TSTP Solution File: LCL088-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL088-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art08.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 13:41:47 EDT 2009
% Result : Unsatisfiable 3.7s
% Output : Refutation 3.7s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of formulae : 37 ( 22 unt; 0 def)
% Number of atoms : 54 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 19 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 105 ( 41 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_ic_3,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL088-1.tptp',unknown),
[] ).
cnf(170406920,plain,
~ is_a_theorem(implies(implies(implies(a,b),a),a)),
inference(rewrite,[status(thm)],[prove_ic_3]),
[] ).
fof(condensed_detachment,plain,
! [A,B] :
( ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL088-1.tptp',unknown),
[] ).
cnf(170397880,plain,
( ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[condensed_detachment]),
[] ).
fof(ic_JLukasiewicz_4,plain,
! [A,B,C,D,E] : is_a_theorem(implies(implies(implies(A,B),implies(C,D)),implies(E,implies(implies(D,A),implies(C,A))))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL088-1.tptp',unknown),
[] ).
cnf(170402864,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,D)),implies(E,implies(implies(D,A),implies(C,A))))),
inference(rewrite,[status(thm)],[ic_JLukasiewicz_4]),
[] ).
cnf(178222208,plain,
( ~ is_a_theorem(implies(implies(A,B),implies(C,D)))
| is_a_theorem(implies(E,implies(implies(D,A),implies(C,A)))) ),
inference(resolution,[status(thm)],[170397880,170402864]),
[] ).
cnf(178241912,plain,
( ~ is_a_theorem(implies(implies(implies(implies(B,C),implies(D,E)),implies(F,implies(implies(E,B),implies(D,B)))),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[170397880,170402864]),
[] ).
cnf(178895672,plain,
is_a_theorem(implies(B,implies(implies(implies(implies(F,C),implies(E,C)),implies(C,D)),implies(A,implies(C,D))))),
inference(resolution,[status(thm)],[178222208,170402864]),
[] ).
cnf(180239088,plain,
is_a_theorem(implies(implies(implies(implies(J,G),implies(I,G)),implies(G,H)),implies(F,implies(G,H)))),
inference(resolution,[status(thm)],[178241912,178895672]),
[] ).
cnf(180257656,plain,
( ~ is_a_theorem(implies(implies(implies(J,G),implies(I,G)),implies(G,H)))
| is_a_theorem(implies(F,implies(G,H))) ),
inference(resolution,[status(thm)],[170397880,180239088]),
[] ).
cnf(180352960,plain,
is_a_theorem(implies(F,implies(implies(M,G),implies(G,implies(M,G))))),
inference(resolution,[status(thm)],[180257656,180239088]),
[] ).
cnf(180621544,plain,
( ~ is_a_theorem(A)
| is_a_theorem(implies(implies(M,G),implies(G,implies(M,G)))) ),
inference(resolution,[status(thm)],[170397880,180352960]),
[] ).
cnf(180698312,plain,
is_a_theorem(implies(implies(L,F),implies(F,implies(L,F)))),
inference(resolution,[status(thm)],[180621544,170402864]),
[] ).
cnf(180792352,plain,
is_a_theorem(implies(C,implies(implies(implies(A,B),A),implies(B,A)))),
inference(resolution,[status(thm)],[178222208,180698312]),
[] ).
cnf(180905600,plain,
( ~ is_a_theorem(A)
| is_a_theorem(implies(implies(implies(B,C),B),implies(C,B))) ),
inference(resolution,[status(thm)],[170397880,180792352]),
[] ).
cnf(180999360,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(B,A))),
inference(resolution,[status(thm)],[180905600,170402864]),
[] ).
cnf(181030288,plain,
( ~ is_a_theorem(implies(implies(A,B),A))
| is_a_theorem(implies(B,A)) ),
inference(resolution,[status(thm)],[170397880,180999360]),
[] ).
cnf(181131224,plain,
is_a_theorem(implies(A,implies(A,A))),
inference(resolution,[status(thm)],[181030288,180999360]),
[] ).
cnf(181212960,plain,
( ~ is_a_theorem(implies(implies(B,implies(B,B)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[170397880,181131224]),
[] ).
cnf(181048664,plain,
( ~ is_a_theorem(implies(implies(implies(implies(B,C),B),implies(C,B)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[170397880,180999360]),
[] ).
cnf(181178736,plain,
is_a_theorem(implies(G,implies(A,implies(H,A)))),
inference(resolution,[status(thm)],[181048664,180239088]),
[] ).
cnf(181353984,plain,
( ~ is_a_theorem(A)
| is_a_theorem(implies(B,implies(H,B))) ),
inference(resolution,[status(thm)],[170397880,181178736]),
[] ).
cnf(181394960,plain,
is_a_theorem(implies(A,implies(G,A))),
inference(resolution,[status(thm)],[181353984,181131224]),
[] ).
cnf(181656216,plain,
is_a_theorem(implies(D,implies(implies(implies(A,B),A),implies(C,A)))),
inference(resolution,[status(thm)],[178222208,181394960]),
[] ).
cnf(184055184,plain,
is_a_theorem(implies(implies(implies(B,C),B),implies(D,B))),
inference(resolution,[status(thm)],[181212960,181656216]),
[] ).
cnf(184156424,plain,
( ~ is_a_theorem(implies(implies(B,C),B))
| is_a_theorem(implies(D,B)) ),
inference(resolution,[status(thm)],[170397880,184055184]),
[] ).
cnf(184237712,plain,
is_a_theorem(implies(C,implies(B,B))),
inference(resolution,[status(thm)],[184156424,180999360]),
[] ).
cnf(184320256,plain,
( ~ is_a_theorem(A)
| is_a_theorem(implies(C,C)) ),
inference(resolution,[status(thm)],[170397880,184237712]),
[] ).
cnf(184377672,plain,
is_a_theorem(implies(B,B)),
inference(resolution,[status(thm)],[184320256,181131224]),
[] ).
cnf(184547560,plain,
( ~ is_a_theorem(implies(implies(C,C),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[170397880,184377672]),
[] ).
cnf(184213840,plain,
is_a_theorem(implies(C,implies(implies(A,implies(A,E)),implies(B,implies(A,E))))),
inference(resolution,[status(thm)],[178222208,184055184]),
[] ).
cnf(188615912,plain,
is_a_theorem(implies(implies(C,implies(C,F)),implies(D,implies(C,F)))),
inference(resolution,[status(thm)],[184547560,184213840]),
[] ).
cnf(197158640,plain,
( ~ is_a_theorem(implies(C,implies(C,F)))
| is_a_theorem(implies(D,implies(C,F))) ),
inference(resolution,[status(thm)],[170397880,188615912]),
[] ).
cnf(197295712,plain,
is_a_theorem(implies(C,implies(implies(implies(E,G),E),E))),
inference(resolution,[status(thm)],[197158640,184055184]),
[] ).
cnf(197811440,plain,
is_a_theorem(implies(implies(implies(F,H),F),F)),
inference(resolution,[status(thm)],[184547560,197295712]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[170406920,197811440]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 3 seconds
% START OF PROOF SEQUENCE
% fof(prove_ic_3,plain,(~is_a_theorem(implies(implies(implies(a,b),a),a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL088-1.tptp',unknown),[]).
%
% cnf(170406920,plain,(~is_a_theorem(implies(implies(implies(a,b),a),a))),inference(rewrite,[status(thm)],[prove_ic_3]),[]).
%
% fof(condensed_detachment,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(A)|is_a_theorem(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL088-1.tptp',unknown),[]).
%
% cnf(170397880,plain,(~is_a_theorem(implies(A,B))|~is_a_theorem(A)|is_a_theorem(B)),inference(rewrite,[status(thm)],[condensed_detachment]),[]).
%
% fof(ic_JLukasiewicz_4,plain,(is_a_theorem(implies(implies(implies(A,B),implies(C,D)),implies(E,implies(implies(D,A),implies(C,A)))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL088-1.tptp',unknown),[]).
%
% cnf(170402864,plain,(is_a_theorem(implies(implies(implies(A,B),implies(C,D)),implies(E,implies(implies(D,A),implies(C,A)))))),inference(rewrite,[status(thm)],[ic_JLukasiewicz_4]),[]).
%
% cnf(178222208,plain,(~is_a_theorem(implies(implies(A,B),implies(C,D)))|is_a_theorem(implies(E,implies(implies(D,A),implies(C,A))))),inference(resolution,[status(thm)],[170397880,170402864]),[]).
%
% cnf(178241912,plain,(~is_a_theorem(implies(implies(implies(implies(B,C),implies(D,E)),implies(F,implies(implies(E,B),implies(D,B)))),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[170397880,170402864]),[]).
%
% cnf(178895672,plain,(is_a_theorem(implies(B,implies(implies(implies(implies(F,C),implies(E,C)),implies(C,D)),implies(A,implies(C,D)))))),inference(resolution,[status(thm)],[178222208,170402864]),[]).
%
% cnf(180239088,plain,(is_a_theorem(implies(implies(implies(implies(J,G),implies(I,G)),implies(G,H)),implies(F,implies(G,H))))),inference(resolution,[status(thm)],[178241912,178895672]),[]).
%
% cnf(180257656,plain,(~is_a_theorem(implies(implies(implies(J,G),implies(I,G)),implies(G,H)))|is_a_theorem(implies(F,implies(G,H)))),inference(resolution,[status(thm)],[170397880,180239088]),[]).
%
% cnf(180352960,plain,(is_a_theorem(implies(F,implies(implies(M,G),implies(G,implies(M,G)))))),inference(resolution,[status(thm)],[180257656,180239088]),[]).
%
% cnf(180621544,plain,(~is_a_theorem(A)|is_a_theorem(implies(implies(M,G),implies(G,implies(M,G))))),inference(resolution,[status(thm)],[170397880,180352960]),[]).
%
% cnf(180698312,plain,(is_a_theorem(implies(implies(L,F),implies(F,implies(L,F))))),inference(resolution,[status(thm)],[180621544,170402864]),[]).
%
% cnf(180792352,plain,(is_a_theorem(implies(C,implies(implies(implies(A,B),A),implies(B,A))))),inference(resolution,[status(thm)],[178222208,180698312]),[]).
%
% cnf(180905600,plain,(~is_a_theorem(A)|is_a_theorem(implies(implies(implies(B,C),B),implies(C,B)))),inference(resolution,[status(thm)],[170397880,180792352]),[]).
%
% cnf(180999360,plain,(is_a_theorem(implies(implies(implies(A,B),A),implies(B,A)))),inference(resolution,[status(thm)],[180905600,170402864]),[]).
%
% cnf(181030288,plain,(~is_a_theorem(implies(implies(A,B),A))|is_a_theorem(implies(B,A))),inference(resolution,[status(thm)],[170397880,180999360]),[]).
%
% cnf(181131224,plain,(is_a_theorem(implies(A,implies(A,A)))),inference(resolution,[status(thm)],[181030288,180999360]),[]).
%
% cnf(181212960,plain,(~is_a_theorem(implies(implies(B,implies(B,B)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[170397880,181131224]),[]).
%
% cnf(181048664,plain,(~is_a_theorem(implies(implies(implies(implies(B,C),B),implies(C,B)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[170397880,180999360]),[]).
%
% cnf(181178736,plain,(is_a_theorem(implies(G,implies(A,implies(H,A))))),inference(resolution,[status(thm)],[181048664,180239088]),[]).
%
% cnf(181353984,plain,(~is_a_theorem(A)|is_a_theorem(implies(B,implies(H,B)))),inference(resolution,[status(thm)],[170397880,181178736]),[]).
%
% cnf(181394960,plain,(is_a_theorem(implies(A,implies(G,A)))),inference(resolution,[status(thm)],[181353984,181131224]),[]).
%
% cnf(181656216,plain,(is_a_theorem(implies(D,implies(implies(implies(A,B),A),implies(C,A))))),inference(resolution,[status(thm)],[178222208,181394960]),[]).
%
% cnf(184055184,plain,(is_a_theorem(implies(implies(implies(B,C),B),implies(D,B)))),inference(resolution,[status(thm)],[181212960,181656216]),[]).
%
% cnf(184156424,plain,(~is_a_theorem(implies(implies(B,C),B))|is_a_theorem(implies(D,B))),inference(resolution,[status(thm)],[170397880,184055184]),[]).
%
% cnf(184237712,plain,(is_a_theorem(implies(C,implies(B,B)))),inference(resolution,[status(thm)],[184156424,180999360]),[]).
%
% cnf(184320256,plain,(~is_a_theorem(A)|is_a_theorem(implies(C,C))),inference(resolution,[status(thm)],[170397880,184237712]),[]).
%
% cnf(184377672,plain,(is_a_theorem(implies(B,B))),inference(resolution,[status(thm)],[184320256,181131224]),[]).
%
% cnf(184547560,plain,(~is_a_theorem(implies(implies(C,C),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[170397880,184377672]),[]).
%
% cnf(184213840,plain,(is_a_theorem(implies(C,implies(implies(A,implies(A,E)),implies(B,implies(A,E)))))),inference(resolution,[status(thm)],[178222208,184055184]),[]).
%
% cnf(188615912,plain,(is_a_theorem(implies(implies(C,implies(C,F)),implies(D,implies(C,F))))),inference(resolution,[status(thm)],[184547560,184213840]),[]).
%
% cnf(197158640,plain,(~is_a_theorem(implies(C,implies(C,F)))|is_a_theorem(implies(D,implies(C,F)))),inference(resolution,[status(thm)],[170397880,188615912]),[]).
%
% cnf(197295712,plain,(is_a_theorem(implies(C,implies(implies(implies(E,G),E),E)))),inference(resolution,[status(thm)],[197158640,184055184]),[]).
%
% cnf(197811440,plain,(is_a_theorem(implies(implies(implies(F,H),F),F))),inference(resolution,[status(thm)],[184547560,197295712]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[170406920,197811440]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------