TSTP Solution File: GRP012-2 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP012-2 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 12:17:48 EDT 2009
% Result : Unsatisfiable 358.5s
% Output : Refutation 358.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 21 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 77 ( 43 ~; 34 |; 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; 5 con; 0-1 aty)
% Number of variables : 74 ( 1 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(left_identity,plain,
! [A] : product(identity,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-2.tptp',unknown),
[] ).
cnf(162043720,plain,
product(identity,A,A),
inference(rewrite,[status(thm)],[left_identity]),
[] ).
fof(inverse_b_multiply_inverse_a_is_d,plain,
product(inverse(b),inverse(a),d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-2.tptp',unknown),
[] ).
cnf(162041240,plain,
product(inverse(b),inverse(a),d),
inference(rewrite,[status(thm)],[inverse_b_multiply_inverse_a_is_d]),
[] ).
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/GRP012-2.tptp',unknown),
[] ).
cnf(162085440,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
inference(rewrite,[status(thm)],[associativity2]),
[] ).
fof(left_inverse,plain,
! [A] : product(inverse(A),A,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-2.tptp',unknown),
[] ).
cnf(162051504,plain,
product(inverse(A),A,identity),
inference(rewrite,[status(thm)],[left_inverse]),
[] ).
cnf(170235280,plain,
( ~ product(A,inverse(C),B)
| ~ product(A,identity,D)
| product(B,C,D) ),
inference(resolution,[status(thm)],[162085440,162051504]),
[] ).
fof(right_identity,plain,
! [A] : product(A,identity,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-2.tptp',unknown),
[] ).
cnf(162047856,plain,
product(A,identity,A),
inference(rewrite,[status(thm)],[right_identity]),
[] ).
cnf(170279088,plain,
( ~ product(A,inverse(C),B)
| product(B,C,A) ),
inference(resolution,[status(thm)],[170235280,162047856]),
[] ).
cnf(232916624,plain,
product(d,a,inverse(b)),
inference(resolution,[status(thm)],[162041240,170279088]),
[] ).
cnf(170024640,plain,
( ~ product(identity,B,C)
| ~ product(A,C,D)
| product(A,B,D) ),
inference(resolution,[status(thm)],[162085440,162047856]),
[] ).
cnf(265038760,plain,
( ~ product(identity,A,a)
| product(d,A,inverse(b)) ),
inference(resolution,[status(thm)],[232916624,170024640]),
[] ).
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/GRP012-2.tptp',unknown),
[] ).
cnf(162077000,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
inference(rewrite,[status(thm)],[associativity1]),
[] ).
cnf(170134240,plain,
( ~ product(A,B,C)
| ~ product(identity,B,D)
| product(inverse(A),C,D) ),
inference(resolution,[status(thm)],[162077000,162051504]),
[] ).
cnf(169987048,plain,
( ~ product(identity,B,C)
| ~ product(A,B,D)
| product(A,C,D) ),
inference(resolution,[status(thm)],[162077000,162047856]),
[] ).
cnf(170009768,plain,
( ~ product(identity,A,B)
| product(identity,B,A) ),
inference(resolution,[status(thm)],[169987048,162043720]),
[] ).
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/GRP012-2.tptp',unknown),
[] ).
cnf(162070200,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| $equal(D,C) ),
inference(rewrite,[status(thm)],[total_function2]),
[] ).
cnf(169881224,plain,
( ~ product(identity,A,B)
| $equal(B,A) ),
inference(resolution,[status(thm)],[162070200,162043720]),
[] ).
fof(prove_c_inverse_equals_d,plain,
~ $equal(inverse(c),d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-2.tptp',unknown),
[] ).
cnf(162097240,plain,
~ $equal(inverse(c),d),
inference(rewrite,[status(thm)],[prove_c_inverse_equals_d]),
[] ).
cnf(171023840,plain,
~ product(identity,d,inverse(c)),
inference(resolution,[status(thm)],[169881224,162097240]),
[] ).
cnf(170220576,plain,
( ~ product(A,B,C)
| ~ product(inverse(A),C,D)
| product(identity,B,D) ),
inference(resolution,[status(thm)],[162085440,162051504]),
[] ).
cnf(170256728,plain,
( ~ product(A,B,identity)
| product(identity,B,inverse(A)) ),
inference(resolution,[status(thm)],[170220576,162047856]),
[] ).
cnf(191483456,plain,
~ product(c,d,identity),
inference(resolution,[status(thm)],[171023840,170256728]),
[] ).
cnf(233093712,plain,
~ product(identity,inverse(d),c),
inference(resolution,[status(thm)],[191483456,170279088]),
[] ).
cnf(233954032,plain,
~ product(identity,c,inverse(d)),
inference(resolution,[status(thm)],[170009768,233093712]),
[] ).
fof(a_multiply_b_is_c,plain,
product(a,b,c),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-2.tptp',unknown),
[] ).
cnf(162088704,plain,
product(a,b,c),
inference(rewrite,[status(thm)],[a_multiply_b_is_c]),
[] ).
cnf(169894520,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| product(identity,C,D) ),
inference(resolution,[status(thm)],[162077000,162043720]),
[] ).
cnf(178128232,plain,
( ~ product(a,b,A)
| product(identity,c,A) ),
inference(resolution,[status(thm)],[162088704,169894520]),
[] ).
cnf(314731400,plain,
~ product(a,b,inverse(d)),
inference(resolution,[status(thm)],[233954032,178128232]),
[] ).
cnf(318507992,plain,
~ product(inverse(d),inverse(b),a),
inference(resolution,[status(thm)],[170279088,314731400]),
[] ).
cnf(628825560,plain,
~ product(identity,A,a),
inference(forward_subsumption_resolution__resolution,[status(thm)],[265038760,170134240,318507992]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[162043720,628825560]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 358 seconds
% START OF PROOF SEQUENCE
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-2.tptp',unknown),[]).
%
% cnf(162043720,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
%
% fof(inverse_b_multiply_inverse_a_is_d,plain,(product(inverse(b),inverse(a),d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-2.tptp',unknown),[]).
%
% cnf(162041240,plain,(product(inverse(b),inverse(a),d)),inference(rewrite,[status(thm)],[inverse_b_multiply_inverse_a_is_d]),[]).
%
% 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/GRP012-2.tptp',unknown),[]).
%
% cnf(162085440,plain,(~product(A,B,C)|~product(B,D,E)|~product(A,E,F)|product(C,D,F)),inference(rewrite,[status(thm)],[associativity2]),[]).
%
% fof(left_inverse,plain,(product(inverse(A),A,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-2.tptp',unknown),[]).
%
% cnf(162051504,plain,(product(inverse(A),A,identity)),inference(rewrite,[status(thm)],[left_inverse]),[]).
%
% cnf(170235280,plain,(~product(A,inverse(C),B)|~product(A,identity,D)|product(B,C,D)),inference(resolution,[status(thm)],[162085440,162051504]),[]).
%
% fof(right_identity,plain,(product(A,identity,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-2.tptp',unknown),[]).
%
% cnf(162047856,plain,(product(A,identity,A)),inference(rewrite,[status(thm)],[right_identity]),[]).
%
% cnf(170279088,plain,(~product(A,inverse(C),B)|product(B,C,A)),inference(resolution,[status(thm)],[170235280,162047856]),[]).
%
% cnf(232916624,plain,(product(d,a,inverse(b))),inference(resolution,[status(thm)],[162041240,170279088]),[]).
%
% cnf(170024640,plain,(~product(identity,B,C)|~product(A,C,D)|product(A,B,D)),inference(resolution,[status(thm)],[162085440,162047856]),[]).
%
% cnf(265038760,plain,(~product(identity,A,a)|product(d,A,inverse(b))),inference(resolution,[status(thm)],[232916624,170024640]),[]).
%
% 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/GRP012-2.tptp',unknown),[]).
%
% cnf(162077000,plain,(~product(A,B,C)|~product(B,D,E)|~product(C,D,F)|product(A,E,F)),inference(rewrite,[status(thm)],[associativity1]),[]).
%
% cnf(170134240,plain,(~product(A,B,C)|~product(identity,B,D)|product(inverse(A),C,D)),inference(resolution,[status(thm)],[162077000,162051504]),[]).
%
% cnf(169987048,plain,(~product(identity,B,C)|~product(A,B,D)|product(A,C,D)),inference(resolution,[status(thm)],[162077000,162047856]),[]).
%
% cnf(170009768,plain,(~product(identity,A,B)|product(identity,B,A)),inference(resolution,[status(thm)],[169987048,162043720]),[]).
%
% fof(total_function2,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-2.tptp',unknown),[]).
%
% cnf(162070200,plain,(~product(A,B,C)|~product(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[total_function2]),[]).
%
% cnf(169881224,plain,(~product(identity,A,B)|$equal(B,A)),inference(resolution,[status(thm)],[162070200,162043720]),[]).
%
% fof(prove_c_inverse_equals_d,plain,(~$equal(inverse(c),d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-2.tptp',unknown),[]).
%
% cnf(162097240,plain,(~$equal(inverse(c),d)),inference(rewrite,[status(thm)],[prove_c_inverse_equals_d]),[]).
%
% cnf(171023840,plain,(~product(identity,d,inverse(c))),inference(resolution,[status(thm)],[169881224,162097240]),[]).
%
% cnf(170220576,plain,(~product(A,B,C)|~product(inverse(A),C,D)|product(identity,B,D)),inference(resolution,[status(thm)],[162085440,162051504]),[]).
%
% cnf(170256728,plain,(~product(A,B,identity)|product(identity,B,inverse(A))),inference(resolution,[status(thm)],[170220576,162047856]),[]).
%
% cnf(191483456,plain,(~product(c,d,identity)),inference(resolution,[status(thm)],[171023840,170256728]),[]).
%
% cnf(233093712,plain,(~product(identity,inverse(d),c)),inference(resolution,[status(thm)],[191483456,170279088]),[]).
%
% cnf(233954032,plain,(~product(identity,c,inverse(d))),inference(resolution,[status(thm)],[170009768,233093712]),[]).
%
% fof(a_multiply_b_is_c,plain,(product(a,b,c)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP012-2.tptp',unknown),[]).
%
% cnf(162088704,plain,(product(a,b,c)),inference(rewrite,[status(thm)],[a_multiply_b_is_c]),[]).
%
% cnf(169894520,plain,(~product(A,B,C)|~product(A,B,D)|product(identity,C,D)),inference(resolution,[status(thm)],[162077000,162043720]),[]).
%
% cnf(178128232,plain,(~product(a,b,A)|product(identity,c,A)),inference(resolution,[status(thm)],[162088704,169894520]),[]).
%
% cnf(314731400,plain,(~product(a,b,inverse(d))),inference(resolution,[status(thm)],[233954032,178128232]),[]).
%
% cnf(318507992,plain,(~product(inverse(d),inverse(b),a)),inference(resolution,[status(thm)],[170279088,314731400]),[]).
%
% cnf(628825560,plain,(~product(identity,A,a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[265038760,170134240,318507992]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[162043720,628825560]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------