TSTP Solution File: ALG054+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG054+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 18:02:09 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 82
% Syntax : Number of clauses : 227 ( 147 unt; 69 nHn; 227 RR)
% Number of literals : 424 ( 0 equ; 115 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 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('ALG054+1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(e2,e0),
file('ALG054+1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(e3,e0),
file('ALG054+1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(e4,e0),
file('ALG054+1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(e2,e1),
file('ALG054+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(e3,e1),
file('ALG054+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(e4,e1),
file('ALG054+1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(e3,e2),
file('ALG054+1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(e4,e2),
file('ALG054+1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(e4,e3),
file('ALG054+1.p',unknown),
[] ).
cnf(11,axiom,
equal(op(unit,e0),e0),
file('ALG054+1.p',unknown),
[] ).
cnf(12,axiom,
equal(op(e0,unit),e0),
file('ALG054+1.p',unknown),
[] ).
cnf(13,axiom,
equal(op(unit,e1),e1),
file('ALG054+1.p',unknown),
[] ).
cnf(15,axiom,
equal(op(unit,e2),e2),
file('ALG054+1.p',unknown),
[] ).
cnf(16,axiom,
equal(op(e2,unit),e2),
file('ALG054+1.p',unknown),
[] ).
cnf(17,axiom,
equal(op(unit,e3),e3),
file('ALG054+1.p',unknown),
[] ).
cnf(18,axiom,
equal(op(e3,unit),e3),
file('ALG054+1.p',unknown),
[] ).
cnf(19,axiom,
equal(op(unit,e4),e4),
file('ALG054+1.p',unknown),
[] ).
cnf(20,axiom,
equal(op(e4,unit),e4),
file('ALG054+1.p',unknown),
[] ).
cnf(21,axiom,
equal(op(e1,e1),e4),
file('ALG054+1.p',unknown),
[] ).
cnf(24,axiom,
~ equal(op(e3,e0),op(e0,e0)),
file('ALG054+1.p',unknown),
[] ).
cnf(27,axiom,
~ equal(op(e3,e0),op(e1,e0)),
file('ALG054+1.p',unknown),
[] ).
cnf(29,axiom,
~ equal(op(e3,e0),op(e2,e0)),
file('ALG054+1.p',unknown),
[] ).
cnf(32,axiom,
~ equal(op(e1,e1),op(e0,e1)),
file('ALG054+1.p',unknown),
[] ).
cnf(34,axiom,
~ equal(op(e3,e1),op(e0,e1)),
file('ALG054+1.p',unknown),
[] ).
cnf(40,axiom,
~ equal(op(e4,e1),op(e2,e1)),
file('ALG054+1.p',unknown),
[] ).
cnf(42,axiom,
~ equal(op(e1,e2),op(e0,e2)),
file('ALG054+1.p',unknown),
[] ).
cnf(43,axiom,
~ equal(op(e2,e2),op(e0,e2)),
file('ALG054+1.p',unknown),
[] ).
cnf(44,axiom,
~ equal(op(e3,e2),op(e0,e2)),
file('ALG054+1.p',unknown),
[] ).
cnf(45,axiom,
~ equal(op(e4,e2),op(e0,e2)),
file('ALG054+1.p',unknown),
[] ).
cnf(49,axiom,
~ equal(op(e3,e2),op(e2,e2)),
file('ALG054+1.p',unknown),
[] ).
cnf(56,axiom,
~ equal(op(e2,e3),op(e1,e3)),
file('ALG054+1.p',unknown),
[] ).
cnf(58,axiom,
~ equal(op(e4,e3),op(e1,e3)),
file('ALG054+1.p',unknown),
[] ).
cnf(63,axiom,
~ equal(op(e2,e4),op(e0,e4)),
file('ALG054+1.p',unknown),
[] ).
cnf(66,axiom,
~ equal(op(e2,e4),op(e1,e4)),
file('ALG054+1.p',unknown),
[] ).
cnf(70,axiom,
~ equal(op(e4,e4),op(e2,e4)),
file('ALG054+1.p',unknown),
[] ).
cnf(71,axiom,
~ equal(op(e4,e4),op(e3,e4)),
file('ALG054+1.p',unknown),
[] ).
cnf(72,axiom,
~ equal(op(e0,e1),op(e0,e0)),
file('ALG054+1.p',unknown),
[] ).
cnf(73,axiom,
~ equal(op(e0,e2),op(e0,e0)),
file('ALG054+1.p',unknown),
[] ).
cnf(75,axiom,
~ equal(op(e0,e4),op(e0,e0)),
file('ALG054+1.p',unknown),
[] ).
cnf(76,axiom,
~ equal(op(e0,e2),op(e0,e1)),
file('ALG054+1.p',unknown),
[] ).
cnf(78,axiom,
~ equal(op(e0,e4),op(e0,e1)),
file('ALG054+1.p',unknown),
[] ).
cnf(81,axiom,
~ equal(op(e0,e4),op(e0,e3)),
file('ALG054+1.p',unknown),
[] ).
cnf(87,axiom,
~ equal(op(e1,e3),op(e1,e1)),
file('ALG054+1.p',unknown),
[] ).
cnf(91,axiom,
~ equal(op(e1,e4),op(e1,e3)),
file('ALG054+1.p',unknown),
[] ).
cnf(98,axiom,
~ equal(op(e2,e4),op(e2,e1)),
file('ALG054+1.p',unknown),
[] ).
cnf(100,axiom,
~ equal(op(e2,e4),op(e2,e2)),
file('ALG054+1.p',unknown),
[] ).
cnf(104,axiom,
~ equal(op(e3,e3),op(e3,e0)),
file('ALG054+1.p',unknown),
[] ).
cnf(105,axiom,
~ equal(op(e3,e4),op(e3,e0)),
file('ALG054+1.p',unknown),
[] ).
cnf(106,axiom,
~ equal(op(e3,e2),op(e3,e1)),
file('ALG054+1.p',unknown),
[] ).
cnf(108,axiom,
~ equal(op(e3,e4),op(e3,e1)),
file('ALG054+1.p',unknown),
[] ).
cnf(110,axiom,
~ equal(op(e3,e4),op(e3,e2)),
file('ALG054+1.p',unknown),
[] ).
cnf(119,axiom,
~ equal(op(e4,e3),op(e4,e2)),
file('ALG054+1.p',unknown),
[] ).
cnf(122,axiom,
equal(op(op(e1,e1),op(e1,e1)),e2),
file('ALG054+1.p',unknown),
[] ).
cnf(124,axiom,
( ~ equal(op(e0,e0),e2)
| equal(op(e0,e2),e0) ),
file('ALG054+1.p',unknown),
[] ).
cnf(126,axiom,
( ~ equal(op(e0,e0),e4)
| equal(op(e0,e4),e0) ),
file('ALG054+1.p',unknown),
[] ).
cnf(130,axiom,
( ~ equal(op(e1,e1),e4)
| equal(op(e1,e4),e1) ),
file('ALG054+1.p',unknown),
[] ).
cnf(133,axiom,
( ~ equal(op(e2,e2),e3)
| equal(op(e2,e3),e2) ),
file('ALG054+1.p',unknown),
[] ).
cnf(135,axiom,
( ~ equal(op(e3,e3),e0)
| equal(op(e3,e0),e3) ),
file('ALG054+1.p',unknown),
[] ).
cnf(136,axiom,
( ~ equal(op(e3,e3),e1)
| equal(op(e3,e1),e3) ),
file('ALG054+1.p',unknown),
[] ).
cnf(137,axiom,
( ~ equal(op(e3,e3),e2)
| equal(op(e3,e2),e3) ),
file('ALG054+1.p',unknown),
[] ).
cnf(141,axiom,
( ~ equal(op(e4,e4),e2)
| equal(op(e4,e2),e4) ),
file('ALG054+1.p',unknown),
[] ).
cnf(143,axiom,
equal(op(e1,op(op(e1,e1),op(e1,e1))),e0),
file('ALG054+1.p',unknown),
[] ).
cnf(144,axiom,
( equal(e4,unit)
| equal(e3,unit)
| equal(e2,unit)
| equal(e1,unit)
| equal(e0,unit) ),
file('ALG054+1.p',unknown),
[] ).
cnf(145,axiom,
equal(op(op(op(e1,e1),op(e1,e1)),op(op(e1,e1),op(e1,e1))),e3),
file('ALG054+1.p',unknown),
[] ).
cnf(148,axiom,
( equal(op(e0,e4),e3)
| equal(op(e1,e4),e3)
| equal(op(e2,e4),e3)
| equal(op(e3,e4),e3)
| equal(op(e4,e4),e3) ),
file('ALG054+1.p',unknown),
[] ).
cnf(149,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('ALG054+1.p',unknown),
[] ).
cnf(156,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('ALG054+1.p',unknown),
[] ).
cnf(161,axiom,
( equal(op(e3,e0),e2)
| equal(op(e3,e1),e2)
| equal(op(e3,e2),e2)
| equal(op(e3,e3),e2)
| equal(op(e3,e4),e2) ),
file('ALG054+1.p',unknown),
[] ).
cnf(162,axiom,
( equal(op(e0,e3),e1)
| equal(op(e1,e3),e1)
| equal(op(e2,e3),e1)
| equal(op(e3,e3),e1)
| equal(op(e4,e3),e1) ),
file('ALG054+1.p',unknown),
[] ).
cnf(173,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('ALG054+1.p',unknown),
[] ).
cnf(179,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('ALG054+1.p',unknown),
[] ).
cnf(181,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('ALG054+1.p',unknown),
[] ).
cnf(182,axiom,
( equal(op(e0,e1),e1)
| equal(op(e1,e1),e1)
| equal(op(e2,e1),e1)
| equal(op(e3,e1),e1)
| equal(op(e4,e1),e1) ),
file('ALG054+1.p',unknown),
[] ).
cnf(184,axiom,
( equal(op(e0,e1),e0)
| equal(op(e1,e1),e0)
| equal(op(e2,e1),e0)
| equal(op(e3,e1),e0)
| equal(op(e4,e1),e0) ),
file('ALG054+1.p',unknown),
[] ).
cnf(205,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('ALG054+1.p',unknown),
[] ).
cnf(206,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('ALG054+1.p',unknown),
[] ).
cnf(218,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('ALG054+1.p',unknown),
[] ).
cnf(219,axiom,
( equal(op(e0,e1),e0)
| equal(op(e0,e1),e1)
| equal(op(e0,e1),e2)
| equal(op(e0,e1),e3)
| equal(op(e0,e1),e4) ),
file('ALG054+1.p',unknown),
[] ).
cnf(220,axiom,
( equal(op(e0,e0),e0)
| equal(op(e0,e0),e1)
| equal(op(e0,e0),e2)
| equal(op(e0,e0),e3)
| equal(op(e0,e0),e4) ),
file('ALG054+1.p',unknown),
[] ).
cnf(224,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('ALG054+1.p',unknown),
[] ).
cnf(225,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('ALG054+1.p',unknown),
[] ).
cnf(227,plain,
~ equal(op(e1,e3),e4),
inference(rew,[status(thm),theory(equality)],[21,87]),
[iquote('0:Rew:21.0,87.0')] ).
cnf(233,plain,
~ equal(op(e0,e1),e4),
inference(rew,[status(thm),theory(equality)],[21,32]),
[iquote('0:Rew:21.0,32.0')] ).
cnf(234,plain,
equal(op(e4,e4),e2),
inference(rew,[status(thm),theory(equality)],[21,122]),
[iquote('0:Rew:21.0,122.0')] ).
cnf(239,plain,
~ equal(op(e3,e4),e2),
inference(rew,[status(thm),theory(equality)],[234,71]),
[iquote('0:Rew:234.0,71.0')] ).
cnf(240,plain,
~ equal(op(e2,e4),e2),
inference(rew,[status(thm),theory(equality)],[234,70]),
[iquote('0:Rew:234.0,70.0')] ).
cnf(243,plain,
equal(op(e1,e2),e0),
inference(rew,[status(thm),theory(equality)],[234,143,21]),
[iquote('0:Rew:234.0,143.0,21.0,143.0')] ).
cnf(251,plain,
~ equal(op(e0,e2),e0),
inference(rew,[status(thm),theory(equality)],[243,42]),
[iquote('0:Rew:243.0,42.0')] ).
cnf(253,plain,
( ~ equal(e2,e2)
| equal(op(e4,e2),e4) ),
inference(rew,[status(thm),theory(equality)],[234,141]),
[iquote('0:Rew:234.0,141.0')] ).
cnf(254,plain,
equal(op(e4,e2),e4),
inference(obv,[status(thm),theory(equality)],[253]),
[iquote('0:Obv:253.0')] ).
cnf(255,plain,
~ equal(op(e4,e3),e4),
inference(rew,[status(thm),theory(equality)],[254,119]),
[iquote('0:Rew:254.0,119.0')] ).
cnf(260,plain,
~ equal(op(e0,e2),e4),
inference(rew,[status(thm),theory(equality)],[254,45]),
[iquote('0:Rew:254.0,45.0')] ).
cnf(265,plain,
( ~ equal(e4,e4)
| equal(op(e1,e4),e1) ),
inference(rew,[status(thm),theory(equality)],[21,130]),
[iquote('0:Rew:21.0,130.0')] ).
cnf(266,plain,
equal(op(e1,e4),e1),
inference(obv,[status(thm),theory(equality)],[265]),
[iquote('0:Obv:265.0')] ).
cnf(267,plain,
~ equal(op(e1,e3),e1),
inference(rew,[status(thm),theory(equality)],[266,91]),
[iquote('0:Rew:266.0,91.0')] ).
cnf(271,plain,
~ equal(op(e2,e4),e1),
inference(rew,[status(thm),theory(equality)],[266,66]),
[iquote('0:Rew:266.0,66.0')] ).
cnf(278,plain,
~ equal(op(e0,e0),e2),
inference(mrr,[status(thm)],[124,251]),
[iquote('0:MRR:124.1,251.0')] ).
cnf(279,plain,
equal(op(e2,e2),e3),
inference(rew,[status(thm),theory(equality)],[234,145,21]),
[iquote('0:Rew:234.0,145.0,21.0,145.0')] ).
cnf(280,plain,
~ equal(op(e2,e4),e3),
inference(rew,[status(thm),theory(equality)],[279,100]),
[iquote('0:Rew:279.0,100.0')] ).
cnf(284,plain,
~ equal(op(e3,e2),e3),
inference(rew,[status(thm),theory(equality)],[279,49]),
[iquote('0:Rew:279.0,49.0')] ).
cnf(285,plain,
~ equal(op(e0,e2),e3),
inference(rew,[status(thm),theory(equality)],[279,43]),
[iquote('0:Rew:279.0,43.0')] ).
cnf(288,plain,
( ~ equal(e3,e3)
| equal(op(e2,e3),e2) ),
inference(rew,[status(thm),theory(equality)],[279,133]),
[iquote('0:Rew:279.0,133.0')] ).
cnf(290,plain,
~ equal(op(e3,e3),e2),
inference(mrr,[status(thm)],[137,284]),
[iquote('0:MRR:137.1,284.0')] ).
cnf(291,plain,
equal(op(e2,e3),e2),
inference(obv,[status(thm),theory(equality)],[288]),
[iquote('0:Obv:288.0')] ).
cnf(297,plain,
~ equal(op(e1,e3),e2),
inference(rew,[status(thm),theory(equality)],[291,56]),
[iquote('0:Rew:291.0,56.0')] ).
cnf(302,plain,
( equal(op(e0,e4),e3)
| equal(e3,e1)
| equal(op(e2,e4),e3)
| equal(op(e3,e4),e3)
| equal(e3,e2) ),
inference(rew,[status(thm),theory(equality)],[234,148,266]),
[iquote('0:Rew:234.0,148.4,266.0,148.1')] ).
cnf(303,plain,
( equal(op(e3,e4),e3)
| equal(op(e0,e4),e3) ),
inference(mrr,[status(thm)],[302,6,280,8]),
[iquote('0:MRR:302.1,302.2,302.4,6.0,280.0,8.0')] ).
cnf(304,plain,
( equal(op(e4,e0),e3)
| equal(op(e4,e1),e3)
| equal(e4,e3)
| equal(op(e4,e3),e3)
| equal(e3,e2) ),
inference(rew,[status(thm),theory(equality)],[234,149,254]),
[iquote('0:Rew:234.0,149.4,254.0,149.2')] ).
cnf(305,plain,
( equal(op(e4,e0),e3)
| equal(op(e4,e1),e3)
| equal(op(e4,e3),e3) ),
inference(mrr,[status(thm)],[304,10,8]),
[iquote('0:MRR:304.2,304.4,10.0,8.0')] ).
cnf(312,plain,
( equal(op(e0,e3),e4)
| equal(op(e1,e3),e4)
| equal(e4,e2)
| equal(op(e3,e3),e4)
| equal(op(e4,e3),e4) ),
inference(rew,[status(thm),theory(equality)],[291,156]),
[iquote('0:Rew:291.0,156.2')] ).
cnf(313,plain,
( equal(op(e3,e3),e4)
| equal(op(e0,e3),e4) ),
inference(mrr,[status(thm)],[312,227,9,255]),
[iquote('0:MRR:312.1,312.2,312.4,227.0,9.0,255.0')] ).
cnf(318,plain,
( equal(op(e3,e0),e2)
| equal(op(e3,e1),e2)
| equal(op(e3,e2),e2) ),
inference(mrr,[status(thm)],[161,290,239]),
[iquote('0:MRR:161.3,161.4,290.0,239.0')] ).
cnf(319,plain,
( equal(op(e0,e3),e1)
| equal(op(e1,e3),e1)
| equal(e2,e1)
| equal(op(e3,e3),e1)
| equal(op(e4,e3),e1) ),
inference(rew,[status(thm),theory(equality)],[291,162]),
[iquote('0:Rew:291.0,162.2')] ).
cnf(320,plain,
( equal(op(e3,e3),e1)
| equal(op(e4,e3),e1)
| equal(op(e0,e3),e1) ),
inference(mrr,[status(thm)],[319,267,5]),
[iquote('0:MRR:319.1,319.2,267.0,5.0')] ).
cnf(331,plain,
( equal(op(e2,e0),e1)
| equal(op(e2,e1),e1)
| equal(e3,e1)
| equal(e2,e1)
| equal(op(e2,e4),e1) ),
inference(rew,[status(thm),theory(equality)],[291,173,279]),
[iquote('0:Rew:291.0,173.3,279.0,173.2')] ).
cnf(332,plain,
( equal(op(e2,e1),e1)
| equal(op(e2,e0),e1) ),
inference(mrr,[status(thm)],[331,6,5,271]),
[iquote('0:MRR:331.2,331.3,331.4,6.0,5.0,271.0')] ).
cnf(337,plain,
( equal(op(e1,e0),e3)
| equal(e4,e3)
| equal(e3,e0)
| equal(op(e1,e3),e3)
| equal(e3,e1) ),
inference(rew,[status(thm),theory(equality)],[266,179,243,21]),
[iquote('0:Rew:266.0,179.4,243.0,179.2,21.0,179.1')] ).
cnf(338,plain,
( equal(op(e1,e0),e3)
| equal(op(e1,e3),e3) ),
inference(mrr,[status(thm)],[337,10,3,6]),
[iquote('0:MRR:337.1,337.2,337.4,10.0,3.0,6.0')] ).
cnf(341,plain,
( equal(op(e1,e0),e2)
| equal(e4,e2)
| equal(e2,e0)
| equal(op(e1,e3),e2)
| equal(e2,e1) ),
inference(rew,[status(thm),theory(equality)],[266,181,243,21]),
[iquote('0:Rew:266.0,181.4,243.0,181.2,21.0,181.1')] ).
cnf(342,plain,
equal(op(e1,e0),e2),
inference(mrr,[status(thm)],[341,9,2,297,5]),
[iquote('0:MRR:341.1,341.2,341.3,341.4,9.0,2.0,297.0,5.0')] ).
cnf(346,plain,
~ equal(op(e3,e0),e2),
inference(rew,[status(thm),theory(equality)],[342,27]),
[iquote('0:Rew:342.0,27.0')] ).
cnf(351,plain,
( equal(e3,e2)
| equal(op(e1,e3),e3) ),
inference(rew,[status(thm),theory(equality)],[342,338]),
[iquote('0:Rew:342.0,338.0')] ).
cnf(352,plain,
( equal(op(e3,e2),e2)
| equal(op(e3,e1),e2) ),
inference(mrr,[status(thm)],[318,346]),
[iquote('0:MRR:318.0,346.0')] ).
cnf(353,plain,
equal(op(e1,e3),e3),
inference(mrr,[status(thm)],[351,8]),
[iquote('0:MRR:351.0,8.0')] ).
cnf(355,plain,
~ equal(op(e4,e3),e3),
inference(rew,[status(thm),theory(equality)],[353,58]),
[iquote('0:Rew:353.0,58.0')] ).
cnf(361,plain,
( equal(op(e4,e1),e3)
| equal(op(e4,e0),e3) ),
inference(mrr,[status(thm)],[305,355]),
[iquote('0:MRR:305.2,355.0')] ).
cnf(363,plain,
( equal(op(e0,e1),e1)
| equal(e4,e1)
| equal(op(e2,e1),e1)
| equal(op(e3,e1),e1)
| equal(op(e4,e1),e1) ),
inference(rew,[status(thm),theory(equality)],[21,182]),
[iquote('0:Rew:21.0,182.1')] ).
cnf(364,plain,
( equal(op(e4,e1),e1)
| equal(op(e3,e1),e1)
| equal(op(e2,e1),e1)
| equal(op(e0,e1),e1) ),
inference(mrr,[status(thm)],[363,7]),
[iquote('0:MRR:363.1,7.0')] ).
cnf(365,plain,
( equal(op(e0,e1),e0)
| equal(e4,e0)
| equal(op(e2,e1),e0)
| equal(op(e3,e1),e0)
| equal(op(e4,e1),e0) ),
inference(rew,[status(thm),theory(equality)],[21,184]),
[iquote('0:Rew:21.0,184.1')] ).
cnf(366,plain,
( equal(op(e0,e1),e0)
| equal(op(e4,e1),e0)
| equal(op(e3,e1),e0)
| equal(op(e2,e1),e0) ),
inference(mrr,[status(thm)],[365,4]),
[iquote('0:MRR:365.1,4.0')] ).
cnf(387,plain,
( equal(op(e3,e0),e3)
| equal(op(e3,e0),e0)
| equal(op(e3,e0),e4)
| equal(op(e3,e0),e1) ),
inference(mrr,[status(thm)],[205,346]),
[iquote('0:MRR:205.2,346.0')] ).
cnf(388,plain,
( equal(op(e2,e4),e4)
| equal(op(e2,e4),e0) ),
inference(mrr,[status(thm)],[206,271,240,280]),
[iquote('0:MRR:206.1,206.2,206.3,271.0,240.0,280.0')] ).
cnf(393,plain,
( equal(op(e0,e2),e2)
| equal(op(e0,e2),e1) ),
inference(mrr,[status(thm)],[218,251,285,260]),
[iquote('0:MRR:218.0,218.3,218.4,251.0,285.0,260.0')] ).
cnf(394,plain,
( equal(op(e0,e1),e1)
| equal(op(e0,e1),e0)
| equal(op(e0,e1),e3)
| equal(op(e0,e1),e2) ),
inference(mrr,[status(thm)],[219,233]),
[iquote('0:MRR:219.4,233.0')] ).
cnf(395,plain,
( equal(op(e0,e0),e0)
| equal(op(e0,e0),e4)
| equal(op(e0,e0),e3)
| equal(op(e0,e0),e1) ),
inference(mrr,[status(thm)],[220,278]),
[iquote('0:MRR:220.2,278.0')] ).
cnf(396,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)],[234,224,279,21]),
[iquote('0:Rew:234.0,224.4,279.0,224.2,21.0,224.1')] ).
cnf(397,plain,
( equal(op(e3,e3),e1)
| equal(op(e0,e0),e1) ),
inference(mrr,[status(thm)],[396,7,6,5]),
[iquote('0:MRR:396.1,396.2,396.4,7.0,6.0,5.0')] ).
cnf(398,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)],[234,225,279,21]),
[iquote('0:Rew:234.0,225.4,279.0,225.2,21.0,225.1')] ).
cnf(399,plain,
( equal(op(e0,e0),e0)
| equal(op(e3,e3),e0) ),
inference(mrr,[status(thm)],[398,4,3,2]),
[iquote('0:MRR:398.1,398.2,398.4,4.0,3.0,2.0')] ).
cnf(400,plain,
equal(e0,unit),
inference(spt,[spt(split,[position(s1)])],[144]),
[iquote('1:Spt:144.4')] ).
cnf(405,plain,
( equal(op(e4,e1),e3)
| equal(op(e4,unit),e3) ),
inference(rew,[status(thm),theory(equality)],[400,361]),
[iquote('1:Rew:400.0,361.1')] ).
cnf(448,plain,
~ equal(op(e2,e4),op(unit,e4)),
inference(rew,[status(thm),theory(equality)],[400,63]),
[iquote('1:Rew:400.0,63.0')] ).
cnf(457,plain,
~ equal(op(e3,e2),op(unit,e2)),
inference(rew,[status(thm),theory(equality)],[400,44]),
[iquote('1:Rew:400.0,44.0')] ).
cnf(488,plain,
( equal(op(unit,e1),unit)
| equal(op(e4,e1),e0)
| equal(op(e3,e1),e0)
| equal(op(e2,e1),e0) ),
inference(rew,[status(thm),theory(equality)],[400,366]),
[iquote('1:Rew:400.0,366.0')] ).
cnf(490,plain,
( equal(op(e2,e4),e4)
| equal(op(e2,e4),unit) ),
inference(rew,[status(thm),theory(equality)],[400,388]),
[iquote('1:Rew:400.0,388.1')] ).
cnf(499,plain,
~ equal(e3,unit),
inference(rew,[status(thm),theory(equality)],[400,3]),
[iquote('1:Rew:400.0,3.0')] ).
cnf(500,plain,
~ equal(e2,unit),
inference(rew,[status(thm),theory(equality)],[400,2]),
[iquote('1:Rew:400.0,2.0')] ).
cnf(501,plain,
~ equal(e1,unit),
inference(rew,[status(thm),theory(equality)],[400,1]),
[iquote('1:Rew:400.0,1.0')] ).
cnf(544,plain,
~ equal(op(e2,e4),e4),
inference(rew,[status(thm),theory(equality)],[19,448]),
[iquote('1:Rew:19.0,448.0')] ).
cnf(547,plain,
~ equal(op(e3,e2),e2),
inference(rew,[status(thm),theory(equality)],[15,457]),
[iquote('1:Rew:15.0,457.0')] ).
cnf(548,plain,
equal(op(e3,e1),e2),
inference(mrr,[status(thm)],[352,547]),
[iquote('1:MRR:352.0,547.0')] ).
cnf(577,plain,
( equal(op(e4,e1),e3)
| equal(e4,e3) ),
inference(rew,[status(thm),theory(equality)],[20,405]),
[iquote('1:Rew:20.0,405.1')] ).
cnf(578,plain,
equal(op(e4,e1),e3),
inference(mrr,[status(thm)],[577,10]),
[iquote('1:MRR:577.1,10.0')] ).
cnf(595,plain,
equal(op(e2,e4),unit),
inference(mrr,[status(thm)],[490,544]),
[iquote('1:MRR:490.0,544.0')] ).
cnf(599,plain,
~ equal(op(e2,e1),unit),
inference(rew,[status(thm),theory(equality)],[595,98]),
[iquote('1:Rew:595.0,98.0')] ).
cnf(642,plain,
( equal(e1,unit)
| equal(e3,unit)
| equal(e2,unit)
| equal(op(e2,e1),unit) ),
inference(rew,[status(thm),theory(equality)],[400,488,548,578,13]),
[iquote('1:Rew:400.0,488.3,548.0,488.2,400.0,488.2,578.0,488.1,400.0,488.1,13.0,488.0')] ).
cnf(643,plain,
$false,
inference(mrr,[status(thm)],[642,501,499,500,599]),
[iquote('1:MRR:642.0,642.1,642.2,642.3,501.0,499.0,500.0,599.0')] ).
cnf(645,plain,
~ equal(e0,unit),
inference(spt,[spt(split,[position(sa)])],[643,400]),
[iquote('1:Spt:643.0,144.4,400.0')] ).
cnf(646,plain,
( equal(e4,unit)
| equal(e3,unit)
| equal(e2,unit)
| equal(e1,unit) ),
inference(spt,[spt(split,[position(s2)])],[144]),
[iquote('1:Spt:643.0,144.0,144.1,144.2,144.3')] ).
cnf(647,plain,
equal(e4,unit),
inference(spt,[spt(split,[position(s2s1)])],[646]),
[iquote('2:Spt:646.0')] ).
cnf(650,plain,
~ equal(op(e3,e0),op(e3,unit)),
inference(rew,[status(thm),theory(equality)],[647,105]),
[iquote('2:Rew:647.0,105.0')] ).
cnf(651,plain,
~ equal(op(e3,e1),op(e3,unit)),
inference(rew,[status(thm),theory(equality)],[647,108]),
[iquote('2:Rew:647.0,108.0')] ).
cnf(662,plain,
~ equal(e1,unit),
inference(rew,[status(thm),theory(equality)],[647,7]),
[iquote('2:Rew:647.0,7.0')] ).
cnf(702,plain,
~ equal(op(e2,e1),op(unit,e1)),
inference(rew,[status(thm),theory(equality)],[647,40]),
[iquote('2:Rew:647.0,40.0')] ).
cnf(723,plain,
( equal(op(e3,e3),e1)
| equal(op(unit,e3),e1)
| equal(op(e0,e3),e1) ),
inference(rew,[status(thm),theory(equality)],[647,320]),
[iquote('2:Rew:647.0,320.1')] ).
cnf(731,plain,
( equal(op(e3,e3),unit)
| equal(op(e0,e3),e4) ),
inference(rew,[status(thm),theory(equality)],[647,313]),
[iquote('2:Rew:647.0,313.0')] ).
cnf(737,plain,
( equal(op(e3,e0),e3)
| equal(op(e3,e0),e0)
| equal(op(e3,e0),unit)
| equal(op(e3,e0),e1) ),
inference(rew,[status(thm),theory(equality)],[647,387]),
[iquote('2:Rew:647.0,387.2')] ).
cnf(758,plain,
~ equal(op(e3,e0),e3),
inference(rew,[status(thm),theory(equality)],[18,650]),
[iquote('2:Rew:18.0,650.0')] ).
cnf(759,plain,
~ equal(op(e3,e3),e0),
inference(mrr,[status(thm)],[135,758]),
[iquote('2:MRR:135.1,758.0')] ).
cnf(760,plain,
equal(op(e0,e0),e0),
inference(mrr,[status(thm)],[399,759]),
[iquote('2:MRR:399.1,759.0')] ).
cnf(763,plain,
~ equal(op(e3,e0),e0),
inference(rew,[status(thm),theory(equality)],[760,24]),
[iquote('2:Rew:760.0,24.0')] ).
cnf(772,plain,
~ equal(op(e3,e1),e3),
inference(rew,[status(thm),theory(equality)],[18,651]),
[iquote('2:Rew:18.0,651.0')] ).
cnf(773,plain,
~ equal(op(e3,e3),e1),
inference(mrr,[status(thm)],[136,772]),
[iquote('2:MRR:136.1,772.0')] ).
cnf(791,plain,
~ equal(op(e2,e1),e1),
inference(rew,[status(thm),theory(equality)],[13,702]),
[iquote('2:Rew:13.0,702.0')] ).
cnf(793,plain,
equal(op(e2,e0),e1),
inference(mrr,[status(thm)],[332,791]),
[iquote('2:MRR:332.0,791.0')] ).
cnf(803,plain,
~ equal(op(e3,e0),e1),
inference(rew,[status(thm),theory(equality)],[793,29]),
[iquote('2:Rew:793.0,29.0')] ).
cnf(823,plain,
( equal(op(e3,e3),unit)
| equal(op(e0,e3),unit) ),
inference(rew,[status(thm),theory(equality)],[647,731]),
[iquote('2:Rew:647.0,731.1')] ).
cnf(866,plain,
( equal(op(e3,e3),e1)
| equal(e3,e1)
| equal(op(e0,e3),e1) ),
inference(rew,[status(thm),theory(equality)],[17,723]),
[iquote('2:Rew:17.0,723.1')] ).
cnf(867,plain,
equal(op(e0,e3),e1),
inference(mrr,[status(thm)],[866,773,6]),
[iquote('2:MRR:866.0,866.1,773.0,6.0')] ).
cnf(872,plain,
( equal(op(e3,e3),unit)
| equal(e1,unit) ),
inference(rew,[status(thm),theory(equality)],[867,823]),
[iquote('2:Rew:867.0,823.1')] ).
cnf(873,plain,
equal(op(e3,e3),unit),
inference(mrr,[status(thm)],[872,662]),
[iquote('2:MRR:872.1,662.0')] ).
cnf(876,plain,
~ equal(op(e3,e0),unit),
inference(rew,[status(thm),theory(equality)],[873,104]),
[iquote('2:Rew:873.0,104.0')] ).
cnf(890,plain,
$false,
inference(mrr,[status(thm)],[737,758,763,876,803]),
[iquote('2:MRR:737.0,737.1,737.2,737.3,758.0,763.0,876.0,803.0')] ).
cnf(891,plain,
~ equal(e4,unit),
inference(spt,[spt(split,[position(s2sa)])],[890,647]),
[iquote('2:Spt:890.0,646.0,647.0')] ).
cnf(892,plain,
( equal(e3,unit)
| equal(e2,unit)
| equal(e1,unit) ),
inference(spt,[spt(split,[position(s2s2)])],[646]),
[iquote('2:Spt:890.0,646.1,646.2,646.3')] ).
cnf(893,plain,
equal(e3,unit),
inference(spt,[spt(split,[position(s2s2s1)])],[892]),
[iquote('3:Spt:892.0')] ).
cnf(904,plain,
~ equal(op(e0,e0),op(unit,e0)),
inference(rew,[status(thm),theory(equality)],[893,24]),
[iquote('3:Rew:893.0,24.0')] ).
cnf(927,plain,
~ equal(op(e0,e2),op(unit,e2)),
inference(rew,[status(thm),theory(equality)],[893,44]),
[iquote('3:Rew:893.0,44.0')] ).
cnf(959,plain,
~ equal(op(e0,e4),op(e0,unit)),
inference(rew,[status(thm),theory(equality)],[893,81]),
[iquote('3:Rew:893.0,81.0')] ).
cnf(990,plain,
( equal(op(unit,e4),unit)
| equal(op(e0,e4),e3) ),
inference(rew,[status(thm),theory(equality)],[893,303]),
[iquote('3:Rew:893.0,303.0')] ).
cnf(993,plain,
( equal(op(e0,e0),e0)
| equal(op(e0,e0),e4)
| equal(op(e0,e0),unit)
| equal(op(e0,e0),e1) ),
inference(rew,[status(thm),theory(equality)],[893,395]),
[iquote('3:Rew:893.0,395.2')] ).
cnf(1014,plain,
~ equal(op(e0,e0),e0),
inference(rew,[status(thm),theory(equality)],[11,904]),
[iquote('3:Rew:11.0,904.0')] ).
cnf(1020,plain,
~ equal(op(e0,e2),e2),
inference(rew,[status(thm),theory(equality)],[15,927]),
[iquote('3:Rew:15.0,927.0')] ).
cnf(1022,plain,
equal(op(e0,e2),e1),
inference(mrr,[status(thm)],[393,1020]),
[iquote('3:MRR:393.0,1020.0')] ).
cnf(1033,plain,
~ equal(op(e0,e0),e1),
inference(rew,[status(thm),theory(equality)],[1022,73]),
[iquote('3:Rew:1022.0,73.0')] ).
cnf(1073,plain,
~ equal(op(e0,e4),e0),
inference(rew,[status(thm),theory(equality)],[12,959]),
[iquote('3:Rew:12.0,959.0')] ).
cnf(1074,plain,
~ equal(op(e0,e0),e4),
inference(mrr,[status(thm)],[126,1073]),
[iquote('3:MRR:126.1,1073.0')] ).
cnf(1093,plain,
( equal(e4,unit)
| equal(op(e0,e4),unit) ),
inference(rew,[status(thm),theory(equality)],[893,990,19]),
[iquote('3:Rew:893.0,990.1,19.0,990.0')] ).
cnf(1094,plain,
equal(op(e0,e4),unit),
inference(mrr,[status(thm)],[1093,891]),
[iquote('3:MRR:1093.0,891.0')] ).
cnf(1097,plain,
~ equal(op(e0,e0),unit),
inference(rew,[status(thm),theory(equality)],[1094,75]),
[iquote('3:Rew:1094.0,75.0')] ).
cnf(1136,plain,
$false,
inference(mrr,[status(thm)],[993,1014,1074,1097,1033]),
[iquote('3:MRR:993.0,993.1,993.2,993.3,1014.0,1074.0,1097.0,1033.0')] ).
cnf(1137,plain,
~ equal(e3,unit),
inference(spt,[spt(split,[position(s2s2sa)])],[1136,893]),
[iquote('3:Spt:1136.0,892.0,893.0')] ).
cnf(1138,plain,
( equal(e2,unit)
| equal(e1,unit) ),
inference(spt,[spt(split,[position(s2s2s2)])],[892]),
[iquote('3:Spt:1136.0,892.1,892.2')] ).
cnf(1139,plain,
equal(e2,unit),
inference(spt,[spt(split,[position(s2s2s2s1)])],[1138]),
[iquote('4:Spt:1138.0')] ).
cnf(1160,plain,
~ equal(op(e3,e4),op(e3,unit)),
inference(rew,[status(thm),theory(equality)],[1139,110]),
[iquote('4:Rew:1139.0,110.0')] ).
cnf(1161,plain,
~ equal(op(e3,e1),op(e3,unit)),
inference(rew,[status(thm),theory(equality)],[1139,106]),
[iquote('4:Rew:1139.0,106.0')] ).
cnf(1171,plain,
~ equal(op(e0,e1),op(e0,unit)),
inference(rew,[status(thm),theory(equality)],[1139,76]),
[iquote('4:Rew:1139.0,76.0')] ).
cnf(1214,plain,
( equal(op(e3,e2),e2)
| equal(op(e3,e1),unit) ),
inference(rew,[status(thm),theory(equality)],[1139,352]),
[iquote('4:Rew:1139.0,352.1')] ).
cnf(1216,plain,
( equal(op(e0,e1),e1)
| equal(op(e0,e1),e0)
| equal(op(e0,e1),e3)
| equal(op(e0,e1),unit) ),
inference(rew,[status(thm),theory(equality)],[1139,394]),
[iquote('4:Rew:1139.0,394.3')] ).
cnf(1242,plain,
~ equal(op(e3,e4),e3),
inference(rew,[status(thm),theory(equality)],[18,1160]),
[iquote('4:Rew:18.0,1160.0')] ).
cnf(1243,plain,
equal(op(e0,e4),e3),
inference(mrr,[status(thm)],[303,1242]),
[iquote('4:MRR:303.0,1242.0')] ).
cnf(1250,plain,
~ equal(op(e0,e1),e3),
inference(rew,[status(thm),theory(equality)],[1243,78]),
[iquote('4:Rew:1243.0,78.0')] ).
cnf(1272,plain,
~ equal(op(e3,e1),e3),
inference(rew,[status(thm),theory(equality)],[18,1161]),
[iquote('4:Rew:18.0,1161.0')] ).
cnf(1273,plain,
~ equal(op(e3,e3),e1),
inference(mrr,[status(thm)],[136,1272]),
[iquote('4:MRR:136.1,1272.0')] ).
cnf(1274,plain,
equal(op(e0,e0),e1),
inference(mrr,[status(thm)],[397,1273]),
[iquote('4:MRR:397.0,1273.0')] ).
cnf(1277,plain,
~ equal(op(e0,e1),e1),
inference(rew,[status(thm),theory(equality)],[1274,72]),
[iquote('4:Rew:1274.0,72.0')] ).
cnf(1291,plain,
~ equal(op(e0,e1),e0),
inference(rew,[status(thm),theory(equality)],[12,1171]),
[iquote('4:Rew:12.0,1171.0')] ).
cnf(1320,plain,
( equal(e3,unit)
| equal(op(e3,e1),unit) ),
inference(rew,[status(thm),theory(equality)],[18,1214,1139]),
[iquote('4:Rew:18.0,1214.0,1139.0,1214.0')] ).
cnf(1321,plain,
equal(op(e3,e1),unit),
inference(mrr,[status(thm)],[1320,1137]),
[iquote('4:MRR:1320.0,1137.0')] ).
cnf(1326,plain,
~ equal(op(e0,e1),unit),
inference(rew,[status(thm),theory(equality)],[1321,34]),
[iquote('4:Rew:1321.0,34.0')] ).
cnf(1381,plain,
$false,
inference(mrr,[status(thm)],[1216,1277,1291,1250,1326]),
[iquote('4:MRR:1216.0,1216.1,1216.2,1216.3,1277.0,1291.0,1250.0,1326.0')] ).
cnf(1382,plain,
~ equal(e2,unit),
inference(spt,[spt(split,[position(s2s2s2sa)])],[1381,1139]),
[iquote('4:Spt:1381.0,1138.0,1139.0')] ).
cnf(1383,plain,
equal(e1,unit),
inference(spt,[spt(split,[position(s2s2s2s2)])],[1138]),
[iquote('4:Spt:1381.0,1138.1')] ).
cnf(1393,plain,
~ equal(e2,unit),
inference(rew,[status(thm),theory(equality)],[1383,5]),
[iquote('4:Rew:1383.0,5.0')] ).
cnf(1549,plain,
( equal(e4,unit)
| equal(e3,unit)
| equal(e2,unit)
| equal(e0,unit) ),
inference(rew,[status(thm),theory(equality)],[12,364,1383,16,18,20]),
[iquote('4:Rew:12.0,364.3,1383.0,364.3,16.0,364.2,1383.0,364.2,18.0,364.1,1383.0,364.1,20.0,364.0,1383.0,364.0')] ).
cnf(1550,plain,
$false,
inference(mrr,[status(thm)],[1549,891,1137,1393,645]),
[iquote('4:MRR:1549.0,1549.1,1549.2,1549.3,891.0,1137.0,1393.0,645.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG054+1 : TPTP v8.1.0. Released v2.7.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.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 : Thu Jun 9 03:16:32 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.51
% 0.19/0.51 SPASS V 3.9
% 0.19/0.51 SPASS beiseite: Proof found.
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.51 SPASS derived 753 clauses, backtracked 570 clauses, performed 4 splits and kept 989 clauses.
% 0.19/0.51 SPASS allocated 85917 KBytes.
% 0.19/0.51 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.51 0:00:00.04 for the input.
% 0.19/0.51 0:00:00.05 for the FLOTTER CNF translation.
% 0.19/0.51 0:00:00.00 for inferences.
% 0.19/0.51 0:00:00.00 for the backtracking.
% 0.19/0.51 0:00:00.05 for the reduction.
% 0.19/0.51
% 0.19/0.51
% 0.19/0.51 Here is a proof with depth 4, length 227 :
% 0.19/0.51 % SZS output start Refutation
% See solution above
% 0.19/0.51 Formulae used in the proof : ax5 ax2 ax6 ax4 co1 ax3 ax1
% 0.19/0.51
%------------------------------------------------------------------------------