%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL528+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 01:12:59 PM UTC 2026
% Result : Theorem 12.30s 7.96s
% Output : CNFRefutation 12.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 32
% Syntax : Number of formulae : 141 ( 78 unt; 0 def)
% Number of atoms : 253 ( 43 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 189 ( 77 ~; 76 |; 17 &)
% ( 12 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 19 ( 17 usr; 17 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 22 con; 0-2 aty)
% Number of variables : 186 ( 13 sgn 60 !; 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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(hilbert_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(hilbert_and_3,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
fof(implies_2,axiom,
( implies_2
<=> ! [X1,X2] : is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_2) ).
fof(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',use_substitution_of_equivalents) ).
fof(hilbert_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_equiv) ).
fof(hilbert_implies_2,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(and_1,axiom,
( and_1
<=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_1) ).
fof(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
fof(or_1,axiom,
( or_1
<=> ! [X1,X2] : is_a_theorem(implies(X1,or(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',or_1) ).
fof(hilbert_and_1,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_1) ).
fof(modus_tollens,axiom,
( modus_tollens
<=> ! [X1,X2] : is_a_theorem(implies(implies(not(X2),not(X1)),implies(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
fof(hilbert_op_or,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_or) ).
fof(hilbert_or_1,axiom,
or_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_or_1) ).
fof(hilbert_modus_tollens,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_tollens) ).
fof(or_2,axiom,
( or_2
<=> ! [X1,X2] : is_a_theorem(implies(X2,or(X1,X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',or_2) ).
fof(hilbert_or_2,axiom,
or_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_or_2) ).
fof(implies_1,axiom,
( implies_1
<=> ! [X1,X2] : is_a_theorem(implies(X1,implies(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_1) ).
fof(hilbert_implies_1,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_1) ).
fof(axiom_M,axiom,
( axiom_M
<=> ! [X1] : is_a_theorem(implies(necessarily(X1),X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_M) ).
fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X1,X2] : strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL007+0.ax',necessitation) ).
fof(s1_0_axiom_m1,conjecture,
axiom_m1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m1) ).
fof(km5_axiom_M,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax',km5_axiom_M) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(km5_necessitation,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax',km5_necessitation) ).
fof(axiom_m1,axiom,
( axiom_m1
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m1) ).
fof(c_0_32,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_33,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_34,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_35,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_36,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| ~ modus_ponens
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[hilbert_modus_ponens]) ).
cnf(c_0_38,plain,
( ~ and_3
| is_a_theorem(implies(X1,implies(X2,and(X1,X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,plain,
and_3,
inference(split_conjunct,[status(thm)],[hilbert_and_3]) ).
fof(c_0_40,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_41,plain,
( ~ is_a_theorem(equiv(X1,X2))
| ~ substitution_of_equivalents
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents]) ).
cnf(c_0_43,plain,
( ~ op_equiv
| equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[hilbert_op_equiv]) ).
cnf(c_0_45,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_36,c_0_37])]) ).
cnf(c_0_46,plain,
is_a_theorem(implies(X1,implies(X2,and(X1,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
cnf(c_0_47,plain,
( ~ implies_2
| is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_48,plain,
implies_2,
inference(split_conjunct,[status(thm)],[hilbert_implies_2]) ).
fof(c_0_49,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_50,plain,
( ~ is_a_theorem(equiv(X1,X2))
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
cnf(c_0_51,plain,
equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
cnf(c_0_52,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,and(X2,X1))) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
fof(c_0_54,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_55,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_56,plain,
( ~ op_implies_and
| implies(X1,X2) = not(and(X1,not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_57,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
fof(c_0_58,plain,
! [X45,X46] :
( ( or_1
| ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0))) )
& ( is_a_theorem(implies(X45,or(X45,X46)))
| ~ or_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)],[or_1])])])])]) ).
cnf(c_0_59,plain,
( ~ is_a_theorem(and(implies(X1,X2),implies(X2,X1)))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_60,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(X2)
| is_a_theorem(and(X1,X2)) ),
inference(spm,[status(thm)],[c_0_45,c_0_52]) ).
cnf(c_0_61,plain,
( ~ is_a_theorem(implies(X1,implies(X1,X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_45,c_0_53]) ).
cnf(c_0_62,plain,
( ~ and_1
| is_a_theorem(implies(and(X1,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_63,plain,
and_1,
inference(split_conjunct,[status(thm)],[hilbert_and_1]) ).
fof(c_0_64,plain,
! [X15,X16] :
( ( modus_tollens
| ~ is_a_theorem(implies(implies(not(esk6_0),not(esk5_0)),implies(esk5_0,esk6_0))) )
& ( is_a_theorem(implies(implies(not(X16),not(X15)),implies(X15,X16)))
| ~ modus_tollens ) ),
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_tollens])])])])]) ).
cnf(c_0_65,plain,
( ~ op_or
| or(X1,X2) = not(and(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_66,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57])]) ).
cnf(c_0_67,plain,
op_or,
inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).
cnf(c_0_68,plain,
( ~ or_1
| is_a_theorem(implies(X1,or(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_69,plain,
or_1,
inference(split_conjunct,[status(thm)],[hilbert_or_1]) ).
cnf(c_0_70,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X2,X1))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_71,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(spm,[status(thm)],[c_0_61,c_0_46]) ).
cnf(c_0_72,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]) ).
cnf(c_0_73,plain,
( ~ modus_tollens
| is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_74,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66]),c_0_67])]) ).
cnf(c_0_75,plain,
modus_tollens,
inference(split_conjunct,[status(thm)],[hilbert_modus_tollens]) ).
cnf(c_0_76,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69])]) ).
cnf(c_0_77,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72])]) ).
fof(c_0_78,plain,
! [X49,X50] :
( ( or_2
| ~ is_a_theorem(implies(esk23_0,or(esk22_0,esk23_0))) )
& ( is_a_theorem(implies(X50,or(X49,X50)))
| ~ or_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)],[or_2])])])])]) ).
cnf(c_0_79,plain,
is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74]),c_0_75])]) ).
cnf(c_0_80,plain,
is_a_theorem(or(X1,or(not(X1),X2))),
inference(spm,[status(thm)],[c_0_76,c_0_74]) ).
cnf(c_0_81,plain,
not(not(X1)) = or(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_77]),c_0_74]) ).
cnf(c_0_82,plain,
( ~ or_2
| is_a_theorem(implies(X1,or(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_83,plain,
or_2,
inference(split_conjunct,[status(thm)],[hilbert_or_2]) ).
cnf(c_0_84,plain,
and(implies(X1,not(X2)),or(X2,X1)) = equiv(X1,not(X2)),
inference(spm,[status(thm)],[c_0_51,c_0_74]) ).
cnf(c_0_85,plain,
( ~ is_a_theorem(or(X2,not(X1)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_45,c_0_79]) ).
cnf(c_0_86,plain,
is_a_theorem(or(X1,not(not(not(X1))))),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_87,plain,
is_a_theorem(implies(or(X1,or(X1,X2)),or(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_74]),c_0_74]) ).
cnf(c_0_88,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_83])]) ).
cnf(c_0_89,plain,
( ~ is_a_theorem(or(X2,X1))
| ~ is_a_theorem(implies(X1,not(X2)))
| is_a_theorem(equiv(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_60,c_0_84]) ).
cnf(c_0_90,plain,
is_a_theorem(or(not(X1),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_74]) ).
cnf(c_0_91,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_76,c_0_81]) ).
fof(c_0_92,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])])])])]) ).
cnf(c_0_93,plain,
or(X1,or(X1,X2)) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_87]),c_0_88])]) ).
cnf(c_0_94,plain,
is_a_theorem(equiv(X1,not(not(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91])]) ).
cnf(c_0_95,plain,
( ~ implies_1
| is_a_theorem(implies(X1,implies(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_96,plain,
implies_1,
inference(split_conjunct,[status(thm)],[hilbert_implies_1]) ).
cnf(c_0_97,plain,
or(X1,not(not(X1))) = not(not(X1)),
inference(spm,[status(thm)],[c_0_93,c_0_81]) ).
cnf(c_0_98,plain,
not(not(X1)) = X1,
inference(spm,[status(thm)],[c_0_50,c_0_94]) ).
cnf(c_0_99,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_96])]) ).
cnf(c_0_100,plain,
is_a_theorem(implies(or(X1,implies(X2,X3)),implies(and(X2,not(X3)),X1))),
inference(spm,[status(thm)],[c_0_79,c_0_66]) ).
cnf(c_0_101,plain,
or(X1,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98]),c_0_98]) ).
fof(c_0_102,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])])])])]) ).
fof(c_0_103,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_104,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_45,c_0_99]) ).
fof(c_0_105,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])])])])])]) ).
fof(c_0_106,negated_conjecture,
~ axiom_m1,
inference(assume_negation,[status(cth)],[s1_0_axiom_m1]) ).
cnf(c_0_107,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_77]),c_0_74]),c_0_74]),c_0_101]) ).
cnf(c_0_108,plain,
( ~ axiom_M
| is_a_theorem(implies(necessarily(X1),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_109,plain,
axiom_M,
inference(split_conjunct,[status(thm)],[km5_axiom_M]) ).
cnf(c_0_110,plain,
( ~ op_strict_implies
| strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_111,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(c_0_112,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_70,c_0_104]) ).
cnf(c_0_113,plain,
( ~ is_a_theorem(X1)
| ~ necessitation
| is_a_theorem(necessarily(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_114,plain,
necessitation,
inference(split_conjunct,[status(thm)],[km5_necessitation]) ).
fof(c_0_115,negated_conjecture,
~ axiom_m1,
inference(fof_simplification,[status(thm)],[c_0_106]) ).
cnf(c_0_116,plain,
not(and(X1,X2)) = implies(X1,not(X2)),
inference(spm,[status(thm)],[c_0_66,c_0_98]) ).
cnf(c_0_117,plain,
or(not(X1),X2) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_74,c_0_98]) ).
cnf(c_0_118,plain,
or(X1,X2) = or(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_107]),c_0_107])]) ).
cnf(c_0_119,plain,
is_a_theorem(implies(necessarily(X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_109])]) ).
cnf(c_0_120,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_111])]) ).
cnf(c_0_121,plain,
( ~ is_a_theorem(X2)
| implies(X1,X2) = X2 ),
inference(spm,[status(thm)],[c_0_112,c_0_99]) ).
cnf(c_0_122,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(necessarily(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114])]) ).
fof(c_0_123,plain,
! [X169,X170] :
( ( axiom_m1
| ~ is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0))) )
& ( is_a_theorem(strict_implies(and(X169,X170),and(X170,X169)))
| ~ axiom_m1 ) ),
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_m1])])])])]) ).
fof(c_0_124,negated_conjecture,
~ axiom_m1,
inference(fof_nnf,[status(thm)],[c_0_115]) ).
cnf(c_0_125,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(spm,[status(thm)],[c_0_98,c_0_116]) ).
cnf(c_0_126,plain,
or(X1,not(X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_127,plain,
is_a_theorem(implies(strict_implies(X1,X2),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_128,plain,
implies(X1,implies(X2,X2)) = implies(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_71]),c_0_77]),c_0_77]) ).
cnf(c_0_129,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_122,c_0_120]) ).
cnf(c_0_130,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_61,c_0_99]) ).
cnf(c_0_131,plain,
( ~ is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0)))
| axiom_m1 ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_132,negated_conjecture,
~ axiom_m1,
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_133,plain,
and(not(X1),X2) = not(implies(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_74]),c_0_126]) ).
cnf(c_0_134,plain,
( ~ is_a_theorem(strict_implies(X1,X2))
| strict_implies(X1,X2) = implies(X1,X2) ),
inference(spm,[status(thm)],[c_0_112,c_0_127]) ).
cnf(c_0_135,plain,
strict_implies(X1,implies(X2,X2)) = strict_implies(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_128]),c_0_120]) ).
cnf(c_0_136,plain,
is_a_theorem(strict_implies(X1,X1)),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_137,plain,
~ is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0))),
inference(sr,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_138,plain,
and(X1,X2) = and(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_98]),c_0_125]) ).
cnf(c_0_139,plain,
strict_implies(X1,X1) = implies(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_128]),c_0_136])]) ).
cnf(c_0_140,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_139]),c_0_130])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL528+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/5.38 % Computer : n011.cluster.edu
% 0.13/5.38 % Model : x86_64 x86_64
% 0.13/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.38 % Memory : 8046.5625MB
% 0.13/5.38 % OS : Linux 6.8.0-71-generic
% 0.13/5.38 % CPULimit : 300
% 0.13/5.38 % WCLimit : 300
% 0.13/5.38 % DateTime : Mon Sep 21 00:37:15 UTC 2026
% 0.13/5.38 % CPUTime :
% 0.13/5.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/5.43 Running first-order theorem proving
% 0.17/5.43 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 12.30/7.96 % Version: 3.5.1
% 12.30/7.96 % Preprocessing class: FSLSSLSSSSSNFFN.
% 12.30/7.96 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.30/7.96 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 12.30/7.96 % Starting new_bool_3 with 300s (1) cores
% 12.30/7.96 % Starting new_bool_1 with 300s (1) cores
% 12.30/7.96 % Starting sh5l with 300s (1) cores
% 12.30/7.96 % new_bool_1 with pid 587047 completed with status 9
% 12.30/7.96 % new_bool_3 with pid 587046 completed with status 9
% 12.30/7.96 % sh5l with pid 587048 completed with status 9
% 12.30/7.96 % H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with pid 587045 completed with status 0
% 12.30/7.96 % Result found by H----_102_C18_F1_PI_AE_CS_SP_PS_S2S
% 12.30/7.96 % Preprocessing class: FSLSSLSSSSSNFFN.
% 12.30/7.96 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.30/7.96 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 12.30/7.96 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 12.30/7.96 % No SInE strategy applied
% 12.30/7.96 % Search class: FGUSF-FFMM21-MFFFFFNN
% 12.30/7.96 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 12.30/7.96 % Starting SubtermCWHack with 136s (1) cores
% 12.30/7.96 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 151s (1) cores
% 12.30/7.96 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 136s (1) cores
% 12.30/7.96 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 12.30/7.96 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 12.30/7.96 % H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with pid 587056 completed with status 0
% 12.30/7.96 % Result found by H----_102_C18_F1_PI_AE_CS_SP_PS_S2S
% 12.30/7.96 % Preprocessing class: FSLSSLSSSSSNFFN.
% 12.30/7.96 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.30/7.96 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 12.30/7.96 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 12.30/7.96 % No SInE strategy applied
% 12.30/7.96 % Search class: FGUSF-FFMM21-MFFFFFNN
% 12.30/7.96 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 12.30/7.96 % Starting SubtermCWHack with 136s (1) cores
% 12.30/7.96 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 151s (1) cores
% 12.30/7.96 % Preprocessing time : 0.003 s
% 12.30/7.96 % Presaturation interreduction done
% 12.30/7.96
% 12.30/7.96 % Proof found!
% 12.30/7.96 % SZS status Theorem
% 12.30/7.96 % SZS output start CNFRefutation
% See solution above
% 12.30/7.96 % Parsed axioms : 88
% 12.30/7.96 % Removed by relevancy pruning/SinE : 0
% 12.30/7.96 % Initial clauses : 146
% 12.30/7.96 % Removed in clause preprocessing : 0
% 12.30/7.96 % Initial clauses in saturation : 146
% 12.30/7.96 % Processed clauses : 8196
% 12.30/7.96 % ...of these trivial : 363
% 12.30/7.96 % ...subsumed : 6188
% 12.30/7.96 % ...remaining for further processing : 1645
% 12.30/7.96 % Other redundant clauses eliminated : 0
% 12.30/7.96 % Clauses deleted for lack of memory : 0
% 12.30/7.96 % Backward-subsumed : 42
% 12.30/7.96 % Backward-rewritten : 667
% 12.30/7.96 % Generated clauses : 125227
% 12.30/7.96 % ...of the previous two non-redundant : 113191
% 12.30/7.96 % ...aggressively subsumed : 0
% 12.30/7.96 % Contextual simplify-reflections : 45
% 12.30/7.96 % Paramodulations : 125227
% 12.30/7.96 % Factorizations : 0
% 12.30/7.96 % NegExts : 0
% 12.30/7.96 % Equation resolutions : 0
% 12.30/7.96 % Disequality decompositions : 0
% 12.30/7.96 % Total rewrite steps : 74263
% 12.30/7.96 % ...of those cached : 63462
% 12.30/7.96 % Propositional unsat checks : 0
% 12.30/7.96 % Propositional check models : 0
% 12.30/7.96 % Propositional check unsatisfiable : 0
% 12.30/7.96 % Propositional clauses : 0
% 12.30/7.96 % Propositional clauses after purity: 0
% 12.30/7.96 % Propositional unsat core size : 0
% 12.30/7.96 % Propositional preprocessing time : 0.000
% 12.30/7.96 % Propositional encoding time : 0.000
% 12.30/7.96 % Propositional solver time : 0.000
% 12.30/7.96 % Success case prop preproc time : 0.000
% 12.30/7.96 % Success case prop encoding time : 0.000
% 12.30/7.96 % Success case prop solver time : 0.000
% 12.30/7.96 % Current number of processed clauses : 821
% 12.30/7.96 % Positive orientable unit clauses : 300
% 12.30/7.96 % Positive unorientable unit clauses: 4
% 12.30/7.96 % Negative unit clauses : 3
% 12.30/7.96 % Non-unit-clauses : 514
% 12.30/7.96 % Current number of unprocessed clauses: 101964
% 12.30/7.96 % ...number of literals in the above : 254253
% 12.30/7.96 % Current number of archived formulas : 0
% 12.30/7.96 % Current number of archived clauses : 824
% 12.30/7.96 % Clause-clause subsumption calls (NU) : 186832
% 12.30/7.96 % Rec. Clause-clause subsumption calls : 131261
% 12.30/7.96 % Non-unit clause-clause subsumptions : 6205
% 12.30/7.96 % Unit Clause-clause subsumption calls : 5377
% 12.30/7.96 % Rewrite failures with RHS unbound : 104
% 12.30/7.96 % BW rewrite match attempts : 2446
% 12.30/7.96 % BW rewrite match successes : 581
% 12.30/7.96 % Condensation attempts : 0
% 12.30/7.96 % Condensation successes : 0
% 12.30/7.96 % Termbank termtop insertions : 1691047
% 12.30/7.96 % Search garbage collected termcells : 2057
% 12.30/7.96
% 12.30/7.96 % -------------------------------------------------
% 12.30/7.96 % User time : 2.341 s
% 12.30/7.96 % System time : 0.111 s
% 12.30/7.96 % Total time : 2.453 s
% 12.30/7.96 % Maximum resident set size: 3992 pages
% 12.30/7.96
% 12.30/7.96 % -------------------------------------------------
% 12.30/7.96 % User time : 11.745 s
% 12.30/7.96 % System time : 0.630 s
% 12.30/7.96 % Total time : 12.375 s
% 12.30/7.96 % Maximum resident set size: 4864 pages
% 12.30/7.96 % E exiting
%------------------------------------------------------------------------------