%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : NUM004-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art07.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 14:50:22 EDT 2009
% Result : Unsatisfiable 487.4s
% Output : Refutation 487.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 14 unt; 0 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 21 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(subtract_substitution1,plain,
! [A,B,C,D] :
( ~ equalish(A,B)
| ~ equalish(C,subtract(A,D))
| equalish(C,subtract(B,D)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM004-1.tptp',unknown),
[] ).
cnf(154423056,plain,
( ~ equalish(A,B)
| ~ equalish(C,subtract(A,D))
| equalish(C,subtract(B,D)) ),
inference(rewrite,[status(thm)],[subtract_substitution1]),
[] ).
fof(commutativity1,plain,
! [A,B,C] : equalish(add(subtract(A,B),C),subtract(add(A,C),B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM004-1.tptp',unknown),
[] ).
cnf(154385544,plain,
equalish(add(subtract(A,B),C),subtract(add(A,C),B)),
inference(rewrite,[status(thm)],[commutativity1]),
[] ).
cnf(162667640,plain,
( ~ equalish(add(C,D),A)
| equalish(add(subtract(C,B),D),subtract(A,B)) ),
inference(resolution,[status(thm)],[154423056,154385544]),
[] ).
fof(commutativity_of_addition,plain,
! [A,B] : equalish(add(A,B),add(B,A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM004-1.tptp',unknown),
[] ).
cnf(154366072,plain,
equalish(add(A,B),add(B,A)),
inference(rewrite,[status(thm)],[commutativity_of_addition]),
[] ).
cnf(162682864,plain,
equalish(add(subtract(B,A),C),subtract(add(C,B),A)),
inference(resolution,[status(thm)],[162667640,154366072]),
[] ).
fof(prove_equation,plain,
~ equalish(subtract(add(a,b),c),add(a,subtract(b,c))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM004-1.tptp',unknown),
[] ).
cnf(154434672,plain,
~ equalish(subtract(add(a,b),c),add(a,subtract(b,c))),
inference(rewrite,[status(thm)],[prove_equation]),
[] ).
fof(transitivity,plain,
! [A,B,C] :
( ~ equalish(A,B)
| ~ equalish(B,C)
| equalish(A,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM004-1.tptp',unknown),
[] ).
cnf(154362128,plain,
( ~ equalish(A,B)
| ~ equalish(B,C)
| equalish(A,C) ),
inference(rewrite,[status(thm)],[transitivity]),
[] ).
cnf(162260512,plain,
( ~ equalish(A,add(B,C))
| equalish(A,add(C,B)) ),
inference(resolution,[status(thm)],[154362128,154366072]),
[] ).
cnf(173430232,plain,
~ equalish(subtract(add(a,b),c),add(subtract(b,c),a)),
inference(resolution,[status(thm)],[154434672,162260512]),
[] ).
fof(subtract_substitution2,plain,
! [A,B,C,D] :
( ~ equalish(A,B)
| ~ equalish(C,subtract(D,A))
| equalish(C,subtract(D,B)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM004-1.tptp',unknown),
[] ).
cnf(154431128,plain,
( ~ equalish(A,B)
| ~ equalish(C,subtract(D,A))
| equalish(C,subtract(D,B)) ),
inference(rewrite,[status(thm)],[subtract_substitution2]),
[] ).
fof(addition_inverts_subtraction2,plain,
! [A,B] : equalish(A,subtract(add(A,B),B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM004-1.tptp',unknown),
[] ).
cnf(154377736,plain,
equalish(A,subtract(add(A,B),B)),
inference(rewrite,[status(thm)],[addition_inverts_subtraction2]),
[] ).
cnf(163471200,plain,
( ~ equalish(add(B,C),A)
| equalish(B,subtract(A,C)) ),
inference(resolution,[status(thm)],[154423056,154377736]),
[] ).
cnf(163497144,plain,
equalish(A,subtract(add(B,A),B)),
inference(resolution,[status(thm)],[163471200,154366072]),
[] ).
cnf(164462368,plain,
( ~ equalish(A,B)
| equalish(C,subtract(add(A,C),B)) ),
inference(resolution,[status(thm)],[154431128,163497144]),
[] ).
fof(addition_inverts_subtraction1,plain,
! [A,B] : equalish(subtract(add(A,B),B),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM004-1.tptp',unknown),
[] ).
cnf(154373824,plain,
equalish(subtract(add(A,B),B),A),
inference(rewrite,[status(thm)],[addition_inverts_subtraction1]),
[] ).
cnf(163630952,plain,
( ~ equalish(A,subtract(add(B,C),C))
| equalish(A,B) ),
inference(resolution,[status(thm)],[154362128,154373824]),
[] ).
cnf(195798224,plain,
( ~ equalish(A,B)
| equalish(B,A) ),
inference(resolution,[status(thm)],[164462368,163630952]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[162682864,173430232,195798224]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 487 seconds
% START OF PROOF SEQUENCE
% fof(subtract_substitution1,plain,(~equalish(A,B)|~equalish(C,subtract(A,D))|equalish(C,subtract(B,D))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM004-1.tptp',unknown),[]).
%
% cnf(154423056,plain,(~equalish(A,B)|~equalish(C,subtract(A,D))|equalish(C,subtract(B,D))),inference(rewrite,[status(thm)],[subtract_substitution1]),[]).
%
% fof(commutativity1,plain,(equalish(add(subtract(A,B),C),subtract(add(A,C),B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM004-1.tptp',unknown),[]).
%
% cnf(154385544,plain,(equalish(add(subtract(A,B),C),subtract(add(A,C),B))),inference(rewrite,[status(thm)],[commutativity1]),[]).
%
% cnf(162667640,plain,(~equalish(add(C,D),A)|equalish(add(subtract(C,B),D),subtract(A,B))),inference(resolution,[status(thm)],[154423056,154385544]),[]).
%
% fof(commutativity_of_addition,plain,(equalish(add(A,B),add(B,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM004-1.tptp',unknown),[]).
%
% cnf(154366072,plain,(equalish(add(A,B),add(B,A))),inference(rewrite,[status(thm)],[commutativity_of_addition]),[]).
%
% cnf(162682864,plain,(equalish(add(subtract(B,A),C),subtract(add(C,B),A))),inference(resolution,[status(thm)],[162667640,154366072]),[]).
%
% fof(prove_equation,plain,(~equalish(subtract(add(a,b),c),add(a,subtract(b,c)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM004-1.tptp',unknown),[]).
%
% cnf(154434672,plain,(~equalish(subtract(add(a,b),c),add(a,subtract(b,c)))),inference(rewrite,[status(thm)],[prove_equation]),[]).
%
% fof(transitivity,plain,(~equalish(A,B)|~equalish(B,C)|equalish(A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM004-1.tptp',unknown),[]).
%
% cnf(154362128,plain,(~equalish(A,B)|~equalish(B,C)|equalish(A,C)),inference(rewrite,[status(thm)],[transitivity]),[]).
%
% cnf(162260512,plain,(~equalish(A,add(B,C))|equalish(A,add(C,B))),inference(resolution,[status(thm)],[154362128,154366072]),[]).
%
% cnf(173430232,plain,(~equalish(subtract(add(a,b),c),add(subtract(b,c),a))),inference(resolution,[status(thm)],[154434672,162260512]),[]).
%
% fof(subtract_substitution2,plain,(~equalish(A,B)|~equalish(C,subtract(D,A))|equalish(C,subtract(D,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM004-1.tptp',unknown),[]).
%
% cnf(154431128,plain,(~equalish(A,B)|~equalish(C,subtract(D,A))|equalish(C,subtract(D,B))),inference(rewrite,[status(thm)],[subtract_substitution2]),[]).
%
% fof(addition_inverts_subtraction2,plain,(equalish(A,subtract(add(A,B),B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM004-1.tptp',unknown),[]).
%
% cnf(154377736,plain,(equalish(A,subtract(add(A,B),B))),inference(rewrite,[status(thm)],[addition_inverts_subtraction2]),[]).
%
% cnf(163471200,plain,(~equalish(add(B,C),A)|equalish(B,subtract(A,C))),inference(resolution,[status(thm)],[154423056,154377736]),[]).
%
% cnf(163497144,plain,(equalish(A,subtract(add(B,A),B))),inference(resolution,[status(thm)],[163471200,154366072]),[]).
%
% cnf(164462368,plain,(~equalish(A,B)|equalish(C,subtract(add(A,C),B))),inference(resolution,[status(thm)],[154431128,163497144]),[]).
%
% fof(addition_inverts_subtraction1,plain,(equalish(subtract(add(A,B),B),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM004-1.tptp',unknown),[]).
%
% cnf(154373824,plain,(equalish(subtract(add(A,B),B),A)),inference(rewrite,[status(thm)],[addition_inverts_subtraction1]),[]).
%
% cnf(163630952,plain,(~equalish(A,subtract(add(B,C),C))|equalish(A,B)),inference(resolution,[status(thm)],[154362128,154373824]),[]).
%
% cnf(195798224,plain,(~equalish(A,B)|equalish(B,A)),inference(resolution,[status(thm)],[164462368,163630952]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[162682864,173430232,195798224]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------