TSTP Solution File: LCL528+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : LCL528+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n029.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 10:11:42 EDT 2022
% Result : Theorem 0.41s 25.60s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 31
% Syntax : Number of formulae : 133 ( 58 unt; 0 def)
% Number of atoms : 272 ( 32 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 234 ( 95 ~; 97 |; 21 &)
% ( 13 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 18 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 25 con; 0-2 aty)
% Number of variables : 165 ( 6 sgn 66 !; 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(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(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(adjunction,axiom,
( adjunction
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(X2) )
=> is_a_theorem(and(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',adjunction) ).
fof(hilbert_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_equiv) ).
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,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(hilbert_implies_2,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
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(substitution_of_equivalents_001,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',substitution_of_equivalents) ).
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_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(hilbert_and_1,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_1) ).
fof(r3,axiom,
( r3
<=> ! [X4,X5] : is_a_theorem(implies(or(X4,X5),or(X5,X4))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r3) ).
fof(hilbert_op_or,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_op_or) ).
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(or_3,axiom,
( or_3
<=> ! [X1,X2,X3] : is_a_theorem(implies(implies(X1,X3),implies(implies(X2,X3),implies(or(X1,X2),X3)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',or_3) ).
fof(hilbert_implies_1,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_1) ).
fof(hilbert_or_3,axiom,
or_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_or_3) ).
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(cn3,axiom,
( cn3
<=> ! [X4] : is_a_theorem(implies(implies(not(X4),X4),X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',cn3) ).
fof(hilbert_or_1,axiom,
or_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_or_1) ).
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(s1_0_axiom_m1,conjecture,
axiom_m1,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',s1_0_axiom_m1) ).
fof(axiom_m1,axiom,
( axiom_m1
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m1) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL007+0.ax',necessitation) ).
fof(km5_necessitation,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+2.ax',km5_necessitation) ).
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,
! [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_33,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_34,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[hilbert_modus_ponens]) ).
cnf(c_0_35,plain,
( is_a_theorem(implies(X1,implies(X2,and(X1,X2))))
| ~ and_3 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
and_3,
inference(split_conjunct,[status(thm)],[hilbert_and_3]) ).
fof(c_0_37,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_38,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_33,c_0_34])]) ).
cnf(c_0_39,plain,
is_a_theorem(implies(X1,implies(X2,and(X1,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
fof(c_0_40,plain,
! [X3,X4] :
( ( ~ adjunction
| ~ is_a_theorem(X3)
| ~ is_a_theorem(X4)
| is_a_theorem(and(X3,X4)) )
& ( is_a_theorem(esk59_0)
| adjunction )
& ( is_a_theorem(esk60_0)
| adjunction )
& ( ~ is_a_theorem(and(esk59_0,esk60_0))
| adjunction ) ),
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)],[adjunction])])])])])])]) ).
cnf(c_0_41,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[hilbert_op_equiv]) ).
cnf(c_0_43,plain,
( is_a_theorem(implies(X1,and(X2,X1)))
| ~ is_a_theorem(X2) ),
inference(pm,[status(thm)],[c_0_38,c_0_39]) ).
fof(c_0_44,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_45,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_46,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ adjunction ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
cnf(c_0_48,plain,
( adjunction
| ~ is_a_theorem(and(esk59_0,esk60_0)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(pm,[status(thm)],[c_0_38,c_0_43]) ).
cnf(c_0_50,plain,
( adjunction
| is_a_theorem(esk59_0) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_51,plain,
( adjunction
| is_a_theorem(esk60_0) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_52,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_53,plain,
implies_2,
inference(split_conjunct,[status(thm)],[hilbert_implies_2]) ).
fof(c_0_54,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_55,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2))
| ~ substitution_of_equivalents ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_56,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[substitution_of_equivalents]) ).
cnf(c_0_57,plain,
( is_a_theorem(equiv(X1,X2))
| ~ adjunction
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(pm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_58,plain,
adjunction,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(pm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_51]) ).
cnf(c_0_59,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53])]) ).
fof(c_0_60,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])])])])])]) ).
fof(c_0_61,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_62,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_63,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
cnf(c_0_64,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]) ).
cnf(c_0_65,plain,
( is_a_theorem(equiv(X1,X2))
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).
cnf(c_0_66,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(X1,X2))) ),
inference(pm,[status(thm)],[c_0_38,c_0_59]) ).
cnf(c_0_67,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ and_1 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_68,plain,
and_1,
inference(split_conjunct,[status(thm)],[hilbert_and_1]) ).
fof(c_0_69,plain,
! [X6,X7] :
( ( ~ r3
| is_a_theorem(implies(or(X6,X7),or(X7,X6))) )
& ( ~ is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0)))
| r3 ) ),
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)],[r3])])])])])]) ).
cnf(c_0_70,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_71,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]) ).
cnf(c_0_72,plain,
op_or,
inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).
fof(c_0_73,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])])])])])]) ).
fof(c_0_74,plain,
! [X4,X5,X6] :
( ( ~ or_3
| is_a_theorem(implies(implies(X4,X6),implies(implies(X5,X6),implies(or(X4,X5),X6)))) )
& ( ~ is_a_theorem(implies(implies(esk24_0,esk26_0),implies(implies(esk25_0,esk26_0),implies(or(esk24_0,esk25_0),esk26_0))))
| or_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)],[or_3])])])])])]) ).
cnf(c_0_75,plain,
( X1 = X2
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(pm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_76,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(pm,[status(thm)],[c_0_66,c_0_39]) ).
cnf(c_0_77,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]) ).
cnf(c_0_78,plain,
( is_a_theorem(implies(or(X1,X2),or(X2,X1)))
| ~ r3 ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_79,plain,
or(X1,X2) = implies(not(X1),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71]),c_0_72])]) ).
cnf(c_0_80,plain,
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ implies_1 ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_81,plain,
implies_1,
inference(split_conjunct,[status(thm)],[hilbert_implies_1]) ).
cnf(c_0_82,plain,
( is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(or(X1,X3),X2))))
| ~ or_3 ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_83,plain,
or_3,
inference(split_conjunct,[status(thm)],[hilbert_or_3]) ).
fof(c_0_84,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])])])])])]) ).
fof(c_0_85,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_86,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(pm,[status(thm)],[c_0_75,c_0_76]),c_0_77])]) ).
cnf(c_0_87,plain,
( is_a_theorem(implies(implies(not(X1),X2),implies(not(X2),X1)))
| ~ r3 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79]),c_0_79]) ).
cnf(c_0_88,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81])]) ).
cnf(c_0_89,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),implies(implies(not(X1),X3),X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_79]),c_0_83])]) ).
cnf(c_0_90,plain,
( is_a_theorem(implies(X1,or(X1,X2)))
| ~ or_1 ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_91,plain,
or_1,
inference(split_conjunct,[status(thm)],[hilbert_or_1]) ).
cnf(c_0_92,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(esk44_0),esk44_0),esk44_0)) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_93,plain,
implies(not(X1),X1) = not(not(X1)),
inference(pm,[status(thm)],[c_0_71,c_0_86]) ).
cnf(c_0_94,plain,
( is_a_theorem(implies(not(X1),X2))
| ~ r3
| ~ is_a_theorem(implies(not(X2),X1)) ),
inference(pm,[status(thm)],[c_0_38,c_0_87]) ).
cnf(c_0_95,plain,
is_a_theorem(implies(X1,X1)),
inference(pm,[status(thm)],[c_0_66,c_0_88]) ).
cnf(c_0_96,plain,
( r3
| ~ is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0))) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_97,plain,
( is_a_theorem(implies(implies(X1,X2),implies(implies(not(X3),X1),X2)))
| ~ is_a_theorem(implies(X3,X2)) ),
inference(pm,[status(thm)],[c_0_38,c_0_89]) ).
cnf(c_0_98,plain,
( is_a_theorem(implies(implies(not(X1),X1),X1))
| ~ cn3 ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_99,plain,
is_a_theorem(implies(X1,implies(not(X1),X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_79]),c_0_91])]) ).
cnf(c_0_100,plain,
( cn3
| ~ is_a_theorem(implies(not(not(esk44_0)),esk44_0)) ),
inference(rw,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_101,plain,
( is_a_theorem(implies(not(not(X1)),X1))
| ~ r3 ),
inference(pm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_102,plain,
( r3
| ~ is_a_theorem(implies(implies(not(esk48_0),esk49_0),implies(not(esk49_0),esk48_0))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_79]),c_0_79]) ).
cnf(c_0_103,plain,
( is_a_theorem(implies(implies(not(X1),X2),X3))
| ~ is_a_theorem(implies(X2,X3))
| ~ is_a_theorem(implies(X1,X3)) ),
inference(pm,[status(thm)],[c_0_38,c_0_97]) ).
fof(c_0_104,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])])])])]) ).
fof(c_0_105,negated_conjecture,
~ axiom_m1,
inference(assume_negation,[status(cth)],[s1_0_axiom_m1]) ).
cnf(c_0_106,plain,
( implies(not(X1),X1) = X1
| ~ cn3 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(pm,[status(thm)],[c_0_75,c_0_98]),c_0_99])]) ).
cnf(c_0_107,plain,
( cn3
| ~ r3 ),
inference(pm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_108,plain,
r3,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(pm,[status(thm)],[c_0_102,c_0_103]),c_0_99]),c_0_88])]) ).
fof(c_0_109,plain,
! [X3,X4] :
( ( ~ axiom_m1
| is_a_theorem(strict_implies(and(X3,X4),and(X4,X3))) )
& ( ~ 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(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m1])])])])])]) ).
cnf(c_0_110,plain,
( strict_implies(X1,X2) = necessarily(implies(X1,X2))
| ~ op_strict_implies ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_111,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
fof(c_0_112,negated_conjecture,
~ axiom_m1,
inference(fof_simplification,[status(thm)],[c_0_105]) ).
fof(c_0_113,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_114,plain,
( not(not(X1)) = X1
| ~ cn3 ),
inference(pm,[status(thm)],[c_0_106,c_0_93]) ).
cnf(c_0_115,plain,
cn3,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_108])]) ).
cnf(c_0_116,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_109]) ).
cnf(c_0_117,plain,
strict_implies(X1,X2) = necessarily(implies(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_111])]) ).
cnf(c_0_118,negated_conjecture,
~ axiom_m1,
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_119,plain,
( is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X1)
| ~ necessitation ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_120,plain,
necessitation,
inference(split_conjunct,[status(thm)],[km5_necessitation]) ).
cnf(c_0_121,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_115])]) ).
cnf(c_0_122,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(not(X2),X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_108])]) ).
cnf(c_0_123,plain,
~ is_a_theorem(necessarily(implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0)))),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_117]),c_0_118]) ).
cnf(c_0_124,plain,
( is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_120])]) ).
cnf(c_0_125,plain,
not(and(X1,X2)) = implies(X1,not(X2)),
inference(pm,[status(thm)],[c_0_71,c_0_121]) ).
cnf(c_0_126,plain,
implies(not(X1),X2) = implies(not(X2),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(pm,[status(thm)],[c_0_75,c_0_122]),c_0_122])]) ).
cnf(c_0_127,plain,
~ is_a_theorem(implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0))),
inference(pm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_128,plain,
and(X1,X2) = not(implies(X1,not(X2))),
inference(pm,[status(thm)],[c_0_121,c_0_125]) ).
cnf(c_0_129,plain,
implies(X1,X2) = implies(not(X2),not(X1)),
inference(pm,[status(thm)],[c_0_126,c_0_121]) ).
cnf(c_0_130,plain,
~ is_a_theorem(implies(not(implies(esk77_0,not(esk78_0))),not(implies(esk78_0,not(esk77_0))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_128]),c_0_128]) ).
cnf(c_0_131,plain,
implies(X1,not(X2)) = implies(X2,not(X1)),
inference(pm,[status(thm)],[c_0_129,c_0_121]) ).
cnf(c_0_132,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_130,c_0_131]),c_0_129]),c_0_95])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL528+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 3 03:44:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.40/23.43 eprover: CPU time limit exceeded, terminating
% 0.40/23.44 eprover: CPU time limit exceeded, terminating
% 0.40/23.45 eprover: CPU time limit exceeded, terminating
% 0.40/23.50 eprover: CPU time limit exceeded, terminating
% 0.41/25.60 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.41/25.60 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.41/25.60 # Preprocessing time : 0.016 s
% 0.41/25.60
% 0.41/25.60 # Failure: Out of unprocessed clauses!
% 0.41/25.60 # OLD status GaveUp
% 0.41/25.60 # Parsed axioms : 88
% 0.41/25.60 # Removed by relevancy pruning/SinE : 86
% 0.41/25.60 # Initial clauses : 3
% 0.41/25.60 # Removed in clause preprocessing : 0
% 0.41/25.60 # Initial clauses in saturation : 3
% 0.41/25.60 # Processed clauses : 3
% 0.41/25.60 # ...of these trivial : 0
% 0.41/25.60 # ...subsumed : 1
% 0.41/25.60 # ...remaining for further processing : 2
% 0.41/25.60 # Other redundant clauses eliminated : 0
% 0.41/25.60 # Clauses deleted for lack of memory : 0
% 0.41/25.60 # Backward-subsumed : 0
% 0.41/25.60 # Backward-rewritten : 0
% 0.41/25.60 # Generated clauses : 0
% 0.41/25.60 # ...of the previous two non-trivial : 0
% 0.41/25.60 # Contextual simplify-reflections : 0
% 0.41/25.60 # Paramodulations : 0
% 0.41/25.60 # Factorizations : 0
% 0.41/25.60 # Equation resolutions : 0
% 0.41/25.60 # Current number of processed clauses : 2
% 0.41/25.60 # Positive orientable unit clauses : 0
% 0.41/25.60 # Positive unorientable unit clauses: 0
% 0.41/25.60 # Negative unit clauses : 2
% 0.41/25.60 # Non-unit-clauses : 0
% 0.41/25.60 # Current number of unprocessed clauses: 0
% 0.41/25.60 # ...number of literals in the above : 0
% 0.41/25.60 # Current number of archived formulas : 0
% 0.41/25.60 # Current number of archived clauses : 0
% 0.41/25.60 # Clause-clause subsumption calls (NU) : 0
% 0.41/25.60 # Rec. Clause-clause subsumption calls : 0
% 0.41/25.60 # Non-unit clause-clause subsumptions : 0
% 0.41/25.60 # Unit Clause-clause subsumption calls : 0
% 0.41/25.60 # Rewrite failures with RHS unbound : 0
% 0.41/25.60 # BW rewrite match attempts : 0
% 0.41/25.60 # BW rewrite match successes : 0
% 0.41/25.60 # Condensation attempts : 0
% 0.41/25.60 # Condensation successes : 0
% 0.41/25.60 # Termbank termtop insertions : 819
% 0.41/25.60
% 0.41/25.60 # -------------------------------------------------
% 0.41/25.60 # User time : 0.012 s
% 0.41/25.60 # System time : 0.004 s
% 0.41/25.60 # Total time : 0.016 s
% 0.41/25.60 # Maximum resident set size: 2852 pages
% 0.41/25.60 # Running protocol protocol_eprover_f171197f65f27d1ba69648a20c844832c84a5dd7 for 23 seconds:
% 0.41/25.60
% 0.41/25.60 # Failure: Resource limit exceeded (time)
% 0.41/25.60 # OLD status Res
% 0.41/25.60 # Preprocessing time : 0.023 s
% 0.41/25.60 # Running protocol protocol_eprover_eb48853eb71ccd2a6fdade56c25b63f5692e1a0c for 23 seconds:
% 0.41/25.60 # Preprocessing time : 0.023 s
% 0.41/25.60
% 0.41/25.60 # Proof found!
% 0.41/25.60 # SZS status Theorem
% 0.41/25.60 # SZS output start CNFRefutation
% See solution above
% 0.41/25.60 # Proof object total steps : 133
% 0.41/25.60 # Proof object clause steps : 83
% 0.41/25.60 # Proof object formula steps : 50
% 0.41/25.60 # Proof object conjectures : 4
% 0.41/25.60 # Proof object clause conjectures : 1
% 0.41/25.60 # Proof object formula conjectures : 3
% 0.41/25.60 # Proof object initial clauses used : 36
% 0.41/25.60 # Proof object initial formulas used : 31
% 0.41/25.60 # Proof object generating inferences : 24
% 0.41/25.60 # Proof object simplifying inferences : 61
% 0.41/25.60 # Training examples: 0 positive, 0 negative
% 0.41/25.60 # Parsed axioms : 88
% 0.41/25.60 # Removed by relevancy pruning/SinE : 0
% 0.41/25.60 # Initial clauses : 146
% 0.41/25.60 # Removed in clause preprocessing : 0
% 0.41/25.60 # Initial clauses in saturation : 146
% 0.41/25.60 # Processed clauses : 3658
% 0.41/25.60 # ...of these trivial : 71
% 0.41/25.60 # ...subsumed : 1763
% 0.41/25.60 # ...remaining for further processing : 1824
% 0.41/25.60 # Other redundant clauses eliminated : 0
% 0.41/25.60 # Clauses deleted for lack of memory : 0
% 0.41/25.60 # Backward-subsumed : 85
% 0.41/25.60 # Backward-rewritten : 1343
% 0.41/25.60 # Generated clauses : 98855
% 0.41/25.60 # ...of the previous two non-trivial : 96340
% 0.41/25.60 # Contextual simplify-reflections : 1192
% 0.41/25.60 # Paramodulations : 98852
% 0.41/25.60 # Factorizations : 0
% 0.41/25.60 # Equation resolutions : 0
% 0.41/25.60 # Current number of processed clauses : 395
% 0.41/25.60 # Positive orientable unit clauses : 79
% 0.41/25.60 # Positive unorientable unit clauses: 4
% 0.41/25.60 # Negative unit clauses : 8
% 0.41/25.60 # Non-unit-clauses : 304
% 0.41/25.60 # Current number of unprocessed clauses: 5267
% 0.41/25.60 # ...number of literals in the above : 14966
% 0.41/25.60 # Current number of archived formulas : 0
% 0.41/25.60 # Current number of archived clauses : 1428
% 0.41/25.60 # Clause-clause subsumption calls (NU) : 257255
% 0.41/25.60 # Rec. Clause-clause subsumption calls : 190623
% 0.41/25.60 # Non-unit clause-clause subsumptions : 2836
% 0.41/25.60 # Unit Clause-clause subsumption calls : 14150
% 0.41/25.60 # Rewrite failures with RHS unbound : 0
% 0.41/25.60 # BW rewrite match attempts : 11801
% 0.41/25.60 # BW rewrite match successes : 1464
% 0.41/25.60 # Condensation attempts : 0
% 0.41/25.60 # Condensation successes : 0
% 0.41/25.60 # Termbank termtop insertions : 1753450
% 0.41/25.60
% 0.41/25.60 # -------------------------------------------------
% 0.41/25.60 # User time : 1.671 s
% 0.41/25.60 # System time : 0.040 s
% 0.41/25.60 # Total time : 1.711 s
% 0.41/25.60 # Maximum resident set size: 90864 pages
%------------------------------------------------------------------------------