TSTP Solution File: LCL518+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL518+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n001.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 : 300s
% DateTime : Thu Aug 31 06:54:28 EDT 2023
% Result : Theorem 0.19s 0.61s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 114
% Syntax : Number of formulae : 190 ( 46 unt; 92 typ; 0 def)
% Number of atoms : 179 ( 36 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 139 ( 58 ~; 58 |; 10 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 34 ( 32 usr; 32 prp; 0-2 aty)
% Number of functors : 60 ( 60 usr; 55 con; 0-2 aty)
% Number of variables : 141 ( 6 sgn; 42 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
modus_ponens: $o ).
tff(decl_23,type,
is_a_theorem: $i > $o ).
tff(decl_24,type,
implies: ( $i * $i ) > $i ).
tff(decl_25,type,
substitution_of_equivalents: $o ).
tff(decl_26,type,
equiv: ( $i * $i ) > $i ).
tff(decl_27,type,
modus_tollens: $o ).
tff(decl_28,type,
not: $i > $i ).
tff(decl_29,type,
implies_1: $o ).
tff(decl_30,type,
implies_2: $o ).
tff(decl_31,type,
implies_3: $o ).
tff(decl_32,type,
and_1: $o ).
tff(decl_33,type,
and: ( $i * $i ) > $i ).
tff(decl_34,type,
and_2: $o ).
tff(decl_35,type,
and_3: $o ).
tff(decl_36,type,
or_1: $o ).
tff(decl_37,type,
or: ( $i * $i ) > $i ).
tff(decl_38,type,
or_2: $o ).
tff(decl_39,type,
or_3: $o ).
tff(decl_40,type,
equivalence_1: $o ).
tff(decl_41,type,
equivalence_2: $o ).
tff(decl_42,type,
equivalence_3: $o ).
tff(decl_43,type,
kn1: $o ).
tff(decl_44,type,
kn2: $o ).
tff(decl_45,type,
kn3: $o ).
tff(decl_46,type,
cn1: $o ).
tff(decl_47,type,
cn2: $o ).
tff(decl_48,type,
cn3: $o ).
tff(decl_49,type,
r1: $o ).
tff(decl_50,type,
r2: $o ).
tff(decl_51,type,
r3: $o ).
tff(decl_52,type,
r4: $o ).
tff(decl_53,type,
r5: $o ).
tff(decl_54,type,
op_or: $o ).
tff(decl_55,type,
op_and: $o ).
tff(decl_56,type,
op_implies_and: $o ).
tff(decl_57,type,
op_implies_or: $o ).
tff(decl_58,type,
op_equiv: $o ).
tff(decl_59,type,
esk1_0: $i ).
tff(decl_60,type,
esk2_0: $i ).
tff(decl_61,type,
esk3_0: $i ).
tff(decl_62,type,
esk4_0: $i ).
tff(decl_63,type,
esk5_0: $i ).
tff(decl_64,type,
esk6_0: $i ).
tff(decl_65,type,
esk7_0: $i ).
tff(decl_66,type,
esk8_0: $i ).
tff(decl_67,type,
esk9_0: $i ).
tff(decl_68,type,
esk10_0: $i ).
tff(decl_69,type,
esk11_0: $i ).
tff(decl_70,type,
esk12_0: $i ).
tff(decl_71,type,
esk13_0: $i ).
tff(decl_72,type,
esk14_0: $i ).
tff(decl_73,type,
esk15_0: $i ).
tff(decl_74,type,
esk16_0: $i ).
tff(decl_75,type,
esk17_0: $i ).
tff(decl_76,type,
esk18_0: $i ).
tff(decl_77,type,
esk19_0: $i ).
tff(decl_78,type,
esk20_0: $i ).
tff(decl_79,type,
esk21_0: $i ).
tff(decl_80,type,
esk22_0: $i ).
tff(decl_81,type,
esk23_0: $i ).
tff(decl_82,type,
esk24_0: $i ).
tff(decl_83,type,
esk25_0: $i ).
tff(decl_84,type,
esk26_0: $i ).
tff(decl_85,type,
esk27_0: $i ).
tff(decl_86,type,
esk28_0: $i ).
tff(decl_87,type,
esk29_0: $i ).
tff(decl_88,type,
esk30_0: $i ).
tff(decl_89,type,
esk31_0: $i ).
tff(decl_90,type,
esk32_0: $i ).
tff(decl_91,type,
esk33_0: $i ).
tff(decl_92,type,
esk34_0: $i ).
tff(decl_93,type,
esk35_0: $i ).
tff(decl_94,type,
esk36_0: $i ).
tff(decl_95,type,
esk37_0: $i ).
tff(decl_96,type,
esk38_0: $i ).
tff(decl_97,type,
esk39_0: $i ).
tff(decl_98,type,
esk40_0: $i ).
tff(decl_99,type,
esk41_0: $i ).
tff(decl_100,type,
esk42_0: $i ).
tff(decl_101,type,
esk43_0: $i ).
tff(decl_102,type,
esk44_0: $i ).
tff(decl_103,type,
esk45_0: $i ).
tff(decl_104,type,
esk46_0: $i ).
tff(decl_105,type,
esk47_0: $i ).
tff(decl_106,type,
esk48_0: $i ).
tff(decl_107,type,
esk49_0: $i ).
tff(decl_108,type,
esk50_0: $i ).
tff(decl_109,type,
esk51_0: $i ).
tff(decl_110,type,
esk52_0: $i ).
tff(decl_111,type,
esk53_0: $i ).
tff(decl_112,type,
esk54_0: $i ).
tff(decl_113,type,
esk55_0: $i ).
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(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_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(principia_op_implies_or,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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(rosser_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_op_implies_and) ).
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(kn2,axiom,
( kn2
<=> ! [X4,X5] : is_a_theorem(implies(and(X4,X5),X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn2) ).
fof(principia_op_and,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).
fof(rosser_op_or,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_op_or) ).
fof(rosser_modus_ponens,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_modus_ponens) ).
fof(rosser_kn2,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn2) ).
fof(kn1,axiom,
( kn1
<=> ! [X4] : is_a_theorem(implies(X4,and(X4,X4))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn1) ).
fof(rosser_kn1,axiom,
kn1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn1) ).
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(rosser_op_equiv,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_op_equiv) ).
fof(kn3,axiom,
( kn3
<=> ! [X4,X5,X6] : is_a_theorem(implies(implies(X4,X5),implies(not(and(X5,X6)),not(and(X6,X4))))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn3) ).
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(rosser_kn3,axiom,
kn3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn3) ).
fof(substitution_of_equivalents_001,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',substitution_of_equivalents) ).
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_r1,conjecture,
r1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r1) ).
fof(c_0_22,plain,
! [X123,X124] :
( ~ op_implies_or
| implies(X123,X124) = or(not(X123),X124) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_or])])]) ).
fof(c_0_23,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])])]) ).
fof(c_0_24,plain,
! [X119,X120] :
( ~ op_and
| and(X119,X120) = not(or(not(X119),not(X120))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_and])])]) ).
cnf(c_0_25,plain,
( implies(X1,X2) = or(not(X1),X2)
| ~ op_implies_or ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,plain,
op_implies_or,
inference(split_conjunct,[status(thm)],[principia_op_implies_or]) ).
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_23]) ).
cnf(c_0_29,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[rosser_op_implies_and]) ).
fof(c_0_30,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_31,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])])])]) ).
cnf(c_0_32,plain,
( and(X1,X2) = not(or(not(X1),not(X2)))
| ~ op_and ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
or(not(X1),X2) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).
cnf(c_0_34,plain,
op_and,
inference(split_conjunct,[status(thm)],[principia_op_and]) ).
cnf(c_0_35,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,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_37,plain,
op_or,
inference(split_conjunct,[status(thm)],[rosser_op_or]) ).
cnf(c_0_38,plain,
( is_a_theorem(X2)
| ~ modus_ponens
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[rosser_modus_ponens]) ).
cnf(c_0_40,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ kn2 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,plain,
kn2,
inference(split_conjunct,[status(thm)],[rosser_kn2]) ).
cnf(c_0_42,plain,
not(implies(X1,not(X2))) = and(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_43,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
fof(c_0_44,plain,
! [X71] :
( ( ~ kn1
| is_a_theorem(implies(X71,and(X71,X71))) )
& ( ~ is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0)))
| kn1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn1])])])]) ).
cnf(c_0_45,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_46,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]) ).
cnf(c_0_47,plain,
not(or(X1,not(X2))) = and(not(X1),X2),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,plain,
( is_a_theorem(implies(X1,and(X1,X1)))
| ~ kn1 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_49,plain,
kn1,
inference(split_conjunct,[status(thm)],[rosser_kn1]) ).
cnf(c_0_50,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(and(X1,X2)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,plain,
and(not(not(X1)),X2) = and(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_33]),c_0_42]) ).
cnf(c_0_52,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]) ).
cnf(c_0_53,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(and(X1,X2)) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,plain,
( is_a_theorem(and(X1,X1))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_52]) ).
fof(c_0_55,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_56,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_58,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[rosser_op_equiv]) ).
cnf(c_0_59,plain,
or(and(X1,X2),X3) = implies(implies(X1,not(X2)),X3),
inference(spm,[status(thm)],[c_0_33,c_0_42]) ).
fof(c_0_60,plain,
! [X77,X78,X79] :
( ( ~ kn3
| is_a_theorem(implies(implies(X77,X78),implies(not(and(X78,X79)),not(and(X79,X77))))) )
& ( ~ is_a_theorem(implies(implies(esk36_0,esk37_0),implies(not(and(esk37_0,esk38_0)),not(and(esk38_0,esk36_0)))))
| kn3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn3])])])]) ).
fof(c_0_61,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_62,plain,
( is_a_theorem(not(implies(X1,X2)))
| ~ is_a_theorem(and(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_56,c_0_36]) ).
cnf(c_0_63,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).
cnf(c_0_64,plain,
and(X1,implies(X2,not(X3))) = not(implies(X1,and(X2,X3))),
inference(spm,[status(thm)],[c_0_42,c_0_42]) ).
cnf(c_0_65,plain,
implies(implies(X1,not(not(X2))),X3) = implies(implies(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_36]),c_0_59]) ).
cnf(c_0_66,plain,
( is_a_theorem(implies(implies(X1,X2),implies(not(and(X2,X3)),not(and(X3,X1)))))
| ~ kn3 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_67,plain,
kn3,
inference(split_conjunct,[status(thm)],[rosser_kn3]) ).
cnf(c_0_68,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_69,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[substitution_of_equivalents]) ).
cnf(c_0_70,plain,
( is_a_theorem(not(implies(X1,and(X2,not(X3)))))
| ~ is_a_theorem(and(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_62,c_0_36]) ).
cnf(c_0_71,plain,
not(implies(or(X1,X2),and(X2,X1))) = equiv(not(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_43]),c_0_64]) ).
cnf(c_0_72,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_45,c_0_65]) ).
cnf(c_0_73,plain,
is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_43]),c_0_67])]) ).
cnf(c_0_74,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69])]) ).
cnf(c_0_75,plain,
( is_a_theorem(equiv(not(not(X1)),X2))
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_33]),c_0_63]) ).
cnf(c_0_76,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(and(X2,X3),X2),X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_46]),c_0_51]) ).
cnf(c_0_77,plain,
( is_a_theorem(implies(implies(X1,not(X2)),not(and(X2,X3))))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_73]),c_0_59]) ).
cnf(c_0_78,plain,
( not(not(X1)) = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_79,plain,
( is_a_theorem(equiv(X1,X1))
| ~ is_a_theorem(implies(X1,X1)) ),
inference(spm,[status(thm)],[c_0_54,c_0_63]) ).
cnf(c_0_80,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(implies(X2,and(not(X1),X3))) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_81,plain,
( not(not(X1)) = X1
| ~ is_a_theorem(implies(X1,X1)) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_82,plain,
is_a_theorem(implies(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_52]),c_0_36]) ).
cnf(c_0_83,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82])]) ).
cnf(c_0_84,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,X2),X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_82]),c_0_43]),c_0_33]) ).
cnf(c_0_85,plain,
not(and(X1,X2)) = implies(X1,not(X2)),
inference(spm,[status(thm)],[c_0_36,c_0_83]) ).
fof(c_0_86,plain,
! [X95] :
( ( ~ r1
| is_a_theorem(implies(or(X95,X95),X95)) )
& ( ~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0))
| r1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r1])])])]) ).
fof(c_0_87,negated_conjecture,
~ r1,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[principia_r1])]) ).
cnf(c_0_88,plain,
( is_a_theorem(implies(X1,not(X2)))
| ~ is_a_theorem(implies(X2,not(X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_77]),c_0_85]) ).
cnf(c_0_89,plain,
is_a_theorem(or(X1,and(not(X1),not(X1)))),
inference(spm,[status(thm)],[c_0_52,c_0_43]) ).
cnf(c_0_90,plain,
and(X1,not(X2)) = not(implies(X1,X2)),
inference(spm,[status(thm)],[c_0_42,c_0_83]) ).
cnf(c_0_91,plain,
( r1
| ~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0)) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_92,negated_conjecture,
~ r1,
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_93,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,not(X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_43]),c_0_83]) ).
cnf(c_0_94,plain,
is_a_theorem(or(X1,not(or(X1,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_43]) ).
cnf(c_0_95,plain,
~ is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0)),
inference(sr,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_96,plain,
is_a_theorem(implies(or(X1,X1),X1)),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_97,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_96])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL518+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.34 % Computer : n001.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Thu Aug 24 20:09:56 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.19/0.53 start to proof: theBenchmark
% 0.19/0.61 % Version : CSE_E---1.5
% 0.19/0.61 % Problem : theBenchmark.p
% 0.19/0.61 % Proof found
% 0.19/0.61 % SZS status Theorem for theBenchmark.p
% 0.19/0.61 % SZS output start Proof
% See solution above
% 0.19/0.62 % Total time : 0.069000 s
% 0.19/0.62 % SZS output end Proof
% 0.19/0.62 % Total time : 0.073000 s
%------------------------------------------------------------------------------