TSTP Solution File: LCL536+1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL536+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.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 13:52:19 EDT 2009
% Result : Theorem 2.5s
% Output : Refutation 2.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 35 ( 20 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 68 ( 30 ~; 30 |; 8 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 0 con; 1-2 aty)
% Number of variables : 28 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(axiom_5,plain,
! [A] :
( ( ~ axiom_5
| is_a_theorem(implies(possibly(A),necessarily(possibly(A)))) )
& ( axiom_5
| ~ is_a_theorem(implies(possibly(x(A)),necessarily(possibly(x(A))))) ) ),
file('/tmp/SystemOnTPTP12038/LCL536+1.p',unknown),
[] ).
cnf(164020096,plain,
( ~ axiom_5
| is_a_theorem(implies(possibly(A),necessarily(possibly(A)))) ),
inference(rewrite,[status(thm)],[axiom_5]),
[] ).
fof(km5_axiom_5,plain,
axiom_5,
file('/tmp/SystemOnTPTP12038/LCL536+1.p',unknown),
[] ).
cnf(164771976,plain,
axiom_5,
inference(rewrite,[status(thm)],[km5_axiom_5]),
[] ).
cnf(173978608,plain,
is_a_theorem(implies(possibly(A),necessarily(possibly(A)))),
inference(resolution,[status(thm)],[164020096,164771976]),
[] ).
fof(necessitation,plain,
! [A] :
( ( ~ necessitation
| ~ is_a_theorem(A)
| is_a_theorem(necessarily(A)) )
& ( ~ is_a_theorem(necessarily(x(A)))
| necessitation )
& ( is_a_theorem(x(A))
| necessitation ) ),
file('/tmp/SystemOnTPTP12038/LCL536+1.p',unknown),
[] ).
cnf(163605072,plain,
( ~ necessitation
| ~ is_a_theorem(A)
| is_a_theorem(necessarily(A)) ),
inference(rewrite,[status(thm)],[necessitation]),
[] ).
fof(km5_necessitation,plain,
necessitation,
file('/tmp/SystemOnTPTP12038/LCL536+1.p',unknown),
[] ).
cnf(164718544,plain,
necessitation,
inference(rewrite,[status(thm)],[km5_necessitation]),
[] ).
cnf(173936720,plain,
( ~ is_a_theorem(A)
| is_a_theorem(necessarily(A)) ),
inference(resolution,[status(thm)],[163605072,164718544]),
[] ).
cnf(176065856,plain,
is_a_theorem(necessarily(implies(possibly(A),necessarily(possibly(A))))),
inference(resolution,[status(thm)],[173978608,173936720]),
[] ).
fof(op_strict_implies,plain,
! [A,B] :
( ~ op_strict_implies
| $equal(necessarily(implies(A,B)),strict_implies(A,B)) ),
file('/tmp/SystemOnTPTP12038/LCL536+1.p',unknown),
[] ).
cnf(164665552,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/SystemOnTPTP12038/LCL536+1.p',unknown),
[] ).
cnf(164809144,plain,
op_strict_implies,
inference(rewrite,[status(thm)],[s1_0_op_strict_implies]),
[] ).
cnf(173990072,plain,
$equal(necessarily(implies(A,B)),strict_implies(A,B)),
inference(resolution,[status(thm)],[164665552,164809144]),
[] ).
cnf(177895496,plain,
is_a_theorem(strict_implies(possibly(A),necessarily(possibly(A)))),
inference(paramodulation,[status(thm)],[176065856,173990072,theory(equality)]),
[] ).
cnf(177917648,plain,
is_a_theorem(necessarily(strict_implies(possibly(A),necessarily(possibly(A))))),
inference(resolution,[status(thm)],[177895496,173936720]),
[] ).
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/SystemOnTPTP12038/LCL536+1.p',unknown),
[] ).
cnf(163893352,plain,
( ~ axiom_m
| is_a_theorem(implies(necessarily(A),A)) ),
inference(rewrite,[status(thm)],[axiom_M]),
[] ).
fof(km5_axiom_M,plain,
axiom_m,
file('/tmp/SystemOnTPTP12038/LCL536+1.p',unknown),
[] ).
cnf(164754120,plain,
axiom_m,
inference(rewrite,[status(thm)],[km5_axiom_M]),
[] ).
cnf(173966896,plain,
is_a_theorem(implies(necessarily(A),A)),
inference(resolution,[status(thm)],[163893352,164754120]),
[] ).
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/SystemOnTPTP12038/LCL536+1.p',unknown),
[] ).
cnf(162046424,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/SystemOnTPTP12038/LCL536+1.p',unknown),
[] ).
cnf(163309312,plain,
modus_ponens,
inference(rewrite,[status(thm)],[hilbert_modus_ponens]),
[] ).
cnf(173738632,plain,
( ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B))
| is_a_theorem(B) ),
inference(resolution,[status(thm)],[162046424,163309312]),
[] ).
cnf(185601072,plain,
( ~ is_a_theorem(necessarily(A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[173966896,173738632]),
[] ).
fof(axiom_m10,plain,
! [A] :
( ( ~ axiom_m10
| is_a_theorem(strict_implies(possibly(A),necessarily(possibly(A)))) )
& ( axiom_m10
| ~ is_a_theorem(strict_implies(possibly(x(A)),necessarily(possibly(x(A))))) ) ),
file('/tmp/SystemOnTPTP12038/LCL536+1.p',unknown),
[] ).
cnf(164584312,plain,
( axiom_m10
| ~ is_a_theorem(strict_implies(possibly(x(A)),necessarily(possibly(x(A))))) ),
inference(rewrite,[status(thm)],[axiom_m10]),
[] ).
fof(s1_0_m10_axiom_m10,plain,
~ axiom_m10,
file('/tmp/SystemOnTPTP12038/LCL536+1.p',unknown),
[] ).
cnf(164844184,plain,
~ axiom_m10,
inference(rewrite,[status(thm)],[s1_0_m10_axiom_m10]),
[] ).
cnf(174013328,plain,
~ is_a_theorem(strict_implies(possibly(x(A)),necessarily(possibly(x(A))))),
inference(resolution,[status(thm)],[164584312,164844184]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[177917648,185601072,174013328]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 seconds
% START OF PROOF SEQUENCE
% fof(axiom_5,plain,(((~axiom_5|is_a_theorem(implies(possibly(A),necessarily(possibly(A)))))&(axiom_5|~is_a_theorem(implies(possibly(x(A)),necessarily(possibly(x(A)))))))),file('/tmp/SystemOnTPTP12038/LCL536+1.p',unknown),[]).
%
% cnf(164020096,plain,(~axiom_5|is_a_theorem(implies(possibly(A),necessarily(possibly(A))))),inference(rewrite,[status(thm)],[axiom_5]),[]).
%
% fof(km5_axiom_5,plain,(axiom_5),file('/tmp/SystemOnTPTP12038/LCL536+1.p',unknown),[]).
%
% cnf(164771976,plain,(axiom_5),inference(rewrite,[status(thm)],[km5_axiom_5]),[]).
%
% cnf(173978608,plain,(is_a_theorem(implies(possibly(A),necessarily(possibly(A))))),inference(resolution,[status(thm)],[164020096,164771976]),[]).
%
% fof(necessitation,plain,(((~necessitation|~is_a_theorem(A)|is_a_theorem(necessarily(A)))&(~is_a_theorem(necessarily(x(A)))|necessitation)&(is_a_theorem(x(A))|necessitation))),file('/tmp/SystemOnTPTP12038/LCL536+1.p',unknown),[]).
%
% cnf(163605072,plain,(~necessitation|~is_a_theorem(A)|is_a_theorem(necessarily(A))),inference(rewrite,[status(thm)],[necessitation]),[]).
%
% fof(km5_necessitation,plain,(necessitation),file('/tmp/SystemOnTPTP12038/LCL536+1.p',unknown),[]).
%
% cnf(164718544,plain,(necessitation),inference(rewrite,[status(thm)],[km5_necessitation]),[]).
%
% cnf(173936720,plain,(~is_a_theorem(A)|is_a_theorem(necessarily(A))),inference(resolution,[status(thm)],[163605072,164718544]),[]).
%
% cnf(176065856,plain,(is_a_theorem(necessarily(implies(possibly(A),necessarily(possibly(A)))))),inference(resolution,[status(thm)],[173978608,173936720]),[]).
%
% fof(op_strict_implies,plain,(~op_strict_implies|$equal(necessarily(implies(A,B)),strict_implies(A,B))),file('/tmp/SystemOnTPTP12038/LCL536+1.p',unknown),[]).
%
% cnf(164665552,plain,(~op_strict_implies|$equal(necessarily(implies(A,B)),strict_implies(A,B))),inference(rewrite,[status(thm)],[op_strict_implies]),[]).
%
% fof(s1_0_op_strict_implies,plain,(op_strict_implies),file('/tmp/SystemOnTPTP12038/LCL536+1.p',unknown),[]).
%
% cnf(164809144,plain,(op_strict_implies),inference(rewrite,[status(thm)],[s1_0_op_strict_implies]),[]).
%
% cnf(173990072,plain,($equal(necessarily(implies(A,B)),strict_implies(A,B))),inference(resolution,[status(thm)],[164665552,164809144]),[]).
%
% cnf(177895496,plain,(is_a_theorem(strict_implies(possibly(A),necessarily(possibly(A))))),inference(paramodulation,[status(thm)],[176065856,173990072,theory(equality)]),[]).
%
% cnf(177917648,plain,(is_a_theorem(necessarily(strict_implies(possibly(A),necessarily(possibly(A)))))),inference(resolution,[status(thm)],[177895496,173936720]),[]).
%
% 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/SystemOnTPTP12038/LCL536+1.p',unknown),[]).
%
% cnf(163893352,plain,(~axiom_m|is_a_theorem(implies(necessarily(A),A))),inference(rewrite,[status(thm)],[axiom_M]),[]).
%
% fof(km5_axiom_M,plain,(axiom_m),file('/tmp/SystemOnTPTP12038/LCL536+1.p',unknown),[]).
%
% cnf(164754120,plain,(axiom_m),inference(rewrite,[status(thm)],[km5_axiom_M]),[]).
%
% cnf(173966896,plain,(is_a_theorem(implies(necessarily(A),A))),inference(resolution,[status(thm)],[163893352,164754120]),[]).
%
% 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/SystemOnTPTP12038/LCL536+1.p',unknown),[]).
%
% cnf(162046424,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/SystemOnTPTP12038/LCL536+1.p',unknown),[]).
%
% cnf(163309312,plain,(modus_ponens),inference(rewrite,[status(thm)],[hilbert_modus_ponens]),[]).
%
% cnf(173738632,plain,(~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B)),inference(resolution,[status(thm)],[162046424,163309312]),[]).
%
% cnf(185601072,plain,(~is_a_theorem(necessarily(A))|is_a_theorem(A)),inference(resolution,[status(thm)],[173966896,173738632]),[]).
%
% fof(axiom_m10,plain,(((~axiom_m10|is_a_theorem(strict_implies(possibly(A),necessarily(possibly(A)))))&(axiom_m10|~is_a_theorem(strict_implies(possibly(x(A)),necessarily(possibly(x(A)))))))),file('/tmp/SystemOnTPTP12038/LCL536+1.p',unknown),[]).
%
% cnf(164584312,plain,(axiom_m10|~is_a_theorem(strict_implies(possibly(x(A)),necessarily(possibly(x(A)))))),inference(rewrite,[status(thm)],[axiom_m10]),[]).
%
% fof(s1_0_m10_axiom_m10,plain,(~axiom_m10),file('/tmp/SystemOnTPTP12038/LCL536+1.p',unknown),[]).
%
% cnf(164844184,plain,(~axiom_m10),inference(rewrite,[status(thm)],[s1_0_m10_axiom_m10]),[]).
%
% cnf(174013328,plain,(~is_a_theorem(strict_implies(possibly(x(A)),necessarily(possibly(x(A)))))),inference(resolution,[status(thm)],[164584312,164844184]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[177917648,185601072,174013328]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------