skC13
| equal(e2,unit) ),
inference(rew,[status(thm),theory(equality)],[556,436]),
[iquote('1:Rew:556.0,436.1')] ).
cnf(575,plain,
~ skC13,
inference(mrr,[status(thm)],[574,553]),
[iquote('1:MRR:574.1,553.0')] ).
cnf(576,plain,
( skC17
| skC15
| skC3 ),
inference(mrr,[status(thm)],[431,575]),
[iquote('1:MRR:431.2,575.0')] ).
cnf(577,plain,
( ~ skC17
| equal(e2,unit) ),
inference(rew,[status(thm),theory(equality)],[556,437]),
[iquote('1:Rew:556.0,437.1')] ).
cnf(578,plain,
~ skC17,
inference(mrr,[status(thm)],[577,553]),
[iquote('1:MRR:577.1,553.0')] ).
cnf(579,plain,
( skC15
| skC3 ),
inference(mrr,[status(thm)],[576,578]),
[iquote('1:MRR:576.0,578.0')] ).
cnf(580,plain,
( ~ skC3
| equal(e0,unit) ),
inference(rew,[status(thm),theory(equality)],[556,441]),
[iquote('1:Rew:556.0,441.1')] ).
cnf(581,plain,
~ skC3,
inference(mrr,[status(thm)],[580,555]),
[iquote('1:MRR:580.1,555.0')] ).
cnf(582,plain,
skC15,
inference(mrr,[status(thm)],[579,581]),
[iquote('1:MRR:579.1,581.0')] ).
cnf(585,plain,
equal(op(e0,e0),unit),
inference(mrr,[status(thm)],[452,582]),
[iquote('1:MRR:452.0,582.0')] ).
cnf(592,plain,
~ equal(op(e4,e2),e4),
inference(rew,[status(thm),theory(equality)],[20,458]),
[iquote('1:Rew:20.0,458.0')] ).
cnf(593,plain,
equal(op(e4,e2),e1),
inference(mrr,[status(thm)],[410,592]),
[iquote('1:MRR:410.0,592.0')] ).
cnf(598,plain,
~ equal(op(e0,e2),e1),
inference(rew,[status(thm),theory(equality)],[593,113]),
[iquote('1:Rew:593.0,113.0')] ).
cnf(601,plain,
( equal(op(e0,e2),e2)
| equal(op(e0,e2),e4) ),
inference(mrr,[status(thm)],[424,598]),
[iquote('1:MRR:424.2,598.0')] ).
cnf(606,plain,
~ equal(op(e2,e4),e4),
inference(rew,[status(thm),theory(equality)],[19,468]),
[iquote('1:Rew:19.0,468.0')] ).
cnf(607,plain,
( equal(op(e2,e4),e1)
| equal(op(e2,e4),e0) ),
inference(mrr,[status(thm)],[416,606]),
[iquote('1:MRR:416.0,606.0')] ).
cnf(613,plain,
~ equal(op(e0,e2),e2),
inference(rew,[status(thm),theory(equality)],[15,479]),
[iquote('1:Rew:15.0,479.0')] ).
cnf(618,plain,
~ equal(op(e2,e1),e1),
inference(rew,[status(thm),theory(equality)],[13,489]),
[iquote('1:Rew:13.0,489.0')] ).
cnf(619,plain,
( equal(op(e2,e1),e2)
| equal(op(e2,e1),e0) ),
inference(mrr,[status(thm)],[418,618]),
[iquote('1:MRR:418.1,618.0')] ).
cnf(631,plain,
~ equal(op(e2,e1),e2),
inference(rew,[status(thm),theory(equality)],[16,511]),
[iquote('1:Rew:16.0,511.0')] ).
cnf(671,plain,
equal(op(e0,e2),e4),
inference(mrr,[status(thm)],[601,613]),
[iquote('1:MRR:601.0,613.0')] ).
cnf(678,plain,
equal(op(e2,e1),e0),
inference(mrr,[status(thm)],[619,631]),
[iquote('1:MRR:619.0,631.0')] ).
cnf(680,plain,
~ equal(op(e2,e4),e0),
inference(rew,[status(thm),theory(equality)],[678,166]),
[iquote('1:Rew:678.0,166.0')] ).
cnf(687,plain,
equal(op(e2,e4),e1),
inference(mrr,[status(thm)],[607,680]),
[iquote('1:MRR:607.1,680.0')] ).
cnf(690,plain,
~ equal(op(e0,e4),e1),
inference(rew,[status(thm),theory(equality)],[687,131]),
[iquote('1:Rew:687.0,131.0')] ).
cnf(699,plain,
( equal(e2,e0)
| equal(e2,e1)
| equal(op(e0,e1),e2) ),
inference(rew,[status(thm),theory(equality)],[13,481,678]),
[iquote('1:Rew:13.0,481.1,678.0,481.0')] ).
cnf(700,plain,
equal(op(e0,e1),e2),
inference(mrr,[status(thm)],[699,2,5]),
[iquote('1:MRR:699.0,699.1,2.0,5.0')] ).
cnf(740,plain,
( equal(e2,e1)
| equal(e1,unit)
| equal(op(e0,e4),e1)
| equal(e1,e0)
| equal(e4,e1) ),
inference(rew,[status(thm),theory(equality)],[671,530,12,585,700]),
[iquote('1:Rew:671.0,530.4,12.0,530.3,585.0,530.1,700.0,530.0')] ).
cnf(741,plain,
$false,
inference(mrr,[status(thm)],[740,5,554,690,1,7]),
[iquote('1:MRR:740.0,740.1,740.2,740.3,740.4,5.0,554.0,690.0,1.0,7.0')] ).
cnf(742,plain,
~ equal(e3,unit),
inference(spt,[spt(split,[position(sa)])],[741,432]),
[iquote('1:Spt:741.0,192.1,432.0')] ).
cnf(743,plain,
( equal(e4,unit)
| equal(e2,unit)
| equal(e1,unit)
| equal(e0,unit) ),
inference(spt,[spt(split,[position(s2)])],[192]),
[iquote('1:Spt:741.0,192.0,192.2,192.3,192.4')] ).
cnf(744,plain,
equal(e4,unit),
inference(spt,[spt(split,[position(s2s1)])],[743]),
[iquote('2:Spt:743.0')] ).
cnf(746,plain,
~ equal(op(e3,e0),op(unit,e0)),
inference(rew,[status(thm),theory(equality)],[744,99]),
[iquote('2:Rew:744.0,99.0')] ).
cnf(747,plain,
~ equal(op(e0,e0),op(unit,e0)),
inference(rew,[status(thm),theory(equality)],[744,93]),
[iquote('2:Rew:744.0,93.0')] ).
cnf(769,plain,
~ equal(e2,unit),
inference(rew,[status(thm),theory(equality)],[744,9]),
[iquote('2:Rew:744.0,9.0')] ).
cnf(770,plain,
~ equal(e1,unit),
inference(rew,[status(thm),theory(equality)],[744,7]),
[iquote('2:Rew:744.0,7.0')] ).
cnf(780,plain,
~ equal(op(e3,e2),op(unit,e2)),
inference(rew,[status(thm),theory(equality)],[744,119]),
[iquote('2:Rew:744.0,119.0')] ).
cnf(788,plain,
~ equal(op(e2,e1),op(e2,unit)),
inference(rew,[status(thm),theory(equality)],[744,166]),
[iquote('2:Rew:744.0,166.0')] ).
cnf(793,plain,
( equal(op(e2,e1),e1)
| equal(op(e2,unit),e1)
| equal(op(e2,e3),e1)
| equal(op(e2,e0),e1) ),
inference(rew,[status(thm),theory(equality)],[744,384]),
[iquote('2:Rew:744.0,384.1')] ).
cnf(797,plain,
~ equal(op(e3,e0),op(e3,unit)),
inference(rew,[status(thm),theory(equality)],[744,173]),
[iquote('2:Rew:744.0,173.0')] ).
cnf(836,plain,
~ equal(op(e2,e1),op(unit,e1)),
inference(rew,[status(thm),theory(equality)],[744,108]),
[iquote('2:Rew:744.0,108.0')] ).
cnf(847,plain,
( equal(op(e2,unit),unit)
| equal(op(e2,e3),e4)
| equal(op(e2,e0),e4) ),
inference(rew,[status(thm),theory(equality)],[744,376]),
[iquote('2:Rew:744.0,376.0')] ).
cnf(858,plain,
( equal(op(e3,e0),e3)
| equal(op(e3,e0),e0)
| equal(op(e3,e0),unit)
| equal(op(e3,e0),e2)
| equal(op(e3,e0),e1) ),
inference(rew,[status(thm),theory(equality)],[744,253]),
[iquote('2:Rew:744.0,253.2')] ).
cnf(878,plain,
~ equal(op(e3,e0),e0),
inference(rew,[status(thm),theory(equality)],[11,746]),
[iquote('2:Rew:11.0,746.0')] ).
cnf(879,plain,
~ equal(op(e0,e0),e0),
inference(rew,[status(thm),theory(equality)],[11,747]),
[iquote('2:Rew:11.0,747.0')] ).
cnf(880,plain,
equal(op(e3,e3),e0),
inference(mrr,[status(thm)],[429,879]),
[iquote('2:MRR:429.0,879.0')] ).
cnf(891,plain,
( equal(e1,e0)
| equal(op(e0,e0),e1) ),
inference(rew,[status(thm),theory(equality)],[880,427]),
[iquote('2:Rew:880.0,427.0')] ).
cnf(904,plain,
~ equal(op(e3,e2),e2),
inference(rew,[status(thm),theory(equality)],[15,780]),
[iquote('2:Rew:15.0,780.0')] ).
cnf(905,plain,
equal(op(e0,e2),e2),
inference(mrr,[status(thm)],[378,904]),
[iquote('2:MRR:378.0,904.0')] ).
cnf(911,plain,
~ equal(op(e0,e1),e2),
inference(rew,[status(thm),theory(equality)],[905,144]),
[iquote('2:Rew:905.0,144.0')] ).
cnf(913,plain,
( equal(op(e2,e1),e2)
| equal(op(e3,e1),e2) ),
inference(mrr,[status(thm)],[392,911]),
[iquote('2:MRR:392.2,911.0')] ).
cnf(919,plain,
~ equal(op(e2,e1),e2),
inference(rew,[status(thm),theory(equality)],[16,788]),
[iquote('2:Rew:16.0,788.0')] ).
cnf(920,plain,
( equal(op(e2,e1),e1)
| equal(op(e2,e1),e0) ),
inference(mrr,[status(thm)],[418,919]),
[iquote('2:MRR:418.0,919.0')] ).
cnf(923,plain,
~ equal(op(e3,e0),e3),
inference(rew,[status(thm),theory(equality)],[18,797]),
[iquote('2:Rew:18.0,797.0')] ).
cnf(945,plain,
~ equal(op(e2,e1),e1),
inference(rew,[status(thm),theory(equality)],[13,836]),
[iquote('2:Rew:13.0,836.0')] ).
cnf(948,plain,
equal(op(e0,e0),e1),
inference(mrr,[status(thm)],[891,1]),
[iquote('2:MRR:891.0,1.0')] ).
cnf(952,plain,
~ equal(op(e3,e0),e1),
inference(rew,[status(thm),theory(equality)],[948,92]),
[iquote('2:Rew:948.0,92.0')] ).
cnf(954,plain,
~ equal(op(e2,e0),e1),
inference(rew,[status(thm),theory(equality)],[948,91]),
[iquote('2:Rew:948.0,91.0')] ).
cnf(963,plain,
equal(op(e3,e1),e2),
inference(mrr,[status(thm)],[913,919]),
[iquote('2:MRR:913.0,919.0')] ).
cnf(964,plain,
~ equal(op(e3,e0),e2),
inference(rew,[status(thm),theory(equality)],[963,170]),
[iquote('2:Rew:963.0,170.0')] ).
cnf(973,plain,
equal(op(e2,e1),e0),
inference(mrr,[status(thm)],[920,945]),
[iquote('2:MRR:920.0,945.0')] ).
cnf(1022,plain,
( equal(e2,unit)
| equal(op(e2,e3),unit)
| equal(op(e2,e0),unit) ),
inference(rew,[status(thm),theory(equality)],[744,847,16]),
[iquote('2:Rew:744.0,847.2,744.0,847.1,16.0,847.0')] ).
cnf(1023,plain,
( equal(op(e2,e3),unit)
| equal(op(e2,e0),unit) ),
inference(mrr,[status(thm)],[1022,769]),
[iquote('2:MRR:1022.0,769.0')] ).
cnf(1030,plain,
( equal(e1,e0)
| equal(e2,e1)
| equal(op(e2,e3),e1)
| equal(op(e2,e0),e1) ),
inference(rew,[status(thm),theory(equality)],[16,793,973]),
[iquote('2:Rew:16.0,793.1,973.0,793.0')] ).
cnf(1031,plain,
equal(op(e2,e3),e1),
inference(mrr,[status(thm)],[1030,1,5,954]),
[iquote('2:MRR:1030.0,1030.1,1030.3,1.0,5.0,954.0')] ).
cnf(1037,plain,
( equal(e1,unit)
| equal(op(e2,e0),unit) ),
inference(rew,[status(thm),theory(equality)],[1031,1023]),
[iquote('2:Rew:1031.0,1023.0')] ).
cnf(1038,plain,
equal(op(e2,e0),unit),
inference(mrr,[status(thm)],[1037,770]),
[iquote('2:MRR:1037.0,770.0')] ).
cnf(1040,plain,
~ equal(op(e3,e0),unit),
inference(rew,[status(thm),theory(equality)],[1038,97]),
[iquote('2:Rew:1038.0,97.0')] ).
cnf(1053,plain,
$false,
inference(mrr,[status(thm)],[858,923,878,1040,964,952]),
[iquote('2:MRR:858.0,858.1,858.2,858.3,858.4,923.0,878.0,1040.0,964.0,952.0')] ).
cnf(1054,plain,
~ equal(e4,unit),
inference(spt,[spt(split,[position(s2sa)])],[1053,744]),
[iquote('2:Spt:1053.0,743.0,744.0')] ).
cnf(1055,plain,
( equal(e2,unit)
| equal(e1,unit)
| equal(e0,unit) ),
inference(spt,[spt(split,[position(s2s2)])],[743]),
[iquote('2:Spt:1053.0,743.1,743.2,743.3')] ).
cnf(1056,plain,
equal(e2,unit),
inference(spt,[spt(split,[position(s2s2s1)])],[1055]),
[iquote('3:Spt:1055.0')] ).
cnf(1057,plain,
~ equal(e1,unit),
inference(rew,[status(thm),theory(equality)],[1056,5]),
[iquote('3:Rew:1056.0,5.0')] ).
cnf(1058,plain,
~ equal(e0,unit),
inference(rew,[status(thm),theory(equality)],[1056,2]),
[iquote('3:Rew:1056.0,2.0')] ).
cnf(1083,plain,
~ equal(op(e0,e4),op(unit,e4)),
inference(rew,[status(thm),theory(equality)],[1056,131]),
[iquote('3:Rew:1056.0,131.0')] ).
cnf(1109,plain,
~ equal(op(e0,e0),op(e0,unit)),
inference(rew,[status(thm),theory(equality)],[1056,141]),
[iquote('3:Rew:1056.0,141.0')] ).
cnf(1111,plain,
( equal(op(e0,e4),e4)
| equal(op(e0,e0),e4)
| equal(op(e0,e3),e4)
| equal(op(e0,unit),e4) ),
inference(rew,[status(thm),theory(equality)],[1056,402]),
[iquote('3:Rew:1056.0,402.3')] ).
cnf(1120,plain,
~ equal(op(e3,e1),op(e3,unit)),
inference(rew,[status(thm),theory(equality)],[1056,174]),
[iquote('3:Rew:1056.0,174.0')] ).
cnf(1138,plain,
~ equal(op(e4,e0),op(unit,e0)),
inference(rew,[status(thm),theory(equality)],[1056,98]),
[iquote('3:Rew:1056.0,98.0')] ).
cnf(1156,plain,
( equal(op(e0,unit),unit)
| equal(op(e0,e0),e2)
| equal(op(e0,e3),e2)
| equal(op(e0,e1),e2) ),
inference(rew,[status(thm),theory(equality)],[1056,406]),
[iquote('3:Rew:1056.0,406.0')] ).
cnf(1194,plain,
~ equal(op(e0,e4),e4),
inference(rew,[status(thm),theory(equality)],[19,1083]),
[iquote('3:Rew:19.0,1083.0')] ).
cnf(1206,plain,
~ equal(op(e0,e0),e0),
inference(rew,[status(thm),theory(equality)],[12,1109]),
[iquote('3:Rew:12.0,1109.0')] ).
cnf(1207,plain,
equal(op(e3,e3),e0),
inference(mrr,[status(thm)],[429,1206]),
[iquote('3:MRR:429.0,1206.0')] ).
cnf(1208,plain,
~ equal(op(e4,e3),e0),
inference(rew,[status(thm),theory(equality)],[1207,129]),
[iquote('3:Rew:1207.0,129.0')] ).
cnf(1214,plain,
( equal(e1,e0)
| equal(op(e0,e0),e1) ),
inference(rew,[status(thm),theory(equality)],[1207,427]),
[iquote('3:Rew:1207.0,427.0')] ).
cnf(1223,plain,
( equal(op(e4,e0),e0)
| equal(op(e4,e1),e0) ),
inference(mrr,[status(thm)],[364,1208]),
[iquote('3:MRR:364.1,1208.0')] ).
cnf(1230,plain,
~ equal(op(e3,e1),e3),
inference(rew,[status(thm),theory(equality)],[18,1120]),
[iquote('3:Rew:18.0,1120.0')] ).
cnf(1231,plain,
( equal(op(e4,e1),e3)
| equal(op(e0,e1),e3) ),
inference(mrr,[status(thm)],[388,1230]),
[iquote('3:MRR:388.0,1230.0')] ).
cnf(1244,plain,
~ equal(op(e4,e0),e0),
inference(rew,[status(thm),theory(equality)],[11,1138]),
[iquote('3:Rew:11.0,1138.0')] ).
cnf(1250,plain,
equal(op(e0,e0),e1),
inference(mrr,[status(thm)],[1214,1]),
[iquote('3:MRR:1214.0,1.0')] ).
cnf(1267,plain,
equal(op(e4,e1),e0),
inference(mrr,[status(thm)],[1223,1244]),
[iquote('3:MRR:1223.0,1244.0')] ).
cnf(1275,plain,
( equal(e3,e0)
| equal(op(e0,e1),e3) ),
inference(rew,[status(thm),theory(equality)],[1267,1231]),
[iquote('3:Rew:1267.0,1231.0')] ).
cnf(1276,plain,
equal(op(e0,e1),e3),
inference(mrr,[status(thm)],[1275,3]),
[iquote('3:MRR:1275.0,3.0')] ).
cnf(1351,plain,
( equal(op(e0,e4),e4)
| equal(e4,e1)
| equal(op(e0,e3),e4)
| equal(e4,e0) ),
inference(rew,[status(thm),theory(equality)],[12,1111,1250]),
[iquote('3:Rew:12.0,1111.3,1250.0,1111.1')] ).
cnf(1352,plain,
equal(op(e0,e3),e4),
inference(mrr,[status(thm)],[1351,1194,7,4]),
[iquote('3:MRR:1351.0,1351.1,1351.3,1194.0,7.0,4.0')] ).
cnf(1370,plain,
( equal(e0,unit)
| equal(e1,unit)
| equal(e4,unit)
| equal(e3,unit) ),
inference(rew,[status(thm),theory(equality)],[1276,1156,1056,1352,1250,12]),
[iquote('3:Rew:1276.0,1156.3,1056.0,1156.3,1352.0,1156.2,1056.0,1156.2,1250.0,1156.1,1056.0,1156.1,12.0,1156.0')] ).
cnf(1371,plain,
$false,
inference(mrr,[status(thm)],[1370,1058,1057,1054,742]),
[iquote('3:MRR:1370.0,1370.1,1370.2,1370.3,1058.0,1057.0,1054.0,742.0')] ).
cnf(1372,plain,
~ equal(e2,unit),
inference(spt,[spt(split,[position(s2s2sa)])],[1371,1056]),
[iquote('3:Spt:1371.0,1055.0,1056.0')] ).
cnf(1373,plain,
( equal(e1,unit)
| equal(e0,unit) ),
inference(spt,[spt(split,[position(s2s2s2)])],[1055]),
[iquote('3:Spt:1371.0,1055.1,1055.2')] ).
cnf(1374,plain,
equal(e1,unit),
inference(spt,[spt(split,[position(s2s2s2s1)])],[1373]),
[iquote('4:Spt:1373.0')] ).
cnf(1375,plain,
~ equal(e0,unit),
inference(rew,[status(thm),theory(equality)],[1374,1]),
[iquote('4:Rew:1374.0,1.0')] ).
cnf(1395,plain,
~ equal(op(e2,e3),op(e2,unit)),
inference(rew,[status(thm),theory(equality)],[1374,165]),
[iquote('4:Rew:1374.0,165.0')] ).
cnf(1404,plain,
~ equal(op(e4,e2),op(e4,unit)),
inference(rew,[status(thm),theory(equality)],[1374,184]),
[iquote('4:Rew:1374.0,184.0')] ).
cnf(1406,plain,
~ equal(op(e4,e3),op(e4,unit)),
inference(rew,[status(thm),theory(equality)],[1374,185]),
[iquote('4:Rew:1374.0,185.0')] ).
cnf(1415,plain,
~ equal(op(e0,e0),op(e0,unit)),
inference(rew,[status(thm),theory(equality)],[1374,140]),
[iquote('4:Rew:1374.0,140.0')] ).
cnf(1430,plain,
( equal(op(e3,e3),e2)
| equal(op(e2,e3),e2)
| equal(op(unit,e3),e2)
| equal(op(e0,e3),e2) ),
inference(rew,[status(thm),theory(equality)],[1374,369]),
[iquote('4:Rew:1374.0,369.2')] ).
cnf(1459,plain,
( equal(op(e4,e2),e4)
| equal(op(e4,e2),unit) ),
inference(rew,[status(thm),theory(equality)],[1374,410]),
[iquote('4:Rew:1374.0,410.1')] ).
cnf(1461,plain,
( equal(op(e3,e3),unit)
| equal(op(e1,e3),e1)
| equal(op(e4,e3),e1)
| equal(op(e2,e3),e1)
| equal(op(e0,e3),e1) ),
inference(rew,[status(thm),theory(equality)],[1374,210]),
[iquote('4:Rew:1374.0,210.0')] ).
cnf(1510,plain,
~ equal(op(e2,e3),e2),
inference(rew,[status(thm),theory(equality)],[16,1395]),
[iquote('4:Rew:16.0,1395.0')] ).
cnf(1512,plain,
~ equal(op(e4,e2),e4),
inference(rew,[status(thm),theory(equality)],[20,1404]),
[iquote('4:Rew:20.0,1404.0')] ).
cnf(1516,plain,
~ equal(op(e4,e3),e4),
inference(rew,[status(thm),theory(equality)],[20,1406]),
[iquote('4:Rew:20.0,1406.0')] ).
cnf(1517,plain,
( equal(op(e3,e3),e4)
| equal(op(e2,e3),e4)
| equal(op(e0,e3),e4) ),
inference(mrr,[status(thm)],[365,1516]),
[iquote('4:MRR:365.0,1516.0')] ).
cnf(1522,plain,
~ equal(op(e0,e0),e0),
inference(rew,[status(thm),theory(equality)],[12,1415]),
[iquote('4:Rew:12.0,1415.0')] ).
cnf(1523,plain,
equal(op(e3,e3),e0),
inference(mrr,[status(thm)],[429,1522]),
[iquote('4:MRR:429.0,1522.0')] ).
cnf(1563,plain,
equal(op(e4,e2),unit),
inference(mrr,[status(thm)],[1459,1512]),
[iquote('4:MRR:1459.0,1512.0')] ).
cnf(1570,plain,
~ equal(op(e4,e3),unit),
inference(rew,[status(thm),theory(equality)],[1563,187]),
[iquote('4:Rew:1563.0,187.0')] ).
cnf(1631,plain,
( equal(e4,e0)
| equal(op(e2,e3),e4)
| equal(op(e0,e3),e4) ),
inference(rew,[status(thm),theory(equality)],[1523,1517]),
[iquote('4:Rew:1523.0,1517.0')] ).
cnf(1632,plain,
( equal(op(e2,e3),e4)
| equal(op(e0,e3),e4) ),
inference(mrr,[status(thm)],[1631,4]),
[iquote('4:MRR:1631.0,4.0')] ).
cnf(1641,plain,
( equal(e2,e0)
| equal(op(e2,e3),e2)
| equal(e3,e2)
| equal(op(e0,e3),e2) ),
inference(rew,[status(thm),theory(equality)],[17,1430,1523]),
[iquote('4:Rew:17.0,1430.2,1523.0,1430.0')] ).
cnf(1642,plain,
equal(op(e0,e3),e2),
inference(mrr,[status(thm)],[1641,2,1510,8]),
[iquote('4:MRR:1641.0,1641.1,1641.2,2.0,1510.0,8.0')] ).
cnf(1649,plain,
( equal(op(e2,e3),e4)
| equal(e4,e2) ),
inference(rew,[status(thm),theory(equality)],[1642,1632]),
[iquote('4:Rew:1642.0,1632.1')] ).
cnf(1666,plain,
equal(op(e2,e3),e4),
inference(mrr,[status(thm)],[1649,9]),
[iquote('4:MRR:1649.1,9.0')] ).
cnf(1694,plain,
( equal(e0,unit)
| equal(e3,unit)
| equal(op(e4,e3),unit)
| equal(e4,unit)
| equal(e2,unit) ),
inference(rew,[status(thm),theory(equality)],[1642,1461,1374,1666,17,1523]),
[iquote('4:Rew:1642.0,1461.4,1374.0,1461.4,1666.0,1461.3,1374.0,1461.3,1374.0,1461.2,17.0,1461.1,1374.0,1461.1,1523.0,1461.0')] ).
cnf(1695,plain,
$false,
inference(mrr,[status(thm)],[1694,1375,742,1570,1054,1372]),
[iquote('4:MRR:1694.0,1694.1,1694.2,1694.3,1694.4,1375.0,742.0,1570.0,1054.0,1372.0')] ).
cnf(1697,plain,
~ equal(e1,unit),
inference(spt,[spt(split,[position(s2s2s2sa)])],[1695,1374]),
[iquote('4:Spt:1695.0,1373.0,1374.0')] ).
cnf(1698,plain,
equal(e0,unit),
inference(spt,[spt(split,[position(s2s2s2s2)])],[1373]),
[iquote('4:Spt:1695.0,1373.1')] ).
cnf(1699,plain,
equal(op(unit,unit),unit),
inference(rew,[status(thm),theory(equality)],[1698,12]),
[iquote('4:Rew:1698.0,12.0')] ).
cnf(1705,plain,
~ equal(e1,unit),
inference(rew,[status(thm),theory(equality)],[1698,1]),
[iquote('4:Rew:1698.0,1.0')] ).
cnf(1721,plain,
( ~ skC15
| equal(e3,unit) ),
inference(rew,[status(thm),theory(equality)],[1699,50,1698]),
[iquote('4:Rew:1699.0,50.1,1698.0,50.1')] ).
cnf(1722,plain,
~ skC15,
inference(mrr,[status(thm)],[1721,742]),
[iquote('4:MRR:1721.1,742.0')] ).
cnf(1723,plain,
( skC17
| skC13
| skC3 ),
inference(mrr,[status(thm)],[431,1722]),
[iquote('4:MRR:431.1,1722.0')] ).
cnf(1724,plain,
( ~ skC3
| equal(e3,unit) ),
inference(rew,[status(thm),theory(equality)],[1699,27,1698]),
[iquote('4:Rew:1699.0,27.1,1698.0,27.1')] ).
cnf(1725,plain,
~ skC3,
inference(mrr,[status(thm)],[1724,742]),
[iquote('4:MRR:1724.1,742.0')] ).
cnf(1726,plain,
( skC17
| skC13 ),
inference(mrr,[status(thm)],[1723,1725]),
[iquote('4:MRR:1723.2,1725.0')] ).
cnf(1771,plain,
( equal(op(e3,e3),e1)
| equal(e1,unit) ),
inference(rew,[status(thm),theory(equality)],[1699,427,1698]),
[iquote('4:Rew:1699.0,427.1,1698.0,427.1')] ).
cnf(1772,plain,
equal(op(e3,e3),e1),
inference(mrr,[status(thm)],[1771,1705]),
[iquote('4:MRR:1771.1,1705.0')] ).
cnf(1773,plain,
( ~ skC13
| equal(e2,e1) ),
inference(rew,[status(thm),theory(equality)],[1772,46]),
[iquote('4:Rew:1772.0,46.1')] ).
cnf(1774,plain,
( ~ skC17
| equal(e2,e1) ),
inference(rew,[status(thm),theory(equality)],[1772,53]),
[iquote('4:Rew:1772.0,53.1')] ).
cnf(1782,plain,
~ skC13,
inference(mrr,[status(thm)],[1773,5]),
[iquote('4:MRR:1773.1,5.0')] ).
cnf(1783,plain,
skC17,
inference(mrr,[status(thm)],[1726,1782]),
[iquote('4:MRR:1726.1,1782.0')] ).
cnf(1784,plain,
$false,
inference(mrr,[status(thm)],[1774,1783,5]),
[iquote('4:MRR:1774.0,1774.1,1783.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ALG063+1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n027.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 01:58:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.37/0.55
% 0.37/0.55 SPASS V 3.9
% 0.37/0.55 SPASS beiseite: Proof found.
% 0.37/0.55 % SZS status Theorem
% 0.37/0.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.37/0.55 SPASS derived 944 clauses, backtracked 728 clauses, performed 4 splits and kept 1237 clauses.
% 0.37/0.55 SPASS allocated 86089 KBytes.
% 0.37/0.55 SPASS spent 0:00:00.22 on the problem.
% 0.37/0.55 0:00:00.04 for the input.
% 0.37/0.55 0:00:00.06 for the FLOTTER CNF translation.
% 0.37/0.55 0:00:00.00 for inferences.
% 0.37/0.55 0:00:00.00 for the backtracking.
% 0.37/0.55 0:00:00.09 for the reduction.
% 0.37/0.55
% 0.37/0.55
% 0.37/0.55 Here is a proof with depth 4, length 351 :
% 0.37/0.55 % SZS output start Refutation
% See solution above
% 0.37/0.56 Formulae used in the proof : ax5 ax2 ax6 co1 ax4 ax3 ax1
% 0.37/0.56
%------------------------------------------------------------------------------