TSTP Solution File: ALG045+1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ALG045+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n017.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 18:02:06 EDT 2022

% Result   : Unsatisfiable 0.19s 0.48s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   49
% Syntax   : Number of clauses     :  155 (  93 unt;  22 nHn; 155 RR)
%            Number of literals    :  255 (   0 equ; 115 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   4 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ equal(e1,e0),
    file('ALG045+1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(e2,e0),
    file('ALG045+1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(e3,e0),
    file('ALG045+1.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(e2,e1),
    file('ALG045+1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(e3,e1),
    file('ALG045+1.p',unknown),
    [] ).

cnf(6,axiom,
    ~ equal(e3,e2),
    file('ALG045+1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(op(unit,e0),e0),
    file('ALG045+1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(op(e0,unit),e0),
    file('ALG045+1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(op(unit,e1),e1),
    file('ALG045+1.p',unknown),
    [] ).

cnf(10,axiom,
    equal(op(e1,unit),e1),
    file('ALG045+1.p',unknown),
    [] ).

cnf(11,axiom,
    equal(op(unit,e2),e2),
    file('ALG045+1.p',unknown),
    [] ).

cnf(12,axiom,
    equal(op(e2,unit),e2),
    file('ALG045+1.p',unknown),
    [] ).

cnf(13,axiom,
    equal(op(unit,e3),e3),
    file('ALG045+1.p',unknown),
    [] ).

cnf(14,axiom,
    equal(op(e3,unit),e3),
    file('ALG045+1.p',unknown),
    [] ).

cnf(16,axiom,
    ( ~ skC0
    | equal(op(e1,e1),e0) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ skC0
    | equal(op(e2,e2),e0) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(18,axiom,
    ( ~ skC0
    | equal(op(e3,e3),e0) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ skC1
    | equal(op(e0,e0),e1) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(21,axiom,
    ( ~ skC1
    | equal(op(e2,e2),e1) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ skC1
    | equal(op(e3,e3),e1) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(23,axiom,
    ( ~ skC2
    | equal(op(e0,e0),e2) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(24,axiom,
    ( ~ skC2
    | equal(op(e1,e1),e2) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ skC2
    | equal(op(e3,e3),e2) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(30,axiom,
    ~ equal(op(e2,e0),op(e1,e0)),
    file('ALG045+1.p',unknown),
    [] ).

cnf(38,axiom,
    ~ equal(op(e3,e1),op(e2,e1)),
    file('ALG045+1.p',unknown),
    [] ).

cnf(41,axiom,
    ~ equal(op(e3,e2),op(e0,e2)),
    file('ALG045+1.p',unknown),
    [] ).

cnf(44,axiom,
    ~ equal(op(e3,e2),op(e2,e2)),
    file('ALG045+1.p',unknown),
    [] ).

cnf(46,axiom,
    ~ equal(op(e2,e3),op(e0,e3)),
    file('ALG045+1.p',unknown),
    [] ).

cnf(47,axiom,
    ~ equal(op(e3,e3),op(e0,e3)),
    file('ALG045+1.p',unknown),
    [] ).

cnf(49,axiom,
    ~ equal(op(e3,e3),op(e1,e3)),
    file('ALG045+1.p',unknown),
    [] ).

cnf(56,axiom,
    ~ equal(op(e0,e3),op(e0,e2)),
    file('ALG045+1.p',unknown),
    [] ).

cnf(63,axiom,
    ~ equal(op(e2,e1),op(e2,e0)),
    file('ALG045+1.p',unknown),
    [] ).

cnf(64,axiom,
    ~ equal(op(e2,e2),op(e2,e0)),
    file('ALG045+1.p',unknown),
    [] ).

cnf(66,axiom,
    ~ equal(op(e2,e2),op(e2,e1)),
    file('ALG045+1.p',unknown),
    [] ).

cnf(67,axiom,
    ~ equal(op(e2,e3),op(e2,e1)),
    file('ALG045+1.p',unknown),
    [] ).

cnf(70,axiom,
    ~ equal(op(e3,e2),op(e3,e0)),
    file('ALG045+1.p',unknown),
    [] ).

cnf(75,axiom,
    ( skC2
    | skC1
    | skC0
    | equal(op(e0,e0),e3) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(76,axiom,
    ( skC2
    | skC1
    | skC0
    | equal(op(e1,e1),e3) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(77,axiom,
    ( skC2
    | skC1
    | skC0
    | equal(op(e2,e2),e3) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(78,axiom,
    ( skC2
    | skC1
    | skC0
    | equal(op(e3,e3),e3) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(79,axiom,
    ( equal(e3,unit)
    | equal(e2,unit)
    | equal(e1,unit)
    | equal(e0,unit) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(82,axiom,
    ( ~ equal(op(e2,e2),e0)
    | ~ equal(op(e3,e2),e1) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(87,axiom,
    ( ~ equal(op(e0,e0),e1)
    | ~ equal(op(e2,e0),e3) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(97,axiom,
    ( ~ equal(op(e3,e3),e2)
    | ~ equal(op(e0,e3),e1) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(100,axiom,
    ( ~ equal(op(e1,e1),e3)
    | ~ equal(op(e2,e1),e0) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(137,axiom,
    ( equal(op(e3,e2),e3)
    | equal(op(e3,e2),e2)
    | equal(op(e3,e2),e1)
    | equal(op(e3,e2),e0) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(142,axiom,
    ( equal(op(e2,e1),e2)
    | equal(op(e2,e1),e1)
    | equal(op(e2,e1),e3)
    | equal(op(e2,e1),e0) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(143,axiom,
    ( equal(op(e2,e0),e2)
    | equal(op(e2,e0),e0)
    | equal(op(e2,e0),e3)
    | equal(op(e2,e0),e1) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(148,axiom,
    ( equal(op(e0,e3),e3)
    | equal(op(e0,e3),e0)
    | equal(op(e0,e3),e2)
    | equal(op(e0,e3),e1) ),
    file('ALG045+1.p',unknown),
    [] ).

cnf(152,plain,
    equal(e3,unit),
    inference(spt,[spt(split,[position(s1)])],[79]),
    [iquote('1:Spt:79.0')] ).

cnf(158,plain,
    ( ~ skC2
    | equal(op(unit,unit),e2) ),
    inference(rew,[status(thm),theory(equality)],[152,26]),
    [iquote('1:Rew:152.0,26.1')] ).

cnf(163,plain,
    ( ~ skC1
    | equal(op(unit,unit),e1) ),
    inference(rew,[status(thm),theory(equality)],[152,22]),
    [iquote('1:Rew:152.0,22.1')] ).

cnf(168,plain,
    ( ~ skC0
    | equal(op(unit,unit),e0) ),
    inference(rew,[status(thm),theory(equality)],[152,18]),
    [iquote('1:Rew:152.0,18.1')] ).

cnf(177,plain,
    ( skC2
    | skC1
    | skC0
    | equal(op(e2,e2),unit) ),
    inference(rew,[status(thm),theory(equality)],[152,77]),
    [iquote('1:Rew:152.0,77.3')] ).

cnf(181,plain,
    ( ~ equal(op(e1,e1),unit)
    | ~ equal(op(e2,e1),e0) ),
    inference(rew,[status(thm),theory(equality)],[152,100]),
    [iquote('1:Rew:152.0,100.0')] ).

cnf(183,plain,
    ( skC2
    | skC1
    | skC0
    | equal(op(e1,e1),unit) ),
    inference(rew,[status(thm),theory(equality)],[152,76]),
    [iquote('1:Rew:152.0,76.3')] ).

cnf(208,plain,
    ~ equal(op(e2,e1),op(unit,e1)),
    inference(rew,[status(thm),theory(equality)],[152,38]),
    [iquote('1:Rew:152.0,38.0')] ).

cnf(228,plain,
    ~ equal(op(e2,e1),op(e2,unit)),
    inference(rew,[status(thm),theory(equality)],[152,67]),
    [iquote('1:Rew:152.0,67.0')] ).

cnf(260,plain,
    ( equal(op(e2,e1),e2)
    | equal(op(e2,e1),e1)
    | equal(op(e2,e1),unit)
    | equal(op(e2,e1),e0) ),
    inference(rew,[status(thm),theory(equality)],[152,142]),
    [iquote('1:Rew:152.0,142.2')] ).

cnf(262,plain,
    ~ equal(e2,unit),
    inference(rew,[status(thm),theory(equality)],[152,6]),
    [iquote('1:Rew:152.0,6.0')] ).

cnf(263,plain,
    ~ equal(e1,unit),
    inference(rew,[status(thm),theory(equality)],[152,5]),
    [iquote('1:Rew:152.0,5.0')] ).

cnf(264,plain,
    ~ equal(e0,unit),
    inference(rew,[status(thm),theory(equality)],[152,3]),
    [iquote('1:Rew:152.0,3.0')] ).

cnf(265,plain,
    equal(op(unit,unit),unit),
    inference(rew,[status(thm),theory(equality)],[152,14]),
    [iquote('1:Rew:152.0,14.0')] ).

cnf(267,plain,
    ( ~ skC2
    | equal(e2,unit) ),
    inference(rew,[status(thm),theory(equality)],[265,158]),
    [iquote('1:Rew:265.0,158.1')] ).

cnf(268,plain,
    ~ skC2,
    inference(mrr,[status(thm)],[267,262]),
    [iquote('1:MRR:267.1,262.0')] ).

cnf(269,plain,
    ( ~ skC1
    | equal(e1,unit) ),
    inference(rew,[status(thm),theory(equality)],[265,163]),
    [iquote('1:Rew:265.0,163.1')] ).

cnf(270,plain,
    ~ skC1,
    inference(mrr,[status(thm)],[269,263]),
    [iquote('1:MRR:269.1,263.0')] ).

cnf(271,plain,
    ( ~ skC0
    | equal(e0,unit) ),
    inference(rew,[status(thm),theory(equality)],[265,168]),
    [iquote('1:Rew:265.0,168.1')] ).

cnf(272,plain,
    ~ skC0,
    inference(mrr,[status(thm)],[271,264]),
    [iquote('1:MRR:271.1,264.0')] ).

cnf(273,plain,
    equal(op(e2,e2),unit),
    inference(mrr,[status(thm)],[177,268,270,272]),
    [iquote('1:MRR:177.0,177.1,177.2,268.0,270.0,272.0')] ).

cnf(274,plain,
    ~ equal(op(e2,e1),unit),
    inference(rew,[status(thm),theory(equality)],[273,66]),
    [iquote('1:Rew:273.0,66.0')] ).

cnf(278,plain,
    equal(op(e1,e1),unit),
    inference(mrr,[status(thm)],[183,268,270,272]),
    [iquote('1:MRR:183.0,183.1,183.2,268.0,270.0,272.0')] ).

cnf(294,plain,
    ~ equal(op(e2,e1),e1),
    inference(rew,[status(thm),theory(equality)],[9,208]),
    [iquote('1:Rew:9.0,208.0')] ).

cnf(304,plain,
    ~ equal(op(e2,e1),e2),
    inference(rew,[status(thm),theory(equality)],[12,228]),
    [iquote('1:Rew:12.0,228.0')] ).

cnf(328,plain,
    ( ~ equal(unit,unit)
    | ~ equal(op(e2,e1),e0) ),
    inference(rew,[status(thm),theory(equality)],[278,181]),
    [iquote('1:Rew:278.0,181.0')] ).

cnf(329,plain,
    ~ equal(op(e2,e1),e0),
    inference(obv,[status(thm),theory(equality)],[328]),
    [iquote('1:Obv:328.0')] ).

cnf(384,plain,
    $false,
    inference(mrr,[status(thm)],[260,304,294,274,329]),
    [iquote('1:MRR:260.0,260.1,260.2,260.3,304.0,294.0,274.0,329.0')] ).

cnf(385,plain,
    ~ equal(e3,unit),
    inference(spt,[spt(split,[position(sa)])],[384,152]),
    [iquote('1:Spt:384.0,79.0,152.0')] ).

cnf(386,plain,
    ( equal(e2,unit)
    | equal(e1,unit)
    | equal(e0,unit) ),
    inference(spt,[spt(split,[position(s2)])],[79]),
    [iquote('1:Spt:384.0,79.1,79.2,79.3')] ).

cnf(387,plain,
    equal(e2,unit),
    inference(spt,[spt(split,[position(s2s1)])],[386]),
    [iquote('2:Spt:386.0')] ).

cnf(424,plain,
    ~ equal(op(e0,e3),op(e0,unit)),
    inference(rew,[status(thm),theory(equality)],[387,56]),
    [iquote('2:Rew:387.0,56.0')] ).

cnf(432,plain,
    ~ equal(e1,unit),
    inference(rew,[status(thm),theory(equality)],[387,4]),
    [iquote('2:Rew:387.0,4.0')] ).

cnf(433,plain,
    ~ equal(e0,unit),
    inference(rew,[status(thm),theory(equality)],[387,2]),
    [iquote('2:Rew:387.0,2.0')] ).

cnf(434,plain,
    equal(op(unit,unit),unit),
    inference(rew,[status(thm),theory(equality)],[387,12]),
    [iquote('2:Rew:387.0,12.0')] ).

cnf(441,plain,
    ( ~ equal(op(e3,e3),unit)
    | ~ equal(op(e0,e3),e1) ),
    inference(rew,[status(thm),theory(equality)],[387,97]),
    [iquote('2:Rew:387.0,97.0')] ).

cnf(442,plain,
    ( ~ skC2
    | equal(op(e3,e3),unit) ),
    inference(rew,[status(thm),theory(equality)],[387,26]),
    [iquote('2:Rew:387.0,26.1')] ).

cnf(445,plain,
    ( ~ skC1
    | equal(op(unit,unit),e1) ),
    inference(rew,[status(thm),theory(equality)],[387,21]),
    [iquote('2:Rew:387.0,21.1')] ).

cnf(447,plain,
    ( ~ skC0
    | equal(op(unit,unit),e0) ),
    inference(rew,[status(thm),theory(equality)],[387,17]),
    [iquote('2:Rew:387.0,17.1')] ).

cnf(448,plain,
    ( skC2
    | skC1
    | skC0
    | equal(op(unit,unit),e3) ),
    inference(rew,[status(thm),theory(equality)],[387,77]),
    [iquote('2:Rew:387.0,77.3')] ).

cnf(468,plain,
    ~ equal(op(e0,e3),op(unit,e3)),
    inference(rew,[status(thm),theory(equality)],[387,46]),
    [iquote('2:Rew:387.0,46.0')] ).

cnf(500,plain,
    ( equal(op(e0,e3),e3)
    | equal(op(e0,e3),e0)
    | equal(op(e0,e3),unit)
    | equal(op(e0,e3),e1) ),
    inference(rew,[status(thm),theory(equality)],[387,148]),
    [iquote('2:Rew:387.0,148.2')] ).

cnf(502,plain,
    ( ~ skC1
    | equal(e1,unit) ),
    inference(rew,[status(thm),theory(equality)],[434,445]),
    [iquote('2:Rew:434.0,445.1')] ).

cnf(503,plain,
    ~ skC1,
    inference(mrr,[status(thm)],[502,432]),
    [iquote('2:MRR:502.1,432.0')] ).

cnf(507,plain,
    ( ~ skC0
    | equal(e0,unit) ),
    inference(rew,[status(thm),theory(equality)],[434,447]),
    [iquote('2:Rew:434.0,447.1')] ).

cnf(508,plain,
    ~ skC0,
    inference(mrr,[status(thm)],[507,433]),
    [iquote('2:MRR:507.1,433.0')] ).

cnf(524,plain,
    ~ equal(op(e0,e3),e0),
    inference(rew,[status(thm),theory(equality)],[8,424]),
    [iquote('2:Rew:8.0,424.0')] ).

cnf(526,plain,
    ( skC2
    | skC1
    | skC0
    | equal(e3,unit) ),
    inference(rew,[status(thm),theory(equality)],[434,448]),
    [iquote('2:Rew:434.0,448.3')] ).

cnf(527,plain,
    skC2,
    inference(mrr,[status(thm)],[526,503,508,385]),
    [iquote('2:MRR:526.1,526.2,526.3,503.0,508.0,385.0')] ).

cnf(528,plain,
    equal(op(e3,e3),unit),
    inference(mrr,[status(thm)],[442,527]),
    [iquote('2:MRR:442.0,527.0')] ).

cnf(531,plain,
    ~ equal(op(e0,e3),unit),
    inference(rew,[status(thm),theory(equality)],[528,47]),
    [iquote('2:Rew:528.0,47.0')] ).

cnf(549,plain,
    ~ equal(op(e0,e3),e3),
    inference(rew,[status(thm),theory(equality)],[13,468]),
    [iquote('2:Rew:13.0,468.0')] ).

cnf(571,plain,
    ( ~ equal(unit,unit)
    | ~ equal(op(e0,e3),e1) ),
    inference(rew,[status(thm),theory(equality)],[528,441]),
    [iquote('2:Rew:528.0,441.0')] ).

cnf(572,plain,
    ~ equal(op(e0,e3),e1),
    inference(obv,[status(thm),theory(equality)],[571]),
    [iquote('2:Obv:571.0')] ).

cnf(625,plain,
    $false,
    inference(mrr,[status(thm)],[500,549,524,531,572]),
    [iquote('2:MRR:500.0,500.1,500.2,500.3,549.0,524.0,531.0,572.0')] ).

cnf(626,plain,
    ~ equal(e2,unit),
    inference(spt,[spt(split,[position(s2sa)])],[625,387]),
    [iquote('2:Spt:625.0,386.0,387.0')] ).

cnf(627,plain,
    ( equal(e1,unit)
    | equal(e0,unit) ),
    inference(spt,[spt(split,[position(s2s2)])],[386]),
    [iquote('2:Spt:625.0,386.1,386.2')] ).

cnf(628,plain,
    equal(e1,unit),
    inference(spt,[spt(split,[position(s2s2s1)])],[627]),
    [iquote('3:Spt:627.0')] ).

cnf(630,plain,
    ~ equal(op(e2,e0),op(unit,e0)),
    inference(rew,[status(thm),theory(equality)],[628,30]),
    [iquote('3:Rew:628.0,30.0')] ).

cnf(653,plain,
    ~ equal(e0,unit),
    inference(rew,[status(thm),theory(equality)],[628,1]),
    [iquote('3:Rew:628.0,1.0')] ).

cnf(654,plain,
    equal(op(unit,unit),unit),
    inference(rew,[status(thm),theory(equality)],[628,10]),
    [iquote('3:Rew:628.0,10.0')] ).

cnf(660,plain,
    ~ equal(op(e3,e3),op(unit,e3)),
    inference(rew,[status(thm),theory(equality)],[628,49]),
    [iquote('3:Rew:628.0,49.0')] ).

cnf(679,plain,
    ( ~ skC2
    | equal(op(unit,unit),e2) ),
    inference(rew,[status(thm),theory(equality)],[628,24]),
    [iquote('3:Rew:628.0,24.1')] ).

cnf(681,plain,
    ( ~ skC0
    | equal(op(unit,unit),e0) ),
    inference(rew,[status(thm),theory(equality)],[628,16]),
    [iquote('3:Rew:628.0,16.1')] ).

cnf(693,plain,
    ( ~ skC1
    | equal(op(e2,e2),unit) ),
    inference(rew,[status(thm),theory(equality)],[628,21]),
    [iquote('3:Rew:628.0,21.1')] ).

cnf(706,plain,
    ( ~ equal(op(e0,e0),unit)
    | ~ equal(op(e2,e0),e3) ),
    inference(rew,[status(thm),theory(equality)],[628,87]),
    [iquote('3:Rew:628.0,87.0')] ).

cnf(708,plain,
    ( ~ skC1
    | equal(op(e0,e0),unit) ),
    inference(rew,[status(thm),theory(equality)],[628,19]),
    [iquote('3:Rew:628.0,19.1')] ).

cnf(723,plain,
    ~ equal(op(e2,e0),op(e2,unit)),
    inference(rew,[status(thm),theory(equality)],[628,63]),
    [iquote('3:Rew:628.0,63.0')] ).

cnf(741,plain,
    ( equal(op(e2,e0),e2)
    | equal(op(e2,e0),e0)
    | equal(op(e2,e0),e3)
    | equal(op(e2,e0),unit) ),
    inference(rew,[status(thm),theory(equality)],[628,143]),
    [iquote('3:Rew:628.0,143.3')] ).

cnf(743,plain,
    ( ~ skC2
    | equal(e2,unit) ),
    inference(rew,[status(thm),theory(equality)],[654,679]),
    [iquote('3:Rew:654.0,679.1')] ).

cnf(744,plain,
    ~ skC2,
    inference(mrr,[status(thm)],[743,626]),
    [iquote('3:MRR:743.1,626.0')] ).

cnf(746,plain,
    ( skC1
    | skC0
    | equal(op(e3,e3),e3) ),
    inference(mrr,[status(thm)],[78,744]),
    [iquote('3:MRR:78.0,744.0')] ).

cnf(748,plain,
    ( ~ skC0
    | equal(e0,unit) ),
    inference(rew,[status(thm),theory(equality)],[654,681]),
    [iquote('3:Rew:654.0,681.1')] ).

cnf(749,plain,
    ~ skC0,
    inference(mrr,[status(thm)],[748,653]),
    [iquote('3:MRR:748.1,653.0')] ).

cnf(751,plain,
    ( skC1
    | equal(op(e3,e3),e3) ),
    inference(mrr,[status(thm)],[746,749]),
    [iquote('3:MRR:746.1,749.0')] ).

cnf(754,plain,
    ~ equal(op(e2,e0),e0),
    inference(rew,[status(thm),theory(equality)],[7,630]),
    [iquote('3:Rew:7.0,630.0')] ).

cnf(762,plain,
    ~ equal(op(e3,e3),e3),
    inference(rew,[status(thm),theory(equality)],[13,660]),
    [iquote('3:Rew:13.0,660.0')] ).

cnf(763,plain,
    skC1,
    inference(mrr,[status(thm)],[751,762]),
    [iquote('3:MRR:751.1,762.0')] ).

cnf(764,plain,
    equal(op(e2,e2),unit),
    inference(mrr,[status(thm)],[693,763]),
    [iquote('3:MRR:693.0,763.0')] ).

cnf(766,plain,
    equal(op(e0,e0),unit),
    inference(mrr,[status(thm)],[708,763]),
    [iquote('3:MRR:708.0,763.0')] ).

cnf(769,plain,
    ~ equal(op(e2,e0),unit),
    inference(rew,[status(thm),theory(equality)],[764,64]),
    [iquote('3:Rew:764.0,64.0')] ).

cnf(797,plain,
    ~ equal(op(e2,e0),e2),
    inference(rew,[status(thm),theory(equality)],[12,723]),
    [iquote('3:Rew:12.0,723.0')] ).

cnf(819,plain,
    ( ~ equal(unit,unit)
    | ~ equal(op(e2,e0),e3) ),
    inference(rew,[status(thm),theory(equality)],[766,706]),
    [iquote('3:Rew:766.0,706.0')] ).

cnf(820,plain,
    ~ equal(op(e2,e0),e3),
    inference(obv,[status(thm),theory(equality)],[819]),
    [iquote('3:Obv:819.0')] ).

cnf(865,plain,
    $false,
    inference(mrr,[status(thm)],[741,797,754,820,769]),
    [iquote('3:MRR:741.0,741.1,741.2,741.3,797.0,754.0,820.0,769.0')] ).

cnf(866,plain,
    ~ equal(e1,unit),
    inference(spt,[spt(split,[position(s2s2sa)])],[865,628]),
    [iquote('3:Spt:865.0,627.0,628.0')] ).

cnf(867,plain,
    equal(e0,unit),
    inference(spt,[spt(split,[position(s2s2s2)])],[627]),
    [iquote('3:Spt:865.0,627.1')] ).

cnf(868,plain,
    equal(op(unit,unit),unit),
    inference(rew,[status(thm),theory(equality)],[867,8]),
    [iquote('3:Rew:867.0,8.0')] ).

cnf(872,plain,
    ~ equal(op(e3,e2),op(e3,unit)),
    inference(rew,[status(thm),theory(equality)],[867,70]),
    [iquote('3:Rew:867.0,70.0')] ).

cnf(874,plain,
    ~ equal(op(e3,e2),op(unit,e2)),
    inference(rew,[status(thm),theory(equality)],[867,41]),
    [iquote('3:Rew:867.0,41.0')] ).

cnf(878,plain,
    ~ equal(e1,unit),
    inference(rew,[status(thm),theory(equality)],[867,1]),
    [iquote('3:Rew:867.0,1.0')] ).

cnf(879,plain,
    ( ~ skC1
    | equal(e1,unit) ),
    inference(rew,[status(thm),theory(equality)],[868,19,867]),
    [iquote('3:Rew:868.0,19.1,867.0,19.1')] ).

cnf(880,plain,
    ~ skC1,
    inference(mrr,[status(thm)],[879,878]),
    [iquote('3:MRR:879.1,878.0')] ).

cnf(882,plain,
    ( ~ skC2
    | equal(e2,unit) ),
    inference(rew,[status(thm),theory(equality)],[868,23,867]),
    [iquote('3:Rew:868.0,23.1,867.0,23.1')] ).

cnf(883,plain,
    ~ skC2,
    inference(mrr,[status(thm)],[882,626]),
    [iquote('3:MRR:882.1,626.0')] ).

cnf(884,plain,
    ( ~ skC0
    | equal(op(e2,e2),unit) ),
    inference(rew,[status(thm),theory(equality)],[867,17]),
    [iquote('3:Rew:867.0,17.1')] ).

cnf(904,plain,
    ( skC2
    | skC1
    | skC0
    | equal(e3,unit) ),
    inference(rew,[status(thm),theory(equality)],[868,75,867]),
    [iquote('3:Rew:868.0,75.3,867.0,75.3')] ).

cnf(905,plain,
    skC0,
    inference(mrr,[status(thm)],[904,883,880,385]),
    [iquote('3:MRR:904.0,904.1,904.3,883.0,880.0,385.0')] ).

cnf(907,plain,
    equal(op(e2,e2),unit),
    inference(mrr,[status(thm)],[884,905]),
    [iquote('3:MRR:884.0,905.0')] ).

cnf(921,plain,
    ~ equal(op(e3,e2),unit),
    inference(rew,[status(thm),theory(equality)],[907,44]),
    [iquote('3:Rew:907.0,44.0')] ).

cnf(931,plain,
    ~ equal(op(e3,e2),e3),
    inference(rew,[status(thm),theory(equality)],[14,872]),
    [iquote('3:Rew:14.0,872.0')] ).

cnf(932,plain,
    ~ equal(op(e3,e2),e2),
    inference(rew,[status(thm),theory(equality)],[11,874]),
    [iquote('3:Rew:11.0,874.0')] ).

cnf(939,plain,
    ( ~ equal(unit,unit)
    | ~ equal(op(e3,e2),e1) ),
    inference(rew,[status(thm),theory(equality)],[907,82,867]),
    [iquote('3:Rew:907.0,82.0,867.0,82.0')] ).

cnf(940,plain,
    ~ equal(op(e3,e2),e1),
    inference(obv,[status(thm),theory(equality)],[939]),
    [iquote('3:Obv:939.0')] ).

cnf(1027,plain,
    ( equal(op(e3,e2),e3)
    | equal(op(e3,e2),e2)
    | equal(op(e3,e2),e1)
    | equal(op(e3,e2),unit) ),
    inference(rew,[status(thm),theory(equality)],[867,137]),
    [iquote('3:Rew:867.0,137.3')] ).

cnf(1028,plain,
    $false,
    inference(mrr,[status(thm)],[1027,931,932,940,921]),
    [iquote('3:MRR:1027.0,1027.1,1027.2,1027.3,931.0,932.0,940.0,921.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ALG045+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n017.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
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Wed Jun  8 12:33:33 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.48  
% 0.19/0.48  SPASS V 3.9 
% 0.19/0.48  SPASS beiseite: Proof found.
% 0.19/0.48  % SZS status Theorem
% 0.19/0.48  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.48  SPASS derived 420 clauses, backtracked 411 clauses, performed 3 splits and kept 672 clauses.
% 0.19/0.48  SPASS allocated 85650 KBytes.
% 0.19/0.48  SPASS spent	0:00:00.13 on the problem.
% 0.19/0.48  		0:00:00.04 for the input.
% 0.19/0.48  		0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.48  		0:00:00.00 for inferences.
% 0.19/0.48  		0:00:00.00 for the backtracking.
% 0.19/0.48  		0:00:00.04 for the reduction.
% 0.19/0.48  
% 0.19/0.48  
% 0.19/0.48  Here is a proof with depth 3, length 155 :
% 0.19/0.48  % SZS output start Refutation
% See solution above
% 0.19/0.48  Formulae used in the proof : ax5 ax2 ax6 ax4 ax9 ax14 ax24 ax27 ax1
% 0.19/0.48  
%------------------------------------------------------------------------------