TSTP Solution File: SEU615^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU615^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n019.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  : 300s
% DateTime : Tue May 21 03:28:35 EDT 2024

% Result   : Theorem 0.21s 0.53s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :  141
% Syntax   : Number of formulae    :  148 (   4 unt; 136 typ;   0 def)
%            Number of atoms       :  463 (   0 equ;   0 cnn)
%            Maximal formula atoms :  160 (  38 avg)
%            Number of connectives :  716 (  48   ~;  35   |; 141   &; 196   @)
%                                         (   4 <=>; 292  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  159 (  42 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  137 ( 136 usr; 135 con; 0-2 aty)
%            Number of variables   :   48 (   0   ^  48   !;   0   ?;  48   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    in: $i > $i > $o ).

thf(decl_24,type,
    setextAx: $o ).

thf(decl_26,type,
    emptysetAx: $o ).

thf(decl_28,type,
    setadjoinAx: $o ).

thf(decl_30,type,
    powersetAx: $o ).

thf(decl_32,type,
    setunionAx: $o ).

thf(decl_34,type,
    omega0Ax: $o ).

thf(decl_35,type,
    omegaSAx: $o ).

thf(decl_36,type,
    omegaIndAx: $o ).

thf(decl_37,type,
    replAx: $o ).

thf(decl_38,type,
    foundationAx: $o ).

thf(decl_39,type,
    wellorderingAx: $o ).

thf(decl_41,type,
    descrp: $o ).

thf(decl_43,type,
    dsetconstrI: $o ).

thf(decl_44,type,
    dsetconstrEL: $o ).

thf(decl_45,type,
    dsetconstrER: $o ).

thf(decl_46,type,
    exuE1: $o ).

thf(decl_48,type,
    prop2setE: $o ).

thf(decl_49,type,
    emptysetE: $o ).

thf(decl_50,type,
    emptysetimpfalse: $o ).

thf(decl_51,type,
    notinemptyset: $o ).

thf(decl_52,type,
    exuE3e: $o ).

thf(decl_53,type,
    setext: $o ).

thf(decl_54,type,
    emptyI: $o ).

thf(decl_55,type,
    noeltsimpempty: $o ).

thf(decl_56,type,
    setbeta: $o ).

thf(decl_58,type,
    nonemptyE1: $o ).

thf(decl_59,type,
    nonemptyI: $o ).

thf(decl_60,type,
    nonemptyI1: $o ).

thf(decl_61,type,
    setadjoinIL: $o ).

thf(decl_62,type,
    emptyinunitempty: $o ).

thf(decl_63,type,
    setadjoinIR: $o ).

thf(decl_64,type,
    setadjoinE: $o ).

thf(decl_65,type,
    setadjoinOr: $o ).

thf(decl_66,type,
    setoftrueEq: $o ).

thf(decl_67,type,
    powersetI: $o ).

thf(decl_68,type,
    emptyinPowerset: $o ).

thf(decl_69,type,
    emptyInPowerset: $o ).

thf(decl_70,type,
    powersetE: $o ).

thf(decl_71,type,
    setunionI: $o ).

thf(decl_72,type,
    setunionE: $o ).

thf(decl_73,type,
    subPowSU: $o ).

thf(decl_74,type,
    exuE2: $o ).

thf(decl_75,type,
    nonemptyImpWitness: $o ).

thf(decl_76,type,
    uniqinunit: $o ).

thf(decl_77,type,
    notinsingleton: $o ).

thf(decl_78,type,
    eqinunit: $o ).

thf(decl_79,type,
    singletonsswitch: $o ).

thf(decl_80,type,
    upairsetE: $o ).

thf(decl_81,type,
    upairsetIL: $o ).

thf(decl_82,type,
    upairsetIR: $o ).

thf(decl_83,type,
    emptyE1: $o ).

thf(decl_84,type,
    vacuousDall: $o ).

thf(decl_85,type,
    quantDeMorgan1: $o ).

thf(decl_86,type,
    quantDeMorgan2: $o ).

thf(decl_87,type,
    quantDeMorgan3: $o ).

thf(decl_88,type,
    quantDeMorgan4: $o ).

thf(decl_89,type,
    prop2setI: $o ).

thf(decl_91,type,
    prop2set2propI: $o ).

thf(decl_92,type,
    notdexE: $o ).

thf(decl_93,type,
    notdallE: $o ).

thf(decl_94,type,
    exuI1: $o ).

thf(decl_95,type,
    exuI3: $o ).

thf(decl_96,type,
    exuI2: $o ).

thf(decl_97,type,
    inCongP: $o ).

thf(decl_98,type,
    in__Cong: $o ).

thf(decl_99,type,
    exuE3u: $o ).

thf(decl_100,type,
    exu__Cong: $o ).

thf(decl_101,type,
    emptyset__Cong: $o ).

thf(decl_102,type,
    setadjoin__Cong: $o ).

thf(decl_103,type,
    powerset__Cong: $o ).

thf(decl_104,type,
    setunion__Cong: $o ).

thf(decl_105,type,
    omega__Cong: $o ).

thf(decl_106,type,
    exuEu: $o ).

thf(decl_107,type,
    descr__Cong: $o ).

thf(decl_108,type,
    dsetconstr__Cong: $o ).

thf(decl_112,type,
    subsetI1: $o ).

thf(decl_113,type,
    eqimpsubset2: $o ).

thf(decl_114,type,
    eqimpsubset1: $o ).

thf(decl_115,type,
    subsetI2: $o ).

thf(decl_116,type,
    emptysetsubset: $o ).

thf(decl_117,type,
    subsetE: $o ).

thf(decl_118,type,
    subsetE2: $o ).

thf(decl_119,type,
    notsubsetI: $o ).

thf(decl_120,type,
    notequalI1: $o ).

thf(decl_121,type,
    notequalI2: $o ).

thf(decl_122,type,
    subsetRefl: $o ).

thf(decl_123,type,
    subsetTrans: $o ).

thf(decl_124,type,
    setadjoinSub: $o ).

thf(decl_125,type,
    setadjoinSub2: $o ).

thf(decl_126,type,
    subset2powerset: $o ).

thf(decl_127,type,
    setextsub: $o ).

thf(decl_128,type,
    subsetemptysetimpeq: $o ).

thf(decl_129,type,
    powersetI1: $o ).

thf(decl_130,type,
    powersetE1: $o ).

thf(decl_131,type,
    inPowerset: $o ).

thf(decl_132,type,
    powersetsubset: $o ).

thf(decl_133,type,
    sepInPowerset: $o ).

thf(decl_134,type,
    sepSubset: $o ).

thf(decl_136,type,
    binunionIL: $o ).

thf(decl_137,type,
    upairset2IR: $o ).

thf(decl_138,type,
    binunionIR: $o ).

thf(decl_139,type,
    binunionEcases: $o ).

thf(decl_140,type,
    binunionE: $o ).

thf(decl_141,type,
    binunionLsub: $o ).

thf(decl_142,type,
    binunionRsub: $o ).

thf(decl_144,type,
    binintersectI: $o ).

thf(decl_145,type,
    binintersectSubset5: $o ).

thf(decl_146,type,
    binintersectEL: $o ).

thf(decl_147,type,
    binintersectLsub: $o ).

thf(decl_148,type,
    binintersectSubset2: $o ).

thf(decl_149,type,
    binintersectSubset3: $o ).

thf(decl_150,type,
    binintersectER: $o ).

thf(decl_151,type,
    disjointsetsI1: $o ).

thf(decl_152,type,
    binintersectRsub: $o ).

thf(decl_153,type,
    binintersectSubset4: $o ).

thf(decl_154,type,
    binintersectSubset1: $o ).

thf(decl_155,type,
    bs114d: $o ).

thf(decl_158,type,
    setminusI: $o ).

thf(decl_159,type,
    setminusEL: $o ).

thf(decl_160,type,
    setminusER: $o ).

thf(decl_161,type,
    setminusSubset2: $o ).

thf(decl_162,type,
    setminusERneg: $o ).

thf(decl_163,type,
    setminusELneg: $o ).

thf(decl_164,type,
    setminusILneg: $o ).

thf(decl_165,type,
    setminusIRneg: $o ).

thf(decl_166,type,
    setminusLsub: $o ).

thf(decl_167,type,
    setminusSubset1: $o ).

thf(decl_168,type,
    symdiff: $i > $i > $i ).

thf(decl_169,type,
    symdiffE: $o ).

thf(decl_170,type,
    symdiffI1: $o ).

thf(decl_171,type,
    symdiffI2: $o ).

thf(decl_172,type,
    symdiffIneg1: $o ).

thf(decl_173,type,
    esk1_0: $i ).

thf(decl_174,type,
    esk2_0: $i ).

thf(decl_175,type,
    esk3_0: $i ).

thf(symdiffIneg2,conjecture,
    ( setextAx
   => ( emptysetAx
     => ( setadjoinAx
       => ( powersetAx
         => ( setunionAx
           => ( omega0Ax
             => ( omegaSAx
               => ( omegaIndAx
                 => ( replAx
                   => ( foundationAx
                     => ( wellorderingAx
                       => ( descrp
                         => ( dsetconstrI
                           => ( dsetconstrEL
                             => ( dsetconstrER
                               => ( exuE1
                                 => ( prop2setE
                                   => ( emptysetE
                                     => ( emptysetimpfalse
                                       => ( notinemptyset
                                         => ( exuE3e
                                           => ( setext
                                             => ( emptyI
                                               => ( noeltsimpempty
                                                 => ( setbeta
                                                   => ( nonemptyE1
                                                     => ( nonemptyI
                                                       => ( nonemptyI1
                                                         => ( setadjoinIL
                                                           => ( emptyinunitempty
                                                             => ( setadjoinIR
                                                               => ( setadjoinE
                                                                 => ( setadjoinOr
                                                                   => ( setoftrueEq
                                                                     => ( powersetI
                                                                       => ( emptyinPowerset
                                                                         => ( emptyInPowerset
                                                                           => ( powersetE
                                                                             => ( setunionI
                                                                               => ( setunionE
                                                                                 => ( subPowSU
                                                                                   => ( exuE2
                                                                                     => ( nonemptyImpWitness
                                                                                       => ( uniqinunit
                                                                                         => ( notinsingleton
                                                                                           => ( eqinunit
                                                                                             => ( singletonsswitch
                                                                                               => ( upairsetE
                                                                                                 => ( upairsetIL
                                                                                                   => ( upairsetIR
                                                                                                     => ( emptyE1
                                                                                                       => ( vacuousDall
                                                                                                         => ( quantDeMorgan1
                                                                                                           => ( quantDeMorgan2
                                                                                                             => ( quantDeMorgan3
                                                                                                               => ( quantDeMorgan4
                                                                                                                 => ( prop2setI
                                                                                                                   => ( prop2set2propI
                                                                                                                     => ( notdexE
                                                                                                                       => ( notdallE
                                                                                                                         => ( exuI1
                                                                                                                           => ( exuI3
                                                                                                                             => ( exuI2
                                                                                                                               => ( inCongP
                                                                                                                                 => ( in__Cong
                                                                                                                                   => ( exuE3u
                                                                                                                                     => ( exu__Cong
                                                                                                                                       => ( emptyset__Cong
                                                                                                                                         => ( setadjoin__Cong
                                                                                                                                           => ( powerset__Cong
                                                                                                                                             => ( setunion__Cong
                                                                                                                                               => ( omega__Cong
                                                                                                                                                 => ( exuEu
                                                                                                                                                   => ( descr__Cong
                                                                                                                                                     => ( dsetconstr__Cong
                                                                                                                                                       => ( subsetI1
                                                                                                                                                         => ( eqimpsubset2
                                                                                                                                                           => ( eqimpsubset1
                                                                                                                                                             => ( subsetI2
                                                                                                                                                               => ( emptysetsubset
                                                                                                                                                                 => ( subsetE
                                                                                                                                                                   => ( subsetE2
                                                                                                                                                                     => ( notsubsetI
                                                                                                                                                                       => ( notequalI1
                                                                                                                                                                         => ( notequalI2
                                                                                                                                                                           => ( subsetRefl
                                                                                                                                                                             => ( subsetTrans
                                                                                                                                                                               => ( setadjoinSub
                                                                                                                                                                                 => ( setadjoinSub2
                                                                                                                                                                                   => ( subset2powerset
                                                                                                                                                                                     => ( setextsub
                                                                                                                                                                                       => ( subsetemptysetimpeq
                                                                                                                                                                                         => ( powersetI1
                                                                                                                                                                                           => ( powersetE1
                                                                                                                                                                                             => ( inPowerset
                                                                                                                                                                                               => ( powersetsubset
                                                                                                                                                                                                 => ( sepInPowerset
                                                                                                                                                                                                   => ( sepSubset
                                                                                                                                                                                                     => ( binunionIL
                                                                                                                                                                                                       => ( upairset2IR
                                                                                                                                                                                                         => ( binunionIR
                                                                                                                                                                                                           => ( binunionEcases
                                                                                                                                                                                                             => ( binunionE
                                                                                                                                                                                                               => ( binunionLsub
                                                                                                                                                                                                                 => ( binunionRsub
                                                                                                                                                                                                                   => ( binintersectI
                                                                                                                                                                                                                     => ( binintersectSubset5
                                                                                                                                                                                                                       => ( binintersectEL
                                                                                                                                                                                                                         => ( binintersectLsub
                                                                                                                                                                                                                           => ( binintersectSubset2
                                                                                                                                                                                                                             => ( binintersectSubset3
                                                                                                                                                                                                                               => ( binintersectER
                                                                                                                                                                                                                                 => ( disjointsetsI1
                                                                                                                                                                                                                                   => ( binintersectRsub
                                                                                                                                                                                                                                     => ( binintersectSubset4
                                                                                                                                                                                                                                       => ( binintersectSubset1
                                                                                                                                                                                                                                         => ( bs114d
                                                                                                                                                                                                                                           => ( setminusI
                                                                                                                                                                                                                                             => ( setminusEL
                                                                                                                                                                                                                                               => ( setminusER
                                                                                                                                                                                                                                                 => ( setminusSubset2
                                                                                                                                                                                                                                                   => ( setminusERneg
                                                                                                                                                                                                                                                     => ( setminusELneg
                                                                                                                                                                                                                                                       => ( setminusILneg
                                                                                                                                                                                                                                                         => ( setminusIRneg
                                                                                                                                                                                                                                                           => ( setminusLsub
                                                                                                                                                                                                                                                             => ( setminusSubset1
                                                                                                                                                                                                                                                               => ( symdiffE
                                                                                                                                                                                                                                                                 => ( symdiffI1
                                                                                                                                                                                                                                                                   => ( symdiffI2
                                                                                                                                                                                                                                                                     => ( symdiffIneg1
                                                                                                                                                                                                                                                                       => ! [X4: $i,X5: $i,X2: $i] :
                                                                                                                                                                                                                                                                            ( ~ ( in @ X2 @ X4 )
                                                                                                                                                                                                                                                                           => ( ~ ( in @ X2 @ X5 )
                                                                                                                                                                                                                                                                             => ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).

thf(symdiffE,axiom,
    ( symdiffE
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
       => ! [X20: $o] :
            ( ( ( in @ X2 @ X4 )
             => ( ~ ( in @ X2 @ X5 )
               => X20 ) )
           => ( ( ~ ( in @ X2 @ X4 )
               => ( ( in @ X2 @ X5 )
                 => X20 ) )
             => X20 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).

thf(symdiffIneg1,axiom,
    ( symdiffIneg1
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( in @ X2 @ X5 )
         => ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).

thf(symdiffI2,axiom,
    ( symdiffI2
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ~ ( in @ X2 @ X4 )
       => ( ( in @ X2 @ X5 )
         => ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).

thf(symdiffI1,axiom,
    ( symdiffI1
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ~ ( in @ X2 @ X5 )
         => ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).

thf(c_0_5,negated_conjecture,
    ~ ( setextAx
     => ( emptysetAx
       => ( setadjoinAx
         => ( powersetAx
           => ( setunionAx
             => ( omega0Ax
               => ( omegaSAx
                 => ( omegaIndAx
                   => ( replAx
                     => ( foundationAx
                       => ( wellorderingAx
                         => ( descrp
                           => ( dsetconstrI
                             => ( dsetconstrEL
                               => ( dsetconstrER
                                 => ( exuE1
                                   => ( prop2setE
                                     => ( emptysetE
                                       => ( emptysetimpfalse
                                         => ( notinemptyset
                                           => ( exuE3e
                                             => ( setext
                                               => ( emptyI
                                                 => ( noeltsimpempty
                                                   => ( setbeta
                                                     => ( nonemptyE1
                                                       => ( nonemptyI
                                                         => ( nonemptyI1
                                                           => ( setadjoinIL
                                                             => ( emptyinunitempty
                                                               => ( setadjoinIR
                                                                 => ( setadjoinE
                                                                   => ( setadjoinOr
                                                                     => ( setoftrueEq
                                                                       => ( powersetI
                                                                         => ( emptyinPowerset
                                                                           => ( emptyInPowerset
                                                                             => ( powersetE
                                                                               => ( setunionI
                                                                                 => ( setunionE
                                                                                   => ( subPowSU
                                                                                     => ( exuE2
                                                                                       => ( nonemptyImpWitness
                                                                                         => ( uniqinunit
                                                                                           => ( notinsingleton
                                                                                             => ( eqinunit
                                                                                               => ( singletonsswitch
                                                                                                 => ( upairsetE
                                                                                                   => ( upairsetIL
                                                                                                     => ( upairsetIR
                                                                                                       => ( emptyE1
                                                                                                         => ( vacuousDall
                                                                                                           => ( quantDeMorgan1
                                                                                                             => ( quantDeMorgan2
                                                                                                               => ( quantDeMorgan3
                                                                                                                 => ( quantDeMorgan4
                                                                                                                   => ( prop2setI
                                                                                                                     => ( prop2set2propI
                                                                                                                       => ( notdexE
                                                                                                                         => ( notdallE
                                                                                                                           => ( exuI1
                                                                                                                             => ( exuI3
                                                                                                                               => ( exuI2
                                                                                                                                 => ( inCongP
                                                                                                                                   => ( in__Cong
                                                                                                                                     => ( exuE3u
                                                                                                                                       => ( exu__Cong
                                                                                                                                         => ( emptyset__Cong
                                                                                                                                           => ( setadjoin__Cong
                                                                                                                                             => ( powerset__Cong
                                                                                                                                               => ( setunion__Cong
                                                                                                                                                 => ( omega__Cong
                                                                                                                                                   => ( exuEu
                                                                                                                                                     => ( descr__Cong
                                                                                                                                                       => ( dsetconstr__Cong
                                                                                                                                                         => ( subsetI1
                                                                                                                                                           => ( eqimpsubset2
                                                                                                                                                             => ( eqimpsubset1
                                                                                                                                                               => ( subsetI2
                                                                                                                                                                 => ( emptysetsubset
                                                                                                                                                                   => ( subsetE
                                                                                                                                                                     => ( subsetE2
                                                                                                                                                                       => ( notsubsetI
                                                                                                                                                                         => ( notequalI1
                                                                                                                                                                           => ( notequalI2
                                                                                                                                                                             => ( subsetRefl
                                                                                                                                                                               => ( subsetTrans
                                                                                                                                                                                 => ( setadjoinSub
                                                                                                                                                                                   => ( setadjoinSub2
                                                                                                                                                                                     => ( subset2powerset
                                                                                                                                                                                       => ( setextsub
                                                                                                                                                                                         => ( subsetemptysetimpeq
                                                                                                                                                                                           => ( powersetI1
                                                                                                                                                                                             => ( powersetE1
                                                                                                                                                                                               => ( inPowerset
                                                                                                                                                                                                 => ( powersetsubset
                                                                                                                                                                                                   => ( sepInPowerset
                                                                                                                                                                                                     => ( sepSubset
                                                                                                                                                                                                       => ( binunionIL
                                                                                                                                                                                                         => ( upairset2IR
                                                                                                                                                                                                           => ( binunionIR
                                                                                                                                                                                                             => ( binunionEcases
                                                                                                                                                                                                               => ( binunionE
                                                                                                                                                                                                                 => ( binunionLsub
                                                                                                                                                                                                                   => ( binunionRsub
                                                                                                                                                                                                                     => ( binintersectI
                                                                                                                                                                                                                       => ( binintersectSubset5
                                                                                                                                                                                                                         => ( binintersectEL
                                                                                                                                                                                                                           => ( binintersectLsub
                                                                                                                                                                                                                             => ( binintersectSubset2
                                                                                                                                                                                                                               => ( binintersectSubset3
                                                                                                                                                                                                                                 => ( binintersectER
                                                                                                                                                                                                                                   => ( disjointsetsI1
                                                                                                                                                                                                                                     => ( binintersectRsub
                                                                                                                                                                                                                                       => ( binintersectSubset4
                                                                                                                                                                                                                                         => ( binintersectSubset1
                                                                                                                                                                                                                                           => ( bs114d
                                                                                                                                                                                                                                             => ( setminusI
                                                                                                                                                                                                                                               => ( setminusEL
                                                                                                                                                                                                                                                 => ( setminusER
                                                                                                                                                                                                                                                   => ( setminusSubset2
                                                                                                                                                                                                                                                     => ( setminusERneg
                                                                                                                                                                                                                                                       => ( setminusELneg
                                                                                                                                                                                                                                                         => ( setminusILneg
                                                                                                                                                                                                                                                           => ( setminusIRneg
                                                                                                                                                                                                                                                             => ( setminusLsub
                                                                                                                                                                                                                                                               => ( setminusSubset1
                                                                                                                                                                                                                                                                 => ( ! [X37: $i,X38: $i,X39: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X39 @ ( symdiff @ X37 @ X38 ) )
                                                                                                                                                                                                                                                                       => ! [X40: $o] :
                                                                                                                                                                                                                                                                            ( ( ( in @ X39 @ X37 )
                                                                                                                                                                                                                                                                             => ( ~ ( in @ X39 @ X38 )
                                                                                                                                                                                                                                                                               => X40 ) )
                                                                                                                                                                                                                                                                           => ( ( ~ ( in @ X39 @ X37 )
                                                                                                                                                                                                                                                                               => ( ( in @ X39 @ X38 )
                                                                                                                                                                                                                                                                                 => X40 ) )
                                                                                                                                                                                                                                                                             => X40 ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X41: $i,X42: $i,X43: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X43 @ X41 )
                                                                                                                                                                                                                                                                         => ( ~ ( in @ X43 @ X42 )
                                                                                                                                                                                                                                                                           => ( in @ X43 @ ( symdiff @ X41 @ X42 ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X44: $i,X45: $i,X46: $i] :
                                                                                                                                                                                                                                                                            ( ~ ( in @ X46 @ X44 )
                                                                                                                                                                                                                                                                           => ( ( in @ X46 @ X45 )
                                                                                                                                                                                                                                                                             => ( in @ X46 @ ( symdiff @ X44 @ X45 ) ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X47: $i,X48: $i,X49: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X49 @ X47 )
                                                                                                                                                                                                                                                                             => ( ( in @ X49 @ X48 )
                                                                                                                                                                                                                                                                               => ~ ( in @ X49 @ ( symdiff @ X47 @ X48 ) ) ) )
                                                                                                                                                                                                                                                                         => ! [X4: $i,X5: $i,X2: $i] :
                                                                                                                                                                                                                                                                              ( ~ ( in @ X2 @ X4 )
                                                                                                                                                                                                                                                                             => ( ~ ( in @ X2 @ X5 )
                                                                                                                                                                                                                                                                               => ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[symdiffIneg2]),symdiffE]),symdiffIneg1]),symdiffI2]),symdiffI1])]) ).

thf(c_0_6,negated_conjecture,
    ! [X50: $i,X51: $i,X52: $i,X53: $o,X54: $i,X55: $i,X56: $i,X57: $i,X58: $i,X59: $i,X60: $i,X61: $i,X62: $i] :
      ( setextAx
      & emptysetAx
      & setadjoinAx
      & powersetAx
      & setunionAx
      & omega0Ax
      & omegaSAx
      & omegaIndAx
      & replAx
      & foundationAx
      & wellorderingAx
      & descrp
      & dsetconstrI
      & dsetconstrEL
      & dsetconstrER
      & exuE1
      & prop2setE
      & emptysetE
      & emptysetimpfalse
      & notinemptyset
      & exuE3e
      & setext
      & emptyI
      & noeltsimpempty
      & setbeta
      & nonemptyE1
      & nonemptyI
      & nonemptyI1
      & setadjoinIL
      & emptyinunitempty
      & setadjoinIR
      & setadjoinE
      & setadjoinOr
      & setoftrueEq
      & powersetI
      & emptyinPowerset
      & emptyInPowerset
      & powersetE
      & setunionI
      & setunionE
      & subPowSU
      & exuE2
      & nonemptyImpWitness
      & uniqinunit
      & notinsingleton
      & eqinunit
      & singletonsswitch
      & upairsetE
      & upairsetIL
      & upairsetIR
      & emptyE1
      & vacuousDall
      & quantDeMorgan1
      & quantDeMorgan2
      & quantDeMorgan3
      & quantDeMorgan4
      & prop2setI
      & prop2set2propI
      & notdexE
      & notdallE
      & exuI1
      & exuI3
      & exuI2
      & inCongP
      & in__Cong
      & exuE3u
      & exu__Cong
      & emptyset__Cong
      & setadjoin__Cong
      & powerset__Cong
      & setunion__Cong
      & omega__Cong
      & exuEu
      & descr__Cong
      & dsetconstr__Cong
      & subsetI1
      & eqimpsubset2
      & eqimpsubset1
      & subsetI2
      & emptysetsubset
      & subsetE
      & subsetE2
      & notsubsetI
      & notequalI1
      & notequalI2
      & subsetRefl
      & subsetTrans
      & setadjoinSub
      & setadjoinSub2
      & subset2powerset
      & setextsub
      & subsetemptysetimpeq
      & powersetI1
      & powersetE1
      & inPowerset
      & powersetsubset
      & sepInPowerset
      & sepSubset
      & binunionIL
      & upairset2IR
      & binunionIR
      & binunionEcases
      & binunionE
      & binunionLsub
      & binunionRsub
      & binintersectI
      & binintersectSubset5
      & binintersectEL
      & binintersectLsub
      & binintersectSubset2
      & binintersectSubset3
      & binintersectER
      & disjointsetsI1
      & binintersectRsub
      & binintersectSubset4
      & binintersectSubset1
      & bs114d
      & setminusI
      & setminusEL
      & setminusER
      & setminusSubset2
      & setminusERneg
      & setminusELneg
      & setminusILneg
      & setminusIRneg
      & setminusLsub
      & setminusSubset1
      & ( ~ ( in @ X52 @ X50 )
        | X53
        | ( in @ X52 @ X50 )
        | ~ ( in @ X52 @ ( symdiff @ X50 @ X51 ) ) )
      & ( ( in @ X52 @ X51 )
        | X53
        | ( in @ X52 @ X50 )
        | ~ ( in @ X52 @ ( symdiff @ X50 @ X51 ) ) )
      & ( ~ X53
        | X53
        | ( in @ X52 @ X50 )
        | ~ ( in @ X52 @ ( symdiff @ X50 @ X51 ) ) )
      & ( ~ ( in @ X52 @ X50 )
        | X53
        | ~ ( in @ X52 @ X51 )
        | ~ ( in @ X52 @ ( symdiff @ X50 @ X51 ) ) )
      & ( ( in @ X52 @ X51 )
        | X53
        | ~ ( in @ X52 @ X51 )
        | ~ ( in @ X52 @ ( symdiff @ X50 @ X51 ) ) )
      & ( ~ X53
        | X53
        | ~ ( in @ X52 @ X51 )
        | ~ ( in @ X52 @ ( symdiff @ X50 @ X51 ) ) )
      & ( ~ ( in @ X52 @ X50 )
        | X53
        | ~ X53
        | ~ ( in @ X52 @ ( symdiff @ X50 @ X51 ) ) )
      & ( ( in @ X52 @ X51 )
        | X53
        | ~ X53
        | ~ ( in @ X52 @ ( symdiff @ X50 @ X51 ) ) )
      & ( ~ X53
        | X53
        | ~ X53
        | ~ ( in @ X52 @ ( symdiff @ X50 @ X51 ) ) )
      & ( ~ ( in @ X56 @ X54 )
        | ( in @ X56 @ X55 )
        | ( in @ X56 @ ( symdiff @ X54 @ X55 ) ) )
      & ( ( in @ X59 @ X57 )
        | ~ ( in @ X59 @ X58 )
        | ( in @ X59 @ ( symdiff @ X57 @ X58 ) ) )
      & ( ~ ( in @ X62 @ X60 )
        | ~ ( in @ X62 @ X61 )
        | ~ ( in @ X62 @ ( symdiff @ X60 @ X61 ) ) )
      & ~ ( in @ esk3_0 @ esk1_0 )
      & ~ ( in @ esk3_0 @ esk2_0 )
      & ( in @ esk3_0 @ ( symdiff @ esk1_0 @ esk2_0 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])])]) ).

thf(c_0_7,negated_conjecture,
    ! [X2: $i,X4: $i,X3: $i] :
      ( ( in @ X2 @ X3 )
      | ( in @ X2 @ X4 )
      | ~ ( in @ X2 @ ( symdiff @ X4 @ X3 ) ) ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_6])])]) ).

thf(c_0_8,negated_conjecture,
    in @ esk3_0 @ ( symdiff @ esk1_0 @ esk2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_9,negated_conjecture,
    ~ ( in @ esk3_0 @ esk1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_10,negated_conjecture,
    ~ ( in @ esk3_0 @ esk2_0 ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

thf(c_0_11,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]),c_0_10]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SEU615^1 : TPTP v8.2.0. Released v3.7.0.
% 0.14/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n019.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 19 16:11:53 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  Running higher-order theorem proving
% 0.21/0.49  Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.53  # Version: 3.1.0-ho
% 0.21/0.53  # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.21/0.53  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53  # Starting ehoh_best5 with 300s (1) cores
% 0.21/0.53  # Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.53  # Starting new_bool_5 with 300s (1) cores
% 0.21/0.53  # Starting pre_casc_3 with 300s (1) cores
% 0.21/0.53  # Starting ho_unfolding_8 with 300s (1) cores
% 0.21/0.53  # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.21/0.53  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.53  # Starting new_ho_5 with 300s (1) cores
% 0.21/0.53  # new_ho_5 with pid 568 completed with status 0
% 0.21/0.53  # Result found by new_ho_5
% 0.21/0.53  # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.21/0.53  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53  # Starting ehoh_best5 with 300s (1) cores
% 0.21/0.53  # Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.53  # Starting new_bool_5 with 300s (1) cores
% 0.21/0.53  # Starting pre_casc_3 with 300s (1) cores
% 0.21/0.53  # Starting ho_unfolding_8 with 300s (1) cores
% 0.21/0.53  # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.21/0.53  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.53  # Starting new_ho_5 with 300s (1) cores
% 0.21/0.53  # SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 0.21/0.53  # Search class: HGHNF-FFSM22-SHFMMFNN
% 0.21/0.53  # partial match(3): HGHNF-FFSF22-SHSSMFNN
% 0.21/0.53  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.53  # Starting new_ho_10 with 163s (1) cores
% 0.21/0.53  # new_ho_10 with pid 578 completed with status 0
% 0.21/0.53  # Result found by new_ho_10
% 0.21/0.53  # Preprocessing class: HSLMSLSSLLLCHFA.
% 0.21/0.53  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.53  # Starting ehoh_best5 with 300s (1) cores
% 0.21/0.53  # Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.53  # Starting new_bool_5 with 300s (1) cores
% 0.21/0.53  # Starting pre_casc_3 with 300s (1) cores
% 0.21/0.53  # Starting ho_unfolding_8 with 300s (1) cores
% 0.21/0.53  # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.21/0.53  # Starting new_bool_3 with 300s (1) cores
% 0.21/0.53  # Starting new_ho_5 with 300s (1) cores
% 0.21/0.53  # SinE strategy is GSinE(CountFormulas,hypos,7,,3,20000,1.0,true)
% 0.21/0.53  # Search class: HGHNF-FFSM22-SHFMMFNN
% 0.21/0.53  # partial match(3): HGHNF-FFSF22-SHSSMFNN
% 0.21/0.53  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.53  # Starting new_ho_10 with 163s (1) cores
% 0.21/0.53  # Preprocessing time       : 0.003 s
% 0.21/0.53  # Presaturation interreduction done
% 0.21/0.53  
% 0.21/0.53  # Proof found!
% 0.21/0.53  # SZS status Theorem
% 0.21/0.53  # SZS output start CNFRefutation
% See solution above
% 0.21/0.53  # Parsed axioms                        : 285
% 0.21/0.53  # Removed by relevancy pruning/SinE    : 280
% 0.21/0.53  # Initial clauses                      : 142
% 0.21/0.53  # Removed in clause preprocessing      : 7
% 0.21/0.53  # Initial clauses in saturation        : 135
% 0.21/0.53  # Processed clauses                    : 267
% 0.21/0.53  # ...of these trivial                  : 0
% 0.21/0.53  # ...subsumed                          : 1
% 0.21/0.53  # ...remaining for further processing  : 266
% 0.21/0.53  # Other redundant clauses eliminated   : 0
% 0.21/0.53  # Clauses deleted for lack of memory   : 0
% 0.21/0.53  # Backward-subsumed                    : 0
% 0.21/0.53  # Backward-rewritten                   : 0
% 0.21/0.53  # Generated clauses                    : 2
% 0.21/0.53  # ...of the previous two non-redundant : 1
% 0.21/0.53  # ...aggressively subsumed             : 0
% 0.21/0.53  # Contextual simplify-reflections      : 0
% 0.21/0.53  # Paramodulations                      : 2
% 0.21/0.53  # Factorizations                       : 0
% 0.21/0.53  # NegExts                              : 0
% 0.21/0.53  # Equation resolutions                 : 0
% 0.21/0.53  # Disequality decompositions           : 0
% 0.21/0.53  # Total rewrite steps                  : 0
% 0.21/0.53  # ...of those cached                   : 0
% 0.21/0.53  # Propositional unsat checks           : 0
% 0.21/0.53  #    Propositional check models        : 0
% 0.21/0.53  #    Propositional check unsatisfiable : 0
% 0.21/0.53  #    Propositional clauses             : 0
% 0.21/0.53  #    Propositional clauses after purity: 0
% 0.21/0.53  #    Propositional unsat core size     : 0
% 0.21/0.53  #    Propositional preprocessing time  : 0.000
% 0.21/0.53  #    Propositional encoding time       : 0.000
% 0.21/0.53  #    Propositional solver time         : 0.000
% 0.21/0.53  #    Success case prop preproc time    : 0.000
% 0.21/0.53  #    Success case prop encoding time   : 0.000
% 0.21/0.53  #    Success case prop solver time     : 0.000
% 0.21/0.53  # Current number of processed clauses  : 132
% 0.21/0.53  #    Positive orientable unit clauses  : 128
% 0.21/0.53  #    Positive unorientable unit clauses: 0
% 0.21/0.53  #    Negative unit clauses             : 2
% 0.21/0.53  #    Non-unit-clauses                  : 2
% 0.21/0.53  # Current number of unprocessed clauses: 3
% 0.21/0.53  # ...number of literals in the above   : 8
% 0.21/0.53  # Current number of archived formulas  : 0
% 0.21/0.53  # Current number of archived clauses   : 134
% 0.21/0.53  # Clause-clause subsumption calls (NU) : 10
% 0.21/0.53  # Rec. Clause-clause subsumption calls : 7
% 0.21/0.53  # Non-unit clause-clause subsumptions  : 1
% 0.21/0.53  # Unit Clause-clause subsumption calls : 2
% 0.21/0.53  # Rewrite failures with RHS unbound    : 0
% 0.21/0.53  # BW rewrite match attempts            : 0
% 0.21/0.53  # BW rewrite match successes           : 0
% 0.21/0.53  # Condensation attempts                : 267
% 0.21/0.53  # Condensation successes               : 0
% 0.21/0.53  # Termbank termtop insertions          : 7979
% 0.21/0.53  # Search garbage collected termcells   : 3288
% 0.21/0.53  
% 0.21/0.53  # -------------------------------------------------
% 0.21/0.53  # User time                : 0.014 s
% 0.21/0.53  # System time              : 0.007 s
% 0.21/0.53  # Total time               : 0.021 s
% 0.21/0.53  # Maximum resident set size: 2624 pages
% 0.21/0.53  
% 0.21/0.53  # -------------------------------------------------
% 0.21/0.53  # User time                : 0.021 s
% 0.21/0.53  # System time              : 0.010 s
% 0.21/0.53  # Total time               : 0.031 s
% 0.21/0.53  # Maximum resident set size: 2020 pages
% 0.21/0.53  % E---3.1 exiting
% 0.21/0.53  % E exiting
%------------------------------------------------------------------------------