TSTP Solution File: SET734+4 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET734+4 : TPTP v5.0.0. Bugfixed v2.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art03.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 03:22:16 EST 2010

% Result   : Theorem 0.21s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   37 (   5 unt;   0 def)
%            Number of atoms       :  199 (   0 equ)
%            Maximal formula atoms :   18 (   5 avg)
%            Number of connectives :  261 (  99   ~;  97   |;  57   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   8 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-7 aty)
%            Number of variables   :  161 (   1 sgn 102   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2,X3] :
      ( surjective(X1,X2,X3)
    <=> ! [X4] :
          ( member(X4,X3)
         => ? [X5] :
              ( member(X5,X2)
              & apply(X1,X5,X4) ) ) ),
    file('/tmp/tmpBXUeKs/sel_SET734+4.p_1',surjective) ).

fof(5,axiom,
    ! [X1,X2] :
      ( identity(X1,X2)
    <=> ! [X6] :
          ( member(X6,X2)
         => apply(X1,X6,X6) ) ),
    file('/tmp/tmpBXUeKs/sel_SET734+4.p_1',identity) ).

fof(6,axiom,
    ! [X11,X1,X2,X3,X12,X6,X13] :
      ( ( member(X6,X2)
        & member(X13,X12) )
     => ( apply(compose_function(X11,X1,X2,X3,X12),X6,X13)
      <=> ? [X4] :
            ( member(X4,X3)
            & apply(X1,X6,X4)
            & apply(X11,X4,X13) ) ) ),
    file('/tmp/tmpBXUeKs/sel_SET734+4.p_1',compose_function) ).

fof(7,conjecture,
    ! [X1,X11,X2,X3] :
      ( ( maps(X11,X2,X3)
        & maps(X1,X3,X2)
        & identity(compose_function(X11,X1,X3,X2,X3),X3) )
     => surjective(X11,X2,X3) ),
    file('/tmp/tmpBXUeKs/sel_SET734+4.p_1',thII25) ).

fof(8,negated_conjecture,
    ~ ! [X1,X11,X2,X3] :
        ( ( maps(X11,X2,X3)
          & maps(X1,X3,X2)
          & identity(compose_function(X11,X1,X3,X2,X3),X3) )
       => surjective(X11,X2,X3) ),
    inference(assume_negation,[status(cth)],[7]) ).

fof(9,plain,
    ! [X1,X2,X3] :
      ( ( ~ surjective(X1,X2,X3)
        | ! [X4] :
            ( ~ member(X4,X3)
            | ? [X5] :
                ( member(X5,X2)
                & apply(X1,X5,X4) ) ) )
      & ( ? [X4] :
            ( member(X4,X3)
            & ! [X5] :
                ( ~ member(X5,X2)
                | ~ apply(X1,X5,X4) ) )
        | surjective(X1,X2,X3) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(10,plain,
    ! [X6,X7,X8] :
      ( ( ~ surjective(X6,X7,X8)
        | ! [X9] :
            ( ~ member(X9,X8)
            | ? [X10] :
                ( member(X10,X7)
                & apply(X6,X10,X9) ) ) )
      & ( ? [X11] :
            ( member(X11,X8)
            & ! [X12] :
                ( ~ member(X12,X7)
                | ~ apply(X6,X12,X11) ) )
        | surjective(X6,X7,X8) ) ),
    inference(variable_rename,[status(thm)],[9]) ).

fof(11,plain,
    ! [X6,X7,X8] :
      ( ( ~ surjective(X6,X7,X8)
        | ! [X9] :
            ( ~ member(X9,X8)
            | ( member(esk1_4(X6,X7,X8,X9),X7)
              & apply(X6,esk1_4(X6,X7,X8,X9),X9) ) ) )
      & ( ( member(esk2_3(X6,X7,X8),X8)
          & ! [X12] :
              ( ~ member(X12,X7)
              | ~ apply(X6,X12,esk2_3(X6,X7,X8)) ) )
        | surjective(X6,X7,X8) ) ),
    inference(skolemize,[status(esa)],[10]) ).

fof(12,plain,
    ! [X6,X7,X8,X9,X12] :
      ( ( ( ( ~ member(X12,X7)
            | ~ apply(X6,X12,esk2_3(X6,X7,X8)) )
          & member(esk2_3(X6,X7,X8),X8) )
        | surjective(X6,X7,X8) )
      & ( ~ member(X9,X8)
        | ( member(esk1_4(X6,X7,X8,X9),X7)
          & apply(X6,esk1_4(X6,X7,X8,X9),X9) )
        | ~ surjective(X6,X7,X8) ) ),
    inference(shift_quantors,[status(thm)],[11]) ).

fof(13,plain,
    ! [X6,X7,X8,X9,X12] :
      ( ( ~ member(X12,X7)
        | ~ apply(X6,X12,esk2_3(X6,X7,X8))
        | surjective(X6,X7,X8) )
      & ( member(esk2_3(X6,X7,X8),X8)
        | surjective(X6,X7,X8) )
      & ( member(esk1_4(X6,X7,X8,X9),X7)
        | ~ member(X9,X8)
        | ~ surjective(X6,X7,X8) )
      & ( apply(X6,esk1_4(X6,X7,X8,X9),X9)
        | ~ member(X9,X8)
        | ~ surjective(X6,X7,X8) ) ),
    inference(distribute,[status(thm)],[12]) ).

cnf(16,plain,
    ( surjective(X1,X2,X3)
    | member(esk2_3(X1,X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[13]) ).

cnf(17,plain,
    ( surjective(X1,X2,X3)
    | ~ apply(X1,X4,esk2_3(X1,X2,X3))
    | ~ member(X4,X2) ),
    inference(split_conjunct,[status(thm)],[13]) ).

fof(56,plain,
    ! [X1,X2] :
      ( ( ~ identity(X1,X2)
        | ! [X6] :
            ( ~ member(X6,X2)
            | apply(X1,X6,X6) ) )
      & ( ? [X6] :
            ( member(X6,X2)
            & ~ apply(X1,X6,X6) )
        | identity(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(57,plain,
    ! [X7,X8] :
      ( ( ~ identity(X7,X8)
        | ! [X9] :
            ( ~ member(X9,X8)
            | apply(X7,X9,X9) ) )
      & ( ? [X10] :
            ( member(X10,X8)
            & ~ apply(X7,X10,X10) )
        | identity(X7,X8) ) ),
    inference(variable_rename,[status(thm)],[56]) ).

fof(58,plain,
    ! [X7,X8] :
      ( ( ~ identity(X7,X8)
        | ! [X9] :
            ( ~ member(X9,X8)
            | apply(X7,X9,X9) ) )
      & ( ( member(esk11_2(X7,X8),X8)
          & ~ apply(X7,esk11_2(X7,X8),esk11_2(X7,X8)) )
        | identity(X7,X8) ) ),
    inference(skolemize,[status(esa)],[57]) ).

fof(59,plain,
    ! [X7,X8,X9] :
      ( ( ~ member(X9,X8)
        | apply(X7,X9,X9)
        | ~ identity(X7,X8) )
      & ( ( member(esk11_2(X7,X8),X8)
          & ~ apply(X7,esk11_2(X7,X8),esk11_2(X7,X8)) )
        | identity(X7,X8) ) ),
    inference(shift_quantors,[status(thm)],[58]) ).

fof(60,plain,
    ! [X7,X8,X9] :
      ( ( ~ member(X9,X8)
        | apply(X7,X9,X9)
        | ~ identity(X7,X8) )
      & ( member(esk11_2(X7,X8),X8)
        | identity(X7,X8) )
      & ( ~ apply(X7,esk11_2(X7,X8),esk11_2(X7,X8))
        | identity(X7,X8) ) ),
    inference(distribute,[status(thm)],[59]) ).

cnf(63,plain,
    ( apply(X1,X3,X3)
    | ~ identity(X1,X2)
    | ~ member(X3,X2) ),
    inference(split_conjunct,[status(thm)],[60]) ).

fof(64,plain,
    ! [X11,X1,X2,X3,X12,X6,X13] :
      ( ~ member(X6,X2)
      | ~ member(X13,X12)
      | ( ( ~ apply(compose_function(X11,X1,X2,X3,X12),X6,X13)
          | ? [X4] :
              ( member(X4,X3)
              & apply(X1,X6,X4)
              & apply(X11,X4,X13) ) )
        & ( ! [X4] :
              ( ~ member(X4,X3)
              | ~ apply(X1,X6,X4)
              | ~ apply(X11,X4,X13) )
          | apply(compose_function(X11,X1,X2,X3,X12),X6,X13) ) ) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(65,plain,
    ! [X14,X15,X16,X17,X18,X19,X20] :
      ( ~ member(X19,X16)
      | ~ member(X20,X18)
      | ( ( ~ apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
          | ? [X21] :
              ( member(X21,X17)
              & apply(X15,X19,X21)
              & apply(X14,X21,X20) ) )
        & ( ! [X22] :
              ( ~ member(X22,X17)
              | ~ apply(X15,X19,X22)
              | ~ apply(X14,X22,X20) )
          | apply(compose_function(X14,X15,X16,X17,X18),X19,X20) ) ) ),
    inference(variable_rename,[status(thm)],[64]) ).

fof(66,plain,
    ! [X14,X15,X16,X17,X18,X19,X20] :
      ( ~ member(X19,X16)
      | ~ member(X20,X18)
      | ( ( ~ apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
          | ( member(esk12_7(X14,X15,X16,X17,X18,X19,X20),X17)
            & apply(X15,X19,esk12_7(X14,X15,X16,X17,X18,X19,X20))
            & apply(X14,esk12_7(X14,X15,X16,X17,X18,X19,X20),X20) ) )
        & ( ! [X22] :
              ( ~ member(X22,X17)
              | ~ apply(X15,X19,X22)
              | ~ apply(X14,X22,X20) )
          | apply(compose_function(X14,X15,X16,X17,X18),X19,X20) ) ) ),
    inference(skolemize,[status(esa)],[65]) ).

fof(67,plain,
    ! [X14,X15,X16,X17,X18,X19,X20,X22] :
      ( ( ( ~ member(X22,X17)
          | ~ apply(X15,X19,X22)
          | ~ apply(X14,X22,X20)
          | apply(compose_function(X14,X15,X16,X17,X18),X19,X20) )
        & ( ~ apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
          | ( member(esk12_7(X14,X15,X16,X17,X18,X19,X20),X17)
            & apply(X15,X19,esk12_7(X14,X15,X16,X17,X18,X19,X20))
            & apply(X14,esk12_7(X14,X15,X16,X17,X18,X19,X20),X20) ) ) )
      | ~ member(X19,X16)
      | ~ member(X20,X18) ),
    inference(shift_quantors,[status(thm)],[66]) ).

fof(68,plain,
    ! [X14,X15,X16,X17,X18,X19,X20,X22] :
      ( ( ~ member(X22,X17)
        | ~ apply(X15,X19,X22)
        | ~ apply(X14,X22,X20)
        | apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
        | ~ member(X19,X16)
        | ~ member(X20,X18) )
      & ( member(esk12_7(X14,X15,X16,X17,X18,X19,X20),X17)
        | ~ apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
        | ~ member(X19,X16)
        | ~ member(X20,X18) )
      & ( apply(X15,X19,esk12_7(X14,X15,X16,X17,X18,X19,X20))
        | ~ apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
        | ~ member(X19,X16)
        | ~ member(X20,X18) )
      & ( apply(X14,esk12_7(X14,X15,X16,X17,X18,X19,X20),X20)
        | ~ apply(compose_function(X14,X15,X16,X17,X18),X19,X20)
        | ~ member(X19,X16)
        | ~ member(X20,X18) ) ),
    inference(distribute,[status(thm)],[67]) ).

cnf(69,plain,
    ( apply(X5,esk12_7(X5,X6,X4,X7,X2,X3,X1),X1)
    | ~ member(X1,X2)
    | ~ member(X3,X4)
    | ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
    inference(split_conjunct,[status(thm)],[68]) ).

cnf(71,plain,
    ( member(esk12_7(X5,X6,X4,X7,X2,X3,X1),X7)
    | ~ member(X1,X2)
    | ~ member(X3,X4)
    | ~ apply(compose_function(X5,X6,X4,X7,X2),X3,X1) ),
    inference(split_conjunct,[status(thm)],[68]) ).

fof(73,negated_conjecture,
    ? [X1,X11,X2,X3] :
      ( maps(X11,X2,X3)
      & maps(X1,X3,X2)
      & identity(compose_function(X11,X1,X3,X2,X3),X3)
      & ~ surjective(X11,X2,X3) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(74,negated_conjecture,
    ? [X12,X13,X14,X15] :
      ( maps(X13,X14,X15)
      & maps(X12,X15,X14)
      & identity(compose_function(X13,X12,X15,X14,X15),X15)
      & ~ surjective(X13,X14,X15) ),
    inference(variable_rename,[status(thm)],[73]) ).

fof(75,negated_conjecture,
    ( maps(esk14_0,esk15_0,esk16_0)
    & maps(esk13_0,esk16_0,esk15_0)
    & identity(compose_function(esk14_0,esk13_0,esk16_0,esk15_0,esk16_0),esk16_0)
    & ~ surjective(esk14_0,esk15_0,esk16_0) ),
    inference(skolemize,[status(esa)],[74]) ).

cnf(76,negated_conjecture,
    ~ surjective(esk14_0,esk15_0,esk16_0),
    inference(split_conjunct,[status(thm)],[75]) ).

cnf(77,negated_conjecture,
    identity(compose_function(esk14_0,esk13_0,esk16_0,esk15_0,esk16_0),esk16_0),
    inference(split_conjunct,[status(thm)],[75]) ).

cnf(80,negated_conjecture,
    ( apply(compose_function(esk14_0,esk13_0,esk16_0,esk15_0,esk16_0),X1,X1)
    | ~ member(X1,esk16_0) ),
    inference(spm,[status(thm)],[63,77,theory(equality)]) ).

cnf(98,plain,
    ( surjective(X1,X2,X3)
    | ~ member(esk12_7(X1,X4,X5,X6,X7,X8,esk2_3(X1,X2,X3)),X2)
    | ~ apply(compose_function(X1,X4,X5,X6,X7),X8,esk2_3(X1,X2,X3))
    | ~ member(X8,X5)
    | ~ member(esk2_3(X1,X2,X3),X7) ),
    inference(spm,[status(thm)],[17,69,theory(equality)]) ).

cnf(352,plain,
    ( surjective(X1,X2,X3)
    | ~ apply(compose_function(X1,X4,X5,X2,X6),X7,esk2_3(X1,X2,X3))
    | ~ member(esk2_3(X1,X2,X3),X6)
    | ~ member(X7,X5) ),
    inference(spm,[status(thm)],[98,71,theory(equality)]) ).

cnf(355,negated_conjecture,
    ( surjective(esk14_0,esk15_0,X1)
    | ~ member(esk2_3(esk14_0,esk15_0,X1),esk16_0) ),
    inference(spm,[status(thm)],[352,80,theory(equality)]) ).

cnf(358,negated_conjecture,
    surjective(esk14_0,esk15_0,esk16_0),
    inference(spm,[status(thm)],[355,16,theory(equality)]) ).

cnf(359,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[358,76,theory(equality)]) ).

cnf(360,negated_conjecture,
    $false,
    359,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET734+4.p
% --creating new selector for [SET006+0.ax, SET006+1.ax]
% -running prover on /tmp/tmpBXUeKs/sel_SET734+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET734+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET734+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET734+4.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
% 
%------------------------------------------------------------------------------