TSTP Solution File: GRP009-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP009-1 : 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 @ 2794MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 12:17:38 EDT 2009
% Result : Unsatisfiable 7.9s
% Output : Refutation 7.9s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 20 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 58 ( 32 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 1 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(left_inverse,plain,
! [A] : product(inverse(A),A,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP009-1.tptp',unknown),
[] ).
cnf(169734608,plain,
product(inverse(A),A,identity),
inference(rewrite,[status(thm)],[left_inverse]),
[] ).
fof(c_is_an_inverse_of_b,plain,
product(c,b,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP009-1.tptp',unknown),
[] ).
cnf(169724320,plain,
product(c,b,identity),
inference(rewrite,[status(thm)],[c_is_an_inverse_of_b]),
[] ).
fof(associativity1,plain,
! [A,B,C,D,E,F] :
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP009-1.tptp',unknown),
[] ).
cnf(169760072,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
inference(rewrite,[status(thm)],[associativity1]),
[] ).
fof(left_identity,plain,
! [A] : product(identity,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP009-1.tptp',unknown),
[] ).
cnf(169726856,plain,
product(identity,A,A),
inference(rewrite,[status(thm)],[left_identity]),
[] ).
cnf(177630168,plain,
( ~ product(A,B,identity)
| ~ product(B,C,D)
| product(A,D,C) ),
inference(resolution,[status(thm)],[169760072,169726856]),
[] ).
cnf(198748264,plain,
( ~ product(A,c,identity)
| product(A,identity,b) ),
inference(resolution,[status(thm)],[169724320,177630168]),
[] ).
fof(total_function2,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(A,B,D)
| $equal(D,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP009-1.tptp',unknown),
[] ).
cnf(169753304,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| $equal(D,C) ),
inference(rewrite,[status(thm)],[total_function2]),
[] ).
fof(a_is_an_inverse_of_b,plain,
product(a,b,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP009-1.tptp',unknown),
[] ).
cnf(169771744,plain,
product(a,b,identity),
inference(rewrite,[status(thm)],[a_is_an_inverse_of_b]),
[] ).
cnf(178386648,plain,
( ~ product(a,b,A)
| $equal(A,identity) ),
inference(resolution,[status(thm)],[169753304,169771744]),
[] ).
fof(total_function1,plain,
! [A,B] : product(A,B,multiply(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP009-1.tptp',unknown),
[] ).
cnf(169742000,plain,
product(A,B,multiply(A,B)),
inference(rewrite,[status(thm)],[total_function1]),
[] ).
cnf(182297312,plain,
$equal(multiply(a,b),identity),
inference(resolution,[status(thm)],[178386648,169742000]),
[] ).
cnf(177563296,plain,
( ~ product(identity,A,B)
| $equal(A,B) ),
inference(resolution,[status(thm)],[169753304,169726856]),
[] ).
fof(prove_a_equals_c,plain,
~ $equal(c,a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP009-1.tptp',unknown),
[] ).
cnf(169780136,plain,
~ $equal(c,a),
inference(rewrite,[status(thm)],[prove_a_equals_c]),
[] ).
cnf(178814320,plain,
~ product(identity,c,a),
inference(resolution,[status(thm)],[177563296,169780136]),
[] ).
cnf(182593552,plain,
~ product(multiply(a,b),c,a),
inference(paramodulation,[status(thm)],[182297312,178814320,theory(equality)]),
[] ).
fof(associativity2,plain,
! [A,B,C,D,E,F] :
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP009-1.tptp',unknown),
[] ).
cnf(169768480,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
inference(rewrite,[status(thm)],[associativity2]),
[] ).
fof(right_identity,plain,
! [A] : product(A,identity,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP009-1.tptp',unknown),
[] ).
cnf(169730960,plain,
product(A,identity,A),
inference(rewrite,[status(thm)],[right_identity]),
[] ).
cnf(177720952,plain,
( ~ product(A,B,C)
| ~ product(B,D,identity)
| product(C,D,A) ),
inference(resolution,[status(thm)],[169768480,169730960]),
[] ).
cnf(178095720,plain,
( ~ product(B,C,identity)
| product(multiply(A,B),C,A) ),
inference(resolution,[status(thm)],[177720952,169742000]),
[] ).
cnf(226096000,plain,
~ product(b,c,identity),
inference(resolution,[status(thm)],[182593552,178095720]),
[] ).
cnf(177640016,plain,
( ~ product(A,identity,B)
| ~ product(A,C,D)
| product(B,C,D) ),
inference(resolution,[status(thm)],[169768480,169726856]),
[] ).
cnf(244107648,plain,
~ product(A,c,identity),
inference(forward_subsumption_resolution__resolution,[status(thm)],[198748264,226096000,177640016]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[169734608,244107648]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 7 seconds
% START OF PROOF SEQUENCE
% fof(left_inverse,plain,(product(inverse(A),A,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP009-1.tptp',unknown),[]).
%
% cnf(169734608,plain,(product(inverse(A),A,identity)),inference(rewrite,[status(thm)],[left_inverse]),[]).
%
% fof(c_is_an_inverse_of_b,plain,(product(c,b,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP009-1.tptp',unknown),[]).
%
% cnf(169724320,plain,(product(c,b,identity)),inference(rewrite,[status(thm)],[c_is_an_inverse_of_b]),[]).
%
% fof(associativity1,plain,(~product(A,B,C)|~product(B,D,E)|~product(C,D,F)|product(A,E,F)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP009-1.tptp',unknown),[]).
%
% cnf(169760072,plain,(~product(A,B,C)|~product(B,D,E)|~product(C,D,F)|product(A,E,F)),inference(rewrite,[status(thm)],[associativity1]),[]).
%
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP009-1.tptp',unknown),[]).
%
% cnf(169726856,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
%
% cnf(177630168,plain,(~product(A,B,identity)|~product(B,C,D)|product(A,D,C)),inference(resolution,[status(thm)],[169760072,169726856]),[]).
%
% cnf(198748264,plain,(~product(A,c,identity)|product(A,identity,b)),inference(resolution,[status(thm)],[169724320,177630168]),[]).
%
% fof(total_function2,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP009-1.tptp',unknown),[]).
%
% cnf(169753304,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[total_function2]),[]).
%
% fof(a_is_an_inverse_of_b,plain,(product(a,b,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP009-1.tptp',unknown),[]).
%
% cnf(169771744,plain,(product(a,b,identity)),inference(rewrite,[status(thm)],[a_is_an_inverse_of_b]),[]).
%
% cnf(178386648,plain,(~product(a,b,A)|$equal(A,identity)),inference(resolution,[status(thm)],[169753304,169771744]),[]).
%
% fof(total_function1,plain,(product(A,B,multiply(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP009-1.tptp',unknown),[]).
%
% cnf(169742000,plain,(product(A,B,multiply(A,B))),inference(rewrite,[status(thm)],[total_function1]),[]).
%
% cnf(182297312,plain,($equal(multiply(a,b),identity)),inference(resolution,[status(thm)],[178386648,169742000]),[]).
%
% cnf(177563296,plain,(~product(identity,A,B)|$equal(A,B)),inference(resolution,[status(thm)],[169753304,169726856]),[]).
%
% fof(prove_a_equals_c,plain,(~$equal(c,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP009-1.tptp',unknown),[]).
%
% cnf(169780136,plain,(~$equal(c,a)),inference(rewrite,[status(thm)],[prove_a_equals_c]),[]).
%
% cnf(178814320,plain,(~product(identity,c,a)),inference(resolution,[status(thm)],[177563296,169780136]),[]).
%
% cnf(182593552,plain,(~product(multiply(a,b),c,a)),inference(paramodulation,[status(thm)],[182297312,178814320,theory(equality)]),[]).
%
% fof(associativity2,plain,(~product(A,B,C)|~product(B,D,E)|~product(A,E,F)|product(C,D,F)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP009-1.tptp',unknown),[]).
%
% cnf(169768480,plain,(~product(A,B,C)|~product(B,D,E)|~product(A,E,F)|product(C,D,F)),inference(rewrite,[status(thm)],[associativity2]),[]).
%
% fof(right_identity,plain,(product(A,identity,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP009-1.tptp',unknown),[]).
%
% cnf(169730960,plain,(product(A,identity,A)),inference(rewrite,[status(thm)],[right_identity]),[]).
%
% cnf(177720952,plain,(~product(A,B,C)|~product(B,D,identity)|product(C,D,A)),inference(resolution,[status(thm)],[169768480,169730960]),[]).
%
% cnf(178095720,plain,(~product(B,C,identity)|product(multiply(A,B),C,A)),inference(resolution,[status(thm)],[177720952,169742000]),[]).
%
% cnf(226096000,plain,(~product(b,c,identity)),inference(resolution,[status(thm)],[182593552,178095720]),[]).
%
% cnf(177640016,plain,(~product(A,identity,B)|~product(A,C,D)|product(B,C,D)),inference(resolution,[status(thm)],[169768480,169726856]),[]).
%
% cnf(244107648,plain,(~product(A,c,identity)),inference(forward_subsumption_resolution__resolution,[status(thm)],[198748264,226096000,177640016]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[169734608,244107648]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------