TSTP Solution File: LCL126-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL126-1 : 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 @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 13:43:11 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 8 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 1 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(q_4,plain,
! [A,B,C] : is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(B,C)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL126-1.tptp',unknown),
[] ).
cnf(141583008,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(B,C)))),
inference(rewrite,[status(thm)],[q_4]),
[] ).
fof(condensed_detachment,plain,
! [A,B] :
( ~ is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL126-1.tptp',unknown),
[] ).
cnf(141573904,plain,
( ~ is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
cnf(149582632,plain,
( ~ is_a_theorem(equivalent(A,B))
| is_a_theorem(equivalent(equivalent(A,C),equivalent(B,C))) ),
inference(resolution,[status(thm)],[141573904,141583008]),
[] ).
cnf(149677408,plain,
( ~ is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(equivalent(A,C))
| is_a_theorem(equivalent(B,C)) ),
inference(resolution,[status(thm)],[149582632,141573904]),
[] ).
fof(q_3,plain,
! [A,B,C] : is_a_theorem(equivalent(A,equivalent(equivalent(A,equivalent(B,C)),equivalent(C,B)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL126-1.tptp',unknown),
[] ).
cnf(141578760,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(A,equivalent(B,C)),equivalent(C,B)))),
inference(rewrite,[status(thm)],[q_3]),
[] ).
cnf(149357928,plain,
( ~ is_a_theorem(A)
| is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(C,B))) ),
inference(resolution,[status(thm)],[141573904,141578760]),
[] ).
cnf(150430392,plain,
( is_a_theorem(equivalent(equivalent(C,B),equivalent(C,B)))
| ~ is_a_theorem(A) ),
inference(resolution,[status(thm)],[149677408,149357928]),
[] ).
cnf(150619184,plain,
is_a_theorem(equivalent(equivalent(B,A),equivalent(B,A))),
inference(resolution,[status(thm)],[150430392,141578760]),
[] ).
cnf(149615048,plain,
( ~ is_a_theorem(A)
| ~ is_a_theorem(equivalent(A,equivalent(B,C)))
| is_a_theorem(equivalent(C,B)) ),
inference(resolution,[status(thm)],[149357928,141573904]),
[] ).
cnf(150712200,plain,
( ~ is_a_theorem(equivalent(B,A))
| is_a_theorem(equivalent(A,B)) ),
inference(resolution,[status(thm)],[150619184,149615048]),
[] ).
fof(prove_q_2,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL126-1.tptp',unknown),
[] ).
cnf(141586752,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))),
inference(rewrite,[status(thm)],[prove_q_2]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[141583008,150712200,141586752]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(q_4,plain,(is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(B,C))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL126-1.tptp',unknown),[]).
%
% cnf(141583008,plain,(is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(B,C))))),inference(rewrite,[status(thm)],[q_4]),[]).
%
% fof(condensed_detachment,plain,(~is_a_theorem(equivalent(A,B))|~is_a_theorem(A)|is_a_theorem(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL126-1.tptp',unknown),[]).
%
% cnf(141573904,plain,(~is_a_theorem(equivalent(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% cnf(149582632,plain,(~is_a_theorem(equivalent(A,B))|is_a_theorem(equivalent(equivalent(A,C),equivalent(B,C)))),inference(resolution,[status(thm)],[141573904,141583008]),[]).
%
% cnf(149677408,plain,(~is_a_theorem(equivalent(A,B))|~is_a_theorem(equivalent(A,C))|is_a_theorem(equivalent(B,C))),inference(resolution,[status(thm)],[149582632,141573904]),[]).
%
% fof(q_3,plain,(is_a_theorem(equivalent(A,equivalent(equivalent(A,equivalent(B,C)),equivalent(C,B))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL126-1.tptp',unknown),[]).
%
% cnf(141578760,plain,(is_a_theorem(equivalent(A,equivalent(equivalent(A,equivalent(B,C)),equivalent(C,B))))),inference(rewrite,[status(thm)],[q_3]),[]).
%
% cnf(149357928,plain,(~is_a_theorem(A)|is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(C,B)))),inference(resolution,[status(thm)],[141573904,141578760]),[]).
%
% cnf(150430392,plain,(is_a_theorem(equivalent(equivalent(C,B),equivalent(C,B)))|~is_a_theorem(A)),inference(resolution,[status(thm)],[149677408,149357928]),[]).
%
% cnf(150619184,plain,(is_a_theorem(equivalent(equivalent(B,A),equivalent(B,A)))),inference(resolution,[status(thm)],[150430392,141578760]),[]).
%
% cnf(149615048,plain,(~is_a_theorem(A)|~is_a_theorem(equivalent(A,equivalent(B,C)))|is_a_theorem(equivalent(C,B))),inference(resolution,[status(thm)],[149357928,141573904]),[]).
%
% cnf(150712200,plain,(~is_a_theorem(equivalent(B,A))|is_a_theorem(equivalent(A,B))),inference(resolution,[status(thm)],[150619184,149615048]),[]).
%
% fof(prove_q_2,plain,(~is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL126-1.tptp',unknown),[]).
%
% cnf(141586752,plain,(~is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c)))),inference(rewrite,[status(thm)],[prove_q_2]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[141583008,150712200,141586752]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------