TSTP Solution File: LCL452+1 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : LCL452+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art05.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 13:50:39 EDT 2009

% Result   : Theorem 23.2s
% Output   : Refutation 23.2s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   36 (  21 unt;   0 def)
%            Number of atoms       :   68 (   0 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :   59 (  27   ~;  26   |;   6   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    9 (   7 usr;   7 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   0 con; 1-2 aty)
%            Number of variables   :   48 (   9 sgn  12   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/SystemOnTPTP4964/LCL452+1.p',unknown),
    [] ).

cnf(150419768,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/SystemOnTPTP4964/LCL452+1.p',unknown),
    [] ).

cnf(151389792,plain,
    modus_ponens,
    inference(rewrite,[status(thm)],[hilbert_modus_ponens]),
    [] ).

cnf(154299392,plain,
    ( ~ is_a_theorem(A)
    | ~ is_a_theorem(implies(A,B))
    | is_a_theorem(B) ),
    inference(resolution,[status(thm)],[150419768,151389792]),
    [] ).

fof(implies_1,plain,
    ! [A,B] :
      ( ( ~ implies_1
        | is_a_theorem(implies(A,implies(B,A))) )
      & ( implies_1
        | ~ is_a_theorem(implies(x(A,B),implies(y(A,B),x(A,B)))) ) ),
    file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),
    [] ).

cnf(150546696,plain,
    ( ~ implies_1
    | is_a_theorem(implies(A,implies(B,A))) ),
    inference(rewrite,[status(thm)],[implies_1]),
    [] ).

fof(hilbert_implies_1,plain,
    implies_1,
    file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),
    [] ).

cnf(150372192,plain,
    implies_1,
    inference(rewrite,[status(thm)],[hilbert_implies_1]),
    [] ).

cnf(160011272,plain,
    is_a_theorem(implies(A,implies(B,A))),
    inference(resolution,[status(thm)],[150546696,150372192]),
    [] ).

cnf(164305936,plain,
    ( ~ is_a_theorem(A)
    | is_a_theorem(implies(B,A)) ),
    inference(resolution,[status(thm)],[154299392,160011272]),
    [] ).

fof(op_or,plain,
    ! [A,B] :
      ( ~ op_or
      | $equal(not(and(not(A),not(B))),or(A,B)) ),
    file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),
    [] ).

cnf(151274520,plain,
    ( ~ op_or
    | $equal(not(and(not(A),not(B))),or(A,B)) ),
    inference(rewrite,[status(thm)],[op_or]),
    [] ).

fof(hilbert_op_or,plain,
    op_or,
    file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),
    [] ).

cnf(151353680,plain,
    op_or,
    inference(rewrite,[status(thm)],[hilbert_op_or]),
    [] ).

cnf(159949592,plain,
    $equal(not(and(not(A),not(B))),or(A,B)),
    inference(resolution,[status(thm)],[151274520,151353680]),
    [] ).

fof(op_implies_and,plain,
    ! [A,B] :
      ( ~ op_implies_and
      | $equal(not(and(A,not(B))),implies(A,B)) ),
    file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),
    [] ).

cnf(151310152,plain,
    ( ~ op_implies_and
    | $equal(not(and(A,not(B))),implies(A,B)) ),
    inference(rewrite,[status(thm)],[op_implies_and]),
    [] ).

fof(hilbert_op_implies_and,plain,
    op_implies_and,
    file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),
    [] ).

cnf(151365872,plain,
    op_implies_and,
    inference(rewrite,[status(thm)],[hilbert_op_implies_and]),
    [] ).

cnf(159961032,plain,
    $equal(not(and(A,not(B))),implies(A,B)),
    inference(resolution,[status(thm)],[151310152,151365872]),
    [] ).

cnf(161853536,plain,
    $equal(or(A,B),implies(not(A),B)),
    inference(paramodulation,[status(thm)],[159949592,159961032,theory(equality)]),
    [] ).

fof(or_1,plain,
    ! [A,B] :
      ( ( ~ or_1
        | is_a_theorem(implies(A,or(A,B))) )
      & ( or_1
        | ~ is_a_theorem(implies(x(A,B),or(x(A,B),y(A,B)))) ) ),
    file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),
    [] ).

cnf(150731472,plain,
    ( ~ or_1
    | is_a_theorem(implies(A,or(A,B))) ),
    inference(rewrite,[status(thm)],[or_1]),
    [] ).

fof(hilbert_or_1,plain,
    or_1,
    file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),
    [] ).

cnf(151484352,plain,
    or_1,
    inference(rewrite,[status(thm)],[hilbert_or_1]),
    [] ).

cnf(160059376,plain,
    is_a_theorem(implies(A,or(A,B))),
    inference(resolution,[status(thm)],[150731472,151484352]),
    [] ).

cnf(162586744,plain,
    is_a_theorem(implies(A,implies(not(A),B))),
    inference(paramodulation,[status(thm)],[161853536,160059376,theory(equality)]),
    [] ).

cnf(165991320,plain,
    is_a_theorem(implies(A,implies(B,implies(not(B),C)))),
    inference(resolution,[status(thm)],[164305936,162586744]),
    [] ).

cnf(164289608,plain,
    ( ~ is_a_theorem(implies(implies(B,implies(C,B)),A))
    | is_a_theorem(A) ),
    inference(resolution,[status(thm)],[154299392,160011272]),
    [] ).

fof(cn2,plain,
    ! [A,B] :
      ( ( ~ cn2
        | is_a_theorem(implies(A,implies(not(A),B))) )
      & ( cn2
        | ~ is_a_theorem(implies(p(A,B),implies(not(p(A,B)),q(A,B)))) ) ),
    file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),
    [] ).

cnf(151050168,plain,
    ( cn2
    | ~ is_a_theorem(implies(p(A,B),implies(not(p(A,B)),q(A,B)))) ),
    inference(rewrite,[status(thm)],[cn2]),
    [] ).

fof(luka_cn2,plain,
    ~ cn2,
    file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),
    [] ).

cnf(151582520,plain,
    ~ cn2,
    inference(rewrite,[status(thm)],[luka_cn2]),
    [] ).

cnf(160118416,plain,
    ~ is_a_theorem(implies(p(A,B),implies(not(p(A,B)),q(A,B)))),
    inference(resolution,[status(thm)],[151050168,151582520]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[165991320,164289608,160118416]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 23 seconds
% START OF PROOF SEQUENCE
% 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/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
% 
% cnf(150419768,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/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
% 
% cnf(151389792,plain,(modus_ponens),inference(rewrite,[status(thm)],[hilbert_modus_ponens]),[]).
% 
% cnf(154299392,plain,(~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B)),inference(resolution,[status(thm)],[150419768,151389792]),[]).
% 
% fof(implies_1,plain,(((~implies_1|is_a_theorem(implies(A,implies(B,A))))&(implies_1|~is_a_theorem(implies(x(A,B),implies(y(A,B),x(A,B))))))),file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
% 
% cnf(150546696,plain,(~implies_1|is_a_theorem(implies(A,implies(B,A)))),inference(rewrite,[status(thm)],[implies_1]),[]).
% 
% fof(hilbert_implies_1,plain,(implies_1),file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
% 
% cnf(150372192,plain,(implies_1),inference(rewrite,[status(thm)],[hilbert_implies_1]),[]).
% 
% cnf(160011272,plain,(is_a_theorem(implies(A,implies(B,A)))),inference(resolution,[status(thm)],[150546696,150372192]),[]).
% 
% cnf(164305936,plain,(~is_a_theorem(A)|is_a_theorem(implies(B,A))),inference(resolution,[status(thm)],[154299392,160011272]),[]).
% 
% fof(op_or,plain,(~op_or|$equal(not(and(not(A),not(B))),or(A,B))),file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
% 
% cnf(151274520,plain,(~op_or|$equal(not(and(not(A),not(B))),or(A,B))),inference(rewrite,[status(thm)],[op_or]),[]).
% 
% fof(hilbert_op_or,plain,(op_or),file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
% 
% cnf(151353680,plain,(op_or),inference(rewrite,[status(thm)],[hilbert_op_or]),[]).
% 
% cnf(159949592,plain,($equal(not(and(not(A),not(B))),or(A,B))),inference(resolution,[status(thm)],[151274520,151353680]),[]).
% 
% fof(op_implies_and,plain,(~op_implies_and|$equal(not(and(A,not(B))),implies(A,B))),file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
% 
% cnf(151310152,plain,(~op_implies_and|$equal(not(and(A,not(B))),implies(A,B))),inference(rewrite,[status(thm)],[op_implies_and]),[]).
% 
% fof(hilbert_op_implies_and,plain,(op_implies_and),file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
% 
% cnf(151365872,plain,(op_implies_and),inference(rewrite,[status(thm)],[hilbert_op_implies_and]),[]).
% 
% cnf(159961032,plain,($equal(not(and(A,not(B))),implies(A,B))),inference(resolution,[status(thm)],[151310152,151365872]),[]).
% 
% cnf(161853536,plain,($equal(or(A,B),implies(not(A),B))),inference(paramodulation,[status(thm)],[159949592,159961032,theory(equality)]),[]).
% 
% fof(or_1,plain,(((~or_1|is_a_theorem(implies(A,or(A,B))))&(or_1|~is_a_theorem(implies(x(A,B),or(x(A,B),y(A,B))))))),file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
% 
% cnf(150731472,plain,(~or_1|is_a_theorem(implies(A,or(A,B)))),inference(rewrite,[status(thm)],[or_1]),[]).
% 
% fof(hilbert_or_1,plain,(or_1),file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
% 
% cnf(151484352,plain,(or_1),inference(rewrite,[status(thm)],[hilbert_or_1]),[]).
% 
% cnf(160059376,plain,(is_a_theorem(implies(A,or(A,B)))),inference(resolution,[status(thm)],[150731472,151484352]),[]).
% 
% cnf(162586744,plain,(is_a_theorem(implies(A,implies(not(A),B)))),inference(paramodulation,[status(thm)],[161853536,160059376,theory(equality)]),[]).
% 
% cnf(165991320,plain,(is_a_theorem(implies(A,implies(B,implies(not(B),C))))),inference(resolution,[status(thm)],[164305936,162586744]),[]).
% 
% cnf(164289608,plain,(~is_a_theorem(implies(implies(B,implies(C,B)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[154299392,160011272]),[]).
% 
% fof(cn2,plain,(((~cn2|is_a_theorem(implies(A,implies(not(A),B))))&(cn2|~is_a_theorem(implies(p(A,B),implies(not(p(A,B)),q(A,B))))))),file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
% 
% cnf(151050168,plain,(cn2|~is_a_theorem(implies(p(A,B),implies(not(p(A,B)),q(A,B))))),inference(rewrite,[status(thm)],[cn2]),[]).
% 
% fof(luka_cn2,plain,(~cn2),file('/tmp/SystemOnTPTP4964/LCL452+1.p',unknown),[]).
% 
% cnf(151582520,plain,(~cn2),inference(rewrite,[status(thm)],[luka_cn2]),[]).
% 
% cnf(160118416,plain,(~is_a_theorem(implies(p(A,B),implies(not(p(A,B)),q(A,B))))),inference(resolution,[status(thm)],[151050168,151582520]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[165991320,164289608,160118416]),[]).
% 
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
% 
%------------------------------------------------------------------------------