TSTP Solution File: ALG028+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ALG028+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n021.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 18:02:01 EDT 2022

% Result   : Theorem 0.20s 0.57s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   42
% Syntax   : Number of clauses     :  126 ( 121 unt;   2 nHn; 126 RR)
%            Number of literals    :  184 (   0 equ;  66 neg)
%            Maximal clause size   :   21 (   1 avg)
%            Maximal term depth    :    5 (   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(35,axiom,
    equal(op(e4,e4),e3),
    file('ALG028+1.p',unknown),
    [] ).

cnf(64,axiom,
    equal(op(e1,e0),op(e0,e1)),
    file('ALG028+1.p',unknown),
    [] ).

cnf(65,axiom,
    equal(op(e2,e0),op(e0,e2)),
    file('ALG028+1.p',unknown),
    [] ).

cnf(66,axiom,
    equal(op(e3,e0),op(e0,e3)),
    file('ALG028+1.p',unknown),
    [] ).

cnf(67,axiom,
    equal(op(e4,e0),op(e0,e4)),
    file('ALG028+1.p',unknown),
    [] ).

cnf(68,axiom,
    equal(op(e5,e0),op(e0,e5)),
    file('ALG028+1.p',unknown),
    [] ).

cnf(70,axiom,
    equal(op(e2,e1),op(e1,e2)),
    file('ALG028+1.p',unknown),
    [] ).

cnf(71,axiom,
    equal(op(e3,e1),op(e1,e3)),
    file('ALG028+1.p',unknown),
    [] ).

cnf(72,axiom,
    equal(op(e4,e1),op(e1,e4)),
    file('ALG028+1.p',unknown),
    [] ).

cnf(73,axiom,
    equal(op(e5,e1),op(e1,e5)),
    file('ALG028+1.p',unknown),
    [] ).

cnf(75,axiom,
    equal(op(e3,e2),op(e2,e3)),
    file('ALG028+1.p',unknown),
    [] ).

cnf(76,axiom,
    equal(op(e4,e2),op(e2,e4)),
    file('ALG028+1.p',unknown),
    [] ).

cnf(77,axiom,
    equal(op(e5,e2),op(e2,e5)),
    file('ALG028+1.p',unknown),
    [] ).

cnf(79,axiom,
    equal(op(e4,e3),op(e3,e4)),
    file('ALG028+1.p',unknown),
    [] ).

cnf(80,axiom,
    equal(op(e5,e3),op(e3,e5)),
    file('ALG028+1.p',unknown),
    [] ).

cnf(82,axiom,
    equal(op(e5,e4),op(e4,e5)),
    file('ALG028+1.p',unknown),
    [] ).

cnf(84,axiom,
    equal(op(op(e4,e4),e4),e1),
    file('ALG028+1.p',unknown),
    [] ).

cnf(235,axiom,
    ~ equal(op(e4,e1),op(e4,e0)),
    file('ALG028+1.p',unknown),
    [] ).

cnf(236,axiom,
    ~ equal(op(e4,e2),op(e4,e0)),
    file('ALG028+1.p',unknown),
    [] ).

cnf(237,axiom,
    ~ equal(op(e4,e3),op(e4,e0)),
    file('ALG028+1.p',unknown),
    [] ).

cnf(238,axiom,
    ~ equal(op(e4,e4),op(e4,e0)),
    file('ALG028+1.p',unknown),
    [] ).

cnf(239,axiom,
    ~ equal(op(e4,e5),op(e4,e0)),
    file('ALG028+1.p',unknown),
    [] ).

cnf(295,axiom,
    equal(op(op(op(e4,e4),e4),e4),e2),
    file('ALG028+1.p',unknown),
    [] ).

cnf(441,axiom,
    equal(op(op(e4,e0),e1),op(e4,op(e0,e1))),
    file('ALG028+1.p',unknown),
    [] ).

cnf(442,axiom,
    equal(op(op(e4,e0),e2),op(e4,op(e0,e2))),
    file('ALG028+1.p',unknown),
    [] ).

cnf(443,axiom,
    equal(op(op(e4,e0),e3),op(e4,op(e0,e3))),
    file('ALG028+1.p',unknown),
    [] ).

cnf(446,axiom,
    equal(op(op(e4,e1),e0),op(e4,op(e1,e0))),
    file('ALG028+1.p',unknown),
    [] ).

cnf(452,axiom,
    equal(op(op(e4,e2),e0),op(e4,op(e2,e0))),
    file('ALG028+1.p',unknown),
    [] ).

cnf(458,axiom,
    equal(op(op(e4,e3),e0),op(e4,op(e3,e0))),
    file('ALG028+1.p',unknown),
    [] ).

cnf(459,axiom,
    equal(op(op(e4,e3),e1),op(e4,op(e3,e1))),
    file('ALG028+1.p',unknown),
    [] ).

cnf(460,axiom,
    equal(op(op(e4,e3),e2),op(e4,op(e3,e2))),
    file('ALG028+1.p',unknown),
    [] ).

cnf(464,axiom,
    equal(op(op(e4,e4),e0),op(e4,op(e4,e0))),
    file('ALG028+1.p',unknown),
    [] ).

cnf(465,axiom,
    equal(op(op(e4,e4),e1),op(e4,op(e4,e1))),
    file('ALG028+1.p',unknown),
    [] ).

cnf(466,axiom,
    equal(op(op(e4,e4),e2),op(e4,op(e4,e2))),
    file('ALG028+1.p',unknown),
    [] ).

cnf(474,axiom,
    equal(op(op(e4,e5),e4),op(e4,op(e5,e4))),
    file('ALG028+1.p',unknown),
    [] ).

cnf(501,axiom,
    equal(op(op(e5,e4),e1),op(e5,op(e4,e1))),
    file('ALG028+1.p',unknown),
    [] ).

cnf(503,axiom,
    equal(op(op(e5,e4),e3),op(e5,op(e4,e3))),
    file('ALG028+1.p',unknown),
    [] ).

cnf(504,axiom,
    equal(op(op(e5,e4),e4),op(e5,op(e4,e4))),
    file('ALG028+1.p',unknown),
    [] ).

cnf(512,axiom,
    equal(op(op(op(op(e4,e4),e4),e4),e4),e5),
    file('ALG028+1.p',unknown),
    [] ).

cnf(513,axiom,
    equal(op(op(op(op(e4,e4),e4),e4),op(e4,e4)),e0),
    file('ALG028+1.p',unknown),
    [] ).

cnf(523,axiom,
    ( equal(op(e5,e3),e0)
    | equal(op(e5,e3),e1)
    | equal(op(e5,e3),e2)
    | equal(op(e5,e3),e3)
    | equal(op(e5,e3),e4)
    | equal(op(e5,e3),e5) ),
    file('ALG028+1.p',unknown),
    [] ).

cnf(557,axiom,
    ( ~ equal(op(e0,e0),op(e0,e0))
    | ~ equal(op(e1,e0),op(e0,e1))
    | ~ equal(op(e2,e0),op(e0,e2))
    | ~ equal(op(e3,e0),op(e0,e3))
    | ~ equal(op(e4,e0),op(e0,e4))
    | ~ equal(op(e5,e0),op(e0,e5))
    | ~ equal(op(e1,e1),op(e1,e1))
    | ~ equal(op(e2,e1),op(e1,e2))
    | ~ equal(op(e3,e1),op(e1,e3))
    | ~ equal(op(e4,e1),op(e1,e4))
    | ~ equal(op(e5,e1),op(e1,e5))
    | ~ equal(op(e2,e2),op(e2,e2))
    | ~ equal(op(e3,e2),op(e2,e3))
    | ~ equal(op(e4,e2),op(e2,e4))
    | ~ equal(op(e5,e2),op(e2,e5))
    | ~ equal(op(e3,e3),op(e3,e3))
    | ~ equal(op(e4,e3),op(e3,e4))
    | ~ equal(op(e5,e3),op(e3,e5))
    | ~ equal(op(e4,e4),op(e4,e4))
    | ~ equal(op(e5,e4),op(e4,e5))
    | ~ equal(op(e5,e5),op(e5,e5)) ),
    file('ALG028+1.p',unknown),
    [] ).

cnf(558,plain,
    equal(op(e3,e4),e1),
    inference(rew,[status(thm),theory(equality)],[35,84]),
    [iquote('0:Rew:35.0,84.0')] ).

cnf(559,plain,
    equal(op(e4,e3),e1),
    inference(rew,[status(thm),theory(equality)],[558,79]),
    [iquote('0:Rew:558.0,79.0')] ).

cnf(585,plain,
    ~ equal(op(e4,e5),op(e0,e4)),
    inference(rew,[status(thm),theory(equality)],[67,239]),
    [iquote('0:Rew:67.0,239.0')] ).

cnf(586,plain,
    ~ equal(op(e0,e4),e3),
    inference(rew,[status(thm),theory(equality)],[35,238,67]),
    [iquote('0:Rew:35.0,238.0,67.0,238.0')] ).

cnf(587,plain,
    ~ equal(op(e0,e4),e1),
    inference(rew,[status(thm),theory(equality)],[559,237,67]),
    [iquote('0:Rew:559.0,237.0,67.0,237.0')] ).

cnf(588,plain,
    ~ equal(op(e2,e4),op(e0,e4)),
    inference(rew,[status(thm),theory(equality)],[76,236,67]),
    [iquote('0:Rew:76.0,236.0,67.0,236.0')] ).

cnf(589,plain,
    ~ equal(op(e1,e4),op(e0,e4)),
    inference(rew,[status(thm),theory(equality)],[72,235,67]),
    [iquote('0:Rew:72.0,235.0,67.0,235.0')] ).

cnf(680,plain,
    equal(op(e1,e4),e2),
    inference(rew,[status(thm),theory(equality)],[558,295,35]),
    [iquote('0:Rew:558.0,295.0,35.0,295.0')] ).

cnf(681,plain,
    equal(op(e4,e1),e2),
    inference(rew,[status(thm),theory(equality)],[680,72]),
    [iquote('0:Rew:680.0,72.0')] ).

cnf(686,plain,
    ~ equal(op(e0,e4),e2),
    inference(rew,[status(thm),theory(equality)],[680,589]),
    [iquote('0:Rew:680.0,589.0')] ).

cnf(692,plain,
    equal(op(e2,e4),e5),
    inference(rew,[status(thm),theory(equality)],[680,512,558,35]),
    [iquote('0:Rew:680.0,512.0,558.0,512.0,35.0,512.0')] ).

cnf(693,plain,
    equal(op(e4,e2),e5),
    inference(rew,[status(thm),theory(equality)],[692,76]),
    [iquote('0:Rew:692.0,76.0')] ).

cnf(697,plain,
    ~ equal(op(e0,e4),e5),
    inference(rew,[status(thm),theory(equality)],[692,588]),
    [iquote('0:Rew:692.0,588.0')] ).

cnf(710,plain,
    equal(op(op(e4,e5),e4),op(e3,e5)),
    inference(rew,[status(thm),theory(equality)],[82,504,80,35]),
    [iquote('0:Rew:82.0,504.0,80.0,504.0,35.0,504.0')] ).

cnf(711,plain,
    equal(op(op(e4,e5),e3),op(e1,e5)),
    inference(rew,[status(thm),theory(equality)],[82,503,73,559]),
    [iquote('0:Rew:82.0,503.0,73.0,503.0,559.0,503.0')] ).

cnf(713,plain,
    equal(op(op(e4,e5),e1),op(e2,e5)),
    inference(rew,[status(thm),theory(equality)],[82,501,77,681]),
    [iquote('0:Rew:82.0,501.0,77.0,501.0,681.0,501.0')] ).

cnf(742,plain,
    equal(op(e4,op(e4,e5)),op(e3,e5)),
    inference(rew,[status(thm),theory(equality)],[710,474,82]),
    [iquote('0:Rew:710.0,474.0,82.0,474.0')] ).

cnf(759,plain,
    equal(op(e4,e5),op(e2,e3)),
    inference(rew,[status(thm),theory(equality)],[75,466,35,693]),
    [iquote('0:Rew:75.0,466.0,35.0,466.0,693.0,466.0')] ).

cnf(760,plain,
    equal(op(e5,e4),op(e2,e3)),
    inference(rew,[status(thm),theory(equality)],[759,82]),
    [iquote('0:Rew:759.0,82.0')] ).

cnf(768,plain,
    ~ equal(op(e2,e3),op(e0,e4)),
    inference(rew,[status(thm),theory(equality)],[759,585]),
    [iquote('0:Rew:759.0,585.0')] ).

cnf(771,plain,
    equal(op(op(e2,e3),e4),op(e3,e5)),
    inference(rew,[status(thm),theory(equality)],[759,710]),
    [iquote('0:Rew:759.0,710.0')] ).

cnf(772,plain,
    equal(op(op(e2,e3),e3),op(e1,e5)),
    inference(rew,[status(thm),theory(equality)],[759,711]),
    [iquote('0:Rew:759.0,711.0')] ).

cnf(774,plain,
    equal(op(op(e2,e3),e1),op(e2,e5)),
    inference(rew,[status(thm),theory(equality)],[759,713]),
    [iquote('0:Rew:759.0,713.0')] ).

cnf(776,plain,
    equal(op(e4,op(e2,e3)),op(e3,e5)),
    inference(rew,[status(thm),theory(equality)],[759,742]),
    [iquote('0:Rew:759.0,742.0')] ).

cnf(777,plain,
    equal(op(e1,e3),e5),
    inference(rew,[status(thm),theory(equality)],[71,465,35,693,681]),
    [iquote('0:Rew:71.0,465.0,35.0,465.0,693.0,465.0,681.0,465.0')] ).

cnf(778,plain,
    equal(op(e3,e1),e5),
    inference(rew,[status(thm),theory(equality)],[777,71]),
    [iquote('0:Rew:777.0,71.0')] ).

cnf(790,plain,
    equal(op(e4,op(e0,e4)),op(e0,e3)),
    inference(rew,[status(thm),theory(equality)],[66,464,35,67]),
    [iquote('0:Rew:66.0,464.0,35.0,464.0,67.0,464.0')] ).

cnf(794,plain,
    equal(op(e3,e5),op(e1,e2)),
    inference(rew,[status(thm),theory(equality)],[559,460,776,75]),
    [iquote('0:Rew:559.0,460.0,776.0,460.0,75.0,460.0')] ).

cnf(795,plain,
    equal(op(e5,e3),op(e1,e2)),
    inference(rew,[status(thm),theory(equality)],[794,80]),
    [iquote('0:Rew:794.0,80.0')] ).

cnf(811,plain,
    equal(op(op(e2,e3),e4),op(e1,e2)),
    inference(rew,[status(thm),theory(equality)],[794,771]),
    [iquote('0:Rew:794.0,771.0')] ).

cnf(815,plain,
    equal(op(e2,e3),op(e1,e1)),
    inference(rew,[status(thm),theory(equality)],[559,459,759,778]),
    [iquote('0:Rew:559.0,459.0,759.0,459.0,778.0,459.0')] ).

cnf(816,plain,
    equal(op(e3,e2),op(e1,e1)),
    inference(rew,[status(thm),theory(equality)],[815,75]),
    [iquote('0:Rew:815.0,75.0')] ).

cnf(826,plain,
    equal(op(e4,e5),op(e1,e1)),
    inference(rew,[status(thm),theory(equality)],[815,759]),
    [iquote('0:Rew:815.0,759.0')] ).

cnf(828,plain,
    equal(op(e5,e4),op(e1,e1)),
    inference(rew,[status(thm),theory(equality)],[815,760]),
    [iquote('0:Rew:815.0,760.0')] ).

cnf(832,plain,
    ~ equal(op(e1,e1),op(e0,e4)),
    inference(rew,[status(thm),theory(equality)],[815,768]),
    [iquote('0:Rew:815.0,768.0')] ).

cnf(833,plain,
    equal(op(op(e1,e1),e3),op(e1,e5)),
    inference(rew,[status(thm),theory(equality)],[815,772]),
    [iquote('0:Rew:815.0,772.0')] ).

cnf(835,plain,
    equal(op(op(e1,e1),e1),op(e2,e5)),
    inference(rew,[status(thm),theory(equality)],[815,774]),
    [iquote('0:Rew:815.0,774.0')] ).

cnf(836,plain,
    equal(op(op(e1,e1),e4),op(e1,e2)),
    inference(rew,[status(thm),theory(equality)],[815,811]),
    [iquote('0:Rew:815.0,811.0')] ).

cnf(838,plain,
    equal(op(e4,op(e0,e3)),op(e0,e1)),
    inference(rew,[status(thm),theory(equality)],[64,458,559,66]),
    [iquote('0:Rew:64.0,458.0,559.0,458.0,66.0,458.0')] ).

cnf(844,plain,
    equal(op(e4,op(e0,e2)),op(e0,e5)),
    inference(rew,[status(thm),theory(equality)],[68,452,693,65]),
    [iquote('0:Rew:68.0,452.0,693.0,452.0,65.0,452.0')] ).

cnf(857,plain,
    equal(op(e4,op(e0,e1)),op(e0,e2)),
    inference(rew,[status(thm),theory(equality)],[65,446,681,64]),
    [iquote('0:Rew:65.0,446.0,681.0,446.0,64.0,446.0')] ).

cnf(860,plain,
    equal(op(op(e0,e4),e3),op(e0,e1)),
    inference(rew,[status(thm),theory(equality)],[67,443,838]),
    [iquote('0:Rew:67.0,443.0,838.0,443.0')] ).

cnf(861,plain,
    equal(op(op(e0,e4),e2),op(e0,e5)),
    inference(rew,[status(thm),theory(equality)],[67,442,844]),
    [iquote('0:Rew:67.0,442.0,844.0,442.0')] ).

cnf(862,plain,
    equal(op(op(e0,e4),e1),op(e0,e2)),
    inference(rew,[status(thm),theory(equality)],[67,441,857]),
    [iquote('0:Rew:67.0,441.0,857.0,441.0')] ).

cnf(1077,plain,
    equal(op(e1,e1),e0),
    inference(rew,[status(thm),theory(equality)],[815,513,680,558,35]),
    [iquote('0:Rew:815.0,513.0,680.0,513.0,558.0,513.0,35.0,513.0')] ).

cnf(1083,plain,
    equal(op(e2,e3),e0),
    inference(rew,[status(thm),theory(equality)],[1077,815]),
    [iquote('0:Rew:1077.0,815.0')] ).

cnf(1086,plain,
    equal(op(e3,e2),e0),
    inference(rew,[status(thm),theory(equality)],[1077,816]),
    [iquote('0:Rew:1077.0,816.0')] ).

cnf(1087,plain,
    equal(op(e4,e5),e0),
    inference(rew,[status(thm),theory(equality)],[1077,826]),
    [iquote('0:Rew:1077.0,826.0')] ).

cnf(1088,plain,
    equal(op(e5,e4),e0),
    inference(rew,[status(thm),theory(equality)],[1077,828]),
    [iquote('0:Rew:1077.0,828.0')] ).

cnf(1094,plain,
    ~ equal(op(e0,e4),e0),
    inference(rew,[status(thm),theory(equality)],[1077,832]),
    [iquote('0:Rew:1077.0,832.0')] ).

cnf(1095,plain,
    equal(op(e1,e5),op(e0,e3)),
    inference(rew,[status(thm),theory(equality)],[1077,833]),
    [iquote('0:Rew:1077.0,833.0')] ).

cnf(1097,plain,
    equal(op(e2,e5),op(e0,e1)),
    inference(rew,[status(thm),theory(equality)],[1077,835]),
    [iquote('0:Rew:1077.0,835.0')] ).

cnf(1098,plain,
    equal(op(e1,e2),op(e0,e4)),
    inference(rew,[status(thm),theory(equality)],[1077,836]),
    [iquote('0:Rew:1077.0,836.0')] ).

cnf(1116,plain,
    equal(op(e5,e1),op(e0,e3)),
    inference(rew,[status(thm),theory(equality)],[1095,73]),
    [iquote('0:Rew:1095.0,73.0')] ).

cnf(1171,plain,
    equal(op(e5,e2),op(e0,e1)),
    inference(rew,[status(thm),theory(equality)],[1097,77]),
    [iquote('0:Rew:1097.0,77.0')] ).

cnf(1187,plain,
    equal(op(e2,e1),op(e0,e4)),
    inference(rew,[status(thm),theory(equality)],[1098,70]),
    [iquote('0:Rew:1098.0,70.0')] ).

cnf(1192,plain,
    equal(op(e3,e5),op(e0,e4)),
    inference(rew,[status(thm),theory(equality)],[1098,794]),
    [iquote('0:Rew:1098.0,794.0')] ).

cnf(1194,plain,
    equal(op(e5,e3),op(e0,e4)),
    inference(rew,[status(thm),theory(equality)],[1098,795]),
    [iquote('0:Rew:1098.0,795.0')] ).

cnf(1261,plain,
    ( equal(op(e0,e4),e0)
    | equal(op(e0,e4),e1)
    | equal(op(e0,e4),e2)
    | equal(op(e0,e4),e3)
    | equal(op(e0,e4),e4)
    | equal(op(e0,e4),e5) ),
    inference(rew,[status(thm),theory(equality)],[1194,523]),
    [iquote('0:Rew:1194.0,523.5,1194.0,523.4,1194.0,523.3,1194.0,523.2,1194.0,523.1,1194.0,523.0')] ).

cnf(1262,plain,
    equal(op(e0,e4),e4),
    inference(mrr,[status(thm)],[1261,1094,587,686,586,697]),
    [iquote('0:MRR:1261.0,1261.1,1261.2,1261.3,1261.5,1094.0,587.0,686.0,586.0,697.0')] ).

cnf(1263,plain,
    equal(op(e4,e0),e4),
    inference(rew,[status(thm),theory(equality)],[1262,67]),
    [iquote('0:Rew:1262.0,67.0')] ).

cnf(1273,plain,
    equal(op(e4,e4),op(e0,e3)),
    inference(rew,[status(thm),theory(equality)],[1262,790]),
    [iquote('0:Rew:1262.0,790.0')] ).

cnf(1275,plain,
    equal(op(e4,e3),op(e0,e1)),
    inference(rew,[status(thm),theory(equality)],[1262,860]),
    [iquote('0:Rew:1262.0,860.0')] ).

cnf(1276,plain,
    equal(op(e4,e2),op(e0,e5)),
    inference(rew,[status(thm),theory(equality)],[1262,861]),
    [iquote('0:Rew:1262.0,861.0')] ).

cnf(1277,plain,
    equal(op(e4,e1),op(e0,e2)),
    inference(rew,[status(thm),theory(equality)],[1262,862]),
    [iquote('0:Rew:1262.0,862.0')] ).

cnf(1293,plain,
    equal(op(e1,e2),e4),
    inference(rew,[status(thm),theory(equality)],[1262,1098]),
    [iquote('0:Rew:1262.0,1098.0')] ).

cnf(1294,plain,
    equal(op(e2,e1),e4),
    inference(rew,[status(thm),theory(equality)],[1262,1187]),
    [iquote('0:Rew:1262.0,1187.0')] ).

cnf(1295,plain,
    equal(op(e3,e5),e4),
    inference(rew,[status(thm),theory(equality)],[1262,1192]),
    [iquote('0:Rew:1262.0,1192.0')] ).

cnf(1296,plain,
    equal(op(e5,e3),e4),
    inference(rew,[status(thm),theory(equality)],[1262,1194]),
    [iquote('0:Rew:1262.0,1194.0')] ).

cnf(1300,plain,
    equal(op(e0,e3),e3),
    inference(rew,[status(thm),theory(equality)],[35,1273]),
    [iquote('0:Rew:35.0,1273.0')] ).

cnf(1301,plain,
    equal(op(e3,e0),e3),
    inference(rew,[status(thm),theory(equality)],[1300,66]),
    [iquote('0:Rew:1300.0,66.0')] ).

cnf(1325,plain,
    equal(op(e1,e5),e3),
    inference(rew,[status(thm),theory(equality)],[1300,1095]),
    [iquote('0:Rew:1300.0,1095.0')] ).

cnf(1326,plain,
    equal(op(e5,e1),e3),
    inference(rew,[status(thm),theory(equality)],[1300,1116]),
    [iquote('0:Rew:1300.0,1116.0')] ).

cnf(1332,plain,
    equal(op(e0,e1),e1),
    inference(rew,[status(thm),theory(equality)],[559,1275]),
    [iquote('0:Rew:559.0,1275.0')] ).

cnf(1333,plain,
    equal(op(e1,e0),e1),
    inference(rew,[status(thm),theory(equality)],[1332,64]),
    [iquote('0:Rew:1332.0,64.0')] ).

cnf(1351,plain,
    equal(op(e2,e5),e1),
    inference(rew,[status(thm),theory(equality)],[1332,1097]),
    [iquote('0:Rew:1332.0,1097.0')] ).

cnf(1352,plain,
    equal(op(e5,e2),e1),
    inference(rew,[status(thm),theory(equality)],[1332,1171]),
    [iquote('0:Rew:1332.0,1171.0')] ).

cnf(1357,plain,
    equal(op(e0,e5),e5),
    inference(rew,[status(thm),theory(equality)],[693,1276]),
    [iquote('0:Rew:693.0,1276.0')] ).

cnf(1358,plain,
    equal(op(e5,e0),e5),
    inference(rew,[status(thm),theory(equality)],[1357,68]),
    [iquote('0:Rew:1357.0,68.0')] ).

cnf(1374,plain,
    equal(op(e0,e2),e2),
    inference(rew,[status(thm),theory(equality)],[681,1277]),
    [iquote('0:Rew:681.0,1277.0')] ).

cnf(1375,plain,
    equal(op(e2,e0),e2),
    inference(rew,[status(thm),theory(equality)],[1374,65]),
    [iquote('0:Rew:1374.0,65.0')] ).

cnf(1454,plain,
    ( ~ equal(op(e1,e0),op(e0,e1))
    | ~ equal(op(e2,e0),op(e0,e2))
    | ~ equal(op(e3,e0),op(e0,e3))
    | ~ equal(op(e4,e0),op(e0,e4))
    | ~ equal(op(e5,e0),op(e0,e5))
    | ~ equal(op(e2,e1),op(e1,e2))
    | ~ equal(op(e3,e1),op(e1,e3))
    | ~ equal(op(e4,e1),op(e1,e4))
    | ~ equal(op(e5,e1),op(e1,e5))
    | ~ equal(op(e3,e2),op(e2,e3))
    | ~ equal(op(e4,e2),op(e2,e4))
    | ~ equal(op(e5,e2),op(e2,e5))
    | ~ equal(op(e4,e3),op(e3,e4))
    | ~ equal(op(e5,e3),op(e3,e5))
    | ~ equal(op(e5,e4),op(e4,e5)) ),
    inference(obv,[status(thm),theory(equality)],[557]),
    [iquote('0:Obv:557.20')] ).

cnf(1455,plain,
    ( ~ equal(e1,e1)
    | ~ equal(e2,e2)
    | ~ equal(e3,e3)
    | ~ equal(e4,e4)
    | ~ equal(e5,e5)
    | ~ equal(e4,e4)
    | ~ equal(e5,e5)
    | ~ equal(e2,e2)
    | ~ equal(e3,e3)
    | ~ equal(e0,e0)
    | ~ equal(e5,e5)
    | ~ equal(e1,e1)
    | ~ equal(e1,e1)
    | ~ equal(e4,e4)
    | ~ equal(e0,e0) ),
    inference(rew,[status(thm),theory(equality)],[1088,1454,1087,1296,1295,559,558,1352,1351,693,692,1086,1083,1326,1325,681,680,778,777,1294,1293,1358,1357,1263,1262,1301,1300,1375,1374,1333,1332]),
    [iquote('0:Rew:1088.0,1454.14,1087.0,1454.14,1296.0,1454.13,1295.0,1454.13,559.0,1454.12,558.0,1454.12,1352.0,1454.11,1351.0,1454.11,693.0,1454.10,692.0,1454.10,1086.0,1454.9,1083.0,1454.9,1326.0,1454.8,1325.0,1454.8,681.0,1454.7,680.0,1454.7,778.0,1454.6,777.0,1454.6,1294.0,1454.5,1293.0,1454.5,1358.0,1454.4,1357.0,1454.4,1263.0,1454.3,1262.0,1454.3,1301.0,1454.2,1300.0,1454.2,1375.0,1454.1,1374.0,1454.1,1333.0,1454.0,1332.0,1454.0')] ).

cnf(1456,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[1455]),
    [iquote('0:Obv:1455.14')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ALG028+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n021.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 07:29:22 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.57  
% 0.20/0.57  SPASS V 3.9 
% 0.20/0.57  SPASS beiseite: Proof found.
% 0.20/0.57  % SZS status Theorem
% 0.20/0.57  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.57  SPASS derived 425 clauses, backtracked 0 clauses, performed 0 splits and kept 560 clauses.
% 0.20/0.57  SPASS allocated 87017 KBytes.
% 0.20/0.57  SPASS spent	0:00:00.22 on the problem.
% 0.20/0.57  		0:00:00.04 for the input.
% 0.20/0.57  		0:00:00.11 for the FLOTTER CNF translation.
% 0.20/0.57  		0:00:00.00 for inferences.
% 0.20/0.57  		0:00:00.00 for the backtracking.
% 0.20/0.57  		0:00:00.04 for the reduction.
% 0.20/0.57  
% 0.20/0.57  
% 0.20/0.57  Here is a proof with depth 0, length 126 :
% 0.20/0.57  % SZS output start Refutation
% See solution above
% 0.20/0.57  Formulae used in the proof : ax11 co1 ax9 ax2 ax1
% 0.20/0.57  
%------------------------------------------------------------------------------