TSTP Solution File: COL066-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : COL066-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art03.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.11-1.1369_FC4
% CPULimit : 600s
% DateTime : Wed May 6 11:33:50 EDT 2009
% Result : Unsatisfiable 80.0s
% Output : Refutation 80.0s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 18 unt; 0 def)
% Number of atoms : 18 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 11 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_p_combinator,plain,
! [A] : ~ $equal(apply(apply(f(A),g(A)),apply(apply(f(A),g(A)),h(A))),apply(apply(apply(apply(A,f(A)),g(A)),g(A)),h(A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL066-1.tptp',unknown),
[] ).
cnf(154996624,plain,
~ $equal(apply(apply(f(A),g(A)),apply(apply(f(A),g(A)),h(A))),apply(apply(apply(apply(A,f(A)),g(A)),g(A)),h(A))),
inference(rewrite,[status(thm)],[prove_p_combinator]),
[] ).
fof(w_definition,plain,
! [A,B] : $equal(apply(apply(w,A),B),apply(apply(A,B),B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL066-1.tptp',unknown),
[] ).
cnf(154987464,plain,
$equal(apply(apply(w,A),B),apply(apply(A,B),B)),
inference(rewrite,[status(thm)],[w_definition]),
[] ).
cnf(162930536,plain,
~ $equal(apply(apply(f(A),g(A)),apply(apply(f(A),g(A)),h(A))),apply(apply(apply(w,apply(A,f(A))),g(A)),h(A))),
inference(paramodulation,[status(thm)],[154996624,154987464,theory(equality)]),
[] ).
fof(b_definition,plain,
! [A,B,C] : $equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL066-1.tptp',unknown),
[] ).
cnf(154979128,plain,
$equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C))),
inference(rewrite,[status(thm)],[b_definition]),
[] ).
cnf(163566256,plain,
~ $equal(apply(apply(apply(b,apply(f(A),g(A))),apply(f(A),g(A))),h(A)),apply(apply(apply(w,apply(A,f(A))),g(A)),h(A))),
inference(paramodulation,[status(thm)],[162930536,154979128,theory(equality)]),
[] ).
fof(q_definition,plain,
! [A,B,C] : $equal(apply(apply(apply(q,A),B),C),apply(B,apply(A,C))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL066-1.tptp',unknown),
[] ).
cnf(154983376,plain,
$equal(apply(apply(apply(q,A),B),C),apply(B,apply(A,C))),
inference(rewrite,[status(thm)],[q_definition]),
[] ).
cnf(165763200,plain,
~ $equal(apply(apply(apply(apply(q,f(A)),apply(b,apply(f(A),g(A)))),g(A)),h(A)),apply(apply(apply(w,apply(A,f(A))),g(A)),h(A))),
inference(paramodulation,[status(thm)],[163566256,154983376,theory(equality)]),
[] ).
cnf(174067312,plain,
~ $equal(apply(apply(apply(apply(apply(q,b),apply(q,f(A))),apply(f(A),g(A))),g(A)),h(A)),apply(apply(apply(w,apply(A,f(A))),g(A)),h(A))),
inference(paramodulation,[status(thm)],[165763200,154983376,theory(equality)]),
[] ).
cnf(200551712,plain,
~ $equal(apply(apply(apply(apply(apply(q,f(A)),apply(apply(q,b),apply(q,f(A)))),g(A)),g(A)),h(A)),apply(apply(apply(w,apply(A,f(A))),g(A)),h(A))),
inference(paramodulation,[status(thm)],[174067312,154983376,theory(equality)]),
[] ).
cnf(275110512,plain,
~ $equal(apply(apply(apply(w,apply(apply(q,f(A)),apply(apply(q,b),apply(q,f(A))))),g(A)),h(A)),apply(apply(apply(w,apply(A,f(A))),g(A)),h(A))),
inference(paramodulation,[status(thm)],[200551712,154987464,theory(equality)]),
[] ).
cnf(351761936,plain,
~ $equal(apply(apply(apply(w,apply(apply(apply(q,apply(q,b)),apply(q,f(A))),apply(q,f(A)))),g(A)),h(A)),apply(apply(apply(w,apply(A,f(A))),g(A)),h(A))),
inference(paramodulation,[status(thm)],[275110512,154983376,theory(equality)]),
[] ).
cnf(578391472,plain,
~ $equal(apply(apply(apply(w,apply(apply(w,apply(q,apply(q,b))),apply(q,f(A)))),g(A)),h(A)),apply(apply(apply(w,apply(A,f(A))),g(A)),h(A))),
inference(paramodulation,[status(thm)],[351761936,154987464,theory(equality)]),
[] ).
cnf(578906656,plain,
~ $equal(apply(apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,b)))),q),f(A))),g(A)),h(A)),apply(apply(apply(w,apply(A,f(A))),g(A)),h(A))),
inference(paramodulation,[status(thm)],[578391472,154979128,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(equality_resolution,[status(thm)],[578906656]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 79 seconds
% START OF PROOF SEQUENCE
% fof(prove_p_combinator,plain,(~$equal(apply(apply(f(A),g(A)),apply(apply(f(A),g(A)),h(A))),apply(apply(apply(apply(A,f(A)),g(A)),g(A)),h(A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL066-1.tptp',unknown),[]).
%
% cnf(154996624,plain,(~$equal(apply(apply(f(A),g(A)),apply(apply(f(A),g(A)),h(A))),apply(apply(apply(apply(A,f(A)),g(A)),g(A)),h(A)))),inference(rewrite,[status(thm)],[prove_p_combinator]),[]).
%
% fof(w_definition,plain,($equal(apply(apply(w,A),B),apply(apply(A,B),B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL066-1.tptp',unknown),[]).
%
% cnf(154987464,plain,($equal(apply(apply(w,A),B),apply(apply(A,B),B))),inference(rewrite,[status(thm)],[w_definition]),[]).
%
% cnf(162930536,plain,(~$equal(apply(apply(f(A),g(A)),apply(apply(f(A),g(A)),h(A))),apply(apply(apply(w,apply(A,f(A))),g(A)),h(A)))),inference(paramodulation,[status(thm)],[154996624,154987464,theory(equality)]),[]).
%
% fof(b_definition,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL066-1.tptp',unknown),[]).
%
% cnf(154979128,plain,($equal(apply(apply(apply(b,A),B),C),apply(A,apply(B,C)))),inference(rewrite,[status(thm)],[b_definition]),[]).
%
% cnf(163566256,plain,(~$equal(apply(apply(apply(b,apply(f(A),g(A))),apply(f(A),g(A))),h(A)),apply(apply(apply(w,apply(A,f(A))),g(A)),h(A)))),inference(paramodulation,[status(thm)],[162930536,154979128,theory(equality)]),[]).
%
% fof(q_definition,plain,($equal(apply(apply(apply(q,A),B),C),apply(B,apply(A,C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/COL/COL066-1.tptp',unknown),[]).
%
% cnf(154983376,plain,($equal(apply(apply(apply(q,A),B),C),apply(B,apply(A,C)))),inference(rewrite,[status(thm)],[q_definition]),[]).
%
% cnf(165763200,plain,(~$equal(apply(apply(apply(apply(q,f(A)),apply(b,apply(f(A),g(A)))),g(A)),h(A)),apply(apply(apply(w,apply(A,f(A))),g(A)),h(A)))),inference(paramodulation,[status(thm)],[163566256,154983376,theory(equality)]),[]).
%
% cnf(174067312,plain,(~$equal(apply(apply(apply(apply(apply(q,b),apply(q,f(A))),apply(f(A),g(A))),g(A)),h(A)),apply(apply(apply(w,apply(A,f(A))),g(A)),h(A)))),inference(paramodulation,[status(thm)],[165763200,154983376,theory(equality)]),[]).
%
% cnf(200551712,plain,(~$equal(apply(apply(apply(apply(apply(q,f(A)),apply(apply(q,b),apply(q,f(A)))),g(A)),g(A)),h(A)),apply(apply(apply(w,apply(A,f(A))),g(A)),h(A)))),inference(paramodulation,[status(thm)],[174067312,154983376,theory(equality)]),[]).
%
% cnf(275110512,plain,(~$equal(apply(apply(apply(w,apply(apply(q,f(A)),apply(apply(q,b),apply(q,f(A))))),g(A)),h(A)),apply(apply(apply(w,apply(A,f(A))),g(A)),h(A)))),inference(paramodulation,[status(thm)],[200551712,154987464,theory(equality)]),[]).
%
% cnf(351761936,plain,(~$equal(apply(apply(apply(w,apply(apply(apply(q,apply(q,b)),apply(q,f(A))),apply(q,f(A)))),g(A)),h(A)),apply(apply(apply(w,apply(A,f(A))),g(A)),h(A)))),inference(paramodulation,[status(thm)],[275110512,154983376,theory(equality)]),[]).
%
% cnf(578391472,plain,(~$equal(apply(apply(apply(w,apply(apply(w,apply(q,apply(q,b))),apply(q,f(A)))),g(A)),h(A)),apply(apply(apply(w,apply(A,f(A))),g(A)),h(A)))),inference(paramodulation,[status(thm)],[351761936,154987464,theory(equality)]),[]).
%
% cnf(578906656,plain,(~$equal(apply(apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,b)))),q),f(A))),g(A)),h(A)),apply(apply(apply(w,apply(A,f(A))),g(A)),h(A)))),inference(paramodulation,[status(thm)],[578391472,154979128,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(equality_resolution,[status(thm)],[578906656]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------