TSTP Solution File: RNG006-1 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : RNG006-1 : 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 @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 15:19:17 EDT 2009
% Result : Unsatisfiable 0.5s
% Output : Refutation 0.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 18 ( 12 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-1 aty)
% Number of variables : 26 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_a_times_bS_Ic_is_aPb_S__IaPc,plain,
~ product(a,bs_ic,apb_s_iapc),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG006-1.tptp',unknown),
[] ).
cnf(143131824,plain,
~ product(a,bs_ic,apb_s_iapc),
inference(rewrite,[status(thm)],[prove_a_times_bS_Ic_is_aPb_S__IaPc]),
[] ).
fof(product_lemma1,plain,
! [A,B,C] :
( ~ product(A,B,C)
| product(A,additive_inverse(B),additive_inverse(C)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG006-1.tptp',unknown),
[] ).
cnf(142990808,plain,
( ~ product(A,B,C)
| product(A,additive_inverse(B),additive_inverse(C)) ),
inference(rewrite,[status(thm)],[product_lemma1]),
[] ).
fof(a_times_c,plain,
product(a,c,apc),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG006-1.tptp',unknown),
[] ).
cnf(143123840,plain,
product(a,c,apc),
inference(rewrite,[status(thm)],[a_times_c]),
[] ).
cnf(151807456,plain,
product(a,additive_inverse(c),additive_inverse(apc)),
inference(resolution,[status(thm)],[142990808,143123840]),
[] ).
fof(distributivity2,plain,
! [A,B,C,D,E,F,G] :
( ~ product(A,B,C)
| ~ product(A,D,E)
| ~ sum(B,D,F)
| ~ sum(C,E,G)
| product(A,F,G) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG006-1.tptp',unknown),
[] ).
cnf(143070256,plain,
( ~ product(A,B,C)
| ~ product(A,D,E)
| ~ sum(B,D,F)
| ~ sum(C,E,G)
| product(A,F,G) ),
inference(rewrite,[status(thm)],[distributivity2]),
[] ).
fof(a_times_b,plain,
product(a,b,apb),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG006-1.tptp',unknown),
[] ).
cnf(143115736,plain,
product(a,b,apb),
inference(rewrite,[status(thm)],[a_times_b]),
[] ).
cnf(151548856,plain,
( ~ product(a,A,B)
| ~ sum(b,A,C)
| ~ sum(apb,B,D)
| product(a,C,D) ),
inference(resolution,[status(thm)],[143070256,143115736]),
[] ).
fof(b_plus_inverse_c,plain,
sum(b,additive_inverse(c),bs_ic),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG006-1.tptp',unknown),
[] ).
cnf(143111848,plain,
sum(b,additive_inverse(c),bs_ic),
inference(rewrite,[status(thm)],[b_plus_inverse_c]),
[] ).
cnf(167187920,plain,
( ~ product(a,additive_inverse(c),A)
| ~ sum(apb,A,B)
| product(a,bs_ic,B) ),
inference(resolution,[status(thm)],[151548856,143111848]),
[] ).
fof(aPb_plus_IaPc,plain,
sum(apb,additive_inverse(apc),apb_s_iapc),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG006-1.tptp',unknown),
[] ).
cnf(143127832,plain,
sum(apb,additive_inverse(apc),apb_s_iapc),
inference(rewrite,[status(thm)],[aPb_plus_IaPc]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[143131824,151807456,167187920,143127832]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(prove_a_times_bS_Ic_is_aPb_S__IaPc,plain,(~product(a,bs_ic,apb_s_iapc)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG006-1.tptp',unknown),[]).
%
% cnf(143131824,plain,(~product(a,bs_ic,apb_s_iapc)),inference(rewrite,[status(thm)],[prove_a_times_bS_Ic_is_aPb_S__IaPc]),[]).
%
% fof(product_lemma1,plain,(~product(A,B,C)|product(A,additive_inverse(B),additive_inverse(C))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG006-1.tptp',unknown),[]).
%
% cnf(142990808,plain,(~product(A,B,C)|product(A,additive_inverse(B),additive_inverse(C))),inference(rewrite,[status(thm)],[product_lemma1]),[]).
%
% fof(a_times_c,plain,(product(a,c,apc)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG006-1.tptp',unknown),[]).
%
% cnf(143123840,plain,(product(a,c,apc)),inference(rewrite,[status(thm)],[a_times_c]),[]).
%
% cnf(151807456,plain,(product(a,additive_inverse(c),additive_inverse(apc))),inference(resolution,[status(thm)],[142990808,143123840]),[]).
%
% fof(distributivity2,plain,(~product(A,B,C)|~product(A,D,E)|~sum(B,D,F)|~sum(C,E,G)|product(A,F,G)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG006-1.tptp',unknown),[]).
%
% cnf(143070256,plain,(~product(A,B,C)|~product(A,D,E)|~sum(B,D,F)|~sum(C,E,G)|product(A,F,G)),inference(rewrite,[status(thm)],[distributivity2]),[]).
%
% fof(a_times_b,plain,(product(a,b,apb)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG006-1.tptp',unknown),[]).
%
% cnf(143115736,plain,(product(a,b,apb)),inference(rewrite,[status(thm)],[a_times_b]),[]).
%
% cnf(151548856,plain,(~product(a,A,B)|~sum(b,A,C)|~sum(apb,B,D)|product(a,C,D)),inference(resolution,[status(thm)],[143070256,143115736]),[]).
%
% fof(b_plus_inverse_c,plain,(sum(b,additive_inverse(c),bs_ic)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG006-1.tptp',unknown),[]).
%
% cnf(143111848,plain,(sum(b,additive_inverse(c),bs_ic)),inference(rewrite,[status(thm)],[b_plus_inverse_c]),[]).
%
% cnf(167187920,plain,(~product(a,additive_inverse(c),A)|~sum(apb,A,B)|product(a,bs_ic,B)),inference(resolution,[status(thm)],[151548856,143111848]),[]).
%
% fof(aPb_plus_IaPc,plain,(sum(apb,additive_inverse(apc),apb_s_iapc)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG006-1.tptp',unknown),[]).
%
% cnf(143127832,plain,(sum(apb,additive_inverse(apc),apb_s_iapc)),inference(rewrite,[status(thm)],[aPb_plus_IaPc]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[143131824,151807456,167187920,143127832]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------