TSTP Solution File: LCL499+1 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : LCL499+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art01.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 13:51:40 EDT 2009

% Result   : Theorem 14.2s
% Output   : Refutation 14.2s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   35 (  21 unt;   0 def)
%            Number of atoms       :   66 (   0 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :   57 (  26   ~;  25   |;   6   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    9 (   7 usr;   7 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   0 con; 1-2 aty)
%            Number of variables   :   34 (   0 sgn  10   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(principia_op_and,plain,
    op_and,
    file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),
    [] ).

cnf(157169656,plain,
    op_and,
    inference(rewrite,[status(thm)],[principia_op_and]),
    [] ).

fof(op_and,plain,
    ! [A,B] :
      ( ~ op_and
      | $equal(not(or(not(A),not(B))),and(A,B)) ),
    file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),
    [] ).

cnf(157096288,plain,
    ( ~ op_and
    | $equal(not(or(not(A),not(B))),and(A,B)) ),
    inference(rewrite,[status(thm)],[op_and]),
    [] ).

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/SystemOnTPTP9980/LCL499+1.p',unknown),
    [] ).

cnf(156230216,plain,
    ( ~ modus_ponens
    | ~ is_a_theorem(A)
    | ~ is_a_theorem(implies(A,B))
    | is_a_theorem(B) ),
    inference(rewrite,[status(thm)],[modus_ponens]),
    [] ).

fof(principia_modus_ponens,plain,
    modus_ponens,
    file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),
    [] ).

cnf(157193544,plain,
    modus_ponens,
    inference(rewrite,[status(thm)],[principia_modus_ponens]),
    [] ).

cnf(165686072,plain,
    ( ~ is_a_theorem(A)
    | ~ is_a_theorem(implies(A,B))
    | is_a_theorem(B) ),
    inference(resolution,[status(thm)],[156230216,157193544]),
    [] ).

fof(r3,plain,
    ! [A,B] :
      ( ( ~ r3
        | is_a_theorem(implies(or(A,B),or(B,A))) )
      & ( r3
        | ~ is_a_theorem(implies(or(p(A,B),q(A,B)),or(q(A,B),p(A,B)))) ) ),
    file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),
    [] ).

cnf(156987992,plain,
    ( ~ r3
    | is_a_theorem(implies(or(A,B),or(B,A))) ),
    inference(rewrite,[status(thm)],[r3]),
    [] ).

fof(principia_r3,plain,
    r3,
    file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),
    [] ).

cnf(157226808,plain,
    r3,
    inference(rewrite,[status(thm)],[principia_r3]),
    [] ).

cnf(165722096,plain,
    is_a_theorem(implies(or(A,B),or(B,A))),
    inference(resolution,[status(thm)],[156987992,157226808]),
    [] ).

cnf(168213016,plain,
    ( ~ is_a_theorem(or(A,B))
    | is_a_theorem(or(B,A)) ),
    inference(resolution,[status(thm)],[165686072,165722096]),
    [] ).

fof(op_implies_or,plain,
    ! [A,B] :
      ( ~ op_implies_or
      | $equal(or(not(A),B),implies(A,B)) ),
    file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),
    [] ).

cnf(157127800,plain,
    ( ~ op_implies_or
    | $equal(or(not(A),B),implies(A,B)) ),
    inference(rewrite,[status(thm)],[op_implies_or]),
    [] ).

fof(principia_op_implies_or,plain,
    op_implies_or,
    file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),
    [] ).

cnf(157157504,plain,
    op_implies_or,
    inference(rewrite,[status(thm)],[principia_op_implies_or]),
    [] ).

cnf(165654744,plain,
    $equal(or(not(A),B),implies(A,B)),
    inference(resolution,[status(thm)],[157127800,157157504]),
    [] ).

fof(r1,plain,
    ! [A] :
      ( ( ~ r1
        | is_a_theorem(implies(or(A,A),A)) )
      & ( r1
        | ~ is_a_theorem(implies(or(p(A),p(A)),p(A))) ) ),
    file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),
    [] ).

cnf(156931160,plain,
    ( ~ r1
    | is_a_theorem(implies(or(A,A),A)) ),
    inference(rewrite,[status(thm)],[r1]),
    [] ).

fof(principia_r1,plain,
    r1,
    file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),
    [] ).

cnf(157204688,plain,
    r1,
    inference(rewrite,[status(thm)],[principia_r1]),
    [] ).

cnf(165701976,plain,
    is_a_theorem(implies(or(A,A),A)),
    inference(resolution,[status(thm)],[156931160,157204688]),
    [] ).

cnf(165908000,plain,
    is_a_theorem(or(not(or(A,A)),A)),
    inference(paramodulation,[status(thm)],[165654744,165701976,theory(equality)]),
    [] ).

cnf(172669184,plain,
    is_a_theorem(or(A,not(or(A,A)))),
    inference(resolution,[status(thm)],[168213016,165908000]),
    [] ).

cnf(173077840,plain,
    is_a_theorem(implies(A,not(or(not(A),not(A))))),
    inference(paramodulation,[status(thm)],[172669184,165654744,theory(equality)]),
    [] ).

cnf(311657224,plain,
    is_a_theorem(implies(A,and(A,A))),
    inference(forward_subsumption_resolution__paramodulation,[status(thm)],[157169656,157096288,173077840,theory(equality)]),
    [] ).

fof(kn1,plain,
    ! [A] :
      ( ( ~ kn1
        | is_a_theorem(implies(A,and(A,A))) )
      & ( kn1
        | ~ is_a_theorem(implies(p(A),and(p(A),p(A)))) ) ),
    file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),
    [] ).

cnf(156183384,plain,
    ( kn1
    | ~ is_a_theorem(implies(p(A),and(p(A),p(A)))) ),
    inference(rewrite,[status(thm)],[kn1]),
    [] ).

fof(rosser_kn1,plain,
    ~ kn1,
    file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),
    [] ).

cnf(157297952,plain,
    ~ kn1,
    inference(rewrite,[status(thm)],[rosser_kn1]),
    [] ).

cnf(165776288,plain,
    ~ is_a_theorem(implies(p(A),and(p(A),p(A)))),
    inference(resolution,[status(thm)],[156183384,157297952]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[311657224,165776288]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 14 seconds
% START OF PROOF SEQUENCE
% fof(principia_op_and,plain,(op_and),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
% 
% cnf(157169656,plain,(op_and),inference(rewrite,[status(thm)],[principia_op_and]),[]).
% 
% fof(op_and,plain,(~op_and|$equal(not(or(not(A),not(B))),and(A,B))),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
% 
% cnf(157096288,plain,(~op_and|$equal(not(or(not(A),not(B))),and(A,B))),inference(rewrite,[status(thm)],[op_and]),[]).
% 
% 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/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
% 
% cnf(156230216,plain,(~modus_ponens|~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B)),inference(rewrite,[status(thm)],[modus_ponens]),[]).
% 
% fof(principia_modus_ponens,plain,(modus_ponens),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
% 
% cnf(157193544,plain,(modus_ponens),inference(rewrite,[status(thm)],[principia_modus_ponens]),[]).
% 
% cnf(165686072,plain,(~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B)),inference(resolution,[status(thm)],[156230216,157193544]),[]).
% 
% fof(r3,plain,(((~r3|is_a_theorem(implies(or(A,B),or(B,A))))&(r3|~is_a_theorem(implies(or(p(A,B),q(A,B)),or(q(A,B),p(A,B))))))),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
% 
% cnf(156987992,plain,(~r3|is_a_theorem(implies(or(A,B),or(B,A)))),inference(rewrite,[status(thm)],[r3]),[]).
% 
% fof(principia_r3,plain,(r3),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
% 
% cnf(157226808,plain,(r3),inference(rewrite,[status(thm)],[principia_r3]),[]).
% 
% cnf(165722096,plain,(is_a_theorem(implies(or(A,B),or(B,A)))),inference(resolution,[status(thm)],[156987992,157226808]),[]).
% 
% cnf(168213016,plain,(~is_a_theorem(or(A,B))|is_a_theorem(or(B,A))),inference(resolution,[status(thm)],[165686072,165722096]),[]).
% 
% fof(op_implies_or,plain,(~op_implies_or|$equal(or(not(A),B),implies(A,B))),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
% 
% cnf(157127800,plain,(~op_implies_or|$equal(or(not(A),B),implies(A,B))),inference(rewrite,[status(thm)],[op_implies_or]),[]).
% 
% fof(principia_op_implies_or,plain,(op_implies_or),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
% 
% cnf(157157504,plain,(op_implies_or),inference(rewrite,[status(thm)],[principia_op_implies_or]),[]).
% 
% cnf(165654744,plain,($equal(or(not(A),B),implies(A,B))),inference(resolution,[status(thm)],[157127800,157157504]),[]).
% 
% fof(r1,plain,(((~r1|is_a_theorem(implies(or(A,A),A)))&(r1|~is_a_theorem(implies(or(p(A),p(A)),p(A)))))),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
% 
% cnf(156931160,plain,(~r1|is_a_theorem(implies(or(A,A),A))),inference(rewrite,[status(thm)],[r1]),[]).
% 
% fof(principia_r1,plain,(r1),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
% 
% cnf(157204688,plain,(r1),inference(rewrite,[status(thm)],[principia_r1]),[]).
% 
% cnf(165701976,plain,(is_a_theorem(implies(or(A,A),A))),inference(resolution,[status(thm)],[156931160,157204688]),[]).
% 
% cnf(165908000,plain,(is_a_theorem(or(not(or(A,A)),A))),inference(paramodulation,[status(thm)],[165654744,165701976,theory(equality)]),[]).
% 
% cnf(172669184,plain,(is_a_theorem(or(A,not(or(A,A))))),inference(resolution,[status(thm)],[168213016,165908000]),[]).
% 
% cnf(173077840,plain,(is_a_theorem(implies(A,not(or(not(A),not(A)))))),inference(paramodulation,[status(thm)],[172669184,165654744,theory(equality)]),[]).
% 
% cnf(311657224,plain,(is_a_theorem(implies(A,and(A,A)))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[157169656,157096288,173077840,theory(equality)]),[]).
% 
% fof(kn1,plain,(((~kn1|is_a_theorem(implies(A,and(A,A))))&(kn1|~is_a_theorem(implies(p(A),and(p(A),p(A))))))),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
% 
% cnf(156183384,plain,(kn1|~is_a_theorem(implies(p(A),and(p(A),p(A))))),inference(rewrite,[status(thm)],[kn1]),[]).
% 
% fof(rosser_kn1,plain,(~kn1),file('/tmp/SystemOnTPTP9980/LCL499+1.p',unknown),[]).
% 
% cnf(157297952,plain,(~kn1),inference(rewrite,[status(thm)],[rosser_kn1]),[]).
% 
% cnf(165776288,plain,(~is_a_theorem(implies(p(A),and(p(A),p(A))))),inference(resolution,[status(thm)],[156183384,157297952]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[311657224,165776288]),[]).
% 
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
% 
%------------------------------------------------------------------------------