TSTP Solution File: LCL538+1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL538+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art02.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 13:52:22 EDT 2009
% Result : Theorem 11.3s
% Output : Refutation 11.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 16 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 56 ( 23 ~; 26 |; 7 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 0 con; 1-2 aty)
% Number of variables : 34 ( 8 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(modus_ponens_strict_implies,plain,
! [A,B] :
( ( ~ modus_ponens_strict_implies
| ~ is_a_theorem(A)
| ~ is_a_theorem(strict_implies(A,B))
| is_a_theorem(B) )
& ( ~ is_a_theorem(y(A,B))
| modus_ponens_strict_implies )
& ( is_a_theorem(x(A,B))
| modus_ponens_strict_implies )
& ( is_a_theorem(strict_implies(x(A,B),y(A,B)))
| modus_ponens_strict_implies ) ),
file('/tmp/SystemOnTPTP10158/LCL538+1.p',unknown),
[] ).
cnf(177677656,plain,
( ~ is_a_theorem(y(A,B))
| modus_ponens_strict_implies ),
inference(rewrite,[status(thm)],[modus_ponens_strict_implies]),
[] ).
fof(s1_0_modus_ponens_strict_implies,plain,
~ modus_ponens_strict_implies,
file('/tmp/SystemOnTPTP10158/LCL538+1.p',unknown),
[] ).
cnf(178882984,plain,
~ modus_ponens_strict_implies,
inference(rewrite,[status(thm)],[s1_0_modus_ponens_strict_implies]),
[] ).
cnf(188074936,plain,
~ is_a_theorem(y(A,B)),
inference(resolution,[status(thm)],[177677656,178882984]),
[] ).
cnf(177665272,plain,
( is_a_theorem(x(A,B))
| modus_ponens_strict_implies ),
inference(rewrite,[status(thm)],[modus_ponens_strict_implies]),
[] ).
cnf(188063344,plain,
is_a_theorem(x(A,B)),
inference(resolution,[status(thm)],[177665272,178882984]),
[] ).
fof(axiom_M,plain,
! [A] :
( ( ~ axiom_m
| is_a_theorem(implies(necessarily(A),A)) )
& ( axiom_m
| ~ is_a_theorem(implies(necessarily(x(A)),x(A))) ) ),
file('/tmp/SystemOnTPTP10158/LCL538+1.p',unknown),
[] ).
cnf(177914232,plain,
( ~ axiom_m
| is_a_theorem(implies(necessarily(A),A)) ),
inference(rewrite,[status(thm)],[axiom_M]),
[] ).
fof(km4b_axiom_M,plain,
axiom_m,
file('/tmp/SystemOnTPTP10158/LCL538+1.p',unknown),
[] ).
cnf(178775000,plain,
axiom_m,
inference(rewrite,[status(thm)],[km4b_axiom_M]),
[] ).
cnf(188005464,plain,
is_a_theorem(implies(necessarily(A),A)),
inference(resolution,[status(thm)],[177914232,178775000]),
[] ).
fof(modus_ponens,plain,
! [A,B] :
( ( ~ modus_ponens
| ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B))
| is_a_theorem(B) )
& ( ~ is_a_theorem(y(A,B))
| modus_ponens )
& ( is_a_theorem(x(A,B))
| modus_ponens )
& ( is_a_theorem(implies(x(A,B),y(A,B)))
| modus_ponens ) ),
file('/tmp/SystemOnTPTP10158/LCL538+1.p',unknown),
[] ).
cnf(176067304,plain,
( ~ modus_ponens
| ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B))
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[modus_ponens]),
[] ).
fof(hilbert_modus_ponens,plain,
modus_ponens,
file('/tmp/SystemOnTPTP10158/LCL538+1.p',unknown),
[] ).
cnf(177330192,plain,
modus_ponens,
inference(rewrite,[status(thm)],[hilbert_modus_ponens]),
[] ).
cnf(187777272,plain,
( ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B))
| is_a_theorem(B) ),
inference(resolution,[status(thm)],[176067304,177330192]),
[] ).
cnf(198590888,plain,
( ~ is_a_theorem(necessarily(A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[188005464,187777272]),
[] ).
cnf(177645640,plain,
( is_a_theorem(strict_implies(x(A,B),y(A,B)))
| modus_ponens_strict_implies ),
inference(rewrite,[status(thm)],[modus_ponens_strict_implies]),
[] ).
cnf(188087664,plain,
is_a_theorem(strict_implies(x(A,B),y(A,B))),
inference(resolution,[status(thm)],[177645640,178882984]),
[] ).
fof(op_strict_implies,plain,
! [A,B] :
( ~ op_strict_implies
| $equal(necessarily(implies(A,B)),strict_implies(A,B)) ),
file('/tmp/SystemOnTPTP10158/LCL538+1.p',unknown),
[] ).
cnf(178686432,plain,
( ~ op_strict_implies
| $equal(necessarily(implies(A,B)),strict_implies(A,B)) ),
inference(rewrite,[status(thm)],[op_strict_implies]),
[] ).
fof(s1_0_op_strict_implies,plain,
op_strict_implies,
file('/tmp/SystemOnTPTP10158/LCL538+1.p',unknown),
[] ).
cnf(178847872,plain,
op_strict_implies,
inference(rewrite,[status(thm)],[s1_0_op_strict_implies]),
[] ).
cnf(188040288,plain,
$equal(necessarily(implies(A,B)),strict_implies(A,B)),
inference(resolution,[status(thm)],[178686432,178847872]),
[] ).
cnf(190814240,plain,
is_a_theorem(necessarily(implies(x(A,B),y(A,B)))),
inference(paramodulation,[status(thm)],[188087664,188040288,theory(equality)]),
[] ).
cnf(221831168,plain,
is_a_theorem(implies(x(A,B),y(A,B))),
inference(resolution,[status(thm)],[198590888,190814240]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[188074936,188063344,221831168,187777272]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 12 seconds
% START OF PROOF SEQUENCE
% fof(modus_ponens_strict_implies,plain,(((~modus_ponens_strict_implies|~is_a_theorem(A)|~is_a_theorem(strict_implies(A,B))|is_a_theorem(B))&(~is_a_theorem(y(A,B))|modus_ponens_strict_implies)&(is_a_theorem(x(A,B))|modus_ponens_strict_implies)&(is_a_theorem(strict_implies(x(A,B),y(A,B)))|modus_ponens_strict_implies))),file('/tmp/SystemOnTPTP10158/LCL538+1.p',unknown),[]).
%
% cnf(177677656,plain,(~is_a_theorem(y(A,B))|modus_ponens_strict_implies),inference(rewrite,[status(thm)],[modus_ponens_strict_implies]),[]).
%
% fof(s1_0_modus_ponens_strict_implies,plain,(~modus_ponens_strict_implies),file('/tmp/SystemOnTPTP10158/LCL538+1.p',unknown),[]).
%
% cnf(178882984,plain,(~modus_ponens_strict_implies),inference(rewrite,[status(thm)],[s1_0_modus_ponens_strict_implies]),[]).
%
% cnf(188074936,plain,(~is_a_theorem(y(A,B))),inference(resolution,[status(thm)],[177677656,178882984]),[]).
%
% cnf(177665272,plain,(is_a_theorem(x(A,B))|modus_ponens_strict_implies),inference(rewrite,[status(thm)],[modus_ponens_strict_implies]),[]).
%
% cnf(188063344,plain,(is_a_theorem(x(A,B))),inference(resolution,[status(thm)],[177665272,178882984]),[]).
%
% fof(axiom_M,plain,(((~axiom_m|is_a_theorem(implies(necessarily(A),A)))&(axiom_m|~is_a_theorem(implies(necessarily(x(A)),x(A)))))),file('/tmp/SystemOnTPTP10158/LCL538+1.p',unknown),[]).
%
% cnf(177914232,plain,(~axiom_m|is_a_theorem(implies(necessarily(A),A))),inference(rewrite,[status(thm)],[axiom_M]),[]).
%
% fof(km4b_axiom_M,plain,(axiom_m),file('/tmp/SystemOnTPTP10158/LCL538+1.p',unknown),[]).
%
% cnf(178775000,plain,(axiom_m),inference(rewrite,[status(thm)],[km4b_axiom_M]),[]).
%
% cnf(188005464,plain,(is_a_theorem(implies(necessarily(A),A))),inference(resolution,[status(thm)],[177914232,178775000]),[]).
%
% fof(modus_ponens,plain,(((~modus_ponens|~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B))&(~is_a_theorem(y(A,B))|modus_ponens)&(is_a_theorem(x(A,B))|modus_ponens)&(is_a_theorem(implies(x(A,B),y(A,B)))|modus_ponens))),file('/tmp/SystemOnTPTP10158/LCL538+1.p',unknown),[]).
%
% cnf(176067304,plain,(~modus_ponens|~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B)),inference(rewrite,[status(thm)],[modus_ponens]),[]).
%
% fof(hilbert_modus_ponens,plain,(modus_ponens),file('/tmp/SystemOnTPTP10158/LCL538+1.p',unknown),[]).
%
% cnf(177330192,plain,(modus_ponens),inference(rewrite,[status(thm)],[hilbert_modus_ponens]),[]).
%
% cnf(187777272,plain,(~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B)),inference(resolution,[status(thm)],[176067304,177330192]),[]).
%
% cnf(198590888,plain,(~is_a_theorem(necessarily(A))|is_a_theorem(A)),inference(resolution,[status(thm)],[188005464,187777272]),[]).
%
% cnf(177645640,plain,(is_a_theorem(strict_implies(x(A,B),y(A,B)))|modus_ponens_strict_implies),inference(rewrite,[status(thm)],[modus_ponens_strict_implies]),[]).
%
% cnf(188087664,plain,(is_a_theorem(strict_implies(x(A,B),y(A,B)))),inference(resolution,[status(thm)],[177645640,178882984]),[]).
%
% fof(op_strict_implies,plain,(~op_strict_implies|$equal(necessarily(implies(A,B)),strict_implies(A,B))),file('/tmp/SystemOnTPTP10158/LCL538+1.p',unknown),[]).
%
% cnf(178686432,plain,(~op_strict_implies|$equal(necessarily(implies(A,B)),strict_implies(A,B))),inference(rewrite,[status(thm)],[op_strict_implies]),[]).
%
% fof(s1_0_op_strict_implies,plain,(op_strict_implies),file('/tmp/SystemOnTPTP10158/LCL538+1.p',unknown),[]).
%
% cnf(178847872,plain,(op_strict_implies),inference(rewrite,[status(thm)],[s1_0_op_strict_implies]),[]).
%
% cnf(188040288,plain,($equal(necessarily(implies(A,B)),strict_implies(A,B))),inference(resolution,[status(thm)],[178686432,178847872]),[]).
%
% cnf(190814240,plain,(is_a_theorem(necessarily(implies(x(A,B),y(A,B))))),inference(paramodulation,[status(thm)],[188087664,188040288,theory(equality)]),[]).
%
% cnf(221831168,plain,(is_a_theorem(implies(x(A,B),y(A,B)))),inference(resolution,[status(thm)],[198590888,190814240]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[188074936,188063344,221831168,187777272]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------