TSTP Solution File: ROB021-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : ROB021-1 : 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 15:21:55 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 11 unt; 0 def)
% Number of atoms : 15 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(negative_equality_implies_positive_equality,plain,
! [B,A] :
( ~ $equal(negate(B),negate(A))
| $equal(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ROB/ROB021-1.tptp',unknown),
[] ).
cnf(145065360,plain,
( ~ $equal(negate(B),negate(A))
| $equal(B,A) ),
inference(rewrite,[status(thm)],[negative_equality_implies_positive_equality]),
[] ).
fof(robbins_axiom,plain,
! [A,B] : $equal(negate(add(negate(add(A,B)),negate(add(A,negate(B))))),A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ROB/ROB021-1.tptp',unknown),
[] ).
cnf(145045952,plain,
$equal(negate(add(negate(add(A,B)),negate(add(A,negate(B))))),A),
inference(rewrite,[status(thm)],[robbins_axiom]),
[] ).
cnf(152911472,plain,
$equal(add(negate(add(negate(A),B)),negate(add(negate(A),negate(B)))),A),
inference(resolution,[status(thm)],[145065360,145045952]),
[] ).
fof(commutativity_of_add,plain,
! [B,A] : $equal(add(B,A),add(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ROB/ROB021-1.tptp',unknown),
[] ).
cnf(145037864,plain,
$equal(add(B,A),add(A,B)),
inference(rewrite,[status(thm)],[commutativity_of_add]),
[] ).
cnf(153174056,plain,
$equal(add(negate(add(negate(A),negate(B))),negate(add(negate(A),B))),A),
inference(paramodulation,[status(thm)],[152911472,145037864,theory(equality)]),
[] ).
cnf(153483368,plain,
$equal(add(negate(add(negate(A),negate(B))),negate(add(B,negate(A)))),A),
inference(paramodulation,[status(thm)],[153174056,145037864,theory(equality)]),
[] ).
fof(prove_huntingtons_axiom,plain,
~ $equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ROB/ROB021-1.tptp',unknown),
[] ).
cnf(145073664,plain,
~ $equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b),
inference(rewrite,[status(thm)],[prove_huntingtons_axiom]),
[] ).
cnf(153089280,plain,
~ $equal(add(negate(add(negate(a),negate(b))),negate(add(a,negate(b)))),b),
inference(paramodulation,[status(thm)],[145073664,145037864,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[153483368,153089280,145037864,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(negative_equality_implies_positive_equality,plain,(~$equal(negate(B),negate(A))|$equal(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ROB/ROB021-1.tptp',unknown),[]).
%
% cnf(145065360,plain,(~$equal(negate(B),negate(A))|$equal(B,A)),inference(rewrite,[status(thm)],[negative_equality_implies_positive_equality]),[]).
%
% fof(robbins_axiom,plain,($equal(negate(add(negate(add(A,B)),negate(add(A,negate(B))))),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ROB/ROB021-1.tptp',unknown),[]).
%
% cnf(145045952,plain,($equal(negate(add(negate(add(A,B)),negate(add(A,negate(B))))),A)),inference(rewrite,[status(thm)],[robbins_axiom]),[]).
%
% cnf(152911472,plain,($equal(add(negate(add(negate(A),B)),negate(add(negate(A),negate(B)))),A)),inference(resolution,[status(thm)],[145065360,145045952]),[]).
%
% fof(commutativity_of_add,plain,($equal(add(B,A),add(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ROB/ROB021-1.tptp',unknown),[]).
%
% cnf(145037864,plain,($equal(add(B,A),add(A,B))),inference(rewrite,[status(thm)],[commutativity_of_add]),[]).
%
% cnf(153174056,plain,($equal(add(negate(add(negate(A),negate(B))),negate(add(negate(A),B))),A)),inference(paramodulation,[status(thm)],[152911472,145037864,theory(equality)]),[]).
%
% cnf(153483368,plain,($equal(add(negate(add(negate(A),negate(B))),negate(add(B,negate(A)))),A)),inference(paramodulation,[status(thm)],[153174056,145037864,theory(equality)]),[]).
%
% fof(prove_huntingtons_axiom,plain,(~$equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/ROB/ROB021-1.tptp',unknown),[]).
%
% cnf(145073664,plain,(~$equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b)),inference(rewrite,[status(thm)],[prove_huntingtons_axiom]),[]).
%
% cnf(153089280,plain,(~$equal(add(negate(add(negate(a),negate(b))),negate(add(a,negate(b)))),b)),inference(paramodulation,[status(thm)],[145073664,145037864,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[153483368,153089280,145037864,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------