TSTP Solution File: COM007+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : COM007+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art06.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 : Sat Dec 25 05:44:19 EST 2010

% Result   : Theorem 0.22s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   63 (  16 unt;   0 def)
%            Number of atoms       :  148 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  149 (  64   ~;  69   |;   9   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   2 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-3 aty)
%            Number of variables   :   93 (   0 sgn  53   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] :
      ( ( reflexive_rewrite(b,X1)
        & reflexive_rewrite(c,X1) )
     => goal ),
    file('/tmp/tmpIlWpqP/sel_COM007+1.p_1',goal_ax) ).

fof(2,axiom,
    ! [X1,X2] :
      ( reflexive_rewrite(X1,X2)
     => ( equalish(X1,X2)
        | rewrite(X1,X2) ) ),
    file('/tmp/tmpIlWpqP/sel_COM007+1.p_1',equalish_or_rewrite) ).

fof(3,axiom,
    ! [X1,X2] :
      ( equalish(X1,X2)
     => reflexive_rewrite(X1,X2) ),
    file('/tmp/tmpIlWpqP/sel_COM007+1.p_1',equalish_in_reflexive_rewrite) ).

fof(4,axiom,
    ! [X1] : equalish(X1,X1),
    file('/tmp/tmpIlWpqP/sel_COM007+1.p_1',reflexivity) ).

fof(5,conjecture,
    goal,
    file('/tmp/tmpIlWpqP/sel_COM007+1.p_1',goal_to_be_proved) ).

fof(6,axiom,
    ! [X1,X2] :
      ( rewrite(X1,X2)
     => reflexive_rewrite(X1,X2) ),
    file('/tmp/tmpIlWpqP/sel_COM007+1.p_1',rewrite_in_reflexive_rewrite) ).

fof(7,axiom,
    ( reflexive_rewrite(a,b)
    & reflexive_rewrite(a,c) ),
    file('/tmp/tmpIlWpqP/sel_COM007+1.p_1',assumption) ).

fof(8,axiom,
    ! [X1,X2,X3] :
      ( ( equalish(X1,X2)
        & reflexive_rewrite(X2,X3) )
     => reflexive_rewrite(X1,X3) ),
    file('/tmp/tmpIlWpqP/sel_COM007+1.p_1',substitution) ).

fof(9,axiom,
    ! [X1,X2] :
      ( equalish(X1,X2)
     => equalish(X2,X1) ),
    file('/tmp/tmpIlWpqP/sel_COM007+1.p_1',symmtery) ).

fof(10,axiom,
    ! [X1,X2,X3] :
      ( ( rewrite(X1,X2)
        & rewrite(X1,X3) )
     => ? [X4] :
          ( rewrite(X2,X4)
          & rewrite(X3,X4) ) ),
    file('/tmp/tmpIlWpqP/sel_COM007+1.p_1',rewrite_diamond) ).

fof(11,negated_conjecture,
    ~ goal,
    inference(assume_negation,[status(cth)],[5]) ).

fof(12,negated_conjecture,
    ~ goal,
    inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).

fof(13,plain,
    ! [X1] :
      ( ~ reflexive_rewrite(b,X1)
      | ~ reflexive_rewrite(c,X1)
      | goal ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(14,plain,
    ! [X2] :
      ( ~ reflexive_rewrite(b,X2)
      | ~ reflexive_rewrite(c,X2)
      | goal ),
    inference(variable_rename,[status(thm)],[13]) ).

cnf(15,plain,
    ( goal
    | ~ reflexive_rewrite(c,X1)
    | ~ reflexive_rewrite(b,X1) ),
    inference(split_conjunct,[status(thm)],[14]) ).

fof(16,plain,
    ! [X1,X2] :
      ( ~ reflexive_rewrite(X1,X2)
      | equalish(X1,X2)
      | rewrite(X1,X2) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(17,plain,
    ! [X3,X4] :
      ( ~ reflexive_rewrite(X3,X4)
      | equalish(X3,X4)
      | rewrite(X3,X4) ),
    inference(variable_rename,[status(thm)],[16]) ).

cnf(18,plain,
    ( rewrite(X1,X2)
    | equalish(X1,X2)
    | ~ reflexive_rewrite(X1,X2) ),
    inference(split_conjunct,[status(thm)],[17]) ).

fof(19,plain,
    ! [X1,X2] :
      ( ~ equalish(X1,X2)
      | reflexive_rewrite(X1,X2) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(20,plain,
    ! [X3,X4] :
      ( ~ equalish(X3,X4)
      | reflexive_rewrite(X3,X4) ),
    inference(variable_rename,[status(thm)],[19]) ).

cnf(21,plain,
    ( reflexive_rewrite(X1,X2)
    | ~ equalish(X1,X2) ),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(22,plain,
    ! [X2] : equalish(X2,X2),
    inference(variable_rename,[status(thm)],[4]) ).

cnf(23,plain,
    equalish(X1,X1),
    inference(split_conjunct,[status(thm)],[22]) ).

cnf(24,negated_conjecture,
    ~ goal,
    inference(split_conjunct,[status(thm)],[12]) ).

fof(25,plain,
    ! [X1,X2] :
      ( ~ rewrite(X1,X2)
      | reflexive_rewrite(X1,X2) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(26,plain,
    ! [X3,X4] :
      ( ~ rewrite(X3,X4)
      | reflexive_rewrite(X3,X4) ),
    inference(variable_rename,[status(thm)],[25]) ).

cnf(27,plain,
    ( reflexive_rewrite(X1,X2)
    | ~ rewrite(X1,X2) ),
    inference(split_conjunct,[status(thm)],[26]) ).

cnf(28,plain,
    reflexive_rewrite(a,c),
    inference(split_conjunct,[status(thm)],[7]) ).

cnf(29,plain,
    reflexive_rewrite(a,b),
    inference(split_conjunct,[status(thm)],[7]) ).

fof(30,plain,
    ! [X1,X2,X3] :
      ( ~ equalish(X1,X2)
      | ~ reflexive_rewrite(X2,X3)
      | reflexive_rewrite(X1,X3) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(31,plain,
    ! [X4,X5,X6] :
      ( ~ equalish(X4,X5)
      | ~ reflexive_rewrite(X5,X6)
      | reflexive_rewrite(X4,X6) ),
    inference(variable_rename,[status(thm)],[30]) ).

cnf(32,plain,
    ( reflexive_rewrite(X1,X2)
    | ~ reflexive_rewrite(X3,X2)
    | ~ equalish(X1,X3) ),
    inference(split_conjunct,[status(thm)],[31]) ).

fof(33,plain,
    ! [X1,X2] :
      ( ~ equalish(X1,X2)
      | equalish(X2,X1) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(34,plain,
    ! [X3,X4] :
      ( ~ equalish(X3,X4)
      | equalish(X4,X3) ),
    inference(variable_rename,[status(thm)],[33]) ).

cnf(35,plain,
    ( equalish(X1,X2)
    | ~ equalish(X2,X1) ),
    inference(split_conjunct,[status(thm)],[34]) ).

fof(36,plain,
    ! [X1,X2,X3] :
      ( ~ rewrite(X1,X2)
      | ~ rewrite(X1,X3)
      | ? [X4] :
          ( rewrite(X2,X4)
          & rewrite(X3,X4) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(37,plain,
    ! [X5,X6,X7] :
      ( ~ rewrite(X5,X6)
      | ~ rewrite(X5,X7)
      | ? [X8] :
          ( rewrite(X6,X8)
          & rewrite(X7,X8) ) ),
    inference(variable_rename,[status(thm)],[36]) ).

fof(38,plain,
    ! [X5,X6,X7] :
      ( ~ rewrite(X5,X6)
      | ~ rewrite(X5,X7)
      | ( rewrite(X6,esk1_3(X5,X6,X7))
        & rewrite(X7,esk1_3(X5,X6,X7)) ) ),
    inference(skolemize,[status(esa)],[37]) ).

fof(39,plain,
    ! [X5,X6,X7] :
      ( ( rewrite(X6,esk1_3(X5,X6,X7))
        | ~ rewrite(X5,X6)
        | ~ rewrite(X5,X7) )
      & ( rewrite(X7,esk1_3(X5,X6,X7))
        | ~ rewrite(X5,X6)
        | ~ rewrite(X5,X7) ) ),
    inference(distribute,[status(thm)],[38]) ).

cnf(40,plain,
    ( rewrite(X2,esk1_3(X1,X3,X2))
    | ~ rewrite(X1,X2)
    | ~ rewrite(X1,X3) ),
    inference(split_conjunct,[status(thm)],[39]) ).

cnf(41,plain,
    ( rewrite(X3,esk1_3(X1,X3,X2))
    | ~ rewrite(X1,X2)
    | ~ rewrite(X1,X3) ),
    inference(split_conjunct,[status(thm)],[39]) ).

cnf(42,plain,
    reflexive_rewrite(X1,X1),
    inference(spm,[status(thm)],[21,23,theory(equality)]) ).

cnf(45,plain,
    ( ~ reflexive_rewrite(b,X1)
    | ~ reflexive_rewrite(c,X1) ),
    inference(sr,[status(thm)],[15,24,theory(equality)]) ).

cnf(47,plain,
    ( equalish(X1,X2)
    | rewrite(X2,X1)
    | ~ reflexive_rewrite(X2,X1) ),
    inference(spm,[status(thm)],[35,18,theory(equality)]) ).

cnf(50,plain,
    ( reflexive_rewrite(X1,esk1_3(X2,X1,X3))
    | ~ rewrite(X2,X1)
    | ~ rewrite(X2,X3) ),
    inference(spm,[status(thm)],[27,41,theory(equality)]) ).

cnf(51,plain,
    ( reflexive_rewrite(X1,esk1_3(X2,X3,X1))
    | ~ rewrite(X2,X3)
    | ~ rewrite(X2,X1) ),
    inference(spm,[status(thm)],[27,40,theory(equality)]) ).

cnf(52,plain,
    ~ reflexive_rewrite(b,c),
    inference(spm,[status(thm)],[45,42,theory(equality)]) ).

cnf(55,plain,
    ( reflexive_rewrite(X1,X2)
    | rewrite(X3,X1)
    | ~ reflexive_rewrite(X3,X2)
    | ~ reflexive_rewrite(X3,X1) ),
    inference(spm,[status(thm)],[32,47,theory(equality)]) ).

cnf(62,plain,
    ( ~ reflexive_rewrite(b,esk1_3(X1,c,X2))
    | ~ rewrite(X1,c)
    | ~ rewrite(X1,X2) ),
    inference(spm,[status(thm)],[45,50,theory(equality)]) ).

cnf(66,plain,
    ( ~ rewrite(X1,c)
    | ~ rewrite(X1,b) ),
    inference(spm,[status(thm)],[62,51,theory(equality)]) ).

cnf(67,plain,
    ( rewrite(a,X1)
    | reflexive_rewrite(X1,b)
    | ~ reflexive_rewrite(a,X1) ),
    inference(spm,[status(thm)],[55,29,theory(equality)]) ).

cnf(68,plain,
    ( rewrite(a,X1)
    | reflexive_rewrite(X1,c)
    | ~ reflexive_rewrite(a,X1) ),
    inference(spm,[status(thm)],[55,28,theory(equality)]) ).

cnf(74,plain,
    ( reflexive_rewrite(c,b)
    | ~ rewrite(a,b)
    | ~ reflexive_rewrite(a,c) ),
    inference(spm,[status(thm)],[66,67,theory(equality)]) ).

cnf(75,plain,
    ( reflexive_rewrite(c,b)
    | ~ rewrite(a,b)
    | $false ),
    inference(rw,[status(thm)],[74,28,theory(equality)]) ).

cnf(76,plain,
    ( reflexive_rewrite(c,b)
    | ~ rewrite(a,b) ),
    inference(cn,[status(thm)],[75,theory(equality)]) ).

cnf(104,plain,
    ( reflexive_rewrite(c,b)
    | reflexive_rewrite(b,c)
    | ~ reflexive_rewrite(a,b) ),
    inference(spm,[status(thm)],[76,68,theory(equality)]) ).

cnf(109,plain,
    ( reflexive_rewrite(c,b)
    | reflexive_rewrite(b,c)
    | $false ),
    inference(rw,[status(thm)],[104,29,theory(equality)]) ).

cnf(110,plain,
    ( reflexive_rewrite(c,b)
    | reflexive_rewrite(b,c) ),
    inference(cn,[status(thm)],[109,theory(equality)]) ).

cnf(111,plain,
    reflexive_rewrite(c,b),
    inference(sr,[status(thm)],[110,52,theory(equality)]) ).

cnf(116,plain,
    ~ reflexive_rewrite(b,b),
    inference(spm,[status(thm)],[45,111,theory(equality)]) ).

cnf(120,plain,
    $false,
    inference(rw,[status(thm)],[116,42,theory(equality)]) ).

cnf(121,plain,
    $false,
    inference(cn,[status(thm)],[120,theory(equality)]) ).

cnf(122,plain,
    $false,
    121,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/COM/COM007+1.p
% --creating new selector for []
% -running prover on /tmp/tmpIlWpqP/sel_COM007+1.p_1 with time limit 29
% -prover status Theorem
% Problem COM007+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/COM/COM007+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/COM/COM007+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
% 
%------------------------------------------------------------------------------