TSTP Solution File: NUM390+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : NUM390+1 : TPTP v7.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : n138.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32218.625MB
% OS       : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan  8 15:21:14 EST 2018

% Result   : Theorem 0.06s
% Output   : CNFRefutation 0.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   84 (  16 unt;   0 def)
%            Number of atoms       :  258 (   7 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  286 ( 112   ~; 110   |;  45   &)
%                                         (   3 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-1 aty)
%            Number of variables   :  135 (   4 sgn  87   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ! [X1] :
      ( ordinal(X1)
     => ( epsilon_transitive(X1)
        & epsilon_connected(X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',cc1_ordinal1) ).

fof(3,axiom,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X2,X3) )
     => subset(X1,X3) ),
    file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',t1_xboole_1) ).

fof(4,axiom,
    ! [X1,X2,X3] :
      ~ ( in(X1,X2)
        & element(X2,powerset(X3))
        & empty(X3) ),
    file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',t5_subset) ).

fof(9,axiom,
    ! [X1,X2] : subset(X1,X1),
    file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',reflexivity_r1_tarski) ).

fof(12,axiom,
    ! [X1,X2,X3] :
      ( ( in(X1,X2)
        & element(X2,powerset(X3)) )
     => element(X1,X3) ),
    file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',t4_subset) ).

fof(15,conjecture,
    ! [X1] :
      ( epsilon_transitive(X1)
     => ! [X2] :
          ( ordinal(X2)
         => ! [X3] :
              ( ordinal(X3)
             => ( ( subset(X1,X2)
                  & in(X2,X3) )
               => in(X1,X3) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',t22_ordinal1) ).

fof(17,axiom,
    ! [X1] :
      ( epsilon_transitive(X1)
    <=> ! [X2] :
          ( in(X2,X1)
         => subset(X2,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',d2_ordinal1) ).

fof(23,axiom,
    ! [X1] :
      ( epsilon_transitive(X1)
     => ! [X2] :
          ( ordinal(X2)
         => ( proper_subset(X1,X2)
           => in(X1,X2) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',t21_ordinal1) ).

fof(24,axiom,
    ! [X1,X2] :
      ( element(X1,X2)
     => ( empty(X2)
        | in(X1,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',t2_subset) ).

fof(25,axiom,
    ! [X1,X2] :
      ( element(X1,powerset(X2))
    <=> subset(X1,X2) ),
    file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',t3_subset) ).

fof(26,axiom,
    ! [X1,X2] :
      ( proper_subset(X1,X2)
    <=> ( subset(X1,X2)
        & ~ equal(X1,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',d8_xboole_0) ).

fof(38,axiom,
    ! [X1,X2] :
      ~ ( in(X1,X2)
        & subset(X2,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1',t7_ordinal1) ).

fof(39,negated_conjecture,
    ~ ! [X1] :
        ( epsilon_transitive(X1)
       => ! [X2] :
            ( ordinal(X2)
           => ! [X3] :
                ( ordinal(X3)
               => ( ( subset(X1,X2)
                    & in(X2,X3) )
                 => in(X1,X3) ) ) ) ),
    inference(assume_negation,[status(cth)],[15]) ).

fof(50,plain,
    ! [X1] :
      ( ~ ordinal(X1)
      | ( epsilon_transitive(X1)
        & epsilon_connected(X1) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(51,plain,
    ! [X2] :
      ( ~ ordinal(X2)
      | ( epsilon_transitive(X2)
        & epsilon_connected(X2) ) ),
    inference(variable_rename,[status(thm)],[50]) ).

fof(52,plain,
    ! [X2] :
      ( ( epsilon_transitive(X2)
        | ~ ordinal(X2) )
      & ( epsilon_connected(X2)
        | ~ ordinal(X2) ) ),
    inference(distribute,[status(thm)],[51]) ).

cnf(54,plain,
    ( epsilon_transitive(X1)
    | ~ ordinal(X1) ),
    inference(split_conjunct,[status(thm)],[52]) ).

fof(55,plain,
    ! [X1,X2,X3] :
      ( ~ subset(X1,X2)
      | ~ subset(X2,X3)
      | subset(X1,X3) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(56,plain,
    ! [X4,X5,X6] :
      ( ~ subset(X4,X5)
      | ~ subset(X5,X6)
      | subset(X4,X6) ),
    inference(variable_rename,[status(thm)],[55]) ).

cnf(57,plain,
    ( subset(X1,X2)
    | ~ subset(X3,X2)
    | ~ subset(X1,X3) ),
    inference(split_conjunct,[status(thm)],[56]) ).

fof(58,plain,
    ! [X1,X2,X3] :
      ( ~ in(X1,X2)
      | ~ element(X2,powerset(X3))
      | ~ empty(X3) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(59,plain,
    ! [X4,X5,X6] :
      ( ~ in(X4,X5)
      | ~ element(X5,powerset(X6))
      | ~ empty(X6) ),
    inference(variable_rename,[status(thm)],[58]) ).

cnf(60,plain,
    ( ~ empty(X1)
    | ~ element(X2,powerset(X1))
    | ~ in(X3,X2) ),
    inference(split_conjunct,[status(thm)],[59]) ).

fof(74,plain,
    ! [X3,X4] : subset(X3,X3),
    inference(variable_rename,[status(thm)],[9]) ).

cnf(75,plain,
    subset(X1,X1),
    inference(split_conjunct,[status(thm)],[74]) ).

fof(83,plain,
    ! [X1,X2,X3] :
      ( ~ in(X1,X2)
      | ~ element(X2,powerset(X3))
      | element(X1,X3) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(84,plain,
    ! [X4,X5,X6] :
      ( ~ in(X4,X5)
      | ~ element(X5,powerset(X6))
      | element(X4,X6) ),
    inference(variable_rename,[status(thm)],[83]) ).

cnf(85,plain,
    ( element(X1,X2)
    | ~ element(X3,powerset(X2))
    | ~ in(X1,X3) ),
    inference(split_conjunct,[status(thm)],[84]) ).

fof(94,negated_conjecture,
    ? [X1] :
      ( epsilon_transitive(X1)
      & ? [X2] :
          ( ordinal(X2)
          & ? [X3] :
              ( ordinal(X3)
              & subset(X1,X2)
              & in(X2,X3)
              & ~ in(X1,X3) ) ) ),
    inference(fof_nnf,[status(thm)],[39]) ).

fof(95,negated_conjecture,
    ? [X4] :
      ( epsilon_transitive(X4)
      & ? [X5] :
          ( ordinal(X5)
          & ? [X6] :
              ( ordinal(X6)
              & subset(X4,X5)
              & in(X5,X6)
              & ~ in(X4,X6) ) ) ),
    inference(variable_rename,[status(thm)],[94]) ).

fof(96,negated_conjecture,
    ( epsilon_transitive(esk6_0)
    & ordinal(esk7_0)
    & ordinal(esk8_0)
    & subset(esk6_0,esk7_0)
    & in(esk7_0,esk8_0)
    & ~ in(esk6_0,esk8_0) ),
    inference(skolemize,[status(esa)],[95]) ).

cnf(97,negated_conjecture,
    ~ in(esk6_0,esk8_0),
    inference(split_conjunct,[status(thm)],[96]) ).

cnf(98,negated_conjecture,
    in(esk7_0,esk8_0),
    inference(split_conjunct,[status(thm)],[96]) ).

cnf(99,negated_conjecture,
    subset(esk6_0,esk7_0),
    inference(split_conjunct,[status(thm)],[96]) ).

cnf(100,negated_conjecture,
    ordinal(esk8_0),
    inference(split_conjunct,[status(thm)],[96]) ).

cnf(102,negated_conjecture,
    epsilon_transitive(esk6_0),
    inference(split_conjunct,[status(thm)],[96]) ).

fof(106,plain,
    ! [X1] :
      ( ( ~ epsilon_transitive(X1)
        | ! [X2] :
            ( ~ in(X2,X1)
            | subset(X2,X1) ) )
      & ( ? [X2] :
            ( in(X2,X1)
            & ~ subset(X2,X1) )
        | epsilon_transitive(X1) ) ),
    inference(fof_nnf,[status(thm)],[17]) ).

fof(107,plain,
    ! [X3] :
      ( ( ~ epsilon_transitive(X3)
        | ! [X4] :
            ( ~ in(X4,X3)
            | subset(X4,X3) ) )
      & ( ? [X5] :
            ( in(X5,X3)
            & ~ subset(X5,X3) )
        | epsilon_transitive(X3) ) ),
    inference(variable_rename,[status(thm)],[106]) ).

fof(108,plain,
    ! [X3] :
      ( ( ~ epsilon_transitive(X3)
        | ! [X4] :
            ( ~ in(X4,X3)
            | subset(X4,X3) ) )
      & ( ( in(esk9_1(X3),X3)
          & ~ subset(esk9_1(X3),X3) )
        | epsilon_transitive(X3) ) ),
    inference(skolemize,[status(esa)],[107]) ).

fof(109,plain,
    ! [X3,X4] :
      ( ( ~ in(X4,X3)
        | subset(X4,X3)
        | ~ epsilon_transitive(X3) )
      & ( ( in(esk9_1(X3),X3)
          & ~ subset(esk9_1(X3),X3) )
        | epsilon_transitive(X3) ) ),
    inference(shift_quantors,[status(thm)],[108]) ).

fof(110,plain,
    ! [X3,X4] :
      ( ( ~ in(X4,X3)
        | subset(X4,X3)
        | ~ epsilon_transitive(X3) )
      & ( in(esk9_1(X3),X3)
        | epsilon_transitive(X3) )
      & ( ~ subset(esk9_1(X3),X3)
        | epsilon_transitive(X3) ) ),
    inference(distribute,[status(thm)],[109]) ).

cnf(113,plain,
    ( subset(X2,X1)
    | ~ epsilon_transitive(X1)
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[110]) ).

fof(132,plain,
    ! [X1] :
      ( ~ epsilon_transitive(X1)
      | ! [X2] :
          ( ~ ordinal(X2)
          | ~ proper_subset(X1,X2)
          | in(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[23]) ).

fof(133,plain,
    ! [X3] :
      ( ~ epsilon_transitive(X3)
      | ! [X4] :
          ( ~ ordinal(X4)
          | ~ proper_subset(X3,X4)
          | in(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[132]) ).

fof(134,plain,
    ! [X3,X4] :
      ( ~ ordinal(X4)
      | ~ proper_subset(X3,X4)
      | in(X3,X4)
      | ~ epsilon_transitive(X3) ),
    inference(shift_quantors,[status(thm)],[133]) ).

cnf(135,plain,
    ( in(X1,X2)
    | ~ epsilon_transitive(X1)
    | ~ proper_subset(X1,X2)
    | ~ ordinal(X2) ),
    inference(split_conjunct,[status(thm)],[134]) ).

fof(136,plain,
    ! [X1,X2] :
      ( ~ element(X1,X2)
      | empty(X2)
      | in(X1,X2) ),
    inference(fof_nnf,[status(thm)],[24]) ).

fof(137,plain,
    ! [X3,X4] :
      ( ~ element(X3,X4)
      | empty(X4)
      | in(X3,X4) ),
    inference(variable_rename,[status(thm)],[136]) ).

cnf(138,plain,
    ( in(X1,X2)
    | empty(X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[137]) ).

fof(139,plain,
    ! [X1,X2] :
      ( ( ~ element(X1,powerset(X2))
        | subset(X1,X2) )
      & ( ~ subset(X1,X2)
        | element(X1,powerset(X2)) ) ),
    inference(fof_nnf,[status(thm)],[25]) ).

fof(140,plain,
    ! [X3,X4] :
      ( ( ~ element(X3,powerset(X4))
        | subset(X3,X4) )
      & ( ~ subset(X3,X4)
        | element(X3,powerset(X4)) ) ),
    inference(variable_rename,[status(thm)],[139]) ).

cnf(141,plain,
    ( element(X1,powerset(X2))
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[140]) ).

fof(143,plain,
    ! [X1,X2] :
      ( ( ~ proper_subset(X1,X2)
        | ( subset(X1,X2)
          & ~ equal(X1,X2) ) )
      & ( ~ subset(X1,X2)
        | equal(X1,X2)
        | proper_subset(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[26]) ).

fof(144,plain,
    ! [X3,X4] :
      ( ( ~ proper_subset(X3,X4)
        | ( subset(X3,X4)
          & ~ equal(X3,X4) ) )
      & ( ~ subset(X3,X4)
        | equal(X3,X4)
        | proper_subset(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[143]) ).

fof(145,plain,
    ! [X3,X4] :
      ( ( subset(X3,X4)
        | ~ proper_subset(X3,X4) )
      & ( ~ equal(X3,X4)
        | ~ proper_subset(X3,X4) )
      & ( ~ subset(X3,X4)
        | equal(X3,X4)
        | proper_subset(X3,X4) ) ),
    inference(distribute,[status(thm)],[144]) ).

cnf(146,plain,
    ( proper_subset(X1,X2)
    | X1 = X2
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[145]) ).

fof(186,plain,
    ! [X1,X2] :
      ( ~ in(X1,X2)
      | ~ subset(X2,X1) ),
    inference(fof_nnf,[status(thm)],[38]) ).

fof(187,plain,
    ! [X3,X4] :
      ( ~ in(X3,X4)
      | ~ subset(X4,X3) ),
    inference(variable_rename,[status(thm)],[186]) ).

cnf(188,plain,
    ( ~ subset(X1,X2)
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[187]) ).

cnf(190,negated_conjecture,
    epsilon_transitive(esk8_0),
    inference(spm,[status(thm)],[54,100,theory(equality)]) ).

cnf(200,plain,
    ~ in(X1,X1),
    inference(spm,[status(thm)],[188,75,theory(equality)]) ).

cnf(217,negated_conjecture,
    ( subset(X1,esk7_0)
    | ~ subset(X1,esk6_0) ),
    inference(spm,[status(thm)],[57,99,theory(equality)]) ).

cnf(232,plain,
    ( in(X1,X2)
    | X1 = X2
    | ~ ordinal(X2)
    | ~ epsilon_transitive(X1)
    | ~ subset(X1,X2) ),
    inference(spm,[status(thm)],[135,146,theory(equality)]) ).

cnf(235,plain,
    ( ~ empty(X1)
    | ~ in(X3,X2)
    | ~ subset(X2,X1) ),
    inference(spm,[status(thm)],[60,141,theory(equality)]) ).

cnf(238,plain,
    ( element(X1,X2)
    | ~ in(X1,X3)
    | ~ subset(X3,X2) ),
    inference(spm,[status(thm)],[85,141,theory(equality)]) ).

cnf(240,negated_conjecture,
    ( subset(X1,esk8_0)
    | ~ in(X1,esk8_0) ),
    inference(spm,[status(thm)],[113,190,theory(equality)]) ).

cnf(270,negated_conjecture,
    ( subset(X1,esk8_0)
    | ~ subset(X1,X2)
    | ~ in(X2,esk8_0) ),
    inference(spm,[status(thm)],[57,240,theory(equality)]) ).

cnf(321,negated_conjecture,
    ( ~ empty(X1)
    | ~ subset(esk8_0,X1) ),
    inference(spm,[status(thm)],[235,98,theory(equality)]) ).

cnf(441,negated_conjecture,
    ( element(esk7_0,X1)
    | ~ subset(esk8_0,X1) ),
    inference(spm,[status(thm)],[238,98,theory(equality)]) ).

cnf(457,negated_conjecture,
    ( empty(X1)
    | in(esk7_0,X1)
    | ~ subset(esk8_0,X1) ),
    inference(spm,[status(thm)],[138,441,theory(equality)]) ).

cnf(460,negated_conjecture,
    ( in(esk7_0,X1)
    | ~ subset(esk8_0,X1) ),
    inference(csr,[status(thm)],[457,321]) ).

cnf(463,negated_conjecture,
    ( in(esk7_0,esk7_0)
    | ~ subset(esk8_0,esk6_0) ),
    inference(spm,[status(thm)],[460,217,theory(equality)]) ).

cnf(470,negated_conjecture,
    ~ subset(esk8_0,esk6_0),
    inference(sr,[status(thm)],[463,200,theory(equality)]) ).

cnf(492,negated_conjecture,
    ( subset(esk6_0,esk8_0)
    | ~ in(esk7_0,esk8_0) ),
    inference(spm,[status(thm)],[270,99,theory(equality)]) ).

cnf(501,negated_conjecture,
    ( subset(esk6_0,esk8_0)
    | $false ),
    inference(rw,[status(thm)],[492,98,theory(equality)]) ).

cnf(502,negated_conjecture,
    subset(esk6_0,esk8_0),
    inference(cn,[status(thm)],[501,theory(equality)]) ).

cnf(516,negated_conjecture,
    ( esk6_0 = esk8_0
    | in(esk6_0,esk8_0)
    | ~ ordinal(esk8_0)
    | ~ epsilon_transitive(esk6_0) ),
    inference(spm,[status(thm)],[232,502,theory(equality)]) ).

cnf(522,negated_conjecture,
    ( esk6_0 = esk8_0
    | in(esk6_0,esk8_0)
    | $false
    | ~ epsilon_transitive(esk6_0) ),
    inference(rw,[status(thm)],[516,100,theory(equality)]) ).

cnf(523,negated_conjecture,
    ( esk6_0 = esk8_0
    | in(esk6_0,esk8_0)
    | $false
    | $false ),
    inference(rw,[status(thm)],[522,102,theory(equality)]) ).

cnf(524,negated_conjecture,
    ( esk6_0 = esk8_0
    | in(esk6_0,esk8_0) ),
    inference(cn,[status(thm)],[523,theory(equality)]) ).

cnf(525,negated_conjecture,
    esk8_0 = esk6_0,
    inference(sr,[status(thm)],[524,97,theory(equality)]) ).

cnf(535,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[470,525,theory(equality)]),75,theory(equality)]) ).

cnf(536,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[535,theory(equality)]) ).

cnf(537,negated_conjecture,
    $false,
    536,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM390+1 : TPTP v7.0.0. Released v3.2.0.
% 0.00/0.03  % Command  : Source/sine.py -e eprover -t %d %s
% 0.02/0.22  % Computer : n138.star.cs.uiowa.edu
% 0.02/0.22  % Model    : x86_64 x86_64
% 0.02/0.22  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.22  % Memory   : 32218.625MB
% 0.02/0.22  % OS       : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.22  % CPULimit : 300
% 0.02/0.22  % DateTime : Fri Jan  5 02:37:15 CST 2018
% 0.02/0.23  % CPUTime  : 
% 0.02/0.27  % SZS status Started for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.27  --creating new selector for []
% 0.06/0.34  -running prover on /export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1 with time limit 29
% 0.06/0.34  -running prover with command ['/export/starexec/sandbox2/solver/bin/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/export/starexec/sandbox2/tmp/tmp8vNz0_/sel_theBenchmark.p_1']
% 0.06/0.34  -prover status Theorem
% 0.06/0.34  Problem theBenchmark.p solved in phase 0.
% 0.06/0.34  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.34  % SZS status Ended for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.34  Solved 1 out of 1.
% 0.06/0.34  # Problem is unsatisfiable (or provable), constructing proof object
% 0.06/0.34  # SZS status Theorem
% 0.06/0.34  # SZS output start CNFRefutation.
% See solution above
% 0.06/0.34  # SZS output end CNFRefutation
%------------------------------------------------------------------------------