TSTP Solution File: LCL525+1 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : LCL525+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art06.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 1003MB
% OS       : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May  6 13:52:05 EDT 2009

% Result   : Theorem 7.4s
% Output   : Refutation 7.4s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   28 (  16 unt;   0 def)
%            Number of atoms       :   61 (   0 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :   56 (  23   ~;  26   |;   7   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    7 (   5 usr;   5 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   0 con; 1-2 aty)
%            Number of variables   :   34 (   8 sgn   7   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(modus_ponens_strict_implies,plain,
    ! [A,B] :
      ( ( ~ modus_ponens_strict_implies
        | ~ is_a_theorem(A)
        | ~ is_a_theorem(strict_implies(A,B))
        | is_a_theorem(B) )
      & ( ~ is_a_theorem(y(A,B))
        | modus_ponens_strict_implies )
      & ( is_a_theorem(x(A,B))
        | modus_ponens_strict_implies )
      & ( is_a_theorem(strict_implies(x(A,B),y(A,B)))
        | modus_ponens_strict_implies ) ),
    file('/tmp/SystemOnTPTP11239/LCL525+1.p',unknown),
    [] ).

cnf(172169120,plain,
    ( ~ is_a_theorem(y(A,B))
    | modus_ponens_strict_implies ),
    inference(rewrite,[status(thm)],[modus_ponens_strict_implies]),
    [] ).

fof(s1_0_modus_ponens_strict_implies,plain,
    ~ modus_ponens_strict_implies,
    file('/tmp/SystemOnTPTP11239/LCL525+1.p',unknown),
    [] ).

cnf(173356600,plain,
    ~ modus_ponens_strict_implies,
    inference(rewrite,[status(thm)],[s1_0_modus_ponens_strict_implies]),
    [] ).

cnf(182536896,plain,
    ~ is_a_theorem(y(A,B)),
    inference(resolution,[status(thm)],[172169120,173356600]),
    [] ).

cnf(172156736,plain,
    ( is_a_theorem(x(A,B))
    | modus_ponens_strict_implies ),
    inference(rewrite,[status(thm)],[modus_ponens_strict_implies]),
    [] ).

cnf(182525304,plain,
    is_a_theorem(x(A,B)),
    inference(resolution,[status(thm)],[172156736,173356600]),
    [] ).

fof(axiom_M,plain,
    ! [A] :
      ( ( ~ axiom_m
        | is_a_theorem(implies(necessarily(A),A)) )
      & ( axiom_m
        | ~ is_a_theorem(implies(necessarily(x(A)),x(A))) ) ),
    file('/tmp/SystemOnTPTP11239/LCL525+1.p',unknown),
    [] ).

cnf(172405696,plain,
    ( ~ axiom_m
    | is_a_theorem(implies(necessarily(A),A)) ),
    inference(rewrite,[status(thm)],[axiom_M]),
    [] ).

fof(km5_axiom_M,plain,
    axiom_m,
    file('/tmp/SystemOnTPTP11239/LCL525+1.p',unknown),
    [] ).

cnf(173266464,plain,
    axiom_m,
    inference(rewrite,[status(thm)],[km5_axiom_M]),
    [] ).

cnf(182479072,plain,
    is_a_theorem(implies(necessarily(A),A)),
    inference(resolution,[status(thm)],[172405696,173266464]),
    [] ).

fof(modus_ponens,plain,
    ! [A,B] :
      ( ( ~ modus_ponens
        | ~ is_a_theorem(A)
        | ~ is_a_theorem(implies(A,B))
        | is_a_theorem(B) )
      & ( ~ is_a_theorem(y(A,B))
        | modus_ponens )
      & ( is_a_theorem(x(A,B))
        | modus_ponens )
      & ( is_a_theorem(implies(x(A,B),y(A,B)))
        | modus_ponens ) ),
    file('/tmp/SystemOnTPTP11239/LCL525+1.p',unknown),
    [] ).

cnf(170558768,plain,
    ( ~ modus_ponens
    | ~ is_a_theorem(A)
    | ~ is_a_theorem(implies(A,B))
    | is_a_theorem(B) ),
    inference(rewrite,[status(thm)],[modus_ponens]),
    [] ).

fof(hilbert_modus_ponens,plain,
    modus_ponens,
    file('/tmp/SystemOnTPTP11239/LCL525+1.p',unknown),
    [] ).

cnf(171821656,plain,
    modus_ponens,
    inference(rewrite,[status(thm)],[hilbert_modus_ponens]),
    [] ).

cnf(182250840,plain,
    ( ~ is_a_theorem(A)
    | ~ is_a_theorem(implies(A,B))
    | is_a_theorem(B) ),
    inference(resolution,[status(thm)],[170558768,171821656]),
    [] ).

cnf(193562088,plain,
    ( ~ is_a_theorem(necessarily(A))
    | is_a_theorem(A) ),
    inference(resolution,[status(thm)],[182479072,182250840]),
    [] ).

cnf(172137104,plain,
    ( is_a_theorem(strict_implies(x(A,B),y(A,B)))
    | modus_ponens_strict_implies ),
    inference(rewrite,[status(thm)],[modus_ponens_strict_implies]),
    [] ).

cnf(182549624,plain,
    is_a_theorem(strict_implies(x(A,B),y(A,B))),
    inference(resolution,[status(thm)],[172137104,173356600]),
    [] ).

fof(op_strict_implies,plain,
    ! [A,B] :
      ( ~ op_strict_implies
      | $equal(necessarily(implies(A,B)),strict_implies(A,B)) ),
    file('/tmp/SystemOnTPTP11239/LCL525+1.p',unknown),
    [] ).

cnf(173177896,plain,
    ( ~ op_strict_implies
    | $equal(necessarily(implies(A,B)),strict_implies(A,B)) ),
    inference(rewrite,[status(thm)],[op_strict_implies]),
    [] ).

fof(s1_0_op_strict_implies,plain,
    op_strict_implies,
    file('/tmp/SystemOnTPTP11239/LCL525+1.p',unknown),
    [] ).

cnf(173321488,plain,
    op_strict_implies,
    inference(rewrite,[status(thm)],[s1_0_op_strict_implies]),
    [] ).

cnf(182502248,plain,
    $equal(necessarily(implies(A,B)),strict_implies(A,B)),
    inference(resolution,[status(thm)],[173177896,173321488]),
    [] ).

cnf(184972328,plain,
    is_a_theorem(necessarily(implies(x(A,B),y(A,B)))),
    inference(paramodulation,[status(thm)],[182549624,182502248,theory(equality)]),
    [] ).

cnf(217329096,plain,
    is_a_theorem(implies(x(A,B),y(A,B))),
    inference(resolution,[status(thm)],[193562088,184972328]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[182536896,182525304,217329096,182250840]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 7 seconds
% START OF PROOF SEQUENCE
% fof(modus_ponens_strict_implies,plain,(((~modus_ponens_strict_implies|~is_a_theorem(A)|~is_a_theorem(strict_implies(A,B))|is_a_theorem(B))&(~is_a_theorem(y(A,B))|modus_ponens_strict_implies)&(is_a_theorem(x(A,B))|modus_ponens_strict_implies)&(is_a_theorem(strict_implies(x(A,B),y(A,B)))|modus_ponens_strict_implies))),file('/tmp/SystemOnTPTP11239/LCL525+1.p',unknown),[]).
% 
% cnf(172169120,plain,(~is_a_theorem(y(A,B))|modus_ponens_strict_implies),inference(rewrite,[status(thm)],[modus_ponens_strict_implies]),[]).
% 
% fof(s1_0_modus_ponens_strict_implies,plain,(~modus_ponens_strict_implies),file('/tmp/SystemOnTPTP11239/LCL525+1.p',unknown),[]).
% 
% cnf(173356600,plain,(~modus_ponens_strict_implies),inference(rewrite,[status(thm)],[s1_0_modus_ponens_strict_implies]),[]).
% 
% cnf(182536896,plain,(~is_a_theorem(y(A,B))),inference(resolution,[status(thm)],[172169120,173356600]),[]).
% 
% cnf(172156736,plain,(is_a_theorem(x(A,B))|modus_ponens_strict_implies),inference(rewrite,[status(thm)],[modus_ponens_strict_implies]),[]).
% 
% cnf(182525304,plain,(is_a_theorem(x(A,B))),inference(resolution,[status(thm)],[172156736,173356600]),[]).
% 
% fof(axiom_M,plain,(((~axiom_m|is_a_theorem(implies(necessarily(A),A)))&(axiom_m|~is_a_theorem(implies(necessarily(x(A)),x(A)))))),file('/tmp/SystemOnTPTP11239/LCL525+1.p',unknown),[]).
% 
% cnf(172405696,plain,(~axiom_m|is_a_theorem(implies(necessarily(A),A))),inference(rewrite,[status(thm)],[axiom_M]),[]).
% 
% fof(km5_axiom_M,plain,(axiom_m),file('/tmp/SystemOnTPTP11239/LCL525+1.p',unknown),[]).
% 
% cnf(173266464,plain,(axiom_m),inference(rewrite,[status(thm)],[km5_axiom_M]),[]).
% 
% cnf(182479072,plain,(is_a_theorem(implies(necessarily(A),A))),inference(resolution,[status(thm)],[172405696,173266464]),[]).
% 
% fof(modus_ponens,plain,(((~modus_ponens|~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B))&(~is_a_theorem(y(A,B))|modus_ponens)&(is_a_theorem(x(A,B))|modus_ponens)&(is_a_theorem(implies(x(A,B),y(A,B)))|modus_ponens))),file('/tmp/SystemOnTPTP11239/LCL525+1.p',unknown),[]).
% 
% cnf(170558768,plain,(~modus_ponens|~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B)),inference(rewrite,[status(thm)],[modus_ponens]),[]).
% 
% fof(hilbert_modus_ponens,plain,(modus_ponens),file('/tmp/SystemOnTPTP11239/LCL525+1.p',unknown),[]).
% 
% cnf(171821656,plain,(modus_ponens),inference(rewrite,[status(thm)],[hilbert_modus_ponens]),[]).
% 
% cnf(182250840,plain,(~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B)),inference(resolution,[status(thm)],[170558768,171821656]),[]).
% 
% cnf(193562088,plain,(~is_a_theorem(necessarily(A))|is_a_theorem(A)),inference(resolution,[status(thm)],[182479072,182250840]),[]).
% 
% cnf(172137104,plain,(is_a_theorem(strict_implies(x(A,B),y(A,B)))|modus_ponens_strict_implies),inference(rewrite,[status(thm)],[modus_ponens_strict_implies]),[]).
% 
% cnf(182549624,plain,(is_a_theorem(strict_implies(x(A,B),y(A,B)))),inference(resolution,[status(thm)],[172137104,173356600]),[]).
% 
% fof(op_strict_implies,plain,(~op_strict_implies|$equal(necessarily(implies(A,B)),strict_implies(A,B))),file('/tmp/SystemOnTPTP11239/LCL525+1.p',unknown),[]).
% 
% cnf(173177896,plain,(~op_strict_implies|$equal(necessarily(implies(A,B)),strict_implies(A,B))),inference(rewrite,[status(thm)],[op_strict_implies]),[]).
% 
% fof(s1_0_op_strict_implies,plain,(op_strict_implies),file('/tmp/SystemOnTPTP11239/LCL525+1.p',unknown),[]).
% 
% cnf(173321488,plain,(op_strict_implies),inference(rewrite,[status(thm)],[s1_0_op_strict_implies]),[]).
% 
% cnf(182502248,plain,($equal(necessarily(implies(A,B)),strict_implies(A,B))),inference(resolution,[status(thm)],[173177896,173321488]),[]).
% 
% cnf(184972328,plain,(is_a_theorem(necessarily(implies(x(A,B),y(A,B))))),inference(paramodulation,[status(thm)],[182549624,182502248,theory(equality)]),[]).
% 
% cnf(217329096,plain,(is_a_theorem(implies(x(A,B),y(A,B)))),inference(resolution,[status(thm)],[193562088,184972328]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[182536896,182525304,217329096,182250840]),[]).
% 
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
% 
%------------------------------------------------------------------------------