TSTP Solution File: LCL481+1 by Enigma---0.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : LCL481+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% 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 09:26:19 EDT 2022
% Result : Timeout 292.01s 38.25s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 18
% Syntax : Number of formulae : 140 ( 65 unt; 0 def)
% Number of atoms : 259 ( 43 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 218 ( 99 ~; 98 |; 10 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-2 aty)
% Number of variables : 259 ( 38 sgn 36 !; 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(cn1,axiom,
( cn1
<=> ! [X4,X5,X6] : is_a_theorem(implies(implies(X4,X5),implies(implies(X5,X6),implies(X4,X6)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',cn1) ).
fof(luka_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+3.ax',luka_modus_ponens) ).
fof(luka_cn1,axiom,
cn1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+3.ax',luka_cn1) ).
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(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(rosser_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_op_implies_and) ).
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(luka_op_or,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+3.ax',luka_op_or) ).
fof(luka_cn3,axiom,
cn3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+3.ax',luka_cn3) ).
fof(cn2,axiom,
( cn2
<=> ! [X4,X5] : is_a_theorem(implies(X4,implies(not(X4),X5))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',cn2) ).
fof(luka_cn2,axiom,
cn2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+3.ax',luka_cn2) ).
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(luka_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+3.ax',luka_op_equiv) ).
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(substitution_of_equivalents_001,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+3.ax',substitution_of_equivalents) ).
fof(rosser_kn2,conjecture,
kn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn2) ).
fof(kn2,axiom,
( kn2
<=> ! [X4,X5] : is_a_theorem(implies(and(X4,X5),X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn2) ).
fof(c_0_18,plain,
! [X7,X8] :
( ( ~ modus_ponens
| ~ is_a_theorem(X7)
| ~ is_a_theorem(implies(X7,X8))
| is_a_theorem(X8) )
& ( 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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens])])])])]) ).
fof(c_0_19,plain,
! [X83,X84,X85] :
( ( ~ cn1
| is_a_theorem(implies(implies(X83,X84),implies(implies(X84,X85),implies(X83,X85)))) )
& ( ~ is_a_theorem(implies(implies(esk39_0,esk40_0),implies(implies(esk40_0,esk41_0),implies(esk39_0,esk41_0))))
| cn1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn1])])])]) ).
cnf(c_0_20,plain,
( is_a_theorem(X2)
| ~ modus_ponens
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[luka_modus_ponens]) ).
cnf(c_0_22,plain,
( is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))
| ~ cn1 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
cn1,
inference(split_conjunct,[status(thm)],[luka_cn1]) ).
fof(c_0_24,plain,
! [X121,X122] :
( ~ op_implies_and
| implies(X121,X122) = not(and(X121,not(X122))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])]) ).
cnf(c_0_25,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_20,c_0_21])]) ).
cnf(c_0_26,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
fof(c_0_27,plain,
! [X117,X118] :
( ~ op_or
| or(X117,X118) = not(and(not(X117),not(X118))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])]) ).
cnf(c_0_28,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[rosser_op_implies_and]) ).
fof(c_0_30,plain,
! [X93] :
( ( ~ cn3
| is_a_theorem(implies(implies(not(X93),X93),X93)) )
& ( ~ is_a_theorem(implies(implies(not(esk44_0),esk44_0),esk44_0))
| cn3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn3])])])]) ).
cnf(c_0_31,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
cnf(c_0_34,plain,
op_or,
inference(split_conjunct,[status(thm)],[luka_op_or]) ).
cnf(c_0_35,plain,
( is_a_theorem(implies(implies(not(X1),X1),X1))
| ~ cn3 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,plain,
cn3,
inference(split_conjunct,[status(thm)],[luka_cn3]) ).
fof(c_0_37,plain,
! [X89,X90] :
( ( ~ cn2
| is_a_theorem(implies(X89,implies(not(X89),X90))) )
& ( ~ is_a_theorem(implies(esk42_0,implies(not(esk42_0),esk43_0)))
| cn2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cn2])])])]) ).
cnf(c_0_38,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X1,X3)) ),
inference(spm,[status(thm)],[c_0_25,c_0_31]) ).
cnf(c_0_39,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_40,plain,
is_a_theorem(implies(implies(not(X1),X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
cnf(c_0_41,plain,
( is_a_theorem(implies(X1,implies(not(X1),X2)))
| ~ cn2 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,plain,
cn2,
inference(split_conjunct,[status(thm)],[luka_cn2]) ).
cnf(c_0_43,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,not(X3)))
| ~ is_a_theorem(or(X3,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(rw,[status(thm)],[c_0_40,c_0_39]) ).
cnf(c_0_45,plain,
is_a_theorem(implies(X1,implies(not(X1),X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
cnf(c_0_46,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X1,not(X3)))
| ~ is_a_theorem(or(X3,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_39]),c_0_39]) ).
cnf(c_0_47,plain,
or(and(X1,not(X2)),X3) = implies(implies(X1,X2),X3),
inference(spm,[status(thm)],[c_0_39,c_0_33]) ).
cnf(c_0_48,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,or(X2,X2))) ),
inference(spm,[status(thm)],[c_0_38,c_0_44]) ).
cnf(c_0_49,plain,
( is_a_theorem(implies(implies(X1,X2),or(X3,X2)))
| ~ is_a_theorem(or(X3,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_39]),c_0_39]) ).
cnf(c_0_50,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(rw,[status(thm)],[c_0_45,c_0_39]) ).
cnf(c_0_51,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X1,implies(X3,X4)))
| ~ is_a_theorem(implies(implies(X3,X4),X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_33]),c_0_47]) ).
cnf(c_0_52,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(or(X2,X1)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_50]) ).
cnf(c_0_54,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X1,or(X3,X4)))
| ~ is_a_theorem(implies(or(X3,X4),X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_39]) ).
cnf(c_0_55,plain,
is_a_theorem(or(X1,or(not(X1),X2))),
inference(spm,[status(thm)],[c_0_50,c_0_39]) ).
cnf(c_0_56,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(implies(or(not(X1),X3),X2)) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_58,plain,
( is_a_theorem(implies(or(X1,X2),X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_39]) ).
cnf(c_0_59,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_60,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_59]) ).
cnf(c_0_61,plain,
( is_a_theorem(implies(implies(X1,or(X2,X2)),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_60]) ).
fof(c_0_62,plain,
! [X125,X126] :
( ~ op_equiv
| equiv(X125,X126) = and(implies(X125,X126),implies(X126,X125)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])]) ).
cnf(c_0_63,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,or(X1,X1)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_61]) ).
cnf(c_0_64,plain,
( is_a_theorem(implies(X1,or(X2,X3)))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_50]) ).
cnf(c_0_65,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_66,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[luka_op_equiv]) ).
cnf(c_0_67,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_63,c_0_49]) ).
cnf(c_0_68,plain,
( is_a_theorem(or(X1,or(X2,X3)))
| ~ is_a_theorem(or(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_39]),c_0_39]) ).
cnf(c_0_69,plain,
not(and(X1,implies(X2,X3))) = implies(X1,and(X2,not(X3))),
inference(spm,[status(thm)],[c_0_33,c_0_33]) ).
cnf(c_0_70,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66])]) ).
fof(c_0_71,plain,
! [X11,X12] :
( ( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X11,X12))
| X11 = X12 )
& ( 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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_of_equivalents])])])])]) ).
cnf(c_0_72,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(or(X2,X3),X1))
| ~ is_a_theorem(or(X1,X2)) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,plain,
( is_a_theorem(implies(or(X1,X2),X2))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_60,c_0_39]) ).
cnf(c_0_74,plain,
implies(implies(X1,X2),and(X2,not(X1))) = not(equiv(X1,X2)),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_75,plain,
( is_a_theorem(implies(X1,or(X2,X3)))
| ~ is_a_theorem(implies(X1,X4))
| ~ is_a_theorem(implies(X4,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_64]) ).
cnf(c_0_76,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(implies(X3,X1))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_64]) ).
cnf(c_0_77,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_78,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[substitution_of_equivalents]) ).
cnf(c_0_79,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(or(X1,X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_80,plain,
( is_a_theorem(or(equiv(X1,X2),and(X2,not(X1))))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_74]),c_0_39]) ).
cnf(c_0_81,plain,
( is_a_theorem(implies(X1,or(X2,X3)))
| ~ is_a_theorem(implies(or(X1,X4),X2)) ),
inference(spm,[status(thm)],[c_0_75,c_0_50]) ).
cnf(c_0_82,plain,
is_a_theorem(implies(or(or(X1,X1),or(X1,X1)),X1)),
inference(spm,[status(thm)],[c_0_48,c_0_44]) ).
cnf(c_0_83,plain,
( is_a_theorem(or(implies(X1,X2),X3))
| ~ is_a_theorem(implies(X4,X2))
| ~ is_a_theorem(implies(X1,X4)) ),
inference(spm,[status(thm)],[c_0_76,c_0_31]) ).
cnf(c_0_84,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78])]) ).
cnf(c_0_85,plain,
( is_a_theorem(equiv(X1,X2))
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_33]) ).
cnf(c_0_86,plain,
( is_a_theorem(implies(X1,or(X2,X3)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_81,c_0_58]) ).
cnf(c_0_87,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,or(or(X2,X2),or(X2,X2)))) ),
inference(spm,[status(thm)],[c_0_38,c_0_82]) ).
cnf(c_0_88,plain,
( is_a_theorem(or(implies(X1,X2),X3))
| ~ is_a_theorem(implies(X1,or(X2,X2))) ),
inference(spm,[status(thm)],[c_0_83,c_0_44]) ).
cnf(c_0_89,plain,
( X1 = X2
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_90,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_86]) ).
cnf(c_0_91,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,X2)) ),
inference(spm,[status(thm)],[c_0_87,c_0_86]) ).
cnf(c_0_92,plain,
is_a_theorem(or(implies(X1,X1),X2)),
inference(spm,[status(thm)],[c_0_88,c_0_50]) ).
cnf(c_0_93,plain,
( implies(X1,X2) = X2
| ~ is_a_theorem(implies(X2,implies(X1,X2)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_89,c_0_60]) ).
cnf(c_0_94,plain,
is_a_theorem(implies(or(X1,X2),implies(implies(X2,X3),or(X1,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_39]),c_0_39]) ).
cnf(c_0_95,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_48,c_0_50]) ).
cnf(c_0_96,plain,
( X1 = X2
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_97,plain,
is_a_theorem(implies(X1,implies(X2,X2))),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_98,plain,
implies(implies(X1,X1),or(X2,X1)) = or(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95])]) ).
cnf(c_0_99,plain,
or(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_44]),c_0_50])]) ).
cnf(c_0_100,plain,
( X1 = implies(X2,X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_101,plain,
implies(implies(X1,X1),X1) = X1,
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_102,plain,
implies(X1,X1) = implies(X2,X2),
inference(spm,[status(thm)],[c_0_100,c_0_95]) ).
cnf(c_0_103,plain,
implies(implies(X1,X1),X2) = X2,
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_104,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_103]),c_0_97])]) ).
cnf(c_0_105,plain,
is_a_theorem(implies(implies(X1,not(X2)),implies(or(X2,X3),implies(X1,X3)))),
inference(spm,[status(thm)],[c_0_26,c_0_39]) ).
cnf(c_0_106,plain,
( implies(X1,X2) = X2
| ~ is_a_theorem(implies(implies(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_89,c_0_104]) ).
cnf(c_0_107,plain,
is_a_theorem(implies(implies(or(not(X1),X2),X1),X1)),
inference(spm,[status(thm)],[c_0_52,c_0_55]) ).
cnf(c_0_108,plain,
( is_a_theorem(implies(implies(or(X1,X2),X3),X3))
| ~ is_a_theorem(or(X3,X1)) ),
inference(spm,[status(thm)],[c_0_52,c_0_68]) ).
cnf(c_0_109,plain,
is_a_theorem(or(X1,implies(or(X1,X2),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_103]),c_0_103]),c_0_39]) ).
cnf(c_0_110,plain,
implies(or(not(X1),X2),X1) = X1,
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_111,plain,
( implies(or(X1,X2),X3) = X3
| ~ is_a_theorem(or(X3,X1)) ),
inference(spm,[status(thm)],[c_0_106,c_0_108]) ).
cnf(c_0_112,plain,
is_a_theorem(or(not(X1),X1)),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_113,plain,
implies(or(X1,X2),not(X1)) = not(X1),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_114,plain,
implies(X1,not(X1)) = not(X1),
inference(spm,[status(thm)],[c_0_113,c_0_99]) ).
cnf(c_0_115,plain,
( or(X1,X2) = X1
| ~ is_a_theorem(implies(or(X1,X2),X1)) ),
inference(spm,[status(thm)],[c_0_89,c_0_50]) ).
cnf(c_0_116,plain,
or(X1,not(not(X1))) = not(not(X1)),
inference(spm,[status(thm)],[c_0_39,c_0_114]) ).
cnf(c_0_117,plain,
is_a_theorem(implies(and(X1,not(X2)),implies(implies(X1,X2),X3))),
inference(spm,[status(thm)],[c_0_50,c_0_47]) ).
cnf(c_0_118,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_39]),c_0_112])]) ).
cnf(c_0_119,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(or(not(X2),X3),X2))) ),
inference(spm,[status(thm)],[c_0_38,c_0_107]) ).
cnf(c_0_120,plain,
is_a_theorem(implies(and(not(X1),not(X2)),implies(or(X1,X2),X3))),
inference(spm,[status(thm)],[c_0_117,c_0_39]) ).
cnf(c_0_121,plain,
not(and(X1,X2)) = implies(X1,not(X2)),
inference(spm,[status(thm)],[c_0_33,c_0_118]) ).
cnf(c_0_122,plain,
is_a_theorem(implies(and(not(not(X1)),not(X2)),X1)),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_123,plain,
implies(X1,and(not(X2),not(X3))) = not(and(X1,or(X2,X3))),
inference(spm,[status(thm)],[c_0_69,c_0_39]) ).
cnf(c_0_124,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(spm,[status(thm)],[c_0_118,c_0_121]) ).
fof(c_0_125,negated_conjecture,
~ kn2,
inference(assume_negation,[status(cth)],[rosser_kn2]) ).
cnf(c_0_126,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(and(X1,or(not(X2),X3)))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_122]),c_0_123]) ).
cnf(c_0_127,plain,
or(not(X1),X2) = implies(X1,X2),
inference(spm,[status(thm)],[c_0_39,c_0_118]) ).
cnf(c_0_128,plain,
and(X1,not(X2)) = not(implies(X1,X2)),
inference(spm,[status(thm)],[c_0_124,c_0_118]) ).
fof(c_0_129,plain,
! [X73,X74] :
( ( ~ kn2
| is_a_theorem(implies(and(X73,X74),X73)) )
& ( ~ is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0))
| kn2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn2])])])]) ).
fof(c_0_130,negated_conjecture,
~ kn2,
inference(fof_simplification,[status(thm)],[c_0_125]) ).
cnf(c_0_131,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,not(implies(X2,X3)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_127]),c_0_69]),c_0_128]) ).
cnf(c_0_132,plain,
is_a_theorem(or(X1,not(X1))),
inference(spm,[status(thm)],[c_0_95,c_0_39]) ).
cnf(c_0_133,plain,
( kn2
| ~ is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0)) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_134,negated_conjecture,
~ kn2,
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_135,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,and(X2,X3))) ),
inference(spm,[status(thm)],[c_0_131,c_0_124]) ).
cnf(c_0_136,plain,
or(X1,not(X1)) = implies(X2,X2),
inference(spm,[status(thm)],[c_0_100,c_0_132]) ).
cnf(c_0_137,plain,
~ is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0)),
inference(sr,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_138,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_132])]) ).
cnf(c_0_139,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_138])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL481+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : enigmatic-eprover.py %s %d 1
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 07:11:42 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45 # ENIGMATIC: Selected SinE mode:
% 0.19/0.46 # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.19/0.46 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.19/0.46 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 292.01/38.25 # ENIGMATIC: Solved by autoschedule:
% 292.01/38.25 # No SInE strategy applied
% 292.01/38.25 # Trying AutoSched0 for 150 seconds
% 292.01/38.25 # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 292.01/38.25 # and selection function SelectComplexExceptUniqMaxHorn.
% 292.01/38.25 #
% 292.01/38.25 # Preprocessing time : 0.029 s
% 292.01/38.25 # Presaturation interreduction done
% 292.01/38.25
% 292.01/38.25 # Proof found!
% 292.01/38.25 # SZS status Theorem
% 292.01/38.25 # SZS output start CNFRefutation
% See solution above
% 292.01/38.25 # Training examples: 0 positive, 0 negative
% 292.01/38.25
% 292.01/38.25 # -------------------------------------------------
% 292.01/38.25 # User time : 34.359 s
% 292.01/38.25 # System time : 1.292 s
% 292.01/38.25 # Total time : 35.651 s
% 292.01/38.25 # Maximum resident set size: 7120 pages
% 292.01/38.25
%------------------------------------------------------------------------------