TSTP Solution File: SEU141+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU141+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art09.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 04:50:58 EST 2010

% Result   : Theorem 5.58s
% Output   : CNFRefutation 5.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   65 (  13 unt;   0 def)
%            Number of atoms       :  285 (  62 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  356 ( 136   ~; 146   |;  66   &)
%                                         (   8 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :  159 (   8 sgn  80   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(4,axiom,
    ! [X1] : set_difference(X1,empty_set) = X1,
    file('/tmp/tmpjRMtxD/sel_SEU141+1.p_1',t3_boole) ).

fof(10,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_difference(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & ~ in(X4,X2) ) ) ),
    file('/tmp/tmpjRMtxD/sel_SEU141+1.p_1',d4_xboole_0) ).

fof(12,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_intersection2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & in(X4,X2) ) ) ),
    file('/tmp/tmpjRMtxD/sel_SEU141+1.p_1',d3_xboole_0) ).

fof(14,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/tmp/tmpjRMtxD/sel_SEU141+1.p_1',commutativity_k3_xboole_0) ).

fof(23,axiom,
    ! [X1,X2] :
      ( ~ ( ~ disjoint(X1,X2)
          & ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
      & ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
          & disjoint(X1,X2) ) ),
    file('/tmp/tmpjRMtxD/sel_SEU141+1.p_1',t4_xboole_0) ).

fof(24,conjecture,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> set_difference(X1,X2) = X1 ),
    file('/tmp/tmpjRMtxD/sel_SEU141+1.p_1',t83_xboole_1) ).

fof(25,negated_conjecture,
    ~ ! [X1,X2] :
        ( disjoint(X1,X2)
      <=> set_difference(X1,X2) = X1 ),
    inference(assume_negation,[status(cth)],[24]) ).

fof(28,plain,
    ! [X1,X2,X3] :
      ( X3 = set_difference(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & ~ in(X4,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).

fof(29,plain,
    ! [X1,X2] :
      ( ~ ( ~ disjoint(X1,X2)
          & ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
      & ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
          & disjoint(X1,X2) ) ),
    inference(fof_simplification,[status(thm)],[23,theory(equality)]) ).

fof(37,plain,
    ! [X2] : set_difference(X2,empty_set) = X2,
    inference(variable_rename,[status(thm)],[4]) ).

cnf(38,plain,
    set_difference(X1,empty_set) = X1,
    inference(split_conjunct,[status(thm)],[37]) ).

fof(49,plain,
    ! [X1,X2,X3] :
      ( ( X3 != set_difference(X1,X2)
        | ! [X4] :
            ( ( ~ in(X4,X3)
              | ( in(X4,X1)
                & ~ in(X4,X2) ) )
            & ( ~ in(X4,X1)
              | in(X4,X2)
              | in(X4,X3) ) ) )
      & ( ? [X4] :
            ( ( ~ in(X4,X3)
              | ~ in(X4,X1)
              | in(X4,X2) )
            & ( in(X4,X3)
              | ( in(X4,X1)
                & ~ in(X4,X2) ) ) )
        | X3 = set_difference(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[28]) ).

fof(50,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_difference(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | ( in(X8,X5)
                & ~ in(X8,X6) ) )
            & ( ~ in(X8,X5)
              | in(X8,X6)
              | in(X8,X7) ) ) )
      & ( ? [X9] :
            ( ( ~ in(X9,X7)
              | ~ in(X9,X5)
              | in(X9,X6) )
            & ( in(X9,X7)
              | ( in(X9,X5)
                & ~ in(X9,X6) ) ) )
        | X7 = set_difference(X5,X6) ) ),
    inference(variable_rename,[status(thm)],[49]) ).

fof(51,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_difference(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | ( in(X8,X5)
                & ~ in(X8,X6) ) )
            & ( ~ in(X8,X5)
              | in(X8,X6)
              | in(X8,X7) ) ) )
      & ( ( ( ~ in(esk2_3(X5,X6,X7),X7)
            | ~ in(esk2_3(X5,X6,X7),X5)
            | in(esk2_3(X5,X6,X7),X6) )
          & ( in(esk2_3(X5,X6,X7),X7)
            | ( in(esk2_3(X5,X6,X7),X5)
              & ~ in(esk2_3(X5,X6,X7),X6) ) ) )
        | X7 = set_difference(X5,X6) ) ),
    inference(skolemize,[status(esa)],[50]) ).

fof(52,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ( ~ in(X8,X7)
            | ( in(X8,X5)
              & ~ in(X8,X6) ) )
          & ( ~ in(X8,X5)
            | in(X8,X6)
            | in(X8,X7) ) )
        | X7 != set_difference(X5,X6) )
      & ( ( ( ~ in(esk2_3(X5,X6,X7),X7)
            | ~ in(esk2_3(X5,X6,X7),X5)
            | in(esk2_3(X5,X6,X7),X6) )
          & ( in(esk2_3(X5,X6,X7),X7)
            | ( in(esk2_3(X5,X6,X7),X5)
              & ~ in(esk2_3(X5,X6,X7),X6) ) ) )
        | X7 = set_difference(X5,X6) ) ),
    inference(shift_quantors,[status(thm)],[51]) ).

fof(53,plain,
    ! [X5,X6,X7,X8] :
      ( ( in(X8,X5)
        | ~ in(X8,X7)
        | X7 != set_difference(X5,X6) )
      & ( ~ in(X8,X6)
        | ~ in(X8,X7)
        | X7 != set_difference(X5,X6) )
      & ( ~ in(X8,X5)
        | in(X8,X6)
        | in(X8,X7)
        | X7 != set_difference(X5,X6) )
      & ( ~ in(esk2_3(X5,X6,X7),X7)
        | ~ in(esk2_3(X5,X6,X7),X5)
        | in(esk2_3(X5,X6,X7),X6)
        | X7 = set_difference(X5,X6) )
      & ( in(esk2_3(X5,X6,X7),X5)
        | in(esk2_3(X5,X6,X7),X7)
        | X7 = set_difference(X5,X6) )
      & ( ~ in(esk2_3(X5,X6,X7),X6)
        | in(esk2_3(X5,X6,X7),X7)
        | X7 = set_difference(X5,X6) ) ),
    inference(distribute,[status(thm)],[52]) ).

cnf(55,plain,
    ( X1 = set_difference(X2,X3)
    | in(esk2_3(X2,X3,X1),X1)
    | in(esk2_3(X2,X3,X1),X2) ),
    inference(split_conjunct,[status(thm)],[53]) ).

cnf(56,plain,
    ( X1 = set_difference(X2,X3)
    | in(esk2_3(X2,X3,X1),X3)
    | ~ in(esk2_3(X2,X3,X1),X2)
    | ~ in(esk2_3(X2,X3,X1),X1) ),
    inference(split_conjunct,[status(thm)],[53]) ).

cnf(58,plain,
    ( X1 != set_difference(X2,X3)
    | ~ in(X4,X1)
    | ~ in(X4,X3) ),
    inference(split_conjunct,[status(thm)],[53]) ).

cnf(59,plain,
    ( in(X4,X2)
    | X1 != set_difference(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[53]) ).

fof(64,plain,
    ! [X1,X2,X3] :
      ( ( X3 != set_intersection2(X1,X2)
        | ! [X4] :
            ( ( ~ in(X4,X3)
              | ( in(X4,X1)
                & in(X4,X2) ) )
            & ( ~ in(X4,X1)
              | ~ in(X4,X2)
              | in(X4,X3) ) ) )
      & ( ? [X4] :
            ( ( ~ in(X4,X3)
              | ~ in(X4,X1)
              | ~ in(X4,X2) )
            & ( in(X4,X3)
              | ( in(X4,X1)
                & in(X4,X2) ) ) )
        | X3 = set_intersection2(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(65,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_intersection2(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | ( in(X8,X5)
                & in(X8,X6) ) )
            & ( ~ in(X8,X5)
              | ~ in(X8,X6)
              | in(X8,X7) ) ) )
      & ( ? [X9] :
            ( ( ~ in(X9,X7)
              | ~ in(X9,X5)
              | ~ in(X9,X6) )
            & ( in(X9,X7)
              | ( in(X9,X5)
                & in(X9,X6) ) ) )
        | X7 = set_intersection2(X5,X6) ) ),
    inference(variable_rename,[status(thm)],[64]) ).

fof(66,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_intersection2(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | ( in(X8,X5)
                & in(X8,X6) ) )
            & ( ~ in(X8,X5)
              | ~ in(X8,X6)
              | in(X8,X7) ) ) )
      & ( ( ( ~ in(esk3_3(X5,X6,X7),X7)
            | ~ in(esk3_3(X5,X6,X7),X5)
            | ~ in(esk3_3(X5,X6,X7),X6) )
          & ( in(esk3_3(X5,X6,X7),X7)
            | ( in(esk3_3(X5,X6,X7),X5)
              & in(esk3_3(X5,X6,X7),X6) ) ) )
        | X7 = set_intersection2(X5,X6) ) ),
    inference(skolemize,[status(esa)],[65]) ).

fof(67,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ( ~ in(X8,X7)
            | ( in(X8,X5)
              & in(X8,X6) ) )
          & ( ~ in(X8,X5)
            | ~ in(X8,X6)
            | in(X8,X7) ) )
        | X7 != set_intersection2(X5,X6) )
      & ( ( ( ~ in(esk3_3(X5,X6,X7),X7)
            | ~ in(esk3_3(X5,X6,X7),X5)
            | ~ in(esk3_3(X5,X6,X7),X6) )
          & ( in(esk3_3(X5,X6,X7),X7)
            | ( in(esk3_3(X5,X6,X7),X5)
              & in(esk3_3(X5,X6,X7),X6) ) ) )
        | X7 = set_intersection2(X5,X6) ) ),
    inference(shift_quantors,[status(thm)],[66]) ).

fof(68,plain,
    ! [X5,X6,X7,X8] :
      ( ( in(X8,X5)
        | ~ in(X8,X7)
        | X7 != set_intersection2(X5,X6) )
      & ( in(X8,X6)
        | ~ in(X8,X7)
        | X7 != set_intersection2(X5,X6) )
      & ( ~ in(X8,X5)
        | ~ in(X8,X6)
        | in(X8,X7)
        | X7 != set_intersection2(X5,X6) )
      & ( ~ in(esk3_3(X5,X6,X7),X7)
        | ~ in(esk3_3(X5,X6,X7),X5)
        | ~ in(esk3_3(X5,X6,X7),X6)
        | X7 = set_intersection2(X5,X6) )
      & ( in(esk3_3(X5,X6,X7),X5)
        | in(esk3_3(X5,X6,X7),X7)
        | X7 = set_intersection2(X5,X6) )
      & ( in(esk3_3(X5,X6,X7),X6)
        | in(esk3_3(X5,X6,X7),X7)
        | X7 = set_intersection2(X5,X6) ) ),
    inference(distribute,[status(thm)],[67]) ).

cnf(72,plain,
    ( in(X4,X1)
    | X1 != set_intersection2(X2,X3)
    | ~ in(X4,X3)
    | ~ in(X4,X2) ),
    inference(split_conjunct,[status(thm)],[68]) ).

cnf(73,plain,
    ( in(X4,X3)
    | X1 != set_intersection2(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[68]) ).

fof(78,plain,
    ! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
    inference(variable_rename,[status(thm)],[14]) ).

cnf(79,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[78]) ).

fof(107,plain,
    ! [X1,X2] :
      ( ( disjoint(X1,X2)
        | ? [X3] : in(X3,set_intersection2(X1,X2)) )
      & ( ! [X3] : ~ in(X3,set_intersection2(X1,X2))
        | ~ disjoint(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[29]) ).

fof(108,plain,
    ! [X4,X5] :
      ( ( disjoint(X4,X5)
        | ? [X6] : in(X6,set_intersection2(X4,X5)) )
      & ( ! [X7] : ~ in(X7,set_intersection2(X4,X5))
        | ~ disjoint(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[107]) ).

fof(109,plain,
    ! [X4,X5] :
      ( ( disjoint(X4,X5)
        | in(esk6_2(X4,X5),set_intersection2(X4,X5)) )
      & ( ! [X7] : ~ in(X7,set_intersection2(X4,X5))
        | ~ disjoint(X4,X5) ) ),
    inference(skolemize,[status(esa)],[108]) ).

fof(110,plain,
    ! [X4,X5,X7] :
      ( ( ~ in(X7,set_intersection2(X4,X5))
        | ~ disjoint(X4,X5) )
      & ( disjoint(X4,X5)
        | in(esk6_2(X4,X5),set_intersection2(X4,X5)) ) ),
    inference(shift_quantors,[status(thm)],[109]) ).

cnf(111,plain,
    ( in(esk6_2(X1,X2),set_intersection2(X1,X2))
    | disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[110]) ).

cnf(112,plain,
    ( ~ disjoint(X1,X2)
    | ~ in(X3,set_intersection2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[110]) ).

fof(113,negated_conjecture,
    ? [X1,X2] :
      ( ( ~ disjoint(X1,X2)
        | set_difference(X1,X2) != X1 )
      & ( disjoint(X1,X2)
        | set_difference(X1,X2) = X1 ) ),
    inference(fof_nnf,[status(thm)],[25]) ).

fof(114,negated_conjecture,
    ? [X3,X4] :
      ( ( ~ disjoint(X3,X4)
        | set_difference(X3,X4) != X3 )
      & ( disjoint(X3,X4)
        | set_difference(X3,X4) = X3 ) ),
    inference(variable_rename,[status(thm)],[113]) ).

fof(115,negated_conjecture,
    ( ( ~ disjoint(esk7_0,esk8_0)
      | set_difference(esk7_0,esk8_0) != esk7_0 )
    & ( disjoint(esk7_0,esk8_0)
      | set_difference(esk7_0,esk8_0) = esk7_0 ) ),
    inference(skolemize,[status(esa)],[114]) ).

cnf(116,negated_conjecture,
    ( set_difference(esk7_0,esk8_0) = esk7_0
    | disjoint(esk7_0,esk8_0) ),
    inference(split_conjunct,[status(thm)],[115]) ).

cnf(117,negated_conjecture,
    ( set_difference(esk7_0,esk8_0) != esk7_0
    | ~ disjoint(esk7_0,esk8_0) ),
    inference(split_conjunct,[status(thm)],[115]) ).

cnf(146,plain,
    ( in(X1,X2)
    | ~ in(X1,set_difference(X2,X3)) ),
    inference(er,[status(thm)],[59,theory(equality)]) ).

cnf(151,plain,
    ( in(X1,X2)
    | ~ in(X1,set_intersection2(X3,X2)) ),
    inference(er,[status(thm)],[73,theory(equality)]) ).

cnf(163,plain,
    ( disjoint(X1,X2)
    | in(esk6_2(X1,X2),set_intersection2(X2,X1)) ),
    inference(spm,[status(thm)],[111,79,theory(equality)]) ).

cnf(178,plain,
    ( in(X1,set_intersection2(X2,X3))
    | ~ in(X1,X3)
    | ~ in(X1,X2) ),
    inference(er,[status(thm)],[72,theory(equality)]) ).

cnf(184,plain,
    ( set_difference(X4,X5) = X4
    | in(esk2_3(X4,X5,X4),X4) ),
    inference(ef,[status(thm)],[55,theory(equality)]) ).

cnf(421,plain,
    ( in(esk6_2(X1,X2),X2)
    | disjoint(X1,X2) ),
    inference(spm,[status(thm)],[151,111,theory(equality)]) ).

cnf(443,plain,
    ( in(esk6_2(X1,set_difference(X2,X3)),X2)
    | disjoint(X1,set_difference(X2,X3)) ),
    inference(spm,[status(thm)],[146,421,theory(equality)]) ).

cnf(657,plain,
    ( in(esk6_2(X1,X2),X1)
    | disjoint(X1,X2) ),
    inference(spm,[status(thm)],[151,163,theory(equality)]) ).

cnf(842,plain,
    ( ~ disjoint(X1,X2)
    | ~ in(X3,X2)
    | ~ in(X3,X1) ),
    inference(spm,[status(thm)],[112,178,theory(equality)]) ).

cnf(959,plain,
    ( set_difference(X1,X2) = X1
    | in(esk2_3(X1,X2,X1),X2)
    | ~ in(esk2_3(X1,X2,X1),X1) ),
    inference(spm,[status(thm)],[56,184,theory(equality)]) ).

cnf(3424,negated_conjecture,
    ( set_difference(esk7_0,esk8_0) = esk7_0
    | ~ in(X1,esk8_0)
    | ~ in(X1,esk7_0) ),
    inference(spm,[status(thm)],[842,116,theory(equality)]) ).

cnf(3581,negated_conjecture,
    ( ~ in(X1,esk8_0)
    | ~ in(X1,esk7_0) ),
    inference(csr,[status(thm)],[3424,58]) ).

cnf(3590,negated_conjecture,
    ( disjoint(X1,esk8_0)
    | ~ in(esk6_2(X1,esk8_0),esk7_0) ),
    inference(spm,[status(thm)],[3581,421,theory(equality)]) ).

cnf(3591,negated_conjecture,
    ( disjoint(esk8_0,X1)
    | ~ in(esk6_2(esk8_0,X1),esk7_0) ),
    inference(spm,[status(thm)],[3581,657,theory(equality)]) ).

cnf(3636,negated_conjecture,
    disjoint(esk7_0,esk8_0),
    inference(spm,[status(thm)],[3590,657,theory(equality)]) ).

cnf(3642,negated_conjecture,
    ( set_difference(esk7_0,esk8_0) != esk7_0
    | $false ),
    inference(rw,[status(thm)],[117,3636,theory(equality)]) ).

cnf(3643,negated_conjecture,
    set_difference(esk7_0,esk8_0) != esk7_0,
    inference(cn,[status(thm)],[3642,theory(equality)]) ).

cnf(3903,negated_conjecture,
    disjoint(esk8_0,set_difference(esk7_0,X1)),
    inference(spm,[status(thm)],[3591,443,theory(equality)]) ).

cnf(3915,negated_conjecture,
    ( ~ in(X2,set_difference(esk7_0,X1))
    | ~ in(X2,esk8_0) ),
    inference(spm,[status(thm)],[842,3903,theory(equality)]) ).

cnf(4160,negated_conjecture,
    ( set_difference(set_difference(esk7_0,X1),X2) = set_difference(esk7_0,X1)
    | ~ in(esk2_3(set_difference(esk7_0,X1),X2,set_difference(esk7_0,X1)),esk8_0) ),
    inference(spm,[status(thm)],[3915,184,theory(equality)]) ).

cnf(22796,plain,
    ( set_difference(X1,X2) = X1
    | in(esk2_3(X1,X2,X1),X2) ),
    inference(csr,[status(thm)],[959,184]) ).

cnf(160143,negated_conjecture,
    set_difference(set_difference(esk7_0,X1),esk8_0) = set_difference(esk7_0,X1),
    inference(spm,[status(thm)],[4160,22796,theory(equality)]) ).

cnf(160165,negated_conjecture,
    set_difference(esk7_0,esk8_0) = esk7_0,
    inference(spm,[status(thm)],[160143,38,theory(equality)]) ).

cnf(160666,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[160165,3643,theory(equality)]) ).

cnf(160667,negated_conjecture,
    $false,
    160666,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU141+1.p
% --creating new selector for []
% -running prover on /tmp/tmpjRMtxD/sel_SEU141+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU141+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU141+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU141+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
%------------------------------------------------------------------------------