TSTP Solution File: GRP010-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP010-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art01.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 12:17:40 EDT 2009
% Result : Unsatisfiable 3.4s
% Output : Refutation 3.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 13 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 16 ~; 14 |; 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 : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 35 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(right_inverse,plain,
! [A] : product(A,inverse(A),identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP010-1.tptp',unknown),
[] ).
cnf(168176728,plain,
product(A,inverse(A),identity),
inference(rewrite,[status(thm)],[right_inverse]),
[] ).
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/GRP010-1.tptp',unknown),
[] ).
cnf(168206704,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
inference(rewrite,[status(thm)],[associativity2]),
[] ).
cnf(176585768,plain,
( ~ product(A,B,C)
| ~ product(A,identity,D)
| product(C,inverse(B),D) ),
inference(resolution,[status(thm)],[168206704,168176728]),
[] ).
fof(right_identity,plain,
! [A] : product(A,identity,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP010-1.tptp',unknown),
[] ).
cnf(168169248,plain,
product(A,identity,A),
inference(rewrite,[status(thm)],[right_identity]),
[] ).
cnf(182934448,plain,
( ~ product(A,B,C)
| product(C,inverse(B),A) ),
inference(resolution,[status(thm)],[176585768,168169248]),
[] ).
fof(a_multiply_b_is_identity,plain,
product(a,b,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP010-1.tptp',unknown),
[] ).
cnf(168209968,plain,
product(a,b,identity),
inference(rewrite,[status(thm)],[a_multiply_b_is_identity]),
[] ).
cnf(182962728,plain,
product(identity,inverse(b),a),
inference(resolution,[status(thm)],[182934448,168209968]),
[] ).
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/GRP010-1.tptp',unknown),
[] ).
cnf(168191592,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| $equal(D,C) ),
inference(rewrite,[status(thm)],[total_function2]),
[] ).
fof(left_identity,plain,
! [A] : product(identity,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP010-1.tptp',unknown),
[] ).
cnf(168165176,plain,
product(identity,A,A),
inference(rewrite,[status(thm)],[left_identity]),
[] ).
cnf(175987984,plain,
( ~ product(identity,A,B)
| $equal(B,A) ),
inference(resolution,[status(thm)],[168191592,168165176]),
[] ).
cnf(224121696,plain,
$equal(a,inverse(b)),
inference(resolution,[status(thm)],[182962728,175987984]),
[] ).
fof(prove_b_multiply_a_is_identity,plain,
~ product(b,a,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP010-1.tptp',unknown),
[] ).
cnf(168162728,plain,
~ product(b,a,identity),
inference(rewrite,[status(thm)],[prove_b_multiply_a_is_identity]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[168176728,224121696,168162728,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 3 seconds
% START OF PROOF SEQUENCE
% fof(right_inverse,plain,(product(A,inverse(A),identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP010-1.tptp',unknown),[]).
%
% cnf(168176728,plain,(product(A,inverse(A),identity)),inference(rewrite,[status(thm)],[right_inverse]),[]).
%
% fof(associativity2,plain,(~product(A,B,C)|~product(B,D,E)|~product(A,E,F)|product(C,D,F)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP010-1.tptp',unknown),[]).
%
% cnf(168206704,plain,(~product(A,B,C)|~product(B,D,E)|~product(A,E,F)|product(C,D,F)),inference(rewrite,[status(thm)],[associativity2]),[]).
%
% cnf(176585768,plain,(~product(A,B,C)|~product(A,identity,D)|product(C,inverse(B),D)),inference(resolution,[status(thm)],[168206704,168176728]),[]).
%
% fof(right_identity,plain,(product(A,identity,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP010-1.tptp',unknown),[]).
%
% cnf(168169248,plain,(product(A,identity,A)),inference(rewrite,[status(thm)],[right_identity]),[]).
%
% cnf(182934448,plain,(~product(A,B,C)|product(C,inverse(B),A)),inference(resolution,[status(thm)],[176585768,168169248]),[]).
%
% fof(a_multiply_b_is_identity,plain,(product(a,b,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP010-1.tptp',unknown),[]).
%
% cnf(168209968,plain,(product(a,b,identity)),inference(rewrite,[status(thm)],[a_multiply_b_is_identity]),[]).
%
% cnf(182962728,plain,(product(identity,inverse(b),a)),inference(resolution,[status(thm)],[182934448,168209968]),[]).
%
% fof(total_function2,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP010-1.tptp',unknown),[]).
%
% cnf(168191592,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[total_function2]),[]).
%
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP010-1.tptp',unknown),[]).
%
% cnf(168165176,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
%
% cnf(175987984,plain,(~product(identity,A,B)|$equal(B,A)),inference(resolution,[status(thm)],[168191592,168165176]),[]).
%
% cnf(224121696,plain,($equal(a,inverse(b))),inference(resolution,[status(thm)],[182962728,175987984]),[]).
%
% fof(prove_b_multiply_a_is_identity,plain,(~product(b,a,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP010-1.tptp',unknown),[]).
%
% cnf(168162728,plain,(~product(b,a,identity)),inference(rewrite,[status(thm)],[prove_b_multiply_a_is_identity]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[168176728,224121696,168162728,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------