TSTP Solution File: RNG003-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : RNG003-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art01.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 15:19:07 EDT 2009
% Result : Unsatisfiable 9.3s
% Output : Refutation 9.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 28 ( 16 unt; 0 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 53 ( 29 ~; 24 |; 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 : 55 ( 1 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(right_inverse,plain,
! [A] : sum(A,additive_inverse(A),additive_identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG003-1.tptp',unknown),
[] ).
cnf(165075480,plain,
sum(A,additive_inverse(A),additive_identity),
inference(rewrite,[status(thm)],[right_inverse]),
[] ).
fof(b_plus_c_is_d,plain,
sum(b,c,d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG003-1.tptp',unknown),
[] ).
cnf(165163704,plain,
sum(b,c,d),
inference(rewrite,[status(thm)],[b_plus_c_is_d]),
[] ).
fof(associativity_of_addition2,plain,
! [A,B,C,D,E,F] :
( ~ sum(A,B,C)
| ~ sum(B,D,E)
| ~ sum(A,E,F)
| sum(C,D,F) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG003-1.tptp',unknown),
[] ).
cnf(165093712,plain,
( ~ sum(A,B,C)
| ~ sum(B,D,E)
| ~ sum(A,E,F)
| sum(C,D,F) ),
inference(rewrite,[status(thm)],[associativity_of_addition2]),
[] ).
fof(additive_identity2,plain,
! [A] : sum(A,additive_identity,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG003-1.tptp',unknown),
[] ).
cnf(165059072,plain,
sum(A,additive_identity,A),
inference(rewrite,[status(thm)],[additive_identity2]),
[] ).
cnf(173215168,plain,
( ~ sum(A,B,C)
| ~ sum(B,D,additive_identity)
| sum(C,D,A) ),
inference(resolution,[status(thm)],[165093712,165059072]),
[] ).
cnf(252326896,plain,
( ~ sum(c,A,additive_identity)
| sum(d,A,b) ),
inference(resolution,[status(thm)],[165163704,173215168]),
[] ).
fof(addition_is_well_defined,plain,
! [A,B,C,D] :
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| $equal(D,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG003-1.tptp',unknown),
[] ).
cnf(165146672,plain,
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| $equal(D,C) ),
inference(rewrite,[status(thm)],[addition_is_well_defined]),
[] ).
fof(additive_identity1,plain,
! [A] : sum(additive_identity,A,A),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG003-1.tptp',unknown),
[] ).
cnf(165054840,plain,
sum(additive_identity,A,A),
inference(rewrite,[status(thm)],[additive_identity1]),
[] ).
cnf(172980320,plain,
( ~ sum(additive_identity,A,B)
| $equal(B,A) ),
inference(resolution,[status(thm)],[165146672,165054840]),
[] ).
fof(prove_a_equals_b,plain,
~ $equal(b,a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG003-1.tptp',unknown),
[] ).
cnf(165168280,plain,
~ $equal(b,a),
inference(rewrite,[status(thm)],[prove_a_equals_b]),
[] ).
cnf(174477696,plain,
~ sum(additive_identity,a,b),
inference(resolution,[status(thm)],[172980320,165168280]),
[] ).
fof(commutativity_of_addition,plain,
! [A,B,C] :
( ~ sum(A,B,C)
| sum(B,A,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG003-1.tptp',unknown),
[] ).
cnf(165097864,plain,
( ~ sum(A,B,C)
| sum(B,A,C) ),
inference(rewrite,[status(thm)],[commutativity_of_addition]),
[] ).
cnf(174612560,plain,
~ sum(a,additive_identity,b),
inference(resolution,[status(thm)],[174477696,165097864]),
[] ).
fof(associativity_of_addition1,plain,
! [A,B,C,D,E,F] :
( ~ sum(A,B,C)
| ~ sum(B,D,E)
| ~ sum(C,D,F)
| sum(A,E,F) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG003-1.tptp',unknown),
[] ).
cnf(165089176,plain,
( ~ sum(A,B,C)
| ~ sum(B,D,E)
| ~ sum(C,D,F)
| sum(A,E,F) ),
inference(rewrite,[status(thm)],[associativity_of_addition1]),
[] ).
fof(a_plus_c_is_d,plain,
sum(a,c,d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG003-1.tptp',unknown),
[] ).
cnf(165051888,plain,
sum(a,c,d),
inference(rewrite,[status(thm)],[a_plus_c_is_d]),
[] ).
cnf(173377992,plain,
( ~ sum(c,A,B)
| ~ sum(d,A,C)
| sum(a,B,C) ),
inference(resolution,[status(thm)],[165089176,165051888]),
[] ).
cnf(257970136,plain,
~ sum(c,A,additive_identity),
inference(forward_subsumption_resolution__resolution,[status(thm)],[252326896,174612560,173377992]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[165075480,257970136]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 9 seconds
% START OF PROOF SEQUENCE
% fof(right_inverse,plain,(sum(A,additive_inverse(A),additive_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG003-1.tptp',unknown),[]).
%
% cnf(165075480,plain,(sum(A,additive_inverse(A),additive_identity)),inference(rewrite,[status(thm)],[right_inverse]),[]).
%
% fof(b_plus_c_is_d,plain,(sum(b,c,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG003-1.tptp',unknown),[]).
%
% cnf(165163704,plain,(sum(b,c,d)),inference(rewrite,[status(thm)],[b_plus_c_is_d]),[]).
%
% fof(associativity_of_addition2,plain,(~sum(A,B,C)|~sum(B,D,E)|~sum(A,E,F)|sum(C,D,F)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG003-1.tptp',unknown),[]).
%
% cnf(165093712,plain,(~sum(A,B,C)|~sum(B,D,E)|~sum(A,E,F)|sum(C,D,F)),inference(rewrite,[status(thm)],[associativity_of_addition2]),[]).
%
% fof(additive_identity2,plain,(sum(A,additive_identity,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG003-1.tptp',unknown),[]).
%
% cnf(165059072,plain,(sum(A,additive_identity,A)),inference(rewrite,[status(thm)],[additive_identity2]),[]).
%
% cnf(173215168,plain,(~sum(A,B,C)|~sum(B,D,additive_identity)|sum(C,D,A)),inference(resolution,[status(thm)],[165093712,165059072]),[]).
%
% cnf(252326896,plain,(~sum(c,A,additive_identity)|sum(d,A,b)),inference(resolution,[status(thm)],[165163704,173215168]),[]).
%
% fof(addition_is_well_defined,plain,(~sum(A,B,C)|~sum(A,B,D)|$equal(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG003-1.tptp',unknown),[]).
%
% cnf(165146672,plain,(~sum(A,B,C)|~sum(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[addition_is_well_defined]),[]).
%
% fof(additive_identity1,plain,(sum(additive_identity,A,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG003-1.tptp',unknown),[]).
%
% cnf(165054840,plain,(sum(additive_identity,A,A)),inference(rewrite,[status(thm)],[additive_identity1]),[]).
%
% cnf(172980320,plain,(~sum(additive_identity,A,B)|$equal(B,A)),inference(resolution,[status(thm)],[165146672,165054840]),[]).
%
% fof(prove_a_equals_b,plain,(~$equal(b,a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG003-1.tptp',unknown),[]).
%
% cnf(165168280,plain,(~$equal(b,a)),inference(rewrite,[status(thm)],[prove_a_equals_b]),[]).
%
% cnf(174477696,plain,(~sum(additive_identity,a,b)),inference(resolution,[status(thm)],[172980320,165168280]),[]).
%
% fof(commutativity_of_addition,plain,(~sum(A,B,C)|sum(B,A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG003-1.tptp',unknown),[]).
%
% cnf(165097864,plain,(~sum(A,B,C)|sum(B,A,C)),inference(rewrite,[status(thm)],[commutativity_of_addition]),[]).
%
% cnf(174612560,plain,(~sum(a,additive_identity,b)),inference(resolution,[status(thm)],[174477696,165097864]),[]).
%
% fof(associativity_of_addition1,plain,(~sum(A,B,C)|~sum(B,D,E)|~sum(C,D,F)|sum(A,E,F)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG003-1.tptp',unknown),[]).
%
% cnf(165089176,plain,(~sum(A,B,C)|~sum(B,D,E)|~sum(C,D,F)|sum(A,E,F)),inference(rewrite,[status(thm)],[associativity_of_addition1]),[]).
%
% fof(a_plus_c_is_d,plain,(sum(a,c,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG003-1.tptp',unknown),[]).
%
% cnf(165051888,plain,(sum(a,c,d)),inference(rewrite,[status(thm)],[a_plus_c_is_d]),[]).
%
% cnf(173377992,plain,(~sum(c,A,B)|~sum(d,A,C)|sum(a,B,C)),inference(resolution,[status(thm)],[165089176,165051888]),[]).
%
% cnf(257970136,plain,(~sum(c,A,additive_identity)),inference(forward_subsumption_resolution__resolution,[status(thm)],[252326896,174612560,173377992]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[165075480,257970136]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------