TSTP Solution File: GRP013-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP013-1 : 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 @ 2794MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 12:17:56 EDT 2009
% Result : Unsatisfiable 0.9s
% Output : Refutation 0.9s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 28 ( 18 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 36 ( 19 ~; 17 |; 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(squareness,plain,
! [A] : product(A,A,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP013-1.tptp',unknown),
[] ).
cnf(166254704,plain,
product(A,A,identity),
inference(rewrite,[status(thm)],[squareness]),
[] ).
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/GRP013-1.tptp',unknown),
[] ).
cnf(166243000,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/GRP013-1.tptp',unknown),
[] ).
cnf(166209720,plain,
product(identity,A,A),
inference(rewrite,[status(thm)],[left_identity]),
[] ).
cnf(174131384,plain,
( ~ product(A,B,identity)
| ~ product(B,C,D)
| product(A,D,C) ),
inference(resolution,[status(thm)],[166243000,166209720]),
[] ).
cnf(174215264,plain,
( ~ product(A,B,C)
| product(A,C,B) ),
inference(resolution,[status(thm)],[174131384,166254704]),
[] ).
fof(total_function1,plain,
! [A,B] : product(A,B,multiply(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP013-1.tptp',unknown),
[] ).
cnf(166224896,plain,
product(A,B,multiply(A,B)),
inference(rewrite,[status(thm)],[total_function1]),
[] ).
cnf(182594344,plain,
product(A,multiply(A,B),B),
inference(resolution,[status(thm)],[174215264,166224896]),
[] ).
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/GRP013-1.tptp',unknown),
[] ).
cnf(166236200,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| $equal(D,C) ),
inference(rewrite,[status(thm)],[total_function2]),
[] ).
fof(inverses_have_property,plain,
! [A,B,C] :
( ~ product(inverse(A),inverse(B),C)
| product(A,C,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP013-1.tptp',unknown),
[] ).
cnf(166271928,plain,
( ~ product(inverse(A),inverse(B),C)
| product(A,C,B) ),
inference(rewrite,[status(thm)],[inverses_have_property]),
[] ).
fof(inverse_a_times_inverse_b_is_d,plain,
product(inverse(a),inverse(b),d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP013-1.tptp',unknown),
[] ).
cnf(166266304,plain,
product(inverse(a),inverse(b),d),
inference(rewrite,[status(thm)],[inverse_a_times_inverse_b_is_d]),
[] ).
cnf(174579128,plain,
product(a,d,b),
inference(resolution,[status(thm)],[166271928,166266304]),
[] ).
cnf(174803456,plain,
( ~ product(a,d,A)
| $equal(A,b) ),
inference(resolution,[status(thm)],[166236200,174579128]),
[] ).
cnf(191195680,plain,
$equal(multiply(a,d),b),
inference(resolution,[status(thm)],[174803456,166224896]),
[] ).
cnf(197327760,plain,
product(a,b,d),
inference(paramodulation,[status(thm)],[182594344,191195680,theory(equality)]),
[] ).
fof(a_times_b_is_c,plain,
product(a,b,c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP013-1.tptp',unknown),
[] ).
cnf(166207136,plain,
product(a,b,c),
inference(rewrite,[status(thm)],[a_times_b_is_c]),
[] ).
cnf(174737120,plain,
( ~ product(a,b,A)
| $equal(A,c) ),
inference(resolution,[status(thm)],[166236200,166207136]),
[] ).
cnf(197394384,plain,
$equal(d,c),
inference(resolution,[status(thm)],[197327760,174737120]),
[] ).
fof(prove_c_times_d_is_identity,plain,
~ product(c,d,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP013-1.tptp',unknown),
[] ).
cnf(166275944,plain,
~ product(c,d,identity),
inference(rewrite,[status(thm)],[prove_c_times_d_is_identity]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[166254704,197394384,166275944,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(squareness,plain,(product(A,A,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP013-1.tptp',unknown),[]).
%
% cnf(166254704,plain,(product(A,A,identity)),inference(rewrite,[status(thm)],[squareness]),[]).
%
% fof(associativity1,plain,(~product(A,B,C)|~product(B,D,E)|~product(C,D,F)|product(A,E,F)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP013-1.tptp',unknown),[]).
%
% cnf(166243000,plain,(~product(A,B,C)|~product(B,D,E)|~product(C,D,F)|product(A,E,F)),inference(rewrite,[status(thm)],[associativity1]),[]).
%
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP013-1.tptp',unknown),[]).
%
% cnf(166209720,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
%
% cnf(174131384,plain,(~product(A,B,identity)|~product(B,C,D)|product(A,D,C)),inference(resolution,[status(thm)],[166243000,166209720]),[]).
%
% cnf(174215264,plain,(~product(A,B,C)|product(A,C,B)),inference(resolution,[status(thm)],[174131384,166254704]),[]).
%
% fof(total_function1,plain,(product(A,B,multiply(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP013-1.tptp',unknown),[]).
%
% cnf(166224896,plain,(product(A,B,multiply(A,B))),inference(rewrite,[status(thm)],[total_function1]),[]).
%
% cnf(182594344,plain,(product(A,multiply(A,B),B)),inference(resolution,[status(thm)],[174215264,166224896]),[]).
%
% fof(total_function2,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP013-1.tptp',unknown),[]).
%
% cnf(166236200,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[total_function2]),[]).
%
% fof(inverses_have_property,plain,(~product(inverse(A),inverse(B),C)|product(A,C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP013-1.tptp',unknown),[]).
%
% cnf(166271928,plain,(~product(inverse(A),inverse(B),C)|product(A,C,B)),inference(rewrite,[status(thm)],[inverses_have_property]),[]).
%
% fof(inverse_a_times_inverse_b_is_d,plain,(product(inverse(a),inverse(b),d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP013-1.tptp',unknown),[]).
%
% cnf(166266304,plain,(product(inverse(a),inverse(b),d)),inference(rewrite,[status(thm)],[inverse_a_times_inverse_b_is_d]),[]).
%
% cnf(174579128,plain,(product(a,d,b)),inference(resolution,[status(thm)],[166271928,166266304]),[]).
%
% cnf(174803456,plain,(~product(a,d,A)|$equal(A,b)),inference(resolution,[status(thm)],[166236200,174579128]),[]).
%
% cnf(191195680,plain,($equal(multiply(a,d),b)),inference(resolution,[status(thm)],[174803456,166224896]),[]).
%
% cnf(197327760,plain,(product(a,b,d)),inference(paramodulation,[status(thm)],[182594344,191195680,theory(equality)]),[]).
%
% fof(a_times_b_is_c,plain,(product(a,b,c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP013-1.tptp',unknown),[]).
%
% cnf(166207136,plain,(product(a,b,c)),inference(rewrite,[status(thm)],[a_times_b_is_c]),[]).
%
% cnf(174737120,plain,(~product(a,b,A)|$equal(A,c)),inference(resolution,[status(thm)],[166236200,166207136]),[]).
%
% cnf(197394384,plain,($equal(d,c)),inference(resolution,[status(thm)],[197327760,174737120]),[]).
%
% fof(prove_c_times_d_is_identity,plain,(~product(c,d,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP013-1.tptp',unknown),[]).
%
% cnf(166275944,plain,(~product(c,d,identity)),inference(rewrite,[status(thm)],[prove_c_times_d_is_identity]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[166254704,197394384,166275944,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------