TSTP Solution File: LCL528+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : LCL528+1 : TPTP v8.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n025.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 : Mon Jun 24 11:05:47 EDT 2024
% Result : Theorem 202.12s 27.43s
% Output : CNFRefutation 202.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 31
% Syntax : Number of formulae : 223 ( 130 unt; 0 def)
% Number of atoms : 343 ( 72 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 212 ( 92 ~; 85 |; 2 &)
% ( 11 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 16 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 322 ( 13 sgn 102 !; 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/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(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_1) ).
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(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_2) ).
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(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(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_equiv) ).
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(f37,axiom,
implies_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_1) ).
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(f41,axiom,
and_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_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(f63,axiom,
( axiom_m1
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m1) ).
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',km5_necessitation) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_M) ).
fof(f83,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_or) ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f86,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_equiv) ).
fof(f88,conjecture,
axiom_m1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m1) ).
fof(f89,negated_conjecture,
~ axiom_m1,
inference(negated_conjecture,[],[f88]) ).
fof(f104,plain,
~ axiom_m1,
inference(flattening,[],[f89]) ).
fof(f105,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
=> axiom_m1 ),
inference(unused_predicate_definition_removal,[],[f63]) ).
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(f116,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f117,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
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(f121,plain,
( implies_1
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
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(f133,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(ennf_transformation,[],[f121]) ).
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(f137,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f117]) ).
fof(f138,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f116]) ).
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(f152,plain,
( axiom_m1
| ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
inference(ennf_transformation,[],[f105]) ).
fof(f154,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f156,plain,
( ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
=> ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
introduced(choice_axiom,[]) ).
fof(f157,plain,
( axiom_m1
| ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[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(f161,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f133]) ).
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(f165,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f137]) ).
fof(f166,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f138]) ).
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(f181,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f182,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f184,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f185,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f186,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
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(f198,plain,
( axiom_m1
| ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
inference(cnf_transformation,[],[f157]) ).
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(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_m1,
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_52,plain,
( ~ implies_1
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(cnf_transformation,[],[f161]) ).
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_56,plain,
( ~ and_2
| is_a_theorem(implies(and(X0,X1),X1)) ),
inference(cnf_transformation,[],[f165]) ).
cnf(c_57,plain,
( ~ and_3
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(cnf_transformation,[],[f166]) ).
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_72,plain,
implies_1,
inference(cnf_transformation,[],[f181]) ).
cnf(c_73,plain,
implies_2,
inference(cnf_transformation,[],[f182]) ).
cnf(c_75,plain,
and_1,
inference(cnf_transformation,[],[f184]) ).
cnf(c_76,plain,
and_2,
inference(cnf_transformation,[],[f185]) ).
cnf(c_77,plain,
and_3,
inference(cnf_transformation,[],[f186]) ).
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_89,plain,
( ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0)))
| axiom_m1 ),
inference(cnf_transformation,[],[f198]) ).
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_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_m1,
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_139,plain,
is_a_theorem(implies(and(X0,X1),X1)),
inference(global_subsumption_just,[status(thm)],[c_56,c_76,c_56]) ).
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_144,plain,
is_a_theorem(implies(X0,implies(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_52,c_72,c_52]) ).
cnf(c_153,plain,
~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))),
inference(global_subsumption_just,[status(thm)],[c_89,c_103,c_89]) ).
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_313,plain,
implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[c_183,c_169]) ).
cnf(c_314,plain,
is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(demodulation,[status(thm)],[c_175,c_313]) ).
cnf(c_6059,plain,
or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[status(thm)],[c_169,c_313]) ).
cnf(c_6819,plain,
is_a_theorem(implies(implies(implies(X0,X1),not(X2)),implies(X2,and(X0,not(X1))))),
inference(superposition,[status(thm)],[c_6059,c_314]) ).
cnf(c_56873,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_163,c_131]) ).
cnf(c_56879,plain,
is_a_theorem(implies(or(X0,not(not(X1))),or(X1,X0))),
inference(superposition,[status(thm)],[c_313,c_314]) ).
cnf(c_56900,plain,
or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[status(thm)],[c_169,c_313]) ).
cnf(c_56902,plain,
implies(X0,and(X1,not(X2))) = not(and(X0,implies(X1,X2))),
inference(superposition,[status(thm)],[c_169,c_169]) ).
cnf(c_56925,plain,
is_a_theorem(strict_implies(and(X0,X1),X1)),
inference(superposition,[status(thm)],[c_139,c_56873]) ).
cnf(c_57082,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,and(X0,X1))) ),
inference(superposition,[status(thm)],[c_160,c_179]) ).
cnf(c_57091,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(superposition,[status(thm)],[c_314,c_179]) ).
cnf(c_57198,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(X1)
| is_a_theorem(and(X0,X1)) ),
inference(superposition,[status(thm)],[c_57082,c_179]) ).
cnf(c_57401,plain,
implies(implies(X0,X1),and(X1,not(X0))) = not(equiv(X0,X1)),
inference(superposition,[status(thm)],[c_189,c_56902]) ).
cnf(c_57403,plain,
implies(X0,and(not(X1),not(X2))) = not(and(X0,or(X1,X2))),
inference(superposition,[status(thm)],[c_313,c_56902]) ).
cnf(c_57586,plain,
is_a_theorem(implies(implies(or(X0,X1),not(X2)),implies(X2,and(not(X0),not(X1))))),
inference(superposition,[status(thm)],[c_313,c_6819]) ).
cnf(c_57598,plain,
is_a_theorem(implies(implies(or(X0,X1),not(X2)),not(and(X2,or(X0,X1))))),
inference(demodulation,[status(thm)],[c_57586,c_57403]) ).
cnf(c_57956,plain,
is_a_theorem(implies(and(X0,not(X1)),not(equiv(X1,X0)))),
inference(superposition,[status(thm)],[c_57401,c_144]) ).
cnf(c_58041,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_57198]) ).
cnf(c_58714,plain,
( ~ is_a_theorem(implies(implies(X0,X1),implies(X0,implies(X0,X1))))
| is_a_theorem(equiv(implies(X0,X1),implies(X0,implies(X0,X1)))) ),
inference(superposition,[status(thm)],[c_172,c_58041]) ).
cnf(c_58744,plain,
( ~ is_a_theorem(implies(and(X0,X1),X1))
| ~ is_a_theorem(X0)
| is_a_theorem(equiv(and(X0,X1),X1)) ),
inference(superposition,[status(thm)],[c_57082,c_58041]) ).
cnf(c_58780,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(equiv(and(X0,X1),X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_58744,c_139]) ).
cnf(c_58784,plain,
is_a_theorem(equiv(implies(X0,X1),implies(X0,implies(X0,X1)))),
inference(forward_subsumption_resolution,[status(thm)],[c_58714,c_144]) ).
cnf(c_58884,plain,
( ~ is_a_theorem(X0)
| and(X0,X1) = X1 ),
inference(superposition,[status(thm)],[c_58780,c_166]) ).
cnf(c_59237,plain,
and(implies(necessarily(X0),X0),X1) = X1,
inference(superposition,[status(thm)],[c_128,c_58884]) ).
cnf(c_59860,plain,
is_a_theorem(strict_implies(X0,X0)),
inference(superposition,[status(thm)],[c_59237,c_56925]) ).
cnf(c_59864,plain,
is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_59237,c_139]) ).
cnf(c_59942,plain,
and(strict_implies(X0,X0),X1) = X1,
inference(superposition,[status(thm)],[c_59860,c_58884]) ).
cnf(c_59945,plain,
and(implies(X0,X0),X1) = X1,
inference(superposition,[status(thm)],[c_59864,c_58884]) ).
cnf(c_60341,plain,
is_a_theorem(implies(X0,strict_implies(X1,X1))),
inference(superposition,[status(thm)],[c_59942,c_142]) ).
cnf(c_60353,plain,
is_a_theorem(implies(not(X0),not(equiv(X0,strict_implies(X1,X1))))),
inference(superposition,[status(thm)],[c_59942,c_57956]) ).
cnf(c_60364,plain,
implies(strict_implies(X0,X0),X1) = not(not(X1)),
inference(superposition,[status(thm)],[c_59942,c_169]) ).
cnf(c_60412,plain,
is_a_theorem(or(X0,not(equiv(X0,strict_implies(X1,X1))))),
inference(demodulation,[status(thm)],[c_60353,c_313]) ).
cnf(c_60657,plain,
and(implies(X0,strict_implies(X1,X1)),X2) = X2,
inference(superposition,[status(thm)],[c_60341,c_58884]) ).
cnf(c_60688,plain,
is_a_theorem(implies(X0,implies(X1,X1))),
inference(superposition,[status(thm)],[c_59945,c_142]) ).
cnf(c_60712,plain,
implies(implies(X0,X0),X1) = not(not(X1)),
inference(superposition,[status(thm)],[c_59945,c_169]) ).
cnf(c_60790,plain,
and(implies(X0,implies(X1,X1)),X2) = X2,
inference(superposition,[status(thm)],[c_60688,c_58884]) ).
cnf(c_64136,plain,
is_a_theorem(implies(equiv(X0,strict_implies(X1,X1)),X0)),
inference(superposition,[status(thm)],[c_60412,c_57091]) ).
cnf(c_68025,plain,
implies(X0,implies(X0,X1)) = implies(X0,X1),
inference(superposition,[status(thm)],[c_58784,c_166]) ).
cnf(c_131492,plain,
and(implies(X0,strict_implies(X1,X1)),not(not(X0))) = equiv(X0,strict_implies(X1,X1)),
inference(superposition,[status(thm)],[c_60364,c_189]) ).
cnf(c_131496,plain,
is_a_theorem(implies(X0,not(not(X0)))),
inference(superposition,[status(thm)],[c_60364,c_144]) ).
cnf(c_132020,plain,
equiv(X0,strict_implies(X1,X1)) = not(not(X0)),
inference(demodulation,[status(thm)],[c_131492,c_60657]) ).
cnf(c_132168,plain,
is_a_theorem(implies(not(not(X0)),X0)),
inference(demodulation,[status(thm)],[c_64136,c_132020]) ).
cnf(c_132170,plain,
is_a_theorem(or(not(X0),X0)),
inference(demodulation,[status(thm)],[c_132168,c_313]) ).
cnf(c_133751,plain,
( ~ is_a_theorem(implies(not(not(X0)),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(superposition,[status(thm)],[c_131496,c_58041]) ).
cnf(c_133755,plain,
( ~ is_a_theorem(or(not(X0),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(demodulation,[status(thm)],[c_133751,c_313]) ).
cnf(c_133756,plain,
is_a_theorem(equiv(not(not(X0)),X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_133755,c_132170]) ).
cnf(c_136410,plain,
not(not(X0)) = X0,
inference(superposition,[status(thm)],[c_133756,c_166]) ).
cnf(c_136444,plain,
is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(demodulation,[status(thm)],[c_56879,c_136410]) ).
cnf(c_136471,plain,
not(implies(X0,X1)) = and(X0,not(X1)),
inference(superposition,[status(thm)],[c_169,c_136410]) ).
cnf(c_136580,plain,
or(not(X0),X1) = implies(X0,X1),
inference(superposition,[status(thm)],[c_136410,c_313]) ).
cnf(c_136694,plain,
implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(superposition,[status(thm)],[c_136410,c_56900]) ).
cnf(c_136713,plain,
implies(X0,not(X1)) = not(and(X0,X1)),
inference(superposition,[status(thm)],[c_136410,c_169]) ).
cnf(c_136998,plain,
implies(X0,not(implies(not(X1),X2))) = not(and(X0,or(X1,X2))),
inference(demodulation,[status(thm)],[c_57403,c_136471]) ).
cnf(c_137012,plain,
implies(X0,not(or(X1,X2))) = not(and(X0,or(X1,X2))),
inference(demodulation,[status(thm)],[c_136998,c_313]) ).
cnf(c_137015,plain,
is_a_theorem(implies(implies(or(X0,X1),not(X2)),implies(X2,not(or(X0,X1))))),
inference(demodulation,[status(thm)],[c_57598,c_137012]) ).
cnf(c_144949,plain,
( ~ is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| is_a_theorem(equiv(or(X0,X1),or(X1,X0))) ),
inference(superposition,[status(thm)],[c_136444,c_58041]) ).
cnf(c_144952,plain,
is_a_theorem(equiv(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_144949,c_136444]) ).
cnf(c_147342,plain,
or(X0,X1) = or(X1,X0),
inference(superposition,[status(thm)],[c_144952,c_166]) ).
cnf(c_150421,plain,
or(X0,not(X1)) = implies(X1,X0),
inference(superposition,[status(thm)],[c_136580,c_147342]) ).
cnf(c_151626,plain,
implies(implies(X0,X0),X1) = X1,
inference(demodulation,[status(thm)],[c_60712,c_136410]) ).
cnf(c_151642,plain,
and(implies(X0,implies(X1,X1)),X0) = equiv(X0,implies(X1,X1)),
inference(superposition,[status(thm)],[c_151626,c_189]) ).
cnf(c_151702,plain,
is_a_theorem(implies(X0,and(X0,implies(X1,X1)))),
inference(superposition,[status(thm)],[c_151626,c_160]) ).
cnf(c_151885,plain,
equiv(X0,implies(X1,X1)) = X0,
inference(demodulation,[status(thm)],[c_151642,c_60790]) ).
cnf(c_152676,plain,
( ~ is_a_theorem(X0)
| implies(X1,X1) = X0 ),
inference(superposition,[status(thm)],[c_151885,c_166]) ).
cnf(c_152856,plain,
implies(and(X0,X1),X0) = implies(X2,X2),
inference(superposition,[status(thm)],[c_142,c_152676]) ).
cnf(c_152944,plain,
implies(X0,X0) = strict_implies(X1,X1),
inference(superposition,[status(thm)],[c_59860,c_152676]) ).
cnf(c_153183,plain,
implies(X0,X0) = sP0_iProver_def,
inference(splitting,[splitting(split),new_symbols(definition,[sP0_iProver_def])],[c_152944]) ).
cnf(c_153208,plain,
implies(and(X0,X1),X0) = sP0_iProver_def,
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_152856]) ).
cnf(c_153453,plain,
and(sP0_iProver_def,X0) = X0,
inference(demodulation,[status(thm)],[c_59945,c_153183]) ).
cnf(c_153454,plain,
is_a_theorem(sP0_iProver_def),
inference(demodulation,[status(thm)],[c_59864,c_153183]) ).
cnf(c_153455,plain,
( ~ is_a_theorem(X0)
| X0 = sP0_iProver_def ),
inference(demodulation,[status(thm)],[c_152676,c_153183]) ).
cnf(c_153462,plain,
is_a_theorem(implies(X0,and(X0,sP0_iProver_def))),
inference(demodulation,[status(thm)],[c_151702,c_153183]) ).
cnf(c_155468,plain,
implies(X0,and(X0,sP0_iProver_def)) = sP0_iProver_def,
inference(superposition,[status(thm)],[c_153462,c_153455]) ).
cnf(c_157071,plain,
and(sP0_iProver_def,implies(and(X0,sP0_iProver_def),X0)) = equiv(X0,and(X0,sP0_iProver_def)),
inference(superposition,[status(thm)],[c_155468,c_189]) ).
cnf(c_157103,plain,
equiv(X0,and(X0,sP0_iProver_def)) = sP0_iProver_def,
inference(demodulation,[status(thm)],[c_157071,c_153208,c_153453]) ).
cnf(c_157142,plain,
( ~ is_a_theorem(sP0_iProver_def)
| and(X0,sP0_iProver_def) = X0 ),
inference(superposition,[status(thm)],[c_157103,c_166]) ).
cnf(c_157157,plain,
and(X0,sP0_iProver_def) = X0,
inference(forward_subsumption_resolution,[status(thm)],[c_157142,c_153454]) ).
cnf(c_157176,plain,
implies(X0,not(sP0_iProver_def)) = not(X0),
inference(superposition,[status(thm)],[c_157157,c_136713]) ).
cnf(c_157217,plain,
implies(X0,not(X0)) = not(X0),
inference(superposition,[status(thm)],[c_157176,c_68025]) ).
cnf(c_157277,plain,
implies(not(X0),X0) = X0,
inference(superposition,[status(thm)],[c_136410,c_157217]) ).
cnf(c_157320,plain,
or(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_157277,c_313]) ).
cnf(c_172265,plain,
or(X0,implies(X1,not(X2))) = implies(and(X1,X2),X0),
inference(superposition,[status(thm)],[c_136713,c_150421]) ).
cnf(c_173440,plain,
is_a_theorem(implies(and(X0,or(X1,X2)),and(or(X1,X2),X0))),
inference(demodulation,[status(thm)],[c_137015,c_136694,c_172265]) ).
cnf(c_173463,plain,
is_a_theorem(implies(and(X0,X1),and(X1,X0))),
inference(superposition,[status(thm)],[c_157320,c_173440]) ).
cnf(c_173610,plain,
is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))),
inference(superposition,[status(thm)],[c_173463,c_56873]) ).
cnf(c_173627,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_153,c_173610]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL528+1 : TPTP v8.2.0. Released v3.3.0.
% 0.12/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Jun 22 13:17:39 EDT 2024
% 0.19/0.34 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 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
% 202.12/27.43 % SZS status Started for theBenchmark.p
% 202.12/27.43 % SZS status Theorem for theBenchmark.p
% 202.12/27.43
% 202.12/27.43 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 202.12/27.43
% 202.12/27.43 ------ iProver source info
% 202.12/27.43
% 202.12/27.43 git: date: 2024-06-12 09:56:46 +0000
% 202.12/27.43 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 202.12/27.43 git: non_committed_changes: false
% 202.12/27.43
% 202.12/27.43 ------ Parsing...
% 202.12/27.43 ------ Clausification by vclausify_rel & Parsing by iProver...
% 202.12/27.43
% 202.12/27.43 ------ 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
% 202.12/27.43
% 202.12/27.43 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 202.12/27.43
% 202.12/27.43 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 202.12/27.43 ------ Proving...
% 202.12/27.43 ------ Problem Properties
% 202.12/27.43
% 202.12/27.43
% 202.12/27.43 clauses 26
% 202.12/27.43 conjectures 0
% 202.12/27.43 EPR 0
% 202.12/27.43 Horn 26
% 202.12/27.43 unary 23
% 202.12/27.43 binary 2
% 202.12/27.43 lits 30
% 202.12/27.43 lits eq 7
% 202.12/27.43 fd_pure 0
% 202.12/27.43 fd_pseudo 0
% 202.12/27.43 fd_cond 0
% 202.12/27.43 fd_pseudo_cond 1
% 202.12/27.43 AC symbols 0
% 202.12/27.43
% 202.12/27.43 ------ Input Options Time Limit: Unbounded
% 202.12/27.43
% 202.12/27.43
% 202.12/27.43 ------
% 202.12/27.43 Current options:
% 202.12/27.43 ------
% 202.12/27.43
% 202.12/27.43
% 202.12/27.43
% 202.12/27.43
% 202.12/27.43 ------ Proving...
% 202.12/27.43
% 202.12/27.43
% 202.12/27.43 % SZS status Theorem for theBenchmark.p
% 202.12/27.43
% 202.12/27.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 202.12/27.43
% 202.12/27.44
%------------------------------------------------------------------------------