TSTP Solution File: NUM001-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : NUM001-1 : TPTP v3.4.2. Released v1.0.0.
% 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 14:50:14 EDT 2009
% Result : Unsatisfiable 15.8s
% Output : Refutation 15.8s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 26 ( 15 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 19 ~; 17 |; 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 : 62 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(associativity_of_addition,plain,
! [A,B,C] : equalish(add(A,add(B,C)),add(add(A,B),C)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM001-1.tptp',unknown),
[] ).
cnf(165761008,plain,
equalish(add(A,add(B,C)),add(add(A,B),C)),
inference(rewrite,[status(thm)],[associativity_of_addition]),
[] ).
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/NUM001-1.tptp',unknown),
[] ).
cnf(165814032,plain,
( ~ equalish(A,B)
| ~ equalish(C,subtract(A,D))
| equalish(C,subtract(B,D)) ),
inference(rewrite,[status(thm)],[subtract_substitution1]),
[] ).
fof(commutativity_of_addition,plain,
! [A,B] : equalish(add(A,B),add(B,A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM001-1.tptp',unknown),
[] ).
cnf(165757048,plain,
equalish(add(A,B),add(B,A)),
inference(rewrite,[status(thm)],[commutativity_of_addition]),
[] ).
cnf(173778304,plain,
( ~ equalish(A,subtract(add(C,D),B))
| equalish(A,subtract(add(D,C),B)) ),
inference(resolution,[status(thm)],[165814032,165757048]),
[] ).
fof(reflexivity,plain,
! [A] : equalish(A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM001-1.tptp',unknown),
[] ).
cnf(165744896,plain,
equalish(A,A),
inference(rewrite,[status(thm)],[reflexivity]),
[] ).
cnf(173791056,plain,
equalish(subtract(add(B,C),A),subtract(add(C,B),A)),
inference(resolution,[status(thm)],[173778304,165744896]),
[] ).
fof(transitivity,plain,
! [A,B,C] :
( ~ equalish(A,B)
| ~ equalish(B,C)
| equalish(A,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM001-1.tptp',unknown),
[] ).
cnf(165753104,plain,
( ~ equalish(A,B)
| ~ equalish(B,C)
| equalish(A,C) ),
inference(rewrite,[status(thm)],[transitivity]),
[] ).
fof(addition_inverts_subtraction1,plain,
! [A,B] : equalish(subtract(add(A,B),B),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM001-1.tptp',unknown),
[] ).
cnf(165764800,plain,
equalish(subtract(add(A,B),B),A),
inference(rewrite,[status(thm)],[addition_inverts_subtraction1]),
[] ).
cnf(174856032,plain,
( ~ equalish(A,subtract(add(B,C),C))
| equalish(A,B) ),
inference(resolution,[status(thm)],[165753104,165764800]),
[] ).
cnf(180721432,plain,
equalish(subtract(add(A,B),A),B),
inference(resolution,[status(thm)],[173791056,174856032]),
[] ).
cnf(180935600,plain,
( ~ equalish(C,subtract(add(A,B),A))
| equalish(C,B) ),
inference(resolution,[status(thm)],[180721432,165753104]),
[] ).
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/NUM001-1.tptp',unknown),
[] ).
cnf(165822104,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/NUM001-1.tptp',unknown),
[] ).
cnf(165768712,plain,
equalish(A,subtract(add(A,B),B)),
inference(rewrite,[status(thm)],[addition_inverts_subtraction2]),
[] ).
cnf(174034128,plain,
( ~ equalish(A,B)
| equalish(C,subtract(add(C,A),B)) ),
inference(resolution,[status(thm)],[165822104,165768712]),
[] ).
cnf(257434848,plain,
( equalish(A,B)
| ~ equalish(B,A) ),
inference(resolution,[status(thm)],[180935600,174034128]),
[] ).
fof(prove_equation,plain,
~ equalish(add(add(a,b),c),add(a,add(b,c))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM001-1.tptp',unknown),
[] ).
cnf(165825648,plain,
~ equalish(add(add(a,b),c),add(a,add(b,c))),
inference(rewrite,[status(thm)],[prove_equation]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[165761008,257434848,165825648]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 15 seconds
% START OF PROOF SEQUENCE
% fof(associativity_of_addition,plain,(equalish(add(A,add(B,C)),add(add(A,B),C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM001-1.tptp',unknown),[]).
%
% cnf(165761008,plain,(equalish(add(A,add(B,C)),add(add(A,B),C))),inference(rewrite,[status(thm)],[associativity_of_addition]),[]).
%
% 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/NUM001-1.tptp',unknown),[]).
%
% cnf(165814032,plain,(~equalish(A,B)|~equalish(C,subtract(A,D))|equalish(C,subtract(B,D))),inference(rewrite,[status(thm)],[subtract_substitution1]),[]).
%
% fof(commutativity_of_addition,plain,(equalish(add(A,B),add(B,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM001-1.tptp',unknown),[]).
%
% cnf(165757048,plain,(equalish(add(A,B),add(B,A))),inference(rewrite,[status(thm)],[commutativity_of_addition]),[]).
%
% cnf(173778304,plain,(~equalish(A,subtract(add(C,D),B))|equalish(A,subtract(add(D,C),B))),inference(resolution,[status(thm)],[165814032,165757048]),[]).
%
% fof(reflexivity,plain,(equalish(A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM001-1.tptp',unknown),[]).
%
% cnf(165744896,plain,(equalish(A,A)),inference(rewrite,[status(thm)],[reflexivity]),[]).
%
% cnf(173791056,plain,(equalish(subtract(add(B,C),A),subtract(add(C,B),A))),inference(resolution,[status(thm)],[173778304,165744896]),[]).
%
% fof(transitivity,plain,(~equalish(A,B)|~equalish(B,C)|equalish(A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM001-1.tptp',unknown),[]).
%
% cnf(165753104,plain,(~equalish(A,B)|~equalish(B,C)|equalish(A,C)),inference(rewrite,[status(thm)],[transitivity]),[]).
%
% fof(addition_inverts_subtraction1,plain,(equalish(subtract(add(A,B),B),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM001-1.tptp',unknown),[]).
%
% cnf(165764800,plain,(equalish(subtract(add(A,B),B),A)),inference(rewrite,[status(thm)],[addition_inverts_subtraction1]),[]).
%
% cnf(174856032,plain,(~equalish(A,subtract(add(B,C),C))|equalish(A,B)),inference(resolution,[status(thm)],[165753104,165764800]),[]).
%
% cnf(180721432,plain,(equalish(subtract(add(A,B),A),B)),inference(resolution,[status(thm)],[173791056,174856032]),[]).
%
% cnf(180935600,plain,(~equalish(C,subtract(add(A,B),A))|equalish(C,B)),inference(resolution,[status(thm)],[180721432,165753104]),[]).
%
% 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/NUM001-1.tptp',unknown),[]).
%
% cnf(165822104,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/NUM001-1.tptp',unknown),[]).
%
% cnf(165768712,plain,(equalish(A,subtract(add(A,B),B))),inference(rewrite,[status(thm)],[addition_inverts_subtraction2]),[]).
%
% cnf(174034128,plain,(~equalish(A,B)|equalish(C,subtract(add(C,A),B))),inference(resolution,[status(thm)],[165822104,165768712]),[]).
%
% cnf(257434848,plain,(equalish(A,B)|~equalish(B,A)),inference(resolution,[status(thm)],[180935600,174034128]),[]).
%
% fof(prove_equation,plain,(~equalish(add(add(a,b),c),add(a,add(b,c)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM001-1.tptp',unknown),[]).
%
% cnf(165825648,plain,(~equalish(add(add(a,b),c),add(a,add(b,c)))),inference(rewrite,[status(thm)],[prove_equation]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[165761008,257434848,165825648]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------