TSTP Solution File: GRP043-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP043-2 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.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 12:19:22 EDT 2009
% Result : Unsatisfiable 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 13 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 26 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_transitivity,plain,
~ equalish(a,c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP043-2.tptp',unknown),
[] ).
cnf(172840536,plain,
~ equalish(a,c),
inference(rewrite,[status(thm)],[prove_transitivity]),
[] ).
fof(product_substitution3,plain,
! [A,B,C,D] :
( ~ equalish(A,B)
| ~ product(C,D,A)
| product(C,D,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP043-2.tptp',unknown),
[] ).
cnf(172881624,plain,
( ~ equalish(A,B)
| ~ product(C,D,A)
| product(C,D,B) ),
inference(rewrite,[status(thm)],[product_substitution3]),
[] ).
fof(left_identity,plain,
! [A] : product(identity,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP043-2.tptp',unknown),
[] ).
cnf(172843072,plain,
product(identity,A,A),
inference(rewrite,[status(thm)],[left_identity]),
[] ).
cnf(181689000,plain,
( ~ equalish(A,B)
| product(identity,A,B) ),
inference(resolution,[status(thm)],[172881624,172843072]),
[] ).
fof(total_function2,plain,
! [A,B,C,D] :
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP043-2.tptp',unknown),
[] ).
cnf(172858992,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[total_function2]),
[] ).
cnf(182035464,plain,
( ~ equalish(A,B)
| ~ product(identity,A,C)
| equalish(B,C) ),
inference(resolution,[status(thm)],[181689000,172858992]),
[] ).
fof(a_equals_b,plain,
equalish(a,b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP043-2.tptp',unknown),
[] ).
cnf(172886176,plain,
equalish(a,b),
inference(rewrite,[status(thm)],[a_equals_b]),
[] ).
cnf(181698280,plain,
product(identity,a,b),
inference(resolution,[status(thm)],[181689000,172886176]),
[] ).
cnf(181761592,plain,
( ~ equalish(b,A)
| product(identity,a,A) ),
inference(resolution,[status(thm)],[172881624,181698280]),
[] ).
fof(b_equals_c,plain,
equalish(b,c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP043-2.tptp',unknown),
[] ).
cnf(172890128,plain,
equalish(b,c),
inference(rewrite,[status(thm)],[b_equals_c]),
[] ).
cnf(181767120,plain,
product(identity,a,c),
inference(resolution,[status(thm)],[181761592,172890128]),
[] ).
cnf(182231784,plain,
( ~ equalish(a,A)
| equalish(A,c) ),
inference(resolution,[status(thm)],[182035464,181767120]),
[] ).
cnf(180711384,plain,
equalish(A,A),
inference(resolution,[status(thm)],[172858992,172843072]),
[] ).
cnf(183512608,plain,
equalish(a,c),
inference(resolution,[status(thm)],[182231784,180711384]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[172840536,183512608]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_transitivity,plain,(~equalish(a,c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP043-2.tptp',unknown),[]).
%
% cnf(172840536,plain,(~equalish(a,c)),inference(rewrite,[status(thm)],[prove_transitivity]),[]).
%
% fof(product_substitution3,plain,(~equalish(A,B)|~product(C,D,A)|product(C,D,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP043-2.tptp',unknown),[]).
%
% cnf(172881624,plain,(~equalish(A,B)|~product(C,D,A)|product(C,D,B)),inference(rewrite,[status(thm)],[product_substitution3]),[]).
%
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP043-2.tptp',unknown),[]).
%
% cnf(172843072,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
%
% cnf(181689000,plain,(~equalish(A,B)|product(identity,A,B)),inference(resolution,[status(thm)],[172881624,172843072]),[]).
%
% fof(total_function2,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP043-2.tptp',unknown),[]).
%
% cnf(172858992,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[total_function2]),[]).
%
% cnf(182035464,plain,(~equalish(A,B)|~product(identity,A,C)|equalish(B,C)),inference(resolution,[status(thm)],[181689000,172858992]),[]).
%
% fof(a_equals_b,plain,(equalish(a,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP043-2.tptp',unknown),[]).
%
% cnf(172886176,plain,(equalish(a,b)),inference(rewrite,[status(thm)],[a_equals_b]),[]).
%
% cnf(181698280,plain,(product(identity,a,b)),inference(resolution,[status(thm)],[181689000,172886176]),[]).
%
% cnf(181761592,plain,(~equalish(b,A)|product(identity,a,A)),inference(resolution,[status(thm)],[172881624,181698280]),[]).
%
% fof(b_equals_c,plain,(equalish(b,c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP043-2.tptp',unknown),[]).
%
% cnf(172890128,plain,(equalish(b,c)),inference(rewrite,[status(thm)],[b_equals_c]),[]).
%
% cnf(181767120,plain,(product(identity,a,c)),inference(resolution,[status(thm)],[181761592,172890128]),[]).
%
% cnf(182231784,plain,(~equalish(a,A)|equalish(A,c)),inference(resolution,[status(thm)],[182035464,181767120]),[]).
%
% cnf(180711384,plain,(equalish(A,A)),inference(resolution,[status(thm)],[172858992,172843072]),[]).
%
% cnf(183512608,plain,(equalish(a,c)),inference(resolution,[status(thm)],[182231784,180711384]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[172840536,183512608]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------