%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL548+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 : Thu Sep 24 01:13:01 PM UTC 2026
% Result : Theorem 0.45s 0.76s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 35
% Syntax : Number of formulae : 140 ( 72 unt; 0 def)
% Number of atoms : 258 ( 44 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 198 ( 80 ~; 79 |; 18 &)
% ( 13 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 21 ( 19 usr; 19 prp; 0-2 aty)
% Number of functors : 31 ( 31 usr; 23 con; 0-2 aty)
% Number of variables : 169 ( 11 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X1,X2] :
( ( is_a_theorem(implies(X1,X2))
& is_a_theorem(X1) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(and_3,axiom,
( and_3
<=> ! [X1,X2] : is_a_theorem(implies(X1,implies(X2,and(X1,X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_3) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X1,X2] :
( is_a_theorem(equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X1,X2] : equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(hilbert_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(hilbert_and_3,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
fof(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',use_substitution_of_equivalents) ).
fof(hilbert_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_equiv) ).
fof(implies_1,axiom,
( implies_1
<=> ! [X1,X2] : is_a_theorem(implies(X1,implies(X2,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_1) ).
fof(implies_2,axiom,
( implies_2
<=> ! [X1,X2] : is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_2) ).
fof(hilbert_implies_1,axiom,
implies_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_1) ).
fof(hilbert_implies_2,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
fof(and_1,axiom,
( and_1
<=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_1) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(hilbert_and_1,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_1) ).
fof(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
fof(or_3,axiom,
( or_3
<=> ! [X1,X2,X3] : is_a_theorem(implies(implies(X1,X3),implies(implies(X2,X3),implies(or(X1,X2),X3)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_3) ).
fof(hilbert_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_or) ).
fof(hilbert_or_3,axiom,
or_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_or_3) ).
fof(and_2,axiom,
( and_2
<=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_2) ).
fof(hilbert_and_2,axiom,
and_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_2) ).
fof(op_possibly,axiom,
( op_possibly
=> ! [X1] : possibly(X1) = not(necessarily(not(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_possibly) ).
fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X1,X2] : strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
fof(necessitation,axiom,
( necessitation
<=> ! [X1] :
( is_a_theorem(X1)
=> is_a_theorem(necessarily(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',necessitation) ).
fof(km4b_op_possibly,axiom,
op_possibly,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+3.ax',km4b_op_possibly) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(axiom_4,axiom,
( axiom_4
<=> ! [X1] : is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_4) ).
fof(axiom_M,axiom,
( axiom_M
<=> ! [X1] : is_a_theorem(implies(necessarily(X1),X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_M) ).
fof(km4b_necessitation,axiom,
necessitation,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+3.ax',km4b_necessitation) ).
fof(s1_0_m6s3m9b_axiom_m9,conjecture,
axiom_m9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m9) ).
fof(km4b_axiom_4,axiom,
axiom_4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+3.ax',km4b_axiom_4) ).
fof(km4b_axiom_M,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+3.ax',km4b_axiom_M) ).
fof(axiom_m2,axiom,
( axiom_m2
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m2) ).
fof(axiom_m9,axiom,
( axiom_m9
<=> ! [X1] : is_a_theorem(strict_implies(possibly(possibly(X1)),possibly(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m9) ).
fof(c_0_35,plain,
! [X7,X8] :
( ( modus_ponens
| ~ is_a_theorem(esk2_0) )
& ( modus_ponens
| is_a_theorem(implies(esk1_0,esk2_0)) )
& ( modus_ponens
| is_a_theorem(esk1_0) )
& ( is_a_theorem(X8)
| ~ is_a_theorem(implies(X7,X8))
| ~ is_a_theorem(X7)
| ~ modus_ponens ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens])])])])])]) ).
fof(c_0_36,plain,
! [X41,X42] :
( ( and_3
| ~ is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0)))) )
& ( is_a_theorem(implies(X41,implies(X42,and(X41,X42))))
| ~ and_3 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_3])])])])]) ).
fof(c_0_37,plain,
! [X11,X12] :
( ( substitution_of_equivalents
| esk3_0 != esk4_0 )
& ( substitution_of_equivalents
| is_a_theorem(equiv(esk3_0,esk4_0)) )
& ( X11 = X12
| ~ is_a_theorem(equiv(X11,X12))
| ~ substitution_of_equivalents ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_of_equivalents])])])])])]) ).
fof(c_0_38,plain,
! [X125,X126] :
( equiv(X125,X126) = and(implies(X125,X126),implies(X126,X125))
| ~ op_equiv ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])])]) ).
cnf(c_0_39,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| ~ modus_ponens
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[hilbert_modus_ponens]) ).
cnf(c_0_41,plain,
( ~ and_3
| is_a_theorem(implies(X1,implies(X2,and(X1,X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,plain,
and_3,
inference(split_conjunct,[status(thm)],[hilbert_and_3]) ).
cnf(c_0_43,plain,
( ~ is_a_theorem(equiv(X1,X2))
| ~ substitution_of_equivalents
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_44,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents]) ).
cnf(c_0_45,plain,
( ~ op_equiv
| equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[hilbert_op_equiv]) ).
cnf(c_0_47,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]) ).
cnf(c_0_48,plain,
is_a_theorem(implies(X1,implies(X2,and(X1,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
fof(c_0_49,plain,
! [X19,X20] :
( ( implies_1
| ~ is_a_theorem(implies(esk7_0,implies(esk8_0,esk7_0))) )
& ( is_a_theorem(implies(X19,implies(X20,X19)))
| ~ implies_1 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_1])])])])]) ).
fof(c_0_50,plain,
! [X23,X24] :
( ( implies_2
| ~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0))) )
& ( is_a_theorem(implies(implies(X23,implies(X23,X24)),implies(X23,X24)))
| ~ implies_2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_2])])])])]) ).
cnf(c_0_51,plain,
( ~ is_a_theorem(equiv(X1,X2))
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
cnf(c_0_52,plain,
equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
cnf(c_0_53,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,and(X2,X1))) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,plain,
( ~ implies_1
| is_a_theorem(implies(X1,implies(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_55,plain,
implies_1,
inference(split_conjunct,[status(thm)],[hilbert_implies_1]) ).
cnf(c_0_56,plain,
( ~ implies_2
| is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_57,plain,
implies_2,
inference(split_conjunct,[status(thm)],[hilbert_implies_2]) ).
cnf(c_0_58,plain,
( ~ is_a_theorem(and(implies(X1,X2),implies(X2,X1)))
| X1 = X2 ),
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(X2)
| is_a_theorem(and(X1,X2)) ),
inference(spm,[status(thm)],[c_0_47,c_0_53]) ).
cnf(c_0_60,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
cnf(c_0_61,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]) ).
fof(c_0_62,plain,
! [X33,X34] :
( ( and_1
| ~ is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0)) )
& ( is_a_theorem(implies(and(X33,X34),X33))
| ~ and_1 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_1])])])])]) ).
fof(c_0_63,plain,
! [X121,X122] :
( implies(X121,X122) = not(and(X121,not(X122)))
| ~ op_implies_and ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])]) ).
cnf(c_0_64,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X2,X1))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_47,c_0_60]) ).
cnf(c_0_66,plain,
( ~ is_a_theorem(implies(X1,implies(X1,X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_47,c_0_61]) ).
cnf(c_0_67,plain,
( ~ and_1
| is_a_theorem(implies(and(X1,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_68,plain,
and_1,
inference(split_conjunct,[status(thm)],[hilbert_and_1]) ).
fof(c_0_69,plain,
! [X117,X118] :
( or(X117,X118) = not(and(not(X117),not(X118)))
| ~ op_or ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])])]) ).
cnf(c_0_70,plain,
( ~ op_implies_and
| implies(X1,X2) = not(and(X1,not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_71,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
cnf(c_0_72,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_73,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(spm,[status(thm)],[c_0_66,c_0_48]) ).
cnf(c_0_74,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
fof(c_0_75,plain,
! [X53,X54,X55] :
( ( or_3
| ~ is_a_theorem(implies(implies(esk24_0,esk26_0),implies(implies(esk25_0,esk26_0),implies(or(esk24_0,esk25_0),esk26_0)))) )
& ( is_a_theorem(implies(implies(X53,X55),implies(implies(X54,X55),implies(or(X53,X54),X55))))
| ~ or_3 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_3])])])])]) ).
cnf(c_0_76,plain,
( ~ op_or
| or(X1,X2) = not(and(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_77,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71])]) ).
cnf(c_0_78,plain,
op_or,
inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).
cnf(c_0_79,plain,
( ~ is_a_theorem(X2)
| implies(X1,X2) = X2 ),
inference(spm,[status(thm)],[c_0_72,c_0_60]) ).
cnf(c_0_80,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_73]),c_0_74])]) ).
cnf(c_0_81,plain,
( ~ or_3
| is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(or(X1,X3),X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_82,plain,
or(X1,X2) = implies(not(X1),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77]),c_0_78])]) ).
cnf(c_0_83,plain,
or_3,
inference(split_conjunct,[status(thm)],[hilbert_or_3]) ).
cnf(c_0_84,plain,
implies(X1,implies(X2,X2)) = implies(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_73]),c_0_80]),c_0_80]) ).
cnf(c_0_85,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_66,c_0_60]) ).
fof(c_0_86,plain,
! [X37,X38] :
( ( and_2
| ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0)) )
& ( is_a_theorem(implies(and(X37,X38),X38))
| ~ and_2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_2])])])])]) ).
cnf(c_0_87,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(implies(not(X1),X3),X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82]),c_0_83])]) ).
cnf(c_0_88,plain,
( ~ is_a_theorem(implies(implies(X1,X1),X2))
| implies(X1,X1) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_84]),c_0_85])]) ).
cnf(c_0_89,plain,
( ~ and_2
| is_a_theorem(implies(and(X1,X2),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_90,plain,
and_2,
inference(split_conjunct,[status(thm)],[hilbert_and_2]) ).
fof(c_0_91,plain,
! [X205] :
( possibly(X205) = not(necessarily(not(X205)))
| ~ op_possibly ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_possibly])])])]) ).
fof(c_0_92,plain,
! [X207,X208] :
( strict_implies(X207,X208) = necessarily(implies(X207,X208))
| ~ op_strict_implies ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_implies])])])]) ).
cnf(c_0_93,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(not(X1),X1),X2))),
inference(spm,[status(thm)],[c_0_66,c_0_87]) ).
cnf(c_0_94,plain,
implies(X1,and(implies(X2,X2),X1)) = implies(X2,X2),
inference(spm,[status(thm)],[c_0_88,c_0_48]) ).
cnf(c_0_95,plain,
is_a_theorem(implies(and(X1,X2),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_90])]) ).
fof(c_0_96,plain,
! [X127] :
( ( necessitation
| ~ is_a_theorem(necessarily(esk56_0)) )
& ( necessitation
| is_a_theorem(esk56_0) )
& ( is_a_theorem(necessarily(X127))
| ~ is_a_theorem(X127)
| ~ necessitation ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[necessitation])])])])])]) ).
cnf(c_0_97,plain,
( ~ op_possibly
| possibly(X1) = not(necessarily(not(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_98,plain,
op_possibly,
inference(split_conjunct,[status(thm)],[km4b_op_possibly]) ).
cnf(c_0_99,plain,
( ~ op_strict_implies
| strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_100,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(c_0_101,plain,
implies(implies(not(X1),X1),X1) = implies(X1,X1),
inference(spm,[status(thm)],[c_0_88,c_0_93]) ).
cnf(c_0_102,plain,
and(implies(X1,X1),X2) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_94]),c_0_85]),c_0_95])]) ).
fof(c_0_103,plain,
! [X147] :
( ( axiom_4
| ~ is_a_theorem(implies(necessarily(esk66_0),necessarily(necessarily(esk66_0)))) )
& ( is_a_theorem(implies(necessarily(X147),necessarily(necessarily(X147))))
| ~ axiom_4 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_4])])])])]) ).
fof(c_0_104,plain,
! [X145] :
( ( axiom_M
| ~ is_a_theorem(implies(necessarily(esk65_0),esk65_0)) )
& ( is_a_theorem(implies(necessarily(X145),X145))
| ~ axiom_M ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_M])])])])]) ).
cnf(c_0_105,plain,
( ~ is_a_theorem(X1)
| ~ necessitation
| is_a_theorem(necessarily(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_106,plain,
necessitation,
inference(split_conjunct,[status(thm)],[km4b_necessitation]) ).
fof(c_0_107,negated_conjecture,
~ axiom_m9,
inference(assume_negation,[status(cth)],[s1_0_m6s3m9b_axiom_m9]) ).
cnf(c_0_108,plain,
not(necessarily(not(X1))) = possibly(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98])]) ).
cnf(c_0_109,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_100])]) ).
cnf(c_0_110,plain,
implies(not(X1),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_101]),c_0_102]),c_0_60])]) ).
cnf(c_0_111,plain,
( ~ axiom_4
| is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_112,plain,
axiom_4,
inference(split_conjunct,[status(thm)],[km4b_axiom_4]) ).
cnf(c_0_113,plain,
( ~ axiom_M
| is_a_theorem(implies(necessarily(X1),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_114,plain,
axiom_M,
inference(split_conjunct,[status(thm)],[km4b_axiom_M]) ).
fof(c_0_115,plain,
! [X173,X174] :
( ( axiom_m2
| ~ is_a_theorem(strict_implies(and(esk79_0,esk80_0),esk79_0)) )
& ( is_a_theorem(strict_implies(and(X173,X174),X173))
| ~ axiom_m2 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m2])])])])]) ).
cnf(c_0_116,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(necessarily(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106])]) ).
fof(c_0_117,negated_conjecture,
~ axiom_m9,
inference(fof_simplification,[status(thm)],[c_0_107]) ).
cnf(c_0_118,plain,
not(strict_implies(X1,X2)) = possibly(and(X1,not(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_77]),c_0_109]) ).
cnf(c_0_119,plain,
strict_implies(not(X1),X1) = necessarily(X1),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_120,plain,
is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_112])]) ).
cnf(c_0_121,plain,
is_a_theorem(implies(necessarily(X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114])]) ).
cnf(c_0_122,plain,
( ~ is_a_theorem(strict_implies(and(esk79_0,esk80_0),esk79_0))
| axiom_m2 ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_123,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_116,c_0_109]) ).
fof(c_0_124,plain,
! [X201] :
( ( axiom_m9
| ~ is_a_theorem(strict_implies(possibly(possibly(esk93_0)),possibly(esk93_0))) )
& ( is_a_theorem(strict_implies(possibly(possibly(X201)),possibly(X201)))
| ~ axiom_m9 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m9])])])])]) ).
fof(c_0_125,negated_conjecture,
~ axiom_m9,
inference(fof_nnf,[status(thm)],[c_0_117]) ).
cnf(c_0_126,plain,
not(necessarily(X1)) = possibly(not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_80]) ).
cnf(c_0_127,plain,
necessarily(necessarily(X1)) = necessarily(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_120]),c_0_121])]) ).
cnf(c_0_128,plain,
not(not(X1)) = implies(not(X1),X1),
inference(spm,[status(thm)],[c_0_77,c_0_80]) ).
cnf(c_0_129,plain,
( ~ axiom_m2
| is_a_theorem(strict_implies(and(X1,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_130,plain,
axiom_m2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_74])]) ).
cnf(c_0_131,plain,
( ~ is_a_theorem(strict_implies(possibly(possibly(esk93_0)),possibly(esk93_0)))
| axiom_m9 ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_132,negated_conjecture,
~ axiom_m9,
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_133,plain,
possibly(possibly(not(X1))) = possibly(not(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_126]),c_0_126]) ).
cnf(c_0_134,plain,
not(not(X1)) = X1,
inference(rw,[status(thm)],[c_0_128,c_0_110]) ).
cnf(c_0_135,plain,
is_a_theorem(strict_implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_130])]) ).
cnf(c_0_136,plain,
~ is_a_theorem(strict_implies(possibly(possibly(esk93_0)),possibly(esk93_0))),
inference(sr,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_137,plain,
possibly(possibly(X1)) = possibly(X1),
inference(spm,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_138,plain,
is_a_theorem(strict_implies(X1,X1)),
inference(spm,[status(thm)],[c_0_135,c_0_80]) ).
cnf(c_0_139,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_138])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL548+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.47 % Computer : n010.cluster.edu
% 0.21/0.47 % Model : x86_64 x86_64
% 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.47 % Memory : 8046.5625MB
% 0.21/0.47 % OS : Linux 6.8.0-71-generic
% 0.21/0.47 % CPULimit : 300
% 0.21/0.47 % WCLimit : 300
% 0.21/0.47 % DateTime : Mon Sep 21 00:38:24 UTC 2026
% 0.21/0.47 % CPUTime :
% 0.21/0.47 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.53 Running first-order theorem proving
% 0.25/0.53 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.45/0.76 % Version: 3.5.1
% 0.45/0.76 % Preprocessing class: FSLSSLSSSSSNFFN.
% 0.45/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.76 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 0.45/0.76 % Starting new_bool_3 with 300s (1) cores
% 0.45/0.76 % Starting new_bool_1 with 300s (1) cores
% 0.45/0.76 % Starting sh5l with 300s (1) cores
% 0.45/0.76 % new_bool_3 with pid 3883224 completed with status 9
% 0.45/0.76 % new_bool_1 with pid 3883225 completed with status 9
% 0.45/0.76 % H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with pid 3883223 completed with status 0
% 0.45/0.76 % Result found by H----_102_C18_F1_PI_AE_CS_SP_PS_S2S
% 0.45/0.76 % Preprocessing class: FSLSSLSSSSSNFFN.
% 0.45/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.76 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 0.45/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.45/0.76 % No SInE strategy applied
% 0.45/0.76 % Search class: FGUSF-FFMM21-MFFFFFNN
% 0.45/0.76 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.45/0.76 % Starting SubtermCWHack with 136s (1) cores
% 0.45/0.76 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 151s (1) cores
% 0.45/0.76 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 136s (1) cores
% 0.45/0.76 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 0.45/0.76 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.45/0.76 % U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 3883243 completed with status 0
% 0.45/0.76 % Result found by U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.45/0.76 % Preprocessing class: FSLSSLSSSSSNFFN.
% 0.45/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.45/0.76 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 0.45/0.76 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.45/0.76 % No SInE strategy applied
% 0.45/0.76 % Search class: FGUSF-FFMM21-MFFFFFNN
% 0.45/0.76 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.45/0.76 % Starting SubtermCWHack with 136s (1) cores
% 0.45/0.76 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 151s (1) cores
% 0.45/0.76 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 136s (1) cores
% 0.45/0.76 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 0.45/0.76 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.45/0.76 % Preprocessing time : 0.004 s
% 0.45/0.76 % Presaturation interreduction done
% 0.45/0.76
% 0.45/0.76 % Proof found!
% 0.45/0.76 % SZS status Theorem
% 0.45/0.76 % SZS output start CNFRefutation
% See solution above
% 0.45/0.76 % Parsed axioms : 89
% 0.45/0.76 % Removed by relevancy pruning/SinE : 0
% 0.45/0.76 % Initial clauses : 147
% 0.45/0.76 % Removed in clause preprocessing : 0
% 0.45/0.76 % Initial clauses in saturation : 147
% 0.45/0.76 % Processed clauses : 705
% 0.45/0.76 % ...of these trivial : 89
% 0.45/0.76 % ...subsumed : 183
% 0.45/0.76 % ...remaining for further processing : 433
% 0.45/0.76 % Other redundant clauses eliminated : 0
% 0.45/0.76 % Clauses deleted for lack of memory : 0
% 0.45/0.76 % Backward-subsumed : 2
% 0.45/0.76 % Backward-rewritten : 65
% 0.45/0.76 % Generated clauses : 5253
% 0.45/0.76 % ...of the previous two non-redundant : 3449
% 0.45/0.76 % ...aggressively subsumed : 0
% 0.45/0.76 % Contextual simplify-reflections : 6
% 0.45/0.76 % Paramodulations : 5253
% 0.45/0.76 % Factorizations : 0
% 0.45/0.76 % NegExts : 0
% 0.45/0.76 % Equation resolutions : 0
% 0.45/0.76 % Disequality decompositions : 0
% 0.45/0.76 % Total rewrite steps : 6167
% 0.45/0.76 % ...of those cached : 4719
% 0.45/0.76 % Propositional unsat checks : 0
% 0.45/0.76 % Propositional check models : 0
% 0.45/0.76 % Propositional check unsatisfiable : 0
% 0.45/0.76 % Propositional clauses : 0
% 0.45/0.76 % Propositional clauses after purity: 0
% 0.45/0.76 % Propositional unsat core size : 0
% 0.45/0.76 % Propositional preprocessing time : 0.000
% 0.45/0.76 % Propositional encoding time : 0.000
% 0.45/0.76 % Propositional solver time : 0.000
% 0.45/0.76 % Success case prop preproc time : 0.000
% 0.45/0.76 % Success case prop encoding time : 0.000
% 0.45/0.76 % Success case prop solver time : 0.000
% 0.45/0.76 % Current number of processed clauses : 253
% 0.45/0.76 % Positive orientable unit clauses : 142
% 0.45/0.76 % Positive unorientable unit clauses: 4
% 0.45/0.76 % Negative unit clauses : 5
% 0.45/0.76 % Non-unit-clauses : 102
% 0.45/0.76 % Current number of unprocessed clauses: 2952
% 0.45/0.76 % ...number of literals in the above : 4010
% 0.45/0.76 % Current number of archived formulas : 0
% 0.45/0.76 % Current number of archived clauses : 180
% 0.45/0.76 % Clause-clause subsumption calls (NU) : 3783
% 0.45/0.76 % Rec. Clause-clause subsumption calls : 2246
% 0.45/0.76 % Non-unit clause-clause subsumptions : 134
% 0.45/0.76 % Unit Clause-clause subsumption calls : 989
% 0.45/0.76 % Rewrite failures with RHS unbound : 0
% 0.45/0.76 % BW rewrite match attempts : 1284
% 0.45/0.76 % BW rewrite match successes : 52
% 0.45/0.76 % Condensation attempts : 0
% 0.45/0.76 % Condensation successes : 0
% 0.45/0.76 % Termbank termtop insertions : 70427
% 0.45/0.76 % Search garbage collected termcells : 2057
% 0.45/0.76
% 0.45/0.76 % -------------------------------------------------
% 0.45/0.76 % User time : 0.155 s
% 0.45/0.76 % System time : 0.014 s
% 0.45/0.76 % Total time : 0.168 s
% 0.45/0.76 % Maximum resident set size: 3992 pages
% 0.45/0.76
% 0.45/0.76 % -------------------------------------------------
% 0.45/0.76 % User time : 0.691 s
% 0.45/0.76 % System time : 0.120 s
% 0.45/0.76 % Total time : 0.810 s
% 0.45/0.76 % Maximum resident set size: 4864 pages
% 0.45/0.76 % E exiting
%------------------------------------------------------------------------------