TSTP Solution File: ALG121+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG121+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 18:02:32 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 75
% Syntax : Number of clauses : 196 ( 109 unt; 67 nHn; 196 RR)
% Number of literals : 410 ( 0 equ; 109 neg)
% Maximal clause size : 20 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(e11,e10),
file('ALG121+1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(e12,e10),
file('ALG121+1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(e13,e10),
file('ALG121+1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(e12,e11),
file('ALG121+1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(e13,e11),
file('ALG121+1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(e13,e12),
file('ALG121+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(e21,e20),
file('ALG121+1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(e22,e20),
file('ALG121+1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(e23,e20),
file('ALG121+1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(e22,e21),
file('ALG121+1.p',unknown),
[] ).
cnf(11,axiom,
~ equal(e23,e21),
file('ALG121+1.p',unknown),
[] ).
cnf(12,axiom,
~ equal(e23,e22),
file('ALG121+1.p',unknown),
[] ).
cnf(32,axiom,
equal(h4(e13),e23),
file('ALG121+1.p',unknown),
[] ).
cnf(33,axiom,
equal(op1(e13,e13),e10),
file('ALG121+1.p',unknown),
[] ).
cnf(34,axiom,
equal(op2(e23,e23),e20),
file('ALG121+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ equal(h4(e10),e20)
| skC39 ),
file('ALG121+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ equal(h4(e11),e21)
| skC40 ),
file('ALG121+1.p',unknown),
[] ).
cnf(81,axiom,
( ~ equal(h4(e12),e22)
| skC41 ),
file('ALG121+1.p',unknown),
[] ).
cnf(83,axiom,
equal(op2(e20,e20),h1(e10)),
file('ALG121+1.p',unknown),
[] ).
cnf(84,axiom,
equal(op2(e21,e21),h2(e10)),
file('ALG121+1.p',unknown),
[] ).
cnf(85,axiom,
equal(op2(e22,e22),h3(e10)),
file('ALG121+1.p',unknown),
[] ).
cnf(86,axiom,
equal(op2(e23,e23),h4(e10)),
file('ALG121+1.p',unknown),
[] ).
cnf(146,axiom,
~ equal(op1(e13,e10),op1(e12,e10)),
file('ALG121+1.p',unknown),
[] ).
cnf(162,axiom,
~ equal(op1(e12,e13),op1(e11,e13)),
file('ALG121+1.p',unknown),
[] ).
cnf(166,axiom,
~ equal(op1(e10,e12),op1(e10,e10)),
file('ALG121+1.p',unknown),
[] ).
cnf(167,axiom,
~ equal(op1(e10,e13),op1(e10,e10)),
file('ALG121+1.p',unknown),
[] ).
cnf(168,axiom,
~ equal(op1(e10,e12),op1(e10,e11)),
file('ALG121+1.p',unknown),
[] ).
cnf(170,axiom,
~ equal(op1(e10,e13),op1(e10,e12)),
file('ALG121+1.p',unknown),
[] ).
cnf(182,axiom,
~ equal(op1(e12,e13),op1(e12,e12)),
file('ALG121+1.p',unknown),
[] ).
cnf(184,axiom,
~ equal(op1(e13,e12),op1(e13,e10)),
file('ALG121+1.p',unknown),
[] ).
cnf(194,axiom,
~ equal(op2(e23,e20),op2(e22,e20)),
file('ALG121+1.p',unknown),
[] ).
cnf(210,axiom,
~ equal(op2(e22,e23),op2(e21,e23)),
file('ALG121+1.p',unknown),
[] ).
cnf(214,axiom,
~ equal(op2(e20,e22),op2(e20,e20)),
file('ALG121+1.p',unknown),
[] ).
cnf(215,axiom,
~ equal(op2(e20,e23),op2(e20,e20)),
file('ALG121+1.p',unknown),
[] ).
cnf(216,axiom,
~ equal(op2(e20,e22),op2(e20,e21)),
file('ALG121+1.p',unknown),
[] ).
cnf(218,axiom,
~ equal(op2(e20,e23),op2(e20,e22)),
file('ALG121+1.p',unknown),
[] ).
cnf(230,axiom,
~ equal(op2(e22,e23),op2(e22,e22)),
file('ALG121+1.p',unknown),
[] ).
cnf(232,axiom,
~ equal(op2(e23,e22),op2(e23,e20)),
file('ALG121+1.p',unknown),
[] ).
cnf(267,axiom,
equal(op1(op1(e13,e13),op1(e13,e13)),e11),
file('ALG121+1.p',unknown),
[] ).
cnf(268,axiom,
equal(op2(op2(e23,e23),op2(e23,e23)),e21),
file('ALG121+1.p',unknown),
[] ).
cnf(269,axiom,
equal(op2(op2(e20,e20),op2(e20,e20)),h1(e11)),
file('ALG121+1.p',unknown),
[] ).
cnf(272,axiom,
equal(op2(op2(e23,e23),op2(e23,e23)),h4(e11)),
file('ALG121+1.p',unknown),
[] ).
cnf(273,axiom,
( ~ equal(op1(e10,e10),e11)
| equal(op1(e10,e11),e10) ),
file('ALG121+1.p',unknown),
[] ).
cnf(281,axiom,
( ~ equal(op1(e12,e12),e13)
| equal(op1(e12,e13),e12) ),
file('ALG121+1.p',unknown),
[] ).
cnf(282,axiom,
( ~ equal(op1(e13,e13),e10)
| equal(op1(e13,e10),e13) ),
file('ALG121+1.p',unknown),
[] ).
cnf(285,axiom,
( ~ equal(op2(e20,e20),e21)
| equal(op2(e20,e21),e20) ),
file('ALG121+1.p',unknown),
[] ).
cnf(293,axiom,
( ~ equal(op2(e22,e22),e23)
| equal(op2(e22,e23),e22) ),
file('ALG121+1.p',unknown),
[] ).
cnf(294,axiom,
( ~ equal(op2(e23,e23),e20)
| equal(op2(e23,e20),e23) ),
file('ALG121+1.p',unknown),
[] ).
cnf(297,axiom,
equal(op1(op1(op1(e13,e13),op1(e13,e13)),e13),e12),
file('ALG121+1.p',unknown),
[] ).
cnf(298,axiom,
equal(op2(op2(op2(e23,e23),op2(e23,e23)),e23),e22),
file('ALG121+1.p',unknown),
[] ).
cnf(299,axiom,
equal(op2(op2(op2(e20,e20),op2(e20,e20)),e20),h1(e12)),
file('ALG121+1.p',unknown),
[] ).
cnf(302,axiom,
equal(op2(op2(op2(e23,e23),op2(e23,e23)),e23),h4(e12)),
file('ALG121+1.p',unknown),
[] ).
cnf(304,axiom,
( equal(op2(e20,e20),e20)
| equal(op2(e21,e21),e21)
| equal(op2(e22,e22),e22)
| equal(op2(e23,e23),e23) ),
file('ALG121+1.p',unknown),
[] ).
cnf(306,axiom,
( equal(op1(e10,e10),e10)
| equal(op1(e11,e11),e11)
| equal(op1(e12,e12),e12)
| equal(op1(e13,e13),e13) ),
file('ALG121+1.p',unknown),
[] ).
cnf(307,axiom,
( equal(op2(e20,e23),e23)
| equal(op2(e21,e23),e23)
| equal(op2(e22,e23),e23)
| equal(op2(e23,e23),e23) ),
file('ALG121+1.p',unknown),
[] ).
cnf(310,axiom,
( equal(op2(e23,e20),e22)
| equal(op2(e23,e21),e22)
| equal(op2(e23,e22),e22)
| equal(op2(e23,e23),e22) ),
file('ALG121+1.p',unknown),
[] ).
cnf(311,axiom,
( equal(op2(e20,e23),e21)
| equal(op2(e21,e23),e21)
| equal(op2(e22,e23),e21)
| equal(op2(e23,e23),e21) ),
file('ALG121+1.p',unknown),
[] ).
cnf(315,axiom,
( equal(op2(e20,e22),e23)
| equal(op2(e21,e22),e23)
| equal(op2(e22,e22),e23)
| equal(op2(e23,e22),e23) ),
file('ALG121+1.p',unknown),
[] ).
cnf(316,axiom,
( equal(op2(e22,e20),e23)
| equal(op2(e22,e21),e23)
| equal(op2(e22,e22),e23)
| equal(op2(e22,e23),e23) ),
file('ALG121+1.p',unknown),
[] ).
cnf(317,axiom,
( equal(op2(e20,e22),e22)
| equal(op2(e21,e22),e22)
| equal(op2(e22,e22),e22)
| equal(op2(e23,e22),e22) ),
file('ALG121+1.p',unknown),
[] ).
cnf(318,axiom,
( equal(op2(e22,e20),e22)
| equal(op2(e22,e21),e22)
| equal(op2(e22,e22),e22)
| equal(op2(e22,e23),e22) ),
file('ALG121+1.p',unknown),
[] ).
cnf(319,axiom,
( equal(op2(e20,e22),e21)
| equal(op2(e21,e22),e21)
| equal(op2(e22,e22),e21)
| equal(op2(e23,e22),e21) ),
file('ALG121+1.p',unknown),
[] ).
cnf(321,axiom,
( equal(op2(e20,e22),e20)
| equal(op2(e21,e22),e20)
| equal(op2(e22,e22),e20)
| equal(op2(e23,e22),e20) ),
file('ALG121+1.p',unknown),
[] ).
cnf(330,axiom,
( equal(op2(e21,e20),e20)
| equal(op2(e21,e21),e20)
| equal(op2(e21,e22),e20)
| equal(op2(e21,e23),e20) ),
file('ALG121+1.p',unknown),
[] ).
cnf(355,axiom,
( equal(op1(e10,e13),e13)
| equal(op1(e11,e13),e13)
| equal(op1(e12,e13),e13)
| equal(op1(e13,e13),e13) ),
file('ALG121+1.p',unknown),
[] ).
cnf(358,axiom,
( equal(op1(e13,e10),e12)
| equal(op1(e13,e11),e12)
| equal(op1(e13,e12),e12)
| equal(op1(e13,e13),e12) ),
file('ALG121+1.p',unknown),
[] ).
cnf(359,axiom,
( equal(op1(e10,e13),e11)
| equal(op1(e11,e13),e11)
| equal(op1(e12,e13),e11)
| equal(op1(e13,e13),e11) ),
file('ALG121+1.p',unknown),
[] ).
cnf(363,axiom,
( equal(op1(e10,e12),e13)
| equal(op1(e11,e12),e13)
| equal(op1(e12,e12),e13)
| equal(op1(e13,e12),e13) ),
file('ALG121+1.p',unknown),
[] ).
cnf(364,axiom,
( equal(op1(e12,e10),e13)
| equal(op1(e12,e11),e13)
| equal(op1(e12,e12),e13)
| equal(op1(e12,e13),e13) ),
file('ALG121+1.p',unknown),
[] ).
cnf(365,axiom,
( equal(op1(e10,e12),e12)
| equal(op1(e11,e12),e12)
| equal(op1(e12,e12),e12)
| equal(op1(e13,e12),e12) ),
file('ALG121+1.p',unknown),
[] ).
cnf(366,axiom,
( equal(op1(e12,e10),e12)
| equal(op1(e12,e11),e12)
| equal(op1(e12,e12),e12)
| equal(op1(e12,e13),e12) ),
file('ALG121+1.p',unknown),
[] ).
cnf(367,axiom,
( equal(op1(e10,e12),e11)
| equal(op1(e11,e12),e11)
| equal(op1(e12,e12),e11)
| equal(op1(e13,e12),e11) ),
file('ALG121+1.p',unknown),
[] ).
cnf(369,axiom,
( equal(op1(e10,e12),e10)
| equal(op1(e11,e12),e10)
| equal(op1(e12,e12),e10)
| equal(op1(e13,e12),e10) ),
file('ALG121+1.p',unknown),
[] ).
cnf(378,axiom,
( equal(op1(e11,e10),e10)
| equal(op1(e11,e11),e10)
| equal(op1(e11,e12),e10)
| equal(op1(e11,e13),e10) ),
file('ALG121+1.p',unknown),
[] ).
cnf(405,axiom,
( ~ equal(h4(e13),e23)
| ~ equal(op2(h4(e10),h4(e10)),h4(op1(e10,e10)))
| ~ equal(op2(h4(e10),h4(e11)),h4(op1(e10,e11)))
| ~ equal(op2(h4(e10),h4(e12)),h4(op1(e10,e12)))
| ~ equal(op2(h4(e10),h4(e13)),h4(op1(e10,e13)))
| ~ equal(op2(h4(e11),h4(e10)),h4(op1(e11,e10)))
| ~ equal(op2(h4(e11),h4(e11)),h4(op1(e11,e11)))
| ~ equal(op2(h4(e11),h4(e12)),h4(op1(e11,e12)))
| ~ equal(op2(h4(e11),h4(e13)),h4(op1(e11,e13)))
| ~ equal(op2(h4(e12),h4(e10)),h4(op1(e12,e10)))
| ~ equal(op2(h4(e12),h4(e11)),h4(op1(e12,e11)))
| ~ equal(op2(h4(e12),h4(e12)),h4(op1(e12,e12)))
| ~ equal(op2(h4(e12),h4(e13)),h4(op1(e12,e13)))
| ~ equal(op2(h4(e13),h4(e10)),h4(op1(e13,e10)))
| ~ equal(op2(h4(e13),h4(e11)),h4(op1(e13,e11)))
| ~ equal(op2(h4(e13),h4(e12)),h4(op1(e13,e12)))
| ~ equal(op2(h4(e13),h4(e13)),h4(op1(e13,e13)))
| ~ skC39
| ~ skC40
| ~ skC41 ),
file('ALG121+1.p',unknown),
[] ).
cnf(421,plain,
equal(h4(e10),e20),
inference(rew,[status(thm),theory(equality)],[34,86]),
[iquote('0:Rew:34.0,86.0')] ).
cnf(427,plain,
( ~ equal(e20,e20)
| skC39 ),
inference(rew,[status(thm),theory(equality)],[421,71]),
[iquote('0:Rew:421.0,71.0')] ).
cnf(428,plain,
skC39,
inference(obv,[status(thm),theory(equality)],[427]),
[iquote('0:Obv:427.0')] ).
cnf(475,plain,
~ equal(op2(e22,e23),h3(e10)),
inference(rew,[status(thm),theory(equality)],[85,230]),
[iquote('0:Rew:85.0,230.0')] ).
cnf(481,plain,
~ equal(op2(e20,e23),h1(e10)),
inference(rew,[status(thm),theory(equality)],[83,215]),
[iquote('0:Rew:83.0,215.0')] ).
cnf(482,plain,
~ equal(op2(e20,e22),h1(e10)),
inference(rew,[status(thm),theory(equality)],[83,214]),
[iquote('0:Rew:83.0,214.0')] ).
cnf(503,plain,
equal(h1(e10),e21),
inference(rew,[status(thm),theory(equality)],[83,268,34]),
[iquote('0:Rew:83.0,268.0,34.0,268.0')] ).
cnf(504,plain,
equal(op2(e20,e20),e21),
inference(rew,[status(thm),theory(equality)],[503,83]),
[iquote('0:Rew:503.0,83.0')] ).
cnf(510,plain,
~ equal(op2(e20,e23),e21),
inference(rew,[status(thm),theory(equality)],[503,481]),
[iquote('0:Rew:503.0,481.0')] ).
cnf(511,plain,
~ equal(op2(e20,e22),e21),
inference(rew,[status(thm),theory(equality)],[503,482]),
[iquote('0:Rew:503.0,482.0')] ).
cnf(518,plain,
equal(op1(e10,e10),e11),
inference(rew,[status(thm),theory(equality)],[33,267]),
[iquote('0:Rew:33.0,267.0')] ).
cnf(522,plain,
~ equal(op1(e10,e13),e11),
inference(rew,[status(thm),theory(equality)],[518,167]),
[iquote('0:Rew:518.0,167.0')] ).
cnf(523,plain,
~ equal(op1(e10,e12),e11),
inference(rew,[status(thm),theory(equality)],[518,166]),
[iquote('0:Rew:518.0,166.0')] ).
cnf(529,plain,
equal(h4(e11),e21),
inference(rew,[status(thm),theory(equality)],[504,272,34]),
[iquote('0:Rew:504.0,272.0,34.0,272.0')] ).
cnf(531,plain,
( ~ equal(e21,e21)
| skC40 ),
inference(rew,[status(thm),theory(equality)],[529,76]),
[iquote('0:Rew:529.0,76.0')] ).
cnf(532,plain,
skC40,
inference(obv,[status(thm),theory(equality)],[531]),
[iquote('0:Obv:531.0')] ).
cnf(535,plain,
equal(h2(e10),h1(e11)),
inference(rew,[status(thm),theory(equality)],[84,269,504]),
[iquote('0:Rew:84.0,269.0,504.0,269.0')] ).
cnf(536,plain,
equal(op2(e21,e21),h1(e11)),
inference(rew,[status(thm),theory(equality)],[535,84]),
[iquote('0:Rew:535.0,84.0')] ).
cnf(549,plain,
equal(op2(e21,e23),e22),
inference(rew,[status(thm),theory(equality)],[504,298,34]),
[iquote('0:Rew:504.0,298.0,34.0,298.0')] ).
cnf(555,plain,
~ equal(op2(e22,e23),e22),
inference(rew,[status(thm),theory(equality)],[549,210]),
[iquote('0:Rew:549.0,210.0')] ).
cnf(562,plain,
equal(op1(e11,e13),e12),
inference(rew,[status(thm),theory(equality)],[518,297,33]),
[iquote('0:Rew:518.0,297.0,33.0,297.0')] ).
cnf(569,plain,
~ equal(op1(e12,e13),e12),
inference(rew,[status(thm),theory(equality)],[562,162]),
[iquote('0:Rew:562.0,162.0')] ).
cnf(577,plain,
( ~ equal(e20,e20)
| equal(op2(e23,e20),e23) ),
inference(rew,[status(thm),theory(equality)],[34,294]),
[iquote('0:Rew:34.0,294.0')] ).
cnf(578,plain,
equal(op2(e23,e20),e23),
inference(obv,[status(thm),theory(equality)],[577]),
[iquote('0:Obv:577.0')] ).
cnf(580,plain,
~ equal(op2(e23,e22),e23),
inference(rew,[status(thm),theory(equality)],[578,232]),
[iquote('0:Rew:578.0,232.0')] ).
cnf(582,plain,
~ equal(op2(e22,e20),e23),
inference(rew,[status(thm),theory(equality)],[578,194]),
[iquote('0:Rew:578.0,194.0')] ).
cnf(586,plain,
( ~ equal(h3(e10),e23)
| equal(op2(e22,e23),e22) ),
inference(rew,[status(thm),theory(equality)],[85,293]),
[iquote('0:Rew:85.0,293.0')] ).
cnf(587,plain,
~ equal(h3(e10),e23),
inference(mrr,[status(thm)],[586,555]),
[iquote('0:MRR:586.1,555.0')] ).
cnf(597,plain,
( ~ equal(e21,e21)
| equal(op2(e20,e21),e20) ),
inference(rew,[status(thm),theory(equality)],[504,285]),
[iquote('0:Rew:504.0,285.0')] ).
cnf(598,plain,
equal(op2(e20,e21),e20),
inference(obv,[status(thm),theory(equality)],[597]),
[iquote('0:Obv:597.0')] ).
cnf(600,plain,
~ equal(op2(e20,e22),e20),
inference(rew,[status(thm),theory(equality)],[598,216]),
[iquote('0:Rew:598.0,216.0')] ).
cnf(608,plain,
( ~ equal(e10,e10)
| equal(op1(e13,e10),e13) ),
inference(rew,[status(thm),theory(equality)],[33,282]),
[iquote('0:Rew:33.0,282.0')] ).
cnf(609,plain,
equal(op1(e13,e10),e13),
inference(obv,[status(thm),theory(equality)],[608]),
[iquote('0:Obv:608.0')] ).
cnf(611,plain,
~ equal(op1(e13,e12),e13),
inference(rew,[status(thm),theory(equality)],[609,184]),
[iquote('0:Rew:609.0,184.0')] ).
cnf(613,plain,
~ equal(op1(e12,e10),e13),
inference(rew,[status(thm),theory(equality)],[609,146]),
[iquote('0:Rew:609.0,146.0')] ).
cnf(617,plain,
~ equal(op1(e12,e12),e13),
inference(mrr,[status(thm)],[281,569]),
[iquote('0:MRR:281.1,569.0')] ).
cnf(623,plain,
( ~ equal(e11,e11)
| equal(op1(e10,e11),e10) ),
inference(rew,[status(thm),theory(equality)],[518,273]),
[iquote('0:Rew:518.0,273.0')] ).
cnf(624,plain,
equal(op1(e10,e11),e10),
inference(obv,[status(thm),theory(equality)],[623]),
[iquote('0:Obv:623.0')] ).
cnf(626,plain,
~ equal(op1(e10,e12),e10),
inference(rew,[status(thm),theory(equality)],[624,168]),
[iquote('0:Rew:624.0,168.0')] ).
cnf(632,plain,
equal(h4(e12),e22),
inference(rew,[status(thm),theory(equality)],[549,302,504,34]),
[iquote('0:Rew:549.0,302.0,504.0,302.0,34.0,302.0')] ).
cnf(633,plain,
( ~ equal(e22,e22)
| skC41 ),
inference(rew,[status(thm),theory(equality)],[632,81]),
[iquote('0:Rew:632.0,81.0')] ).
cnf(634,plain,
skC41,
inference(obv,[status(thm),theory(equality)],[633]),
[iquote('0:Obv:633.0')] ).
cnf(637,plain,
equal(op2(h1(e11),e20),h1(e12)),
inference(rew,[status(thm),theory(equality)],[536,299,504]),
[iquote('0:Rew:536.0,299.0,504.0,299.0')] ).
cnf(640,plain,
( equal(e21,e20)
| equal(h1(e11),e21)
| equal(h3(e10),e22)
| equal(e23,e20) ),
inference(rew,[status(thm),theory(equality)],[34,304,85,536,504]),
[iquote('0:Rew:34.0,304.3,85.0,304.2,536.0,304.1,504.0,304.0')] ).
cnf(641,plain,
( equal(h1(e11),e21)
| equal(h3(e10),e22) ),
inference(mrr,[status(thm)],[640,7,9]),
[iquote('0:MRR:640.0,640.3,7.0,9.0')] ).
cnf(644,plain,
( equal(e11,e10)
| equal(op1(e11,e11),e11)
| equal(op1(e12,e12),e12)
| equal(e13,e10) ),
inference(rew,[status(thm),theory(equality)],[33,306,518]),
[iquote('0:Rew:33.0,306.3,518.0,306.0')] ).
cnf(645,plain,
( equal(op1(e11,e11),e11)
| equal(op1(e12,e12),e12) ),
inference(mrr,[status(thm)],[644,1,3]),
[iquote('0:MRR:644.0,644.3,1.0,3.0')] ).
cnf(646,plain,
( equal(op2(e20,e23),e23)
| equal(e23,e22)
| equal(op2(e22,e23),e23)
| equal(e23,e20) ),
inference(rew,[status(thm),theory(equality)],[34,307,549]),
[iquote('0:Rew:34.0,307.3,549.0,307.1')] ).
cnf(647,plain,
( equal(op2(e20,e23),e23)
| equal(op2(e22,e23),e23) ),
inference(mrr,[status(thm)],[646,12,9]),
[iquote('0:MRR:646.1,646.3,12.0,9.0')] ).
cnf(648,plain,
( equal(e23,e22)
| equal(op2(e23,e21),e22)
| equal(op2(e23,e22),e22)
| equal(e22,e20) ),
inference(rew,[status(thm),theory(equality)],[34,310,578]),
[iquote('0:Rew:34.0,310.3,578.0,310.0')] ).
cnf(649,plain,
( equal(op2(e23,e21),e22)
| equal(op2(e23,e22),e22) ),
inference(mrr,[status(thm)],[648,12,8]),
[iquote('0:MRR:648.0,648.3,12.0,8.0')] ).
cnf(650,plain,
( equal(op2(e20,e23),e21)
| equal(e22,e21)
| equal(op2(e22,e23),e21)
| equal(e21,e20) ),
inference(rew,[status(thm),theory(equality)],[34,311,549]),
[iquote('0:Rew:34.0,311.3,549.0,311.1')] ).
cnf(651,plain,
equal(op2(e22,e23),e21),
inference(mrr,[status(thm)],[650,510,10,7]),
[iquote('0:MRR:650.0,650.1,650.3,510.0,10.0,7.0')] ).
cnf(652,plain,
~ equal(h3(e10),e21),
inference(rew,[status(thm),theory(equality)],[651,475]),
[iquote('0:Rew:651.0,475.0')] ).
cnf(658,plain,
( equal(op2(e20,e23),e23)
| equal(e23,e21) ),
inference(rew,[status(thm),theory(equality)],[651,647]),
[iquote('0:Rew:651.0,647.1')] ).
cnf(661,plain,
equal(op2(e20,e23),e23),
inference(mrr,[status(thm)],[658,11]),
[iquote('0:MRR:658.1,11.0')] ).
cnf(662,plain,
~ equal(op2(e20,e22),e23),
inference(rew,[status(thm),theory(equality)],[661,218]),
[iquote('0:Rew:661.0,218.0')] ).
cnf(668,plain,
( equal(op2(e20,e22),e23)
| equal(op2(e21,e22),e23)
| equal(h3(e10),e23)
| equal(op2(e23,e22),e23) ),
inference(rew,[status(thm),theory(equality)],[85,315]),
[iquote('0:Rew:85.0,315.2')] ).
cnf(669,plain,
equal(op2(e21,e22),e23),
inference(mrr,[status(thm)],[668,662,587,580]),
[iquote('0:MRR:668.0,668.2,668.3,662.0,587.0,580.0')] ).
cnf(676,plain,
( equal(op2(e22,e20),e23)
| equal(op2(e22,e21),e23)
| equal(h3(e10),e23)
| equal(e23,e21) ),
inference(rew,[status(thm),theory(equality)],[651,316,85]),
[iquote('0:Rew:651.0,316.3,85.0,316.2')] ).
cnf(677,plain,
equal(op2(e22,e21),e23),
inference(mrr,[status(thm)],[676,582,587,11]),
[iquote('0:MRR:676.0,676.2,676.3,582.0,587.0,11.0')] ).
cnf(684,plain,
( equal(op2(e20,e22),e22)
| equal(e23,e22)
| equal(h3(e10),e22)
| equal(op2(e23,e22),e22) ),
inference(rew,[status(thm),theory(equality)],[85,317,669]),
[iquote('0:Rew:85.0,317.2,669.0,317.1')] ).
cnf(685,plain,
( equal(op2(e20,e22),e22)
| equal(h3(e10),e22)
| equal(op2(e23,e22),e22) ),
inference(mrr,[status(thm)],[684,12]),
[iquote('0:MRR:684.1,12.0')] ).
cnf(686,plain,
( equal(op2(e22,e20),e22)
| equal(e23,e22)
| equal(h3(e10),e22)
| equal(e22,e21) ),
inference(rew,[status(thm),theory(equality)],[651,318,85,677]),
[iquote('0:Rew:651.0,318.3,85.0,318.2,677.0,318.1')] ).
cnf(687,plain,
( equal(op2(e22,e20),e22)
| equal(h3(e10),e22) ),
inference(mrr,[status(thm)],[686,12,10]),
[iquote('0:MRR:686.1,686.3,12.0,10.0')] ).
cnf(689,plain,
( equal(op2(e20,e22),e21)
| equal(e23,e21)
| equal(h3(e10),e21)
| equal(op2(e23,e22),e21) ),
inference(rew,[status(thm),theory(equality)],[85,319,669]),
[iquote('0:Rew:85.0,319.2,669.0,319.1')] ).
cnf(690,plain,
equal(op2(e23,e22),e21),
inference(mrr,[status(thm)],[689,511,11,652]),
[iquote('0:MRR:689.0,689.1,689.2,511.0,11.0,652.0')] ).
cnf(696,plain,
( equal(op2(e20,e22),e22)
| equal(h3(e10),e22)
| equal(e22,e21) ),
inference(rew,[status(thm),theory(equality)],[690,685]),
[iquote('0:Rew:690.0,685.2')] ).
cnf(697,plain,
( equal(op2(e23,e21),e22)
| equal(e22,e21) ),
inference(rew,[status(thm),theory(equality)],[690,649]),
[iquote('0:Rew:690.0,649.1')] ).
cnf(698,plain,
equal(op2(e23,e21),e22),
inference(mrr,[status(thm)],[697,10]),
[iquote('0:MRR:697.1,10.0')] ).
cnf(703,plain,
( equal(op2(e20,e22),e22)
| equal(h3(e10),e22) ),
inference(mrr,[status(thm)],[696,10]),
[iquote('0:MRR:696.2,10.0')] ).
cnf(704,plain,
( equal(op2(e20,e22),e20)
| equal(e23,e20)
| equal(h3(e10),e20)
| equal(e21,e20) ),
inference(rew,[status(thm),theory(equality)],[690,321,85,669]),
[iquote('0:Rew:690.0,321.3,85.0,321.2,669.0,321.1')] ).
cnf(705,plain,
equal(h3(e10),e20),
inference(mrr,[status(thm)],[704,600,9,7]),
[iquote('0:MRR:704.0,704.1,704.3,600.0,9.0,7.0')] ).
cnf(706,plain,
equal(op2(e22,e22),e20),
inference(rew,[status(thm),theory(equality)],[705,85]),
[iquote('0:Rew:705.0,85.0')] ).
cnf(708,plain,
( equal(op2(e20,e22),e22)
| equal(e22,e20) ),
inference(rew,[status(thm),theory(equality)],[705,703]),
[iquote('0:Rew:705.0,703.1')] ).
cnf(709,plain,
( equal(op2(e22,e20),e22)
| equal(e22,e20) ),
inference(rew,[status(thm),theory(equality)],[705,687]),
[iquote('0:Rew:705.0,687.1')] ).
cnf(710,plain,
( equal(h1(e11),e21)
| equal(e22,e20) ),
inference(rew,[status(thm),theory(equality)],[705,641]),
[iquote('0:Rew:705.0,641.1')] ).
cnf(722,plain,
equal(h1(e11),e21),
inference(mrr,[status(thm)],[710,8]),
[iquote('0:MRR:710.1,8.0')] ).
cnf(724,plain,
equal(op2(e21,e21),e21),
inference(rew,[status(thm),theory(equality)],[722,536]),
[iquote('0:Rew:722.0,536.0')] ).
cnf(731,plain,
equal(op2(e21,e20),h1(e12)),
inference(rew,[status(thm),theory(equality)],[722,637]),
[iquote('0:Rew:722.0,637.0')] ).
cnf(745,plain,
equal(op2(e20,e22),e22),
inference(mrr,[status(thm)],[708,8]),
[iquote('0:MRR:708.1,8.0')] ).
cnf(749,plain,
equal(op2(e22,e20),e22),
inference(mrr,[status(thm)],[709,8]),
[iquote('0:MRR:709.1,8.0')] ).
cnf(754,plain,
( equal(h1(e12),e20)
| equal(e21,e20)
| equal(e23,e20)
| equal(e22,e20) ),
inference(rew,[status(thm),theory(equality)],[549,330,669,724,731]),
[iquote('0:Rew:549.0,330.3,669.0,330.2,724.0,330.1,731.0,330.0')] ).
cnf(755,plain,
equal(h1(e12),e20),
inference(mrr,[status(thm)],[754,7,9,8]),
[iquote('0:MRR:754.1,754.2,754.3,7.0,9.0,8.0')] ).
cnf(756,plain,
equal(op2(e21,e20),e20),
inference(rew,[status(thm),theory(equality)],[755,731]),
[iquote('0:Rew:755.0,731.0')] ).
cnf(760,plain,
( equal(op1(e10,e13),e13)
| equal(e13,e12)
| equal(op1(e12,e13),e13)
| equal(e13,e10) ),
inference(rew,[status(thm),theory(equality)],[33,355,562]),
[iquote('0:Rew:33.0,355.3,562.0,355.1')] ).
cnf(761,plain,
( equal(op1(e10,e13),e13)
| equal(op1(e12,e13),e13) ),
inference(mrr,[status(thm)],[760,6,3]),
[iquote('0:MRR:760.1,760.3,6.0,3.0')] ).
cnf(762,plain,
( equal(e13,e12)
| equal(op1(e13,e11),e12)
| equal(op1(e13,e12),e12)
| equal(e12,e10) ),
inference(rew,[status(thm),theory(equality)],[33,358,609]),
[iquote('0:Rew:33.0,358.3,609.0,358.0')] ).
cnf(763,plain,
( equal(op1(e13,e11),e12)
| equal(op1(e13,e12),e12) ),
inference(mrr,[status(thm)],[762,6,2]),
[iquote('0:MRR:762.0,762.3,6.0,2.0')] ).
cnf(764,plain,
( equal(op1(e10,e13),e11)
| equal(e12,e11)
| equal(op1(e12,e13),e11)
| equal(e11,e10) ),
inference(rew,[status(thm),theory(equality)],[33,359,562]),
[iquote('0:Rew:33.0,359.3,562.0,359.1')] ).
cnf(765,plain,
equal(op1(e12,e13),e11),
inference(mrr,[status(thm)],[764,522,4,1]),
[iquote('0:MRR:764.0,764.1,764.3,522.0,4.0,1.0')] ).
cnf(766,plain,
~ equal(op1(e12,e12),e11),
inference(rew,[status(thm),theory(equality)],[765,182]),
[iquote('0:Rew:765.0,182.0')] ).
cnf(772,plain,
( equal(op1(e10,e13),e13)
| equal(e13,e11) ),
inference(rew,[status(thm),theory(equality)],[765,761]),
[iquote('0:Rew:765.0,761.1')] ).
cnf(775,plain,
equal(op1(e10,e13),e13),
inference(mrr,[status(thm)],[772,5]),
[iquote('0:MRR:772.1,5.0')] ).
cnf(776,plain,
~ equal(op1(e10,e12),e13),
inference(rew,[status(thm),theory(equality)],[775,170]),
[iquote('0:Rew:775.0,170.0')] ).
cnf(782,plain,
equal(op1(e11,e12),e13),
inference(mrr,[status(thm)],[363,776,617,611]),
[iquote('0:MRR:363.0,363.2,363.3,776.0,617.0,611.0')] ).
cnf(789,plain,
( equal(op1(e12,e10),e13)
| equal(op1(e12,e11),e13)
| equal(op1(e12,e12),e13)
| equal(e13,e11) ),
inference(rew,[status(thm),theory(equality)],[765,364]),
[iquote('0:Rew:765.0,364.3')] ).
cnf(790,plain,
equal(op1(e12,e11),e13),
inference(mrr,[status(thm)],[789,613,617,5]),
[iquote('0:MRR:789.0,789.2,789.3,613.0,617.0,5.0')] ).
cnf(797,plain,
( equal(op1(e10,e12),e12)
| equal(e13,e12)
| equal(op1(e12,e12),e12)
| equal(op1(e13,e12),e12) ),
inference(rew,[status(thm),theory(equality)],[782,365]),
[iquote('0:Rew:782.0,365.1')] ).
cnf(798,plain,
( equal(op1(e10,e12),e12)
| equal(op1(e12,e12),e12)
| equal(op1(e13,e12),e12) ),
inference(mrr,[status(thm)],[797,6]),
[iquote('0:MRR:797.1,6.0')] ).
cnf(799,plain,
( equal(op1(e12,e10),e12)
| equal(e13,e12)
| equal(op1(e12,e12),e12)
| equal(e12,e11) ),
inference(rew,[status(thm),theory(equality)],[765,366,790]),
[iquote('0:Rew:765.0,366.3,790.0,366.1')] ).
cnf(800,plain,
( equal(op1(e12,e10),e12)
| equal(op1(e12,e12),e12) ),
inference(mrr,[status(thm)],[799,6,4]),
[iquote('0:MRR:799.1,799.3,6.0,4.0')] ).
cnf(802,plain,
( equal(op1(e10,e12),e11)
| equal(e13,e11)
| equal(op1(e12,e12),e11)
| equal(op1(e13,e12),e11) ),
inference(rew,[status(thm),theory(equality)],[782,367]),
[iquote('0:Rew:782.0,367.1')] ).
cnf(803,plain,
equal(op1(e13,e12),e11),
inference(mrr,[status(thm)],[802,523,5,766]),
[iquote('0:MRR:802.0,802.1,802.2,523.0,5.0,766.0')] ).
cnf(809,plain,
( equal(op1(e10,e12),e12)
| equal(op1(e12,e12),e12)
| equal(e12,e11) ),
inference(rew,[status(thm),theory(equality)],[803,798]),
[iquote('0:Rew:803.0,798.2')] ).
cnf(810,plain,
( equal(op1(e13,e11),e12)
| equal(e12,e11) ),
inference(rew,[status(thm),theory(equality)],[803,763]),
[iquote('0:Rew:803.0,763.1')] ).
cnf(811,plain,
equal(op1(e13,e11),e12),
inference(mrr,[status(thm)],[810,4]),
[iquote('0:MRR:810.1,4.0')] ).
cnf(816,plain,
( equal(op1(e10,e12),e12)
| equal(op1(e12,e12),e12) ),
inference(mrr,[status(thm)],[809,4]),
[iquote('0:MRR:809.2,4.0')] ).
cnf(817,plain,
( equal(op1(e10,e12),e10)
| equal(e13,e10)
| equal(op1(e12,e12),e10)
| equal(e11,e10) ),
inference(rew,[status(thm),theory(equality)],[803,369,782]),
[iquote('0:Rew:803.0,369.3,782.0,369.1')] ).
cnf(818,plain,
equal(op1(e12,e12),e10),
inference(mrr,[status(thm)],[817,626,3,1]),
[iquote('0:MRR:817.0,817.1,817.3,626.0,3.0,1.0')] ).
cnf(819,plain,
( equal(op1(e10,e12),e12)
| equal(e12,e10) ),
inference(rew,[status(thm),theory(equality)],[818,816]),
[iquote('0:Rew:818.0,816.1')] ).
cnf(820,plain,
( equal(op1(e12,e10),e12)
| equal(e12,e10) ),
inference(rew,[status(thm),theory(equality)],[818,800]),
[iquote('0:Rew:818.0,800.1')] ).
cnf(821,plain,
( equal(op1(e11,e11),e11)
| equal(e12,e10) ),
inference(rew,[status(thm),theory(equality)],[818,645]),
[iquote('0:Rew:818.0,645.1')] ).
cnf(826,plain,
equal(op1(e10,e12),e12),
inference(mrr,[status(thm)],[819,2]),
[iquote('0:MRR:819.1,2.0')] ).
cnf(830,plain,
equal(op1(e12,e10),e12),
inference(mrr,[status(thm)],[820,2]),
[iquote('0:MRR:820.1,2.0')] ).
cnf(835,plain,
equal(op1(e11,e11),e11),
inference(mrr,[status(thm)],[821,2]),
[iquote('0:MRR:821.1,2.0')] ).
cnf(843,plain,
( equal(op1(e11,e10),e10)
| equal(e11,e10)
| equal(e13,e10)
| equal(e12,e10) ),
inference(rew,[status(thm),theory(equality)],[562,378,782,835]),
[iquote('0:Rew:562.0,378.3,782.0,378.2,835.0,378.1')] ).
cnf(844,plain,
equal(op1(e11,e10),e10),
inference(mrr,[status(thm)],[843,1,3,2]),
[iquote('0:MRR:843.1,843.2,843.3,1.0,3.0,2.0')] ).
cnf(848,plain,
( ~ equal(e23,e23)
| ~ equal(e21,e21)
| ~ equal(e20,e20)
| ~ equal(e22,e22)
| ~ equal(e23,e23)
| ~ equal(e20,e20)
| ~ equal(e21,e21)
| ~ equal(e23,e23)
| ~ equal(e22,e22)
| ~ equal(e22,e22)
| ~ equal(e23,e23)
| ~ equal(e20,e20)
| ~ equal(e21,e21)
| ~ equal(e23,e23)
| ~ equal(e22,e22)
| ~ equal(e21,e21)
| ~ equal(e20,e20)
| ~ skC39
| ~ skC40
| ~ skC41 ),
inference(rew,[status(thm),theory(equality)],[34,405,32,421,33,690,632,529,803,698,811,578,609,651,765,706,818,677,790,749,830,549,562,669,782,724,835,756,844,661,775,745,826,598,624,504,518]),
[iquote('0:Rew:34.0,405.16,32.0,405.16,421.0,405.16,33.0,405.16,690.0,405.15,32.0,405.15,632.0,405.15,529.0,405.15,803.0,405.15,698.0,405.14,32.0,405.14,529.0,405.14,632.0,405.14,811.0,405.14,578.0,405.13,421.0,405.13,32.0,405.13,609.0,405.13,651.0,405.12,632.0,405.12,32.0,405.12,529.0,405.12,765.0,405.12,706.0,405.11,632.0,405.11,421.0,405.11,818.0,405.11,677.0,405.10,632.0,405.10,529.0,405.10,32.0,405.10,790.0,405.10,749.0,405.9,421.0,405.9,632.0,405.9,830.0,405.9,549.0,405.8,529.0,405.8,32.0,405.8,632.0,405.8,562.0,405.8,669.0,405.7,529.0,405.7,632.0,405.7,32.0,405.7,782.0,405.7,724.0,405.6,529.0,405.6,835.0,405.6,756.0,405.5,529.0,405.5,421.0,405.5,844.0,405.5,661.0,405.4,421.0,405.4,32.0,405.4,775.0,405.4,745.0,405.3,421.0,405.3,632.0,405.3,826.0,405.3,598.0,405.2,529.0,405.2,421.0,405.2,624.0,405.2,504.0,405.1,421.0,405.1,529.0,405.1,518.0,405.1,32.0,405.0')] ).
cnf(849,plain,
( ~ skC39
| ~ skC40
| ~ skC41 ),
inference(obv,[status(thm),theory(equality)],[848]),
[iquote('0:Obv:848.16')] ).
cnf(850,plain,
$false,
inference(mrr,[status(thm)],[849,428,532,634]),
[iquote('0:MRR:849.0,849.1,849.2,428.0,532.0,634.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ALG121+1 : TPTP v8.1.0. Released v2.7.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.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 00:55:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.52
% 0.19/0.52 SPASS V 3.9
% 0.19/0.52 SPASS beiseite: Proof found.
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.52 SPASS derived 228 clauses, backtracked 0 clauses, performed 0 splits and kept 405 clauses.
% 0.19/0.52 SPASS allocated 86328 KBytes.
% 0.19/0.52 SPASS spent 0:00:00.18 on the problem.
% 0.19/0.52 0:00:00.04 for the input.
% 0.19/0.52 0:00:00.09 for the FLOTTER CNF translation.
% 0.19/0.52 0:00:00.00 for inferences.
% 0.19/0.52 0:00:00.00 for the backtracking.
% 0.19/0.52 0:00:00.02 for the reduction.
% 0.19/0.52
% 0.19/0.52
% 0.19/0.52 Here is a proof with depth 0, length 196 :
% 0.19/0.52 % SZS output start Refutation
% See solution above
% 0.19/0.53 Formulae used in the proof : ax7 ax8 ax17 ax12 ax13 co1 ax14 ax15 ax16 ax5 ax6 ax10 ax11 ax4 ax2
% 0.19/0.53
%------------------------------------------------------------------------------