TSTP Solution File: LCL528+1 by E---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : LCL528+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 18:13:03 EDT 2023
% Result : Theorem 8.66s 1.53s
% Output : CNFRefutation 8.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 36
% Syntax : Number of formulae : 151 ( 76 unt; 0 def)
% Number of atoms : 280 ( 51 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 217 ( 88 ~; 89 |; 19 &)
% ( 14 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 21 ( 19 usr; 19 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 26 con; 0-2 aty)
% Number of variables : 203 ( 12 sgn; 68 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(implies(X1,X2)) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',modus_ponens) ).
fof(and_3,axiom,
( and_3
<=> ! [X1,X2] : is_a_theorem(implies(X1,implies(X2,and(X1,X2)))) ),
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',and_3) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X1,X2] :
( is_a_theorem(equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',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/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',op_equiv) ).
fof(hilbert_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',hilbert_modus_ponens) ).
fof(hilbert_and_3,axiom,
and_3,
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',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/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',implies_2) ).
fof(substitution_of_equivalents_0001,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',substitution_of_equivalents_0001) ).
fof(hilbert_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',hilbert_op_equiv) ).
fof(hilbert_implies_2,axiom,
implies_2,
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',hilbert_implies_2) ).
fof(and_1,axiom,
( and_1
<=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',and_1) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X1,X2] : implies(X1,X2) = not(and(X1,not(X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',op_implies_and) ).
fof(hilbert_and_1,axiom,
and_1,
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',hilbert_and_1) ).
fof(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',op_or) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',hilbert_op_implies_and) ).
fof(or_1,axiom,
( or_1
<=> ! [X1,X2] : is_a_theorem(implies(X1,or(X1,X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',or_1) ).
fof(hilbert_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',hilbert_op_or) ).
fof(modus_tollens,axiom,
( modus_tollens
<=> ! [X1,X2] : is_a_theorem(implies(implies(not(X2),not(X1)),implies(X1,X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',modus_tollens) ).
fof(hilbert_or_1,axiom,
or_1,
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',hilbert_or_1) ).
fof(implies_1,axiom,
( implies_1
<=> ! [X1,X2] : is_a_theorem(implies(X1,implies(X2,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',implies_1) ).
fof(hilbert_modus_tollens,axiom,
modus_tollens,
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',hilbert_modus_tollens) ).
fof(hilbert_implies_1,axiom,
implies_1,
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',hilbert_implies_1) ).
fof(and_2,axiom,
( and_2
<=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',and_2) ).
fof(axiom_M,axiom,
( axiom_M
<=> ! [X1] : is_a_theorem(implies(necessarily(X1),X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',axiom_M) ).
fof(hilbert_and_2,axiom,
and_2,
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',hilbert_and_2) ).
fof(necessitation,axiom,
( necessitation
<=> ! [X1] :
( is_a_theorem(X1)
=> is_a_theorem(necessarily(X1)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',necessitation) ).
fof(km5_axiom_M,axiom,
axiom_M,
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',km5_axiom_M) ).
fof(km5_necessitation,axiom,
necessitation,
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',km5_necessitation) ).
fof(axiom_5,axiom,
( axiom_5
<=> ! [X1] : is_a_theorem(implies(possibly(X1),necessarily(possibly(X1)))) ),
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',axiom_5) ).
fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X1,X2] : strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',op_strict_implies) ).
fof(km5_axiom_5,axiom,
axiom_5,
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',km5_axiom_5) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',s1_0_op_strict_implies) ).
fof(implies_3,axiom,
( implies_3
<=> ! [X1,X2,X3] : is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) ),
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',implies_3) ).
fof(hilbert_implies_3,axiom,
implies_3,
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',hilbert_implies_3) ).
fof(axiom_m1,axiom,
( axiom_m1
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))) ),
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',axiom_m1) ).
fof(s1_0_axiom_m1,conjecture,
axiom_m1,
file('/export/starexec/sandbox2/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p',s1_0_axiom_m1) ).
fof(c_0_36,plain,
! [X7,X8] :
( ( ~ modus_ponens
| ~ is_a_theorem(X7)
| ~ is_a_theorem(implies(X7,X8))
| is_a_theorem(X8) )
& ( is_a_theorem(esk1_0)
| modus_ponens )
& ( is_a_theorem(implies(esk1_0,esk2_0))
| modus_ponens )
& ( ~ is_a_theorem(esk2_0)
| modus_ponens ) ),
inference(distribute,[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_37,plain,
! [X41,X42] :
( ( ~ and_3
| is_a_theorem(implies(X41,implies(X42,and(X41,X42)))) )
& ( ~ is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0))))
| and_3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_3])])])]) ).
fof(c_0_38,plain,
! [X11,X12] :
( ( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X11,X12))
| X11 = X12 )
& ( is_a_theorem(equiv(esk3_0,esk4_0))
| substitution_of_equivalents )
& ( esk3_0 != esk4_0
| substitution_of_equivalents ) ),
inference(distribute,[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_39,plain,
! [X125,X126] :
( ~ op_equiv
| equiv(X125,X126) = and(implies(X125,X126),implies(X126,X125)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])]) ).
cnf(c_0_40,plain,
( is_a_theorem(X2)
| ~ modus_ponens
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[hilbert_modus_ponens]) ).
cnf(c_0_42,plain,
( is_a_theorem(implies(X1,implies(X2,and(X1,X2))))
| ~ and_3 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,plain,
and_3,
inference(split_conjunct,[status(thm)],[hilbert_and_3]) ).
fof(c_0_44,plain,
! [X23,X24] :
( ( ~ implies_2
| is_a_theorem(implies(implies(X23,implies(X23,X24)),implies(X23,X24))) )
& ( ~ is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0)))
| implies_2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_2])])])]) ).
cnf(c_0_45,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[substitution_of_equivalents_0001]) ).
cnf(c_0_47,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[hilbert_op_equiv]) ).
cnf(c_0_49,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]) ).
cnf(c_0_50,plain,
is_a_theorem(implies(X1,implies(X2,and(X1,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).
cnf(c_0_51,plain,
( is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))
| ~ implies_2 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,plain,
implies_2,
inference(split_conjunct,[status(thm)],[hilbert_implies_2]) ).
cnf(c_0_53,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
cnf(c_0_54,plain,
equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
cnf(c_0_55,plain,
( is_a_theorem(implies(X1,and(X2,X1)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
fof(c_0_57,plain,
! [X33,X34] :
( ( ~ and_1
| is_a_theorem(implies(and(X33,X34),X33)) )
& ( ~ is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0))
| and_1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_1])])])]) ).
fof(c_0_58,plain,
! [X121,X122] :
( ~ op_implies_and
| implies(X121,X122) = not(and(X121,not(X122))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])]) ).
cnf(c_0_59,plain,
( X1 = X2
| ~ is_a_theorem(and(implies(X1,X2),implies(X2,X1))) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_55]) ).
cnf(c_0_61,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_49,c_0_56]) ).
cnf(c_0_62,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ and_1 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_63,plain,
and_1,
inference(split_conjunct,[status(thm)],[hilbert_and_1]) ).
fof(c_0_64,plain,
! [X117,X118] :
( ~ op_or
| or(X117,X118) = not(and(not(X117),not(X118))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])]) ).
cnf(c_0_65,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_66,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
fof(c_0_67,plain,
! [X45,X46] :
( ( ~ or_1
| is_a_theorem(implies(X45,or(X45,X46))) )
& ( ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0)))
| or_1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_1])])])]) ).
cnf(c_0_68,plain,
( X1 = X2
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_69,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(spm,[status(thm)],[c_0_61,c_0_50]) ).
cnf(c_0_70,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_71,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_72,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66])]) ).
cnf(c_0_73,plain,
op_or,
inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).
fof(c_0_74,plain,
! [X15,X16] :
( ( ~ modus_tollens
| is_a_theorem(implies(implies(not(X16),not(X15)),implies(X15,X16))) )
& ( ~ is_a_theorem(implies(implies(not(esk6_0),not(esk5_0)),implies(esk5_0,esk6_0)))
| modus_tollens ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_tollens])])])]) ).
cnf(c_0_75,plain,
( is_a_theorem(implies(X1,or(X1,X2)))
| ~ or_1 ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_76,plain,
or_1,
inference(split_conjunct,[status(thm)],[hilbert_or_1]) ).
fof(c_0_77,plain,
! [X19,X20] :
( ( ~ implies_1
| is_a_theorem(implies(X19,implies(X20,X19))) )
& ( ~ is_a_theorem(implies(esk7_0,implies(esk8_0,esk7_0)))
| implies_1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_1])])])]) ).
cnf(c_0_78,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70])]) ).
cnf(c_0_79,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).
cnf(c_0_80,plain,
( is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))
| ~ modus_tollens ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_81,plain,
modus_tollens,
inference(split_conjunct,[status(thm)],[hilbert_modus_tollens]) ).
cnf(c_0_82,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76])]) ).
cnf(c_0_83,plain,
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ implies_1 ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_84,plain,
implies_1,
inference(split_conjunct,[status(thm)],[hilbert_implies_1]) ).
cnf(c_0_85,plain,
not(not(X1)) = or(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_78]),c_0_79]) ).
cnf(c_0_86,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_80,c_0_79]),c_0_81])]) ).
cnf(c_0_87,plain,
is_a_theorem(or(X1,or(not(X1),X2))),
inference(spm,[status(thm)],[c_0_82,c_0_79]) ).
fof(c_0_88,plain,
! [X37,X38] :
( ( ~ and_2
| is_a_theorem(implies(and(X37,X38),X38)) )
& ( ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0))
| and_2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_2])])])]) ).
cnf(c_0_89,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84])]) ).
fof(c_0_90,plain,
! [X145] :
( ( ~ axiom_M
| is_a_theorem(implies(necessarily(X145),X145)) )
& ( ~ is_a_theorem(implies(necessarily(esk65_0),esk65_0))
| axiom_M ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_M])])])]) ).
cnf(c_0_91,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_82,c_0_85]) ).
cnf(c_0_92,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_49,c_0_86]) ).
cnf(c_0_93,plain,
is_a_theorem(or(X1,not(not(not(X1))))),
inference(spm,[status(thm)],[c_0_87,c_0_85]) ).
cnf(c_0_94,plain,
( is_a_theorem(implies(and(X1,X2),X2))
| ~ and_2 ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_95,plain,
and_2,
inference(split_conjunct,[status(thm)],[hilbert_and_2]) ).
cnf(c_0_96,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_89]) ).
fof(c_0_97,plain,
! [X127] :
( ( ~ necessitation
| ~ is_a_theorem(X127)
| is_a_theorem(necessarily(X127)) )
& ( is_a_theorem(esk56_0)
| necessitation )
& ( ~ is_a_theorem(necessarily(esk56_0))
| necessitation ) ),
inference(distribute,[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_98,plain,
( is_a_theorem(implies(necessarily(X1),X1))
| ~ axiom_M ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_99,plain,
axiom_M,
inference(split_conjunct,[status(thm)],[km5_axiom_M]) ).
cnf(c_0_100,plain,
( not(not(X1)) = X1
| ~ is_a_theorem(or(not(X1),X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_91]),c_0_79]) ).
cnf(c_0_101,plain,
is_a_theorem(or(not(X1),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_79]) ).
cnf(c_0_102,plain,
is_a_theorem(implies(and(X1,X2),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95])]) ).
cnf(c_0_103,plain,
( X1 = X2
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_96]) ).
cnf(c_0_104,plain,
( is_a_theorem(necessarily(X1))
| ~ necessitation
| ~ is_a_theorem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_105,plain,
necessitation,
inference(split_conjunct,[status(thm)],[km5_necessitation]) ).
fof(c_0_106,plain,
! [X151] :
( ( ~ axiom_5
| is_a_theorem(implies(possibly(X151),necessarily(possibly(X151)))) )
& ( ~ is_a_theorem(implies(possibly(esk68_0),necessarily(possibly(esk68_0))))
| axiom_5 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_5])])])]) ).
cnf(c_0_107,plain,
is_a_theorem(implies(necessarily(X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_99])]) ).
fof(c_0_108,plain,
! [X207,X208] :
( ~ op_strict_implies
| strict_implies(X207,X208) = necessarily(implies(X207,X208)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_implies])])]) ).
cnf(c_0_109,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_101])]) ).
cnf(c_0_110,plain,
( and(X1,X2) = X2
| ~ is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_55]),c_0_102])]) ).
cnf(c_0_111,plain,
( X1 = X2
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_103,c_0_96]) ).
cnf(c_0_112,plain,
( is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_105])]) ).
cnf(c_0_113,plain,
( is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))
| ~ axiom_5 ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_114,plain,
axiom_5,
inference(split_conjunct,[status(thm)],[km5_axiom_5]) ).
cnf(c_0_115,plain,
( necessarily(X1) = X1
| ~ is_a_theorem(necessarily(X1)) ),
inference(spm,[status(thm)],[c_0_103,c_0_107]) ).
cnf(c_0_116,plain,
( strict_implies(X1,X2) = necessarily(implies(X1,X2))
| ~ op_strict_implies ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_117,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(c_0_118,plain,
not(and(X1,X2)) = implies(X1,not(X2)),
inference(spm,[status(thm)],[c_0_72,c_0_109]) ).
cnf(c_0_119,plain,
and(implies(X1,X1),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_69]),c_0_78]) ).
cnf(c_0_120,plain,
( necessarily(X1) = X2
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_121,plain,
is_a_theorem(implies(possibly(X1),necessarily(possibly(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114])]) ).
cnf(c_0_122,plain,
( implies(X1,X1) = X2
| ~ is_a_theorem(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_69]),c_0_78]) ).
cnf(c_0_123,plain,
( necessarily(X1) = X1
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_115,c_0_112]) ).
cnf(c_0_124,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_117])]) ).
fof(c_0_125,plain,
! [X27,X28,X29] :
( ( ~ implies_3
| is_a_theorem(implies(implies(X27,X28),implies(implies(X28,X29),implies(X27,X29)))) )
& ( ~ is_a_theorem(implies(implies(esk11_0,esk12_0),implies(implies(esk12_0,esk13_0),implies(esk11_0,esk13_0))))
| implies_3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_3])])])]) ).
cnf(c_0_126,plain,
implies(implies(X1,X1),not(X2)) = not(X2),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_127,plain,
( necessarily(X1) = implies(and(X2,X3),X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_120,c_0_70]) ).
cnf(c_0_128,plain,
necessarily(possibly(X1)) = possibly(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_121]),c_0_107])]) ).
cnf(c_0_129,plain,
implies(X1,X1) = implies(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_69]),c_0_78]) ).
cnf(c_0_130,plain,
strict_implies(X1,X1) = implies(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_69]),c_0_78]),c_0_124]),c_0_78]) ).
cnf(c_0_131,plain,
( is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))
| ~ implies_3 ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_132,plain,
implies_3,
inference(split_conjunct,[status(thm)],[hilbert_implies_3]) ).
cnf(c_0_133,plain,
( implies(X1,and(X2,X1)) = X2
| ~ is_a_theorem(implies(implies(X1,and(X2,X1)),X2)) ),
inference(spm,[status(thm)],[c_0_68,c_0_50]) ).
cnf(c_0_134,plain,
implies(implies(X1,X1),X2) = X2,
inference(spm,[status(thm)],[c_0_126,c_0_109]) ).
cnf(c_0_135,plain,
implies(and(X1,X2),X1) = implies(esk1_0,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_121]),c_0_128]),c_0_129]),c_0_124]),c_0_130]) ).
cnf(c_0_136,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_61,c_0_89]) ).
cnf(c_0_137,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_132])]) ).
cnf(c_0_138,plain,
and(X1,implies(X2,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135]),c_0_136])]) ).
cnf(c_0_139,plain,
( implies(implies(X1,X2),implies(X3,X2)) = implies(X3,X1)
| ~ is_a_theorem(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X3,X1))) ),
inference(spm,[status(thm)],[c_0_68,c_0_137]) ).
cnf(c_0_140,plain,
implies(X1,not(implies(X2,X2))) = not(X1),
inference(spm,[status(thm)],[c_0_118,c_0_138]) ).
fof(c_0_141,plain,
! [X169,X170] :
( ( ~ axiom_m1
| is_a_theorem(strict_implies(and(X169,X170),and(X170,X169))) )
& ( ~ is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0)))
| axiom_m1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m1])])])]) ).
fof(c_0_142,negated_conjecture,
~ axiom_m1,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[s1_0_axiom_m1])]) ).
cnf(c_0_143,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(spm,[status(thm)],[c_0_109,c_0_118]) ).
cnf(c_0_144,plain,
or(X1,not(X2)) = implies(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_140]),c_0_79]),c_0_140]),c_0_79]),c_0_86])]) ).
cnf(c_0_145,plain,
( axiom_m1
| ~ is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0))) ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_146,negated_conjecture,
~ axiom_m1,
inference(split_conjunct,[status(thm)],[c_0_142]) ).
cnf(c_0_147,plain,
and(not(X1),X2) = not(implies(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_79]),c_0_144]) ).
cnf(c_0_148,plain,
~ is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0))),
inference(sr,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_149,plain,
and(X1,X2) = and(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_109]),c_0_143]) ).
cnf(c_0_150,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_130]),c_0_136])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : LCL528+1 : TPTP v8.1.2. Released v3.3.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n011.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 2400
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Oct 2 12:12:38 EDT 2023
% 0.16/0.31 % CPUTime :
% 0.16/0.43 Running first-order theorem proving
% 0.16/0.43 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/tmp/tmp.F0ZrQ3aUgH/E---3.1_20709.p
% 8.66/1.53 # Version: 3.1pre001
% 8.66/1.53 # Preprocessing class: FSLSSLSSSSSNFFN.
% 8.66/1.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.66/1.53 # Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 8.66/1.53 # Starting new_bool_3 with 300s (1) cores
% 8.66/1.53 # Starting new_bool_1 with 300s (1) cores
% 8.66/1.53 # Starting sh5l with 300s (1) cores
% 8.66/1.53 # H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with pid 20787 completed with status 0
% 8.66/1.53 # Result found by H----_102_C18_F1_PI_AE_CS_SP_PS_S2S
% 8.66/1.53 # Preprocessing class: FSLSSLSSSSSNFFN.
% 8.66/1.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.66/1.53 # Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 8.66/1.53 # No SInE strategy applied
% 8.66/1.53 # Search class: FGUSF-FFMM21-MFFFFFNN
% 8.66/1.53 # Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 8.66/1.53 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 675s (1) cores
% 8.66/1.53 # Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 151s (1) cores
% 8.66/1.53 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 8.66/1.53 # Starting U----_207d_00_B07_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 8.66/1.53 # Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 136s (1) cores
% 8.66/1.53 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with pid 20796 completed with status 0
% 8.66/1.53 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 8.66/1.53 # Preprocessing class: FSLSSLSSSSSNFFN.
% 8.66/1.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.66/1.53 # Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 1500s (5) cores
% 8.66/1.53 # No SInE strategy applied
% 8.66/1.53 # Search class: FGUSF-FFMM21-MFFFFFNN
% 8.66/1.53 # Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 8.66/1.53 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI with 675s (1) cores
% 8.66/1.53 # Preprocessing time : 0.002 s
% 8.66/1.53 # Presaturation interreduction done
% 8.66/1.53
% 8.66/1.53 # Proof found!
% 8.66/1.53 # SZS status Theorem
% 8.66/1.53 # SZS output start CNFRefutation
% See solution above
% 8.66/1.53 # Parsed axioms : 88
% 8.66/1.53 # Removed by relevancy pruning/SinE : 0
% 8.66/1.53 # Initial clauses : 146
% 8.66/1.53 # Removed in clause preprocessing : 0
% 8.66/1.53 # Initial clauses in saturation : 146
% 8.66/1.53 # Processed clauses : 10660
% 8.66/1.53 # ...of these trivial : 329
% 8.66/1.53 # ...subsumed : 8420
% 8.66/1.53 # ...remaining for further processing : 1911
% 8.66/1.53 # Other redundant clauses eliminated : 0
% 8.66/1.53 # Clauses deleted for lack of memory : 0
% 8.66/1.53 # Backward-subsumed : 76
% 8.66/1.53 # Backward-rewritten : 400
% 8.66/1.53 # Generated clauses : 81875
% 8.66/1.53 # ...of the previous two non-redundant : 72286
% 8.66/1.53 # ...aggressively subsumed : 0
% 8.66/1.53 # Contextual simplify-reflections : 1
% 8.66/1.53 # Paramodulations : 81875
% 8.66/1.53 # Factorizations : 0
% 8.66/1.53 # NegExts : 0
% 8.66/1.53 # Equation resolutions : 0
% 8.66/1.53 # Total rewrite steps : 83895
% 8.66/1.53 # Propositional unsat checks : 0
% 8.66/1.53 # Propositional check models : 0
% 8.66/1.53 # Propositional check unsatisfiable : 0
% 8.66/1.53 # Propositional clauses : 0
% 8.66/1.53 # Propositional clauses after purity: 0
% 8.66/1.53 # Propositional unsat core size : 0
% 8.66/1.53 # Propositional preprocessing time : 0.000
% 8.66/1.53 # Propositional encoding time : 0.000
% 8.66/1.53 # Propositional solver time : 0.000
% 8.66/1.53 # Success case prop preproc time : 0.000
% 8.66/1.53 # Success case prop encoding time : 0.000
% 8.66/1.53 # Success case prop solver time : 0.000
% 8.66/1.53 # Current number of processed clauses : 1319
% 8.66/1.53 # Positive orientable unit clauses : 162
% 8.66/1.53 # Positive unorientable unit clauses: 16
% 8.66/1.53 # Negative unit clauses : 3
% 8.66/1.53 # Non-unit-clauses : 1138
% 8.66/1.53 # Current number of unprocessed clauses: 59151
% 8.66/1.53 # ...number of literals in the above : 116867
% 8.66/1.53 # Current number of archived formulas : 0
% 8.66/1.53 # Current number of archived clauses : 592
% 8.66/1.53 # Clause-clause subsumption calls (NU) : 161658
% 8.66/1.53 # Rec. Clause-clause subsumption calls : 113181
% 8.66/1.53 # Non-unit clause-clause subsumptions : 6894
% 8.66/1.53 # Unit Clause-clause subsumption calls : 1626
% 8.66/1.53 # Rewrite failures with RHS unbound : 0
% 8.66/1.53 # BW rewrite match attempts : 3315
% 8.66/1.53 # BW rewrite match successes : 707
% 8.66/1.53 # Condensation attempts : 0
% 8.66/1.53 # Condensation successes : 0
% 8.66/1.53 # Termbank termtop insertions : 1028610
% 8.66/1.53
% 8.66/1.53 # -------------------------------------------------
% 8.66/1.53 # User time : 1.019 s
% 8.66/1.53 # System time : 0.041 s
% 8.66/1.53 # Total time : 1.060 s
% 8.66/1.53 # Maximum resident set size: 2256 pages
% 8.66/1.53
% 8.66/1.53 # -------------------------------------------------
% 8.66/1.53 # User time : 5.115 s
% 8.66/1.53 # System time : 0.229 s
% 8.66/1.53 # Total time : 5.343 s
% 8.66/1.53 # Maximum resident set size: 1768 pages
% 8.66/1.53 % E---3.1 exiting
% 8.66/1.53 % E---3.1 exiting
%------------------------------------------------------------------------------