TSTP Solution File: LCL549+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : LCL549+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n008.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 10:11:49 EDT 2022
% Result : Theorem 0.29s 7.47s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 32
% Syntax : Number of formulae : 119 ( 60 unt; 0 def)
% Number of atoms : 227 ( 20 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 181 ( 73 ~; 71 |; 18 &)
% ( 13 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 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 : 136 ( 3 sgn 54 !; 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/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(implies_2,axiom,
( implies_2
<=> ! [X1,X2] : is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_2) ).
fof(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/benchmark/Axioms/LCL006+0.ax',implies_3) ).
fof(hilbert_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(hilbert_implies_2,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
fof(and_3,axiom,
( and_3
<=> ! [X1,X2] : is_a_theorem(implies(X1,implies(X2,and(X1,X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_3) ).
fof(modus_tollens,axiom,
( modus_tollens
<=> ! [X1,X2] : is_a_theorem(implies(implies(not(X2),not(X1)),implies(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
fof(hilbert_implies_3,axiom,
implies_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_3) ).
fof(hilbert_and_3,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
fof(hilbert_modus_tollens,axiom,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_tollens) ).
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(equivalence_3,axiom,
( equivalence_3
<=> ! [X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X1),equiv(X1,X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',equivalence_3) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
fof(implies_1,axiom,
( implies_1
<=> ! [X1,X2] : is_a_theorem(implies(X1,implies(X2,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_1) ).
fof(hilbert_equivalence_3,axiom,
equivalence_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_equivalence_3) ).
fof(hilbert_implies_1,axiom,
implies_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_1) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X1,X2] :
( is_a_theorem(equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
fof(s1_0_m10_axiom_m10,conjecture,
axiom_m10,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',s1_0_m10_axiom_m10) ).
fof(axiom_B,axiom,
( axiom_B
<=> ! [X1] : is_a_theorem(implies(X1,necessarily(possibly(X1)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_B) ).
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(substitution_of_equivalents_001,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',substitution_of_equivalents) ).
fof(axiom_m10,axiom,
( axiom_m10
<=> ! [X1] : is_a_theorem(strict_implies(possibly(X1),necessarily(possibly(X1)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m10) ).
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(km4b_axiom_B,axiom,
axiom_B,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+3.ax',km4b_axiom_B) ).
fof(km4b_op_possibly,axiom,
op_possibly,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+3.ax',km4b_op_possibly) ).
fof(axiom_4,axiom,
( axiom_4
<=> ! [X1] : is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_4) ).
fof(axiom_M,axiom,
( axiom_M
<=> ! [X1] : is_a_theorem(implies(necessarily(X1),X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_M) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',s1_0_op_strict_implies) ).
fof(necessitation,axiom,
( necessitation
<=> ! [X1] :
( is_a_theorem(X1)
=> is_a_theorem(necessarily(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',necessitation) ).
fof(km4b_axiom_4,axiom,
axiom_4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+3.ax',km4b_axiom_4) ).
fof(km4b_axiom_M,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+3.ax',km4b_axiom_M) ).
fof(km4b_necessitation,axiom,
necessitation,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+3.ax',km4b_necessitation) ).
fof(c_0_32,plain,
! [X3,X4] :
( ( ~ modus_ponens
| ~ is_a_theorem(X3)
| ~ is_a_theorem(implies(X3,X4))
| is_a_theorem(X4) )
& ( 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(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens])])])])])])]) ).
fof(c_0_33,plain,
! [X3,X4] :
( ( ~ implies_2
| is_a_theorem(implies(implies(X3,implies(X3,X4)),implies(X3,X4))) )
& ( ~ 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(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_2])])])])])]) ).
fof(c_0_34,plain,
! [X4,X5,X6] :
( ( ~ implies_3
| is_a_theorem(implies(implies(X4,X5),implies(implies(X5,X6),implies(X4,X6)))) )
& ( ~ 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(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_3])])])])])]) ).
cnf(c_0_35,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2)
| ~ modus_ponens ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[hilbert_modus_ponens]) ).
cnf(c_0_37,plain,
( is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))
| ~ implies_2 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,plain,
implies_2,
inference(split_conjunct,[status(thm)],[hilbert_implies_2]) ).
fof(c_0_39,plain,
! [X3,X4] :
( ( ~ and_3
| is_a_theorem(implies(X3,implies(X4,and(X3,X4)))) )
& ( ~ 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(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_3])])])])])]) ).
fof(c_0_40,plain,
! [X3,X4] :
( ( ~ modus_tollens
| is_a_theorem(implies(implies(not(X4),not(X3)),implies(X3,X4))) )
& ( ~ 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(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_tollens])])])])])]) ).
cnf(c_0_41,plain,
( is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))
| ~ implies_3 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
implies_3,
inference(split_conjunct,[status(thm)],[hilbert_implies_3]) ).
cnf(c_0_43,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_35,c_0_36])]) ).
cnf(c_0_44,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_45,plain,
( is_a_theorem(implies(X1,implies(X2,and(X1,X2))))
| ~ and_3 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,plain,
and_3,
inference(split_conjunct,[status(thm)],[hilbert_and_3]) ).
cnf(c_0_47,plain,
( is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))
| ~ modus_tollens ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_48,plain,
modus_tollens,
inference(split_conjunct,[status(thm)],[hilbert_modus_tollens]) ).
fof(c_0_49,plain,
! [X3,X4] :
( ~ op_implies_and
| implies(X3,X4) = not(and(X3,not(X4))) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])])]) ).
fof(c_0_50,plain,
! [X3,X4] :
( ( ~ equivalence_3
| is_a_theorem(implies(implies(X3,X4),implies(implies(X4,X3),equiv(X3,X4)))) )
& ( ~ is_a_theorem(implies(implies(esk31_0,esk32_0),implies(implies(esk32_0,esk31_0),equiv(esk31_0,esk32_0))))
| equivalence_3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_3])])])])])]) ).
cnf(c_0_51,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_41,c_0_42])]) ).
cnf(c_0_52,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_53,plain,
is_a_theorem(implies(X1,implies(X2,and(X1,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
cnf(c_0_54,plain,
is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
cnf(c_0_55,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
fof(c_0_57,plain,
! [X3,X4] :
( ( ~ implies_1
| is_a_theorem(implies(X3,implies(X4,X3))) )
& ( ~ is_a_theorem(implies(esk7_0,implies(esk8_0,esk7_0)))
| implies_1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_1])])])])])]) ).
cnf(c_0_58,plain,
( is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X1),equiv(X1,X2))))
| ~ equivalence_3 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_59,plain,
equivalence_3,
inference(split_conjunct,[status(thm)],[hilbert_equivalence_3]) ).
cnf(c_0_60,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_43,c_0_51]) ).
cnf(c_0_61,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_62,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(not(X2),not(X1))) ),
inference(spm,[status(thm)],[c_0_43,c_0_54]) ).
cnf(c_0_63,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_64,plain,
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ implies_1 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_65,plain,
implies_1,
inference(split_conjunct,[status(thm)],[hilbert_implies_1]) ).
fof(c_0_66,plain,
! [X3,X4] :
( ( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X3,X4))
| X3 = X4 )
& ( 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(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_of_equivalents])])])])])])]) ).
cnf(c_0_67,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X1),equiv(X1,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]) ).
cnf(c_0_68,plain,
is_a_theorem(implies(implies(and(X1,X1),X2),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_69,plain,
( is_a_theorem(implies(and(X1,not(X2)),X3))
| ~ is_a_theorem(implies(not(X3),implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_70,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]) ).
fof(c_0_71,negated_conjecture,
~ axiom_m10,
inference(assume_negation,[status(cth)],[s1_0_m10_axiom_m10]) ).
fof(c_0_72,plain,
! [X2] :
( ( ~ axiom_B
| is_a_theorem(implies(X2,necessarily(possibly(X2)))) )
& ( ~ is_a_theorem(implies(esk67_0,necessarily(possibly(esk67_0))))
| axiom_B ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_B])])])])])]) ).
fof(c_0_73,plain,
! [X2] :
( ~ op_possibly
| possibly(X2) = not(necessarily(not(X2))) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_possibly])])])])]) ).
cnf(c_0_74,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2))
| ~ substitution_of_equivalents ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_75,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[substitution_of_equivalents]) ).
cnf(c_0_76,plain,
( is_a_theorem(implies(implies(X1,X2),equiv(X2,X1)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_43,c_0_67]) ).
cnf(c_0_77,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(and(X1,X1),X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_68]) ).
cnf(c_0_78,plain,
is_a_theorem(implies(and(X1,not(not(X2))),X2)),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
fof(c_0_79,plain,
! [X2] :
( ( ~ axiom_m10
| is_a_theorem(strict_implies(possibly(X2),necessarily(possibly(X2)))) )
& ( ~ is_a_theorem(strict_implies(possibly(esk94_0),necessarily(possibly(esk94_0))))
| axiom_m10 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m10])])])])])]) ).
fof(c_0_80,negated_conjecture,
~ axiom_m10,
inference(fof_simplification,[status(thm)],[c_0_71]) ).
fof(c_0_81,plain,
! [X3,X4] :
( ~ op_strict_implies
| strict_implies(X3,X4) = necessarily(implies(X3,X4)) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_implies])])])])]) ).
cnf(c_0_82,plain,
( is_a_theorem(implies(X1,necessarily(possibly(X1))))
| ~ axiom_B ),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_83,plain,
axiom_B,
inference(split_conjunct,[status(thm)],[km4b_axiom_B]) ).
cnf(c_0_84,plain,
( possibly(X1) = not(necessarily(not(X1)))
| ~ op_possibly ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_85,plain,
op_possibly,
inference(split_conjunct,[status(thm)],[km4b_op_possibly]) ).
cnf(c_0_86,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]) ).
cnf(c_0_87,plain,
( is_a_theorem(equiv(X1,X2))
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_76]) ).
cnf(c_0_88,plain,
is_a_theorem(implies(not(not(X1)),X1)),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
fof(c_0_89,plain,
! [X2] :
( ( ~ axiom_4
| is_a_theorem(implies(necessarily(X2),necessarily(necessarily(X2)))) )
& ( ~ is_a_theorem(implies(necessarily(esk66_0),necessarily(necessarily(esk66_0))))
| axiom_4 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_4])])])])])]) ).
fof(c_0_90,plain,
! [X2] :
( ( ~ axiom_M
| is_a_theorem(implies(necessarily(X2),X2)) )
& ( ~ is_a_theorem(implies(necessarily(esk65_0),esk65_0))
| axiom_M ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_M])])])])])]) ).
cnf(c_0_91,plain,
( axiom_m10
| ~ is_a_theorem(strict_implies(possibly(esk94_0),necessarily(possibly(esk94_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_92,negated_conjecture,
~ axiom_m10,
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_93,plain,
( strict_implies(X1,X2) = necessarily(implies(X1,X2))
| ~ op_strict_implies ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_94,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
fof(c_0_95,plain,
! [X2] :
( ( ~ necessitation
| ~ is_a_theorem(X2)
| is_a_theorem(necessarily(X2)) )
& ( 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(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[necessitation])])])])])])]) ).
cnf(c_0_96,plain,
is_a_theorem(implies(X1,necessarily(possibly(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_83])]) ).
cnf(c_0_97,plain,
possibly(X1) = not(necessarily(not(X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85])]) ).
cnf(c_0_98,plain,
( X1 = X2
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_99,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_62,c_0_88]) ).
cnf(c_0_100,plain,
( is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1))))
| ~ axiom_4 ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_101,plain,
axiom_4,
inference(split_conjunct,[status(thm)],[km4b_axiom_4]) ).
cnf(c_0_102,plain,
( is_a_theorem(implies(necessarily(X1),X1))
| ~ axiom_M ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_103,plain,
axiom_M,
inference(split_conjunct,[status(thm)],[km4b_axiom_M]) ).
cnf(c_0_104,plain,
~ is_a_theorem(strict_implies(possibly(esk94_0),necessarily(possibly(esk94_0)))),
inference(sr,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_105,plain,
strict_implies(X1,X2) = necessarily(implies(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94])]) ).
cnf(c_0_106,plain,
( is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X1)
| ~ necessitation ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_107,plain,
necessitation,
inference(split_conjunct,[status(thm)],[km4b_necessitation]) ).
cnf(c_0_108,plain,
is_a_theorem(implies(X1,necessarily(not(necessarily(not(X1)))))),
inference(rw,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_109,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_88]),c_0_99])]) ).
cnf(c_0_110,plain,
is_a_theorem(implies(necessarily(X1),necessarily(necessarily(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_101])]) ).
cnf(c_0_111,plain,
is_a_theorem(implies(necessarily(X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_103])]) ).
cnf(c_0_112,plain,
~ is_a_theorem(necessarily(implies(not(necessarily(not(esk94_0))),necessarily(not(necessarily(not(esk94_0))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_105]),c_0_97]),c_0_97]) ).
cnf(c_0_113,plain,
( is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_107])]) ).
cnf(c_0_114,plain,
is_a_theorem(implies(not(X1),necessarily(not(necessarily(X1))))),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_115,plain,
necessarily(necessarily(X1)) = necessarily(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_110]),c_0_111])]) ).
cnf(c_0_116,plain,
~ is_a_theorem(implies(not(necessarily(not(esk94_0))),necessarily(not(necessarily(not(esk94_0)))))),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_117,plain,
is_a_theorem(implies(not(necessarily(X1)),necessarily(not(necessarily(X1))))),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_118,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_117])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL549+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.13 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 17:35:08 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.29/7.47 # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.29/7.47 # Preprocessing time : 0.023 s
% 0.29/7.47
% 0.29/7.47 # Proof found!
% 0.29/7.47 # SZS status Theorem
% 0.29/7.47 # SZS output start CNFRefutation
% See solution above
% 0.29/7.47 # Proof object total steps : 119
% 0.29/7.47 # Proof object clause steps : 69
% 0.29/7.47 # Proof object formula steps : 50
% 0.29/7.47 # Proof object conjectures : 4
% 0.29/7.47 # Proof object clause conjectures : 1
% 0.29/7.47 # Proof object formula conjectures : 3
% 0.29/7.47 # Proof object initial clauses used : 32
% 0.29/7.47 # Proof object initial formulas used : 32
% 0.29/7.47 # Proof object generating inferences : 18
% 0.29/7.47 # Proof object simplifying inferences : 41
% 0.29/7.47 # Training examples: 0 positive, 0 negative
% 0.29/7.47 # Parsed axioms : 89
% 0.29/7.47 # Removed by relevancy pruning/SinE : 0
% 0.29/7.47 # Initial clauses : 147
% 0.29/7.47 # Removed in clause preprocessing : 0
% 0.29/7.47 # Initial clauses in saturation : 147
% 0.29/7.47 # Processed clauses : 3877
% 0.29/7.47 # ...of these trivial : 143
% 0.29/7.47 # ...subsumed : 1887
% 0.29/7.47 # ...remaining for further processing : 1847
% 0.29/7.47 # Other redundant clauses eliminated : 0
% 0.29/7.47 # Clauses deleted for lack of memory : 253030
% 0.29/7.47 # Backward-subsumed : 42
% 0.29/7.47 # Backward-rewritten : 1510
% 0.29/7.47 # Generated clauses : 387640
% 0.29/7.47 # ...of the previous two non-trivial : 382715
% 0.29/7.47 # Contextual simplify-reflections : 620
% 0.29/7.47 # Paramodulations : 387619
% 0.29/7.47 # Factorizations : 0
% 0.29/7.47 # Equation resolutions : 0
% 0.29/7.47 # Current number of processed clauses : 288
% 0.29/7.47 # Positive orientable unit clauses : 87
% 0.29/7.47 # Positive unorientable unit clauses: 0
% 0.29/7.47 # Negative unit clauses : 24
% 0.29/7.47 # Non-unit-clauses : 177
% 0.29/7.47 # Current number of unprocessed clauses: 2184
% 0.29/7.47 # ...number of literals in the above : 4901
% 0.29/7.47 # Current number of archived formulas : 0
% 0.29/7.47 # Current number of archived clauses : 1552
% 0.29/7.47 # Clause-clause subsumption calls (NU) : 129099
% 0.29/7.47 # Rec. Clause-clause subsumption calls : 113616
% 0.29/7.47 # Non-unit clause-clause subsumptions : 2376
% 0.29/7.47 # Unit Clause-clause subsumption calls : 13586
% 0.29/7.47 # Rewrite failures with RHS unbound : 0
% 0.29/7.47 # BW rewrite match attempts : 11930
% 0.29/7.47 # BW rewrite match successes : 604
% 0.29/7.47 # Condensation attempts : 0
% 0.29/7.47 # Condensation successes : 0
% 0.29/7.47 # Termbank termtop insertions : 10558179
% 0.29/7.47
% 0.29/7.47 # -------------------------------------------------
% 0.29/7.47 # User time : 6.275 s
% 0.29/7.47 # System time : 0.113 s
% 0.29/7.47 # Total time : 6.388 s
% 0.29/7.47 # Maximum resident set size: 137768 pages
% 0.29/23.44 eprover: CPU time limit exceeded, terminating
% 0.29/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.29/23.45 eprover: No such file or directory
% 0.29/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.29/23.46 eprover: No such file or directory
% 0.29/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.29/23.47 eprover: No such file or directory
% 0.29/23.47 eprover: CPU time limit exceeded, terminating
% 0.29/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.29/23.47 eprover: No such file or directory
% 0.29/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.29/23.48 eprover: No such file or directory
% 0.29/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.29/23.48 eprover: No such file or directory
% 0.29/23.49 eprover: CPU time limit exceeded, terminating
% 0.29/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.49 eprover: No such file or directory
% 0.29/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.29/23.49 eprover: No such file or directory
% 0.29/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.49 eprover: No such file or directory
% 0.29/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.29/23.50 eprover: No such file or directory
% 0.29/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.50 eprover: No such file or directory
% 0.29/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.50 eprover: No such file or directory
% 0.29/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.29/23.50 eprover: No such file or directory
% 0.29/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.50 eprover: No such file or directory
% 0.29/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.51 eprover: No such file or directory
% 0.29/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.29/23.51 eprover: No such file or directory
% 0.29/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.51 eprover: No such file or directory
% 0.29/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.51 eprover: No such file or directory
% 0.29/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.51 eprover: No such file or directory
% 0.29/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.51 eprover: No such file or directory
% 0.29/23.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.52 eprover: No such file or directory
% 0.29/23.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.52 eprover: No such file or directory
% 0.29/23.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.52 eprover: No such file or directory
% 0.29/23.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.52 eprover: No such file or directory
% 0.29/23.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.52 eprover: No such file or directory
% 0.29/23.53 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.53 eprover: No such file or directory
% 0.29/23.53 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.53 eprover: No such file or directory
% 0.29/23.53 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.53 eprover: No such file or directory
% 0.29/23.53 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.29/23.53 eprover: No such file or directory
%------------------------------------------------------------------------------