%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : LCL523+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 10:11:40 EDT 2022
% Result : Theorem 0.43s 33.61s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 34
% Syntax : Number of formulae : 136 ( 73 unt; 0 def)
% Number of atoms : 244 ( 43 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 181 ( 73 ~; 72 |; 17 &)
% ( 13 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 18 prp; 0-2 aty)
% Number of functors : 31 ( 31 usr; 24 con; 0-2 aty)
% Number of variables : 172 ( 11 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(implies(X1,X2)) )
=> is_a_theorem(X2) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL006+0.ax',and_3) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X1,X2] :
( is_a_theorem(equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X1,X2] : equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(hilbert_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(hilbert_and_3,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
fof(substitution_of_equivalents_001,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',substitution_of_equivalents) ).
fof(hilbert_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_equiv) ).
fof(and_2,axiom,
( and_2
<=> ! [X1,X2] : is_a_theorem(implies(and(X1,X2),X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_2) ).
fof(hilbert_and_2,axiom,
and_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_2) ).
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(axiom_K,axiom,
( axiom_K
<=> ! [X1,X2] : is_a_theorem(implies(necessarily(implies(X1,X2)),implies(necessarily(X1),necessarily(X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_K) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
fof(km5_axiom_K,axiom,
axiom_K,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_axiom_K) ).
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(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(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(hilbert_implies_1,axiom,
implies_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_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/sandbox2/benchmark/Axioms/LCL006+0.ax',or_3) ).
fof(hilbert_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_or) ).
fof(hilbert_implies_2,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
fof(hilbert_or_3,axiom,
or_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_or_3) ).
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(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_and_1,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_1) ).
fof(hilbert_or_1,axiom,
or_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_or_1) ).
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(km5_op_possibly,axiom,
op_possibly,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_op_possibly) ).
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(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(km5_axiom_5,axiom,
axiom_5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_axiom_5) ).
fof(km5_axiom_M,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_axiom_M) ).
fof(km4b_axiom_4,conjecture,
axiom_4,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',km4b_axiom_4) ).
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(c_0_34,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_35,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_36,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])])])])])])]) ).
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)
| ~ modus_ponens ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[hilbert_modus_ponens]) ).
cnf(c_0_40,plain,
( is_a_theorem(implies(X1,implies(X2,and(X1,X2))))
| ~ and_3 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,plain,
and_3,
inference(split_conjunct,[status(thm)],[hilbert_and_3]) ).
cnf(c_0_42,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2))
| ~ substitution_of_equivalents ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[substitution_of_equivalents]) ).
cnf(c_0_44,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[hilbert_op_equiv]) ).
cnf(c_0_46,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
cnf(c_0_47,plain,
is_a_theorem(implies(X1,implies(X2,and(X1,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]) ).
cnf(c_0_48,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).
cnf(c_0_49,plain,
equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).
cnf(c_0_50,plain,
( is_a_theorem(implies(X1,and(X2,X1)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
fof(c_0_51,plain,
! [X3,X4] :
( ( ~ and_2
| is_a_theorem(implies(and(X3,X4),X4)) )
& ( ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0))
| and_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)],[and_2])])])])])]) ).
cnf(c_0_52,plain,
( X1 = X2
| ~ is_a_theorem(and(implies(X1,X2),implies(X2,X1))) ),
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_50]) ).
cnf(c_0_54,plain,
( is_a_theorem(implies(and(X1,X2),X2))
| ~ and_2 ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_55,plain,
and_2,
inference(split_conjunct,[status(thm)],[hilbert_and_2]) ).
fof(c_0_56,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_57,plain,
( X1 = X2
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,plain,
is_a_theorem(implies(and(X1,X2),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
fof(c_0_59,plain,
! [X3,X4] :
( ( ~ axiom_K
| is_a_theorem(implies(necessarily(implies(X3,X4)),implies(necessarily(X3),necessarily(X4)))) )
& ( ~ is_a_theorem(implies(necessarily(implies(esk63_0,esk64_0)),implies(necessarily(esk63_0),necessarily(esk64_0))))
| axiom_K ) ),
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_K])])])])])]) ).
cnf(c_0_60,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_61,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
cnf(c_0_62,plain,
( and(X1,X2) = X2
| ~ is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_50]),c_0_58])]) ).
cnf(c_0_63,plain,
( is_a_theorem(implies(necessarily(implies(X1,X2)),implies(necessarily(X1),necessarily(X2))))
| ~ axiom_K ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_64,plain,
axiom_K,
inference(split_conjunct,[status(thm)],[km5_axiom_K]) ).
fof(c_0_65,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_66,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])])])])]) ).
fof(c_0_67,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])])])])])]) ).
cnf(c_0_68,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]) ).
cnf(c_0_69,plain,
( is_a_theorem(implies(X1,X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_58,c_0_62]) ).
cnf(c_0_70,plain,
is_a_theorem(implies(necessarily(implies(X1,X2)),implies(necessarily(X1),necessarily(X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]) ).
cnf(c_0_71,plain,
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ implies_1 ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_72,plain,
implies_1,
inference(split_conjunct,[status(thm)],[hilbert_implies_1]) ).
fof(c_0_73,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_74,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_75,plain,
op_or,
inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).
cnf(c_0_76,plain,
( is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))
| ~ implies_2 ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_77,plain,
implies_2,
inference(split_conjunct,[status(thm)],[hilbert_implies_2]) ).
cnf(c_0_78,plain,
( not(not(X1)) = implies(X2,X1)
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_68,c_0_62]) ).
cnf(c_0_79,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_80,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72])]) ).
cnf(c_0_81,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_73]) ).
cnf(c_0_82,plain,
or(X1,X2) = implies(not(X1),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_68]),c_0_75])]) ).
cnf(c_0_83,plain,
or_3,
inference(split_conjunct,[status(thm)],[hilbert_or_3]) ).
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_76,c_0_77])]) ).
cnf(c_0_85,plain,
not(not(X1)) = implies(implies(X2,X2),X1),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
fof(c_0_86,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_87,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_80]) ).
cnf(c_0_88,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_81,c_0_82]),c_0_83])]) ).
cnf(c_0_89,plain,
implies(X1,implies(X1,X2)) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_84]),c_0_80])]) ).
cnf(c_0_90,plain,
implies(implies(X1,X1),X2) = implies(implies(X3,X3),X2),
inference(spm,[status(thm)],[c_0_85,c_0_85]) ).
fof(c_0_91,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_92,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ and_1 ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_93,plain,
and_1,
inference(split_conjunct,[status(thm)],[hilbert_and_1]) ).
cnf(c_0_94,plain,
( X1 = X2
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_87]) ).
cnf(c_0_95,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(not(X1),X1),X2))),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_96,plain,
is_a_theorem(implies(implies(X1,X1),implies(X2,X2))),
inference(spm,[status(thm)],[c_0_79,c_0_90]) ).
cnf(c_0_97,plain,
( is_a_theorem(implies(X1,or(X1,X2)))
| ~ or_1 ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_98,plain,
or_1,
inference(split_conjunct,[status(thm)],[hilbert_or_1]) ).
cnf(c_0_99,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(spm,[status(thm)],[c_0_47,c_0_89]) ).
cnf(c_0_100,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93])]) ).
cnf(c_0_101,plain,
( implies(implies(not(X1),X1),X2) = implies(X1,X2)
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_102,plain,
implies(X1,X1) = implies(X2,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_96]),c_0_96])]) ).
cnf(c_0_103,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98])]) ).
fof(c_0_104,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_105,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_99]),c_0_100])]) ).
cnf(c_0_106,plain,
implies(implies(not(X1),X1),X1) = implies(X2,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_79])]) ).
cnf(c_0_107,plain,
is_a_theorem(implies(X1,implies(not(X1),X2))),
inference(rw,[status(thm)],[c_0_103,c_0_82]) ).
cnf(c_0_108,plain,
( possibly(X1) = not(necessarily(not(X1)))
| ~ op_possibly ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_109,plain,
op_possibly,
inference(split_conjunct,[status(thm)],[km5_op_possibly]) ).
cnf(c_0_110,plain,
not(not(X1)) = implies(not(X1),X1),
inference(spm,[status(thm)],[c_0_68,c_0_105]) ).
cnf(c_0_111,plain,
implies(not(X1),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_106]),c_0_79]),c_0_107])]) ).
fof(c_0_112,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_113,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_114,plain,
not(necessarily(not(X1))) = possibly(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_109])]) ).
cnf(c_0_115,plain,
not(not(X1)) = X1,
inference(rw,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_116,plain,
( is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))
| ~ axiom_5 ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_117,plain,
axiom_5,
inference(split_conjunct,[status(thm)],[km5_axiom_5]) ).
cnf(c_0_118,plain,
( is_a_theorem(implies(necessarily(X1),X1))
| ~ axiom_M ),
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_119,plain,
axiom_M,
inference(split_conjunct,[status(thm)],[km5_axiom_M]) ).
cnf(c_0_120,plain,
not(necessarily(X1)) = possibly(not(X1)),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_121,plain,
is_a_theorem(implies(possibly(X1),necessarily(possibly(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_117])]) ).
cnf(c_0_122,plain,
is_a_theorem(implies(necessarily(X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_119])]) ).
cnf(c_0_123,plain,
not(possibly(not(X1))) = necessarily(X1),
inference(spm,[status(thm)],[c_0_115,c_0_120]) ).
fof(c_0_124,negated_conjecture,
~ axiom_4,
inference(assume_negation,[status(cth)],[km4b_axiom_4]) ).
cnf(c_0_125,plain,
necessarily(possibly(X1)) = possibly(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_121]),c_0_122])]) ).
cnf(c_0_126,plain,
not(possibly(X1)) = necessarily(not(X1)),
inference(spm,[status(thm)],[c_0_123,c_0_115]) ).
fof(c_0_127,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_128,negated_conjecture,
~ axiom_4,
inference(fof_simplification,[status(thm)],[c_0_124]) ).
cnf(c_0_129,plain,
possibly(necessarily(not(X1))) = necessarily(not(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_125]),c_0_126]),c_0_126]) ).
cnf(c_0_130,plain,
( axiom_4
| ~ is_a_theorem(implies(necessarily(esk66_0),necessarily(necessarily(esk66_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_131,negated_conjecture,
~ axiom_4,
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_132,plain,
possibly(necessarily(X1)) = necessarily(X1),
inference(spm,[status(thm)],[c_0_129,c_0_115]) ).
cnf(c_0_133,plain,
~ is_a_theorem(implies(necessarily(esk66_0),necessarily(necessarily(esk66_0)))),
inference(sr,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_134,plain,
necessarily(necessarily(X1)) = necessarily(X1),
inference(spm,[status(thm)],[c_0_125,c_0_132]) ).
cnf(c_0_135,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_134]),c_0_79])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL523+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : run_ET %s %d
% 0.11/0.33 % Computer : n029.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sat Jul 2 11:12:10 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.36/23.39 eprover: CPU time limit exceeded, terminating
% 0.36/23.40 eprover: CPU time limit exceeded, terminating
% 0.36/23.41 eprover: CPU time limit exceeded, terminating
% 0.36/23.44 eprover: CPU time limit exceeded, terminating
% 0.43/33.61 # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.43/33.61
% 0.43/33.61 # Failure: Resource limit exceeded (time)
% 0.43/33.61 # OLD status Res
% 0.43/33.61 # Preprocessing time : 0.022 s
% 0.43/33.61 # Running protocol protocol_eprover_773c90a94152ea2e8c9d3df9c4b1eb6152c40c03 for 23 seconds:
% 0.43/33.61 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,,100,1.0)
% 0.43/33.61 # Preprocessing time : 0.017 s
% 0.43/33.61
% 0.43/33.61 # Failure: Out of unprocessed clauses!
% 0.43/33.61 # OLD status GaveUp
% 0.43/33.61 # Parsed axioms : 82
% 0.43/33.61 # Removed by relevancy pruning/SinE : 80
% 0.43/33.61 # Initial clauses : 3
% 0.43/33.61 # Removed in clause preprocessing : 0
% 0.43/33.61 # Initial clauses in saturation : 3
% 0.43/33.61 # Processed clauses : 3
% 0.43/33.61 # ...of these trivial : 0
% 0.43/33.61 # ...subsumed : 1
% 0.43/33.61 # ...remaining for further processing : 2
% 0.43/33.61 # Other redundant clauses eliminated : 0
% 0.43/33.61 # Clauses deleted for lack of memory : 0
% 0.43/33.61 # Backward-subsumed : 0
% 0.43/33.61 # Backward-rewritten : 0
% 0.43/33.61 # Generated clauses : 0
% 0.43/33.61 # ...of the previous two non-trivial : 0
% 0.43/33.61 # Contextual simplify-reflections : 0
% 0.43/33.61 # Paramodulations : 0
% 0.43/33.61 # Factorizations : 0
% 0.43/33.61 # Equation resolutions : 0
% 0.43/33.61 # Current number of processed clauses : 2
% 0.43/33.61 # Positive orientable unit clauses : 0
% 0.43/33.61 # Positive unorientable unit clauses: 0
% 0.43/33.61 # Negative unit clauses : 2
% 0.43/33.61 # Non-unit-clauses : 0
% 0.43/33.61 # Current number of unprocessed clauses: 0
% 0.43/33.61 # ...number of literals in the above : 0
% 0.43/33.61 # Current number of archived formulas : 0
% 0.43/33.61 # Current number of archived clauses : 0
% 0.43/33.61 # Clause-clause subsumption calls (NU) : 0
% 0.43/33.61 # Rec. Clause-clause subsumption calls : 0
% 0.43/33.61 # Non-unit clause-clause subsumptions : 0
% 0.43/33.61 # Unit Clause-clause subsumption calls : 0
% 0.43/33.61 # Rewrite failures with RHS unbound : 0
% 0.43/33.61 # BW rewrite match attempts : 0
% 0.43/33.61 # BW rewrite match successes : 0
% 0.43/33.61 # Condensation attempts : 0
% 0.43/33.61 # Condensation successes : 0
% 0.43/33.61 # Termbank termtop insertions : 792
% 0.43/33.61
% 0.43/33.61 # -------------------------------------------------
% 0.43/33.61 # User time : 0.011 s
% 0.43/33.61 # System time : 0.006 s
% 0.43/33.61 # Total time : 0.017 s
% 0.43/33.61 # Maximum resident set size: 2844 pages
% 0.43/33.61 # Running protocol protocol_eprover_75515770aeb32f68e33e9fbd9dff93f5a2e34f2e for 23 seconds:
% 0.43/33.61 # Preprocessing time : 0.021 s
% 0.43/33.61
% 0.43/33.61 # Proof found!
% 0.43/33.61 # SZS status Theorem
% 0.43/33.61 # SZS output start CNFRefutation
% See solution above
% 0.43/33.61 # Proof object total steps : 136
% 0.43/33.61 # Proof object clause steps : 83
% 0.43/33.61 # Proof object formula steps : 53
% 0.43/33.61 # Proof object conjectures : 4
% 0.43/33.61 # Proof object clause conjectures : 1
% 0.43/33.61 # Proof object formula conjectures : 3
% 0.43/33.61 # Proof object initial clauses used : 34
% 0.43/33.61 # Proof object initial formulas used : 34
% 0.43/33.61 # Proof object generating inferences : 28
% 0.43/33.61 # Proof object simplifying inferences : 58
% 0.43/33.61 # Training examples: 0 positive, 0 negative
% 0.43/33.61 # Parsed axioms : 82
% 0.43/33.61 # Removed by relevancy pruning/SinE : 0
% 0.43/33.61 # Initial clauses : 140
% 0.43/33.61 # Removed in clause preprocessing : 0
% 0.43/33.61 # Initial clauses in saturation : 140
% 0.43/33.61 # Processed clauses : 180266
% 0.43/33.61 # ...of these trivial : 4947
% 0.43/33.61 # ...subsumed : 171391
% 0.43/33.61 # ...remaining for further processing : 3928
% 0.43/33.61 # Other redundant clauses eliminated : 0
% 0.43/33.61 # Clauses deleted for lack of memory : 590811
% 0.43/33.61 # Backward-subsumed : 715
% 0.43/33.61 # Backward-rewritten : 571
% 0.43/33.61 # Generated clauses : 1030659
% 0.43/33.61 # ...of the previous two non-trivial : 977681
% 0.43/33.61 # Contextual simplify-reflections : 0
% 0.43/33.61 # Paramodulations : 1030659
% 0.43/33.61 # Factorizations : 0
% 0.43/33.61 # Equation resolutions : 0
% 0.43/33.61 # Current number of processed clauses : 2642
% 0.43/33.61 # Positive orientable unit clauses : 157
% 0.43/33.61 # Positive unorientable unit clauses: 320
% 0.43/33.61 # Negative unit clauses : 3
% 0.43/33.61 # Non-unit-clauses : 2162
% 0.43/33.61 # Current number of unprocessed clauses: 82120
% 0.43/33.61 # ...number of literals in the above : 180095
% 0.43/33.61 # Current number of archived formulas : 0
% 0.43/33.61 # Current number of archived clauses : 1286
% 0.43/33.61 # Clause-clause subsumption calls (NU) : 2157040
% 0.43/33.61 # Rec. Clause-clause subsumption calls : 1182951
% 0.43/33.61 # Non-unit clause-clause subsumptions : 52359
% 0.43/33.61 # Unit Clause-clause subsumption calls : 20992
% 0.43/33.61 # Rewrite failures with RHS unbound : 17729
% 0.43/33.61 # BW rewrite match attempts : 98358
% 0.43/33.61 # BW rewrite match successes : 2966
% 0.43/33.61 # Condensation attempts : 0
% 0.43/33.61 # Condensation successes : 0
% 0.43/33.61 # Termbank termtop insertions : 10140927
% 0.43/33.61
% 0.43/33.61 # -------------------------------------------------
% 0.43/33.61 # User time : 9.495 s
% 0.43/33.61 # System time : 0.118 s
% 0.43/33.61 # Total time : 9.613 s
% 0.43/33.61 # Maximum resident set size: 134616 pages
% 0.43/46.43 eprover: CPU time limit exceeded, terminating
% 0.43/46.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.43/46.44 eprover: No such file or directory
% 0.43/46.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.43/46.45 eprover: No such file or directory
% 0.43/46.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.43/46.45 eprover: No such file or directory
% 0.43/46.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.43/46.46 eprover: No such file or directory
% 0.43/46.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.43/46.46 eprover: No such file or directory
% 0.43/46.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.43/46.47 eprover: No such file or directory
% 0.43/46.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.43/46.48 eprover: No such file or directory
% 0.43/46.48 eprover: CPU time limit exceeded, terminating
% 0.43/46.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.43/46.48 eprover: No such file or directory
% 0.43/46.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.43/46.49 eprover: No such file or directory
% 0.43/46.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.43/46.49 eprover: No such file or directory
% 0.43/46.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.43/46.50 eprover: No such file or directory
% 0.43/46.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.43/46.51 eprover: No such file or directory
% 0.43/46.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.43/46.51 eprover: No such file or directory
% 0.43/46.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.43/46.52 eprover: No such file or directory
% 0.43/46.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.43/46.52 eprover: No such file or directory
%------------------------------------------------------------------------------