TSTP Solution File: RNG002-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : RNG002-1 : 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 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 15:19:05 EDT 2009
% Result : Unsatisfiable 17.3s
% Output : Refutation 17.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 15 unt; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 35 ( 19 ~; 16 |; 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 : 39 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/RNG002-1.tptp',unknown),
[] ).
cnf(159596936,plain,
( ~ sum(A,B,C)
| sum(B,A,C) ),
inference(rewrite,[status(thm)],[commutativity_of_addition]),
[] ).
fof(a_plus_c_is_d,plain,
sum(a,c,d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG002-1.tptp',unknown),
[] ).
cnf(159662696,plain,
sum(a,c,d),
inference(rewrite,[status(thm)],[a_plus_c_is_d]),
[] ).
cnf(168511544,plain,
sum(c,a,d),
inference(resolution,[status(thm)],[159596936,159662696]),
[] ).
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/RNG002-1.tptp',unknown),
[] ).
cnf(159592784,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/RNG002-1.tptp',unknown),
[] ).
cnf(159558144,plain,
sum(A,additive_identity,A),
inference(rewrite,[status(thm)],[additive_identity2]),
[] ).
cnf(167714144,plain,
( ~ sum(A,B,C)
| ~ sum(B,D,additive_identity)
| sum(C,D,A) ),
inference(resolution,[status(thm)],[159592784,159558144]),
[] ).
fof(right_inverse,plain,
! [A] : sum(A,additive_inverse(A),additive_identity),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG002-1.tptp',unknown),
[] ).
cnf(159574552,plain,
sum(A,additive_inverse(A),additive_identity),
inference(rewrite,[status(thm)],[right_inverse]),
[] ).
cnf(168026912,plain,
( ~ sum(A,B,C)
| sum(C,additive_inverse(B),A) ),
inference(resolution,[status(thm)],[167714144,159574552]),
[] ).
cnf(261169192,plain,
sum(d,additive_inverse(a),c),
inference(resolution,[status(thm)],[168511544,168026912]),
[] ).
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/RNG002-1.tptp',unknown),
[] ).
cnf(159645744,plain,
( ~ sum(A,B,C)
| ~ sum(A,B,D)
| $equal(D,C) ),
inference(rewrite,[status(thm)],[addition_is_well_defined]),
[] ).
fof(prove_b_equals_c,plain,
~ $equal(c,b),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG002-1.tptp',unknown),
[] ).
cnf(159667256,plain,
~ $equal(c,b),
inference(rewrite,[status(thm)],[prove_b_equals_c]),
[] ).
cnf(168606488,plain,
( ~ sum(A,B,b)
| ~ sum(A,B,c) ),
inference(resolution,[status(thm)],[159645744,159667256]),
[] ).
fof(a_plus_b_is_d,plain,
sum(a,b,d),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG002-1.tptp',unknown),
[] ).
cnf(159550960,plain,
sum(a,b,d),
inference(rewrite,[status(thm)],[a_plus_b_is_d]),
[] ).
cnf(168500672,plain,
sum(b,a,d),
inference(resolution,[status(thm)],[159596936,159550960]),
[] ).
cnf(261159904,plain,
sum(d,additive_inverse(a),b),
inference(resolution,[status(thm)],[168500672,168026912]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[261169192,168606488,261159904]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 17 seconds
% START OF PROOF SEQUENCE
% fof(commutativity_of_addition,plain,(~sum(A,B,C)|sum(B,A,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG002-1.tptp',unknown),[]).
%
% cnf(159596936,plain,(~sum(A,B,C)|sum(B,A,C)),inference(rewrite,[status(thm)],[commutativity_of_addition]),[]).
%
% fof(a_plus_c_is_d,plain,(sum(a,c,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG002-1.tptp',unknown),[]).
%
% cnf(159662696,plain,(sum(a,c,d)),inference(rewrite,[status(thm)],[a_plus_c_is_d]),[]).
%
% cnf(168511544,plain,(sum(c,a,d)),inference(resolution,[status(thm)],[159596936,159662696]),[]).
%
% 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/RNG002-1.tptp',unknown),[]).
%
% cnf(159592784,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/RNG002-1.tptp',unknown),[]).
%
% cnf(159558144,plain,(sum(A,additive_identity,A)),inference(rewrite,[status(thm)],[additive_identity2]),[]).
%
% cnf(167714144,plain,(~sum(A,B,C)|~sum(B,D,additive_identity)|sum(C,D,A)),inference(resolution,[status(thm)],[159592784,159558144]),[]).
%
% fof(right_inverse,plain,(sum(A,additive_inverse(A),additive_identity)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG002-1.tptp',unknown),[]).
%
% cnf(159574552,plain,(sum(A,additive_inverse(A),additive_identity)),inference(rewrite,[status(thm)],[right_inverse]),[]).
%
% cnf(168026912,plain,(~sum(A,B,C)|sum(C,additive_inverse(B),A)),inference(resolution,[status(thm)],[167714144,159574552]),[]).
%
% cnf(261169192,plain,(sum(d,additive_inverse(a),c)),inference(resolution,[status(thm)],[168511544,168026912]),[]).
%
% 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/RNG002-1.tptp',unknown),[]).
%
% cnf(159645744,plain,(~sum(A,B,C)|~sum(A,B,D)|$equal(D,C)),inference(rewrite,[status(thm)],[addition_is_well_defined]),[]).
%
% fof(prove_b_equals_c,plain,(~$equal(c,b)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG002-1.tptp',unknown),[]).
%
% cnf(159667256,plain,(~$equal(c,b)),inference(rewrite,[status(thm)],[prove_b_equals_c]),[]).
%
% cnf(168606488,plain,(~sum(A,B,b)|~sum(A,B,c)),inference(resolution,[status(thm)],[159645744,159667256]),[]).
%
% fof(a_plus_b_is_d,plain,(sum(a,b,d)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/RNG/RNG002-1.tptp',unknown),[]).
%
% cnf(159550960,plain,(sum(a,b,d)),inference(rewrite,[status(thm)],[a_plus_b_is_d]),[]).
%
% cnf(168500672,plain,(sum(b,a,d)),inference(resolution,[status(thm)],[159596936,159550960]),[]).
%
% cnf(261159904,plain,(sum(d,additive_inverse(a),b)),inference(resolution,[status(thm)],[168500672,168026912]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[261169192,168606488,261159904]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------