TSTP Solution File: LCL130-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL130-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art10.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 13:43:16 EDT 2009
% Result : Unsatisfiable 1.9s
% Output : Refutation 1.9s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 16 unt; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_lg_2,plain,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL130-1.tptp',unknown),
[] ).
cnf(158637128,plain,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e)))))),
inference(rewrite,[status(thm)],[prove_lg_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/LCL130-1.tptp',unknown),
[] ).
cnf(158627696,plain,
( ~ is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
fof(p_4,plain,
! [A,B,C,D] : is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(B,D),equivalent(C,D)))),A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL130-1.tptp',unknown),
[] ).
cnf(158632624,plain,
is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(B,D),equivalent(C,D)))),A)),
inference(rewrite,[status(thm)],[p_4]),
[] ).
cnf(166417200,plain,
( ~ is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(B,D),equivalent(C,D)))))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[158627696,158632624]),
[] ).
cnf(166656624,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(B,C))),equivalent(equivalent(D,E),equivalent(equivalent(D,F),equivalent(E,F))))),
inference(resolution,[status(thm)],[166417200,158632624]),
[] ).
cnf(168969024,plain,
is_a_theorem(equivalent(equivalent(D,E),equivalent(equivalent(D,F),equivalent(E,F)))),
inference(resolution,[status(thm)],[166417200,166656624]),
[] ).
cnf(169009208,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(E,F),equivalent(equivalent(E,G),equivalent(F,G))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[158627696,168969024]),
[] ).
cnf(168990592,plain,
( ~ is_a_theorem(equivalent(D,E))
| is_a_theorem(equivalent(equivalent(D,F),equivalent(E,F))) ),
inference(resolution,[status(thm)],[158627696,168969024]),
[] ).
cnf(169075456,plain,
is_a_theorem(equivalent(equivalent(equivalent(H,I),D),equivalent(equivalent(equivalent(H,J),equivalent(I,J)),D))),
inference(resolution,[status(thm)],[168990592,168969024]),
[] ).
cnf(169268104,plain,
is_a_theorem(equivalent(equivalent(equivalent(D,M),equivalent(E,M)),equivalent(equivalent(D,F),equivalent(E,F)))),
inference(resolution,[status(thm)],[169009208,169075456]),
[] ).
cnf(169600064,plain,
( ~ is_a_theorem(equivalent(equivalent(D,M),equivalent(E,M)))
| is_a_theorem(equivalent(equivalent(D,F),equivalent(E,F))) ),
inference(resolution,[status(thm)],[158627696,169268104]),
[] ).
cnf(169729080,plain,
is_a_theorem(equivalent(equivalent(equivalent(N,P),D),equivalent(equivalent(N,P),D))),
inference(resolution,[status(thm)],[169600064,169268104]),
[] ).
cnf(169762288,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(O,Q),E),equivalent(equivalent(O,Q),E)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[158627696,169729080]),
[] ).
cnf(169128224,plain,
( ~ is_a_theorem(equivalent(equivalent(H,I),D))
| is_a_theorem(equivalent(equivalent(equivalent(H,J),equivalent(I,J)),D)) ),
inference(resolution,[status(thm)],[158627696,169075456]),
[] ).
cnf(169783776,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(U,W),H),equivalent(G,H)),equivalent(equivalent(U,W),G))),
inference(resolution,[status(thm)],[169128224,169729080]),
[] ).
cnf(169949800,plain,
is_a_theorem(equivalent(equivalent(N,P),equivalent(N,P))),
inference(resolution,[status(thm)],[169762288,169783776]),
[] ).
cnf(169987688,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(O,Q),equivalent(O,Q)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[158627696,169949800]),
[] ).
cnf(170010912,plain,
is_a_theorem(equivalent(equivalent(equivalent(N,W),equivalent(P,W)),equivalent(N,P))),
inference(resolution,[status(thm)],[169987688,169075456]),
[] ).
cnf(170084016,plain,
is_a_theorem(equivalent(N,N)),
inference(resolution,[status(thm)],[169987688,170010912]),
[] ).
cnf(170158688,plain,
( ~ is_a_theorem(equivalent(equivalent(O,O),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[158627696,170084016]),
[] ).
cnf(166436816,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(B,equivalent(equivalent(C,D),equivalent(equivalent(C,E),equivalent(D,E)))),B),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[158627696,158632624]),
[] ).
cnf(169038992,plain,
is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(B,D),equivalent(C,D)))),H),equivalent(A,H))),
inference(resolution,[status(thm)],[166436816,168969024]),
[] ).
cnf(172380872,plain,
is_a_theorem(equivalent(N,equivalent(N,equivalent(equivalent(O,P),equivalent(equivalent(O,Q),equivalent(P,Q)))))),
inference(resolution,[status(thm)],[170158688,169038992]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[158637128,172380872]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 seconds
% START OF PROOF SEQUENCE
% fof(prove_lg_2,plain,(~is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e))))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL130-1.tptp',unknown),[]).
%
% cnf(158637128,plain,(~is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(b,e),equivalent(c,e))))))),inference(rewrite,[status(thm)],[prove_lg_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/LCL130-1.tptp',unknown),[]).
%
% cnf(158627696,plain,(~is_a_theorem(equivalent(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% fof(p_4,plain,(is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(B,D),equivalent(C,D)))),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL130-1.tptp',unknown),[]).
%
% cnf(158632624,plain,(is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(B,D),equivalent(C,D)))),A))),inference(rewrite,[status(thm)],[p_4]),[]).
%
% cnf(166417200,plain,(~is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(B,D),equivalent(C,D)))))|is_a_theorem(A)),inference(resolution,[status(thm)],[158627696,158632624]),[]).
%
% cnf(166656624,plain,(is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(A,C),equivalent(B,C))),equivalent(equivalent(D,E),equivalent(equivalent(D,F),equivalent(E,F)))))),inference(resolution,[status(thm)],[166417200,158632624]),[]).
%
% cnf(168969024,plain,(is_a_theorem(equivalent(equivalent(D,E),equivalent(equivalent(D,F),equivalent(E,F))))),inference(resolution,[status(thm)],[166417200,166656624]),[]).
%
% cnf(169009208,plain,(~is_a_theorem(equivalent(equivalent(equivalent(E,F),equivalent(equivalent(E,G),equivalent(F,G))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[158627696,168969024]),[]).
%
% cnf(168990592,plain,(~is_a_theorem(equivalent(D,E))|is_a_theorem(equivalent(equivalent(D,F),equivalent(E,F)))),inference(resolution,[status(thm)],[158627696,168969024]),[]).
%
% cnf(169075456,plain,(is_a_theorem(equivalent(equivalent(equivalent(H,I),D),equivalent(equivalent(equivalent(H,J),equivalent(I,J)),D)))),inference(resolution,[status(thm)],[168990592,168969024]),[]).
%
% cnf(169268104,plain,(is_a_theorem(equivalent(equivalent(equivalent(D,M),equivalent(E,M)),equivalent(equivalent(D,F),equivalent(E,F))))),inference(resolution,[status(thm)],[169009208,169075456]),[]).
%
% cnf(169600064,plain,(~is_a_theorem(equivalent(equivalent(D,M),equivalent(E,M)))|is_a_theorem(equivalent(equivalent(D,F),equivalent(E,F)))),inference(resolution,[status(thm)],[158627696,169268104]),[]).
%
% cnf(169729080,plain,(is_a_theorem(equivalent(equivalent(equivalent(N,P),D),equivalent(equivalent(N,P),D)))),inference(resolution,[status(thm)],[169600064,169268104]),[]).
%
% cnf(169762288,plain,(~is_a_theorem(equivalent(equivalent(equivalent(equivalent(O,Q),E),equivalent(equivalent(O,Q),E)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[158627696,169729080]),[]).
%
% cnf(169128224,plain,(~is_a_theorem(equivalent(equivalent(H,I),D))|is_a_theorem(equivalent(equivalent(equivalent(H,J),equivalent(I,J)),D))),inference(resolution,[status(thm)],[158627696,169075456]),[]).
%
% cnf(169783776,plain,(is_a_theorem(equivalent(equivalent(equivalent(equivalent(U,W),H),equivalent(G,H)),equivalent(equivalent(U,W),G)))),inference(resolution,[status(thm)],[169128224,169729080]),[]).
%
% cnf(169949800,plain,(is_a_theorem(equivalent(equivalent(N,P),equivalent(N,P)))),inference(resolution,[status(thm)],[169762288,169783776]),[]).
%
% cnf(169987688,plain,(~is_a_theorem(equivalent(equivalent(equivalent(O,Q),equivalent(O,Q)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[158627696,169949800]),[]).
%
% cnf(170010912,plain,(is_a_theorem(equivalent(equivalent(equivalent(N,W),equivalent(P,W)),equivalent(N,P)))),inference(resolution,[status(thm)],[169987688,169075456]),[]).
%
% cnf(170084016,plain,(is_a_theorem(equivalent(N,N))),inference(resolution,[status(thm)],[169987688,170010912]),[]).
%
% cnf(170158688,plain,(~is_a_theorem(equivalent(equivalent(O,O),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[158627696,170084016]),[]).
%
% cnf(166436816,plain,(~is_a_theorem(equivalent(equivalent(equivalent(B,equivalent(equivalent(C,D),equivalent(equivalent(C,E),equivalent(D,E)))),B),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[158627696,158632624]),[]).
%
% cnf(169038992,plain,(is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(B,D),equivalent(C,D)))),H),equivalent(A,H)))),inference(resolution,[status(thm)],[166436816,168969024]),[]).
%
% cnf(172380872,plain,(is_a_theorem(equivalent(N,equivalent(N,equivalent(equivalent(O,P),equivalent(equivalent(O,Q),equivalent(P,Q))))))),inference(resolution,[status(thm)],[170158688,169038992]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[158637128,172380872]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------