%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG065+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 0.59s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 97
% Syntax : Number of clauses : 301 ( 180 unt; 97 nHn; 301 RR)
% Number of literals : 578 ( 0 equ; 168 neg)
% Maximal clause size : 5 ( 1 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('ALG065+1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(e2,e0),
file('ALG065+1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(e3,e0),
file('ALG065+1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(e4,e0),
file('ALG065+1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(e2,e1),
file('ALG065+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(e3,e1),
file('ALG065+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(e4,e1),
file('ALG065+1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(e3,e2),
file('ALG065+1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(e4,e2),
file('ALG065+1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(e4,e3),
file('ALG065+1.p',unknown),
[] ).
cnf(11,axiom,
equal(op(unit,e0),e0),
file('ALG065+1.p',unknown),
[] ).
cnf(12,axiom,
equal(op(e0,unit),e0),
file('ALG065+1.p',unknown),
[] ).
cnf(13,axiom,
equal(op(unit,e1),e1),
file('ALG065+1.p',unknown),
[] ).
cnf(14,axiom,
equal(op(e1,unit),e1),
file('ALG065+1.p',unknown),
[] ).
cnf(15,axiom,
equal(op(unit,e2),e2),
file('ALG065+1.p',unknown),
[] ).
cnf(16,axiom,
equal(op(e2,unit),e2),
file('ALG065+1.p',unknown),
[] ).
cnf(17,axiom,
equal(op(unit,e3),e3),
file('ALG065+1.p',unknown),
[] ).
cnf(18,axiom,
equal(op(e3,unit),e3),
file('ALG065+1.p',unknown),
[] ).
cnf(19,axiom,
equal(op(unit,e4),e4),
file('ALG065+1.p',unknown),
[] ).
cnf(20,axiom,
equal(op(e4,unit),e4),
file('ALG065+1.p',unknown),
[] ).
cnf(21,axiom,
equal(op(e4,e2),e1),
file('ALG065+1.p',unknown),
[] ).
cnf(22,axiom,
equal(op(e2,e4),e3),
file('ALG065+1.p',unknown),
[] ).
cnf(27,axiom,
~ equal(op(e2,e0),op(e1,e0)),
file('ALG065+1.p',unknown),
[] ).
cnf(28,axiom,
~ equal(op(e3,e0),op(e1,e0)),
file('ALG065+1.p',unknown),
[] ).
cnf(30,axiom,
~ equal(op(e3,e0),op(e2,e0)),
file('ALG065+1.p',unknown),
[] ).
cnf(31,axiom,
~ equal(op(e4,e0),op(e2,e0)),
file('ALG065+1.p',unknown),
[] ).
cnf(32,axiom,
~ equal(op(e4,e0),op(e3,e0)),
file('ALG065+1.p',unknown),
[] ).
cnf(37,axiom,
~ equal(op(e2,e1),op(e1,e1)),
file('ALG065+1.p',unknown),
[] ).
cnf(40,axiom,
~ equal(op(e3,e1),op(e2,e1)),
file('ALG065+1.p',unknown),
[] ).
cnf(41,axiom,
~ equal(op(e4,e1),op(e2,e1)),
file('ALG065+1.p',unknown),
[] ).
cnf(50,axiom,
~ equal(op(e3,e2),op(e2,e2)),
file('ALG065+1.p',unknown),
[] ).
cnf(51,axiom,
~ equal(op(e4,e2),op(e2,e2)),
file('ALG065+1.p',unknown),
[] ).
cnf(52,axiom,
~ equal(op(e4,e2),op(e3,e2)),
file('ALG065+1.p',unknown),
[] ).
cnf(58,axiom,
~ equal(op(e3,e3),op(e1,e3)),
file('ALG065+1.p',unknown),
[] ).
cnf(59,axiom,
~ equal(op(e4,e3),op(e1,e3)),
file('ALG065+1.p',unknown),
[] ).
cnf(60,axiom,
~ equal(op(e3,e3),op(e2,e3)),
file('ALG065+1.p',unknown),
[] ).
cnf(61,axiom,
~ equal(op(e4,e3),op(e2,e3)),
file('ALG065+1.p',unknown),
[] ).
cnf(62,axiom,
~ equal(op(e4,e3),op(e3,e3)),
file('ALG065+1.p',unknown),
[] ).
cnf(67,axiom,
~ equal(op(e2,e4),op(e1,e4)),
file('ALG065+1.p',unknown),
[] ).
cnf(70,axiom,
~ equal(op(e3,e4),op(e2,e4)),
file('ALG065+1.p',unknown),
[] ).
cnf(71,axiom,
~ equal(op(e4,e4),op(e2,e4)),
file('ALG065+1.p',unknown),
[] ).
cnf(77,axiom,
~ equal(op(e0,e2),op(e0,e1)),
file('ALG065+1.p',unknown),
[] ).
cnf(81,axiom,
~ equal(op(e0,e4),op(e0,e2)),
file('ALG065+1.p',unknown),
[] ).
cnf(86,axiom,
~ equal(op(e1,e4),op(e1,e0)),
file('ALG065+1.p',unknown),
[] ).
cnf(89,axiom,
~ equal(op(e1,e4),op(e1,e1)),
file('ALG065+1.p',unknown),
[] ).
cnf(93,axiom,
~ equal(op(e2,e1),op(e2,e0)),
file('ALG065+1.p',unknown),
[] ).
cnf(94,axiom,
~ equal(op(e2,e2),op(e2,e0)),
file('ALG065+1.p',unknown),
[] ).
cnf(95,axiom,
~ equal(op(e2,e3),op(e2,e0)),
file('ALG065+1.p',unknown),
[] ).
cnf(96,axiom,
~ equal(op(e2,e4),op(e2,e0)),
file('ALG065+1.p',unknown),
[] ).
cnf(99,axiom,
~ equal(op(e2,e4),op(e2,e1)),
file('ALG065+1.p',unknown),
[] ).
cnf(101,axiom,
~ equal(op(e2,e4),op(e2,e2)),
file('ALG065+1.p',unknown),
[] ).
cnf(103,axiom,
~ equal(op(e3,e1),op(e3,e0)),
file('ALG065+1.p',unknown),
[] ).
cnf(104,axiom,
~ equal(op(e3,e2),op(e3,e0)),
file('ALG065+1.p',unknown),
[] ).
cnf(105,axiom,
~ equal(op(e3,e3),op(e3,e0)),
file('ALG065+1.p',unknown),
[] ).
cnf(106,axiom,
~ equal(op(e3,e4),op(e3,e0)),
file('ALG065+1.p',unknown),
[] ).
cnf(107,axiom,
~ equal(op(e3,e2),op(e3,e1)),
file('ALG065+1.p',unknown),
[] ).
cnf(109,axiom,
~ equal(op(e3,e4),op(e3,e1)),
file('ALG065+1.p',unknown),
[] ).
cnf(112,axiom,
~ equal(op(e3,e4),op(e3,e3)),
file('ALG065+1.p',unknown),
[] ).
cnf(116,axiom,
~ equal(op(e4,e4),op(e4,e0)),
file('ALG065+1.p',unknown),
[] ).
cnf(118,axiom,
~ equal(op(e4,e3),op(e4,e1)),
file('ALG065+1.p',unknown),
[] ).
cnf(121,axiom,
~ equal(op(e4,e4),op(e4,e2)),
file('ALG065+1.p',unknown),
[] ).
cnf(123,axiom,
( ~ skC0
| equal(op(e0,op(e0,e0)),e0) ),
file('ALG065+1.p',unknown),
[] ).
cnf(143,axiom,
equal(op(op(e4,e2),op(e4,e2)),e0),
file('ALG065+1.p',unknown),
[] ).
cnf(144,axiom,
( ~ equal(op(e0,op(e0,e0)),e0)
| ~ skC0 ),
file('ALG065+1.p',unknown),
[] ).
cnf(145,axiom,
( ~ equal(op(e1,op(e1,e0)),e0)
| ~ skC1 ),
file('ALG065+1.p',unknown),
[] ).
cnf(146,axiom,
( ~ skC2
| ~ equal(op(e2,op(e2,e0)),e0) ),
file('ALG065+1.p',unknown),
[] ).
cnf(147,axiom,
( ~ skC3
| ~ equal(op(e3,op(e3,e0)),e0) ),
file('ALG065+1.p',unknown),
[] ).
cnf(168,axiom,
( ~ equal(op(e1,e1),e0)
| equal(op(e1,e0),e1) ),
file('ALG065+1.p',unknown),
[] ).
cnf(172,axiom,
( ~ equal(op(e2,e2),e0)
| equal(op(e2,e0),e2) ),
file('ALG065+1.p',unknown),
[] ).
cnf(175,axiom,
( ~ equal(op(e2,e2),e4)
| equal(op(e2,e4),e2) ),
file('ALG065+1.p',unknown),
[] ).
cnf(176,axiom,
( ~ equal(op(e3,e3),e0)
| equal(op(e3,e0),e3) ),
file('ALG065+1.p',unknown),
[] ).
cnf(177,axiom,
( ~ equal(op(e3,e3),e1)
| equal(op(e3,e1),e3) ),
file('ALG065+1.p',unknown),
[] ).
cnf(178,axiom,
( ~ equal(op(e3,e3),e2)
| equal(op(e3,e2),e3) ),
file('ALG065+1.p',unknown),
[] ).
cnf(179,axiom,
( ~ equal(op(e3,e3),e4)
| equal(op(e3,e4),e3) ),
file('ALG065+1.p',unknown),
[] ).
cnf(180,axiom,
( ~ equal(op(e4,e4),e0)
| equal(op(e4,e0),e4) ),
file('ALG065+1.p',unknown),
[] ).
cnf(182,axiom,
( ~ equal(op(e4,e4),e2)
| equal(op(e4,e2),e4) ),
file('ALG065+1.p',unknown),
[] ).
cnf(189,axiom,
( ~ equal(op(e4,op(e4,e0)),e0)
| skC0
| skC1
| skC2
| skC3 ),
file('ALG065+1.p',unknown),
[] ).
cnf(194,axiom,
( equal(e4,unit)
| equal(e3,unit)
| equal(e2,unit)
| equal(e1,unit)
| equal(e0,unit) ),
file('ALG065+1.p',unknown),
[] ).
cnf(198,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('ALG065+1.p',unknown),
[] ).
cnf(200,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('ALG065+1.p',unknown),
[] ).
cnf(201,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('ALG065+1.p',unknown),
[] ).
cnf(203,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('ALG065+1.p',unknown),
[] ).
cnf(212,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('ALG065+1.p',unknown),
[] ).
cnf(215,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('ALG065+1.p',unknown),
[] ).
cnf(216,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('ALG065+1.p',unknown),
[] ).
cnf(219,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('ALG065+1.p',unknown),
[] ).
cnf(222,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('ALG065+1.p',unknown),
[] ).
cnf(224,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('ALG065+1.p',unknown),
[] ).
cnf(225,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('ALG065+1.p',unknown),
[] ).
cnf(227,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('ALG065+1.p',unknown),
[] ).
cnf(228,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('ALG065+1.p',unknown),
[] ).
cnf(229,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('ALG065+1.p',unknown),
[] ).
cnf(245,axiom,
( equal(op(e4,e4),e0)
| equal(op(e4,e4),e1)
| equal(op(e4,e4),e2)
| equal(op(e4,e4),e3)
| equal(op(e4,e4),e4) ),
file('ALG065+1.p',unknown),
[] ).
cnf(251,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('ALG065+1.p',unknown),
[] ).
cnf(254,axiom,
( equal(op(e3,e0),e0)
| equal(op(e3,e0),e1)
| equal(op(e3,e0),e2)
| equal(op(e3,e0),e3)
| equal(op(e3,e0),e4) ),
file('ALG065+1.p',unknown),
[] ).
cnf(257,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('ALG065+1.p',unknown),
[] ).
cnf(259,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('ALG065+1.p',unknown),
[] ).
cnf(270,plain,
~ equal(op(e4,e4),e1),
inference(rew,[status(thm),theory(equality)],[21,121]),
[iquote('0:Rew:21.0,121.0')] ).
cnf(275,plain,
~ equal(op(e2,e2),e3),
inference(rew,[status(thm),theory(equality)],[22,101]),
[iquote('0:Rew:22.0,101.0')] ).
cnf(276,plain,
~ equal(op(e2,e1),e3),
inference(rew,[status(thm),theory(equality)],[22,99]),
[iquote('0:Rew:22.0,99.0')] ).
cnf(277,plain,
~ equal(op(e2,e0),e3),
inference(rew,[status(thm),theory(equality)],[22,96]),
[iquote('0:Rew:22.0,96.0')] ).
cnf(278,plain,
~ equal(op(e4,e4),e3),
inference(rew,[status(thm),theory(equality)],[22,71]),
[iquote('0:Rew:22.0,71.0')] ).
cnf(279,plain,
~ equal(op(e3,e4),e3),
inference(rew,[status(thm),theory(equality)],[22,70]),
[iquote('0:Rew:22.0,70.0')] ).
cnf(280,plain,
~ equal(op(e1,e4),e3),
inference(rew,[status(thm),theory(equality)],[22,67]),
[iquote('0:Rew:22.0,67.0')] ).
cnf(282,plain,
~ equal(op(e3,e2),e1),
inference(rew,[status(thm),theory(equality)],[21,52]),
[iquote('0:Rew:21.0,52.0')] ).
cnf(283,plain,
~ equal(op(e2,e2),e1),
inference(rew,[status(thm),theory(equality)],[21,51]),
[iquote('0:Rew:21.0,51.0')] ).
cnf(286,plain,
equal(op(e1,e1),e0),
inference(rew,[status(thm),theory(equality)],[21,143]),
[iquote('0:Rew:21.0,143.0')] ).
cnf(287,plain,
~ equal(op(e1,e4),e0),
inference(rew,[status(thm),theory(equality)],[286,89]),
[iquote('0:Rew:286.0,89.0')] ).
cnf(293,plain,
~ equal(op(e2,e1),e0),
inference(rew,[status(thm),theory(equality)],[286,37]),
[iquote('0:Rew:286.0,37.0')] ).
cnf(304,plain,
( ~ equal(e0,e0)
| ~ skC0 ),
inference(rew,[status(thm),theory(equality)],[123,144]),
[iquote('0:Rew:123.1,144.0')] ).
cnf(305,plain,
~ skC0,
inference(obv,[status(thm),theory(equality)],[304]),
[iquote('0:Obv:304.0')] ).
cnf(311,plain,
( ~ equal(op(e4,e4),e2)
| equal(e4,e1) ),
inference(rew,[status(thm),theory(equality)],[21,182]),
[iquote('0:Rew:21.0,182.1')] ).
cnf(312,plain,
~ equal(op(e4,e4),e2),
inference(mrr,[status(thm)],[311,7]),
[iquote('0:MRR:311.1,7.0')] ).
cnf(313,plain,
~ equal(op(e3,e3),e4),
inference(mrr,[status(thm)],[179,279]),
[iquote('0:MRR:179.1,279.0')] ).
cnf(314,plain,
( ~ equal(op(e2,e2),e4)
| equal(e3,e2) ),
inference(rew,[status(thm),theory(equality)],[22,175]),
[iquote('0:Rew:22.0,175.1')] ).
cnf(315,plain,
~ equal(op(e2,e2),e4),
inference(mrr,[status(thm)],[314,8]),
[iquote('0:MRR:314.1,8.0')] ).
cnf(319,plain,
( ~ equal(e0,e0)
| equal(op(e1,e0),e1) ),
inference(rew,[status(thm),theory(equality)],[286,168]),
[iquote('0:Rew:286.0,168.0')] ).
cnf(320,plain,
equal(op(e1,e0),e1),
inference(obv,[status(thm),theory(equality)],[319]),
[iquote('0:Obv:319.0')] ).
cnf(321,plain,
~ equal(op(e1,e4),e1),
inference(rew,[status(thm),theory(equality)],[320,86]),
[iquote('0:Rew:320.0,86.0')] ).
cnf(325,plain,
~ equal(op(e3,e0),e1),
inference(rew,[status(thm),theory(equality)],[320,28]),
[iquote('0:Rew:320.0,28.0')] ).
cnf(326,plain,
~ equal(op(e2,e0),e1),
inference(rew,[status(thm),theory(equality)],[320,27]),
[iquote('0:Rew:320.0,27.0')] ).
cnf(330,plain,
( ~ equal(op(e1,e1),e0)
| ~ skC1 ),
inference(rew,[status(thm),theory(equality)],[320,145]),
[iquote('0:Rew:320.0,145.0')] ).
cnf(331,plain,
( ~ equal(e0,e0)
| ~ skC1 ),
inference(rew,[status(thm),theory(equality)],[286,330]),
[iquote('0:Rew:286.0,330.0')] ).
cnf(332,plain,
~ skC1,
inference(obv,[status(thm),theory(equality)],[331]),
[iquote('0:Obv:331.0')] ).
cnf(340,plain,
( ~ equal(op(e4,op(e4,e0)),e0)
| skC3
| skC2 ),
inference(mrr,[status(thm)],[189,305,332]),
[iquote('0:MRR:189.1,189.2,305.0,332.0')] ).
cnf(345,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)],[21,198]),
[iquote('0:Rew:21.0,198.2')] ).
cnf(346,plain,
( equal(op(e4,e3),e3)
| equal(op(e4,e1),e3)
| equal(op(e4,e0),e3) ),
inference(mrr,[status(thm)],[345,6,278]),
[iquote('0:MRR:345.2,345.4,6.0,278.0')] ).
cnf(349,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)],[21,200]),
[iquote('0:Rew:21.0,200.2')] ).
cnf(350,plain,
( equal(op(e4,e3),e2)
| equal(op(e4,e1),e2)
| equal(op(e4,e0),e2) ),
inference(mrr,[status(thm)],[349,5,312]),
[iquote('0:MRR:349.2,349.4,5.0,312.0')] ).
cnf(351,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)],[22,201]),
[iquote('0:Rew:22.0,201.2')] ).
cnf(352,plain,
( equal(op(e3,e4),e1)
| equal(op(e0,e4),e1) ),
inference(mrr,[status(thm)],[351,321,6,270]),
[iquote('0:MRR:351.1,351.2,351.4,321.0,6.0,270.0')] ).
cnf(353,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)],[22,203]),
[iquote('0:Rew:22.0,203.2')] ).
cnf(354,plain,
( equal(op(e4,e4),e0)
| equal(op(e0,e4),e0)
| equal(op(e3,e4),e0) ),
inference(mrr,[status(thm)],[353,287,3]),
[iquote('0:MRR:353.1,353.2,287.0,3.0')] ).
cnf(362,plain,
( equal(op(e3,e3),e1)
| equal(op(e3,e1),e1)
| equal(op(e3,e4),e1) ),
inference(mrr,[status(thm)],[212,325,282]),
[iquote('0:MRR:212.0,212.2,325.0,282.0')] ).
cnf(365,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)],[21,215]),
[iquote('0:Rew:21.0,215.4')] ).
cnf(366,plain,
( equal(op(e3,e2),e4)
| equal(op(e1,e2),e4)
| equal(op(e0,e2),e4) ),
inference(mrr,[status(thm)],[365,315,7]),
[iquote('0:MRR:365.2,365.4,315.0,7.0')] ).
cnf(367,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)],[22,216]),
[iquote('0:Rew:22.0,216.4')] ).
cnf(368,plain,
( equal(op(e2,e3),e4)
| equal(op(e2,e1),e4)
| equal(op(e2,e0),e4) ),
inference(mrr,[status(thm)],[367,315,10]),
[iquote('0:MRR:367.2,367.4,315.0,10.0')] ).
cnf(371,plain,
( equal(op(e0,e2),e2)
| equal(op(e1,e2),e2)
| equal(op(e2,e2),e2)
| equal(op(e3,e2),e2)
| equal(e2,e1) ),
inference(rew,[status(thm),theory(equality)],[21,219]),
[iquote('0:Rew:21.0,219.4')] ).
cnf(372,plain,
( equal(op(e2,e2),e2)
| equal(op(e3,e2),e2)
| equal(op(e1,e2),e2)
| equal(op(e0,e2),e2) ),
inference(mrr,[status(thm)],[371,5]),
[iquote('0:MRR:371.4,5.0')] ).
cnf(375,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)],[22,222]),
[iquote('0:Rew:22.0,222.4')] ).
cnf(376,plain,
( equal(op(e2,e1),e1)
| equal(op(e2,e3),e1) ),
inference(mrr,[status(thm)],[375,326,283,6]),
[iquote('0:MRR:375.0,375.2,375.4,326.0,283.0,6.0')] ).
cnf(379,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)],[22,224]),
[iquote('0:Rew:22.0,224.4')] ).
cnf(380,plain,
( equal(op(e2,e2),e0)
| equal(op(e2,e0),e0)
| equal(op(e2,e3),e0) ),
inference(mrr,[status(thm)],[379,293,3]),
[iquote('0:MRR:379.1,379.4,293.0,3.0')] ).
cnf(381,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)],[286,225]),
[iquote('0:Rew:286.0,225.1')] ).
cnf(382,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)],[381,4]),
[iquote('0:MRR:381.1,4.0')] ).
cnf(385,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)],[286,227]),
[iquote('0:Rew:286.0,227.1')] ).
cnf(386,plain,
( equal(op(e3,e1),e3)
| equal(op(e4,e1),e3)
| equal(op(e0,e1),e3) ),
inference(mrr,[status(thm)],[385,3,276]),
[iquote('0:MRR:385.1,385.2,3.0,276.0')] ).
cnf(387,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)],[286,228,320]),
[iquote('0:Rew:286.0,228.1,320.0,228.0')] ).
cnf(388,plain,
( equal(op(e1,e3),e3)
| equal(op(e1,e2),e3) ),
inference(mrr,[status(thm)],[387,6,3,280]),
[iquote('0:MRR:387.0,387.1,387.4,6.0,3.0,280.0')] ).
cnf(389,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)],[286,229]),
[iquote('0:Rew:286.0,229.1')] ).
cnf(390,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)],[389,2]),
[iquote('0:MRR:389.1,2.0')] ).
cnf(406,plain,
( equal(op(e4,e4),e4)
| equal(op(e4,e4),e0) ),
inference(mrr,[status(thm)],[245,270,312,278]),
[iquote('0:MRR:245.1,245.2,245.3,270.0,312.0,278.0')] ).
cnf(411,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)],[251,313]),
[iquote('0:MRR:251.4,313.0')] ).
cnf(414,plain,
( equal(op(e3,e0),e3)
| equal(op(e3,e0),e0)
| equal(op(e3,e0),e4)
| equal(op(e3,e0),e2) ),
inference(mrr,[status(thm)],[254,325]),
[iquote('0:MRR:254.1,325.0')] ).
cnf(416,plain,
( equal(op(e2,e2),e2)
| equal(op(e2,e2),e0) ),
inference(mrr,[status(thm)],[257,283,275,315]),
[iquote('0:MRR:257.1,257.3,257.4,283.0,275.0,315.0')] ).
cnf(418,plain,
( equal(op(e2,e0),e2)
| equal(op(e2,e0),e0)
| equal(op(e2,e0),e4) ),
inference(mrr,[status(thm)],[259,326,277]),
[iquote('0:MRR:259.1,259.3,326.0,277.0')] ).
cnf(426,plain,
equal(e3,unit),
inference(spt,[spt(split,[position(s1)])],[194]),
[iquote('1:Spt:194.1')] ).
cnf(437,plain,
~ equal(op(e4,e1),op(e4,unit)),
inference(rew,[status(thm),theory(equality)],[426,118]),
[iquote('1:Rew:426.0,118.0')] ).
cnf(460,plain,
( equal(op(unit,e2),e4)
| equal(op(e1,e2),e4)
| equal(op(e0,e2),e4) ),
inference(rew,[status(thm),theory(equality)],[426,366]),
[iquote('1:Rew:426.0,366.0')] ).
cnf(466,plain,
~ equal(op(e2,e2),op(unit,e2)),
inference(rew,[status(thm),theory(equality)],[426,50]),
[iquote('1:Rew:426.0,50.0')] ).
cnf(469,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)],[426,382]),
[iquote('1:Rew:426.0,382.1')] ).
cnf(500,plain,
~ equal(op(e2,e0),op(e2,unit)),
inference(rew,[status(thm),theory(equality)],[426,95]),
[iquote('1:Rew:426.0,95.0')] ).
cnf(537,plain,
( equal(op(e1,unit),unit)
| equal(op(e1,e2),e3) ),
inference(rew,[status(thm),theory(equality)],[426,388]),
[iquote('1:Rew:426.0,388.0')] ).
cnf(541,plain,
~ equal(e4,unit),
inference(rew,[status(thm),theory(equality)],[426,10]),
[iquote('1:Rew:426.0,10.0')] ).
cnf(543,plain,
~ equal(e1,unit),
inference(rew,[status(thm),theory(equality)],[426,6]),
[iquote('1:Rew:426.0,6.0')] ).
cnf(598,plain,
~ equal(op(e4,e1),e4),
inference(rew,[status(thm),theory(equality)],[20,437]),
[iquote('1:Rew:20.0,437.0')] ).
cnf(616,plain,
~ equal(op(e2,e2),e2),
inference(rew,[status(thm),theory(equality)],[15,466]),
[iquote('1:Rew:15.0,466.0')] ).
cnf(617,plain,
equal(op(e2,e2),e0),
inference(mrr,[status(thm)],[416,616]),
[iquote('1:MRR:416.0,616.0')] ).
cnf(622,plain,
~ equal(op(e2,e0),e0),
inference(rew,[status(thm),theory(equality)],[617,94]),
[iquote('1:Rew:617.0,94.0')] ).
cnf(627,plain,
( equal(op(e2,e0),e2)
| equal(op(e2,e0),e4) ),
inference(mrr,[status(thm)],[418,622]),
[iquote('1:MRR:418.1,622.0')] ).
cnf(647,plain,
~ equal(op(e2,e0),e2),
inference(rew,[status(thm),theory(equality)],[16,500]),
[iquote('1:Rew:16.0,500.0')] ).
cnf(698,plain,
( equal(e1,unit)
| equal(op(e1,e2),unit) ),
inference(rew,[status(thm),theory(equality)],[426,537,14]),
[iquote('1:Rew:426.0,537.1,14.0,537.0')] ).
cnf(699,plain,
equal(op(e1,e2),unit),
inference(mrr,[status(thm)],[698,543]),
[iquote('1:MRR:698.0,543.0')] ).
cnf(719,plain,
equal(op(e2,e0),e4),
inference(mrr,[status(thm)],[627,647]),
[iquote('1:MRR:627.0,647.0')] ).
cnf(721,plain,
~ equal(op(e2,e1),e4),
inference(rew,[status(thm),theory(equality)],[719,93]),
[iquote('1:Rew:719.0,93.0')] ).
cnf(746,plain,
( equal(e4,e2)
| equal(e4,unit)
| equal(op(e0,e2),e4) ),
inference(rew,[status(thm),theory(equality)],[699,460,15]),
[iquote('1:Rew:699.0,460.1,15.0,460.0')] ).
cnf(747,plain,
equal(op(e0,e2),e4),
inference(mrr,[status(thm)],[746,9,541]),
[iquote('1:MRR:746.0,746.1,9.0,541.0')] ).
cnf(749,plain,
~ equal(op(e0,e1),e4),
inference(rew,[status(thm),theory(equality)],[747,77]),
[iquote('1:Rew:747.0,77.0')] ).
cnf(776,plain,
( equal(op(e4,e1),e4)
| equal(e4,e1)
| equal(op(e2,e1),e4)
| equal(op(e0,e1),e4) ),
inference(rew,[status(thm),theory(equality)],[13,469]),
[iquote('1:Rew:13.0,469.1')] ).
cnf(777,plain,
$false,
inference(mrr,[status(thm)],[776,598,7,721,749]),
[iquote('1:MRR:776.0,776.1,776.2,776.3,598.0,7.0,721.0,749.0')] ).
cnf(831,plain,
~ equal(e3,unit),
inference(spt,[spt(split,[position(sa)])],[777,426]),
[iquote('1:Spt:777.0,194.1,426.0')] ).
cnf(832,plain,
( equal(e4,unit)
| equal(e2,unit)
| equal(e1,unit)
| equal(e0,unit) ),
inference(spt,[spt(split,[position(s2)])],[194]),
[iquote('1:Spt:777.0,194.0,194.2,194.3,194.4')] ).
cnf(833,plain,
equal(e4,unit),
inference(spt,[spt(split,[position(s2s1)])],[832]),
[iquote('2:Spt:832.0')] ).
cnf(834,plain,
~ equal(e2,unit),
inference(rew,[status(thm),theory(equality)],[833,9]),
[iquote('2:Rew:833.0,9.0')] ).
cnf(835,plain,
~ equal(e1,unit),
inference(rew,[status(thm),theory(equality)],[833,7]),
[iquote('2:Rew:833.0,7.0')] ).
cnf(864,plain,
~ equal(op(e3,e0),op(e3,unit)),
inference(rew,[status(thm),theory(equality)],[833,106]),
[iquote('2:Rew:833.0,106.0')] ).
cnf(865,plain,
~ equal(op(e3,e1),op(e3,unit)),
inference(rew,[status(thm),theory(equality)],[833,109]),
[iquote('2:Rew:833.0,109.0')] ).
cnf(890,plain,
~ equal(op(e1,e3),op(unit,e3)),
inference(rew,[status(thm),theory(equality)],[833,59]),
[iquote('2:Rew:833.0,59.0')] ).
cnf(899,plain,
~ equal(op(e3,e0),op(unit,e0)),
inference(rew,[status(thm),theory(equality)],[833,32]),
[iquote('2:Rew:833.0,32.0')] ).
cnf(902,plain,
~ equal(op(e2,e0),op(unit,e0)),
inference(rew,[status(thm),theory(equality)],[833,31]),
[iquote('2:Rew:833.0,31.0')] ).
cnf(915,plain,
~ equal(op(e2,e1),op(unit,e1)),
inference(rew,[status(thm),theory(equality)],[833,41]),
[iquote('2:Rew:833.0,41.0')] ).
cnf(916,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)],[833,390]),
[iquote('2:Rew:833.0,390.1')] ).
cnf(919,plain,
( equal(op(e3,e1),e3)
| equal(op(unit,e1),e3)
| equal(op(e0,e1),e3) ),
inference(rew,[status(thm),theory(equality)],[833,386]),
[iquote('2:Rew:833.0,386.1')] ).
cnf(922,plain,
( equal(op(e2,e3),unit)
| equal(op(e2,e1),e4)
| equal(op(e2,e0),e4) ),
inference(rew,[status(thm),theory(equality)],[833,368]),
[iquote('2:Rew:833.0,368.0')] ).
cnf(945,plain,
( equal(op(e3,e2),e4)
| equal(op(e1,e2),unit)
| equal(op(e0,e2),e4) ),
inference(rew,[status(thm),theory(equality)],[833,366]),
[iquote('2:Rew:833.0,366.1')] ).
cnf(954,plain,
( equal(op(e3,e0),e3)
| equal(op(e3,e0),e0)
| equal(op(e3,e0),unit)
| equal(op(e3,e0),e2) ),
inference(rew,[status(thm),theory(equality)],[833,414]),
[iquote('2:Rew:833.0,414.2')] ).
cnf(989,plain,
~ equal(op(e3,e0),e3),
inference(rew,[status(thm),theory(equality)],[18,864]),
[iquote('2:Rew:18.0,864.0')] ).
cnf(993,plain,
~ equal(op(e3,e1),e3),
inference(rew,[status(thm),theory(equality)],[18,865]),
[iquote('2:Rew:18.0,865.0')] ).
cnf(1006,plain,
~ equal(op(e1,e3),e3),
inference(rew,[status(thm),theory(equality)],[17,890]),
[iquote('2:Rew:17.0,890.0')] ).
cnf(1007,plain,
equal(op(e1,e2),e3),
inference(mrr,[status(thm)],[388,1006]),
[iquote('2:MRR:388.0,1006.0')] ).
cnf(1016,plain,
( equal(op(e2,e2),e2)
| equal(op(e3,e2),e2)
| equal(e3,e2)
| equal(op(e0,e2),e2) ),
inference(rew,[status(thm),theory(equality)],[1007,372]),
[iquote('2:Rew:1007.0,372.2')] ).
cnf(1020,plain,
~ equal(op(e3,e0),e0),
inference(rew,[status(thm),theory(equality)],[11,899]),
[iquote('2:Rew:11.0,899.0')] ).
cnf(1023,plain,
~ equal(op(e2,e0),e0),
inference(rew,[status(thm),theory(equality)],[11,902]),
[iquote('2:Rew:11.0,902.0')] ).
cnf(1024,plain,
( equal(op(e2,e2),e0)
| equal(op(e2,e3),e0) ),
inference(mrr,[status(thm)],[380,1023]),
[iquote('2:MRR:380.1,1023.0')] ).
cnf(1032,plain,
~ equal(op(e2,e1),e1),
inference(rew,[status(thm),theory(equality)],[13,915]),
[iquote('2:Rew:13.0,915.0')] ).
cnf(1033,plain,
equal(op(e2,e3),e1),
inference(mrr,[status(thm)],[376,1032]),
[iquote('2:MRR:376.0,1032.0')] ).
cnf(1063,plain,
( equal(op(e2,e2),e0)
| equal(e1,e0) ),
inference(rew,[status(thm),theory(equality)],[1033,1024]),
[iquote('2:Rew:1033.0,1024.1')] ).
cnf(1064,plain,
equal(op(e2,e2),e0),
inference(mrr,[status(thm)],[1063,1]),
[iquote('2:MRR:1063.1,1.0')] ).
cnf(1071,plain,
( ~ equal(e0,e0)
| equal(op(e2,e0),e2) ),
inference(rew,[status(thm),theory(equality)],[1064,172]),
[iquote('2:Rew:1064.0,172.0')] ).
cnf(1073,plain,
equal(op(e2,e0),e2),
inference(obv,[status(thm),theory(equality)],[1071]),
[iquote('2:Obv:1071.0')] ).
cnf(1076,plain,
~ equal(op(e3,e0),e2),
inference(rew,[status(thm),theory(equality)],[1073,30]),
[iquote('2:Rew:1073.0,30.0')] ).
cnf(1116,plain,
( equal(op(e3,e1),e3)
| equal(e3,e1)
| equal(op(e0,e1),e3) ),
inference(rew,[status(thm),theory(equality)],[13,919]),
[iquote('2:Rew:13.0,919.1')] ).
cnf(1117,plain,
equal(op(e0,e1),e3),
inference(mrr,[status(thm)],[1116,993,6]),
[iquote('2:MRR:1116.0,1116.1,993.0,6.0')] ).
cnf(1130,plain,
( equal(e1,unit)
| equal(op(e2,e1),unit)
| equal(e2,unit) ),
inference(rew,[status(thm),theory(equality)],[1073,922,833,1033]),
[iquote('2:Rew:1073.0,922.2,833.0,922.2,833.0,922.1,1033.0,922.0')] ).
cnf(1131,plain,
equal(op(e2,e1),unit),
inference(mrr,[status(thm)],[1130,835,834]),
[iquote('2:MRR:1130.0,1130.2,835.0,834.0')] ).
cnf(1146,plain,
( equal(op(e3,e2),unit)
| equal(e3,unit)
| equal(op(e0,e2),unit) ),
inference(rew,[status(thm),theory(equality)],[833,945,1007]),
[iquote('2:Rew:833.0,945.2,1007.0,945.1,833.0,945.0')] ).
cnf(1147,plain,
( equal(op(e3,e2),unit)
| equal(op(e0,e2),unit) ),
inference(mrr,[status(thm)],[1146,831]),
[iquote('2:MRR:1146.1,831.0')] ).
cnf(1150,plain,
( equal(e2,e0)
| equal(op(e3,e2),e2)
| equal(e3,e2)
| equal(op(e0,e2),e2) ),
inference(rew,[status(thm),theory(equality)],[1064,1016]),
[iquote('2:Rew:1064.0,1016.0')] ).
cnf(1151,plain,
( equal(op(e3,e2),e2)
| equal(op(e0,e2),e2) ),
inference(mrr,[status(thm)],[1150,2,8]),
[iquote('2:MRR:1150.0,1150.2,2.0,8.0')] ).
cnf(1161,plain,
( equal(e2,unit)
| equal(e2,e1)
| equal(op(e3,e1),e2)
| equal(e3,e2) ),
inference(rew,[status(thm),theory(equality)],[1117,916,13,1131]),
[iquote('2:Rew:1117.0,916.3,13.0,916.1,1131.0,916.0')] ).
cnf(1162,plain,
equal(op(e3,e1),e2),
inference(mrr,[status(thm)],[1161,834,5,8]),
[iquote('2:MRR:1161.0,1161.1,1161.3,834.0,5.0,8.0')] ).
cnf(1165,plain,
~ equal(op(e3,e2),e2),
inference(rew,[status(thm),theory(equality)],[1162,107]),
[iquote('2:Rew:1162.0,107.0')] ).
cnf(1172,plain,
equal(op(e0,e2),e2),
inference(mrr,[status(thm)],[1151,1165]),
[iquote('2:MRR:1151.0,1165.0')] ).
cnf(1181,plain,
( equal(op(e3,e2),unit)
| equal(e2,unit) ),
inference(rew,[status(thm),theory(equality)],[1172,1147]),
[iquote('2:Rew:1172.0,1147.1')] ).
cnf(1184,plain,
equal(op(e3,e2),unit),
inference(mrr,[status(thm)],[1181,834]),
[iquote('2:MRR:1181.1,834.0')] ).
cnf(1186,plain,
~ equal(op(e3,e0),unit),
inference(rew,[status(thm),theory(equality)],[1184,104]),
[iquote('2:Rew:1184.0,104.0')] ).
cnf(1211,plain,
$false,
inference(mrr,[status(thm)],[954,989,1020,1186,1076]),
[iquote('2:MRR:954.0,954.1,954.2,954.3,989.0,1020.0,1186.0,1076.0')] ).
cnf(1213,plain,
~ equal(e4,unit),
inference(spt,[spt(split,[position(s2sa)])],[1211,833]),
[iquote('2:Spt:1211.0,832.0,833.0')] ).
cnf(1214,plain,
( equal(e2,unit)
| equal(e1,unit)
| equal(e0,unit) ),
inference(spt,[spt(split,[position(s2s2)])],[832]),
[iquote('2:Spt:1211.0,832.1,832.2,832.3')] ).
cnf(1215,plain,
equal(e2,unit),
inference(spt,[spt(split,[position(s2s2s1)])],[1214]),
[iquote('3:Spt:1214.0')] ).
cnf(1247,plain,
~ equal(op(e4,e3),op(unit,e3)),
inference(rew,[status(thm),theory(equality)],[1215,61]),
[iquote('3:Rew:1215.0,61.0')] ).
cnf(1249,plain,
~ equal(op(e3,e3),op(unit,e3)),
inference(rew,[status(thm),theory(equality)],[1215,60]),
[iquote('3:Rew:1215.0,60.0')] ).
cnf(1275,plain,
~ equal(op(e3,e1),op(unit,e1)),
inference(rew,[status(thm),theory(equality)],[1215,40]),
[iquote('3:Rew:1215.0,40.0')] ).
cnf(1278,plain,
~ equal(op(e0,e4),op(e0,unit)),
inference(rew,[status(thm),theory(equality)],[1215,81]),
[iquote('3:Rew:1215.0,81.0')] ).
cnf(1293,plain,
~ equal(op(e3,e1),op(e3,unit)),
inference(rew,[status(thm),theory(equality)],[1215,107]),
[iquote('3:Rew:1215.0,107.0')] ).
cnf(1296,plain,
~ equal(op(e3,e0),op(e3,unit)),
inference(rew,[status(thm),theory(equality)],[1215,104]),
[iquote('3:Rew:1215.0,104.0')] ).
cnf(1304,plain,
( equal(op(e4,e3),unit)
| equal(op(e4,e1),e2)
| equal(op(e4,e0),e2) ),
inference(rew,[status(thm),theory(equality)],[1215,350]),
[iquote('3:Rew:1215.0,350.0')] ).
cnf(1330,plain,
( equal(op(e3,e3),e3)
| equal(op(e3,e3),unit)
| equal(op(e3,e3),e1)
| equal(op(e3,e3),e0) ),
inference(rew,[status(thm),theory(equality)],[1215,411]),
[iquote('3:Rew:1215.0,411.1')] ).
cnf(1361,plain,
~ equal(op(e4,e3),e3),
inference(rew,[status(thm),theory(equality)],[17,1247]),
[iquote('3:Rew:17.0,1247.0')] ).
cnf(1362,plain,
( equal(op(e4,e1),e3)
| equal(op(e4,e0),e3) ),
inference(mrr,[status(thm)],[346,1361]),
[iquote('3:MRR:346.0,1361.0')] ).
cnf(1365,plain,
~ equal(op(e3,e3),e3),
inference(rew,[status(thm),theory(equality)],[17,1249]),
[iquote('3:Rew:17.0,1249.0')] ).
cnf(1382,plain,
~ equal(op(e3,e1),e1),
inference(rew,[status(thm),theory(equality)],[13,1275]),
[iquote('3:Rew:13.0,1275.0')] ).
cnf(1383,plain,
( equal(op(e3,e3),e1)
| equal(op(e3,e4),e1) ),
inference(mrr,[status(thm)],[362,1382]),
[iquote('3:MRR:362.1,1382.0')] ).
cnf(1384,plain,
~ equal(op(e0,e4),e0),
inference(rew,[status(thm),theory(equality)],[12,1278]),
[iquote('3:Rew:12.0,1278.0')] ).
cnf(1386,plain,
( equal(op(e4,e4),e0)
| equal(op(e3,e4),e0) ),
inference(mrr,[status(thm)],[354,1384]),
[iquote('3:MRR:354.1,1384.0')] ).
cnf(1397,plain,
~ equal(op(e3,e1),e3),
inference(rew,[status(thm),theory(equality)],[18,1293]),
[iquote('3:Rew:18.0,1293.0')] ).
cnf(1398,plain,
~ equal(op(e3,e3),e1),
inference(mrr,[status(thm)],[177,1397]),
[iquote('3:MRR:177.1,1397.0')] ).
cnf(1402,plain,
~ equal(op(e3,e0),e3),
inference(rew,[status(thm),theory(equality)],[18,1296]),
[iquote('3:Rew:18.0,1296.0')] ).
cnf(1403,plain,
~ equal(op(e3,e3),e0),
inference(mrr,[status(thm)],[176,1402]),
[iquote('3:MRR:176.1,1402.0')] ).
cnf(1428,plain,
equal(op(e3,e4),e1),
inference(mrr,[status(thm)],[1383,1398]),
[iquote('3:MRR:1383.0,1398.0')] ).
cnf(1452,plain,
( equal(op(e4,e4),e0)
| equal(e1,e0) ),
inference(rew,[status(thm),theory(equality)],[1428,1386]),
[iquote('3:Rew:1428.0,1386.1')] ).
cnf(1453,plain,
equal(op(e4,e4),e0),
inference(mrr,[status(thm)],[1452,1]),
[iquote('3:MRR:1452.1,1.0')] ).
cnf(1462,plain,
( ~ equal(e0,e0)
| equal(op(e4,e0),e4) ),
inference(rew,[status(thm),theory(equality)],[1453,180]),
[iquote('3:Rew:1453.0,180.0')] ).
cnf(1464,plain,
equal(op(e4,e0),e4),
inference(obv,[status(thm),theory(equality)],[1462]),
[iquote('3:Obv:1462.0')] ).
cnf(1473,plain,
( equal(op(e4,e1),e3)
| equal(e4,e3) ),
inference(rew,[status(thm),theory(equality)],[1464,1362]),
[iquote('3:Rew:1464.0,1362.1')] ).
cnf(1478,plain,
equal(op(e4,e1),e3),
inference(mrr,[status(thm)],[1473,10]),
[iquote('3:MRR:1473.1,10.0')] ).
cnf(1503,plain,
( equal(op(e4,e3),unit)
| equal(e3,unit)
| equal(e4,unit) ),
inference(rew,[status(thm),theory(equality)],[1464,1304,1215,1478]),
[iquote('3:Rew:1464.0,1304.2,1215.0,1304.2,1478.0,1304.1,1215.0,1304.1')] ).
cnf(1504,plain,
equal(op(e4,e3),unit),
inference(mrr,[status(thm)],[1503,831,1213]),
[iquote('3:MRR:1503.1,1503.2,831.0,1213.0')] ).
cnf(1506,plain,
~ equal(op(e3,e3),unit),
inference(rew,[status(thm),theory(equality)],[1504,62]),
[iquote('3:Rew:1504.0,62.0')] ).
cnf(1604,plain,
$false,
inference(mrr,[status(thm)],[1330,1365,1506,1398,1403]),
[iquote('3:MRR:1330.0,1330.1,1330.2,1330.3,1365.0,1506.0,1398.0,1403.0')] ).
cnf(1607,plain,
~ equal(e2,unit),
inference(spt,[spt(split,[position(s2s2sa)])],[1604,1215]),
[iquote('3:Spt:1604.0,1214.0,1215.0')] ).
cnf(1608,plain,
( equal(e1,unit)
| equal(e0,unit) ),
inference(spt,[spt(split,[position(s2s2s2)])],[1214]),
[iquote('3:Spt:1604.0,1214.1,1214.2')] ).
cnf(1609,plain,
equal(e1,unit),
inference(spt,[spt(split,[position(s2s2s2s1)])],[1608]),
[iquote('4:Spt:1608.0')] ).
cnf(1678,plain,
~ equal(op(e3,e3),op(unit,e3)),
inference(rew,[status(thm),theory(equality)],[1609,58]),
[iquote('4:Rew:1609.0,58.0')] ).
cnf(1685,plain,
~ equal(op(e3,e2),op(e3,unit)),
inference(rew,[status(thm),theory(equality)],[1609,107]),
[iquote('4:Rew:1609.0,107.0')] ).
cnf(1689,plain,
~ equal(op(e3,e0),op(e3,unit)),
inference(rew,[status(thm),theory(equality)],[1609,103]),
[iquote('4:Rew:1609.0,103.0')] ).
cnf(1718,plain,
( equal(op(e2,unit),unit)
| equal(op(e2,e3),e1) ),
inference(rew,[status(thm),theory(equality)],[1609,376]),
[iquote('4:Rew:1609.0,376.0')] ).
cnf(1731,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)],[1609,411]),
[iquote('4:Rew:1609.0,411.2')] ).
cnf(1810,plain,
~ equal(op(e3,e3),e3),
inference(rew,[status(thm),theory(equality)],[17,1678]),
[iquote('4:Rew:17.0,1678.0')] ).
cnf(1811,plain,
~ equal(op(e3,e2),e3),
inference(rew,[status(thm),theory(equality)],[18,1685]),
[iquote('4:Rew:18.0,1685.0')] ).
cnf(1812,plain,
~ equal(op(e3,e3),e2),
inference(mrr,[status(thm)],[178,1811]),
[iquote('4:MRR:178.1,1811.0')] ).
cnf(1816,plain,
~ equal(op(e3,e0),e3),
inference(rew,[status(thm),theory(equality)],[18,1689]),
[iquote('4:Rew:18.0,1689.0')] ).
cnf(1817,plain,
~ equal(op(e3,e3),e0),
inference(mrr,[status(thm)],[176,1816]),
[iquote('4:MRR:176.1,1816.0')] ).
cnf(1844,plain,
( equal(e2,unit)
| equal(op(e2,e3),unit) ),
inference(rew,[status(thm),theory(equality)],[1609,1718,16]),
[iquote('4:Rew:1609.0,1718.1,16.0,1718.0')] ).
cnf(1845,plain,
equal(op(e2,e3),unit),
inference(mrr,[status(thm)],[1844,1607]),
[iquote('4:MRR:1844.0,1607.0')] ).
cnf(1849,plain,
~ equal(op(e3,e3),unit),
inference(rew,[status(thm),theory(equality)],[1845,60]),
[iquote('4:Rew:1845.0,60.0')] ).
cnf(2005,plain,
$false,
inference(mrr,[status(thm)],[1731,1810,1812,1849,1817]),
[iquote('4:MRR:1731.0,1731.1,1731.2,1731.3,1810.0,1812.0,1849.0,1817.0')] ).
cnf(2006,plain,
~ equal(e1,unit),
inference(spt,[spt(split,[position(s2s2s2sa)])],[2005,1609]),
[iquote('4:Spt:2005.0,1608.0,1609.0')] ).
cnf(2007,plain,
equal(e0,unit),
inference(spt,[spt(split,[position(s2s2s2s2)])],[1608]),
[iquote('4:Spt:2005.0,1608.1')] ).
cnf(2043,plain,
~ equal(op(e2,e2),e2),
inference(rew,[status(thm),theory(equality)],[16,94,2007]),
[iquote('4:Rew:16.0,94.0,2007.0,94.0')] ).
cnf(2045,plain,
~ equal(op(e4,e4),e4),
inference(rew,[status(thm),theory(equality)],[20,116,2007]),
[iquote('4:Rew:20.0,116.0,2007.0,116.0')] ).
cnf(2050,plain,
~ equal(op(e3,e2),e3),
inference(rew,[status(thm),theory(equality)],[18,104,2007]),
[iquote('4:Rew:18.0,104.0,2007.0,104.0')] ).
cnf(2066,plain,
~ equal(op(e3,e3),e3),
inference(rew,[status(thm),theory(equality)],[18,105,2007]),
[iquote('4:Rew:18.0,105.0,2007.0,105.0')] ).
cnf(2078,plain,
( equal(op(e3,e4),e1)
| equal(e4,e1) ),
inference(rew,[status(thm),theory(equality)],[19,352,2007]),
[iquote('4:Rew:19.0,352.1,2007.0,352.1')] ).
cnf(2079,plain,
equal(op(e3,e4),e1),
inference(mrr,[status(thm)],[2078,7]),
[iquote('4:MRR:2078.1,7.0')] ).
cnf(2085,plain,
~ equal(op(e3,e3),e1),
inference(rew,[status(thm),theory(equality)],[2079,112]),
[iquote('4:Rew:2079.0,112.0')] ).
cnf(2119,plain,
( equal(op(e2,e2),e2)
| equal(op(e2,e2),unit) ),
inference(rew,[status(thm),theory(equality)],[2007,416]),
[iquote('4:Rew:2007.0,416.1')] ).
cnf(2120,plain,
equal(op(e2,e2),unit),
inference(mrr,[status(thm)],[2119,2043]),
[iquote('4:MRR:2119.0,2043.0')] ).
cnf(2127,plain,
( equal(op(e4,e4),e4)
| equal(op(e4,e4),unit) ),
inference(rew,[status(thm),theory(equality)],[2007,406]),
[iquote('4:Rew:2007.0,406.1')] ).
cnf(2128,plain,
equal(op(e4,e4),unit),
inference(mrr,[status(thm)],[2127,2045]),
[iquote('4:MRR:2127.0,2045.0')] ).
cnf(2140,plain,
( ~ skC2
| ~ equal(unit,unit) ),
inference(rew,[status(thm),theory(equality)],[2120,146,16,2007]),
[iquote('4:Rew:2120.0,146.1,16.0,146.1,2007.0,146.1')] ).
cnf(2141,plain,
~ skC2,
inference(obv,[status(thm),theory(equality)],[2140]),
[iquote('4:Obv:2140.1')] ).
cnf(2142,plain,
( ~ equal(unit,unit)
| skC3
| skC2 ),
inference(rew,[status(thm),theory(equality)],[2128,340,20,2007]),
[iquote('4:Rew:2128.0,340.0,20.0,340.0,2007.0,340.0')] ).
cnf(2143,plain,
( skC3
| skC2 ),
inference(obv,[status(thm),theory(equality)],[2142]),
[iquote('4:Obv:2142.0')] ).
cnf(2144,plain,
skC3,
inference(mrr,[status(thm)],[2143,2141]),
[iquote('4:MRR:2143.1,2141.0')] ).
cnf(2152,plain,
( ~ skC3
| ~ equal(op(e3,e3),unit) ),
inference(rew,[status(thm),theory(equality)],[18,147,2007]),
[iquote('4:Rew:18.0,147.1,2007.0,147.1')] ).
cnf(2153,plain,
~ equal(op(e3,e3),unit),
inference(mrr,[status(thm)],[2152,2144]),
[iquote('4:MRR:2152.0,2144.0')] ).
cnf(2158,plain,
~ equal(op(e3,e3),e2),
inference(mrr,[status(thm)],[178,2050]),
[iquote('4:MRR:178.1,2050.0')] ).
cnf(2253,plain,
( equal(op(e3,e3),e3)
| equal(op(e3,e3),e2)
| equal(op(e3,e3),e1)
| equal(op(e3,e3),unit) ),
inference(rew,[status(thm),theory(equality)],[2007,411]),
[iquote('4:Rew:2007.0,411.3')] ).
cnf(2254,plain,
$false,
inference(mrr,[status(thm)],[2253,2066,2158,2085,2153]),
[iquote('4:MRR:2253.0,2253.1,2253.2,2253.3,2066.0,2158.0,2085.0,2153.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : ALG065+1 : TPTP v8.1.0. Released v2.7.0.
% 0.08/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 8 02:09:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.37/0.59
% 0.37/0.59 SPASS V 3.9
% 0.37/0.59 SPASS beiseite: Proof found.
% 0.37/0.59 % SZS status Theorem
% 0.37/0.59 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.37/0.59 SPASS derived 1143 clauses, backtracked 872 clauses, performed 4 splits and kept 1467 clauses.
% 0.37/0.59 SPASS allocated 86210 KBytes.
% 0.37/0.59 SPASS spent 0:00:00.24 on the problem.
% 0.37/0.59 0:00:00.04 for the input.
% 0.37/0.59 0:00:00.06 for the FLOTTER CNF translation.
% 0.37/0.59 0:00:00.00 for inferences.
% 0.37/0.59 0:00:00.00 for the backtracking.
% 0.37/0.59 0:00:00.11 for the reduction.
% 0.37/0.59
% 0.37/0.59
% 0.37/0.59 Here is a proof with depth 4, length 301 :
% 0.37/0.59 % SZS output start Refutation
% See solution above
% 0.37/0.60 Formulae used in the proof : ax5 ax2 ax6 ax4 co1 ax3 ax1
% 0.37/0.60
%------------------------------------------------------------------------------