TSTP Solution File: LCL106-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL106-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art05.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 13:42:15 EDT 2009
% Result : Unsatisfiable 0.4s
% Output : Refutation 0.4s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 10 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 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 : 44 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_q_2,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(c,b)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL106-1.tptp',unknown),
[] ).
cnf(151058344,plain,
~ is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(c,b)))),
inference(rewrite,[status(thm)],[prove_q_2]),
[] ).
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/LCL106-1.tptp',unknown),
[] ).
cnf(151045496,plain,
( ~ is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
fof(q_4,plain,
! [A,B,C] : is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(B,C))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL106-1.tptp',unknown),
[] ).
cnf(151054600,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(B,C))),
inference(rewrite,[status(thm)],[q_4]),
[] ).
cnf(158959872,plain,
( ~ is_a_theorem(equivalent(equivalent(A,B),equivalent(A,C)))
| is_a_theorem(equivalent(B,C)) ),
inference(resolution,[status(thm)],[151045496,151054600]),
[] ).
cnf(159218264,plain,
( is_a_theorem(equivalent(B,C))
| ~ is_a_theorem(equivalent(equivalent(D,equivalent(A,B)),equivalent(D,equivalent(A,C)))) ),
inference(resolution,[status(thm)],[158959872,158959872]),
[] ).
cnf(158979208,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(B,C),equivalent(B,D)),equivalent(C,D)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[151045496,151054600]),
[] ).
fof(q_1,plain,
! [A,B,C] : is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(C,B),A)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL106-1.tptp',unknown),
[] ).
cnf(151050352,plain,
is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(C,B),A)))),
inference(rewrite,[status(thm)],[q_1]),
[] ).
cnf(158844272,plain,
( ~ is_a_theorem(A)
| is_a_theorem(equivalent(equivalent(B,C),equivalent(equivalent(C,B),A))) ),
inference(resolution,[status(thm)],[151045496,151050352]),
[] ).
cnf(159064680,plain,
is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(B,A),equivalent(C,equivalent(equivalent(D,E),equivalent(equivalent(E,D),C)))))),
inference(resolution,[status(thm)],[158844272,151050352]),
[] ).
cnf(163970128,plain,
is_a_theorem(equivalent(equivalent(equivalent(B,C),equivalent(equivalent(A,B),equivalent(A,C))),equivalent(D,equivalent(equivalent(E,F),equivalent(equivalent(F,E),D))))),
inference(resolution,[status(thm)],[158979208,159064680]),
[] ).
cnf(165634144,plain,
is_a_theorem(equivalent(equivalent(A,C),equivalent(equivalent(B,A),equivalent(B,C)))),
inference(resolution,[status(thm)],[159218264,163970128]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[151058344,165634144]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(prove_q_2,plain,(~is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(c,b))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL106-1.tptp',unknown),[]).
%
% cnf(151058344,plain,(~is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(c,b))))),inference(rewrite,[status(thm)],[prove_q_2]),[]).
%
% 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/LCL106-1.tptp',unknown),[]).
%
% cnf(151045496,plain,(~is_a_theorem(equivalent(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% fof(q_4,plain,(is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL106-1.tptp',unknown),[]).
%
% cnf(151054600,plain,(is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(A,C)),equivalent(B,C)))),inference(rewrite,[status(thm)],[q_4]),[]).
%
% cnf(158959872,plain,(~is_a_theorem(equivalent(equivalent(A,B),equivalent(A,C)))|is_a_theorem(equivalent(B,C))),inference(resolution,[status(thm)],[151045496,151054600]),[]).
%
% cnf(159218264,plain,(is_a_theorem(equivalent(B,C))|~is_a_theorem(equivalent(equivalent(D,equivalent(A,B)),equivalent(D,equivalent(A,C))))),inference(resolution,[status(thm)],[158959872,158959872]),[]).
%
% cnf(158979208,plain,(~is_a_theorem(equivalent(equivalent(equivalent(equivalent(B,C),equivalent(B,D)),equivalent(C,D)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[151045496,151054600]),[]).
%
% fof(q_1,plain,(is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(C,B),A))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL106-1.tptp',unknown),[]).
%
% cnf(151050352,plain,(is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(C,B),A))))),inference(rewrite,[status(thm)],[q_1]),[]).
%
% cnf(158844272,plain,(~is_a_theorem(A)|is_a_theorem(equivalent(equivalent(B,C),equivalent(equivalent(C,B),A)))),inference(resolution,[status(thm)],[151045496,151050352]),[]).
%
% cnf(159064680,plain,(is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(B,A),equivalent(C,equivalent(equivalent(D,E),equivalent(equivalent(E,D),C))))))),inference(resolution,[status(thm)],[158844272,151050352]),[]).
%
% cnf(163970128,plain,(is_a_theorem(equivalent(equivalent(equivalent(B,C),equivalent(equivalent(A,B),equivalent(A,C))),equivalent(D,equivalent(equivalent(E,F),equivalent(equivalent(F,E),D)))))),inference(resolution,[status(thm)],[158979208,159064680]),[]).
%
% cnf(165634144,plain,(is_a_theorem(equivalent(equivalent(A,C),equivalent(equivalent(B,A),equivalent(B,C))))),inference(resolution,[status(thm)],[159218264,163970128]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[151058344,165634144]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------