TSTP Solution File: LCL524+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : LCL524+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n021.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 10:11:41 EDT 2022
% Result : Theorem 0.73s 65.91s
% Output : CNFRefutation 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 31
% Syntax : Number of formulae : 126 ( 59 unt; 0 def)
% Number of atoms : 237 ( 28 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 192 ( 81 ~; 77 |; 16 &)
% ( 12 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 19 ( 17 usr; 17 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 21 con; 0-2 aty)
% Number of variables : 152 ( 6 sgn 56 !; 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_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(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(hilbert_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(hilbert_implies_3,axiom,
implies_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_3) ).
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(hilbert_and_3,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
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(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/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
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(op_equiv,axiom,
( op_equiv
=> ! [X1,X2] : equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(km5_axiom_M,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_axiom_M) ).
fof(cn3,axiom,
( cn3
<=> ! [X4] : is_a_theorem(implies(implies(not(X4),X4),X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',cn3) ).
fof(hilbert_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_or) ).
fof(km5_op_possibly,axiom,
op_possibly,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_op_possibly) ).
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(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(hilbert_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_equiv) ).
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_2,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
fof(km4b_axiom_B,conjecture,
axiom_B,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',km4b_axiom_B) ).
fof(substitution_of_equivalents_001,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',substitution_of_equivalents) ).
fof(axiom_5,axiom,
( axiom_5
<=> ! [X1] : is_a_theorem(implies(possibly(X1),necessarily(possibly(X1)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_5) ).
fof(and_1,axiom,
( and_1
<=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_1) ).
fof(hilbert_modus_tollens,axiom,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_tollens) ).
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(km5_axiom_5,axiom,
axiom_5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_axiom_5) ).
fof(hilbert_and_1,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_1) ).
fof(or_1,axiom,
( or_1
<=> ! [X1,X2] : is_a_theorem(implies(X1,or(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_1) ).
fof(hilbert_or_1,axiom,
or_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_or_1) ).
fof(c_0_31,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_32,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])])])])])]) ).
fof(c_0_33,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])])])])])]) ).
cnf(c_0_34,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2)
| ~ modus_ponens ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[hilbert_modus_ponens]) ).
cnf(c_0_36,plain,
( is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))
| ~ implies_3 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
implies_3,
inference(split_conjunct,[status(thm)],[hilbert_implies_3]) ).
fof(c_0_38,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])])])])]) ).
cnf(c_0_39,plain,
( is_a_theorem(implies(X1,implies(X2,and(X1,X2))))
| ~ and_3 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,plain,
and_3,
inference(split_conjunct,[status(thm)],[hilbert_and_3]) ).
cnf(c_0_41,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_34,c_0_35])]) ).
cnf(c_0_42,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_36,c_0_37])]) ).
fof(c_0_43,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])])])])])]) ).
fof(c_0_44,plain,
! [X3,X4] :
( ~ op_or
| or(X3,X4) = not(and(not(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_or])])])])]) ).
cnf(c_0_45,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
fof(c_0_47,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_48,plain,
is_a_theorem(implies(X1,implies(X2,and(X1,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]) ).
fof(c_0_49,plain,
! [X3,X4] :
( ~ op_equiv
| equiv(X3,X4) = and(implies(X3,X4),implies(X4,X3)) ),
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_equiv])])])])]) ).
cnf(c_0_50,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_51,plain,
( is_a_theorem(implies(necessarily(X1),X1))
| ~ axiom_M ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,plain,
axiom_M,
inference(split_conjunct,[status(thm)],[km5_axiom_M]) ).
fof(c_0_53,plain,
! [X5] :
( ( ~ cn3
| is_a_theorem(implies(implies(not(X5),X5),X5)) )
& ( ~ is_a_theorem(implies(implies(not(esk44_0),esk44_0),esk44_0))
| cn3 ) ),
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)],[cn3])])])])])]) ).
cnf(c_0_54,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_55,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
cnf(c_0_56,plain,
op_or,
inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).
cnf(c_0_57,plain,
( possibly(X1) = not(necessarily(not(X1)))
| ~ op_possibly ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_58,plain,
op_possibly,
inference(split_conjunct,[status(thm)],[km5_op_possibly]) ).
fof(c_0_59,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_60,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_61,plain,
( is_a_theorem(implies(X1,and(X2,X1)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_48]) ).
cnf(c_0_62,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_63,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[hilbert_op_equiv]) ).
fof(c_0_64,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_65,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X1,X3)) ),
inference(spm,[status(thm)],[c_0_41,c_0_50]) ).
cnf(c_0_66,plain,
is_a_theorem(implies(necessarily(X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
cnf(c_0_67,plain,
( is_a_theorem(implies(implies(not(X1),X1),X1))
| ~ cn3 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_68,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55]),c_0_56])]) ).
cnf(c_0_69,plain,
not(necessarily(not(X1))) = possibly(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).
cnf(c_0_70,plain,
( is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))
| ~ implies_2 ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_71,plain,
implies_2,
inference(split_conjunct,[status(thm)],[hilbert_implies_2]) ).
fof(c_0_72,negated_conjecture,
~ axiom_B,
inference(assume_negation,[status(cth)],[km4b_axiom_B]) ).
cnf(c_0_73,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2))
| ~ substitution_of_equivalents ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_74,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[substitution_of_equivalents]) ).
cnf(c_0_75,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_61]) ).
cnf(c_0_76,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]) ).
fof(c_0_77,plain,
! [X2] :
( ( ~ axiom_5
| is_a_theorem(implies(possibly(X2),necessarily(possibly(X2)))) )
& ( ~ is_a_theorem(implies(possibly(esk68_0),necessarily(possibly(esk68_0))))
| axiom_5 ) ),
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_5])])])])])]) ).
fof(c_0_78,plain,
! [X3,X4] :
( ( ~ and_1
| is_a_theorem(implies(and(X3,X4),X3)) )
& ( ~ is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0))
| and_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)],[and_1])])])])])]) ).
cnf(c_0_79,plain,
( is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))
| ~ modus_tollens ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_80,plain,
modus_tollens,
inference(split_conjunct,[status(thm)],[hilbert_modus_tollens]) ).
cnf(c_0_81,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,necessarily(X2))) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_82,plain,
( is_a_theorem(implies(or(X1,X1),X1))
| ~ cn3 ),
inference(rw,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_83,plain,
not(and(X1,possibly(X2))) = implies(X1,necessarily(not(X2))),
inference(spm,[status(thm)],[c_0_55,c_0_69]) ).
cnf(c_0_84,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71])]) ).
fof(c_0_85,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_86,negated_conjecture,
~ axiom_B,
inference(fof_simplification,[status(thm)],[c_0_72]) ).
cnf(c_0_87,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74])]) ).
cnf(c_0_88,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_75,c_0_76]) ).
cnf(c_0_89,plain,
( is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))
| ~ axiom_5 ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_90,plain,
axiom_5,
inference(split_conjunct,[status(thm)],[km5_axiom_5]) ).
cnf(c_0_91,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ and_1 ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_92,plain,
and_1,
inference(split_conjunct,[status(thm)],[hilbert_and_1]) ).
cnf(c_0_93,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_79,c_0_68]),c_0_80])]) ).
cnf(c_0_94,plain,
( is_a_theorem(implies(or(necessarily(X1),necessarily(X1)),X1))
| ~ cn3 ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_95,plain,
or(necessarily(not(X1)),X2) = implies(possibly(X1),X2),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_96,plain,
implies(implies(X1,necessarily(not(X2))),X3) = or(and(X1,possibly(X2)),X3),
inference(spm,[status(thm)],[c_0_68,c_0_83]) ).
fof(c_0_97,plain,
! [X3,X4] :
( ( ~ or_1
| is_a_theorem(implies(X3,or(X3,X4))) )
& ( ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0)))
| or_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)],[or_1])])])])])]) ).
cnf(c_0_98,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_41,c_0_84]) ).
cnf(c_0_99,plain,
( axiom_B
| ~ is_a_theorem(implies(esk67_0,necessarily(possibly(esk67_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_100,negated_conjecture,
~ axiom_B,
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_101,plain,
( X1 = X2
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_102,plain,
is_a_theorem(implies(possibly(X1),necessarily(possibly(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_90])]) ).
cnf(c_0_103,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92])]) ).
cnf(c_0_104,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_41,c_0_93]) ).
cnf(c_0_105,plain,
( is_a_theorem(or(and(possibly(X1),possibly(X1)),not(X1)))
| ~ cn3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96]) ).
cnf(c_0_106,plain,
( is_a_theorem(implies(X1,or(X1,X2)))
| ~ or_1 ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_107,plain,
or_1,
inference(split_conjunct,[status(thm)],[hilbert_or_1]) ).
cnf(c_0_108,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(spm,[status(thm)],[c_0_98,c_0_48]) ).
cnf(c_0_109,plain,
~ is_a_theorem(implies(esk67_0,necessarily(possibly(esk67_0)))),
inference(sr,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_110,plain,
necessarily(possibly(X1)) = possibly(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_66])]) ).
cnf(c_0_111,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,and(X2,X3))) ),
inference(spm,[status(thm)],[c_0_65,c_0_103]) ).
cnf(c_0_112,plain,
( is_a_theorem(implies(X1,and(possibly(X1),possibly(X1))))
| ~ cn3 ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_113,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_107])]) ).
cnf(c_0_114,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_108]),c_0_103])]) ).
cnf(c_0_115,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(esk44_0),esk44_0),esk44_0)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_116,plain,
~ is_a_theorem(implies(esk67_0,possibly(esk67_0))),
inference(rw,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_117,plain,
( is_a_theorem(implies(X1,possibly(X1)))
| ~ cn3 ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_118,plain,
is_a_theorem(or(X1,or(not(X1),X2))),
inference(spm,[status(thm)],[c_0_113,c_0_68]) ).
cnf(c_0_119,plain,
or(X1,X1) = not(not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_114]),c_0_68]) ).
cnf(c_0_120,plain,
( cn3
| ~ is_a_theorem(implies(or(esk44_0,esk44_0),esk44_0)) ),
inference(rw,[status(thm)],[c_0_115,c_0_68]) ).
cnf(c_0_121,plain,
~ cn3,
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_122,plain,
is_a_theorem(or(X1,not(not(not(X1))))),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_123,plain,
~ is_a_theorem(or(not(esk44_0),esk44_0)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_119]),c_0_68]),c_0_121]) ).
cnf(c_0_124,plain,
is_a_theorem(or(not(X1),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_122]),c_0_68]) ).
cnf(c_0_125,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_124])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL524+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : run_ET %s %d
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jul 3 03:43:15 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.42/23.43 eprover: CPU time limit exceeded, terminating
% 0.42/23.43 eprover: CPU time limit exceeded, terminating
% 0.42/23.44 eprover: CPU time limit exceeded, terminating
% 0.42/23.49 eprover: CPU time limit exceeded, terminating
% 0.58/46.46 eprover: CPU time limit exceeded, terminating
% 0.58/46.46 eprover: CPU time limit exceeded, terminating
% 0.58/46.47 eprover: CPU time limit exceeded, terminating
% 0.58/46.52 eprover: CPU time limit exceeded, terminating
% 0.73/65.91 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.73/65.91
% 0.73/65.91 # Failure: Resource limit exceeded (time)
% 0.73/65.91 # OLD status Res
% 0.73/65.91 # Preprocessing time : 0.013 s
% 0.73/65.91 # Running protocol protocol_eprover_f6eb5f7f05126ea361481ae651a4823314e3d740 for 23 seconds:
% 0.73/65.91 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,02,20000,1.0)
% 0.73/65.91 # Preprocessing time : 0.016 s
% 0.73/65.91
% 0.73/65.91 # Failure: Out of unprocessed clauses!
% 0.73/65.91 # OLD status GaveUp
% 0.73/65.91 # Parsed axioms : 82
% 0.73/65.91 # Removed by relevancy pruning/SinE : 80
% 0.73/65.91 # Initial clauses : 3
% 0.73/65.91 # Removed in clause preprocessing : 0
% 0.73/65.91 # Initial clauses in saturation : 3
% 0.73/65.91 # Processed clauses : 3
% 0.73/65.91 # ...of these trivial : 0
% 0.73/65.91 # ...subsumed : 1
% 0.73/65.91 # ...remaining for further processing : 2
% 0.73/65.91 # Other redundant clauses eliminated : 0
% 0.73/65.91 # Clauses deleted for lack of memory : 0
% 0.73/65.91 # Backward-subsumed : 0
% 0.73/65.91 # Backward-rewritten : 0
% 0.73/65.91 # Generated clauses : 0
% 0.73/65.91 # ...of the previous two non-trivial : 0
% 0.73/65.91 # Contextual simplify-reflections : 0
% 0.73/65.91 # Paramodulations : 0
% 0.73/65.91 # Factorizations : 0
% 0.73/65.91 # Equation resolutions : 0
% 0.73/65.91 # Current number of processed clauses : 2
% 0.73/65.91 # Positive orientable unit clauses : 0
% 0.73/65.91 # Positive unorientable unit clauses: 0
% 0.73/65.91 # Negative unit clauses : 2
% 0.73/65.91 # Non-unit-clauses : 0
% 0.73/65.91 # Current number of unprocessed clauses: 0
% 0.73/65.91 # ...number of literals in the above : 0
% 0.73/65.91 # Current number of archived formulas : 0
% 0.73/65.91 # Current number of archived clauses : 0
% 0.73/65.91 # Clause-clause subsumption calls (NU) : 0
% 0.73/65.91 # Rec. Clause-clause subsumption calls : 0
% 0.73/65.91 # Non-unit clause-clause subsumptions : 0
% 0.73/65.91 # Unit Clause-clause subsumption calls : 0
% 0.73/65.91 # Rewrite failures with RHS unbound : 0
% 0.73/65.91 # BW rewrite match attempts : 0
% 0.73/65.91 # BW rewrite match successes : 0
% 0.73/65.91 # Condensation attempts : 0
% 0.73/65.91 # Condensation successes : 0
% 0.73/65.91 # Termbank termtop insertions : 784
% 0.73/65.91
% 0.73/65.91 # -------------------------------------------------
% 0.73/65.91 # User time : 0.013 s
% 0.73/65.91 # System time : 0.003 s
% 0.73/65.91 # Total time : 0.016 s
% 0.73/65.91 # Maximum resident set size: 2896 pages
% 0.73/65.91 # Running protocol protocol_eprover_a172c605141d0894bf6fdc293a5220c6c2a32117 for 23 seconds:
% 0.73/65.91
% 0.73/65.91 # Failure: Resource limit exceeded (time)
% 0.73/65.91 # OLD status Res
% 0.73/65.91 # Preprocessing time : 0.023 s
% 0.73/65.91 # Running protocol protocol_eprover_f8b0f932169414d689b89e2a8b18d4600533b975 for 23 seconds:
% 0.73/65.91 # Preprocessing time : 0.012 s
% 0.73/65.91
% 0.73/65.91 # Proof found!
% 0.73/65.91 # SZS status Theorem
% 0.73/65.91 # SZS output start CNFRefutation
% See solution above
% 0.73/65.91 # Proof object total steps : 126
% 0.73/65.91 # Proof object clause steps : 77
% 0.73/65.91 # Proof object formula steps : 49
% 0.73/65.91 # Proof object conjectures : 4
% 0.73/65.91 # Proof object clause conjectures : 1
% 0.73/65.91 # Proof object formula conjectures : 3
% 0.73/65.91 # Proof object initial clauses used : 32
% 0.73/65.91 # Proof object initial formulas used : 31
% 0.73/65.91 # Proof object generating inferences : 25
% 0.73/65.91 # Proof object simplifying inferences : 46
% 0.73/65.91 # Training examples: 0 positive, 0 negative
% 0.73/65.91 # Parsed axioms : 82
% 0.73/65.91 # Removed by relevancy pruning/SinE : 0
% 0.73/65.91 # Initial clauses : 140
% 0.73/65.91 # Removed in clause preprocessing : 0
% 0.73/65.91 # Initial clauses in saturation : 140
% 0.73/65.91 # Processed clauses : 21222
% 0.73/65.91 # ...of these trivial : 115
% 0.73/65.91 # ...subsumed : 15927
% 0.73/65.91 # ...remaining for further processing : 5180
% 0.73/65.91 # Other redundant clauses eliminated : 0
% 0.73/65.91 # Clauses deleted for lack of memory : 1066037
% 0.73/65.91 # Backward-subsumed : 990
% 0.73/65.91 # Backward-rewritten : 744
% 0.73/65.91 # Generated clauses : 1264382
% 0.73/65.91 # ...of the previous two non-trivial : 1254094
% 0.73/65.91 # Contextual simplify-reflections : 19117
% 0.73/65.91 # Paramodulations : 1264382
% 0.73/65.91 # Factorizations : 0
% 0.73/65.91 # Equation resolutions : 0
% 0.73/65.91 # Current number of processed clauses : 3446
% 0.73/65.91 # Positive orientable unit clauses : 242
% 0.73/65.91 # Positive unorientable unit clauses: 0
% 0.73/65.91 # Negative unit clauses : 27
% 0.73/65.91 # Non-unit-clauses : 3177
% 0.73/65.91 # Current number of unprocessed clauses: 86414
% 0.73/65.91 # ...number of literals in the above : 294984
% 0.73/65.91 # Current number of archived formulas : 0
% 0.73/65.91 # Current number of archived clauses : 1734
% 0.73/65.91 # Clause-clause subsumption calls (NU) : 2257546
% 0.73/65.91 # Rec. Clause-clause subsumption calls : 1244477
% 0.73/65.91 # Non-unit clause-clause subsumptions : 35827
% 0.73/65.91 # Unit Clause-clause subsumption calls : 36169
% 0.73/65.91 # Rewrite failures with RHS unbound : 0
% 0.73/65.91 # BW rewrite match attempts : 8912
% 0.73/65.91 # BW rewrite match successes : 180
% 0.73/65.91 # Condensation attempts : 0
% 0.73/65.91 # Condensation successes : 0
% 0.73/65.91 # Termbank termtop insertions : 23694006
% 0.73/65.91
% 0.73/65.91 # -------------------------------------------------
% 0.73/65.91 # User time : 18.292 s
% 0.73/65.91 # System time : 0.147 s
% 0.73/65.91 # Total time : 18.439 s
% 0.73/65.91 # Maximum resident set size: 143116 pages
% 0.73/69.48 eprover: CPU time limit exceeded, terminating
% 0.73/69.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.50 eprover: No such file or directory
% 0.73/69.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.51 eprover: No such file or directory
% 0.73/69.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.51 eprover: No such file or directory
% 0.73/69.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.52 eprover: No such file or directory
% 0.73/69.53 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.53 eprover: No such file or directory
% 0.73/69.53 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.53 eprover: No such file or directory
% 0.73/69.54 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.54 eprover: No such file or directory
% 0.73/69.54 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.54 eprover: No such file or directory
% 0.73/69.56 eprover: CPU time limit exceeded, terminating
% 0.73/69.58 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.58 eprover: No such file or directory
% 0.73/69.59 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.59 eprover: No such file or directory
% 0.73/69.59 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.59 eprover: No such file or directory
% 0.73/69.59 eprover: CPU time limit exceeded, terminating
% 0.73/69.60 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.73/69.60 eprover: No such file or directory
% 0.73/69.61 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.73/69.61 eprover: No such file or directory
% 0.73/69.61 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.73/69.61 eprover: No such file or directory
% 0.73/69.62 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.73/69.62 eprover: No such file or directory
%------------------------------------------------------------------------------