%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL535+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:06:51 PM UTC 2026
% Result : Theorem 18.64s 3.32s
% Output : CNFRefutation 18.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 34
% Syntax : Number of formulae : 192 ( 96 unt; 0 def)
% Number of atoms : 313 ( 39 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 210 ( 89 ~; 83 |; 2 &)
% ( 13 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 20 ( 18 usr; 18 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 214 ( 0 sgn 213 !; 1 ?; 104 :)
% 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/Axioms/LCL006+0.ax',modus_ponens) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',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/Axioms/LCL006+0.ax',modus_tollens) ).
fof(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',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/Axioms/LCL006+0.ax',implies_2) ).
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_1) ).
fof(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_3) ).
fof(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',or_1) ).
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/Axioms/LCL006+0.ax',equivalence_3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_tollens) ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_1) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_1) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
fof(f43,axiom,
or_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_or_1) ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_equivalence_3) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',use_substitution_of_equivalents) ).
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',necessitation) ).
fof(f55,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_M) ).
fof(f58,axiom,
( axiom_5
<=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_5) ).
fof(f71,axiom,
( axiom_m9
<=> ! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m9) ).
fof(f73,axiom,
( op_possibly
=> ! [X0] : possibly(X0) = not(necessarily(not(X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_possibly) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax',km5_necessitation) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax',km5_axiom_M) ).
fof(f81,axiom,
axiom_5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax',km5_axiom_5) ).
fof(f82,axiom,
op_possibly,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_possibly) ).
fof(f83,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_or) ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f88,conjecture,
axiom_m9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m9) ).
fof(f89,negated_conjecture,
~ axiom_m9,
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f90,plain,
~ axiom_m9,
inference(flattening,[],[f89]) ).
fof(f91,plain,
( ! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0)))
=> axiom_m9 ),
inference(unused_predicate_definition_removal,[],[f71]) ).
fof(f92,plain,
( axiom_5
=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(unused_predicate_definition_removal,[],[f58]) ).
fof(f93,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f95,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f96,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(f101,plain,
( or_1
=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f102,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f104,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f106,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f107,plain,
( implies_1
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f108,plain,
( modus_tollens
=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f109,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f110,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(f115,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f110]) ).
fof(f116,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(flattening,[],[f115]) ).
fof(f117,plain,
( ~ substitution_of_equivalents
| ! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ) ),
inference(ennf_transformation,[],[f109]) ).
fof(f118,plain,
( ~ modus_tollens
| ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(ennf_transformation,[],[f108]) ).
fof(f119,plain,
( ~ implies_1
| ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(ennf_transformation,[],[f107]) ).
fof(f120,plain,
( ~ implies_2
| ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(ennf_transformation,[],[f106]) ).
fof(f122,plain,
( ~ and_1
| ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(ennf_transformation,[],[f104]) ).
fof(f124,plain,
( ~ and_3
| ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(ennf_transformation,[],[f102]) ).
fof(f125,plain,
( ~ or_1
| ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
inference(ennf_transformation,[],[f101]) ).
fof(f130,plain,
( ~ equivalence_3
| ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(ennf_transformation,[],[f96]) ).
fof(f131,plain,
( ~ op_or
| ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f132,plain,
( ~ op_implies_and
| ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
inference(ennf_transformation,[],[f29]) ).
fof(f134,plain,
( ~ necessitation
| ! [X0] :
( ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ) ),
inference(ennf_transformation,[],[f95]) ).
fof(f136,plain,
( ~ axiom_M
| ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(ennf_transformation,[],[f93]) ).
fof(f137,plain,
( ~ axiom_5
| ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(ennf_transformation,[],[f92]) ).
fof(f138,plain,
( ? [X0] : ~ is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0)))
| axiom_m9 ),
inference(ennf_transformation,[],[f91]) ).
fof(f139,plain,
( ~ op_possibly
| ! [X0] : possibly(X0) = not(necessarily(not(X0))) ),
inference(ennf_transformation,[],[f73]) ).
fof(f140,plain,
( ~ op_strict_implies
| ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(ennf_transformation,[],[f75]) ).
fof(f142,plain,
( ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0)))
| axiom_m9 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f138]) ).
fof(f143,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f144,plain,
! [X0,X1] :
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f117]) ).
fof(f145,plain,
! [X0,X1] :
( ~ modus_tollens
| is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f118]) ).
fof(f146,plain,
! [X0,X1] :
( ~ implies_1
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(cnf_transformation,[],[f119]) ).
fof(f147,plain,
! [X0,X1] :
( ~ implies_2
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f120]) ).
fof(f149,plain,
! [X0,X1] :
( ~ and_1
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f122]) ).
fof(f151,plain,
! [X0,X1] :
( ~ and_3
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(cnf_transformation,[],[f124]) ).
fof(f152,plain,
! [X0,X1] :
( ~ or_1
| is_a_theorem(implies(X0,or(X0,X1))) ),
inference(cnf_transformation,[],[f125]) ).
fof(f157,plain,
! [X0,X1] :
( ~ equivalence_3
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(cnf_transformation,[],[f130]) ).
fof(f158,plain,
! [X0,X1] :
( ~ op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f131]) ).
fof(f159,plain,
! [X0,X1] :
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf_transformation,[],[f132]) ).
fof(f162,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f164,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f165,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f166,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f167,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f169,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f171,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f172,plain,
or_1,
inference(cnf_transformation,[],[f43]) ).
fof(f177,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f178,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f179,plain,
! [X0] :
( ~ necessitation
| ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ),
inference(cnf_transformation,[],[f134]) ).
fof(f181,plain,
! [X0] :
( ~ axiom_M
| is_a_theorem(implies(necessarily(X0),X0)) ),
inference(cnf_transformation,[],[f136]) ).
fof(f182,plain,
! [X0] :
( ~ axiom_5
| is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f183,plain,
( ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0)))
| axiom_m9 ),
inference(cnf_transformation,[],[f142]) ).
fof(f184,plain,
! [X0] :
( ~ op_possibly
| possibly(X0) = not(necessarily(not(X0))) ),
inference(cnf_transformation,[],[f139]) ).
fof(f185,plain,
! [X0,X1] :
( ~ op_strict_implies
| strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(cnf_transformation,[],[f140]) ).
fof(f188,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f190,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f191,plain,
axiom_5,
inference(cnf_transformation,[],[f81]) ).
fof(f192,plain,
op_possibly,
inference(cnf_transformation,[],[f82]) ).
fof(f193,plain,
op_or,
inference(cnf_transformation,[],[f83]) ).
fof(f194,plain,
op_strict_implies,
inference(cnf_transformation,[],[f85]) ).
fof(f197,plain,
~ axiom_m9,
inference(cnf_transformation,[],[f90]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ modus_ponens
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0)))
| ~ modus_tollens ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ( not(and(not(X0),not(X1))) = or(X0,X1) )
| ~ op_or ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( not(and(X0,not(X1))) = implies(X0,X1) )
| ~ op_implies_and ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_68,plain,
op_implies_and,
inference(cnf_transformation,[],[f162]) ).
tcf(c_70,plain,
modus_ponens,
inference(cnf_transformation,[],[f164]) ).
tcf(c_71,plain,
modus_tollens,
inference(cnf_transformation,[],[f165]) ).
tcf(c_72,plain,
implies_1,
inference(cnf_transformation,[],[f166]) ).
tcf(c_73,plain,
implies_2,
inference(cnf_transformation,[],[f167]) ).
tcf(c_75,plain,
and_1,
inference(cnf_transformation,[],[f169]) ).
tcf(c_77,plain,
and_3,
inference(cnf_transformation,[],[f171]) ).
tcf(c_78,plain,
or_1,
inference(cnf_transformation,[],[f172]) ).
tcf(c_83,plain,
equivalence_3,
inference(cnf_transformation,[],[f177]) ).
tcf(c_84,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f178]) ).
tcf(c_85,plain,
! [X0: $i] :
( is_a_theorem(necessarily(X0))
| ~ necessitation
| ~ is_a_theorem(X0) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_87,plain,
! [X0: $i] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_88,plain,
! [X0: $i] :
( is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ axiom_5 ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_89,plain,
( axiom_m9
| ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0))) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_90,plain,
! [X0: $i] :
( ( not(necessarily(not(X0))) = possibly(X0) )
| ~ op_possibly ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( ( necessarily(implies(X0,X1)) = strict_implies(X0,X1) )
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_94,plain,
necessitation,
inference(cnf_transformation,[],[f188]) ).
tcf(c_96,plain,
axiom_M,
inference(cnf_transformation,[],[f190]) ).
tcf(c_97,plain,
axiom_5,
inference(cnf_transformation,[],[f191]) ).
tcf(c_98,plain,
op_possibly,
inference(cnf_transformation,[],[f192]) ).
tcf(c_99,plain,
op_or,
inference(cnf_transformation,[],[f193]) ).
tcf(c_100,plain,
op_strict_implies,
inference(cnf_transformation,[],[f194]) ).
tcf(c_103,negated_conjecture,
~ axiom_m9,
inference(cnf_transformation,[],[f197]) ).
tcf(c_128,plain,
! [X0: $i] : is_a_theorem(implies(necessarily(X0),X0)),
inference(global_subsumption_just,[status(thm)],[c_87,c_96,c_87]) ).
tcf(c_131,plain,
! [X0: $i] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_85,c_94,c_85]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,or(X0,X1))),
inference(global_subsumption_just,[status(thm)],[c_58,c_78,c_58]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption_just,[status(thm)],[c_55,c_75,c_55]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_52,c_72,c_52]) ).
tcf(c_147,plain,
~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0))),
inference(global_subsumption_just,[status(thm)],[c_89,c_103,c_89]) ).
tcf(c_149,plain,
! [X0: $i] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))),
inference(global_subsumption_just,[status(thm)],[c_88,c_97,c_88]) ).
tcf(c_152,plain,
! [X0: $i] : not(necessarily(not(X0))) = possibly(X0),
inference(global_subsumption_just,[status(thm)],[c_90,c_98,c_90]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(global_subsumption_just,[status(thm)],[c_57,c_77,c_57]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] : necessarily(implies(X0,X1)) = strict_implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_91,c_100,c_91]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_84,c_50]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i] : not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_65,c_68,c_65]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(global_subsumption_just,[status(thm)],[c_53,c_73,c_53]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_51,c_71,c_51]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_70,c_49]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(renaming,[status(thm)],[c_178]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] : not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_64,c_99,c_64]) ).
tcf(c_192,plain,
! [X0: $i,X1: $i] : 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]) ).
tcf(c_318,plain,
! [X0: $i,X1: $i] : implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[c_183,c_169]) ).
tcf(c_397,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(demodulation,[status(thm)],[c_175,c_318]) ).
tcf(c_2324,plain,
! [X0: $i] : not(necessarily(possibly(X0))) = possibly(necessarily(not(X0))),
inference(superposition,[status(thm)],[c_152,c_152]) ).
tcf(c_2326,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_163,c_131]) ).
tcf(c_2331,plain,
! [X0: $i,X1: $i] : implies(X0,necessarily(not(X1))) = not(and(X0,possibly(X1))),
inference(superposition,[status(thm)],[c_152,c_169]) ).
tcf(c_2339,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(superposition,[status(thm)],[c_172,c_179]) ).
tcf(c_2355,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_192,c_179]) ).
tcf(c_2363,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_397,c_179]) ).
tcf(c_2405,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,or(not(X0),X1))),
inference(superposition,[status(thm)],[c_318,c_137]) ).
tcf(c_2447,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(necessarily(not(X0)),not(and(X1,possibly(X0))))),
inference(superposition,[status(thm)],[c_2331,c_144]) ).
tcf(c_2520,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_144,c_2339]) ).
tcf(c_2522,plain,
! [X0: $i] : is_a_theorem(implies(X0,and(X0,X0))),
inference(superposition,[status(thm)],[c_160,c_2339]) ).
tcf(c_2559,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_2355,c_179]) ).
tcf(c_2594,plain,
! [X0: $i] : is_a_theorem(strict_implies(X0,X0)),
inference(superposition,[status(thm)],[c_2520,c_2326]) ).
tcf(c_4873,plain,
! [X0: $i] :
( is_a_theorem(equiv(necessarily(possibly(X0)),possibly(X0)))
| ~ is_a_theorem(implies(necessarily(possibly(X0)),possibly(X0))) ),
inference(superposition,[status(thm)],[c_149,c_2559]) ).
tcf(c_4920,plain,
! [X0: $i] :
( is_a_theorem(equiv(and(X0,X0),X0))
| ~ is_a_theorem(implies(and(X0,X0),X0)) ),
inference(superposition,[status(thm)],[c_2522,c_2559]) ).
tcf(c_4930,plain,
! [X0: $i] : is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_4920,c_142]) ).
tcf(c_4931,plain,
! [X0: $i] : is_a_theorem(equiv(necessarily(possibly(X0)),possibly(X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_4873,c_128]) ).
tcf(c_5125,plain,
! [X0: $i] : and(X0,X0) = X0,
inference(superposition,[status(thm)],[c_4930,c_166]) ).
tcf(c_5150,plain,
! [X0: $i] : implies(not(X0),X0) = not(not(X0)),
inference(superposition,[status(thm)],[c_5125,c_169]) ).
tcf(c_5183,plain,
! [X0: $i] : is_a_theorem(implies(necessarily(not(X0)),not(possibly(X0)))),
inference(superposition,[status(thm)],[c_5125,c_2447]) ).
tcf(c_5214,plain,
! [X0: $i] : or(X0,X0) = not(not(X0)),
inference(demodulation,[status(thm)],[c_5150,c_318]) ).
tcf(c_5284,plain,
! [X0: $i] : necessarily(possibly(X0)) = possibly(X0),
inference(superposition,[status(thm)],[c_4931,c_166]) ).
tcf(c_6287,plain,
! [X0: $i] : is_a_theorem(or(X0,not(not(not(X0))))),
inference(superposition,[status(thm)],[c_5214,c_2405]) ).
tcf(c_7176,plain,
! [X0: $i] : is_a_theorem(implies(not(not(X0)),X0)),
inference(superposition,[status(thm)],[c_6287,c_2363]) ).
tcf(c_7177,plain,
! [X0: $i] : is_a_theorem(or(not(X0),X0)),
inference(demodulation,[status(thm)],[c_7176,c_318]) ).
tcf(c_7192,plain,
! [X0: $i] : is_a_theorem(or(possibly(X0),necessarily(not(X0)))),
inference(superposition,[status(thm)],[c_152,c_7177]) ).
tcf(c_7999,plain,
! [X0: $i] :
( is_a_theorem(equiv(not(possibly(X0)),necessarily(not(X0))))
| ~ is_a_theorem(implies(not(possibly(X0)),necessarily(not(X0)))) ),
inference(superposition,[status(thm)],[c_5183,c_2559]) ).
tcf(c_8010,plain,
! [X0: $i] :
( is_a_theorem(equiv(not(possibly(X0)),necessarily(not(X0))))
| ~ is_a_theorem(or(possibly(X0),necessarily(not(X0)))) ),
inference(demodulation,[status(thm)],[c_7999,c_318]) ).
tcf(c_8011,plain,
! [X0: $i] : is_a_theorem(equiv(not(possibly(X0)),necessarily(not(X0)))),
inference(forward_subsumption_resolution,[status(thm)],[c_8010,c_7192]) ).
tcf(c_8824,plain,
! [X0: $i] : not(possibly(X0)) = necessarily(not(X0)),
inference(superposition,[status(thm)],[c_8011,c_166]) ).
tcf(c_8895,plain,
! [X0: $i] : not(necessarily(possibly(X0))) = possibly(not(possibly(X0))),
inference(superposition,[status(thm)],[c_8824,c_2324]) ).
tcf(c_8896,plain,
! [X0: $i] : not(not(possibly(X0))) = possibly(X0),
inference(superposition,[status(thm)],[c_8824,c_152]) ).
tcf(c_8913,plain,
! [X0: $i] : possibly(not(possibly(X0))) = not(possibly(X0)),
inference(demodulation,[status(thm)],[c_8895,c_5284]) ).
tcf(c_9844,plain,
! [X0: $i] : not(necessarily(possibly(not(possibly(X0))))) = possibly(necessarily(possibly(X0))),
inference(superposition,[status(thm)],[c_8896,c_2324]) ).
tcf(c_9981,plain,
! [X0: $i] : possibly(possibly(X0)) = possibly(X0),
inference(demodulation,[status(thm)],[c_9844,c_5284,c_8896,c_8913]) ).
tcf(c_10811,plain,
~ is_a_theorem(strict_implies(possibly(sK0),possibly(sK0))),
inference(superposition,[status(thm)],[c_9981,c_147]) ).
tcf(c_10820,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_10811,c_2594]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL535+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.38 % Computer : n008.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Wed Sep 23 23:41:46 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 18.64/3.32 % SZS status Started for theBenchmark.p
% 18.64/3.32 % SZS status Theorem for theBenchmark.p
% 18.64/3.32
% 18.64/3.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.64/3.32
% 18.64/3.32 % ------ iProver source info
% 18.64/3.32
% 18.64/3.32 % git: date: 2026-07-19 20:42:38 +0200
% 18.64/3.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.64/3.32 % git: non_committed_changes: false
% 18.64/3.32
% 18.64/3.32 % ------ Parsing...
% 18.64/3.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 18.64/3.32
% 18.64/3.32 % ------ Preprocessing... sup_sim: 2 sf_s rm: 27 0s sf_e pe_s pe_e sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 18.64/3.32
% 18.64/3.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 18.64/3.32
% 18.64/3.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 18.64/3.32 % ------ Proving...
% 18.64/3.32 % ------ Problem Properties
% 18.64/3.32
% 18.64/3.32 %
% 18.64/3.32 % clauses 26
% 18.64/3.32 % conjectures 0
% 18.64/3.32 % EPR 0
% 18.64/3.32 % Horn 26
% 18.64/3.32 % unary 23
% 18.64/3.32 % binary 2
% 18.64/3.32 % lits 30
% 18.64/3.32 % lits eq 7
% 18.64/3.32 % fd_pure 0
% 18.64/3.32 % fd_pseudo 0
% 18.64/3.32 % fd_cond 0
% 18.64/3.32 % fd_pseudo_cond 1
% 18.64/3.32 % AC symbols 0
% 18.64/3.32
% 18.64/3.32 % ------ Input Options Time Limit: Unbounded
% 18.64/3.32
% 18.64/3.32
% 18.64/3.32 % ------
% 18.64/3.32 % Current options:
% 18.64/3.32 % ------
% 18.64/3.32
% 18.64/3.32
% 18.64/3.32 %
% 18.64/3.32
% 18.64/3.32 % ------ Proving...
% 18.64/3.32 %
% 18.64/3.32
% 18.64/3.32 % SZS status Theorem for theBenchmark.p
% 18.64/3.32
% 18.64/3.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.64/3.33
% 18.64/3.33
%------------------------------------------------------------------------------