TSTP Solution File: LCL535+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : LCL535+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n022.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 07:44:56 EDT 2023
% Result : Theorem 17.91s 3.19s
% Output : CNFRefutation 17.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 33
% Syntax : Number of formulae : 172 ( 82 unt; 0 def)
% Number of atoms : 288 ( 40 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 203 ( 87 ~; 80 |; 2 &)
% ( 11 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 19 ( 17 usr; 17 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 190 ( 5 sgn; 99 !; 2 ?)
% 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(f3,axiom,
( modus_tollens
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_tollens) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_2) ).
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_1) ).
fof(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_3) ).
fof(f11,axiom,
( or_2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_2) ).
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(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(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(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f44,axiom,
or_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_2) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',necessitation) ).
fof(f55,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_M) ).
fof(f58,axiom,
( axiom_5
<=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f71,axiom,
( axiom_m9
<=> ! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m9) ).
fof(f73,axiom,
( op_possibly
=> ! [X0] : possibly(X0) = not(necessarily(not(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_possibly) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km5_necessitation) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km5_axiom_M) ).
fof(f81,axiom,
axiom_5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km5_axiom_5) ).
fof(f82,axiom,
op_possibly,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_possibly) ).
fof(f83,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_or) ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f86,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_equiv) ).
fof(f88,conjecture,
axiom_m9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m9) ).
fof(f89,negated_conjecture,
~ axiom_m9,
inference(negated_conjecture,[],[f88]) ).
fof(f104,plain,
~ axiom_m9,
inference(flattening,[],[f89]) ).
fof(f105,plain,
( ! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0)))
=> axiom_m9 ),
inference(unused_predicate_definition_removal,[],[f71]) ).
fof(f106,plain,
( axiom_5
=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(unused_predicate_definition_removal,[],[f58]) ).
fof(f107,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f109,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f114,plain,
( or_2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f116,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f118,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f120,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f122,plain,
( modus_tollens
=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f123,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f124,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(f129,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f124]) ).
fof(f130,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f129]) ).
fof(f131,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f123]) ).
fof(f132,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(ennf_transformation,[],[f122]) ).
fof(f134,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f120]) ).
fof(f136,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f118]) ).
fof(f138,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f116]) ).
fof(f140,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(ennf_transformation,[],[f114]) ).
fof(f145,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f146,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f147,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f148,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ necessitation ),
inference(ennf_transformation,[],[f109]) ).
fof(f150,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f107]) ).
fof(f151,plain,
( ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ axiom_5 ),
inference(ennf_transformation,[],[f106]) ).
fof(f152,plain,
( axiom_m9
| ? [X0] : ~ is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))) ),
inference(ennf_transformation,[],[f105]) ).
fof(f153,plain,
( ! [X0] : possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(ennf_transformation,[],[f73]) ).
fof(f154,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f156,plain,
( ? [X0] : ~ is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0)))
=> ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0))) ),
introduced(choice_axiom,[]) ).
fof(f157,plain,
( axiom_m9
| ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f152,f156]) ).
fof(f158,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f130]) ).
fof(f159,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f131]) ).
fof(f160,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(cnf_transformation,[],[f132]) ).
fof(f162,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f134]) ).
fof(f164,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f136]) ).
fof(f166,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f138]) ).
fof(f168,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(cnf_transformation,[],[f140]) ).
fof(f173,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f145]) ).
fof(f174,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f146]) ).
fof(f175,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f147]) ).
fof(f177,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f179,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f180,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f182,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f184,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f186,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f188,plain,
or_2,
inference(cnf_transformation,[],[f44]) ).
fof(f193,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f194,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[],[f148]) ).
fof(f196,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f150]) ).
fof(f197,plain,
! [X0] :
( is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ axiom_5 ),
inference(cnf_transformation,[],[f151]) ).
fof(f198,plain,
( axiom_m9
| ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0))) ),
inference(cnf_transformation,[],[f157]) ).
fof(f199,plain,
! [X0] :
( possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(cnf_transformation,[],[f153]) ).
fof(f200,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f154]) ).
fof(f203,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f205,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f206,plain,
axiom_5,
inference(cnf_transformation,[],[f81]) ).
fof(f207,plain,
op_possibly,
inference(cnf_transformation,[],[f82]) ).
fof(f208,plain,
op_or,
inference(cnf_transformation,[],[f83]) ).
fof(f209,plain,
op_strict_implies,
inference(cnf_transformation,[],[f85]) ).
fof(f210,plain,
op_equiv,
inference(cnf_transformation,[],[f86]) ).
fof(f212,plain,
~ axiom_m9,
inference(cnf_transformation,[],[f104]) ).
cnf(c_49,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f158]) ).
cnf(c_50,plain,
( ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents
| X0 = X1 ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_51,plain,
( ~ modus_tollens
| is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))) ),
inference(cnf_transformation,[],[f160]) ).
cnf(c_53,plain,
( ~ implies_2
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_55,plain,
( ~ and_1
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f164]) ).
cnf(c_57,plain,
( ~ and_3
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(cnf_transformation,[],[f166]) ).
cnf(c_59,plain,
( ~ or_2
| is_a_theorem(implies(X0,or(X1,X0))) ),
inference(cnf_transformation,[],[f168]) ).
cnf(c_64,plain,
( ~ op_or
| not(and(not(X0),not(X1))) = or(X0,X1) ),
inference(cnf_transformation,[],[f173]) ).
cnf(c_65,plain,
( ~ op_implies_and
| not(and(X0,not(X1))) = implies(X0,X1) ),
inference(cnf_transformation,[],[f174]) ).
cnf(c_66,plain,
( ~ op_equiv
| and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) ),
inference(cnf_transformation,[],[f175]) ).
cnf(c_68,plain,
op_implies_and,
inference(cnf_transformation,[],[f177]) ).
cnf(c_70,plain,
modus_ponens,
inference(cnf_transformation,[],[f179]) ).
cnf(c_71,plain,
modus_tollens,
inference(cnf_transformation,[],[f180]) ).
cnf(c_73,plain,
implies_2,
inference(cnf_transformation,[],[f182]) ).
cnf(c_75,plain,
and_1,
inference(cnf_transformation,[],[f184]) ).
cnf(c_77,plain,
and_3,
inference(cnf_transformation,[],[f186]) ).
cnf(c_79,plain,
or_2,
inference(cnf_transformation,[],[f188]) ).
cnf(c_84,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f193]) ).
cnf(c_85,plain,
( ~ is_a_theorem(X0)
| ~ necessitation
| is_a_theorem(necessarily(X0)) ),
inference(cnf_transformation,[],[f194]) ).
cnf(c_87,plain,
( ~ axiom_M
| is_a_theorem(implies(necessarily(X0),X0)) ),
inference(cnf_transformation,[],[f196]) ).
cnf(c_88,plain,
( ~ axiom_5
| is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(cnf_transformation,[],[f197]) ).
cnf(c_89,plain,
( ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0)))
| axiom_m9 ),
inference(cnf_transformation,[],[f198]) ).
cnf(c_90,plain,
( ~ op_possibly
| not(necessarily(not(X0))) = possibly(X0) ),
inference(cnf_transformation,[],[f199]) ).
cnf(c_91,plain,
( ~ op_strict_implies
| necessarily(implies(X0,X1)) = strict_implies(X0,X1) ),
inference(cnf_transformation,[],[f200]) ).
cnf(c_94,plain,
necessitation,
inference(cnf_transformation,[],[f203]) ).
cnf(c_96,plain,
axiom_M,
inference(cnf_transformation,[],[f205]) ).
cnf(c_97,plain,
axiom_5,
inference(cnf_transformation,[],[f206]) ).
cnf(c_98,plain,
op_possibly,
inference(cnf_transformation,[],[f207]) ).
cnf(c_99,plain,
op_or,
inference(cnf_transformation,[],[f208]) ).
cnf(c_100,plain,
op_strict_implies,
inference(cnf_transformation,[],[f209]) ).
cnf(c_101,plain,
op_equiv,
inference(cnf_transformation,[],[f210]) ).
cnf(c_103,negated_conjecture,
~ axiom_m9,
inference(cnf_transformation,[],[f212]) ).
cnf(c_128,plain,
is_a_theorem(implies(necessarily(X0),X0)),
inference(global_subsumption_just,[status(thm)],[c_87,c_96,c_87]) ).
cnf(c_131,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_85,c_94,c_85]) ).
cnf(c_134,plain,
is_a_theorem(implies(X0,or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_59,c_79,c_59]) ).
cnf(c_142,plain,
is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption_just,[status(thm)],[c_55,c_75,c_55]) ).
cnf(c_147,plain,
~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0))),
inference(global_subsumption_just,[status(thm)],[c_89,c_103,c_89]) ).
cnf(c_149,plain,
is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))),
inference(global_subsumption_just,[status(thm)],[c_88,c_97,c_88]) ).
cnf(c_152,plain,
not(necessarily(not(X0))) = possibly(X0),
inference(global_subsumption_just,[status(thm)],[c_90,c_98,c_90]) ).
cnf(c_160,plain,
is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(global_subsumption_just,[status(thm)],[c_57,c_77,c_57]) ).
cnf(c_163,plain,
necessarily(implies(X0,X1)) = strict_implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_91,c_100,c_91]) ).
cnf(c_166,plain,
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(global_subsumption_just,[status(thm)],[c_50,c_84,c_50]) ).
cnf(c_169,plain,
not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_65,c_68,c_65]) ).
cnf(c_172,plain,
is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(global_subsumption_just,[status(thm)],[c_53,c_73,c_53]) ).
cnf(c_175,plain,
is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_51,c_71,c_51]) ).
cnf(c_178,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_70,c_49]) ).
cnf(c_179,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(renaming,[status(thm)],[c_178]) ).
cnf(c_183,plain,
not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_64,c_99,c_64]) ).
cnf(c_189,plain,
and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_66,c_101,c_66]) ).
cnf(c_325,plain,
implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[c_183,c_169]) ).
cnf(c_326,plain,
is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(demodulation,[status(thm)],[c_175,c_325]) ).
cnf(c_9285,plain,
not(necessarily(possibly(X0))) = possibly(necessarily(not(X0))),
inference(superposition,[status(thm)],[c_152,c_152]) ).
cnf(c_9292,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_163,c_131]) ).
cnf(c_9308,plain,
is_a_theorem(or(X0,or(X1,not(X0)))),
inference(superposition,[status(thm)],[c_325,c_134]) ).
cnf(c_9446,plain,
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_172,c_179]) ).
cnf(c_9450,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,and(X0,X1))) ),
inference(superposition,[status(thm)],[c_160,c_179]) ).
cnf(c_9459,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(superposition,[status(thm)],[c_326,c_179]) ).
cnf(c_9585,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(X1)
| is_a_theorem(and(X0,X1)) ),
inference(superposition,[status(thm)],[c_9450,c_179]) ).
cnf(c_9961,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X1,X0))
| is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[status(thm)],[c_189,c_9585]) ).
cnf(c_10047,plain,
is_a_theorem(implies(X0,and(X0,X0))),
inference(superposition,[status(thm)],[c_160,c_9446]) ).
cnf(c_46946,plain,
( ~ is_a_theorem(implies(necessarily(possibly(X0)),possibly(X0)))
| is_a_theorem(equiv(necessarily(possibly(X0)),possibly(X0))) ),
inference(superposition,[status(thm)],[c_149,c_9961]) ).
cnf(c_46989,plain,
( ~ is_a_theorem(implies(and(X0,X0),X0))
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(superposition,[status(thm)],[c_10047,c_9961]) ).
cnf(c_47007,plain,
is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_46989,c_142]) ).
cnf(c_47024,plain,
is_a_theorem(equiv(necessarily(possibly(X0)),possibly(X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_46946,c_128]) ).
cnf(c_48016,plain,
and(X0,X0) = X0,
inference(superposition,[status(thm)],[c_47007,c_166]) ).
cnf(c_48063,plain,
implies(not(X0),X0) = not(not(X0)),
inference(superposition,[status(thm)],[c_48016,c_169]) ).
cnf(c_48481,plain,
necessarily(possibly(X0)) = possibly(X0),
inference(superposition,[status(thm)],[c_47024,c_166]) ).
cnf(c_48490,plain,
possibly(necessarily(not(X0))) = not(possibly(X0)),
inference(demodulation,[status(thm)],[c_9285,c_48481]) ).
cnf(c_49570,plain,
or(X0,X0) = not(not(X0)),
inference(demodulation,[status(thm)],[c_48063,c_325]) ).
cnf(c_49678,plain,
is_a_theorem(or(X0,not(not(not(X0))))),
inference(superposition,[status(thm)],[c_49570,c_9308]) ).
cnf(c_55647,plain,
not(possibly(necessarily(not(X0)))) = possibly(necessarily(possibly(X0))),
inference(superposition,[status(thm)],[c_152,c_48490]) ).
cnf(c_55679,plain,
not(not(possibly(X0))) = possibly(possibly(X0)),
inference(light_normalisation,[status(thm)],[c_55647,c_48481,c_48490]) ).
cnf(c_63434,plain,
is_a_theorem(or(possibly(X0),not(possibly(possibly(X0))))),
inference(superposition,[status(thm)],[c_55679,c_49678]) ).
cnf(c_67388,plain,
is_a_theorem(implies(possibly(possibly(X0)),possibly(X0))),
inference(superposition,[status(thm)],[c_63434,c_9459]) ).
cnf(c_67401,plain,
is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))),
inference(superposition,[status(thm)],[c_67388,c_9292]) ).
cnf(c_67407,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_147,c_67401]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL535+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 05:47:55 EDT 2023
% 0.13/0.34 % 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
% 17.91/3.19 % SZS status Started for theBenchmark.p
% 17.91/3.19 % SZS status Theorem for theBenchmark.p
% 17.91/3.19
% 17.91/3.19 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 17.91/3.19
% 17.91/3.19 ------ iProver source info
% 17.91/3.19
% 17.91/3.19 git: date: 2023-05-31 18:12:56 +0000
% 17.91/3.19 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 17.91/3.19 git: non_committed_changes: false
% 17.91/3.19 git: last_make_outside_of_git: false
% 17.91/3.19
% 17.91/3.19 ------ Parsing...
% 17.91/3.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 17.91/3.19
% 17.91/3.19 ------ Preprocessing... sup_sim: 3 sf_s rm: 27 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 17.91/3.19
% 17.91/3.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 17.91/3.19
% 17.91/3.19 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.91/3.19 ------ Proving...
% 17.91/3.19 ------ Problem Properties
% 17.91/3.19
% 17.91/3.19
% 17.91/3.19 clauses 26
% 17.91/3.19 conjectures 0
% 17.91/3.19 EPR 0
% 17.91/3.19 Horn 26
% 17.91/3.19 unary 23
% 17.91/3.19 binary 2
% 17.91/3.19 lits 30
% 17.91/3.19 lits eq 7
% 17.91/3.19 fd_pure 0
% 17.91/3.19 fd_pseudo 0
% 17.91/3.19 fd_cond 0
% 17.91/3.19 fd_pseudo_cond 1
% 17.91/3.19 AC symbols 0
% 17.91/3.19
% 17.91/3.19 ------ Schedule dynamic 5 is on
% 17.91/3.19
% 17.91/3.19 ------ no conjectures: strip conj schedule
% 17.91/3.19
% 17.91/3.19 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 17.91/3.19
% 17.91/3.19
% 17.91/3.19 ------
% 17.91/3.19 Current options:
% 17.91/3.19 ------
% 17.91/3.19
% 17.91/3.19
% 17.91/3.19
% 17.91/3.19
% 17.91/3.19 ------ Proving...
% 17.91/3.19
% 17.91/3.19
% 17.91/3.19 % SZS status Theorem for theBenchmark.p
% 17.91/3.19
% 17.91/3.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.91/3.20
% 17.91/3.20
%------------------------------------------------------------------------------