TSTP Solution File: LCL519+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : LCL519+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 07:44:52 EDT 2023
% Result : Theorem 71.15s 10.36s
% Output : CNFRefutation 71.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 23
% Syntax : Number of formulae : 229 ( 113 unt; 0 def)
% Number of atoms : 371 ( 55 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 263 ( 121 ~; 114 |; 2 &)
% ( 10 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 392 ( 39 sgn; 84 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f16,axiom,
( kn1
<=> ! [X3] : is_a_theorem(implies(X3,and(X3,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn1) ).
fof(f17,axiom,
( kn2
<=> ! [X3,X4] : is_a_theorem(implies(and(X3,X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn2) ).
fof(f18,axiom,
( kn3
<=> ! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X4),implies(not(and(X4,X5)),not(and(X5,X3))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn3) ).
fof(f23,axiom,
( r2
<=> ! [X3,X4] : is_a_theorem(implies(X4,or(X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
fof(f28,axiom,
( op_and
=> ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_and) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
fof(f30,axiom,
( op_implies_or
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_or) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv) ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_op_or) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_op_implies_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_modus_ponens) ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn1) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn2) ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn3) ).
fof(f39,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f40,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f41,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).
fof(f42,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_equiv) ).
fof(f43,conjecture,
r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r2) ).
fof(f44,negated_conjecture,
~ r2,
inference(negated_conjecture,[],[f43]) ).
fof(f45,plain,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(rectify,[],[f16]) ).
fof(f46,plain,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(rectify,[],[f17]) ).
fof(f47,plain,
( kn3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(rectify,[],[f18]) ).
fof(f52,plain,
( r2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(rectify,[],[f23]) ).
fof(f56,plain,
~ r2,
inference(flattening,[],[f44]) ).
fof(f57,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
=> r2 ),
inference(unused_predicate_definition_removal,[],[f52]) ).
fof(f58,plain,
( kn3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(unused_predicate_definition_removal,[],[f47]) ).
fof(f59,plain,
( kn2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f46]) ).
fof(f60,plain,
( kn1
=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(unused_predicate_definition_removal,[],[f45]) ).
fof(f61,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f62,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f63,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f62]) ).
fof(f64,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f61]) ).
fof(f66,plain,
( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(ennf_transformation,[],[f60]) ).
fof(f67,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(ennf_transformation,[],[f59]) ).
fof(f68,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(ennf_transformation,[],[f58]) ).
fof(f69,plain,
( r2
| ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1))) ),
inference(ennf_transformation,[],[f57]) ).
fof(f70,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f71,plain,
( ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(ennf_transformation,[],[f28]) ).
fof(f72,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f73,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f74,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f75,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1)))
=> ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
( r2
| ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f69,f75]) ).
fof(f77,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f64]) ).
fof(f78,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f65]) ).
fof(f79,plain,
! [X0] :
( is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(cnf_transformation,[],[f66]) ).
fof(f80,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(cnf_transformation,[],[f67]) ).
fof(f81,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(cnf_transformation,[],[f68]) ).
fof(f82,plain,
( r2
| ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
inference(cnf_transformation,[],[f76]) ).
fof(f83,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f70]) ).
fof(f84,plain,
! [X0,X1] :
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[],[f71]) ).
fof(f85,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f72]) ).
fof(f86,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[],[f73]) ).
fof(f87,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f74]) ).
fof(f88,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f89,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f91,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f92,plain,
kn1,
inference(cnf_transformation,[],[f36]) ).
fof(f93,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f94,plain,
kn3,
inference(cnf_transformation,[],[f38]) ).
fof(f95,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f39]) ).
fof(f96,plain,
op_implies_or,
inference(cnf_transformation,[],[f40]) ).
fof(f97,plain,
op_and,
inference(cnf_transformation,[],[f41]) ).
fof(f98,plain,
op_equiv,
inference(cnf_transformation,[],[f42]) ).
fof(f99,plain,
~ r2,
inference(cnf_transformation,[],[f56]) ).
cnf(c_49,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f77]) ).
cnf(c_50,plain,
( ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents
| X0 = X1 ),
inference(cnf_transformation,[],[f78]) ).
cnf(c_51,plain,
( ~ kn1
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(cnf_transformation,[],[f79]) ).
cnf(c_52,plain,
( ~ kn2
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f80]) ).
cnf(c_53,plain,
( ~ kn3
| is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(cnf_transformation,[],[f81]) ).
cnf(c_54,plain,
( ~ is_a_theorem(implies(sK1,or(sK0,sK1)))
| r2 ),
inference(cnf_transformation,[],[f82]) ).
cnf(c_55,plain,
( ~ op_or
| not(and(not(X0),not(X1))) = or(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
cnf(c_56,plain,
( ~ op_and
| not(or(not(X0),not(X1))) = and(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
cnf(c_57,plain,
( ~ op_implies_and
| not(and(X0,not(X1))) = implies(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
cnf(c_58,plain,
( ~ op_implies_or
| or(not(X0),X1) = implies(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
cnf(c_59,plain,
( ~ op_equiv
| and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
cnf(c_60,plain,
op_or,
inference(cnf_transformation,[],[f88]) ).
cnf(c_61,plain,
op_implies_and,
inference(cnf_transformation,[],[f89]) ).
cnf(c_63,plain,
modus_ponens,
inference(cnf_transformation,[],[f91]) ).
cnf(c_64,plain,
kn1,
inference(cnf_transformation,[],[f92]) ).
cnf(c_65,plain,
kn2,
inference(cnf_transformation,[],[f93]) ).
cnf(c_66,plain,
kn3,
inference(cnf_transformation,[],[f94]) ).
cnf(c_67,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f95]) ).
cnf(c_68,plain,
op_implies_or,
inference(cnf_transformation,[],[f96]) ).
cnf(c_69,plain,
op_and,
inference(cnf_transformation,[],[f97]) ).
cnf(c_70,plain,
op_equiv,
inference(cnf_transformation,[],[f98]) ).
cnf(c_71,negated_conjecture,
~ r2,
inference(cnf_transformation,[],[f99]) ).
cnf(c_81,plain,
~ is_a_theorem(implies(sK1,or(sK0,sK1))),
inference(global_subsumption_just,[status(thm)],[c_54,c_71,c_54]) ).
cnf(c_83,plain,
is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption_just,[status(thm)],[c_52,c_65,c_52]) ).
cnf(c_86,plain,
is_a_theorem(implies(X0,and(X0,X0))),
inference(global_subsumption_just,[status(thm)],[c_51,c_64,c_51]) ).
cnf(c_89,plain,
or(not(X0),X1) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_58,c_68,c_58]) ).
cnf(c_92,plain,
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(global_subsumption_just,[status(thm)],[c_50,c_67,c_50]) ).
cnf(c_95,plain,
not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_57,c_61,c_57]) ).
cnf(c_98,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_63,c_49]) ).
cnf(c_99,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(renaming,[status(thm)],[c_98]) ).
cnf(c_100,plain,
not(or(not(X0),not(X1))) = and(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_56,c_69,c_56]) ).
cnf(c_103,plain,
not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_55,c_60,c_55]) ).
cnf(c_106,plain,
and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_59,c_70,c_59]) ).
cnf(c_109,plain,
is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))),
inference(global_subsumption_just,[status(thm)],[c_53,c_66,c_53]) ).
cnf(c_170,plain,
implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[c_103,c_95]) ).
cnf(c_171,plain,
not(implies(X0,not(X1))) = and(X0,X1),
inference(demodulation,[status(thm)],[c_100,c_89]) ).
cnf(c_172,plain,
is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))),
inference(demodulation,[status(thm)],[c_109,c_170]) ).
cnf(c_374,plain,
is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[status(thm)],[c_170,c_86]) ).
cnf(c_376,plain,
is_a_theorem(implies(X0,and(not(not(X0)),not(not(X0))))),
inference(superposition,[status(thm)],[c_89,c_374]) ).
cnf(c_378,plain,
implies(X0,and(X1,not(X2))) = not(and(X0,implies(X1,X2))),
inference(superposition,[status(thm)],[c_95,c_95]) ).
cnf(c_381,plain,
or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[status(thm)],[c_95,c_170]) ).
cnf(c_382,plain,
implies(and(X0,not(X1)),X2) = or(implies(X0,X1),X2),
inference(superposition,[status(thm)],[c_95,c_89]) ).
cnf(c_387,plain,
and(or(X0,X1),implies(X1,not(X0))) = equiv(not(X0),X1),
inference(superposition,[status(thm)],[c_170,c_106]) ).
cnf(c_389,plain,
is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[status(thm)],[c_106,c_86]) ).
cnf(c_395,plain,
not(or(X0,not(X1))) = and(not(X0),X1),
inference(superposition,[status(thm)],[c_170,c_171]) ).
cnf(c_397,plain,
and(X0,implies(X1,not(X2))) = not(implies(X0,and(X1,X2))),
inference(superposition,[status(thm)],[c_171,c_171]) ).
cnf(c_401,plain,
or(implies(X0,not(X1)),X2) = implies(and(X0,X1),X2),
inference(superposition,[status(thm)],[c_171,c_170]) ).
cnf(c_402,plain,
implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(superposition,[status(thm)],[c_171,c_89]) ).
cnf(c_412,plain,
is_a_theorem(implies(implies(not(X0),X1),or(and(X1,X2),implies(X2,X0)))),
inference(superposition,[status(thm)],[c_95,c_172]) ).
cnf(c_414,plain,
is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0)))),
inference(light_normalisation,[status(thm)],[c_412,c_170]) ).
cnf(c_443,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(and(X0,X0)) ),
inference(superposition,[status(thm)],[c_86,c_99]) ).
cnf(c_444,plain,
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_83,c_99]) ).
cnf(c_449,plain,
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X0))
| is_a_theorem(X1) ),
inference(superposition,[status(thm)],[c_170,c_99]) ).
cnf(c_554,plain,
and(not(not(X0)),X1) = not(implies(X0,not(X1))),
inference(superposition,[status(thm)],[c_89,c_395]) ).
cnf(c_557,plain,
and(not(X0),or(X1,not(X2))) = not(or(X0,and(not(X1),X2))),
inference(superposition,[status(thm)],[c_395,c_395]) ).
cnf(c_567,plain,
implies(or(X0,not(X1)),X2) = or(and(not(X0),X1),X2),
inference(superposition,[status(thm)],[c_395,c_89]) ).
cnf(c_568,plain,
and(not(not(X0)),X1) = and(X0,X1),
inference(light_normalisation,[status(thm)],[c_554,c_171]) ).
cnf(c_571,plain,
is_a_theorem(implies(X0,and(X0,not(not(X0))))),
inference(demodulation,[status(thm)],[c_376,c_568]) ).
cnf(c_608,plain,
is_a_theorem(or(X0,and(not(X0),not(not(not(X0)))))),
inference(superposition,[status(thm)],[c_170,c_571]) ).
cnf(c_612,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(and(X0,not(not(X0)))) ),
inference(superposition,[status(thm)],[c_571,c_99]) ).
cnf(c_658,plain,
implies(implies(X0,X1),and(X1,not(X0))) = not(equiv(X0,X1)),
inference(superposition,[status(thm)],[c_106,c_378]) ).
cnf(c_659,plain,
implies(X0,and(not(X1),not(X2))) = not(and(X0,or(X1,X2))),
inference(superposition,[status(thm)],[c_170,c_378]) ).
cnf(c_719,plain,
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(and(X0,not(not(X0)))) ),
inference(superposition,[status(thm)],[c_568,c_443]) ).
cnf(c_721,plain,
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(not(not(X0))) ),
inference(superposition,[status(thm)],[c_568,c_444]) ).
cnf(c_722,plain,
is_a_theorem(implies(and(X0,X1),not(not(X0)))),
inference(superposition,[status(thm)],[c_568,c_83]) ).
cnf(c_802,plain,
is_a_theorem(implies(X0,and(not(not(X0)),not(not(not(not(X0))))))),
inference(superposition,[status(thm)],[c_89,c_608]) ).
cnf(c_838,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(not(not(X0))) ),
inference(superposition,[status(thm)],[c_443,c_721]) ).
cnf(c_841,plain,
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(not(not(not(not(X0))))) ),
inference(superposition,[status(thm)],[c_568,c_721]) ).
cnf(c_860,plain,
( ~ is_a_theorem(and(X0,not(X1)))
| is_a_theorem(not(implies(X0,X1))) ),
inference(superposition,[status(thm)],[c_95,c_838]) ).
cnf(c_1022,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(not(X0)))
| is_a_theorem(X1) ),
inference(superposition,[status(thm)],[c_89,c_449]) ).
cnf(c_1107,plain,
( ~ is_a_theorem(not(X0))
| is_a_theorem(not(implies(not(X0),X0))) ),
inference(superposition,[status(thm)],[c_443,c_860]) ).
cnf(c_1224,plain,
( ~ is_a_theorem(not(X0))
| is_a_theorem(not(or(X0,X0))) ),
inference(demodulation,[status(thm)],[c_1107,c_170]) ).
cnf(c_1229,plain,
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(and(not(not(X0)),X0)) ),
inference(superposition,[status(thm)],[c_395,c_1224]) ).
cnf(c_1292,plain,
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_719,c_444]) ).
cnf(c_1335,plain,
( ~ is_a_theorem(not(and(X0,X1)))
| is_a_theorem(implies(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_171,c_1292]) ).
cnf(c_1429,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(not(not(not(not(X0))))) ),
inference(superposition,[status(thm)],[c_612,c_841]) ).
cnf(c_1459,plain,
is_a_theorem(or(implies(X0,X1),X0)),
inference(superposition,[status(thm)],[c_382,c_83]) ).
cnf(c_1568,plain,
is_a_theorem(or(or(X0,X1),not(X0))),
inference(superposition,[status(thm)],[c_170,c_1459]) ).
cnf(c_1692,plain,
( ~ is_a_theorem(implies(X0,not(X1)))
| is_a_theorem(not(not(not(and(X0,X1))))) ),
inference(superposition,[status(thm)],[c_171,c_1429]) ).
cnf(c_1834,plain,
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(and(X0,X0)) ),
inference(demodulation,[status(thm)],[c_1229,c_568]) ).
cnf(c_1888,plain,
not(implies(or(X0,X1),and(X1,X0))) = equiv(not(X0),X1),
inference(demodulation,[status(thm)],[c_387,c_397]) ).
cnf(c_1889,plain,
not(implies(implies(X0,X1),and(X1,not(X0)))) = equiv(not(not(X0)),X1),
inference(superposition,[status(thm)],[c_89,c_1888]) ).
cnf(c_1943,plain,
equiv(not(not(X0)),X1) = not(not(equiv(X0,X1))),
inference(light_normalisation,[status(thm)],[c_1889,c_658]) ).
cnf(c_2206,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X0,not(not(X1)))) ),
inference(superposition,[status(thm)],[c_95,c_1335]) ).
cnf(c_2379,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(not(not(X1))) ),
inference(superposition,[status(thm)],[c_2206,c_99]) ).
cnf(c_2572,plain,
is_a_theorem(implies(or(X0,X1),or(and(X1,not(X2)),or(X2,X0)))),
inference(superposition,[status(thm)],[c_170,c_414]) ).
cnf(c_2574,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(and(X1,X2),implies(X2,X0))) ),
inference(superposition,[status(thm)],[c_414,c_99]) ).
cnf(c_2705,plain,
is_a_theorem(not(not(implies(X0,and(X0,not(not(X0))))))),
inference(demodulation,[status(thm)],[c_802,c_89,c_397,c_659]) ).
cnf(c_2706,plain,
is_a_theorem(not(not(or(X0,and(not(X0),not(not(not(X0)))))))),
inference(superposition,[status(thm)],[c_170,c_2705]) ).
cnf(c_3090,plain,
( ~ is_a_theorem(not(not(not(X0))))
| ~ is_a_theorem(or(X0,X1))
| is_a_theorem(X1) ),
inference(superposition,[status(thm)],[c_170,c_1022]) ).
cnf(c_5099,plain,
( ~ is_a_theorem(not(not(equiv(X0,X1))))
| not(not(X0)) = X1 ),
inference(superposition,[status(thm)],[c_1943,c_92]) ).
cnf(c_5482,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(not(not(and(X0,X0)))) ),
inference(superposition,[status(thm)],[c_86,c_2379]) ).
cnf(c_5485,plain,
( ~ is_a_theorem(implies(X0,X0))
| is_a_theorem(not(not(equiv(X0,X0)))) ),
inference(superposition,[status(thm)],[c_389,c_2379]) ).
cnf(c_5873,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(and(and(X0,X0),and(X0,X0))) ),
inference(superposition,[status(thm)],[c_5482,c_1834]) ).
cnf(c_6251,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(not(not(not(not(and(X0,X0)))))) ),
inference(superposition,[status(thm)],[c_5873,c_841]) ).
cnf(c_8446,plain,
( ~ is_a_theorem(implies(X0,not(not(X1))))
| is_a_theorem(not(not(implies(X0,X1)))) ),
inference(superposition,[status(thm)],[c_95,c_1692]) ).
cnf(c_8981,plain,
is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X2,X0)))),
inference(demodulation,[status(thm)],[c_2572,c_381]) ).
cnf(c_8982,plain,
is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),or(X2,not(X0))))),
inference(superposition,[status(thm)],[c_89,c_8981]) ).
cnf(c_8986,plain,
is_a_theorem(implies(or(X0,not(X1)),implies(or(X1,X2),or(X2,X0)))),
inference(superposition,[status(thm)],[c_170,c_8981]) ).
cnf(c_10309,plain,
( ~ is_a_theorem(or(not(and(X0,X0)),X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(superposition,[status(thm)],[c_6251,c_3090]) ).
cnf(c_10637,plain,
( ~ is_a_theorem(implies(X0,X0))
| not(not(X0)) = X0 ),
inference(superposition,[status(thm)],[c_5485,c_5099]) ).
cnf(c_13346,plain,
is_a_theorem(not(not(implies(and(X0,X1),X0)))),
inference(superposition,[status(thm)],[c_722,c_8446]) ).
cnf(c_13807,plain,
is_a_theorem(and(implies(and(X0,X1),X0),implies(and(X0,X1),X0))),
inference(superposition,[status(thm)],[c_13346,c_1834]) ).
cnf(c_14070,plain,
not(and(not(X0),or(X1,X2))) = or(X0,and(not(X1),not(X2))),
inference(superposition,[status(thm)],[c_659,c_170]) ).
cnf(c_14137,plain,
is_a_theorem(not(not(not(and(not(X0),or(X0,not(not(X0)))))))),
inference(demodulation,[status(thm)],[c_2706,c_14070]) ).
cnf(c_14728,plain,
is_a_theorem(not(not(not(not(not(and(not(X0),or(X0,X0)))))))),
inference(demodulation,[status(thm)],[c_14137,c_557,c_14070]) ).
cnf(c_14744,plain,
is_a_theorem(not(not(not(and(not(X0),or(X0,X0)))))),
inference(superposition,[status(thm)],[c_14728,c_1292]) ).
cnf(c_14954,plain,
( ~ is_a_theorem(or(and(not(X0),or(X0,X0)),X1))
| is_a_theorem(X1) ),
inference(superposition,[status(thm)],[c_14744,c_3090]) ).
cnf(c_17724,plain,
is_a_theorem(not(not(not(not(implies(and(X0,X1),X0)))))),
inference(superposition,[status(thm)],[c_13807,c_841]) ).
cnf(c_17769,plain,
is_a_theorem(not(not(not(and(and(not(X0),X1),X0))))),
inference(superposition,[status(thm)],[c_171,c_17724]) ).
cnf(c_17784,plain,
( ~ is_a_theorem(or(not(implies(and(X0,X1),X0)),X2))
| is_a_theorem(X2) ),
inference(superposition,[status(thm)],[c_17724,c_3090]) ).
cnf(c_17942,plain,
( ~ is_a_theorem(or(and(and(not(X0),X1),X0),X2))
| is_a_theorem(X2) ),
inference(superposition,[status(thm)],[c_17769,c_3090]) ).
cnf(c_19103,plain,
( ~ is_a_theorem(implies(or(X0,not(or(X0,X0))),X1))
| is_a_theorem(X1) ),
inference(demodulation,[status(thm)],[c_14954,c_567]) ).
cnf(c_19115,plain,
is_a_theorem(implies(or(or(X0,X0),X1),or(X1,X0))),
inference(superposition,[status(thm)],[c_8986,c_19103]) ).
cnf(c_19419,plain,
( ~ is_a_theorem(or(or(X0,X0),X1))
| is_a_theorem(or(X1,X0)) ),
inference(superposition,[status(thm)],[c_19115,c_99]) ).
cnf(c_21342,plain,
is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_1568,c_19419]) ).
cnf(c_21613,plain,
is_a_theorem(implies(X0,X0)),
inference(demodulation,[status(thm)],[c_21342,c_89]) ).
cnf(c_21614,plain,
not(not(X0)) = X0,
inference(backward_subsumption_resolution,[status(thm)],[c_10637,c_21613]) ).
cnf(c_21831,plain,
implies(X0,not(X1)) = not(and(X0,X1)),
inference(superposition,[status(thm)],[c_21614,c_95]) ).
cnf(c_22316,plain,
( ~ is_a_theorem(implies(implies(and(X0,X1),X0),X2))
| is_a_theorem(X2) ),
inference(demodulation,[status(thm)],[c_17784,c_89]) ).
cnf(c_22324,plain,
is_a_theorem(implies(implies(X0,X1),or(X1,not(and(X0,X2))))),
inference(superposition,[status(thm)],[c_8982,c_22316]) ).
cnf(c_22476,plain,
is_a_theorem(implies(implies(X0,X1),or(X1,implies(X0,not(X2))))),
inference(demodulation,[status(thm)],[c_22324,c_21831]) ).
cnf(c_22487,plain,
is_a_theorem(implies(implies(X0,X1),or(X1,implies(X0,X2)))),
inference(superposition,[status(thm)],[c_21614,c_22476]) ).
cnf(c_22502,plain,
is_a_theorem(implies(implies(not(X0),X1),or(X1,or(X0,X2)))),
inference(superposition,[status(thm)],[c_170,c_22487]) ).
cnf(c_22504,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(X1,implies(X0,X2))) ),
inference(superposition,[status(thm)],[c_22487,c_99]) ).
cnf(c_22509,plain,
is_a_theorem(implies(or(X0,X1),or(X1,or(X0,X2)))),
inference(light_normalisation,[status(thm)],[c_22502,c_170]) ).
cnf(c_23281,plain,
is_a_theorem(implies(or(X0,not(X1)),implies(X1,or(X0,X2)))),
inference(superposition,[status(thm)],[c_89,c_22509]) ).
cnf(c_27519,plain,
( ~ is_a_theorem(implies(X0,or(X1,X1)))
| is_a_theorem(or(implies(X0,X2),X1)) ),
inference(superposition,[status(thm)],[c_22504,c_19419]) ).
cnf(c_27716,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,or(X0,X2))) ),
inference(superposition,[status(thm)],[c_23281,c_99]) ).
cnf(c_35576,plain,
( ~ is_a_theorem(or(X0,and(not(X1),X2)))
| is_a_theorem(implies(X1,X0)) ),
inference(superposition,[status(thm)],[c_2574,c_17942]) ).
cnf(c_40246,plain,
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(implies(not(X1),X0)) ),
inference(superposition,[status(thm)],[c_21614,c_35576]) ).
cnf(c_46364,plain,
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(or(X1,X0)) ),
inference(demodulation,[status(thm)],[c_40246,c_170]) ).
cnf(c_46401,plain,
( ~ is_a_theorem(implies(X0,and(X1,X2)))
| is_a_theorem(or(X1,not(X0))) ),
inference(superposition,[status(thm)],[c_89,c_46364]) ).
cnf(c_52590,plain,
( ~ is_a_theorem(implies(and(X0,X0),X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(demodulation,[status(thm)],[c_10309,c_89]) ).
cnf(c_52666,plain,
( ~ is_a_theorem(implies(equiv(X0,X0),X1))
| ~ is_a_theorem(implies(X0,X0))
| is_a_theorem(X1) ),
inference(superposition,[status(thm)],[c_106,c_52590]) ).
cnf(c_52680,plain,
( ~ is_a_theorem(implies(equiv(X0,X0),X1))
| is_a_theorem(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_52666,c_21613]) ).
cnf(c_75824,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(or(implies(X1,X2),X0)) ),
inference(superposition,[status(thm)],[c_27716,c_27519]) ).
cnf(c_106440,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(and(X1,X2),X0)) ),
inference(superposition,[status(thm)],[c_401,c_75824]) ).
cnf(c_106445,plain,
( ~ is_a_theorem(or(X0,not(not(X1))))
| is_a_theorem(or(or(X1,X2),X0)) ),
inference(superposition,[status(thm)],[c_170,c_75824]) ).
cnf(c_113030,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(or(X1,X2),X0)) ),
inference(demodulation,[status(thm)],[c_106445,c_21614]) ).
cnf(c_148403,plain,
( ~ is_a_theorem(or(X0,not(implies(X1,X2))))
| is_a_theorem(implies(equiv(X1,X2),X0)) ),
inference(superposition,[status(thm)],[c_106,c_106440]) ).
cnf(c_151524,plain,
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(implies(equiv(X1,not(X2)),X0)) ),
inference(superposition,[status(thm)],[c_171,c_148403]) ).
cnf(c_152792,plain,
( ~ is_a_theorem(or(X0,and(not(X1),X1)))
| is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_151524,c_52680]) ).
cnf(c_153416,plain,
( ~ is_a_theorem(or(and(not(X0),X0),X1))
| is_a_theorem(or(X1,X2)) ),
inference(superposition,[status(thm)],[c_113030,c_152792]) ).
cnf(c_319466,plain,
( ~ is_a_theorem(implies(or(X0,not(X0)),X1))
| is_a_theorem(or(X1,X2)) ),
inference(demodulation,[status(thm)],[c_153416,c_567]) ).
cnf(c_319479,plain,
is_a_theorem(or(implies(or(X0,X1),or(X1,X0)),X2)),
inference(superposition,[status(thm)],[c_8986,c_319466]) ).
cnf(c_323481,plain,
is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(superposition,[status(thm)],[c_319479,c_152792]) ).
cnf(c_323557,plain,
is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))),
inference(superposition,[status(thm)],[c_89,c_323481]) ).
cnf(c_323591,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,X0)) ),
inference(superposition,[status(thm)],[c_323481,c_99]) ).
cnf(c_323745,plain,
is_a_theorem(implies(implies(X0,not(X1)),implies(X1,not(X0)))),
inference(superposition,[status(thm)],[c_89,c_323557]) ).
cnf(c_323981,plain,
is_a_theorem(or(and(X0,X1),implies(X1,not(X0)))),
inference(demodulation,[status(thm)],[c_323745,c_402]) ).
cnf(c_325728,plain,
is_a_theorem(or(implies(X0,not(X1)),and(X1,X0))),
inference(superposition,[status(thm)],[c_323981,c_323591]) ).
cnf(c_327417,plain,
is_a_theorem(implies(and(X0,X1),and(X1,X0))),
inference(demodulation,[status(thm)],[c_325728,c_401]) ).
cnf(c_327451,plain,
is_a_theorem(or(X0,not(and(X1,X0)))),
inference(superposition,[status(thm)],[c_327417,c_46401]) ).
cnf(c_327791,plain,
is_a_theorem(or(X0,implies(X1,not(X0)))),
inference(demodulation,[status(thm)],[c_327451,c_21831]) ).
cnf(c_327792,plain,
is_a_theorem(implies(X0,implies(X1,not(not(X0))))),
inference(superposition,[status(thm)],[c_89,c_327791]) ).
cnf(c_327829,plain,
is_a_theorem(implies(X0,implies(X1,X0))),
inference(light_normalisation,[status(thm)],[c_327792,c_21614]) ).
cnf(c_328383,plain,
is_a_theorem(implies(X0,or(X1,X0))),
inference(superposition,[status(thm)],[c_170,c_327829]) ).
cnf(c_328412,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_81,c_328383]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL519+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 02:50:35 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 71.15/10.36 % SZS status Started for theBenchmark.p
% 71.15/10.36 % SZS status Theorem for theBenchmark.p
% 71.15/10.36
% 71.15/10.36 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 71.15/10.36
% 71.15/10.36 ------ iProver source info
% 71.15/10.36
% 71.15/10.36 git: date: 2023-05-31 18:12:56 +0000
% 71.15/10.36 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 71.15/10.36 git: non_committed_changes: false
% 71.15/10.36 git: last_make_outside_of_git: false
% 71.15/10.36
% 71.15/10.36 ------ Parsing...
% 71.15/10.36 ------ Clausification by vclausify_rel & Parsing by iProver...
% 71.15/10.36
% 71.15/10.36 ------ Preprocessing... sup_sim: 3 sf_s rm: 12 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 71.15/10.36
% 71.15/10.36 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 71.15/10.36
% 71.15/10.36 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 71.15/10.36 ------ Proving...
% 71.15/10.36 ------ Problem Properties
% 71.15/10.36
% 71.15/10.36
% 71.15/10.36 clauses 11
% 71.15/10.36 conjectures 0
% 71.15/10.36 EPR 0
% 71.15/10.36 Horn 11
% 71.15/10.36 unary 9
% 71.15/10.36 binary 1
% 71.15/10.36 lits 14
% 71.15/10.36 lits eq 6
% 71.15/10.36 fd_pure 0
% 71.15/10.36 fd_pseudo 0
% 71.15/10.36 fd_cond 0
% 71.15/10.36 fd_pseudo_cond 1
% 71.15/10.36 AC symbols 0
% 71.15/10.36
% 71.15/10.36 ------ Schedule dynamic 5 is on
% 71.15/10.36
% 71.15/10.36 ------ no conjectures: strip conj schedule
% 71.15/10.36
% 71.15/10.36 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 71.15/10.36
% 71.15/10.36
% 71.15/10.36 ------
% 71.15/10.36 Current options:
% 71.15/10.36 ------
% 71.15/10.36
% 71.15/10.36
% 71.15/10.36
% 71.15/10.36
% 71.15/10.36 ------ Proving...
% 71.15/10.36
% 71.15/10.36
% 71.15/10.36 % SZS status Theorem for theBenchmark.p
% 71.15/10.36
% 71.15/10.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 71.15/10.36
% 71.15/10.37
%------------------------------------------------------------------------------