TSTP Solution File: LCL541+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : LCL541+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 07:44:58 EDT 2023
% Result : Theorem 159.67s 21.82s
% Output : CNFRefutation 159.67s
% 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/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f3,axiom,
( modus_tollens
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_tollens) ).
fof(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',implies_2) ).
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_1) ).
fof(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_3) ).
fof(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_1) ).
fof(f11,axiom,
( or_2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_2) ).
fof(f14,axiom,
( equivalence_2
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',equivalence_3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_1) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f43,axiom,
or_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f44,axiom,
or_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_2) ).
fof(f47,axiom,
equivalence_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',necessitation) ).
fof(f63,axiom,
( axiom_m1
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m1) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km4b_necessitation) ).
fof(f84,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_or) ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f87,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_equiv) ).
fof(f89,conjecture,
axiom_m1,
file('/export/starexec/sandbox/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_1831,plain,
or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[status(thm)],[c_175,c_323]) ).
cnf(c_2238,plain,
implies(implies(X0,and(X1,not(X2))),X3) = or(and(X0,implies(X1,X2)),X3),
inference(superposition,[status(thm)],[c_175,c_1831]) ).
cnf(c_15655,plain,
is_a_theorem(or(X0,or(X1,not(X0)))),
inference(superposition,[status(thm)],[c_323,c_140]) ).
cnf(c_15673,plain,
is_a_theorem(implies(or(X0,not(not(X1))),or(X1,X0))),
inference(superposition,[status(thm)],[c_323,c_324]) ).
cnf(c_16001,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_16005,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,and(X0,X1))) ),
inference(superposition,[status(thm)],[c_166,c_185]) ).
cnf(c_16115,plain,
is_a_theorem(implies(X0,and(X0,X0))),
inference(superposition,[status(thm)],[c_166,c_16001]) ).
cnf(c_16476,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(X1)
| is_a_theorem(and(X0,X1)) ),
inference(superposition,[status(thm)],[c_16005,c_185]) ).
cnf(c_17612,plain,
( ~ is_a_theorem(or(X0,not(not(X1))))
| is_a_theorem(or(X1,X0)) ),
inference(superposition,[status(thm)],[c_15673,c_185]) ).
cnf(c_18454,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_16476]) ).
cnf(c_42329,plain,
( ~ is_a_theorem(implies(and(X0,X0),X0))
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(superposition,[status(thm)],[c_16115,c_18454]) ).
cnf(c_42444,plain,
is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_42329,c_148]) ).
cnf(c_42976,plain,
and(X0,X0) = X0,
inference(superposition,[status(thm)],[c_42444,c_172]) ).
cnf(c_43034,plain,
implies(not(X0),X0) = not(not(X0)),
inference(superposition,[status(thm)],[c_42976,c_175]) ).
cnf(c_43262,plain,
or(X0,X0) = not(not(X0)),
inference(demodulation,[status(thm)],[c_43034,c_323]) ).
cnf(c_45498,plain,
is_a_theorem(implies(X0,not(not(X0)))),
inference(superposition,[status(thm)],[c_43262,c_143]) ).
cnf(c_45526,plain,
is_a_theorem(or(X0,not(not(not(X0))))),
inference(superposition,[status(thm)],[c_43262,c_15655]) ).
cnf(c_46412,plain,
( ~ is_a_theorem(implies(not(not(X0)),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(superposition,[status(thm)],[c_45498,c_18454]) ).
cnf(c_46416,plain,
( ~ is_a_theorem(or(not(X0),X0))
| is_a_theorem(equiv(not(not(X0)),X0)) ),
inference(demodulation,[status(thm)],[c_46412,c_323]) ).
cnf(c_46483,plain,
is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_45526,c_17612]) ).
cnf(c_46505,plain,
is_a_theorem(equiv(not(not(X0)),X0)),
inference(backward_subsumption_resolution,[status(thm)],[c_46416,c_46483]) ).
cnf(c_46534,plain,
not(not(X0)) = X0,
inference(superposition,[status(thm)],[c_46505,c_172]) ).
cnf(c_47362,plain,
not(implies(X0,X1)) = and(X0,not(X1)),
inference(superposition,[status(thm)],[c_175,c_46534]) ).
cnf(c_49944,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_169,c_137]) ).
cnf(c_49949,plain,
not(not(implies(X0,X1))) = implies(X0,X1),
inference(demodulation,[status(thm)],[c_175,c_47362]) ).
cnf(c_49965,plain,
not(not(or(X0,X1))) = or(X0,X1),
inference(superposition,[status(thm)],[c_323,c_49949]) ).
cnf(c_49974,plain,
is_a_theorem(implies(X0,or(X1,and(X0,not(X1))))),
inference(superposition,[status(thm)],[c_323,c_166]) ).
cnf(c_49980,plain,
is_a_theorem(implies(X0,or(X1,not(implies(X0,X1))))),
inference(demodulation,[status(thm)],[c_49974,c_47362]) ).
cnf(c_50039,plain,
not(implies(X0,not(implies(X1,X2)))) = and(X0,implies(X1,X2)),
inference(superposition,[status(thm)],[c_49949,c_47362]) ).
cnf(c_50112,plain,
implies(implies(X0,not(implies(X1,X2))),X3) = or(and(X0,implies(X1,X2)),X3),
inference(demodulation,[status(thm)],[c_2238,c_47362]) ).
cnf(c_50115,plain,
implies(implies(X0,not(or(X1,X2))),X3) = or(and(X0,or(X1,X2)),X3),
inference(superposition,[status(thm)],[c_323,c_50112]) ).
cnf(c_50496,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_50500,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,and(X0,X1))) ),
inference(superposition,[status(thm)],[c_166,c_185]) ).
cnf(c_50506,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_50510,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(superposition,[status(thm)],[c_324,c_185]) ).
cnf(c_50519,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(or(X1,not(implies(X0,X1)))) ),
inference(superposition,[status(thm)],[c_49980,c_185]) ).
cnf(c_50848,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(X1)
| is_a_theorem(and(X0,X1)) ),
inference(superposition,[status(thm)],[c_50500,c_185]) ).
cnf(c_51500,plain,
or(implies(X0,not(implies(X1,X2))),X3) = implies(and(X0,implies(X1,X2)),X3),
inference(superposition,[status(thm)],[c_50039,c_323]) ).
cnf(c_51865,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(superposition,[status(thm)],[c_50519,c_50510]) ).
cnf(c_51999,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_50848]) ).
cnf(c_53352,plain,
is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_150,c_50496]) ).
cnf(c_53354,plain,
is_a_theorem(implies(X0,and(X0,X0))),
inference(superposition,[status(thm)],[c_166,c_50496]) ).
cnf(c_53387,plain,
is_a_theorem(strict_implies(X0,X0)),
inference(superposition,[status(thm)],[c_53352,c_49944]) ).
cnf(c_53414,plain,
is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[status(thm)],[c_323,c_53354]) ).
cnf(c_53424,plain,
is_a_theorem(or(X0,not(or(X0,X0)))),
inference(demodulation,[status(thm)],[c_53414,c_323,c_47362]) ).
cnf(c_53653,plain,
is_a_theorem(implies(or(X0,X0),X0)),
inference(superposition,[status(thm)],[c_53424,c_50510]) ).
cnf(c_53904,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_51999]) ).
cnf(c_53952,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_51865,c_51999]) ).
cnf(c_53975,plain,
( ~ is_a_theorem(implies(X0,or(X0,X0)))
| is_a_theorem(equiv(X0,or(X0,X0))) ),
inference(superposition,[status(thm)],[c_53653,c_51999]) ).
cnf(c_53979,plain,
is_a_theorem(equiv(X0,or(X0,X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_53975,c_143]) ).
cnf(c_53982,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(equiv(X1,implies(X0,X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53952,c_150]) ).
cnf(c_53998,plain,
or(X0,X0) = X0,
inference(superposition,[status(thm)],[c_53979,c_172]) ).
cnf(c_54065,plain,
not(not(X0)) = X0,
inference(superposition,[status(thm)],[c_53998,c_49965]) ).
cnf(c_54108,plain,
implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(superposition,[status(thm)],[c_53998,c_50115]) ).
cnf(c_54315,plain,
or(not(X0),X1) = implies(X0,X1),
inference(superposition,[status(thm)],[c_54065,c_323]) ).
cnf(c_54323,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(implies(not(X1),X0)) ),
inference(superposition,[status(thm)],[c_54065,c_50510]) ).
cnf(c_54345,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,X0)) ),
inference(demodulation,[status(thm)],[c_54323,c_323]) ).
cnf(c_54438,plain,
is_a_theorem(implies(implies(X0,not(X1)),implies(X1,not(X0)))),
inference(superposition,[status(thm)],[c_54315,c_324]) ).
cnf(c_54496,plain,
is_a_theorem(or(and(X0,X1),implies(X1,not(X0)))),
inference(demodulation,[status(thm)],[c_54438,c_54108]) ).
cnf(c_57296,plain,
( ~ is_a_theorem(X0)
| implies(X0,X1) = X1 ),
inference(superposition,[status(thm)],[c_53982,c_172]) ).
cnf(c_57514,plain,
implies(implies(X0,X0),X1) = X1,
inference(superposition,[status(thm)],[c_53352,c_57296]) ).
cnf(c_58058,plain,
( ~ is_a_theorem(implies(X0,implies(X1,X1)))
| is_a_theorem(implies(X0,equiv(X0,implies(X1,X1)))) ),
inference(superposition,[status(thm)],[c_57514,c_50506]) ).
cnf(c_58078,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_57514,c_53904]) ).
cnf(c_58106,plain,
is_a_theorem(implies(X0,implies(X1,X1))),
inference(superposition,[status(thm)],[c_57514,c_150]) ).
cnf(c_58204,plain,
is_a_theorem(implies(X0,equiv(X0,implies(X1,X1)))),
inference(forward_subsumption_resolution,[status(thm)],[c_58058,c_58106]) ).
cnf(c_58215,plain,
is_a_theorem(equiv(implies(implies(X0,X0),X1),equiv(X1,implies(X0,X0)))),
inference(forward_subsumption_resolution,[status(thm)],[c_58078,c_58204]) ).
cnf(c_58216,plain,
is_a_theorem(equiv(X0,equiv(X0,implies(X1,X1)))),
inference(demodulation,[status(thm)],[c_58215,c_57514]) ).
cnf(c_62888,plain,
equiv(X0,implies(X1,X1)) = X0,
inference(superposition,[status(thm)],[c_58216,c_172]) ).
cnf(c_63017,plain,
( ~ is_a_theorem(X0)
| implies(X1,X1) = X0 ),
inference(superposition,[status(thm)],[c_62888,c_172]) ).
cnf(c_63141,plain,
implies(X0,X0) = strict_implies(X1,X1),
inference(superposition,[status(thm)],[c_53387,c_63017]) ).
cnf(c_63277,plain,
implies(X0,X0) = sP0_iProver_split,
inference(splitting,[splitting(split),new_symbols(definition,[sP0_iProver_split])],[c_63141]) ).
cnf(c_63447,plain,
implies(sP0_iProver_split,X0) = X0,
inference(demodulation,[status(thm)],[c_57514,c_63277]) ).
cnf(c_68537,plain,
or(implies(X0,not(X1)),X2) = implies(and(X0,X1),X2),
inference(superposition,[status(thm)],[c_63447,c_51500]) ).
cnf(c_74497,plain,
is_a_theorem(or(implies(X0,not(X1)),and(X1,X0))),
inference(superposition,[status(thm)],[c_54496,c_54345]) ).
cnf(c_74507,plain,
is_a_theorem(implies(and(X0,X1),and(X1,X0))),
inference(demodulation,[status(thm)],[c_74497,c_68537]) ).
cnf(c_74578,plain,
is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))),
inference(superposition,[status(thm)],[c_74507,c_49944]) ).
cnf(c_74618,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_159,c_74578]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL541+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.14/0.13 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n024.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 Aug 24 17:50:24 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 159.67/21.82 % SZS status Started for theBenchmark.p
% 159.67/21.82 % SZS status Theorem for theBenchmark.p
% 159.67/21.82
% 159.67/21.82 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 159.67/21.82
% 159.67/21.82 ------ iProver source info
% 159.67/21.82
% 159.67/21.82 git: date: 2023-05-31 18:12:56 +0000
% 159.67/21.82 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 159.67/21.82 git: non_committed_changes: false
% 159.67/21.82 git: last_make_outside_of_git: false
% 159.67/21.82
% 159.67/21.82 ------ Parsing...
% 159.67/21.82 ------ Clausification by vclausify_rel & Parsing by iProver...
% 159.67/21.82
% 159.67/21.82 ------ 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
% 159.67/21.82
% 159.67/21.82 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 159.67/21.82
% 159.67/21.82 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 159.67/21.82 ------ Proving...
% 159.67/21.82 ------ Problem Properties
% 159.67/21.82
% 159.67/21.82
% 159.67/21.82 clauses 27
% 159.67/21.82 conjectures 0
% 159.67/21.82 EPR 0
% 159.67/21.82 Horn 27
% 159.67/21.82 unary 24
% 159.67/21.82 binary 2
% 159.67/21.82 lits 31
% 159.67/21.82 lits eq 7
% 159.67/21.82 fd_pure 0
% 159.67/21.82 fd_pseudo 0
% 159.67/21.82 fd_cond 0
% 159.67/21.82 fd_pseudo_cond 1
% 159.67/21.82 AC symbols 0
% 159.67/21.82
% 159.67/21.82 ------ Input Options Time Limit: Unbounded
% 159.67/21.82
% 159.67/21.82
% 159.67/21.82 ------
% 159.67/21.82 Current options:
% 159.67/21.82 ------
% 159.67/21.82
% 159.67/21.82
% 159.67/21.82
% 159.67/21.82
% 159.67/21.82 ------ Proving...
% 159.67/21.82
% 159.67/21.82
% 159.67/21.82 % SZS status Theorem for theBenchmark.p
% 159.67/21.82
% 159.67/21.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 159.67/21.82
% 159.67/21.83
%------------------------------------------------------------------------------