%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : LCL489+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n024.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 10:11:29 EDT 2022
% Result : Theorem 0.40s 24.58s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 26
% Syntax : Number of formulae : 124 ( 72 unt; 0 def)
% Number of atoms : 210 ( 33 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 147 ( 61 ~; 59 |; 12 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 14 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 17 con; 0-2 aty)
% Number of variables : 195 ( 9 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(op_and,axiom,
( op_and
=> ! [X1,X2] : and(X1,X2) = not(or(not(X1),not(X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_and) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X1,X2] : implies(X1,X2) = or(not(X1),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).
fof(principia_op_and,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_op_and) ).
fof(principia_op_implies_or,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_op_implies_or) ).
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(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(r2,axiom,
( r2
<=> ! [X4,X5] : is_a_theorem(implies(X5,or(X4,X5))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r2) ).
fof(hilbert_op_or,axiom,
op_or,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',hilbert_op_or) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',hilbert_op_implies_and) ).
fof(principia_r2,axiom,
r2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r2) ).
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(r1,axiom,
( r1
<=> ! [X4] : is_a_theorem(implies(or(X4,X4),X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r1) ).
fof(principia_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).
fof(r4,axiom,
( r4
<=> ! [X4,X5,X6] : is_a_theorem(implies(or(X4,or(X5,X6)),or(X5,or(X4,X6)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r4) ).
fof(principia_r1,axiom,
r1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r1) ).
fof(principia_r4,axiom,
r4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r4) ).
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(principia_r3,axiom,
r3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
fof(r5,axiom,
( r5
<=> ! [X4,X5,X6] : is_a_theorem(implies(implies(X5,X6),implies(or(X4,X5),or(X4,X6)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r5) ).
fof(principia_r5,axiom,
r5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_r5) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X1,X2] :
( is_a_theorem(equiv(X1,X2))
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X1,X2] : equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(substitution_of_equivalents_001,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',substitution_of_equivalents) ).
fof(principia_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax',principia_op_equiv) ).
fof(hilbert_and_3,conjecture,
and_3,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',hilbert_and_3) ).
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(c_0_26,plain,
! [X3,X4] :
( ~ op_and
| and(X3,X4) = not(or(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_and])])])])]) ).
fof(c_0_27,plain,
! [X3,X4] :
( ~ op_implies_or
| implies(X3,X4) = or(not(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_implies_or])])])])]) ).
cnf(c_0_28,plain,
( and(X1,X2) = not(or(not(X1),not(X2)))
| ~ op_and ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_29,plain,
op_and,
inference(split_conjunct,[status(thm)],[principia_op_and]) ).
cnf(c_0_30,plain,
( implies(X1,X2) = or(not(X1),X2)
| ~ op_implies_or ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,plain,
op_implies_or,
inference(split_conjunct,[status(thm)],[principia_op_implies_or]) ).
fof(c_0_32,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_33,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_34,plain,
and(X1,X2) = not(or(not(X1),not(X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
cnf(c_0_35,plain,
or(not(X1),X2) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
fof(c_0_36,plain,
! [X6,X7] :
( ( ~ r2
| is_a_theorem(implies(X7,or(X6,X7))) )
& ( ~ is_a_theorem(implies(esk47_0,or(esk46_0,esk47_0)))
| r2 ) ),
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)],[r2])])])])])]) ).
cnf(c_0_37,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
op_or,
inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).
cnf(c_0_39,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
cnf(c_0_41,plain,
and(X1,X2) = not(implies(X1,not(X2))),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,plain,
( is_a_theorem(implies(X1,or(X2,X1)))
| ~ r2 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,plain,
r2,
inference(split_conjunct,[status(thm)],[principia_r2]) ).
cnf(c_0_44,plain,
not(and(not(X1),not(X2))) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_45,plain,
not(not(implies(X1,not(not(X2))))) = implies(X1,X2),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]),c_0_41]) ).
cnf(c_0_46,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).
cnf(c_0_47,plain,
or(X1,X2) = implies(not(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_34]),c_0_35]),c_0_45]) ).
cnf(c_0_48,plain,
is_a_theorem(implies(X1,implies(not(X2),X1))),
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_49,plain,
implies(not(not(X1)),X2) = implies(X1,X2),
inference(rw,[status(thm)],[c_0_35,c_0_47]) ).
fof(c_0_50,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])])])])])])]) ).
cnf(c_0_51,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_52,plain,
implies(X1,implies(X2,not(not(X3)))) = not(not(implies(X1,implies(X2,X3)))),
inference(spm,[status(thm)],[c_0_45,c_0_45]) ).
fof(c_0_53,plain,
! [X5] :
( ( ~ r1
| is_a_theorem(implies(or(X5,X5),X5)) )
& ( ~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0))
| r1 ) ),
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)],[r1])])])])])]) ).
cnf(c_0_54,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X2)
| ~ modus_ponens ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_55,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[principia_modus_ponens]) ).
cnf(c_0_56,plain,
is_a_theorem(not(not(implies(X1,implies(X2,X1))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_49]),c_0_52]) ).
fof(c_0_57,plain,
! [X7,X8,X9] :
( ( ~ r4
| is_a_theorem(implies(or(X7,or(X8,X9)),or(X8,or(X7,X9)))) )
& ( ~ is_a_theorem(implies(or(esk50_0,or(esk51_0,esk52_0)),or(esk51_0,or(esk50_0,esk52_0))))
| r4 ) ),
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)],[r4])])])])])]) ).
cnf(c_0_58,plain,
( is_a_theorem(implies(or(X1,X1),X1))
| ~ r1 ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_59,plain,
r1,
inference(split_conjunct,[status(thm)],[principia_r1]) ).
cnf(c_0_60,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_54,c_0_55])]) ).
cnf(c_0_61,plain,
is_a_theorem(not(not(not(not(implies(X1,implies(X2,X1))))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_49]),c_0_52]) ).
cnf(c_0_62,plain,
( is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))
| ~ r4 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_63,plain,
r4,
inference(split_conjunct,[status(thm)],[principia_r4]) ).
cnf(c_0_64,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]) ).
cnf(c_0_65,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(not(X2)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_60,c_0_49]) ).
cnf(c_0_66,plain,
is_a_theorem(not(not(not(not(not(not(implies(X1,implies(X2,X1))))))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_49]),c_0_52]) ).
cnf(c_0_67,plain,
is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]) ).
cnf(c_0_68,plain,
is_a_theorem(implies(implies(not(X1),X1),X1)),
inference(rw,[status(thm)],[c_0_64,c_0_47]) ).
cnf(c_0_69,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,implies(X3,X2)),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_49]),c_0_49]) ).
cnf(c_0_70,plain,
is_a_theorem(implies(implies(not(X1),implies(not(X2),X3)),implies(not(X2),implies(not(X1),X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_47]),c_0_47]),c_0_47]),c_0_47]) ).
cnf(c_0_71,plain,
implies(implies(X1,not(not(X2))),X3) = implies(implies(X1,X2),X3),
inference(spm,[status(thm)],[c_0_49,c_0_45]) ).
cnf(c_0_72,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(not(X1),X1)) ),
inference(spm,[status(thm)],[c_0_60,c_0_68]) ).
cnf(c_0_73,plain,
is_a_theorem(implies(not(X1),implies(not(X2),not(X2)))),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
fof(c_0_74,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_75,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,not(not(X3))))
| ~ is_a_theorem(implies(implies(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_60,c_0_71]) ).
cnf(c_0_76,plain,
is_a_theorem(implies(not(X1),not(X1))),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_77,plain,
( is_a_theorem(implies(or(X1,X2),or(X2,X1)))
| ~ r3 ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_78,plain,
r3,
inference(split_conjunct,[status(thm)],[principia_r3]) ).
cnf(c_0_79,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,X2),X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_49]) ).
cnf(c_0_80,plain,
is_a_theorem(implies(implies(X1,implies(not(X2),X3)),implies(not(X2),implies(X1,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_49]),c_0_49]) ).
cnf(c_0_81,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78])]) ).
cnf(c_0_82,plain,
is_a_theorem(implies(not(X1),implies(implies(not(X1),X2),X2))),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
fof(c_0_83,plain,
! [X7,X8,X9] :
( ( ~ r5
| is_a_theorem(implies(implies(X8,X9),implies(or(X7,X8),or(X7,X9)))) )
& ( ~ is_a_theorem(implies(implies(esk54_0,esk55_0),implies(or(esk53_0,esk54_0),or(esk53_0,esk55_0))))
| r5 ) ),
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)],[r5])])])])])]) ).
cnf(c_0_84,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(not(X2),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_47]),c_0_47]) ).
cnf(c_0_85,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_49]),c_0_49]) ).
cnf(c_0_86,plain,
( is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))
| ~ r5 ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_87,plain,
r5,
inference(split_conjunct,[status(thm)],[principia_r5]) ).
fof(c_0_88,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_89,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_90,plain,
is_a_theorem(implies(implies(X1,X2),implies(not(X2),not(X1)))),
inference(spm,[status(thm)],[c_0_84,c_0_49]) ).
cnf(c_0_91,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),X2)),
inference(spm,[status(thm)],[c_0_79,c_0_85]) ).
cnf(c_0_92,plain,
is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87])]) ).
cnf(c_0_93,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2))
| ~ substitution_of_equivalents ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_94,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[substitution_of_equivalents]) ).
cnf(c_0_95,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_96,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[principia_op_equiv]) ).
cnf(c_0_97,plain,
( is_a_theorem(implies(not(X1),not(X2)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_60,c_0_90]) ).
cnf(c_0_98,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),not(not(X2)))),
inference(spm,[status(thm)],[c_0_91,c_0_71]) ).
cnf(c_0_99,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_85]) ).
cnf(c_0_100,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(not(X3),X1),implies(not(X3),X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_47]),c_0_47]) ).
cnf(c_0_101,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94])]) ).
cnf(c_0_102,plain,
equiv(X1,X2) = not(implies(implies(X1,X2),not(implies(X2,X1)))),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_96])]),c_0_41]) ).
cnf(c_0_103,plain,
is_a_theorem(implies(not(X1),not(implies(implies(X2,X2),X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_49]) ).
fof(c_0_104,negated_conjecture,
~ and_3,
inference(assume_negation,[status(cth)],[hilbert_and_3]) ).
cnf(c_0_105,plain,
is_a_theorem(implies(implies(implies(X1,implies(implies(X1,X2),X2)),X3),X3)),
inference(spm,[status(thm)],[c_0_99,c_0_85]) ).
cnf(c_0_106,plain,
( is_a_theorem(implies(implies(not(X1),X2),implies(not(X1),X3)))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(spm,[status(thm)],[c_0_60,c_0_100]) ).
cnf(c_0_107,plain,
( X1 = X2
| ~ is_a_theorem(not(implies(implies(X1,X2),not(implies(X2,X1))))) ),
inference(rw,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_108,plain,
is_a_theorem(implies(X1,not(implies(implies(X2,X2),not(X1))))),
inference(spm,[status(thm)],[c_0_103,c_0_49]) ).
fof(c_0_109,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_110,negated_conjecture,
~ and_3,
inference(fof_simplification,[status(thm)],[c_0_104]) ).
cnf(c_0_111,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,implies(implies(X2,X3),X3)),X1)) ),
inference(spm,[status(thm)],[c_0_60,c_0_105]) ).
cnf(c_0_112,plain,
is_a_theorem(implies(implies(not(X1),implies(X2,X3)),implies(not(X1),implies(not(X3),not(X2))))),
inference(spm,[status(thm)],[c_0_106,c_0_90]) ).
cnf(c_0_113,plain,
( X1 = not(not(X2))
| ~ is_a_theorem(not(implies(implies(X1,X2),not(implies(X2,X1))))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_49]),c_0_71]) ).
cnf(c_0_114,plain,
is_a_theorem(not(implies(implies(X1,X1),not(implies(X2,X2))))),
inference(spm,[status(thm)],[c_0_79,c_0_108]) ).
cnf(c_0_115,plain,
( and_3
| ~ is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_116,negated_conjecture,
~ and_3,
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_117,plain,
is_a_theorem(implies(not(X1),implies(not(X2),not(implies(not(X1),X2))))),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_118,plain,
not(not(X1)) = X1,
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_119,plain,
~ is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0)))),
inference(sr,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_120,plain,
is_a_theorem(implies(X1,implies(not(X2),not(implies(X1,X2))))),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_121,plain,
~ is_a_theorem(implies(esk18_0,implies(esk19_0,not(implies(esk18_0,not(esk19_0)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_34]),c_0_47]),c_0_49]) ).
cnf(c_0_122,plain,
is_a_theorem(implies(X1,implies(X2,not(implies(X1,not(X2)))))),
inference(spm,[status(thm)],[c_0_120,c_0_118]) ).
cnf(c_0_123,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_122])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL489+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 13:04:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.39/23.41 eprover: CPU time limit exceeded, terminating
% 0.39/23.42 eprover: CPU time limit exceeded, terminating
% 0.39/23.43 eprover: CPU time limit exceeded, terminating
% 0.39/23.47 eprover: CPU time limit exceeded, terminating
% 0.40/24.58 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.40/24.58
% 0.40/24.58 # Failure: Resource limit exceeded (time)
% 0.40/24.58 # OLD status Res
% 0.40/24.58 # Preprocessing time : 0.019 s
% 0.40/24.58 # Running protocol protocol_eprover_f6eb5f7f05126ea361481ae651a4823314e3d740 for 23 seconds:
% 0.40/24.58 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,02,20000,1.0)
% 0.40/24.58 # Preprocessing time : 0.015 s
% 0.40/24.58
% 0.40/24.58 # Failure: Out of unprocessed clauses!
% 0.40/24.58 # OLD status GaveUp
% 0.40/24.58 # Parsed axioms : 45
% 0.40/24.58 # Removed by relevancy pruning/SinE : 43
% 0.40/24.58 # Initial clauses : 3
% 0.40/24.58 # Removed in clause preprocessing : 0
% 0.40/24.58 # Initial clauses in saturation : 3
% 0.40/24.58 # Processed clauses : 3
% 0.40/24.58 # ...of these trivial : 0
% 0.40/24.58 # ...subsumed : 1
% 0.40/24.58 # ...remaining for further processing : 2
% 0.40/24.58 # Other redundant clauses eliminated : 0
% 0.40/24.58 # Clauses deleted for lack of memory : 0
% 0.40/24.58 # Backward-subsumed : 0
% 0.40/24.58 # Backward-rewritten : 0
% 0.40/24.58 # Generated clauses : 0
% 0.40/24.58 # ...of the previous two non-trivial : 0
% 0.40/24.58 # Contextual simplify-reflections : 0
% 0.40/24.58 # Paramodulations : 0
% 0.40/24.58 # Factorizations : 0
% 0.40/24.58 # Equation resolutions : 0
% 0.40/24.58 # Current number of processed clauses : 2
% 0.40/24.58 # Positive orientable unit clauses : 0
% 0.40/24.58 # Positive unorientable unit clauses: 0
% 0.40/24.58 # Negative unit clauses : 2
% 0.40/24.58 # Non-unit-clauses : 0
% 0.40/24.58 # Current number of unprocessed clauses: 0
% 0.40/24.58 # ...number of literals in the above : 0
% 0.40/24.58 # Current number of archived formulas : 0
% 0.40/24.58 # Current number of archived clauses : 0
% 0.40/24.58 # Clause-clause subsumption calls (NU) : 0
% 0.40/24.58 # Rec. Clause-clause subsumption calls : 0
% 0.40/24.58 # Non-unit clause-clause subsumptions : 0
% 0.40/24.58 # Unit Clause-clause subsumption calls : 0
% 0.40/24.58 # Rewrite failures with RHS unbound : 0
% 0.40/24.58 # BW rewrite match attempts : 0
% 0.40/24.58 # BW rewrite match successes : 0
% 0.40/24.58 # Condensation attempts : 0
% 0.40/24.58 # Condensation successes : 0
% 0.40/24.58 # Termbank termtop insertions : 496
% 0.40/24.58
% 0.40/24.58 # -------------------------------------------------
% 0.40/24.58 # User time : 0.011 s
% 0.40/24.58 # System time : 0.004 s
% 0.40/24.58 # Total time : 0.015 s
% 0.40/24.58 # Maximum resident set size: 2860 pages
% 0.40/24.58 # Running protocol protocol_eprover_a172c605141d0894bf6fdc293a5220c6c2a32117 for 23 seconds:
% 0.40/24.58 # Preprocessing time : 0.020 s
% 0.40/24.58
% 0.40/24.58 # Proof found!
% 0.40/24.58 # SZS status Theorem
% 0.40/24.58 # SZS output start CNFRefutation
% See solution above
% 0.40/24.58 # Proof object total steps : 124
% 0.40/24.58 # Proof object clause steps : 83
% 0.40/24.58 # Proof object formula steps : 41
% 0.40/24.58 # Proof object conjectures : 4
% 0.40/24.58 # Proof object clause conjectures : 1
% 0.40/24.58 # Proof object formula conjectures : 3
% 0.40/24.58 # Proof object initial clauses used : 26
% 0.40/24.58 # Proof object initial formulas used : 26
% 0.40/24.58 # Proof object generating inferences : 33
% 0.40/24.58 # Proof object simplifying inferences : 58
% 0.40/24.58 # Training examples: 0 positive, 0 negative
% 0.40/24.58 # Parsed axioms : 45
% 0.40/24.58 # Removed by relevancy pruning/SinE : 0
% 0.40/24.58 # Initial clauses : 74
% 0.40/24.58 # Removed in clause preprocessing : 0
% 0.40/24.58 # Initial clauses in saturation : 74
% 0.40/24.58 # Processed clauses : 1074
% 0.40/24.58 # ...of these trivial : 302
% 0.40/24.58 # ...subsumed : 61
% 0.40/24.58 # ...remaining for further processing : 711
% 0.40/24.58 # Other redundant clauses eliminated : 0
% 0.40/24.58 # Clauses deleted for lack of memory : 0
% 0.40/24.58 # Backward-subsumed : 4
% 0.40/24.58 # Backward-rewritten : 204
% 0.40/24.58 # Generated clauses : 18300
% 0.40/24.58 # ...of the previous two non-trivial : 13245
% 0.40/24.58 # Contextual simplify-reflections : 0
% 0.40/24.58 # Paramodulations : 18300
% 0.40/24.58 # Factorizations : 0
% 0.40/24.58 # Equation resolutions : 0
% 0.40/24.58 # Current number of processed clauses : 503
% 0.40/24.58 # Positive orientable unit clauses : 417
% 0.40/24.58 # Positive unorientable unit clauses: 0
% 0.40/24.58 # Negative unit clauses : 1
% 0.40/24.58 # Non-unit-clauses : 85
% 0.40/24.58 # Current number of unprocessed clauses: 10522
% 0.40/24.58 # ...number of literals in the above : 10720
% 0.40/24.58 # Current number of archived formulas : 0
% 0.40/24.58 # Current number of archived clauses : 208
% 0.40/24.58 # Clause-clause subsumption calls (NU) : 1445
% 0.40/24.58 # Rec. Clause-clause subsumption calls : 1442
% 0.40/24.58 # Non-unit clause-clause subsumptions : 64
% 0.40/24.58 # Unit Clause-clause subsumption calls : 1480
% 0.40/24.58 # Rewrite failures with RHS unbound : 0
% 0.40/24.58 # BW rewrite match attempts : 35300
% 0.40/24.58 # BW rewrite match successes : 218
% 0.40/24.58 # Condensation attempts : 0
% 0.40/24.58 # Condensation successes : 0
% 0.40/24.58 # Termbank termtop insertions : 253073
% 0.40/24.58
% 0.40/24.58 # -------------------------------------------------
% 0.40/24.58 # User time : 0.190 s
% 0.40/24.58 # System time : 0.009 s
% 0.40/24.58 # Total time : 0.199 s
% 0.40/24.58 # Maximum resident set size: 17040 pages
%------------------------------------------------------------------------------