TSTP Solution File: LCL533+1 by Enigma---0.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : LCL533+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n013.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 : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 09:26:38 EDT 2022
% Result : Theorem 9.25s 2.59s
% Output : CNFRefutation 9.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 34
% Syntax : Number of formulae : 147 ( 73 unt; 0 def)
% Number of atoms : 270 ( 44 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 210 ( 87 ~; 86 |; 17 &)
% ( 12 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 18 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 22 con; 0-2 aty)
% Number of variables : 195 ( 8 sgn 62 !; 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/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(substitution_of_equivalents_001,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',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(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_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(hilbert_and_1,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_1) ).
fof(op_or,axiom,
( op_or
=> ! [X1,X2] : or(X1,X2) = not(and(not(X1),not(X2))) ),
file('/export/starexec/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_op_or,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',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/sandbox/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
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(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(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/sandbox/benchmark/Axioms/LCL006+0.ax',implies_3) ).
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(hilbert_implies_3,axiom,
implies_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_3) ).
fof(km5_axiom_M,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax',km5_axiom_M) ).
fof(op_possibly,axiom,
( op_possibly
=> ! [X1] : possibly(X1) = not(necessarily(not(X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_possibly) ).
fof(s1_0_m6s3m9b_axiom_m6,conjecture,
axiom_m6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m6) ).
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(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(km5_op_possibly,axiom,
op_possibly,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax',km5_op_possibly) ).
fof(axiom_m6,axiom,
( axiom_m6
<=> ! [X1] : is_a_theorem(strict_implies(X1,possibly(X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m6) ).
fof(km5_necessitation,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax',km5_necessitation) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(c_0_34,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_35,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_36,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_37,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_38,plain,
( is_a_theorem(X2)
| ~ modus_ponens
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[hilbert_modus_ponens]) ).
cnf(c_0_40,plain,
( is_a_theorem(implies(X1,implies(X2,and(X1,X2))))
| ~ and_3 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,plain,
and_3,
inference(split_conjunct,[status(thm)],[hilbert_and_3]) ).
fof(c_0_42,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_43,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[substitution_of_equivalents]) ).
cnf(c_0_45,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[hilbert_op_equiv]) ).
cnf(c_0_47,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_38,c_0_39])]) ).
cnf(c_0_48,plain,
is_a_theorem(implies(X1,implies(X2,and(X1,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]) ).
cnf(c_0_49,plain,
( is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))
| ~ implies_2 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,plain,
implies_2,
inference(split_conjunct,[status(thm)],[hilbert_implies_2]) ).
cnf(c_0_51,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
cnf(c_0_52,plain,
equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
cnf(c_0_53,plain,
( is_a_theorem(implies(X1,and(X2,X1)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
fof(c_0_55,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_56,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_57,plain,
( X1 = X2
| ~ is_a_theorem(and(implies(X1,X2),implies(X2,X1))) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_58,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_53]) ).
cnf(c_0_59,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_47,c_0_54]) ).
cnf(c_0_60,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ and_1 ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_61,plain,
and_1,
inference(split_conjunct,[status(thm)],[hilbert_and_1]) ).
fof(c_0_62,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_63,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_64,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
fof(c_0_65,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_66,plain,
( X1 = X2
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_67,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(spm,[status(thm)],[c_0_59,c_0_48]) ).
cnf(c_0_68,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]) ).
cnf(c_0_69,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_70,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]) ).
cnf(c_0_71,plain,
op_or,
inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).
fof(c_0_72,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_73,plain,
( is_a_theorem(implies(X1,or(X1,X2)))
| ~ or_1 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_74,plain,
or_1,
inference(split_conjunct,[status(thm)],[hilbert_or_1]) ).
cnf(c_0_75,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68])]) ).
cnf(c_0_76,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70]),c_0_71])]) ).
cnf(c_0_77,plain,
( is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))
| ~ modus_tollens ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_78,plain,
modus_tollens,
inference(split_conjunct,[status(thm)],[hilbert_modus_tollens]) ).
cnf(c_0_79,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74])]) ).
cnf(c_0_80,plain,
not(not(X1)) = or(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_75]),c_0_76]) ).
cnf(c_0_81,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_77,c_0_76]),c_0_78])]) ).
cnf(c_0_82,plain,
is_a_theorem(or(X1,or(not(X1),X2))),
inference(spm,[status(thm)],[c_0_79,c_0_76]) ).
cnf(c_0_83,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_84,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_47,c_0_81]) ).
cnf(c_0_85,plain,
is_a_theorem(or(X1,not(not(not(X1))))),
inference(spm,[status(thm)],[c_0_82,c_0_80]) ).
cnf(c_0_86,plain,
( not(not(X1)) = X1
| ~ is_a_theorem(or(not(X1),X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_83]),c_0_76]) ).
cnf(c_0_87,plain,
is_a_theorem(or(not(X1),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_76]) ).
cnf(c_0_88,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87])]) ).
cnf(c_0_89,plain,
is_a_theorem(implies(or(X1,not(not(X2))),or(X2,X1))),
inference(spm,[status(thm)],[c_0_81,c_0_76]) ).
cnf(c_0_90,plain,
not(and(X1,X2)) = implies(X1,not(X2)),
inference(spm,[status(thm)],[c_0_70,c_0_88]) ).
cnf(c_0_91,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(rw,[status(thm)],[c_0_89,c_0_88]) ).
cnf(c_0_92,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(spm,[status(thm)],[c_0_88,c_0_90]) ).
cnf(c_0_93,plain,
or(not(X1),X2) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_76,c_0_88]) ).
cnf(c_0_94,plain,
or(X1,X2) = or(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_91]),c_0_91])]) ).
fof(c_0_95,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])])])]) ).
fof(c_0_96,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_97,plain,
( is_a_theorem(or(X1,and(X2,not(X1))))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_76]) ).
cnf(c_0_98,plain,
and(X1,not(X2)) = not(implies(X1,X2)),
inference(spm,[status(thm)],[c_0_92,c_0_88]) ).
cnf(c_0_99,plain,
or(X1,not(X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_100,plain,
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ implies_1 ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_101,plain,
implies_1,
inference(split_conjunct,[status(thm)],[hilbert_implies_1]) ).
fof(c_0_102,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_103,plain,
( is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))
| ~ implies_3 ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_104,plain,
implies_3,
inference(split_conjunct,[status(thm)],[hilbert_implies_3]) ).
cnf(c_0_105,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98]),c_0_99]) ).
cnf(c_0_106,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_101])]) ).
cnf(c_0_107,plain,
( is_a_theorem(implies(necessarily(X1),X1))
| ~ axiom_M ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_108,plain,
axiom_M,
inference(split_conjunct,[status(thm)],[km5_axiom_M]) ).
cnf(c_0_109,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_103,c_0_104])]) ).
cnf(c_0_110,plain,
( implies(X1,X2) = X2
| ~ is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_105]),c_0_106])]) ).
cnf(c_0_111,plain,
is_a_theorem(implies(necessarily(X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_108])]) ).
cnf(c_0_112,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_47,c_0_109]) ).
cnf(c_0_113,plain,
implies(implies(necessarily(X1),X1),X2) = X2,
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
fof(c_0_114,plain,
! [X205] :
( ~ op_possibly
| possibly(X205) = not(necessarily(not(X205))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_possibly])])]) ).
cnf(c_0_115,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_106]) ).
fof(c_0_116,negated_conjecture,
~ axiom_m6,
inference(assume_negation,[status(cth)],[s1_0_m6s3m9b_axiom_m6]) ).
fof(c_0_117,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])])])])]) ).
fof(c_0_118,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_119,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,necessarily(X2))) ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_120,plain,
( possibly(X1) = not(necessarily(not(X1)))
| ~ op_possibly ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_121,plain,
op_possibly,
inference(split_conjunct,[status(thm)],[km5_op_possibly]) ).
cnf(c_0_122,plain,
( X1 = X2
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_115]) ).
fof(c_0_123,plain,
! [X191] :
( ( ~ axiom_m6
| is_a_theorem(strict_implies(X191,possibly(X191))) )
& ( ~ is_a_theorem(strict_implies(esk88_0,possibly(esk88_0)))
| axiom_m6 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m6])])])]) ).
fof(c_0_124,negated_conjecture,
~ axiom_m6,
inference(fof_simplification,[status(thm)],[c_0_116]) ).
cnf(c_0_125,plain,
( is_a_theorem(necessarily(X1))
| ~ necessitation
| ~ is_a_theorem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_126,plain,
necessitation,
inference(split_conjunct,[status(thm)],[km5_necessitation]) ).
cnf(c_0_127,plain,
( strict_implies(X1,X2) = necessarily(implies(X1,X2))
| ~ op_strict_implies ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_128,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(c_0_129,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X1,necessarily(X2))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_76]),c_0_76]) ).
cnf(c_0_130,plain,
not(necessarily(not(X1))) = possibly(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_121])]) ).
cnf(c_0_131,plain,
( X1 = X2
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_122,c_0_115]) ).
cnf(c_0_132,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_59,c_0_106]) ).
cnf(c_0_133,plain,
( axiom_m6
| ~ is_a_theorem(strict_implies(esk88_0,possibly(esk88_0))) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_134,negated_conjecture,
~ axiom_m6,
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_135,plain,
( is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_126])]) ).
cnf(c_0_136,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_128])]) ).
cnf(c_0_137,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(necessarily(X2),X1)) ),
inference(spm,[status(thm)],[c_0_129,c_0_94]) ).
cnf(c_0_138,plain,
or(necessarily(not(X1)),X2) = implies(possibly(X1),X2),
inference(spm,[status(thm)],[c_0_76,c_0_130]) ).
cnf(c_0_139,plain,
( implies(X1,X1) = X2
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_140,plain,
~ is_a_theorem(strict_implies(esk88_0,possibly(esk88_0))),
inference(sr,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_141,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_142,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(possibly(X1),X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_99]) ).
cnf(c_0_143,plain,
implies(X1,X1) = implies(necessarily(X2),X2),
inference(spm,[status(thm)],[c_0_139,c_0_111]) ).
cnf(c_0_144,plain,
~ is_a_theorem(implies(esk88_0,possibly(esk88_0))),
inference(spm,[status(thm)],[c_0_140,c_0_141]) ).
cnf(c_0_145,plain,
is_a_theorem(implies(X1,possibly(X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_111])]) ).
cnf(c_0_146,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_144,c_0_145])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : LCL533+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.12 % Command : enigmatic-eprover.py %s %d 1
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 2 20:13:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.43 # ENIGMATIC: Selected SinE mode:
% 0.18/0.44 # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.18/0.44 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.18/0.44 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 9.25/2.59 # ENIGMATIC: Solved by autoschedule:
% 9.25/2.59 # No SInE strategy applied
% 9.25/2.59 # Trying AutoSched0 for 150 seconds
% 9.25/2.59 # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 9.25/2.59 # and selection function SelectComplexExceptUniqMaxHorn.
% 9.25/2.59 #
% 9.25/2.59 # Preprocessing time : 0.018 s
% 9.25/2.59 # Presaturation interreduction done
% 9.25/2.59
% 9.25/2.59 # Proof found!
% 9.25/2.59 # SZS status Theorem
% 9.25/2.59 # SZS output start CNFRefutation
% See solution above
% 9.25/2.59 # Training examples: 0 positive, 0 negative
% 9.25/2.59
% 9.25/2.59 # -------------------------------------------------
% 9.25/2.59 # User time : 0.348 s
% 9.25/2.59 # System time : 0.020 s
% 9.25/2.59 # Total time : 0.368 s
% 9.25/2.59 # Maximum resident set size: 7124 pages
% 9.25/2.59
%------------------------------------------------------------------------------