TSTP Solution File: LCL236-3 by Faust---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : LCL236-3 : TPTP v3.4.2. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art09.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 13:47:09 EDT 2009
% Result : Unsatisfiable 89.8s
% Output : Refutation 89.8s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 29 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 70 ( 13 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(rule_2,plain,
! [A,B] :
( theorem(A)
| ~ theorem(implies(B,A))
| ~ theorem(B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL236-3.tptp',unknown),
[] ).
cnf(173792240,plain,
( theorem(A)
| ~ theorem(implies(B,A))
| ~ theorem(B) ),
inference(rewrite,[status(thm)],[rule_2]),
[] ).
fof(rule_1,plain,
! [A] :
( theorem(A)
| ~ axiom(A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL236-3.tptp',unknown),
[] ).
cnf(173773360,plain,
( theorem(A)
| ~ axiom(A) ),
inference(rewrite,[status(thm)],[rule_1]),
[] ).
fof(axiom_1_3,plain,
! [A,B] : axiom(implies(A,or(B,A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL236-3.tptp',unknown),
[] ).
cnf(173746360,plain,
axiom(implies(A,or(B,A))),
inference(rewrite,[status(thm)],[axiom_1_3]),
[] ).
cnf(181615112,plain,
theorem(implies(A,or(B,A))),
inference(resolution,[status(thm)],[173773360,173746360]),
[] ).
fof(implies_definition,plain,
! [A,B] : $equal(or(not(A),B),implies(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL236-3.tptp',unknown),
[] ).
cnf(173766840,plain,
$equal(or(not(A),B),implies(A,B)),
inference(rewrite,[status(thm)],[implies_definition]),
[] ).
cnf(181899304,plain,
theorem(or(not(A),or(B,A))),
inference(paramodulation,[status(thm)],[181615112,173766840,theory(equality)]),
[] ).
cnf(182229480,plain,
( theorem(A)
| ~ theorem(implies(or(not(B),or(C,B)),A)) ),
inference(resolution,[status(thm)],[173792240,181899304]),
[] ).
fof(axiom_1_5,plain,
! [A,B,C] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL236-3.tptp',unknown),
[] ).
cnf(173754144,plain,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(rewrite,[status(thm)],[axiom_1_5]),
[] ).
cnf(181831144,plain,
theorem(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(resolution,[status(thm)],[173773360,173754144]),
[] ).
cnf(233911664,plain,
theorem(or(B,or(not(A),A))),
inference(resolution,[status(thm)],[182229480,181831144]),
[] ).
fof(axiom_1_2,plain,
! [A] : axiom(implies(or(A,A),A)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL236-3.tptp',unknown),
[] ).
cnf(173742144,plain,
axiom(implies(or(A,A),A)),
inference(rewrite,[status(thm)],[axiom_1_2]),
[] ).
cnf(181607208,plain,
theorem(implies(or(A,A),A)),
inference(resolution,[status(thm)],[173773360,173742144]),
[] ).
cnf(181628512,plain,
( theorem(A)
| ~ theorem(or(A,A)) ),
inference(resolution,[status(thm)],[173792240,181607208]),
[] ).
cnf(260650808,plain,
theorem(or(not(A),A)),
inference(resolution,[status(thm)],[233911664,181628512]),
[] ).
fof(axiom_1_4,plain,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL236-3.tptp',unknown),
[] ).
cnf(173750128,plain,
axiom(implies(or(A,B),or(B,A))),
inference(rewrite,[status(thm)],[axiom_1_4]),
[] ).
cnf(181823488,plain,
theorem(implies(or(A,B),or(B,A))),
inference(resolution,[status(thm)],[173773360,173750128]),
[] ).
cnf(182062272,plain,
theorem(implies(or(A,not(B)),implies(B,A))),
inference(paramodulation,[status(thm)],[181823488,173766840,theory(equality)]),
[] ).
cnf(183530056,plain,
( theorem(implies(B,A))
| ~ theorem(or(A,not(B))) ),
inference(resolution,[status(thm)],[182062272,173792240]),
[] ).
cnf(261317072,plain,
theorem(implies(A,not(not(A)))),
inference(resolution,[status(thm)],[260650808,183530056]),
[] ).
cnf(181882384,plain,
theorem(implies(A,implies(B,A))),
inference(paramodulation,[status(thm)],[181615112,173766840,theory(equality)]),
[] ).
cnf(182170512,plain,
( theorem(implies(B,A))
| ~ theorem(A) ),
inference(resolution,[status(thm)],[173792240,181882384]),
[] ).
cnf(262495864,plain,
theorem(implies(B,implies(A,not(not(A))))),
inference(resolution,[status(thm)],[261317072,182170512]),
[] ).
fof(and_defn,plain,
! [A,B] : $equal(not(or(not(A),not(B))),and(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL236-3.tptp',unknown),
[] ).
cnf(173804488,plain,
$equal(not(or(not(A),not(B))),and(A,B)),
inference(rewrite,[status(thm)],[and_defn]),
[] ).
cnf(494435720,plain,
theorem(implies(A,implies(or(not(B),not(C)),not(and(B,C))))),
inference(paramodulation,[status(thm)],[262495864,173804488,theory(equality)]),
[] ).
cnf(181656832,plain,
( theorem(or(B,A))
| ~ theorem(A) ),
inference(resolution,[status(thm)],[173792240,181615112]),
[] ).
cnf(181703408,plain,
theorem(or(A,implies(or(B,B),B))),
inference(resolution,[status(thm)],[181656832,181607208]),
[] ).
cnf(182697280,plain,
theorem(implies(B,implies(or(A,A),A))),
inference(paramodulation,[status(thm)],[181703408,173766840,theory(equality)]),
[] ).
cnf(183761448,plain,
( theorem(C)
| ~ theorem(implies(implies(B,implies(or(A,A),A)),C)) ),
inference(resolution,[status(thm)],[182697280,173792240]),
[] ).
fof(prove_this,plain,
~ theorem(implies(or(not(p),not(q)),not(and(p,q)))),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL236-3.tptp',unknown),
[] ).
cnf(173809288,plain,
~ theorem(implies(or(not(p),not(q)),not(and(p,q)))),
inference(rewrite,[status(thm)],[prove_this]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[494435720,183761448,173809288]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 90 seconds
% START OF PROOF SEQUENCE
% fof(rule_2,plain,(theorem(A)|~theorem(implies(B,A))|~theorem(B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL236-3.tptp',unknown),[]).
%
% cnf(173792240,plain,(theorem(A)|~theorem(implies(B,A))|~theorem(B)),inference(rewrite,[status(thm)],[rule_2]),[]).
%
% fof(rule_1,plain,(theorem(A)|~axiom(A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL236-3.tptp',unknown),[]).
%
% cnf(173773360,plain,(theorem(A)|~axiom(A)),inference(rewrite,[status(thm)],[rule_1]),[]).
%
% fof(axiom_1_3,plain,(axiom(implies(A,or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL236-3.tptp',unknown),[]).
%
% cnf(173746360,plain,(axiom(implies(A,or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_3]),[]).
%
% cnf(181615112,plain,(theorem(implies(A,or(B,A)))),inference(resolution,[status(thm)],[173773360,173746360]),[]).
%
% fof(implies_definition,plain,($equal(or(not(A),B),implies(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL236-3.tptp',unknown),[]).
%
% cnf(173766840,plain,($equal(or(not(A),B),implies(A,B))),inference(rewrite,[status(thm)],[implies_definition]),[]).
%
% cnf(181899304,plain,(theorem(or(not(A),or(B,A)))),inference(paramodulation,[status(thm)],[181615112,173766840,theory(equality)]),[]).
%
% cnf(182229480,plain,(theorem(A)|~theorem(implies(or(not(B),or(C,B)),A))),inference(resolution,[status(thm)],[173792240,181899304]),[]).
%
% fof(axiom_1_5,plain,(axiom(implies(or(A,or(B,C)),or(B,or(A,C))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL236-3.tptp',unknown),[]).
%
% cnf(173754144,plain,(axiom(implies(or(A,or(B,C)),or(B,or(A,C))))),inference(rewrite,[status(thm)],[axiom_1_5]),[]).
%
% cnf(181831144,plain,(theorem(implies(or(A,or(B,C)),or(B,or(A,C))))),inference(resolution,[status(thm)],[173773360,173754144]),[]).
%
% cnf(233911664,plain,(theorem(or(B,or(not(A),A)))),inference(resolution,[status(thm)],[182229480,181831144]),[]).
%
% fof(axiom_1_2,plain,(axiom(implies(or(A,A),A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL236-3.tptp',unknown),[]).
%
% cnf(173742144,plain,(axiom(implies(or(A,A),A))),inference(rewrite,[status(thm)],[axiom_1_2]),[]).
%
% cnf(181607208,plain,(theorem(implies(or(A,A),A))),inference(resolution,[status(thm)],[173773360,173742144]),[]).
%
% cnf(181628512,plain,(theorem(A)|~theorem(or(A,A))),inference(resolution,[status(thm)],[173792240,181607208]),[]).
%
% cnf(260650808,plain,(theorem(or(not(A),A))),inference(resolution,[status(thm)],[233911664,181628512]),[]).
%
% fof(axiom_1_4,plain,(axiom(implies(or(A,B),or(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL236-3.tptp',unknown),[]).
%
% cnf(173750128,plain,(axiom(implies(or(A,B),or(B,A)))),inference(rewrite,[status(thm)],[axiom_1_4]),[]).
%
% cnf(181823488,plain,(theorem(implies(or(A,B),or(B,A)))),inference(resolution,[status(thm)],[173773360,173750128]),[]).
%
% cnf(182062272,plain,(theorem(implies(or(A,not(B)),implies(B,A)))),inference(paramodulation,[status(thm)],[181823488,173766840,theory(equality)]),[]).
%
% cnf(183530056,plain,(theorem(implies(B,A))|~theorem(or(A,not(B)))),inference(resolution,[status(thm)],[182062272,173792240]),[]).
%
% cnf(261317072,plain,(theorem(implies(A,not(not(A))))),inference(resolution,[status(thm)],[260650808,183530056]),[]).
%
% cnf(181882384,plain,(theorem(implies(A,implies(B,A)))),inference(paramodulation,[status(thm)],[181615112,173766840,theory(equality)]),[]).
%
% cnf(182170512,plain,(theorem(implies(B,A))|~theorem(A)),inference(resolution,[status(thm)],[173792240,181882384]),[]).
%
% cnf(262495864,plain,(theorem(implies(B,implies(A,not(not(A)))))),inference(resolution,[status(thm)],[261317072,182170512]),[]).
%
% fof(and_defn,plain,($equal(not(or(not(A),not(B))),and(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL236-3.tptp',unknown),[]).
%
% cnf(173804488,plain,($equal(not(or(not(A),not(B))),and(A,B))),inference(rewrite,[status(thm)],[and_defn]),[]).
%
% cnf(494435720,plain,(theorem(implies(A,implies(or(not(B),not(C)),not(and(B,C)))))),inference(paramodulation,[status(thm)],[262495864,173804488,theory(equality)]),[]).
%
% cnf(181656832,plain,(theorem(or(B,A))|~theorem(A)),inference(resolution,[status(thm)],[173792240,181615112]),[]).
%
% cnf(181703408,plain,(theorem(or(A,implies(or(B,B),B)))),inference(resolution,[status(thm)],[181656832,181607208]),[]).
%
% cnf(182697280,plain,(theorem(implies(B,implies(or(A,A),A)))),inference(paramodulation,[status(thm)],[181703408,173766840,theory(equality)]),[]).
%
% cnf(183761448,plain,(theorem(C)|~theorem(implies(implies(B,implies(or(A,A),A)),C))),inference(resolution,[status(thm)],[182697280,173792240]),[]).
%
% fof(prove_this,plain,(~theorem(implies(or(not(p),not(q)),not(and(p,q))))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/LCL/LCL236-3.tptp',unknown),[]).
%
% cnf(173809288,plain,(~theorem(implies(or(not(p),not(q)),not(and(p,q))))),inference(rewrite,[status(thm)],[prove_this]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[494435720,183761448,173809288]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------