%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL484+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art01.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 13:51:18 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 : 37 ( 21 unt; 0 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 64 ( 29 ~; 28 |; 7 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 0 con; 1-2 aty)
% Number of variables : 46 ( 8 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/SystemOnTPTP9001/LCL484+1.p',unknown),
[] ).
cnf(162685520,plain,
( ~ modus_ponens
| ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B))
| is_a_theorem(B) ),
inference(rewrite,[status(thm)],[modus_ponens]),
[] ).
fof(principia_modus_ponens,plain,
modus_ponens,
file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),
[] ).
cnf(163648848,plain,
modus_ponens,
inference(rewrite,[status(thm)],[principia_modus_ponens]),
[] ).
cnf(172141416,plain,
( ~ is_a_theorem(A)
| ~ is_a_theorem(implies(A,B))
| is_a_theorem(B) ),
inference(resolution,[status(thm)],[162685520,163648848]),
[] ).
fof(r3,plain,
! [A,B] :
( ( ~ r3
| is_a_theorem(implies(or(A,B),or(B,A))) )
& ( r3
| ~ is_a_theorem(implies(or(p(A,B),q(A,B)),or(q(A,B),p(A,B)))) ) ),
file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),
[] ).
cnf(163443296,plain,
( ~ r3
| is_a_theorem(implies(or(A,B),or(B,A))) ),
inference(rewrite,[status(thm)],[r3]),
[] ).
fof(principia_r3,plain,
r3,
file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),
[] ).
cnf(163682112,plain,
r3,
inference(rewrite,[status(thm)],[principia_r3]),
[] ).
cnf(172177440,plain,
is_a_theorem(implies(or(A,B),or(B,A))),
inference(resolution,[status(thm)],[163443296,163682112]),
[] ).
cnf(174770056,plain,
( ~ is_a_theorem(or(A,B))
| is_a_theorem(or(B,A)) ),
inference(resolution,[status(thm)],[172141416,172177440]),
[] ).
fof(r2,plain,
! [B,A] :
( ( ~ r2
| is_a_theorem(implies(B,or(A,B))) )
& ( r2
| ~ is_a_theorem(implies(q(A,B),or(p(A,B),q(A,B)))) ) ),
file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),
[] ).
cnf(163412848,plain,
( ~ r2
| is_a_theorem(implies(B,or(A,B))) ),
inference(rewrite,[status(thm)],[r2]),
[] ).
fof(principia_r2,plain,
r2,
file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),
[] ).
cnf(162637936,plain,
r2,
inference(rewrite,[status(thm)],[principia_r2]),
[] ).
cnf(172172976,plain,
is_a_theorem(implies(B,or(A,B))),
inference(resolution,[status(thm)],[163412848,162637936]),
[] ).
cnf(174422976,plain,
( ~ is_a_theorem(A)
| is_a_theorem(or(B,A)) ),
inference(resolution,[status(thm)],[172141416,172172976]),
[] ).
fof(op_implies_or,plain,
! [A,B] :
( ~ op_implies_or
| $equal(or(not(A),B),implies(A,B)) ),
file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),
[] ).
cnf(163583104,plain,
( ~ op_implies_or
| $equal(or(not(A),B),implies(A,B)) ),
inference(rewrite,[status(thm)],[op_implies_or]),
[] ).
fof(principia_op_implies_or,plain,
op_implies_or,
file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),
[] ).
cnf(163612808,plain,
op_implies_or,
inference(rewrite,[status(thm)],[principia_op_implies_or]),
[] ).
cnf(172110088,plain,
$equal(or(not(A),B),implies(A,B)),
inference(resolution,[status(thm)],[163583104,163612808]),
[] ).
cnf(172372008,plain,
is_a_theorem(implies(B,implies(A,B))),
inference(paramodulation,[status(thm)],[172110088,172172976,theory(equality)]),
[] ).
cnf(175885000,plain,
is_a_theorem(or(A,implies(C,implies(B,C)))),
inference(resolution,[status(thm)],[174422976,172372008]),
[] ).
cnf(180597080,plain,
is_a_theorem(or(implies(C,implies(B,C)),A)),
inference(resolution,[status(thm)],[174770056,175885000]),
[] ).
fof(r1,plain,
! [A] :
( ( ~ r1
| is_a_theorem(implies(or(A,A),A)) )
& ( r1
| ~ is_a_theorem(implies(or(p(A),p(A)),p(A))) ) ),
file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),
[] ).
cnf(163386464,plain,
( ~ r1
| is_a_theorem(implies(or(A,A),A)) ),
inference(rewrite,[status(thm)],[r1]),
[] ).
fof(principia_r1,plain,
r1,
file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),
[] ).
cnf(163659992,plain,
r1,
inference(rewrite,[status(thm)],[principia_r1]),
[] ).
cnf(172157336,plain,
is_a_theorem(implies(or(A,A),A)),
inference(resolution,[status(thm)],[163386464,163659992]),
[] ).
cnf(174389264,plain,
( ~ is_a_theorem(or(A,A))
| is_a_theorem(A) ),
inference(resolution,[status(thm)],[172141416,172157336]),
[] ).
fof(implies_1,plain,
! [A,B] :
( ( ~ implies_1
| is_a_theorem(implies(A,implies(B,A))) )
& ( implies_1
| ~ is_a_theorem(implies(x(A,B),implies(y(A,B),x(A,B)))) ) ),
file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),
[] ).
cnf(162793912,plain,
( implies_1
| ~ is_a_theorem(implies(x(A,B),implies(y(A,B),x(A,B)))) ),
inference(rewrite,[status(thm)],[implies_1]),
[] ).
fof(hilbert_implies_1,plain,
~ implies_1,
file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),
[] ).
cnf(163753256,plain,
~ implies_1,
inference(rewrite,[status(thm)],[hilbert_implies_1]),
[] ).
cnf(172231600,plain,
~ is_a_theorem(implies(x(A,B),implies(y(A,B),x(A,B)))),
inference(resolution,[status(thm)],[162793912,163753256]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[180597080,174389264,172231600]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 2 seconds
% START OF PROOF SEQUENCE
% 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/SystemOnTPTP9001/LCL484+1.p',unknown),[]).
%
% cnf(162685520,plain,(~modus_ponens|~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B)),inference(rewrite,[status(thm)],[modus_ponens]),[]).
%
% fof(principia_modus_ponens,plain,(modus_ponens),file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),[]).
%
% cnf(163648848,plain,(modus_ponens),inference(rewrite,[status(thm)],[principia_modus_ponens]),[]).
%
% cnf(172141416,plain,(~is_a_theorem(A)|~is_a_theorem(implies(A,B))|is_a_theorem(B)),inference(resolution,[status(thm)],[162685520,163648848]),[]).
%
% fof(r3,plain,(((~r3|is_a_theorem(implies(or(A,B),or(B,A))))&(r3|~is_a_theorem(implies(or(p(A,B),q(A,B)),or(q(A,B),p(A,B))))))),file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),[]).
%
% cnf(163443296,plain,(~r3|is_a_theorem(implies(or(A,B),or(B,A)))),inference(rewrite,[status(thm)],[r3]),[]).
%
% fof(principia_r3,plain,(r3),file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),[]).
%
% cnf(163682112,plain,(r3),inference(rewrite,[status(thm)],[principia_r3]),[]).
%
% cnf(172177440,plain,(is_a_theorem(implies(or(A,B),or(B,A)))),inference(resolution,[status(thm)],[163443296,163682112]),[]).
%
% cnf(174770056,plain,(~is_a_theorem(or(A,B))|is_a_theorem(or(B,A))),inference(resolution,[status(thm)],[172141416,172177440]),[]).
%
% fof(r2,plain,(((~r2|is_a_theorem(implies(B,or(A,B))))&(r2|~is_a_theorem(implies(q(A,B),or(p(A,B),q(A,B))))))),file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),[]).
%
% cnf(163412848,plain,(~r2|is_a_theorem(implies(B,or(A,B)))),inference(rewrite,[status(thm)],[r2]),[]).
%
% fof(principia_r2,plain,(r2),file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),[]).
%
% cnf(162637936,plain,(r2),inference(rewrite,[status(thm)],[principia_r2]),[]).
%
% cnf(172172976,plain,(is_a_theorem(implies(B,or(A,B)))),inference(resolution,[status(thm)],[163412848,162637936]),[]).
%
% cnf(174422976,plain,(~is_a_theorem(A)|is_a_theorem(or(B,A))),inference(resolution,[status(thm)],[172141416,172172976]),[]).
%
% fof(op_implies_or,plain,(~op_implies_or|$equal(or(not(A),B),implies(A,B))),file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),[]).
%
% cnf(163583104,plain,(~op_implies_or|$equal(or(not(A),B),implies(A,B))),inference(rewrite,[status(thm)],[op_implies_or]),[]).
%
% fof(principia_op_implies_or,plain,(op_implies_or),file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),[]).
%
% cnf(163612808,plain,(op_implies_or),inference(rewrite,[status(thm)],[principia_op_implies_or]),[]).
%
% cnf(172110088,plain,($equal(or(not(A),B),implies(A,B))),inference(resolution,[status(thm)],[163583104,163612808]),[]).
%
% cnf(172372008,plain,(is_a_theorem(implies(B,implies(A,B)))),inference(paramodulation,[status(thm)],[172110088,172172976,theory(equality)]),[]).
%
% cnf(175885000,plain,(is_a_theorem(or(A,implies(C,implies(B,C))))),inference(resolution,[status(thm)],[174422976,172372008]),[]).
%
% cnf(180597080,plain,(is_a_theorem(or(implies(C,implies(B,C)),A))),inference(resolution,[status(thm)],[174770056,175885000]),[]).
%
% fof(r1,plain,(((~r1|is_a_theorem(implies(or(A,A),A)))&(r1|~is_a_theorem(implies(or(p(A),p(A)),p(A)))))),file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),[]).
%
% cnf(163386464,plain,(~r1|is_a_theorem(implies(or(A,A),A))),inference(rewrite,[status(thm)],[r1]),[]).
%
% fof(principia_r1,plain,(r1),file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),[]).
%
% cnf(163659992,plain,(r1),inference(rewrite,[status(thm)],[principia_r1]),[]).
%
% cnf(172157336,plain,(is_a_theorem(implies(or(A,A),A))),inference(resolution,[status(thm)],[163386464,163659992]),[]).
%
% cnf(174389264,plain,(~is_a_theorem(or(A,A))|is_a_theorem(A)),inference(resolution,[status(thm)],[172141416,172157336]),[]).
%
% fof(implies_1,plain,(((~implies_1|is_a_theorem(implies(A,implies(B,A))))&(implies_1|~is_a_theorem(implies(x(A,B),implies(y(A,B),x(A,B))))))),file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),[]).
%
% cnf(162793912,plain,(implies_1|~is_a_theorem(implies(x(A,B),implies(y(A,B),x(A,B))))),inference(rewrite,[status(thm)],[implies_1]),[]).
%
% fof(hilbert_implies_1,plain,(~implies_1),file('/tmp/SystemOnTPTP9001/LCL484+1.p',unknown),[]).
%
% cnf(163753256,plain,(~implies_1),inference(rewrite,[status(thm)],[hilbert_implies_1]),[]).
%
% cnf(172231600,plain,(~is_a_theorem(implies(x(A,B),implies(y(A,B),x(A,B))))),inference(resolution,[status(thm)],[162793912,163753256]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[180597080,174389264,172231600]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------