TSTP Solution File: RNG024-7 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : RNG024-7 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art04.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 15:20:22 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 10 unt; 0 def)
% Number of atoms : 10 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 12 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(right_additive_inverse,plain,
! [A] : $equal(add(A,additive_inverse(A)),additive_identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG024-7.tptp',unknown),
[] ).
cnf(151812592,plain,
$equal(add(A,additive_inverse(A)),additive_identity),
inference(rewrite,[status(thm)],[right_additive_inverse]),
[] ).
fof(prove_right_alternative,plain,
~ $equal(associator(x,y,y),additive_identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG024-7.tptp',unknown),
[] ).
cnf(151989392,plain,
~ $equal(associator(x,y,y),additive_identity),
inference(rewrite,[status(thm)],[prove_right_alternative]),
[] ).
fof(associator,plain,
! [A,B,C] : $equal(add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C)))),associator(A,B,C)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG024-7.tptp',unknown),
[] ).
cnf(151881624,plain,
$equal(add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C)))),associator(A,B,C)),
inference(rewrite,[status(thm)],[associator]),
[] ).
cnf(159896600,plain,
~ $equal(add(multiply(multiply(x,y),y),additive_inverse(multiply(x,multiply(y,y)))),additive_identity),
inference(paramodulation,[status(thm)],[151989392,151881624,theory(equality)]),
[] ).
fof(right_alternative,plain,
! [A,B] : $equal(multiply(A,multiply(B,B)),multiply(multiply(A,B),B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG024-7.tptp',unknown),
[] ).
cnf(151873600,plain,
$equal(multiply(A,multiply(B,B)),multiply(multiply(A,B),B)),
inference(rewrite,[status(thm)],[right_alternative]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[151812592,159896600,151873600,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(right_additive_inverse,plain,($equal(add(A,additive_inverse(A)),additive_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG024-7.tptp',unknown),[]).
%
% cnf(151812592,plain,($equal(add(A,additive_inverse(A)),additive_identity)),inference(rewrite,[status(thm)],[right_additive_inverse]),[]).
%
% fof(prove_right_alternative,plain,(~$equal(associator(x,y,y),additive_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG024-7.tptp',unknown),[]).
%
% cnf(151989392,plain,(~$equal(associator(x,y,y),additive_identity)),inference(rewrite,[status(thm)],[prove_right_alternative]),[]).
%
% fof(associator,plain,($equal(add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C)))),associator(A,B,C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG024-7.tptp',unknown),[]).
%
% cnf(151881624,plain,($equal(add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C)))),associator(A,B,C))),inference(rewrite,[status(thm)],[associator]),[]).
%
% cnf(159896600,plain,(~$equal(add(multiply(multiply(x,y),y),additive_inverse(multiply(x,multiply(y,y)))),additive_identity)),inference(paramodulation,[status(thm)],[151989392,151881624,theory(equality)]),[]).
%
% fof(right_alternative,plain,($equal(multiply(A,multiply(B,B)),multiply(multiply(A,B),B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG024-7.tptp',unknown),[]).
%
% cnf(151873600,plain,($equal(multiply(A,multiply(B,B)),multiply(multiply(A,B),B))),inference(rewrite,[status(thm)],[right_alternative]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[151812592,159896600,151873600,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------