TSTP Solution File: LCL546+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : LCL546+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n008.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 : Fri May 3 02:38:10 EDT 2024
% Result : Theorem 17.51s 3.17s
% Output : CNFRefutation 17.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 37
% Syntax : Number of formulae : 200 ( 97 unt; 0 def)
% Number of atoms : 328 ( 35 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 222 ( 94 ~; 87 |; 2 &)
% ( 14 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 21 ( 19 usr; 19 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 218 ( 7 sgn 113 !; 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/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',implies_2) ).
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',and_3) ).
fof(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_1) ).
fof(f11,axiom,
( or_2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_2) ).
fof(f15,axiom,
( equivalence_3
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_and) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f43,axiom,
or_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f44,axiom,
or_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_2) ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation) ).
fof(f55,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_M) ).
fof(f56,axiom,
( axiom_4
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(f57,axiom,
( axiom_B
<=> ! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_B) ).
fof(f68,axiom,
( axiom_m6
<=> ! [X0] : is_a_theorem(strict_implies(X0,possibly(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m6) ).
fof(f73,axiom,
( op_possibly
=> ! [X0] : possibly(X0) = not(necessarily(not(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_possibly) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_necessitation) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_axiom_M) ).
fof(f81,axiom,
axiom_4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_axiom_4) ).
fof(f82,axiom,
axiom_B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_axiom_B) ).
fof(f83,axiom,
op_possibly,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_possibly) ).
fof(f84,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_or) ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f89,conjecture,
axiom_m6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m6) ).
fof(f90,negated_conjecture,
~ axiom_m6,
inference(negated_conjecture,[],[f89]) ).
fof(f105,plain,
~ axiom_m6,
inference(flattening,[],[f90]) ).
fof(f106,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,possibly(X0)))
=> axiom_m6 ),
inference(unused_predicate_definition_removal,[],[f68]) ).
fof(f107,plain,
( axiom_B
=> ! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
inference(unused_predicate_definition_removal,[],[f57]) ).
fof(f108,plain,
( axiom_4
=> ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
inference(unused_predicate_definition_removal,[],[f56]) ).
fof(f109,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f111,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f112,plain,
( equivalence_3
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f15]) ).
fof(f116,plain,
( or_2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f117,plain,
( or_1
=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f118,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f120,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f122,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f124,plain,
( modus_tollens
=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f125,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f126,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(f131,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f126]) ).
fof(f132,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f131]) ).
fof(f133,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f125]) ).
fof(f134,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(ennf_transformation,[],[f124]) ).
fof(f136,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f122]) ).
fof(f138,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f120]) ).
fof(f140,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f118]) ).
fof(f141,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(ennf_transformation,[],[f117]) ).
fof(f142,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(ennf_transformation,[],[f116]) ).
fof(f146,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(ennf_transformation,[],[f112]) ).
fof(f147,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f148,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f150,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ necessitation ),
inference(ennf_transformation,[],[f111]) ).
fof(f152,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f109]) ).
fof(f153,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0))))
| ~ axiom_4 ),
inference(ennf_transformation,[],[f108]) ).
fof(f154,plain,
( ! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0))))
| ~ axiom_B ),
inference(ennf_transformation,[],[f107]) ).
fof(f155,plain,
( axiom_m6
| ? [X0] : ~ is_a_theorem(strict_implies(X0,possibly(X0))) ),
inference(ennf_transformation,[],[f106]) ).
fof(f156,plain,
( ! [X0] : possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(ennf_transformation,[],[f73]) ).
fof(f157,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f159,plain,
( ? [X0] : ~ is_a_theorem(strict_implies(X0,possibly(X0)))
=> ~ is_a_theorem(strict_implies(sK0,possibly(sK0))) ),
introduced(choice_axiom,[]) ).
fof(f160,plain,
( axiom_m6
| ~ is_a_theorem(strict_implies(sK0,possibly(sK0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f155,f159]) ).
fof(f161,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f132]) ).
fof(f162,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f133]) ).
fof(f163,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(cnf_transformation,[],[f134]) ).
fof(f165,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f136]) ).
fof(f167,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f138]) ).
fof(f169,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f140]) ).
fof(f170,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(cnf_transformation,[],[f141]) ).
fof(f171,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(cnf_transformation,[],[f142]) ).
fof(f175,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[],[f146]) ).
fof(f176,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f147]) ).
fof(f177,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f148]) ).
fof(f180,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f182,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f183,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f185,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f187,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f189,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f190,plain,
or_1,
inference(cnf_transformation,[],[f43]) ).
fof(f191,plain,
or_2,
inference(cnf_transformation,[],[f44]) ).
fof(f195,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f196,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f197,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[],[f150]) ).
fof(f199,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f152]) ).
fof(f200,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0))))
| ~ axiom_4 ),
inference(cnf_transformation,[],[f153]) ).
fof(f201,plain,
! [X0] :
( is_a_theorem(implies(X0,necessarily(possibly(X0))))
| ~ axiom_B ),
inference(cnf_transformation,[],[f154]) ).
fof(f202,plain,
( axiom_m6
| ~ is_a_theorem(strict_implies(sK0,possibly(sK0))) ),
inference(cnf_transformation,[],[f160]) ).
fof(f203,plain,
! [X0] :
( possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(cnf_transformation,[],[f156]) ).
fof(f204,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f157]) ).
fof(f207,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f209,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f210,plain,
axiom_4,
inference(cnf_transformation,[],[f81]) ).
fof(f211,plain,
axiom_B,
inference(cnf_transformation,[],[f82]) ).
fof(f212,plain,
op_possibly,
inference(cnf_transformation,[],[f83]) ).
fof(f213,plain,
op_or,
inference(cnf_transformation,[],[f84]) ).
fof(f214,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f217,plain,
~ axiom_m6,
inference(cnf_transformation,[],[f105]) ).
cnf(c_49,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_50,plain,
( ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents
| X0 = X1 ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_51,plain,
( ~ modus_tollens
| is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))) ),
inference(cnf_transformation,[],[f163]) ).
cnf(c_53,plain,
( ~ implies_2
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f165]) ).
cnf(c_55,plain,
( ~ and_1
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f167]) ).
cnf(c_57,plain,
( ~ and_3
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(cnf_transformation,[],[f169]) ).
cnf(c_58,plain,
( ~ or_1
| is_a_theorem(implies(X0,or(X0,X1))) ),
inference(cnf_transformation,[],[f170]) ).
cnf(c_59,plain,
( ~ or_2
| is_a_theorem(implies(X0,or(X1,X0))) ),
inference(cnf_transformation,[],[f171]) ).
cnf(c_63,plain,
( ~ equivalence_3
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(cnf_transformation,[],[f175]) ).
cnf(c_64,plain,
( ~ op_or
| not(and(not(X0),not(X1))) = or(X0,X1) ),
inference(cnf_transformation,[],[f176]) ).
cnf(c_65,plain,
( ~ op_implies_and
| not(and(X0,not(X1))) = implies(X0,X1) ),
inference(cnf_transformation,[],[f177]) ).
cnf(c_68,plain,
op_implies_and,
inference(cnf_transformation,[],[f180]) ).
cnf(c_70,plain,
modus_ponens,
inference(cnf_transformation,[],[f182]) ).
cnf(c_71,plain,
modus_tollens,
inference(cnf_transformation,[],[f183]) ).
cnf(c_73,plain,
implies_2,
inference(cnf_transformation,[],[f185]) ).
cnf(c_75,plain,
and_1,
inference(cnf_transformation,[],[f187]) ).
cnf(c_77,plain,
and_3,
inference(cnf_transformation,[],[f189]) ).
cnf(c_78,plain,
or_1,
inference(cnf_transformation,[],[f190]) ).
cnf(c_79,plain,
or_2,
inference(cnf_transformation,[],[f191]) ).
cnf(c_83,plain,
equivalence_3,
inference(cnf_transformation,[],[f195]) ).
cnf(c_84,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f196]) ).
cnf(c_85,plain,
( ~ is_a_theorem(X0)
| ~ necessitation
| is_a_theorem(necessarily(X0)) ),
inference(cnf_transformation,[],[f197]) ).
cnf(c_87,plain,
( ~ axiom_M
| is_a_theorem(implies(necessarily(X0),X0)) ),
inference(cnf_transformation,[],[f199]) ).
cnf(c_88,plain,
( ~ axiom_4
| is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
inference(cnf_transformation,[],[f200]) ).
cnf(c_89,plain,
( ~ axiom_B
| is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
inference(cnf_transformation,[],[f201]) ).
cnf(c_90,plain,
( ~ is_a_theorem(strict_implies(sK0,possibly(sK0)))
| axiom_m6 ),
inference(cnf_transformation,[],[f202]) ).
cnf(c_91,plain,
( ~ op_possibly
| not(necessarily(not(X0))) = possibly(X0) ),
inference(cnf_transformation,[],[f203]) ).
cnf(c_92,plain,
( ~ op_strict_implies
| necessarily(implies(X0,X1)) = strict_implies(X0,X1) ),
inference(cnf_transformation,[],[f204]) ).
cnf(c_95,plain,
necessitation,
inference(cnf_transformation,[],[f207]) ).
cnf(c_97,plain,
axiom_M,
inference(cnf_transformation,[],[f209]) ).
cnf(c_98,plain,
axiom_4,
inference(cnf_transformation,[],[f210]) ).
cnf(c_99,plain,
axiom_B,
inference(cnf_transformation,[],[f211]) ).
cnf(c_100,plain,
op_possibly,
inference(cnf_transformation,[],[f212]) ).
cnf(c_101,plain,
op_or,
inference(cnf_transformation,[],[f213]) ).
cnf(c_102,plain,
op_strict_implies,
inference(cnf_transformation,[],[f214]) ).
cnf(c_105,negated_conjecture,
~ axiom_m6,
inference(cnf_transformation,[],[f217]) ).
cnf(c_131,plain,
~ is_a_theorem(strict_implies(sK0,possibly(sK0))),
inference(global_subsumption_just,[status(thm)],[c_90,c_105,c_90]) ).
cnf(c_133,plain,
is_a_theorem(implies(necessarily(X0),X0)),
inference(global_subsumption_just,[status(thm)],[c_87,c_97,c_87]) ).
cnf(c_136,plain,
is_a_theorem(implies(X0,necessarily(possibly(X0)))),
inference(global_subsumption_just,[status(thm)],[c_89,c_99,c_89]) ).
cnf(c_139,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_85,c_95,c_85]) ).
cnf(c_142,plain,
is_a_theorem(implies(X0,or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_59,c_79,c_59]) ).
cnf(c_145,plain,
is_a_theorem(implies(X0,or(X0,X1))),
inference(global_subsumption_just,[status(thm)],[c_58,c_78,c_58]) ).
cnf(c_150,plain,
is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption_just,[status(thm)],[c_55,c_75,c_55]) ).
cnf(c_155,plain,
is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))),
inference(global_subsumption_just,[status(thm)],[c_88,c_98,c_88]) ).
cnf(c_158,plain,
not(necessarily(not(X0))) = possibly(X0),
inference(global_subsumption_just,[status(thm)],[c_91,c_100,c_91]) ).
cnf(c_166,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_169,plain,
necessarily(implies(X0,X1)) = strict_implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_92,c_102,c_92]) ).
cnf(c_172,plain,
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(global_subsumption_just,[status(thm)],[c_50,c_84,c_50]) ).
cnf(c_175,plain,
not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_65,c_68,c_65]) ).
cnf(c_178,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_181,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_184,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_185,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(renaming,[status(thm)],[c_184]) ).
cnf(c_189,plain,
not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_64,c_101,c_64]) ).
cnf(c_198,plain,
is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(global_subsumption_just,[status(thm)],[c_63,c_83,c_63]) ).
cnf(c_328,plain,
implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[c_189,c_175]) ).
cnf(c_409,plain,
is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(demodulation,[status(thm)],[c_181,c_328]) ).
cnf(c_2120,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_169,c_139]) ).
cnf(c_2133,plain,
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_178,c_185]) ).
cnf(c_2150,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(implies(X1,X0),equiv(X0,X1))) ),
inference(superposition,[status(thm)],[c_198,c_185]) ).
cnf(c_2197,plain,
is_a_theorem(or(X0,or(X1,not(X0)))),
inference(superposition,[status(thm)],[c_328,c_142]) ).
cnf(c_2207,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(superposition,[status(thm)],[c_409,c_185]) ).
cnf(c_2230,plain,
is_a_theorem(strict_implies(X0,necessarily(possibly(X0)))),
inference(superposition,[status(thm)],[c_136,c_2120]) ).
cnf(c_2265,plain,
is_a_theorem(implies(X0,and(X0,X0))),
inference(superposition,[status(thm)],[c_166,c_2133]) ).
cnf(c_2312,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X1,X0))
| is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[status(thm)],[c_2150,c_185]) ).
cnf(c_4391,plain,
( ~ is_a_theorem(implies(necessarily(necessarily(X0)),necessarily(X0)))
| is_a_theorem(equiv(necessarily(necessarily(X0)),necessarily(X0))) ),
inference(superposition,[status(thm)],[c_155,c_2312]) ).
cnf(c_4426,plain,
( ~ is_a_theorem(implies(and(X0,X0),X0))
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(superposition,[status(thm)],[c_2265,c_2312]) ).
cnf(c_4438,plain,
is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_4426,c_150]) ).
cnf(c_4439,plain,
is_a_theorem(equiv(necessarily(necessarily(X0)),necessarily(X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_4391,c_133]) ).
cnf(c_4924,plain,
and(X0,X0) = X0,
inference(superposition,[status(thm)],[c_4438,c_172]) ).
cnf(c_4944,plain,
implies(not(X0),X0) = not(not(X0)),
inference(superposition,[status(thm)],[c_4924,c_175]) ).
cnf(c_4969,plain,
or(X0,X0) = not(not(X0)),
inference(demodulation,[status(thm)],[c_4944,c_328]) ).
cnf(c_5011,plain,
necessarily(necessarily(X0)) = necessarily(X0),
inference(superposition,[status(thm)],[c_4439,c_172]) ).
cnf(c_6287,plain,
is_a_theorem(implies(X0,not(not(X0)))),
inference(superposition,[status(thm)],[c_4969,c_145]) ).
cnf(c_6308,plain,
is_a_theorem(or(X0,not(not(not(X0))))),
inference(superposition,[status(thm)],[c_4969,c_2197]) ).
cnf(c_6530,plain,
is_a_theorem(implies(necessarily(not(X0)),not(possibly(X0)))),
inference(superposition,[status(thm)],[c_158,c_6287]) ).
cnf(c_6589,plain,
is_a_theorem(implies(not(not(X0)),X0)),
inference(superposition,[status(thm)],[c_6308,c_2207]) ).
cnf(c_6590,plain,
is_a_theorem(or(not(X0),X0)),
inference(demodulation,[status(thm)],[c_6589,c_328]) ).
cnf(c_6602,plain,
is_a_theorem(or(possibly(X0),necessarily(not(X0)))),
inference(superposition,[status(thm)],[c_158,c_6590]) ).
cnf(c_12858,plain,
( ~ is_a_theorem(implies(not(possibly(X0)),necessarily(not(X0))))
| is_a_theorem(equiv(not(possibly(X0)),necessarily(not(X0)))) ),
inference(superposition,[status(thm)],[c_6530,c_2312]) ).
cnf(c_12867,plain,
( ~ is_a_theorem(or(possibly(X0),necessarily(not(X0))))
| is_a_theorem(equiv(not(possibly(X0)),necessarily(not(X0)))) ),
inference(demodulation,[status(thm)],[c_12858,c_328]) ).
cnf(c_12868,plain,
is_a_theorem(equiv(not(possibly(X0)),necessarily(not(X0)))),
inference(forward_subsumption_resolution,[status(thm)],[c_12867,c_6602]) ).
cnf(c_15305,plain,
not(possibly(X0)) = necessarily(not(X0)),
inference(superposition,[status(thm)],[c_12868,c_172]) ).
cnf(c_17369,plain,
not(necessarily(necessarily(not(X0)))) = possibly(possibly(X0)),
inference(superposition,[status(thm)],[c_15305,c_158]) ).
cnf(c_17533,plain,
possibly(possibly(X0)) = possibly(X0),
inference(demodulation,[status(thm)],[c_17369,c_158,c_5011]) ).
cnf(c_17941,plain,
is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))),
inference(superposition,[status(thm)],[c_17533,c_136]) ).
cnf(c_18074,plain,
( ~ is_a_theorem(implies(necessarily(possibly(X0)),possibly(X0)))
| is_a_theorem(equiv(necessarily(possibly(X0)),possibly(X0))) ),
inference(superposition,[status(thm)],[c_17941,c_2312]) ).
cnf(c_18080,plain,
is_a_theorem(equiv(necessarily(possibly(X0)),possibly(X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_18074,c_133]) ).
cnf(c_18106,plain,
necessarily(possibly(X0)) = possibly(X0),
inference(superposition,[status(thm)],[c_18080,c_172]) ).
cnf(c_18193,plain,
is_a_theorem(strict_implies(X0,possibly(X0))),
inference(superposition,[status(thm)],[c_18106,c_2230]) ).
cnf(c_20168,plain,
$false,
inference(superposition,[status(thm)],[c_18193,c_131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL546+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n008.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 : Thu May 2 19:05:43 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 17.51/3.17 % SZS status Started for theBenchmark.p
% 17.51/3.17 % SZS status Theorem for theBenchmark.p
% 17.51/3.17
% 17.51/3.17 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 17.51/3.17
% 17.51/3.17 ------ iProver source info
% 17.51/3.17
% 17.51/3.17 git: date: 2024-05-02 19:28:25 +0000
% 17.51/3.17 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 17.51/3.17 git: non_committed_changes: false
% 17.51/3.17
% 17.51/3.17 ------ Parsing...
% 17.51/3.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 17.51/3.17
% 17.51/3.17 ------ Preprocessing... sup_sim: 2 sf_s rm: 28 0s sf_e pe_s pe_e sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e
% 17.51/3.17
% 17.51/3.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 17.51/3.17
% 17.51/3.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.51/3.17 ------ Proving...
% 17.51/3.17 ------ Problem Properties
% 17.51/3.17
% 17.51/3.17
% 17.51/3.17 clauses 27
% 17.51/3.17 conjectures 0
% 17.51/3.17 EPR 0
% 17.51/3.17 Horn 27
% 17.51/3.17 unary 24
% 17.51/3.17 binary 2
% 17.51/3.17 lits 31
% 17.51/3.17 lits eq 7
% 17.51/3.17 fd_pure 0
% 17.51/3.17 fd_pseudo 0
% 17.51/3.17 fd_cond 0
% 17.51/3.17 fd_pseudo_cond 1
% 17.51/3.17 AC symbols 0
% 17.51/3.17
% 17.51/3.17 ------ Input Options Time Limit: Unbounded
% 17.51/3.17
% 17.51/3.17
% 17.51/3.17 ------
% 17.51/3.17 Current options:
% 17.51/3.17 ------
% 17.51/3.17
% 17.51/3.17
% 17.51/3.17
% 17.51/3.17
% 17.51/3.17 ------ Proving...
% 17.51/3.17
% 17.51/3.17
% 17.51/3.17 % SZS status Theorem for theBenchmark.p
% 17.51/3.17
% 17.51/3.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.51/3.18
% 17.51/3.18
%------------------------------------------------------------------------------