%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL568+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 : n015.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 01:13:04 PM UTC 2026
% Result : Theorem 1.70s 0.79s
% Output : CNFRefutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 30
% Syntax : Number of formulae : 136 ( 69 unt; 0 def)
% Number of atoms : 258 ( 46 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 209 ( 87 ~; 87 |; 17 &)
% ( 10 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 16 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 17 con; 0-2 aty)
% Number of variables : 179 ( 9 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(adjunction,axiom,
( adjunction
<=> ! [X1,X2] :
( ( is_a_theorem(X2)
& is_a_theorem(X1) )
=> is_a_theorem(and(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',adjunction) ).
fof(op_strict_equiv,axiom,
( op_strict_equiv
=> ! [X1,X2] : strict_equiv(X1,X2) = and(strict_implies(X1,X2),strict_implies(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_strict_equiv) ).
fof(substitution_strict_equiv,axiom,
( substitution_strict_equiv
<=> ! [X1,X2] :
( is_a_theorem(strict_equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',substitution_strict_equiv) ).
fof(s1_0_adjunction,axiom,
adjunction,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_adjunction) ).
fof(s1_0_op_strict_equiv,axiom,
op_strict_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_strict_equiv) ).
fof(s1_0_substitution_strict_equiv,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_substitution_strict_equiv) ).
fof(axiom_m1,axiom,
( axiom_m1
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m1) ).
fof(modus_ponens_strict_implies,axiom,
( modus_ponens_strict_implies
<=> ! [X1,X2] :
( ( is_a_theorem(strict_implies(X1,X2))
& is_a_theorem(X1) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',modus_ponens_strict_implies) ).
fof(axiom_m5,axiom,
( axiom_m5
<=> ! [X1,X2,X3] : is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m5) ).
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(s1_0_axiom_m1,axiom,
axiom_m1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m1) ).
fof(s1_0_modus_ponens_strict_implies,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_modus_ponens_strict_implies) ).
fof(s1_0_axiom_m5,axiom,
axiom_m5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m5) ).
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(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/theBenchmark.p',hilbert_op_implies_and) ).
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(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_strict_implies) ).
fof(s1_0_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_or) ).
fof(s1_0_axiom_m2,axiom,
axiom_m2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m2) ).
fof(axiom_m4,axiom,
( axiom_m4
<=> ! [X1] : is_a_theorem(strict_implies(X1,and(X1,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m4) ).
fof(s1_0_axiom_m4,axiom,
axiom_m4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_axiom_m4) ).
fof(axiom_m6,axiom,
( axiom_m6
<=> ! [X1] : is_a_theorem(strict_implies(X1,possibly(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m6) ).
fof(s1_0_m6s3m9b_axiom_m6,axiom,
axiom_m6,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+5.ax',s1_0_m6s3m9b_axiom_m6) ).
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(s1_0_op_possibly,axiom,
op_possibly,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+4.ax',s1_0_op_possibly) ).
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(km4b_axiom_4,conjecture,
axiom_4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_axiom_4) ).
fof(s1_0_m6s3m9b_axiom_m9,axiom,
axiom_m9,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+5.ax',s1_0_m6s3m9b_axiom_m9) ).
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(c_0_30,plain,
! [X22,X23] :
( ( adjunction
| ~ is_a_theorem(and(esk4_0,esk5_0)) )
& ( adjunction
| is_a_theorem(esk5_0) )
& ( adjunction
| is_a_theorem(esk4_0) )
& ( is_a_theorem(and(X22,X23))
| ~ is_a_theorem(X23)
| ~ is_a_theorem(X22)
| ~ adjunction ) ),
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)],[adjunction])])])])])]) ).
fof(c_0_31,plain,
! [X98,X99] :
( strict_equiv(X98,X99) = and(strict_implies(X98,X99),strict_implies(X99,X98))
| ~ op_strict_equiv ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_equiv])])])]) ).
fof(c_0_32,plain,
! [X26,X27] :
( ( substitution_strict_equiv
| esk6_0 != esk7_0 )
& ( substitution_strict_equiv
| is_a_theorem(strict_equiv(esk6_0,esk7_0)) )
& ( X26 = X27
| ~ is_a_theorem(strict_equiv(X26,X27))
| ~ substitution_strict_equiv ) ),
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_strict_equiv])])])])])]) ).
cnf(c_0_33,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ adjunction
| is_a_theorem(and(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
adjunction,
inference(split_conjunct,[status(thm)],[s1_0_adjunction]) ).
cnf(c_0_35,plain,
( ~ op_strict_equiv
| strict_equiv(X1,X2) = and(strict_implies(X1,X2),strict_implies(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,plain,
op_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_equiv]) ).
cnf(c_0_37,plain,
( ~ is_a_theorem(strict_equiv(X1,X2))
| ~ substitution_strict_equiv
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
substitution_strict_equiv,
inference(split_conjunct,[status(thm)],[s1_0_substitution_strict_equiv]) ).
cnf(c_0_39,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(X2)
| is_a_theorem(and(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
cnf(c_0_40,plain,
and(strict_implies(X1,X2),strict_implies(X2,X1)) = strict_equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
fof(c_0_41,plain,
! [X58,X59] :
( ( axiom_m1
| ~ is_a_theorem(strict_implies(and(esk22_0,esk23_0),and(esk23_0,esk22_0))) )
& ( is_a_theorem(strict_implies(and(X58,X59),and(X59,X58)))
| ~ 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_42,plain,
! [X18,X19] :
( ( modus_ponens_strict_implies
| ~ is_a_theorem(esk3_0) )
& ( modus_ponens_strict_implies
| is_a_theorem(strict_implies(esk2_0,esk3_0)) )
& ( modus_ponens_strict_implies
| is_a_theorem(esk2_0) )
& ( is_a_theorem(X19)
| ~ is_a_theorem(strict_implies(X18,X19))
| ~ is_a_theorem(X18)
| ~ modus_ponens_strict_implies ) ),
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_strict_implies])])])])])]) ).
fof(c_0_43,plain,
! [X74,X75,X76] :
( ( axiom_m5
| ~ is_a_theorem(strict_implies(and(strict_implies(esk30_0,esk31_0),strict_implies(esk31_0,esk32_0)),strict_implies(esk30_0,esk32_0))) )
& ( is_a_theorem(strict_implies(and(strict_implies(X74,X75),strict_implies(X75,X76)),strict_implies(X74,X76)))
| ~ axiom_m5 ) ),
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_m5])])])])]) ).
fof(c_0_44,plain,
! [X10,X11] :
( implies(X10,X11) = not(and(X10,not(X11)))
| ~ 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_45,plain,
( ~ is_a_theorem(strict_equiv(X1,X2))
| X1 = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_46,plain,
( ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X2,X1))
| is_a_theorem(strict_equiv(X1,X2)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,plain,
( ~ axiom_m1
| is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,plain,
axiom_m1,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m1]) ).
cnf(c_0_49,plain,
( ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(X1)
| ~ modus_ponens_strict_implies
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,plain,
modus_ponens_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_modus_ponens_strict_implies]) ).
cnf(c_0_51,plain,
( ~ axiom_m5
| is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,plain,
axiom_m5,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m5]) ).
fof(c_0_53,plain,
! [X96,X97] :
( strict_implies(X96,X97) = necessarily(implies(X96,X97))
| ~ 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])])])]) ).
fof(c_0_54,plain,
! [X6,X7] :
( or(X6,X7) = not(and(not(X6),not(X7)))
| ~ 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_55,plain,
( ~ op_implies_and
| implies(X1,X2) = not(and(X1,not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_56,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
cnf(c_0_57,plain,
( ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X2,X1))
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_58,plain,
is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
cnf(c_0_59,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(strict_implies(X2,X1))
| is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
cnf(c_0_60,plain,
is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
fof(c_0_61,plain,
! [X62,X63] :
( ( axiom_m2
| ~ is_a_theorem(strict_implies(and(esk24_0,esk25_0),esk24_0)) )
& ( is_a_theorem(strict_implies(and(X62,X63),X62))
| ~ 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_62,plain,
( ~ op_strict_implies
| strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_63,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(c_0_64,plain,
( ~ op_or
| or(X1,X2) = not(and(not(X1),not(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_65,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]) ).
cnf(c_0_66,plain,
op_or,
inference(split_conjunct,[status(thm)],[s1_0_op_or]) ).
cnf(c_0_67,plain,
and(X1,X2) = and(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_58])]) ).
cnf(c_0_68,plain,
( ~ is_a_theorem(and(strict_implies(X1,X3),strict_implies(X3,X2)))
| is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_69,plain,
( ~ axiom_m2
| is_a_theorem(strict_implies(and(X1,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_70,plain,
axiom_m2,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m2]) ).
cnf(c_0_71,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]) ).
cnf(c_0_72,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65]),c_0_66])]) ).
cnf(c_0_73,plain,
not(and(not(X1),X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_65,c_0_67]) ).
fof(c_0_74,plain,
! [X72] :
( ( axiom_m4
| ~ is_a_theorem(strict_implies(esk29_0,and(esk29_0,esk29_0))) )
& ( is_a_theorem(strict_implies(X72,and(X72,X72)))
| ~ axiom_m4 ) ),
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_m4])])])])]) ).
cnf(c_0_75,plain,
( ~ is_a_theorem(strict_implies(X1,X3))
| ~ is_a_theorem(strict_implies(X3,X2))
| is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_68,c_0_39]) ).
cnf(c_0_76,plain,
is_a_theorem(strict_implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70])]) ).
cnf(c_0_77,plain,
necessarily(or(X1,X2)) = strict_implies(not(X1),X2),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_78,plain,
or(X1,X2) = or(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_73]),c_0_72]),c_0_72]) ).
cnf(c_0_79,plain,
( ~ axiom_m4
| is_a_theorem(strict_implies(X1,and(X1,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_80,plain,
axiom_m4,
inference(split_conjunct,[status(thm)],[s1_0_axiom_m4]) ).
cnf(c_0_81,plain,
( ~ is_a_theorem(strict_implies(X1,and(X2,X3)))
| is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_82,plain,
strict_implies(not(X1),X2) = strict_implies(not(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_77]) ).
cnf(c_0_83,plain,
is_a_theorem(strict_implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]) ).
cnf(c_0_84,plain,
( ~ is_a_theorem(strict_implies(not(and(X2,X3)),X1))
| is_a_theorem(strict_implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_85,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_83]),c_0_76])]) ).
cnf(c_0_86,plain,
is_a_theorem(strict_implies(not(X1),not(and(X1,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_83]),c_0_85]),c_0_82]) ).
cnf(c_0_87,plain,
( ~ is_a_theorem(strict_implies(X1,not(X3)))
| ~ is_a_theorem(strict_implies(not(X2),X3))
| is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_75,c_0_82]) ).
cnf(c_0_88,plain,
( ~ is_a_theorem(strict_implies(not(X2),X1))
| is_a_theorem(strict_implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_89,plain,
is_a_theorem(strict_implies(not(not(X1)),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_86,c_0_73]) ).
cnf(c_0_90,plain,
( ~ is_a_theorem(strict_implies(X1,not(X2)))
| ~ is_a_theorem(strict_implies(not(X1),X2))
| X1 = not(X2) ),
inference(spm,[status(thm)],[c_0_57,c_0_82]) ).
cnf(c_0_91,plain,
( ~ is_a_theorem(strict_implies(X1,not(not(X2))))
| is_a_theorem(strict_implies(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_83]),c_0_85]) ).
cnf(c_0_92,plain,
is_a_theorem(strict_implies(not(implies(X1,X2)),not(X2))),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
fof(c_0_93,plain,
! [X80] :
( ( axiom_m6
| ~ is_a_theorem(strict_implies(esk33_0,possibly(esk33_0))) )
& ( is_a_theorem(strict_implies(X80,possibly(X80)))
| ~ axiom_m6 ) ),
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_m6])])])])]) ).
cnf(c_0_94,plain,
( ~ is_a_theorem(strict_implies(X1,not(not(X1))))
| not(not(X1)) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_83]),c_0_85]),c_0_85]) ).
cnf(c_0_95,plain,
not(not(X1)) = or(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_85]),c_0_72]) ).
cnf(c_0_96,plain,
is_a_theorem(strict_implies(not(X1),implies(X2,not(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_82]) ).
cnf(c_0_97,plain,
( ~ axiom_m6
| is_a_theorem(strict_implies(X1,possibly(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_98,plain,
axiom_m6,
inference(split_conjunct,[status(thm)],[s1_0_m6s3m9b_axiom_m6]) ).
cnf(c_0_99,plain,
( ~ is_a_theorem(strict_implies(X1,or(X1,X1)))
| or(X1,X1) = X1 ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_100,plain,
is_a_theorem(strict_implies(not(X1),or(X2,not(X1)))),
inference(spm,[status(thm)],[c_0_96,c_0_72]) ).
cnf(c_0_101,plain,
is_a_theorem(strict_implies(X1,possibly(X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98])]) ).
fof(c_0_102,plain,
! [X94] :
( possibly(X94) = not(necessarily(not(X94)))
| ~ op_possibly ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_possibly])])])]) ).
cnf(c_0_103,plain,
not(not(not(X1))) = not(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_95]) ).
cnf(c_0_104,plain,
( ~ is_a_theorem(not(X2))
| ~ is_a_theorem(strict_implies(not(X1),X2))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_82]) ).
cnf(c_0_105,plain,
( ~ is_a_theorem(strict_implies(X1,X2))
| is_a_theorem(strict_implies(X1,possibly(X2))) ),
inference(spm,[status(thm)],[c_0_75,c_0_101]) ).
cnf(c_0_106,plain,
( ~ op_possibly
| possibly(X1) = not(necessarily(not(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_107,plain,
op_possibly,
inference(split_conjunct,[status(thm)],[s1_0_op_possibly]) ).
fof(c_0_108,plain,
! [X90] :
( ( axiom_m9
| ~ is_a_theorem(strict_implies(possibly(possibly(esk38_0)),possibly(esk38_0))) )
& ( is_a_theorem(strict_implies(possibly(possibly(X90)),possibly(X90)))
| ~ 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])])])])]) ).
cnf(c_0_109,plain,
implies(X1,not(not(X2))) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_103]),c_0_73]) ).
fof(c_0_110,negated_conjecture,
~ axiom_4,
inference(assume_negation,[status(cth)],[km4b_axiom_4]) ).
cnf(c_0_111,plain,
( ~ is_a_theorem(not(possibly(X2)))
| ~ is_a_theorem(strict_implies(not(X1),X2))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_112,plain,
not(necessarily(not(X1))) = possibly(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_107])]) ).
cnf(c_0_113,plain,
( ~ axiom_m9
| is_a_theorem(strict_implies(possibly(possibly(X1)),possibly(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_114,plain,
axiom_m9,
inference(split_conjunct,[status(thm)],[s1_0_m6s3m9b_axiom_m9]) ).
cnf(c_0_115,plain,
strict_implies(X1,not(not(X2))) = strict_implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_109]),c_0_71]) ).
cnf(c_0_116,plain,
is_a_theorem(strict_implies(X1,X1)),
inference(spm,[status(thm)],[c_0_76,c_0_85]) ).
fof(c_0_117,negated_conjecture,
~ axiom_4,
inference(fof_simplification,[status(thm)],[c_0_110]) ).
cnf(c_0_118,plain,
( ~ is_a_theorem(not(possibly(X2)))
| ~ is_a_theorem(strict_implies(not(X2),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_111,c_0_82]) ).
cnf(c_0_119,plain,
possibly(and(X1,not(X2))) = not(strict_implies(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_65]),c_0_71]) ).
cnf(c_0_120,plain,
is_a_theorem(strict_implies(possibly(possibly(X1)),possibly(X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114])]) ).
cnf(c_0_121,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_115]),c_0_116])]) ).
fof(c_0_122,plain,
! [X36] :
( ( axiom_4
| ~ is_a_theorem(implies(necessarily(esk11_0),necessarily(necessarily(esk11_0)))) )
& ( is_a_theorem(implies(necessarily(X36),necessarily(necessarily(X36))))
| ~ 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_123,negated_conjecture,
~ axiom_4,
inference(fof_nnf,[status(thm)],[c_0_117]) ).
cnf(c_0_124,plain,
( ~ is_a_theorem(not(possibly(X1)))
| is_a_theorem(not(X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_83]),c_0_85]) ).
cnf(c_0_125,plain,
possibly(and(not(X1),X2)) = not(strict_implies(X2,X1)),
inference(spm,[status(thm)],[c_0_119,c_0_67]) ).
cnf(c_0_126,plain,
possibly(possibly(X1)) = possibly(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_120]),c_0_101])]) ).
cnf(c_0_127,plain,
possibly(not(X1)) = not(necessarily(X1)),
inference(spm,[status(thm)],[c_0_112,c_0_121]) ).
cnf(c_0_128,plain,
( ~ is_a_theorem(implies(necessarily(esk11_0),necessarily(necessarily(esk11_0))))
| axiom_4 ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_129,negated_conjecture,
~ axiom_4,
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_130,plain,
( ~ is_a_theorem(not(not(strict_implies(X1,X2))))
| is_a_theorem(implies(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_73]) ).
cnf(c_0_131,plain,
not(necessarily(necessarily(X1))) = not(necessarily(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_127]) ).
cnf(c_0_132,plain,
~ is_a_theorem(implies(necessarily(esk11_0),necessarily(necessarily(esk11_0)))),
inference(sr,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_133,plain,
( ~ is_a_theorem(strict_implies(X1,X2))
| is_a_theorem(implies(X1,X2)) ),
inference(rw,[status(thm)],[c_0_130,c_0_121]) ).
cnf(c_0_134,plain,
necessarily(necessarily(X1)) = necessarily(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_131]),c_0_121]) ).
cnf(c_0_135,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_134]),c_0_116])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL568+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 00:42:21 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 1.70/0.79 % Version: 3.5.1
% 1.70/0.79 % Preprocessing class: FSMSSLSSSSSNFFN.
% 1.70/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.70/0.79 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 1.70/0.79 % Starting new_bool_3 with 300s (1) cores
% 1.70/0.79 % Starting new_bool_1 with 300s (1) cores
% 1.70/0.79 % Starting sh5l with 300s (1) cores
% 1.70/0.79 % new_bool_3 with pid 185237 completed with status 9
% 1.70/0.79 % new_bool_1 with pid 185238 completed with status 9
% 1.70/0.79 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 185236 completed with status 0
% 1.70/0.79 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 1.70/0.79 % Preprocessing class: FSMSSLSSSSSNFFN.
% 1.70/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.70/0.79 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 1.70/0.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.70/0.79 % No SInE strategy applied
% 1.70/0.79 % Search class: FGUSF-FFMM21-MFFFFFNN
% 1.70/0.79 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.70/0.79 % Starting SubtermCWHack with 151s (1) cores
% 1.70/0.79 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 1.70/0.79 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0YI with 151s (1) cores
% 1.70/0.79 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 151s (1) cores
% 1.70/0.79 % Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.70/0.79 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 185249 completed with status 0
% 1.70/0.79 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 1.70/0.79 % Preprocessing class: FSMSSLSSSSSNFFN.
% 1.70/0.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.70/0.79 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 1500s (5) cores
% 1.70/0.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.70/0.79 % No SInE strategy applied
% 1.70/0.79 % Search class: FGUSF-FFMM21-MFFFFFNN
% 1.70/0.79 % Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.70/0.79 % Starting SubtermCWHack with 151s (1) cores
% 1.70/0.79 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 750s (1) cores
% 1.70/0.79 % Preprocessing time : 0.002 s
% 1.70/0.79 % Presaturation interreduction done
% 1.70/0.79
% 1.70/0.79 % Proof found!
% 1.70/0.79 % SZS status Theorem
% 1.70/0.79 % SZS output start CNFRefutation
% See solution above
% 1.70/0.80 % Parsed axioms : 55
% 1.70/0.80 % Removed by relevancy pruning/SinE : 0
% 1.70/0.80 % Initial clauses : 84
% 1.70/0.80 % Removed in clause preprocessing : 0
% 1.70/0.80 % Initial clauses in saturation : 84
% 1.70/0.80 % Processed clauses : 3240
% 1.70/0.80 % ...of these trivial : 149
% 1.70/0.80 % ...subsumed : 2310
% 1.70/0.80 % ...remaining for further processing : 781
% 1.70/0.80 % Other redundant clauses eliminated : 0
% 1.70/0.80 % Clauses deleted for lack of memory : 0
% 1.70/0.80 % Backward-subsumed : 16
% 1.70/0.80 % Backward-rewritten : 209
% 1.70/0.80 % Generated clauses : 19951
% 1.70/0.80 % ...of the previous two non-redundant : 18823
% 1.70/0.80 % ...aggressively subsumed : 0
% 1.70/0.80 % Contextual simplify-reflections : 0
% 1.70/0.80 % Paramodulations : 19951
% 1.70/0.80 % Factorizations : 0
% 1.70/0.80 % NegExts : 0
% 1.70/0.80 % Equation resolutions : 0
% 1.70/0.80 % Disequality decompositions : 0
% 1.70/0.80 % Total rewrite steps : 8940
% 1.70/0.80 % ...of those cached : 7565
% 1.70/0.80 % Propositional unsat checks : 0
% 1.70/0.80 % Propositional check models : 0
% 1.70/0.80 % Propositional check unsatisfiable : 0
% 1.70/0.80 % Propositional clauses : 0
% 1.70/0.80 % Propositional clauses after purity: 0
% 1.70/0.80 % Propositional unsat core size : 0
% 1.70/0.80 % Propositional preprocessing time : 0.000
% 1.70/0.80 % Propositional encoding time : 0.000
% 1.70/0.80 % Propositional solver time : 0.000
% 1.70/0.80 % Success case prop preproc time : 0.000
% 1.70/0.80 % Success case prop encoding time : 0.000
% 1.70/0.80 % Success case prop solver time : 0.000
% 1.70/0.80 % Current number of processed clauses : 491
% 1.70/0.80 % Positive orientable unit clauses : 133
% 1.70/0.80 % Positive unorientable unit clauses: 5
% 1.70/0.80 % Negative unit clauses : 4
% 1.70/0.80 % Non-unit-clauses : 349
% 1.70/0.80 % Current number of unprocessed clauses: 15590
% 1.70/0.80 % ...number of literals in the above : 34580
% 1.70/0.80 % Current number of archived formulas : 0
% 1.70/0.80 % Current number of archived clauses : 290
% 1.70/0.80 % Clause-clause subsumption calls (NU) : 59326
% 1.70/0.80 % Rec. Clause-clause subsumption calls : 50436
% 1.70/0.80 % Non-unit clause-clause subsumptions : 2277
% 1.70/0.80 % Unit Clause-clause subsumption calls : 2428
% 1.70/0.80 % Rewrite failures with RHS unbound : 0
% 1.70/0.80 % BW rewrite match attempts : 422
% 1.70/0.80 % BW rewrite match successes : 133
% 1.70/0.80 % Condensation attempts : 0
% 1.70/0.80 % Condensation successes : 0
% 1.70/0.80 % Termbank termtop insertions : 280481
% 1.70/0.80 % Search garbage collected termcells : 1012
% 1.70/0.80
% 1.70/0.80 % -------------------------------------------------
% 1.70/0.80 % User time : 0.330 s
% 1.70/0.80 % System time : 0.019 s
% 1.70/0.80 % Total time : 0.349 s
% 1.70/0.80 % Maximum resident set size: 3436 pages
% 1.70/0.80
% 1.70/0.80 % -------------------------------------------------
% 1.70/0.80 % User time : 1.643 s
% 1.70/0.80 % System time : 0.142 s
% 1.70/0.80 % Total time : 1.785 s
% 1.70/0.80 % Maximum resident set size: 4864 pages
% 1.70/0.80 % E exiting
%------------------------------------------------------------------------------