TSTP Solution File: SET013-4 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET013-4 : TPTP v3.4.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art10.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 15:23:27 EDT 2009

% Result   : Unsatisfiable 291.9s
% Output   : Refutation 291.9s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   30 (  10 unt;   0 def)
%            Number of atoms       :   58 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   52 (  24   ~;  28   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   32 (   2 sgn  13   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_c_equals_d,plain,
    ~ $equal(ds,cs),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),
    [] ).

cnf(168163360,plain,
    ~ $equal(ds,cs),
    inference(rewrite,[status(thm)],[prove_c_equals_d]),
    [] ).

fof(extensionality2,plain,
    ! [A,B] :
      ( member(f1(A,B),A)
      | member(f1(A,B),B)
      | $equal(B,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),
    [] ).

cnf(168107536,plain,
    ( member(f1(A,B),A)
    | member(f1(A,B),B)
    | $equal(B,A) ),
    inference(rewrite,[status(thm)],[extensionality2]),
    [] ).

cnf(176122736,plain,
    ( member(f1(cs,ds),cs)
    | member(f1(cs,ds),ds) ),
    inference(resolution,[status(thm)],[168163360,168107536]),
    [] ).

fof(intersection1,plain,
    ! [A,B,C] :
      ( ~ member(A,intersection(B,C))
      | member(A,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),
    [] ).

cnf(168124776,plain,
    ( ~ member(A,intersection(B,C))
    | member(A,B) ),
    inference(rewrite,[status(thm)],[intersection1]),
    [] ).

fof(intersection_of_a_and_b_is_c,plain,
    $equal(intersection(as,bs),cs),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),
    [] ).

cnf(168084936,plain,
    $equal(intersection(as,bs),cs),
    inference(rewrite,[status(thm)],[intersection_of_a_and_b_is_c]),
    [] ).

cnf(176470344,plain,
    ( ~ member(A,cs)
    | member(A,as) ),
    inference(paramodulation,[status(thm)],[168124776,168084936,theory(equality)]),
    [] ).

cnf(179922136,plain,
    ( member(f1(cs,ds),ds)
    | member(f1(cs,ds),as) ),
    inference(resolution,[status(thm)],[176122736,176470344]),
    [] ).

fof(intersection2,plain,
    ! [A,B,C] :
      ( ~ member(A,intersection(B,C))
      | member(A,C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),
    [] ).

cnf(168129072,plain,
    ( ~ member(A,intersection(B,C))
    | member(A,C) ),
    inference(rewrite,[status(thm)],[intersection2]),
    [] ).

fof(intersection_of_b_and_a_is_d,plain,
    $equal(intersection(bs,as),ds),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),
    [] ).

cnf(168158736,plain,
    $equal(intersection(bs,as),ds),
    inference(rewrite,[status(thm)],[intersection_of_b_and_a_is_d]),
    [] ).

cnf(176791128,plain,
    ( ~ member(A,ds)
    | member(A,as) ),
    inference(paramodulation,[status(thm)],[168129072,168158736,theory(equality)]),
    [] ).

cnf(277974664,plain,
    member(f1(cs,ds),as),
    inference(resolution,[status(thm)],[179922136,176791128]),
    [] ).

cnf(176490664,plain,
    ( ~ member(A,ds)
    | member(A,bs) ),
    inference(paramodulation,[status(thm)],[168124776,168158736,theory(equality)]),
    [] ).

cnf(179931672,plain,
    ( member(f1(cs,ds),cs)
    | member(f1(cs,ds),bs) ),
    inference(resolution,[status(thm)],[176122736,176490664]),
    [] ).

cnf(176786544,plain,
    ( ~ member(A,cs)
    | member(A,bs) ),
    inference(paramodulation,[status(thm)],[168129072,168084936,theory(equality)]),
    [] ).

cnf(278158976,plain,
    member(f1(cs,ds),bs),
    inference(resolution,[status(thm)],[179931672,176786544]),
    [] ).

fof(intersection3,plain,
    ! [A,B,C] :
      ( member(A,intersection(B,C))
      | ~ member(A,B)
      | ~ member(A,C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),
    [] ).

cnf(168136072,plain,
    ( member(A,intersection(B,C))
    | ~ member(A,B)
    | ~ member(A,C) ),
    inference(rewrite,[status(thm)],[intersection3]),
    [] ).

cnf(182647648,plain,
    ( member(A,cs)
    | ~ member(A,as)
    | ~ member(A,bs) ),
    inference(paramodulation,[status(thm)],[168136072,168084936,theory(equality)]),
    [] ).

cnf(595690400,plain,
    member(f1(cs,ds),cs),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[179931672,182647648,277974664]),
    [] ).

cnf(182655632,plain,
    ( member(A,ds)
    | ~ member(A,bs)
    | ~ member(A,as) ),
    inference(paramodulation,[status(thm)],[168136072,168158736,theory(equality)]),
    [] ).

fof(extensionality3,plain,
    ! [A,B] :
      ( ~ member(f1(A,B),A)
      | ~ member(f1(A,B),B)
      | $equal(B,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),
    [] ).

cnf(168115160,plain,
    ( ~ member(f1(A,B),A)
    | ~ member(f1(A,B),B)
    | $equal(B,A) ),
    inference(rewrite,[status(thm)],[extensionality3]),
    [] ).

cnf(176081504,plain,
    ( ~ member(f1(cs,ds),cs)
    | ~ member(f1(cs,ds),ds) ),
    inference(resolution,[status(thm)],[168115160,168163360]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[277974664,278158976,595690400,182655632,176081504]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 290 seconds
% START OF PROOF SEQUENCE
% fof(prove_c_equals_d,plain,(~$equal(ds,cs)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),[]).
% 
% cnf(168163360,plain,(~$equal(ds,cs)),inference(rewrite,[status(thm)],[prove_c_equals_d]),[]).
% 
% fof(extensionality2,plain,(member(f1(A,B),A)|member(f1(A,B),B)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),[]).
% 
% cnf(168107536,plain,(member(f1(A,B),A)|member(f1(A,B),B)|$equal(B,A)),inference(rewrite,[status(thm)],[extensionality2]),[]).
% 
% cnf(176122736,plain,(member(f1(cs,ds),cs)|member(f1(cs,ds),ds)),inference(resolution,[status(thm)],[168163360,168107536]),[]).
% 
% fof(intersection1,plain,(~member(A,intersection(B,C))|member(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),[]).
% 
% cnf(168124776,plain,(~member(A,intersection(B,C))|member(A,B)),inference(rewrite,[status(thm)],[intersection1]),[]).
% 
% fof(intersection_of_a_and_b_is_c,plain,($equal(intersection(as,bs),cs)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),[]).
% 
% cnf(168084936,plain,($equal(intersection(as,bs),cs)),inference(rewrite,[status(thm)],[intersection_of_a_and_b_is_c]),[]).
% 
% cnf(176470344,plain,(~member(A,cs)|member(A,as)),inference(paramodulation,[status(thm)],[168124776,168084936,theory(equality)]),[]).
% 
% cnf(179922136,plain,(member(f1(cs,ds),ds)|member(f1(cs,ds),as)),inference(resolution,[status(thm)],[176122736,176470344]),[]).
% 
% fof(intersection2,plain,(~member(A,intersection(B,C))|member(A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),[]).
% 
% cnf(168129072,plain,(~member(A,intersection(B,C))|member(A,C)),inference(rewrite,[status(thm)],[intersection2]),[]).
% 
% fof(intersection_of_b_and_a_is_d,plain,($equal(intersection(bs,as),ds)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),[]).
% 
% cnf(168158736,plain,($equal(intersection(bs,as),ds)),inference(rewrite,[status(thm)],[intersection_of_b_and_a_is_d]),[]).
% 
% cnf(176791128,plain,(~member(A,ds)|member(A,as)),inference(paramodulation,[status(thm)],[168129072,168158736,theory(equality)]),[]).
% 
% cnf(277974664,plain,(member(f1(cs,ds),as)),inference(resolution,[status(thm)],[179922136,176791128]),[]).
% 
% cnf(176490664,plain,(~member(A,ds)|member(A,bs)),inference(paramodulation,[status(thm)],[168124776,168158736,theory(equality)]),[]).
% 
% cnf(179931672,plain,(member(f1(cs,ds),cs)|member(f1(cs,ds),bs)),inference(resolution,[status(thm)],[176122736,176490664]),[]).
% 
% cnf(176786544,plain,(~member(A,cs)|member(A,bs)),inference(paramodulation,[status(thm)],[168129072,168084936,theory(equality)]),[]).
% 
% cnf(278158976,plain,(member(f1(cs,ds),bs)),inference(resolution,[status(thm)],[179931672,176786544]),[]).
% 
% fof(intersection3,plain,(member(A,intersection(B,C))|~member(A,B)|~member(A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),[]).
% 
% cnf(168136072,plain,(member(A,intersection(B,C))|~member(A,B)|~member(A,C)),inference(rewrite,[status(thm)],[intersection3]),[]).
% 
% cnf(182647648,plain,(member(A,cs)|~member(A,as)|~member(A,bs)),inference(paramodulation,[status(thm)],[168136072,168084936,theory(equality)]),[]).
% 
% cnf(595690400,plain,(member(f1(cs,ds),cs)),inference(forward_subsumption_resolution__resolution,[status(thm)],[179931672,182647648,277974664]),[]).
% 
% cnf(182655632,plain,(member(A,ds)|~member(A,bs)|~member(A,as)),inference(paramodulation,[status(thm)],[168136072,168158736,theory(equality)]),[]).
% 
% fof(extensionality3,plain,(~member(f1(A,B),A)|~member(f1(A,B),B)|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET013-4.tptp',unknown),[]).
% 
% cnf(168115160,plain,(~member(f1(A,B),A)|~member(f1(A,B),B)|$equal(B,A)),inference(rewrite,[status(thm)],[extensionality3]),[]).
% 
% cnf(176081504,plain,(~member(f1(cs,ds),cs)|~member(f1(cs,ds),ds)),inference(resolution,[status(thm)],[168115160,168163360]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[277974664,278158976,595690400,182655632,176081504]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------