TSTP Solution File: GRP046-2 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : GRP046-2 : 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 12:19:28 EDT 2009
% Result : Unsatisfiable 46.7s
% Output : Refutation 46.7s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 14 unt; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 47 ( 26 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 17 !; 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/GRP046-2.tptp',unknown),
[] ).
cnf(161932800,plain,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
inference(rewrite,[status(thm)],[associativity2]),
[] ).
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/GRP046-2.tptp',unknown),
[] ).
cnf(161944336,plain,
( ~ equalish(A,B)
| ~ product(C,D,A)
| product(C,D,B) ),
inference(rewrite,[status(thm)],[product_substitution3]),
[] ).
fof(a_equals_b,plain,
equalish(a,b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP046-2.tptp',unknown),
[] ).
cnf(161948912,plain,
equalish(a,b),
inference(rewrite,[status(thm)],[a_equals_b]),
[] ).
cnf(169737064,plain,
( ~ product(A,B,a)
| product(A,B,b) ),
inference(resolution,[status(thm)],[161944336,161948912]),
[] ).
fof(left_identity,plain,
! [A] : product(identity,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP046-2.tptp',unknown),
[] ).
cnf(161905760,plain,
product(identity,A,A),
inference(rewrite,[status(thm)],[left_identity]),
[] ).
cnf(169784120,plain,
product(identity,a,b),
inference(resolution,[status(thm)],[169737064,161905760]),
[] ).
cnf(170012312,plain,
( ~ product(a,A,B)
| ~ product(identity,B,C)
| product(b,A,C) ),
inference(resolution,[status(thm)],[161932800,169784120]),
[] ).
cnf(170051616,plain,
( ~ product(a,A,B)
| product(b,A,B) ),
inference(resolution,[status(thm)],[170012312,161905760]),
[] ).
fof(total_function1,plain,
! [A,B] : product(A,B,multiply(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP046-2.tptp',unknown),
[] ).
cnf(161913656,plain,
product(A,B,multiply(A,B)),
inference(rewrite,[status(thm)],[total_function1]),
[] ).
cnf(384365984,plain,
product(b,A,multiply(a,A)),
inference(resolution,[status(thm)],[170051616,161913656]),
[] ).
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/GRP046-2.tptp',unknown),
[] ).
cnf(161921680,plain,
( ~ product(A,B,C)
| ~ product(A,B,D)
| equalish(C,D) ),
inference(rewrite,[status(thm)],[total_function2]),
[] ).
cnf(170342744,plain,
( ~ product(A,B,C)
| equalish(multiply(A,B),C) ),
inference(resolution,[status(thm)],[161921680,161913656]),
[] ).
cnf(170495056,plain,
( ~ equalish(A,B)
| product(identity,A,B) ),
inference(resolution,[status(thm)],[161944336,161905760]),
[] ).
cnf(169773352,plain,
( ~ product(identity,A,B)
| equalish(B,A) ),
inference(resolution,[status(thm)],[161921680,161905760]),
[] ).
fof(prove_multiply_substitution1,plain,
~ equalish(multiply(a,c),multiply(b,c)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP046-2.tptp',unknown),
[] ).
cnf(161953000,plain,
~ equalish(multiply(a,c),multiply(b,c)),
inference(rewrite,[status(thm)],[prove_multiply_substitution1]),
[] ).
cnf(170442824,plain,
~ product(identity,multiply(b,c),multiply(a,c)),
inference(resolution,[status(thm)],[169773352,161953000]),
[] ).
cnf(171772800,plain,
~ equalish(multiply(b,c),multiply(a,c)),
inference(resolution,[status(thm)],[170495056,170442824]),
[] ).
cnf(180282168,plain,
~ product(b,c,multiply(a,c)),
inference(resolution,[status(thm)],[170342744,171772800]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[384365984,180282168]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 46 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/GRP046-2.tptp',unknown),[]).
%
% cnf(161932800,plain,(~product(A,B,C)|~product(B,D,E)|~product(A,E,F)|product(C,D,F)),inference(rewrite,[status(thm)],[associativity2]),[]).
%
% fof(product_substitution3,plain,(~equalish(A,B)|~product(C,D,A)|product(C,D,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP046-2.tptp',unknown),[]).
%
% cnf(161944336,plain,(~equalish(A,B)|~product(C,D,A)|product(C,D,B)),inference(rewrite,[status(thm)],[product_substitution3]),[]).
%
% fof(a_equals_b,plain,(equalish(a,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP046-2.tptp',unknown),[]).
%
% cnf(161948912,plain,(equalish(a,b)),inference(rewrite,[status(thm)],[a_equals_b]),[]).
%
% cnf(169737064,plain,(~product(A,B,a)|product(A,B,b)),inference(resolution,[status(thm)],[161944336,161948912]),[]).
%
% fof(left_identity,plain,(product(identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP046-2.tptp',unknown),[]).
%
% cnf(161905760,plain,(product(identity,A,A)),inference(rewrite,[status(thm)],[left_identity]),[]).
%
% cnf(169784120,plain,(product(identity,a,b)),inference(resolution,[status(thm)],[169737064,161905760]),[]).
%
% cnf(170012312,plain,(~product(a,A,B)|~product(identity,B,C)|product(b,A,C)),inference(resolution,[status(thm)],[161932800,169784120]),[]).
%
% cnf(170051616,plain,(~product(a,A,B)|product(b,A,B)),inference(resolution,[status(thm)],[170012312,161905760]),[]).
%
% fof(total_function1,plain,(product(A,B,multiply(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP046-2.tptp',unknown),[]).
%
% cnf(161913656,plain,(product(A,B,multiply(A,B))),inference(rewrite,[status(thm)],[total_function1]),[]).
%
% cnf(384365984,plain,(product(b,A,multiply(a,A))),inference(resolution,[status(thm)],[170051616,161913656]),[]).
%
% fof(total_function2,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP046-2.tptp',unknown),[]).
%
% cnf(161921680,plain,(~product(A,B,C)|~product(A,B,D)|equalish(C,D)),inference(rewrite,[status(thm)],[total_function2]),[]).
%
% cnf(170342744,plain,(~product(A,B,C)|equalish(multiply(A,B),C)),inference(resolution,[status(thm)],[161921680,161913656]),[]).
%
% cnf(170495056,plain,(~equalish(A,B)|product(identity,A,B)),inference(resolution,[status(thm)],[161944336,161905760]),[]).
%
% cnf(169773352,plain,(~product(identity,A,B)|equalish(B,A)),inference(resolution,[status(thm)],[161921680,161905760]),[]).
%
% fof(prove_multiply_substitution1,plain,(~equalish(multiply(a,c),multiply(b,c))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/GRP/GRP046-2.tptp',unknown),[]).
%
% cnf(161953000,plain,(~equalish(multiply(a,c),multiply(b,c))),inference(rewrite,[status(thm)],[prove_multiply_substitution1]),[]).
%
% cnf(170442824,plain,(~product(identity,multiply(b,c),multiply(a,c))),inference(resolution,[status(thm)],[169773352,161953000]),[]).
%
% cnf(171772800,plain,(~equalish(multiply(b,c),multiply(a,c))),inference(resolution,[status(thm)],[170495056,170442824]),[]).
%
% cnf(180282168,plain,(~product(b,c,multiply(a,c))),inference(resolution,[status(thm)],[170342744,171772800]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[384365984,180282168]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------