%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP012-1 : 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 12:17:46 EDT 2009
% Result : Unsatisfiable 37.2s
% Output : Refutation 37.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 41 ( 29 unt; 0 def)
% Number of atoms : 65 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52 ( 28 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 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 : 62 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/GRP012-1.tptp',unknown),
[] ).
cnf(151877992,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
inference(rewrite,[status(thm)],[associativity1]),
[] ).
fof(inverse_b_multiply_inverse_a_is_d,plain,
product(inverse(b),inverse(a),d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-1.tptp',unknown),
[] ).
cnf(151842232,plain,
product(inverse(b),inverse(a),d),
inference(rewrite,[status(thm)],[inverse_b_multiply_inverse_a_is_d]),
[] ).
cnf(169760312,plain,
( ~ product(A,inverse(b),B)
| ~ product(B,inverse(a),C)
| product(A,d,C) ),
inference(resolution,[status(thm)],[151877992,151842232]),
[] ).
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/GRP012-1.tptp',unknown),
[] ).
cnf(151886432,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/GRP012-1.tptp',unknown),
[] ).
cnf(151848848,plain,
product(A,identity,A),
inference(rewrite,[status(thm)],[right_identity]),
[] ).
cnf(165846224,plain,
( ~ product(A,B,C)
| ~ product(B,D,identity)
| product(C,D,A) ),
inference(resolution,[status(thm)],[151886432,151848848]),
[] ).
fof(a_multiply_b_is_c,plain,
product(a,b,c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-1.tptp',unknown),
[] ).
cnf(151889696,plain,
product(a,b,c),
inference(rewrite,[status(thm)],[a_multiply_b_is_c]),
[] ).
cnf(166162000,plain,
( ~ product(b,A,identity)
| product(c,A,a) ),
inference(resolution,[status(thm)],[165846224,151889696]),
[] ).
fof(right_inverse,plain,
! [A] : product(A,inverse(A),identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-1.tptp',unknown),
[] ).
cnf(151856328,plain,
product(A,inverse(A),identity),
inference(rewrite,[status(thm)],[right_inverse]),
[] ).
cnf(166982808,plain,
product(c,inverse(b),a),
inference(resolution,[status(thm)],[166162000,151856328]),
[] ).
cnf(323088952,plain,
( ~ product(a,inverse(a),A)
| product(c,d,A) ),
inference(resolution,[status(thm)],[169760312,166982808]),
[] ).
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/GRP012-1.tptp',unknown),
[] ).
cnf(151871192,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/GRP012-1.tptp',unknown),
[] ).
cnf(151844712,plain,
product(identity,A,A),
inference(rewrite,[status(thm)],[left_identity]),
[] ).
cnf(159681352,plain,
( ~ product(identity,A,B)
| $equal(B,A) ),
inference(resolution,[status(thm)],[151871192,151844712]),
[] ).
cnf(160139600,plain,
$equal(identity,inverse(identity)),
inference(resolution,[status(thm)],[159681352,151856328]),
[] ).
fof(left_inverse,plain,
! [A] : product(inverse(A),A,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-1.tptp',unknown),
[] ).
cnf(151852496,plain,
product(inverse(A),A,identity),
inference(rewrite,[status(thm)],[left_inverse]),
[] ).
cnf(160194488,plain,
product(inverse(A),A,inverse(identity)),
inference(paramodulation,[status(thm)],[160139600,151852496,theory(equality)]),
[] ).
cnf(160352664,plain,
product(identity,identity,inverse(identity)),
inference(paramodulation,[status(thm)],[160194488,160139600,theory(equality)]),
[] ).
cnf(160364432,plain,
$equal(inverse(identity),identity),
inference(resolution,[status(thm)],[160352664,159681352]),
[] ).
cnf(160395968,plain,
$equal(identity,inverse(inverse(identity))),
inference(paramodulation,[status(thm)],[160364432,160139600,theory(equality)]),
[] ).
cnf(160430176,plain,
product(A,inverse(A),inverse(inverse(identity))),
inference(paramodulation,[status(thm)],[160395968,151856328,theory(equality)]),
[] ).
cnf(323124232,plain,
product(c,d,inverse(inverse(identity))),
inference(resolution,[status(thm)],[323088952,160430176]),
[] ).
cnf(160032736,plain,
( ~ product(inverse(A),A,B)
| $equal(B,identity) ),
inference(resolution,[status(thm)],[151871192,151852496]),
[] ).
fof(total_function1,plain,
! [A,B] : product(A,B,multiply(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-1.tptp',unknown),
[] ).
cnf(151859888,plain,
product(A,B,multiply(A,B)),
inference(rewrite,[status(thm)],[total_function1]),
[] ).
cnf(162996232,plain,
$equal(multiply(inverse(A),A),identity),
inference(resolution,[status(thm)],[160032736,151859888]),
[] ).
fof(prove_c_multiply_d_is_identity,plain,
~ product(c,d,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-1.tptp',unknown),
[] ).
cnf(151897496,plain,
~ product(c,d,identity),
inference(rewrite,[status(thm)],[prove_c_multiply_d_is_identity]),
[] ).
cnf(160217232,plain,
~ product(c,d,inverse(identity)),
inference(paramodulation,[status(thm)],[160139600,151897496,theory(equality)]),
[] ).
cnf(163353800,plain,
~ product(c,d,inverse(multiply(inverse(A),A))),
inference(paramodulation,[status(thm)],[162996232,160217232,theory(equality)]),
[] ).
cnf(163158776,plain,
$equal(multiply(inverse(A),A),inverse(identity)),
inference(paramodulation,[status(thm)],[162996232,160139600,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[323124232,163353800,163158776,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 37 seconds
% START OF PROOF SEQUENCE
% 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/GRP012-1.tptp',unknown),[]).
%
% cnf(151877992,plain,(~product(A,B,C)|~product(B,D,E)|~product(C,D,F)|product(A,E,F)),inference(rewrite,[status(thm)],[associativity1]),[]).
%
% fof(inverse_b_multiply_inverse_a_is_d,plain,(product(inverse(b),inverse(a),d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-1.tptp',unknown),[]).
%
% cnf(151842232,plain,(product(inverse(b),inverse(a),d)),inference(rewrite,[status(thm)],[inverse_b_multiply_inverse_a_is_d]),[]).
%
% cnf(169760312,plain,(~product(A,inverse(b),B)|~product(B,inverse(a),C)|product(A,d,C)),inference(resolution,[status(thm)],[151877992,151842232]),[]).
%
% 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/GRP012-1.tptp',unknown),[]).
%
% cnf(151886432,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/GRP012-1.tptp',unknown),[]).
%
% cnf(151848848,plain,(product(A,identity,A)),inference(rewrite,[status(thm)],[right_identity]),[]).
%
% cnf(165846224,plain,(~product(A,B,C)|~product(B,D,identity)|product(C,D,A)),inference(resolution,[status(thm)],[151886432,151848848]),[]).
%
% fof(a_multiply_b_is_c,plain,(product(a,b,c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-1.tptp',unknown),[]).
%
% cnf(151889696,plain,(product(a,b,c)),inference(rewrite,[status(thm)],[a_multiply_b_is_c]),[]).
%
% cnf(166162000,plain,(~product(b,A,identity)|product(c,A,a)),inference(resolution,[status(thm)],[165846224,151889696]),[]).
%
% fof(right_inverse,plain,(product(A,inverse(A),identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-1.tptp',unknown),[]).
%
% cnf(151856328,plain,(product(A,inverse(A),identity)),inference(rewrite,[status(thm)],[right_inverse]),[]).
%
% cnf(166982808,plain,(product(c,inverse(b),a)),inference(resolution,[status(thm)],[166162000,151856328]),[]).
%
% cnf(323088952,plain,(~product(a,inverse(a),A)|product(c,d,A)),inference(resolution,[status(thm)],[169760312,166982808]),[]).
%
% fof(total_function2,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-1.tptp',unknown),[]).
%
% cnf(151871192,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[total_function2]),[]).
%
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-1.tptp',unknown),[]).
%
% cnf(151844712,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
%
% cnf(159681352,plain,(~product(identity,A,B)|$equal(B,A)),inference(resolution,[status(thm)],[151871192,151844712]),[]).
%
% cnf(160139600,plain,($equal(identity,inverse(identity))),inference(resolution,[status(thm)],[159681352,151856328]),[]).
%
% fof(left_inverse,plain,(product(inverse(A),A,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-1.tptp',unknown),[]).
%
% cnf(151852496,plain,(product(inverse(A),A,identity)),inference(rewrite,[status(thm)],[left_inverse]),[]).
%
% cnf(160194488,plain,(product(inverse(A),A,inverse(identity))),inference(paramodulation,[status(thm)],[160139600,151852496,theory(equality)]),[]).
%
% cnf(160352664,plain,(product(identity,identity,inverse(identity))),inference(paramodulation,[status(thm)],[160194488,160139600,theory(equality)]),[]).
%
% cnf(160364432,plain,($equal(inverse(identity),identity)),inference(resolution,[status(thm)],[160352664,159681352]),[]).
%
% cnf(160395968,plain,($equal(identity,inverse(inverse(identity)))),inference(paramodulation,[status(thm)],[160364432,160139600,theory(equality)]),[]).
%
% cnf(160430176,plain,(product(A,inverse(A),inverse(inverse(identity)))),inference(paramodulation,[status(thm)],[160395968,151856328,theory(equality)]),[]).
%
% cnf(323124232,plain,(product(c,d,inverse(inverse(identity)))),inference(resolution,[status(thm)],[323088952,160430176]),[]).
%
% cnf(160032736,plain,(~product(inverse(A),A,B)|$equal(B,identity)),inference(resolution,[status(thm)],[151871192,151852496]),[]).
%
% fof(total_function1,plain,(product(A,B,multiply(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-1.tptp',unknown),[]).
%
% cnf(151859888,plain,(product(A,B,multiply(A,B))),inference(rewrite,[status(thm)],[total_function1]),[]).
%
% cnf(162996232,plain,($equal(multiply(inverse(A),A),identity)),inference(resolution,[status(thm)],[160032736,151859888]),[]).
%
% fof(prove_c_multiply_d_is_identity,plain,(~product(c,d,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-1.tptp',unknown),[]).
%
% cnf(151897496,plain,(~product(c,d,identity)),inference(rewrite,[status(thm)],[prove_c_multiply_d_is_identity]),[]).
%
% cnf(160217232,plain,(~product(c,d,inverse(identity))),inference(paramodulation,[status(thm)],[160139600,151897496,theory(equality)]),[]).
%
% cnf(163353800,plain,(~product(c,d,inverse(multiply(inverse(A),A)))),inference(paramodulation,[status(thm)],[162996232,160217232,theory(equality)]),[]).
%
% cnf(163158776,plain,($equal(multiply(inverse(A),A),inverse(identity))),inference(paramodulation,[status(thm)],[162996232,160139600,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[323124232,163353800,163158776,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------