TSTP Solution File: LCL541+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : LCL541+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n032.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 02:38:09 EDT 2024
% Result : Theorem 177.10s 24.25s
% Output : CNFRefutation 177.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 35
% Syntax : Number of formulae : 234 ( 119 unt; 0 def)
% Number of atoms : 378 ( 52 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 256 ( 112 ~; 105 |; 2 &)
% ( 13 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 18 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 333 ( 10 sgn 122 !; 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(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(f14,axiom,
( equivalence_2
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_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(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(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(f47,axiom,
equivalence_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_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(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',km4b_necessitation) ).
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(f87,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_equiv) ).
fof(f89,conjecture,
axiom_m1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m1) ).
fof(f90,negated_conjecture,
~ axiom_m1,
inference(negated_conjecture,[],[f89]) ).
fof(f105,plain,
~ axiom_m1,
inference(flattening,[],[f90]) ).
fof(f106,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
=> axiom_m1 ),
inference(unused_predicate_definition_removal,[],[f63]) ).
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(f113,plain,
( equivalence_2
=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f14]) ).
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(f123,plain,
( implies_1
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
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(f135,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(ennf_transformation,[],[f123]) ).
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(f145,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(ennf_transformation,[],[f113]) ).
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(f149,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f150,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ necessitation ),
inference(ennf_transformation,[],[f111]) ).
fof(f155,plain,
( axiom_m1
| ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
inference(ennf_transformation,[],[f106]) ).
fof(f157,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f159,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(f160,plain,
( axiom_m1
| ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[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(f164,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f135]) ).
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(f174,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(cnf_transformation,[],[f145]) ).
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(f178,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f149]) ).
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(f184,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
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(f194,plain,
equivalence_2,
inference(cnf_transformation,[],[f47]) ).
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(f202,plain,
( axiom_m1
| ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
inference(cnf_transformation,[],[f160]) ).
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(f213,plain,
op_or,
inference(cnf_transformation,[],[f84]) ).
fof(f214,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f215,plain,
op_equiv,
inference(cnf_transformation,[],[f87]) ).
fof(f217,plain,
~ axiom_m1,
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_52,plain,
( ~ implies_1
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(cnf_transformation,[],[f164]) ).
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_62,plain,
( ~ equivalence_2
| is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
inference(cnf_transformation,[],[f174]) ).
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_66,plain,
( ~ op_equiv
| and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) ),
inference(cnf_transformation,[],[f178]) ).
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_72,plain,
implies_1,
inference(cnf_transformation,[],[f184]) ).
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_82,plain,
equivalence_2,
inference(cnf_transformation,[],[f194]) ).
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_90,plain,
( ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0)))
| axiom_m1 ),
inference(cnf_transformation,[],[f202]) ).
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_101,plain,
op_or,
inference(cnf_transformation,[],[f213]) ).
cnf(c_102,plain,
op_strict_implies,
inference(cnf_transformation,[],[f214]) ).
cnf(c_103,plain,
op_equiv,
inference(cnf_transformation,[],[f215]) ).
cnf(c_105,negated_conjecture,
~ axiom_m1,
inference(cnf_transformation,[],[f217]) ).
cnf(c_137,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_85,c_95,c_85]) ).
cnf(c_140,plain,
is_a_theorem(implies(X0,or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_59,c_79,c_59]) ).
cnf(c_143,plain,
is_a_theorem(implies(X0,or(X0,X1))),
inference(global_subsumption_just,[status(thm)],[c_58,c_78,c_58]) ).
cnf(c_148,plain,
is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption_just,[status(thm)],[c_55,c_75,c_55]) ).
cnf(c_150,plain,
is_a_theorem(implies(X0,implies(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_52,c_72,c_52]) ).
cnf(c_159,plain,
~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))),
inference(global_subsumption_just,[status(thm)],[c_90,c_105,c_90]) ).
cnf(c_161,plain,
is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_62,c_82,c_62]) ).
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_195,plain,
and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_66,c_103,c_66]) ).
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_323,plain,
implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[c_189,c_175]) ).
cnf(c_324,plain,
is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(demodulation,[status(thm)],[c_181,c_323]) ).
cnf(c_2010,plain,
or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[status(thm)],[c_175,c_323]) ).
cnf(c_2417,plain,
implies(implies(X0,and(X1,not(X2))),X3) = or(and(X0,implies(X1,X2)),X3),
inference(superposition,[status(thm)],[c_175,c_2010]) ).
cnf(c_17864,plain,
is_a_theorem(or(X0,or(X1,not(X0)))),
inference(superposition,[status(thm)],[c_323,c_140]) ).
cnf(c_17882,plain,
is_a_theorem(implies(or(X0,not(not(X1))),or(X1,X0))),
inference(superposition,[status(thm)],[c_323,c_324]) ).
cnf(c_18210,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_18214,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,and(X0,X1))) ),
inference(superposition,[status(thm)],[c_166,c_185]) ).
cnf(c_18324,plain,
is_a_theorem(implies(X0,and(X0,X0))),
inference(superposition,[status(thm)],[c_166,c_18210]) ).
cnf(c_18685,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(X1)
| is_a_theorem(and(X0,X1)) ),
inference(superposition,[status(thm)],[c_18214,c_185]) ).
cnf(c_19821,plain,
( ~ is_a_theorem(or(X0,not(not(X1))))
| is_a_theorem(or(X1,X0)) ),
inference(superposition,[status(thm)],[c_17882,c_185]) ).
cnf(c_20663,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X1,X0))
| is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[status(thm)],[c_195,c_18685]) ).
cnf(c_52385,plain,
( ~ is_a_theorem(implies(and(X0,X0),X0))
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(superposition,[status(thm)],[c_18324,c_20663]) ).
cnf(c_52494,plain,
is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_52385,c_148]) ).
cnf(c_53441,plain,
and(X0,X0) = X0,
inference(superposition,[status(thm)],[c_52494,c_172]) ).
cnf(c_53499,plain,
implies(not(X0),X0) = not(not(X0)),
inference(superposition,[status(thm)],[c_53441,c_175]) ).
cnf(c_53727,plain,
or(X0,X0) = not(not(X0)),
inference(demodulation,[status(thm)],[c_53499,c_323]) ).
cnf(c_56365,plain,
is_a_theorem(implies(X0,not(not(X0)))),
inference(superposition,[status(thm)],[c_53727,c_143]) ).
cnf(c_56393,plain,
is_a_theorem(or(X0,not(not(not(X0))))),
inference(superposition,[status(thm)],[c_53727,c_17864]) ).
cnf(c_60068,plain,
( ~ is_a_theorem(implies(not(not(X0)),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(superposition,[status(thm)],[c_56365,c_20663]) ).
cnf(c_60072,plain,
( ~ is_a_theorem(or(not(X0),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(demodulation,[status(thm)],[c_60068,c_323]) ).
cnf(c_60116,plain,
is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_56393,c_19821]) ).
cnf(c_60138,plain,
is_a_theorem(equiv(not(not(X0)),X0)),
inference(backward_subsumption_resolution,[status(thm)],[c_60072,c_60116]) ).
cnf(c_60167,plain,
not(not(X0)) = X0,
inference(superposition,[status(thm)],[c_60138,c_172]) ).
cnf(c_61634,plain,
not(implies(X0,X1)) = and(X0,not(X1)),
inference(superposition,[status(thm)],[c_175,c_60167]) ).
cnf(c_64495,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_169,c_137]) ).
cnf(c_64500,plain,
not(not(implies(X0,X1))) = implies(X0,X1),
inference(demodulation,[status(thm)],[c_175,c_61634]) ).
cnf(c_64516,plain,
not(not(or(X0,X1))) = or(X0,X1),
inference(superposition,[status(thm)],[c_323,c_64500]) ).
cnf(c_64525,plain,
is_a_theorem(implies(X0,or(X1,and(X0,not(X1))))),
inference(superposition,[status(thm)],[c_323,c_166]) ).
cnf(c_64531,plain,
is_a_theorem(implies(X0,or(X1,not(implies(X0,X1))))),
inference(demodulation,[status(thm)],[c_64525,c_61634]) ).
cnf(c_64590,plain,
not(implies(X0,not(implies(X1,X2)))) = and(X0,implies(X1,X2)),
inference(superposition,[status(thm)],[c_64500,c_61634]) ).
cnf(c_64663,plain,
implies(implies(X0,not(implies(X1,X2))),X3) = or(and(X0,implies(X1,X2)),X3),
inference(demodulation,[status(thm)],[c_2417,c_61634]) ).
cnf(c_64666,plain,
implies(implies(X0,not(or(X1,X2))),X3) = or(and(X0,or(X1,X2)),X3),
inference(superposition,[status(thm)],[c_323,c_64663]) ).
cnf(c_65047,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_65051,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,and(X0,X1))) ),
inference(superposition,[status(thm)],[c_166,c_185]) ).
cnf(c_65057,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_65061,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(superposition,[status(thm)],[c_324,c_185]) ).
cnf(c_65070,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(or(X1,not(implies(X0,X1)))) ),
inference(superposition,[status(thm)],[c_64531,c_185]) ).
cnf(c_65399,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(X1)
| is_a_theorem(and(X0,X1)) ),
inference(superposition,[status(thm)],[c_65051,c_185]) ).
cnf(c_66051,plain,
or(implies(X0,not(implies(X1,X2))),X3) = implies(and(X0,implies(X1,X2)),X3),
inference(superposition,[status(thm)],[c_64590,c_323]) ).
cnf(c_66416,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(superposition,[status(thm)],[c_65070,c_65061]) ).
cnf(c_66550,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X1,X0))
| is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[status(thm)],[c_195,c_65399]) ).
cnf(c_67903,plain,
is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_150,c_65047]) ).
cnf(c_67905,plain,
is_a_theorem(implies(X0,and(X0,X0))),
inference(superposition,[status(thm)],[c_166,c_65047]) ).
cnf(c_67938,plain,
is_a_theorem(strict_implies(X0,X0)),
inference(superposition,[status(thm)],[c_67903,c_64495]) ).
cnf(c_67965,plain,
is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[status(thm)],[c_323,c_67905]) ).
cnf(c_67975,plain,
is_a_theorem(or(X0,not(or(X0,X0)))),
inference(demodulation,[status(thm)],[c_67965,c_323,c_61634]) ).
cnf(c_68204,plain,
is_a_theorem(implies(or(X0,X0),X0)),
inference(superposition,[status(thm)],[c_67975,c_65061]) ).
cnf(c_68455,plain,
( ~ is_a_theorem(implies(implies(X0,X1),equiv(X1,X0)))
| is_a_theorem(equiv(implies(X0,X1),equiv(X1,X0))) ),
inference(superposition,[status(thm)],[c_161,c_66550]) ).
cnf(c_68506,plain,
( ~ is_a_theorem(implies(X0,implies(X1,X0)))
| ~ is_a_theorem(X1)
| is_a_theorem(equiv(X0,implies(X1,X0))) ),
inference(superposition,[status(thm)],[c_66416,c_66550]) ).
cnf(c_68526,plain,
( ~ is_a_theorem(implies(X0,or(X0,X0)))
| is_a_theorem(equiv(X0,or(X0,X0))) ),
inference(superposition,[status(thm)],[c_68204,c_66550]) ).
cnf(c_68530,plain,
is_a_theorem(equiv(X0,or(X0,X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_68526,c_143]) ).
cnf(c_68533,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(equiv(X1,implies(X0,X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_68506,c_150]) ).
cnf(c_68549,plain,
or(X0,X0) = X0,
inference(superposition,[status(thm)],[c_68530,c_172]) ).
cnf(c_68616,plain,
not(not(X0)) = X0,
inference(superposition,[status(thm)],[c_68549,c_64516]) ).
cnf(c_68659,plain,
implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(superposition,[status(thm)],[c_68549,c_64666]) ).
cnf(c_68866,plain,
or(not(X0),X1) = implies(X0,X1),
inference(superposition,[status(thm)],[c_68616,c_323]) ).
cnf(c_68874,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(implies(not(X1),X0)) ),
inference(superposition,[status(thm)],[c_68616,c_65061]) ).
cnf(c_68896,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,X0)) ),
inference(demodulation,[status(thm)],[c_68874,c_323]) ).
cnf(c_68989,plain,
is_a_theorem(implies(implies(X0,not(X1)),implies(X1,not(X0)))),
inference(superposition,[status(thm)],[c_68866,c_324]) ).
cnf(c_69047,plain,
is_a_theorem(or(and(X0,X1),implies(X1,not(X0)))),
inference(demodulation,[status(thm)],[c_68989,c_68659]) ).
cnf(c_71847,plain,
( ~ is_a_theorem(X0)
| implies(X0,X1) = X1 ),
inference(superposition,[status(thm)],[c_68533,c_172]) ).
cnf(c_72068,plain,
implies(implies(X0,X0),X1) = X1,
inference(superposition,[status(thm)],[c_67903,c_71847]) ).
cnf(c_72609,plain,
( ~ is_a_theorem(implies(X0,implies(X1,X1)))
| is_a_theorem(implies(X0,equiv(X0,implies(X1,X1)))) ),
inference(superposition,[status(thm)],[c_72068,c_65057]) ).
cnf(c_72629,plain,
( ~ is_a_theorem(implies(X0,equiv(X0,implies(X1,X1))))
| is_a_theorem(equiv(implies(implies(X1,X1),X0),equiv(X0,implies(X1,X1)))) ),
inference(superposition,[status(thm)],[c_72068,c_68455]) ).
cnf(c_72657,plain,
is_a_theorem(implies(X0,implies(X1,X1))),
inference(superposition,[status(thm)],[c_72068,c_150]) ).
cnf(c_72755,plain,
is_a_theorem(implies(X0,equiv(X0,implies(X1,X1)))),
inference(forward_subsumption_resolution,[status(thm)],[c_72609,c_72657]) ).
cnf(c_72766,plain,
is_a_theorem(equiv(implies(implies(X0,X0),X1),equiv(X1,implies(X0,X0)))),
inference(forward_subsumption_resolution,[status(thm)],[c_72629,c_72755]) ).
cnf(c_72767,plain,
is_a_theorem(equiv(X0,equiv(X0,implies(X1,X1)))),
inference(demodulation,[status(thm)],[c_72766,c_72068]) ).
cnf(c_77439,plain,
equiv(X0,implies(X1,X1)) = X0,
inference(superposition,[status(thm)],[c_72767,c_172]) ).
cnf(c_77568,plain,
( ~ is_a_theorem(X0)
| implies(X1,X1) = X0 ),
inference(superposition,[status(thm)],[c_77439,c_172]) ).
cnf(c_77695,plain,
implies(X0,X0) = strict_implies(X1,X1),
inference(superposition,[status(thm)],[c_67938,c_77568]) ).
cnf(c_77828,plain,
implies(X0,X0) = sP0_iProver_def,
inference(splitting,[splitting(split),new_symbols(definition,[sP0_iProver_def])],[c_77695]) ).
cnf(c_77998,plain,
implies(sP0_iProver_def,X0) = X0,
inference(demodulation,[status(thm)],[c_72068,c_77828]) ).
cnf(c_83088,plain,
or(implies(X0,not(X1)),X2) = implies(and(X0,X1),X2),
inference(superposition,[status(thm)],[c_77998,c_66051]) ).
cnf(c_89048,plain,
is_a_theorem(or(implies(X0,not(X1)),and(X1,X0))),
inference(superposition,[status(thm)],[c_69047,c_68896]) ).
cnf(c_89058,plain,
is_a_theorem(implies(and(X0,X1),and(X1,X0))),
inference(demodulation,[status(thm)],[c_89048,c_83088]) ).
cnf(c_89129,plain,
is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))),
inference(superposition,[status(thm)],[c_89058,c_64495]) ).
cnf(c_89169,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_159,c_89129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL541+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.03/0.12 % Command : run_iprover %s %d THM
% 0.11/0.33 % Computer : n032.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu May 2 19:01:38 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.18/0.45 Running first-order theorem proving
% 0.18/0.45 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
% 177.10/24.25 % SZS status Started for theBenchmark.p
% 177.10/24.25 % SZS status Theorem for theBenchmark.p
% 177.10/24.25
% 177.10/24.25 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 177.10/24.25
% 177.10/24.25 ------ iProver source info
% 177.10/24.25
% 177.10/24.25 git: date: 2024-05-02 19:28:25 +0000
% 177.10/24.25 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 177.10/24.25 git: non_committed_changes: false
% 177.10/24.25
% 177.10/24.25 ------ Parsing...
% 177.10/24.25 ------ Clausification by vclausify_rel & Parsing by iProver...
% 177.10/24.25
% 177.10/24.25 ------ Preprocessing... sup_sim: 3 sf_s rm: 28 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 177.10/24.25
% 177.10/24.25 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 177.10/24.25
% 177.10/24.25 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 177.10/24.25 ------ Proving...
% 177.10/24.25 ------ Problem Properties
% 177.10/24.25
% 177.10/24.25
% 177.10/24.25 clauses 27
% 177.10/24.25 conjectures 0
% 177.10/24.25 EPR 0
% 177.10/24.25 Horn 27
% 177.10/24.25 unary 24
% 177.10/24.25 binary 2
% 177.10/24.25 lits 31
% 177.10/24.25 lits eq 7
% 177.10/24.25 fd_pure 0
% 177.10/24.25 fd_pseudo 0
% 177.10/24.25 fd_cond 0
% 177.10/24.25 fd_pseudo_cond 1
% 177.10/24.25 AC symbols 0
% 177.10/24.25
% 177.10/24.25 ------ Input Options Time Limit: Unbounded
% 177.10/24.25
% 177.10/24.25
% 177.10/24.25 ------
% 177.10/24.25 Current options:
% 177.10/24.25 ------
% 177.10/24.25
% 177.10/24.25
% 177.10/24.25
% 177.10/24.25
% 177.10/24.25 ------ Proving...
% 177.10/24.25
% 177.10/24.25
% 177.10/24.25 % SZS status Theorem for theBenchmark.p
% 177.10/24.25
% 177.10/24.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 177.10/24.25
% 177.10/24.26
%------------------------------------------------------------------------------