TSTP Solution File: GRP004-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP004-1 : 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 12:17:27 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 38 ( 20 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 45 ( 1 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/GRP004-1.tptp',unknown),
[] ).
cnf(145053064,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
inference(rewrite,[status(thm)],[associativity2]),
[] ).
fof(left_identity,plain,
! [A] : product(identity,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP004-1.tptp',unknown),
[] ).
cnf(145038984,plain,
product(identity,A,A),
inference(rewrite,[status(thm)],[left_identity]),
[] ).
cnf(152879208,plain,
( ~ product(A,identity,B)
| ~ product(A,C,D)
| product(B,C,D) ),
inference(resolution,[status(thm)],[145053064,145038984]),
[] ).
fof(left_inverse,plain,
! [A] : product(inverse(A),A,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP004-1.tptp',unknown),
[] ).
cnf(145035032,plain,
product(inverse(A),A,identity),
inference(rewrite,[status(thm)],[left_inverse]),
[] ).
cnf(153011568,plain,
( ~ product(inverse(B),identity,A)
| product(A,B,identity) ),
inference(resolution,[status(thm)],[152879208,145035032]),
[] ).
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/GRP004-1.tptp',unknown),
[] ).
cnf(145048704,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
inference(rewrite,[status(thm)],[associativity1]),
[] ).
cnf(152865224,plain,
( ~ product(A,B,identity)
| ~ product(B,C,D)
| product(A,D,C) ),
inference(resolution,[status(thm)],[145048704,145038984]),
[] ).
cnf(152897752,plain,
( ~ product(A,B,C)
| product(inverse(A),C,B) ),
inference(resolution,[status(thm)],[152865224,145035032]),
[] ).
cnf(153802792,plain,
product(inverse(inverse(A)),identity,A),
inference(resolution,[status(thm)],[152897752,145035032]),
[] ).
cnf(155333304,plain,
product(A,inverse(A),identity),
inference(resolution,[status(thm)],[153011568,153802792]),
[] ).
fof(prove_there_is_a_right_inverse,plain,
! [A] : ~ product(a,A,identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP004-1.tptp',unknown),
[] ).
cnf(145056328,plain,
~ product(a,A,identity),
inference(rewrite,[status(thm)],[prove_there_is_a_right_inverse]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[155333304,145056328]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% 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/GRP004-1.tptp',unknown),[]).
%
% cnf(145053064,plain,(~product(A,B,C)|~product(B,D,E)|~product(A,E,F)|product(C,D,F)),inference(rewrite,[status(thm)],[associativity2]),[]).
%
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP004-1.tptp',unknown),[]).
%
% cnf(145038984,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
%
% cnf(152879208,plain,(~product(A,identity,B)|~product(A,C,D)|product(B,C,D)),inference(resolution,[status(thm)],[145053064,145038984]),[]).
%
% fof(left_inverse,plain,(product(inverse(A),A,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP004-1.tptp',unknown),[]).
%
% cnf(145035032,plain,(product(inverse(A),A,identity)),inference(rewrite,[status(thm)],[left_inverse]),[]).
%
% cnf(153011568,plain,(~product(inverse(B),identity,A)|product(A,B,identity)),inference(resolution,[status(thm)],[152879208,145035032]),[]).
%
% 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/GRP004-1.tptp',unknown),[]).
%
% cnf(145048704,plain,(~product(A,B,C)|~product(B,D,E)|~product(C,D,F)|product(A,E,F)),inference(rewrite,[status(thm)],[associativity1]),[]).
%
% cnf(152865224,plain,(~product(A,B,identity)|~product(B,C,D)|product(A,D,C)),inference(resolution,[status(thm)],[145048704,145038984]),[]).
%
% cnf(152897752,plain,(~product(A,B,C)|product(inverse(A),C,B)),inference(resolution,[status(thm)],[152865224,145035032]),[]).
%
% cnf(153802792,plain,(product(inverse(inverse(A)),identity,A)),inference(resolution,[status(thm)],[152897752,145035032]),[]).
%
% cnf(155333304,plain,(product(A,inverse(A),identity)),inference(resolution,[status(thm)],[153011568,153802792]),[]).
%
% fof(prove_there_is_a_right_inverse,plain,(~product(a,A,identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP004-1.tptp',unknown),[]).
%
% cnf(145056328,plain,(~product(a,A,identity)),inference(rewrite,[status(thm)],[prove_there_is_a_right_inverse]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[155333304,145056328]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------