TSTP Solution File: NUM002-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : NUM002-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art03.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 14:50:16 EDT 2009
% Result : Unsatisfiable 51.4s
% Output : Refutation 51.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 20 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 23 ~; 20 |; 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 : 85 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(transitivity,plain,
! [A,B,C] :
( ~ equalish(A,B)
| ~ equalish(B,C)
| equalish(A,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM002-1.tptp',unknown),
[] ).
cnf(153239824,plain,
( ~ equalish(A,B)
| ~ equalish(B,C)
| equalish(A,C) ),
inference(rewrite,[status(thm)],[transitivity]),
[] ).
fof(commutativity2,plain,
! [A,B,C] : equalish(subtract(add(A,B),C),add(subtract(A,C),B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM002-1.tptp',unknown),
[] ).
cnf(153267136,plain,
equalish(subtract(add(A,B),C),add(subtract(A,C),B)),
inference(rewrite,[status(thm)],[commutativity2]),
[] ).
cnf(161964224,plain,
( ~ equalish(A,subtract(add(B,C),D))
| equalish(A,add(subtract(B,D),C)) ),
inference(resolution,[status(thm)],[153239824,153267136]),
[] ).
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/NUM002-1.tptp',unknown),
[] ).
cnf(153300752,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/NUM002-1.tptp',unknown),
[] ).
cnf(153263240,plain,
equalish(add(subtract(A,B),C),subtract(add(A,C),B)),
inference(rewrite,[status(thm)],[commutativity1]),
[] ).
cnf(161545344,plain,
( ~ equalish(add(C,D),A)
| equalish(add(subtract(C,B),D),subtract(A,B)) ),
inference(resolution,[status(thm)],[153300752,153263240]),
[] ).
fof(commutativity_of_addition,plain,
! [A,B] : equalish(add(A,B),add(B,A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM002-1.tptp',unknown),
[] ).
cnf(153243768,plain,
equalish(add(A,B),add(B,A)),
inference(rewrite,[status(thm)],[commutativity_of_addition]),
[] ).
cnf(161560568,plain,
equalish(add(subtract(B,A),C),subtract(add(C,B),A)),
inference(resolution,[status(thm)],[161545344,153243768]),
[] ).
cnf(193375704,plain,
equalish(add(subtract(B,C),A),add(subtract(A,C),B)),
inference(resolution,[status(thm)],[161964224,161560568]),
[] ).
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/NUM002-1.tptp',unknown),
[] ).
cnf(153308824,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/NUM002-1.tptp',unknown),
[] ).
cnf(153255432,plain,
equalish(A,subtract(add(A,B),B)),
inference(rewrite,[status(thm)],[addition_inverts_subtraction2]),
[] ).
cnf(169500376,plain,
( ~ equalish(A,B)
| equalish(C,subtract(add(C,A),B)) ),
inference(resolution,[status(thm)],[153308824,153255432]),
[] ).
cnf(161265016,plain,
( ~ equalish(A,subtract(add(C,D),B))
| equalish(A,subtract(add(D,C),B)) ),
inference(resolution,[status(thm)],[153300752,153243768]),
[] ).
fof(reflexivity,plain,
! [A] : equalish(A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM002-1.tptp',unknown),
[] ).
cnf(153231616,plain,
equalish(A,A),
inference(rewrite,[status(thm)],[reflexivity]),
[] ).
cnf(161277768,plain,
equalish(subtract(add(B,C),A),subtract(add(C,B),A)),
inference(resolution,[status(thm)],[161265016,153231616]),
[] ).
fof(addition_inverts_subtraction1,plain,
! [A,B] : equalish(subtract(add(A,B),B),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM002-1.tptp',unknown),
[] ).
cnf(153251520,plain,
equalish(subtract(add(A,B),B),A),
inference(rewrite,[status(thm)],[addition_inverts_subtraction1]),
[] ).
cnf(161900648,plain,
( ~ equalish(A,subtract(add(B,C),C))
| equalish(A,B) ),
inference(resolution,[status(thm)],[153239824,153251520]),
[] ).
cnf(168746544,plain,
equalish(subtract(add(A,B),A),B),
inference(resolution,[status(thm)],[161277768,161900648]),
[] ).
cnf(168824360,plain,
( ~ equalish(C,subtract(add(A,B),A))
| equalish(C,B) ),
inference(resolution,[status(thm)],[168746544,153239824]),
[] ).
cnf(293488144,plain,
( ~ equalish(A,B)
| equalish(B,A) ),
inference(resolution,[status(thm)],[169500376,168824360]),
[] ).
fof(prove_equation,plain,
~ equalish(add(subtract(a,b),c),add(a,subtract(c,b))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM002-1.tptp',unknown),
[] ).
cnf(153312368,plain,
~ equalish(add(subtract(a,b),c),add(a,subtract(c,b))),
inference(rewrite,[status(thm)],[prove_equation]),
[] ).
cnf(161138352,plain,
( ~ equalish(A,add(B,C))
| equalish(A,add(C,B)) ),
inference(resolution,[status(thm)],[153239824,153243768]),
[] ).
cnf(162159288,plain,
~ equalish(add(subtract(a,b),c),add(subtract(c,b),a)),
inference(resolution,[status(thm)],[153312368,161138352]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[193375704,293488144,162159288]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 51 seconds
% START OF PROOF SEQUENCE
% fof(transitivity,plain,(~equalish(A,B)|~equalish(B,C)|equalish(A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM002-1.tptp',unknown),[]).
%
% cnf(153239824,plain,(~equalish(A,B)|~equalish(B,C)|equalish(A,C)),inference(rewrite,[status(thm)],[transitivity]),[]).
%
% fof(commutativity2,plain,(equalish(subtract(add(A,B),C),add(subtract(A,C),B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM002-1.tptp',unknown),[]).
%
% cnf(153267136,plain,(equalish(subtract(add(A,B),C),add(subtract(A,C),B))),inference(rewrite,[status(thm)],[commutativity2]),[]).
%
% cnf(161964224,plain,(~equalish(A,subtract(add(B,C),D))|equalish(A,add(subtract(B,D),C))),inference(resolution,[status(thm)],[153239824,153267136]),[]).
%
% 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/NUM002-1.tptp',unknown),[]).
%
% cnf(153300752,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/NUM002-1.tptp',unknown),[]).
%
% cnf(153263240,plain,(equalish(add(subtract(A,B),C),subtract(add(A,C),B))),inference(rewrite,[status(thm)],[commutativity1]),[]).
%
% cnf(161545344,plain,(~equalish(add(C,D),A)|equalish(add(subtract(C,B),D),subtract(A,B))),inference(resolution,[status(thm)],[153300752,153263240]),[]).
%
% fof(commutativity_of_addition,plain,(equalish(add(A,B),add(B,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM002-1.tptp',unknown),[]).
%
% cnf(153243768,plain,(equalish(add(A,B),add(B,A))),inference(rewrite,[status(thm)],[commutativity_of_addition]),[]).
%
% cnf(161560568,plain,(equalish(add(subtract(B,A),C),subtract(add(C,B),A))),inference(resolution,[status(thm)],[161545344,153243768]),[]).
%
% cnf(193375704,plain,(equalish(add(subtract(B,C),A),add(subtract(A,C),B))),inference(resolution,[status(thm)],[161964224,161560568]),[]).
%
% 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/NUM002-1.tptp',unknown),[]).
%
% cnf(153308824,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/NUM002-1.tptp',unknown),[]).
%
% cnf(153255432,plain,(equalish(A,subtract(add(A,B),B))),inference(rewrite,[status(thm)],[addition_inverts_subtraction2]),[]).
%
% cnf(169500376,plain,(~equalish(A,B)|equalish(C,subtract(add(C,A),B))),inference(resolution,[status(thm)],[153308824,153255432]),[]).
%
% cnf(161265016,plain,(~equalish(A,subtract(add(C,D),B))|equalish(A,subtract(add(D,C),B))),inference(resolution,[status(thm)],[153300752,153243768]),[]).
%
% fof(reflexivity,plain,(equalish(A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM002-1.tptp',unknown),[]).
%
% cnf(153231616,plain,(equalish(A,A)),inference(rewrite,[status(thm)],[reflexivity]),[]).
%
% cnf(161277768,plain,(equalish(subtract(add(B,C),A),subtract(add(C,B),A))),inference(resolution,[status(thm)],[161265016,153231616]),[]).
%
% fof(addition_inverts_subtraction1,plain,(equalish(subtract(add(A,B),B),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM002-1.tptp',unknown),[]).
%
% cnf(153251520,plain,(equalish(subtract(add(A,B),B),A)),inference(rewrite,[status(thm)],[addition_inverts_subtraction1]),[]).
%
% cnf(161900648,plain,(~equalish(A,subtract(add(B,C),C))|equalish(A,B)),inference(resolution,[status(thm)],[153239824,153251520]),[]).
%
% cnf(168746544,plain,(equalish(subtract(add(A,B),A),B)),inference(resolution,[status(thm)],[161277768,161900648]),[]).
%
% cnf(168824360,plain,(~equalish(C,subtract(add(A,B),A))|equalish(C,B)),inference(resolution,[status(thm)],[168746544,153239824]),[]).
%
% cnf(293488144,plain,(~equalish(A,B)|equalish(B,A)),inference(resolution,[status(thm)],[169500376,168824360]),[]).
%
% fof(prove_equation,plain,(~equalish(add(subtract(a,b),c),add(a,subtract(c,b)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/NUM/NUM002-1.tptp',unknown),[]).
%
% cnf(153312368,plain,(~equalish(add(subtract(a,b),c),add(a,subtract(c,b)))),inference(rewrite,[status(thm)],[prove_equation]),[]).
%
% cnf(161138352,plain,(~equalish(A,add(B,C))|equalish(A,add(C,B))),inference(resolution,[status(thm)],[153239824,153243768]),[]).
%
% cnf(162159288,plain,(~equalish(add(subtract(a,b),c),add(subtract(c,b),a))),inference(resolution,[status(thm)],[153312368,161138352]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[193375704,293488144,162159288]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------