TSTP Solution File: LCL108-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL108-1 : 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 13:42:19 EDT 2009
% Result : Unsatisfiable 1.8s
% Output : Refutation 1.8s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 13 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 8 ( 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 : 111 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_q_3,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),c)),c)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL108-1.tptp',unknown),
[] ).
cnf(159253592,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),c)),c)),
inference(rewrite,[status(thm)],[prove_q_3]),
[] ).
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/LCL108-1.tptp',unknown),
[] ).
cnf(159240080,plain,
( ~ is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
fof(lg_27_1690,plain,
! [A,B,C,D,E,F,G] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,E),equivalent(equivalent(equivalent(F,E),equivalent(F,D)),G))),equivalent(C,equivalent(equivalent(B,A),G)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL108-1.tptp',unknown),
[] ).
cnf(159245192,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,E),equivalent(equivalent(equivalent(F,E),equivalent(F,D)),G))),equivalent(C,equivalent(equivalent(B,A),G)))),
inference(rewrite,[status(thm)],[lg_27_1690]),
[] ).
cnf(167136904,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(B,C),D),equivalent(equivalent(E,F),equivalent(equivalent(equivalent(G,F),equivalent(G,E)),H))),equivalent(D,equivalent(equivalent(C,B),H))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[159240080,159245192]),
[] ).
cnf(167117848,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,E),equivalent(equivalent(equivalent(F,E),equivalent(F,D)),G))))
| is_a_theorem(equivalent(C,equivalent(equivalent(B,A),G))) ),
inference(resolution,[status(thm)],[159240080,159245192]),
[] ).
cnf(169088776,plain,
is_a_theorem(equivalent(equivalent(equivalent(E,F),equivalent(equivalent(equivalent(G,F),equivalent(G,E)),D)),equivalent(equivalent(equivalent(A,B),equivalent(equivalent(C,A),equivalent(C,B))),D))),
inference(resolution,[status(thm)],[167117848,159245192]),
[] ).
cnf(169210880,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(H,B),equivalent(H,A)),equivalent(equivalent(equivalent(C,equivalent(equivalent(G,E),equivalent(G,F))),equivalent(C,equivalent(E,F))),D)),equivalent(equivalent(B,A),D))),
inference(resolution,[status(thm)],[167117848,169088776]),
[] ).
cnf(169234120,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(H,B),equivalent(H,A)),equivalent(equivalent(equivalent(C,equivalent(equivalent(G,E),equivalent(G,F))),equivalent(C,equivalent(E,F))),D)))
| is_a_theorem(equivalent(equivalent(B,A),D)) ),
inference(resolution,[status(thm)],[159240080,169210880]),
[] ).
cnf(169407392,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(B,equivalent(equivalent(F,equivalent(E,C)),equivalent(F,equivalent(E,D)))),equivalent(B,equivalent(C,D))),A),A)),
inference(resolution,[status(thm)],[169234120,169210880]),
[] ).
cnf(169542552,plain,
is_a_theorem(equivalent(equivalent(equivalent(F,equivalent(E,equivalent(equivalent(C,B),equivalent(C,A)))),equivalent(F,equivalent(E,D))),equivalent(equivalent(B,A),D))),
inference(resolution,[status(thm)],[167136904,169407392]),
[] ).
cnf(169962848,plain,
( ~ is_a_theorem(equivalent(equivalent(F,equivalent(E,equivalent(equivalent(C,B),equivalent(C,A)))),equivalent(F,equivalent(E,D))))
| is_a_theorem(equivalent(equivalent(B,A),D)) ),
inference(resolution,[status(thm)],[159240080,169542552]),
[] ).
cnf(170140096,plain,
is_a_theorem(equivalent(equivalent(equivalent(E,equivalent(B,C)),A),equivalent(equivalent(E,equivalent(equivalent(D,B),equivalent(D,C))),A))),
inference(resolution,[status(thm)],[169962848,169088776]),
[] ).
cnf(170256048,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(F,equivalent(C,D)),B),equivalent(equivalent(F,equivalent(equivalent(E,C),equivalent(E,D))),B)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[159240080,170140096]),
[] ).
cnf(170681680,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),D),equivalent(equivalent(equivalent(C,A),equivalent(equivalent(E,C),equivalent(E,B))),D))),
inference(resolution,[status(thm)],[170256048,169210880]),
[] ).
cnf(170738584,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(B,C),E),equivalent(equivalent(equivalent(D,B),equivalent(equivalent(F,D),equivalent(F,C))),E)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[159240080,170681680]),
[] ).
cnf(169424680,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(B,equivalent(equivalent(F,equivalent(E,C)),equivalent(F,equivalent(E,D)))),equivalent(B,equivalent(C,D))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[159240080,169407392]),
[] ).
cnf(169591512,plain,
is_a_theorem(equivalent(equivalent(equivalent(D,equivalent(C,A)),equivalent(equivalent(F,equivalent(E,D)),equivalent(F,equivalent(E,equivalent(C,B))))),equivalent(A,B))),
inference(resolution,[status(thm)],[169424680,169407392]),
[] ).
cnf(171472944,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,C),equivalent(equivalent(C,A),D)),D)),
inference(resolution,[status(thm)],[170738584,169591512]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[159253592,171472944]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 seconds
% START OF PROOF SEQUENCE
% fof(prove_q_3,plain,(~is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),c)),c))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL108-1.tptp',unknown),[]).
%
% cnf(159253592,plain,(~is_a_theorem(equivalent(equivalent(equivalent(a,b),equivalent(equivalent(b,a),c)),c))),inference(rewrite,[status(thm)],[prove_q_3]),[]).
%
% 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/LCL108-1.tptp',unknown),[]).
%
% cnf(159240080,plain,(~is_a_theorem(equivalent(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% fof(lg_27_1690,plain,(is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,E),equivalent(equivalent(equivalent(F,E),equivalent(F,D)),G))),equivalent(C,equivalent(equivalent(B,A),G))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL108-1.tptp',unknown),[]).
%
% cnf(159245192,plain,(is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,E),equivalent(equivalent(equivalent(F,E),equivalent(F,D)),G))),equivalent(C,equivalent(equivalent(B,A),G))))),inference(rewrite,[status(thm)],[lg_27_1690]),[]).
%
% cnf(167136904,plain,(~is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(B,C),D),equivalent(equivalent(E,F),equivalent(equivalent(equivalent(G,F),equivalent(G,E)),H))),equivalent(D,equivalent(equivalent(C,B),H))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[159240080,159245192]),[]).
%
% cnf(167117848,plain,(~is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(equivalent(D,E),equivalent(equivalent(equivalent(F,E),equivalent(F,D)),G))))|is_a_theorem(equivalent(C,equivalent(equivalent(B,A),G)))),inference(resolution,[status(thm)],[159240080,159245192]),[]).
%
% cnf(169088776,plain,(is_a_theorem(equivalent(equivalent(equivalent(E,F),equivalent(equivalent(equivalent(G,F),equivalent(G,E)),D)),equivalent(equivalent(equivalent(A,B),equivalent(equivalent(C,A),equivalent(C,B))),D)))),inference(resolution,[status(thm)],[167117848,159245192]),[]).
%
% cnf(169210880,plain,(is_a_theorem(equivalent(equivalent(equivalent(equivalent(H,B),equivalent(H,A)),equivalent(equivalent(equivalent(C,equivalent(equivalent(G,E),equivalent(G,F))),equivalent(C,equivalent(E,F))),D)),equivalent(equivalent(B,A),D)))),inference(resolution,[status(thm)],[167117848,169088776]),[]).
%
% cnf(169234120,plain,(~is_a_theorem(equivalent(equivalent(equivalent(H,B),equivalent(H,A)),equivalent(equivalent(equivalent(C,equivalent(equivalent(G,E),equivalent(G,F))),equivalent(C,equivalent(E,F))),D)))|is_a_theorem(equivalent(equivalent(B,A),D))),inference(resolution,[status(thm)],[159240080,169210880]),[]).
%
% cnf(169407392,plain,(is_a_theorem(equivalent(equivalent(equivalent(equivalent(B,equivalent(equivalent(F,equivalent(E,C)),equivalent(F,equivalent(E,D)))),equivalent(B,equivalent(C,D))),A),A))),inference(resolution,[status(thm)],[169234120,169210880]),[]).
%
% cnf(169542552,plain,(is_a_theorem(equivalent(equivalent(equivalent(F,equivalent(E,equivalent(equivalent(C,B),equivalent(C,A)))),equivalent(F,equivalent(E,D))),equivalent(equivalent(B,A),D)))),inference(resolution,[status(thm)],[167136904,169407392]),[]).
%
% cnf(169962848,plain,(~is_a_theorem(equivalent(equivalent(F,equivalent(E,equivalent(equivalent(C,B),equivalent(C,A)))),equivalent(F,equivalent(E,D))))|is_a_theorem(equivalent(equivalent(B,A),D))),inference(resolution,[status(thm)],[159240080,169542552]),[]).
%
% cnf(170140096,plain,(is_a_theorem(equivalent(equivalent(equivalent(E,equivalent(B,C)),A),equivalent(equivalent(E,equivalent(equivalent(D,B),equivalent(D,C))),A)))),inference(resolution,[status(thm)],[169962848,169088776]),[]).
%
% cnf(170256048,plain,(~is_a_theorem(equivalent(equivalent(equivalent(equivalent(F,equivalent(C,D)),B),equivalent(equivalent(F,equivalent(equivalent(E,C),equivalent(E,D))),B)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[159240080,170140096]),[]).
%
% cnf(170681680,plain,(is_a_theorem(equivalent(equivalent(equivalent(A,B),D),equivalent(equivalent(equivalent(C,A),equivalent(equivalent(E,C),equivalent(E,B))),D)))),inference(resolution,[status(thm)],[170256048,169210880]),[]).
%
% cnf(170738584,plain,(~is_a_theorem(equivalent(equivalent(equivalent(equivalent(B,C),E),equivalent(equivalent(equivalent(D,B),equivalent(equivalent(F,D),equivalent(F,C))),E)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[159240080,170681680]),[]).
%
% cnf(169424680,plain,(~is_a_theorem(equivalent(equivalent(equivalent(B,equivalent(equivalent(F,equivalent(E,C)),equivalent(F,equivalent(E,D)))),equivalent(B,equivalent(C,D))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[159240080,169407392]),[]).
%
% cnf(169591512,plain,(is_a_theorem(equivalent(equivalent(equivalent(D,equivalent(C,A)),equivalent(equivalent(F,equivalent(E,D)),equivalent(F,equivalent(E,equivalent(C,B))))),equivalent(A,B)))),inference(resolution,[status(thm)],[169424680,169407392]),[]).
%
% cnf(171472944,plain,(is_a_theorem(equivalent(equivalent(equivalent(A,C),equivalent(equivalent(C,A),D)),D))),inference(resolution,[status(thm)],[170738584,169591512]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[159253592,171472944]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------