%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL523+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 : n005.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 02:06:50 PM UTC 2026
% Result : Theorem 21.70s 4.68s
% Output : CNFRefutation 21.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 26
% Syntax : Number of formulae : 154 ( 72 unt; 0 def)
% Number of atoms : 259 ( 39 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 187 ( 82 ~; 76 |; 2 &)
% ( 10 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 14 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 187 ( 0 sgn 186 !; 1 ?; 99 :)
% 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(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(f6,axiom,
( implies_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_3) ).
fof(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_2) ).
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(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(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_equiv) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
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(f39,axiom,
implies_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_3) ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_2) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',use_substitution_of_equivalents) ).
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(f56,axiom,
( axiom_4
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_4) ).
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(f73,axiom,
( op_possibly
=> ! [X0] : possibly(X0) = not(necessarily(not(X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_possibly) ).
fof(f77,axiom,
op_possibly,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax',km5_op_possibly) ).
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,conjecture,
axiom_4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km4b_axiom_4) ).
fof(f83,negated_conjecture,
~ axiom_4,
inference(negated_conjecture,[status(cth)],[f82]) ).
fof(f84,plain,
~ axiom_4,
inference(flattening,[],[f83]) ).
fof(f85,plain,
( axiom_5
=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(unused_predicate_definition_removal,[],[f58]) ).
fof(f86,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0))))
=> axiom_4 ),
inference(unused_predicate_definition_removal,[],[f56]) ).
fof(f87,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f96,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f97,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f99,plain,
( implies_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f100,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f101,plain,
( implies_1
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f103,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f104,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(f110,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f104]) ).
fof(f111,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(flattening,[],[f110]) ).
fof(f112,plain,
( ~ substitution_of_equivalents
| ! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ) ),
inference(ennf_transformation,[],[f103]) ).
fof(f114,plain,
( ~ implies_1
| ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(ennf_transformation,[],[f101]) ).
fof(f115,plain,
( ~ implies_2
| ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(ennf_transformation,[],[f100]) ).
fof(f116,plain,
( ~ implies_3
| ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(ennf_transformation,[],[f99]) ).
fof(f118,plain,
( ~ and_2
| ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(ennf_transformation,[],[f97]) ).
fof(f119,plain,
( ~ and_3
| ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(ennf_transformation,[],[f96]) ).
fof(f127,plain,
( ~ op_implies_and
| ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
inference(ennf_transformation,[],[f29]) ).
fof(f128,plain,
( ~ op_equiv
| ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(ennf_transformation,[],[f31]) ).
fof(f131,plain,
( ~ axiom_M
| ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(ennf_transformation,[],[f87]) ).
fof(f132,plain,
( ? [X0] : ~ is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0))))
| axiom_4 ),
inference(ennf_transformation,[],[f86]) ).
fof(f133,plain,
( ~ axiom_5
| ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(ennf_transformation,[],[f85]) ).
fof(f134,plain,
( ~ op_possibly
| ! [X0] : possibly(X0) = not(necessarily(not(X0))) ),
inference(ennf_transformation,[],[f73]) ).
fof(f135,plain,
( ~ is_a_theorem(implies(necessarily(sK0),necessarily(necessarily(sK0))))
| axiom_4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f132]) ).
fof(f136,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f137,plain,
! [X0,X1] :
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f112]) ).
fof(f139,plain,
! [X0,X1] :
( ~ implies_1
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(cnf_transformation,[],[f114]) ).
fof(f140,plain,
! [X0,X1] :
( ~ implies_2
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f115]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ implies_3
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(cnf_transformation,[],[f116]) ).
fof(f143,plain,
! [X0,X1] :
( ~ and_2
| is_a_theorem(implies(and(X0,X1),X1)) ),
inference(cnf_transformation,[],[f118]) ).
fof(f144,plain,
! [X0,X1] :
( ~ and_3
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(cnf_transformation,[],[f119]) ).
fof(f152,plain,
! [X0,X1] :
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf_transformation,[],[f127]) ).
fof(f153,plain,
! [X0,X1] :
( ~ op_equiv
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(cnf_transformation,[],[f128]) ).
fof(f155,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f156,plain,
op_equiv,
inference(cnf_transformation,[],[f34]) ).
fof(f157,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f159,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f160,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f161,plain,
implies_3,
inference(cnf_transformation,[],[f39]) ).
fof(f163,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f164,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f171,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f174,plain,
! [X0] :
( ~ axiom_M
| is_a_theorem(implies(necessarily(X0),X0)) ),
inference(cnf_transformation,[],[f131]) ).
fof(f175,plain,
( ~ is_a_theorem(implies(necessarily(sK0),necessarily(necessarily(sK0))))
| axiom_4 ),
inference(cnf_transformation,[],[f135]) ).
fof(f176,plain,
! [X0] :
( ~ axiom_5
| is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(cnf_transformation,[],[f133]) ).
fof(f177,plain,
! [X0] :
( ~ op_possibly
| possibly(X0) = not(necessarily(not(X0))) ),
inference(cnf_transformation,[],[f134]) ).
fof(f178,plain,
op_possibly,
inference(cnf_transformation,[],[f77]) ).
fof(f181,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f182,plain,
axiom_5,
inference(cnf_transformation,[],[f81]) ).
fof(f183,plain,
~ axiom_4,
inference(cnf_transformation,[],[f84]) ).
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,[],[f136]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f139]) ).
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,[],[f140]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( not(and(X0,not(X1))) = implies(X0,X1) )
| ~ op_implies_and ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) )
| ~ op_equiv ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_68,plain,
op_implies_and,
inference(cnf_transformation,[],[f155]) ).
tcf(c_69,plain,
op_equiv,
inference(cnf_transformation,[],[f156]) ).
tcf(c_70,plain,
modus_ponens,
inference(cnf_transformation,[],[f157]) ).
tcf(c_72,plain,
implies_1,
inference(cnf_transformation,[],[f159]) ).
tcf(c_73,plain,
implies_2,
inference(cnf_transformation,[],[f160]) ).
tcf(c_74,plain,
implies_3,
inference(cnf_transformation,[],[f161]) ).
tcf(c_76,plain,
and_2,
inference(cnf_transformation,[],[f163]) ).
tcf(c_77,plain,
and_3,
inference(cnf_transformation,[],[f164]) ).
tcf(c_84,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f171]) ).
tcf(c_87,plain,
! [X0: $i] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_88,plain,
( axiom_4
| ~ is_a_theorem(implies(necessarily(sK0),necessarily(necessarily(sK0)))) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_89,plain,
! [X0: $i] :
( is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ axiom_5 ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_90,plain,
! [X0: $i] :
( ( not(necessarily(not(X0))) = possibly(X0) )
| ~ op_possibly ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_91,plain,
op_possibly,
inference(cnf_transformation,[],[f178]) ).
tcf(c_94,plain,
axiom_M,
inference(cnf_transformation,[],[f181]) ).
tcf(c_95,plain,
axiom_5,
inference(cnf_transformation,[],[f182]) ).
tcf(c_96,negated_conjecture,
~ axiom_4,
inference(cnf_transformation,[],[f183]) ).
tcf(c_119,plain,
! [X0: $i] : is_a_theorem(implies(necessarily(X0),X0)),
inference(global_subsumption_just,[status(thm)],[c_87,c_94,c_87]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),X1)),
inference(global_subsumption_just,[status(thm)],[c_56,c_76,c_56]) ).
tcf(c_135,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_138,plain,
! [X0: $i] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))),
inference(global_subsumption_just,[status(thm)],[c_89,c_95,c_89]) ).
tcf(c_141,plain,
~ is_a_theorem(implies(necessarily(sK0),necessarily(necessarily(sK0)))),
inference(global_subsumption_just,[status(thm)],[c_88,c_96,c_88]) ).
tcf(c_143,plain,
! [X0: $i] : not(necessarily(not(X0))) = possibly(X0),
inference(global_subsumption_just,[status(thm)],[c_90,c_91,c_90]) ).
tcf(c_151,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_154,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_157,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_160,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_166,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_167,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(renaming,[status(thm)],[c_166]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i] : and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_66,c_69,c_66]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(global_subsumption_just,[status(thm)],[c_54,c_74,c_54]) ).
tcf(c_600,plain,
! [X0: $i] : not(necessarily(possibly(X0))) = possibly(necessarily(not(X0))),
inference(superposition,[status(thm)],[c_143,c_143]) ).
tcf(c_656,plain,
! [X0: $i,X1: $i] : not(necessarily(implies(X0,X1))) = possibly(and(X0,not(X1))),
inference(superposition,[status(thm)],[c_157,c_143]) ).
tcf(c_706,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_135,c_167]) ).
tcf(c_707,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(superposition,[status(thm)],[c_160,c_167]) ).
tcf(c_710,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_151,c_167]) ).
tcf(c_844,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_180,c_167]) ).
tcf(c_870,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_710,c_167]) ).
tcf(c_1141,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_174,c_870]) ).
tcf(c_1170,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_135,c_707]) ).
tcf(c_3099,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(superposition,[status(thm)],[c_844,c_707]) ).
tcf(c_27668,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_706,c_3099]) ).
tcf(c_35691,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_138,c_1141]) ).
tcf(c_35704,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(and(X0,X1),X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(and(X0,X1),X1)) ),
inference(superposition,[status(thm)],[c_710,c_1141]) ).
tcf(c_35740,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(X0,implies(X1,X0)))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(superposition,[status(thm)],[c_27668,c_1141]) ).
tcf(c_35796,plain,
! [X0: $i] : is_a_theorem(equiv(necessarily(possibly(X0)),possibly(X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_35691,c_119]) ).
tcf(c_35797,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(X1,implies(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35740,c_135]) ).
tcf(c_35803,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(and(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35704,c_130]) ).
tcf(c_36281,plain,
! [X0: $i] : necessarily(possibly(X0)) = possibly(X0),
inference(superposition,[status(thm)],[c_35796,c_154]) ).
tcf(c_36301,plain,
! [X0: $i] : possibly(necessarily(not(X0))) = not(possibly(X0)),
inference(demodulation,[status(thm)],[c_600,c_36281]) ).
tcf(c_36902,plain,
! [X0: $i,X1: $i] :
( ( implies(X0,X1) = X1 )
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_35797,c_154]) ).
tcf(c_36960,plain,
! [X0: $i,X1: $i] :
( ( and(X0,X1) = X1 )
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_35803,c_154]) ).
tcf(c_40393,plain,
! [X0: $i,X1: $i] : implies(implies(X0,X0),X1) = X1,
inference(superposition,[status(thm)],[c_1170,c_36902]) ).
tcf(c_41496,plain,
! [X0: $i,X1: $i] : and(implies(X0,X0),X1) = X1,
inference(superposition,[status(thm)],[c_1170,c_36960]) ).
tcf(c_46641,plain,
! [X0: $i,X1: $i] : not(necessarily(implies(implies(X0,X0),X1))) = possibly(not(X1)),
inference(superposition,[status(thm)],[c_41496,c_656]) ).
tcf(c_46645,plain,
! [X0: $i,X1: $i] : implies(implies(X0,X0),X1) = not(not(X1)),
inference(superposition,[status(thm)],[c_41496,c_157]) ).
tcf(c_46693,plain,
! [X0: $i] : not(not(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_46645,c_40393]) ).
tcf(c_46702,plain,
! [X0: $i] : not(necessarily(X0)) = possibly(not(X0)),
inference(light_normalisation,[status(thm)],[c_46641,c_40393]) ).
tcf(c_46840,plain,
! [X0: $i] : not(possibly(X0)) = necessarily(not(X0)),
inference(superposition,[status(thm)],[c_143,c_46693]) ).
tcf(c_46854,plain,
! [X0: $i] : not(possibly(not(X0))) = possibly(necessarily(X0)),
inference(superposition,[status(thm)],[c_46693,c_36301]) ).
tcf(c_47049,plain,
! [X0: $i] : not(not(necessarily(X0))) = possibly(necessarily(X0)),
inference(light_normalisation,[status(thm)],[c_46854,c_46702]) ).
tcf(c_50215,plain,
! [X0: $i] : not(not(necessarily(X0))) = necessarily(not(not(X0))),
inference(superposition,[status(thm)],[c_46702,c_46840]) ).
tcf(c_50240,plain,
! [X0: $i] : possibly(necessarily(X0)) = necessarily(X0),
inference(light_normalisation,[status(thm)],[c_50215,c_46693,c_47049]) ).
tcf(c_50349,plain,
! [X0: $i] : necessarily(necessarily(X0)) = necessarily(X0),
inference(superposition,[status(thm)],[c_50240,c_36281]) ).
tcf(c_50440,plain,
~ is_a_theorem(implies(necessarily(sK0),necessarily(sK0))),
inference(demodulation,[status(thm)],[c_141,c_50349]) ).
tcf(c_50441,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_50440,c_1170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL523+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 23:38:49 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 21.70/4.68 % SZS status Started for theBenchmark.p
% 21.70/4.68 % SZS status Theorem for theBenchmark.p
% 21.70/4.68
% 21.70/4.68 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 21.70/4.68
% 21.70/4.68 % ------ iProver source info
% 21.70/4.68
% 21.70/4.68 % git: date: 2026-07-19 20:42:38 +0200
% 21.70/4.68 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 21.70/4.68 % git: non_committed_changes: false
% 21.70/4.68
% 21.70/4.68 % ------ Parsing...
% 21.70/4.68 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 21.70/4.68
% 21.70/4.68 % ------ Preprocessing... sup_sim: 2 sf_s rm: 25 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 21.70/4.68
% 21.70/4.68 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 21.70/4.68
% 21.70/4.68 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 21.70/4.68 % ------ Proving...
% 21.70/4.68 % ------ Problem Properties
% 21.70/4.68
% 21.70/4.68 %
% 21.70/4.68 % clauses 24
% 21.70/4.68 % conjectures 0
% 21.70/4.68 % EPR 0
% 21.70/4.68 % Horn 24
% 21.70/4.68 % unary 21
% 21.70/4.68 % binary 2
% 21.70/4.68 % lits 28
% 21.70/4.68 % lits eq 5
% 21.70/4.68 % fd_pure 0
% 21.70/4.68 % fd_pseudo 0
% 21.70/4.68 % fd_cond 0
% 21.70/4.68 % fd_pseudo_cond 1
% 21.70/4.68 % AC symbols 0
% 21.70/4.68
% 21.70/4.68 % ------ Schedule dynamic 5 is on
% 21.70/4.68
% 21.70/4.68 % ------ no conjectures: strip conj schedule
% 21.70/4.68
% 21.70/4.68 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 21.70/4.68
% 21.70/4.68
% 21.70/4.68 % ------
% 21.70/4.68 % Current options:
% 21.70/4.68 % ------
% 21.70/4.68
% 21.70/4.68
% 21.70/4.68 %
% 21.70/4.68
% 21.70/4.68 % ------ Proving...
% 21.70/4.68 %
% 21.70/4.68
% 21.70/4.68 % SZS status Theorem for theBenchmark.p
% 21.70/4.68
% 21.70/4.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 21.70/4.68
%------------------------------------------------------------------------------