TSTP Solution File: LCL089-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL089-1 : 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 13:41:49 EDT 2009
% Result : Unsatisfiable 8.7s
% Output : Refutation 8.7s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 3
% Syntax : Number of formulae : 43 ( 26 unt; 0 def)
% Number of atoms : 62 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 19 |; 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 124 ( 44 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_ic_4,plain,
~ is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL089-1.tptp',unknown),
[] ).
cnf(143703688,plain,
~ is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c)))),
inference(rewrite,[status(thm)],[prove_ic_4]),
[] ).
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/LCL089-1.tptp',unknown),
[] ).
cnf(143694552,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/LCL089-1.tptp',unknown),
[] ).
cnf(143699568,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(151522912,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)],[143694552,143699568]),
[] ).
cnf(151542648,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)],[143694552,143699568]),
[] ).
cnf(152473152,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)],[151522912,143699568]),
[] ).
cnf(154590048,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)],[151542648,152473152]),
[] ).
cnf(154607632,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)],[143694552,154590048]),
[] ).
cnf(154703680,plain,
is_a_theorem(implies(F,implies(implies(M,G),implies(G,implies(M,G))))),
inference(resolution,[status(thm)],[154607632,154590048]),
[] ).
cnf(154969792,plain,
( ~ is_a_theorem(A)
| is_a_theorem(implies(implies(M,G),implies(G,implies(M,G)))) ),
inference(resolution,[status(thm)],[143694552,154703680]),
[] ).
cnf(155047776,plain,
is_a_theorem(implies(implies(L,F),implies(F,implies(L,F)))),
inference(resolution,[status(thm)],[154969792,143699568]),
[] ).
cnf(155123064,plain,
is_a_theorem(implies(C,implies(implies(implies(A,B),A),implies(B,A)))),
inference(resolution,[status(thm)],[151522912,155047776]),
[] ).
cnf(155254504,plain,
( ~ is_a_theorem(A)
| is_a_theorem(implies(implies(implies(B,C),B),implies(C,B))) ),
inference(resolution,[status(thm)],[143694552,155123064]),
[] ).
cnf(155349200,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(B,A))),
inference(resolution,[status(thm)],[155254504,143699568]),
[] ).
cnf(155378544,plain,
( ~ is_a_theorem(implies(implies(A,B),A))
| is_a_theorem(implies(B,A)) ),
inference(resolution,[status(thm)],[143694552,155349200]),
[] ).
cnf(155480296,plain,
is_a_theorem(implies(A,implies(A,A))),
inference(resolution,[status(thm)],[155378544,155349200]),
[] ).
cnf(155561208,plain,
( ~ is_a_theorem(implies(implies(B,implies(B,B)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[143694552,155480296]),
[] ).
cnf(155396920,plain,
( ~ is_a_theorem(implies(implies(implies(implies(B,C),B),implies(C,B)),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[143694552,155349200]),
[] ).
cnf(155527800,plain,
is_a_theorem(implies(G,implies(A,implies(H,A)))),
inference(resolution,[status(thm)],[155396920,154590048]),
[] ).
cnf(155702112,plain,
( ~ is_a_theorem(A)
| is_a_theorem(implies(B,implies(H,B))) ),
inference(resolution,[status(thm)],[143694552,155527800]),
[] ).
cnf(155744032,plain,
is_a_theorem(implies(A,implies(G,A))),
inference(resolution,[status(thm)],[155702112,155480296]),
[] ).
cnf(155990192,plain,
is_a_theorem(implies(D,implies(implies(implies(A,B),A),implies(C,A)))),
inference(resolution,[status(thm)],[151522912,155744032]),
[] ).
cnf(158223568,plain,
is_a_theorem(implies(implies(implies(B,C),B),implies(D,B))),
inference(resolution,[status(thm)],[155561208,155990192]),
[] ).
cnf(158325040,plain,
( ~ is_a_theorem(implies(implies(B,C),B))
| is_a_theorem(implies(D,B)) ),
inference(resolution,[status(thm)],[143694552,158223568]),
[] ).
cnf(158407184,plain,
is_a_theorem(implies(C,implies(B,B))),
inference(resolution,[status(thm)],[158325040,155349200]),
[] ).
cnf(158481480,plain,
( ~ is_a_theorem(A)
| is_a_theorem(implies(C,C)) ),
inference(resolution,[status(thm)],[143694552,158407184]),
[] ).
cnf(158539832,plain,
is_a_theorem(implies(B,B)),
inference(resolution,[status(thm)],[158481480,155480296]),
[] ).
cnf(158701528,plain,
( ~ is_a_theorem(implies(implies(C,C),A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[143694552,158539832]),
[] ).
cnf(158364880,plain,
is_a_theorem(implies(C,implies(implies(A,implies(A,E)),implies(B,implies(A,E))))),
inference(resolution,[status(thm)],[151522912,158223568]),
[] ).
cnf(169659096,plain,
is_a_theorem(implies(implies(C,implies(C,F)),implies(D,implies(C,F)))),
inference(resolution,[status(thm)],[158701528,158364880]),
[] ).
cnf(170031088,plain,
( ~ is_a_theorem(implies(C,implies(C,F)))
| is_a_theorem(implies(D,implies(C,F))) ),
inference(resolution,[status(thm)],[143694552,169659096]),
[] ).
cnf(170347992,plain,
is_a_theorem(implies(C,implies(implies(G,implies(G,I)),implies(G,I)))),
inference(resolution,[status(thm)],[170031088,169659096]),
[] ).
cnf(174826576,plain,
is_a_theorem(implies(implies(H,implies(H,J)),implies(H,J))),
inference(resolution,[status(thm)],[158701528,170347992]),
[] ).
cnf(175225688,plain,
( ~ is_a_theorem(implies(H,implies(H,J)))
| is_a_theorem(implies(H,J)) ),
inference(resolution,[status(thm)],[143694552,174826576]),
[] ).
cnf(155768688,plain,
is_a_theorem(implies(D,implies(implies(implies(J,C),A),implies(C,A)))),
inference(resolution,[status(thm)],[151522912,155527800]),
[] ).
cnf(156485232,plain,
is_a_theorem(implies(implies(implies(J,D),B),implies(D,B))),
inference(resolution,[status(thm)],[155561208,155768688]),
[] ).
cnf(156541296,plain,
( ~ is_a_theorem(implies(implies(J,D),B))
| is_a_theorem(implies(D,B)) ),
inference(resolution,[status(thm)],[143694552,156485232]),
[] ).
cnf(156652272,plain,
is_a_theorem(implies(implies(J,K),implies(L,implies(implies(K,H),implies(J,H))))),
inference(resolution,[status(thm)],[156541296,143699568]),
[] ).
cnf(175389968,plain,
is_a_theorem(implies(implies(R,S),implies(implies(S,P),implies(R,P)))),
inference(resolution,[status(thm)],[175225688,156652272]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[143703688,175389968]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 9 seconds
% START OF PROOF SEQUENCE
% fof(prove_ic_4,plain,(~is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL089-1.tptp',unknown),[]).
%
% cnf(143703688,plain,(~is_a_theorem(implies(implies(a,b),implies(implies(b,c),implies(a,c))))),inference(rewrite,[status(thm)],[prove_ic_4]),[]).
%
% 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/LCL089-1.tptp',unknown),[]).
%
% cnf(143694552,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/LCL089-1.tptp',unknown),[]).
%
% cnf(143699568,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(151522912,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)],[143694552,143699568]),[]).
%
% cnf(151542648,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)],[143694552,143699568]),[]).
%
% cnf(152473152,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)],[151522912,143699568]),[]).
%
% cnf(154590048,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)],[151542648,152473152]),[]).
%
% cnf(154607632,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)],[143694552,154590048]),[]).
%
% cnf(154703680,plain,(is_a_theorem(implies(F,implies(implies(M,G),implies(G,implies(M,G)))))),inference(resolution,[status(thm)],[154607632,154590048]),[]).
%
% cnf(154969792,plain,(~is_a_theorem(A)|is_a_theorem(implies(implies(M,G),implies(G,implies(M,G))))),inference(resolution,[status(thm)],[143694552,154703680]),[]).
%
% cnf(155047776,plain,(is_a_theorem(implies(implies(L,F),implies(F,implies(L,F))))),inference(resolution,[status(thm)],[154969792,143699568]),[]).
%
% cnf(155123064,plain,(is_a_theorem(implies(C,implies(implies(implies(A,B),A),implies(B,A))))),inference(resolution,[status(thm)],[151522912,155047776]),[]).
%
% cnf(155254504,plain,(~is_a_theorem(A)|is_a_theorem(implies(implies(implies(B,C),B),implies(C,B)))),inference(resolution,[status(thm)],[143694552,155123064]),[]).
%
% cnf(155349200,plain,(is_a_theorem(implies(implies(implies(A,B),A),implies(B,A)))),inference(resolution,[status(thm)],[155254504,143699568]),[]).
%
% cnf(155378544,plain,(~is_a_theorem(implies(implies(A,B),A))|is_a_theorem(implies(B,A))),inference(resolution,[status(thm)],[143694552,155349200]),[]).
%
% cnf(155480296,plain,(is_a_theorem(implies(A,implies(A,A)))),inference(resolution,[status(thm)],[155378544,155349200]),[]).
%
% cnf(155561208,plain,(~is_a_theorem(implies(implies(B,implies(B,B)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[143694552,155480296]),[]).
%
% cnf(155396920,plain,(~is_a_theorem(implies(implies(implies(implies(B,C),B),implies(C,B)),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[143694552,155349200]),[]).
%
% cnf(155527800,plain,(is_a_theorem(implies(G,implies(A,implies(H,A))))),inference(resolution,[status(thm)],[155396920,154590048]),[]).
%
% cnf(155702112,plain,(~is_a_theorem(A)|is_a_theorem(implies(B,implies(H,B)))),inference(resolution,[status(thm)],[143694552,155527800]),[]).
%
% cnf(155744032,plain,(is_a_theorem(implies(A,implies(G,A)))),inference(resolution,[status(thm)],[155702112,155480296]),[]).
%
% cnf(155990192,plain,(is_a_theorem(implies(D,implies(implies(implies(A,B),A),implies(C,A))))),inference(resolution,[status(thm)],[151522912,155744032]),[]).
%
% cnf(158223568,plain,(is_a_theorem(implies(implies(implies(B,C),B),implies(D,B)))),inference(resolution,[status(thm)],[155561208,155990192]),[]).
%
% cnf(158325040,plain,(~is_a_theorem(implies(implies(B,C),B))|is_a_theorem(implies(D,B))),inference(resolution,[status(thm)],[143694552,158223568]),[]).
%
% cnf(158407184,plain,(is_a_theorem(implies(C,implies(B,B)))),inference(resolution,[status(thm)],[158325040,155349200]),[]).
%
% cnf(158481480,plain,(~is_a_theorem(A)|is_a_theorem(implies(C,C))),inference(resolution,[status(thm)],[143694552,158407184]),[]).
%
% cnf(158539832,plain,(is_a_theorem(implies(B,B))),inference(resolution,[status(thm)],[158481480,155480296]),[]).
%
% cnf(158701528,plain,(~is_a_theorem(implies(implies(C,C),A))|is_a_theorem(A)),inference(resolution,[status(thm)],[143694552,158539832]),[]).
%
% cnf(158364880,plain,(is_a_theorem(implies(C,implies(implies(A,implies(A,E)),implies(B,implies(A,E)))))),inference(resolution,[status(thm)],[151522912,158223568]),[]).
%
% cnf(169659096,plain,(is_a_theorem(implies(implies(C,implies(C,F)),implies(D,implies(C,F))))),inference(resolution,[status(thm)],[158701528,158364880]),[]).
%
% cnf(170031088,plain,(~is_a_theorem(implies(C,implies(C,F)))|is_a_theorem(implies(D,implies(C,F)))),inference(resolution,[status(thm)],[143694552,169659096]),[]).
%
% cnf(170347992,plain,(is_a_theorem(implies(C,implies(implies(G,implies(G,I)),implies(G,I))))),inference(resolution,[status(thm)],[170031088,169659096]),[]).
%
% cnf(174826576,plain,(is_a_theorem(implies(implies(H,implies(H,J)),implies(H,J)))),inference(resolution,[status(thm)],[158701528,170347992]),[]).
%
% cnf(175225688,plain,(~is_a_theorem(implies(H,implies(H,J)))|is_a_theorem(implies(H,J))),inference(resolution,[status(thm)],[143694552,174826576]),[]).
%
% cnf(155768688,plain,(is_a_theorem(implies(D,implies(implies(implies(J,C),A),implies(C,A))))),inference(resolution,[status(thm)],[151522912,155527800]),[]).
%
% cnf(156485232,plain,(is_a_theorem(implies(implies(implies(J,D),B),implies(D,B)))),inference(resolution,[status(thm)],[155561208,155768688]),[]).
%
% cnf(156541296,plain,(~is_a_theorem(implies(implies(J,D),B))|is_a_theorem(implies(D,B))),inference(resolution,[status(thm)],[143694552,156485232]),[]).
%
% cnf(156652272,plain,(is_a_theorem(implies(implies(J,K),implies(L,implies(implies(K,H),implies(J,H)))))),inference(resolution,[status(thm)],[156541296,143699568]),[]).
%
% cnf(175389968,plain,(is_a_theorem(implies(implies(R,S),implies(implies(S,P),implies(R,P))))),inference(resolution,[status(thm)],[175225688,156652272]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[143703688,175389968]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------