TSTP Solution File: LCL528+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL528+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n007.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 06:54:31 EDT 2023
% Result : Theorem 1.19s 1.27s
% Output : CNFRefutation 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 199
% Syntax : Number of formulae : 314 ( 76 unt; 163 typ; 0 def)
% Number of atoms : 280 ( 51 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 217 ( 88 ~; 89 |; 19 &)
% ( 14 <=>; 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 : 16 ( 10 >; 6 *; 0 +; 0 <<)
% Number of predicates : 62 ( 60 usr; 60 prp; 0-2 aty)
% Number of functors : 103 ( 103 usr; 94 con; 0-2 aty)
% Number of variables : 203 ( 12 sgn; 68 !; 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,
necessitation: $o ).
tff(decl_60,type,
necessarily: $i > $i ).
tff(decl_61,type,
modus_ponens_strict_implies: $o ).
tff(decl_62,type,
strict_implies: ( $i * $i ) > $i ).
tff(decl_63,type,
adjunction: $o ).
tff(decl_64,type,
substitution_strict_equiv: $o ).
tff(decl_65,type,
strict_equiv: ( $i * $i ) > $i ).
tff(decl_66,type,
axiom_K: $o ).
tff(decl_67,type,
axiom_M: $o ).
tff(decl_68,type,
axiom_4: $o ).
tff(decl_69,type,
axiom_B: $o ).
tff(decl_70,type,
possibly: $i > $i ).
tff(decl_71,type,
axiom_5: $o ).
tff(decl_72,type,
axiom_s1: $o ).
tff(decl_73,type,
axiom_s2: $o ).
tff(decl_74,type,
axiom_s3: $o ).
tff(decl_75,type,
axiom_s4: $o ).
tff(decl_76,type,
axiom_m1: $o ).
tff(decl_77,type,
axiom_m2: $o ).
tff(decl_78,type,
axiom_m3: $o ).
tff(decl_79,type,
axiom_m4: $o ).
tff(decl_80,type,
axiom_m5: $o ).
tff(decl_81,type,
axiom_m6: $o ).
tff(decl_82,type,
axiom_m7: $o ).
tff(decl_83,type,
axiom_m8: $o ).
tff(decl_84,type,
axiom_m9: $o ).
tff(decl_85,type,
axiom_m10: $o ).
tff(decl_86,type,
op_possibly: $o ).
tff(decl_87,type,
op_necessarily: $o ).
tff(decl_88,type,
op_strict_implies: $o ).
tff(decl_89,type,
op_strict_equiv: $o ).
tff(decl_90,type,
op_implies: $o ).
tff(decl_91,type,
esk1_0: $i ).
tff(decl_92,type,
esk2_0: $i ).
tff(decl_93,type,
esk3_0: $i ).
tff(decl_94,type,
esk4_0: $i ).
tff(decl_95,type,
esk5_0: $i ).
tff(decl_96,type,
esk6_0: $i ).
tff(decl_97,type,
esk7_0: $i ).
tff(decl_98,type,
esk8_0: $i ).
tff(decl_99,type,
esk9_0: $i ).
tff(decl_100,type,
esk10_0: $i ).
tff(decl_101,type,
esk11_0: $i ).
tff(decl_102,type,
esk12_0: $i ).
tff(decl_103,type,
esk13_0: $i ).
tff(decl_104,type,
esk14_0: $i ).
tff(decl_105,type,
esk15_0: $i ).
tff(decl_106,type,
esk16_0: $i ).
tff(decl_107,type,
esk17_0: $i ).
tff(decl_108,type,
esk18_0: $i ).
tff(decl_109,type,
esk19_0: $i ).
tff(decl_110,type,
esk20_0: $i ).
tff(decl_111,type,
esk21_0: $i ).
tff(decl_112,type,
esk22_0: $i ).
tff(decl_113,type,
esk23_0: $i ).
tff(decl_114,type,
esk24_0: $i ).
tff(decl_115,type,
esk25_0: $i ).
tff(decl_116,type,
esk26_0: $i ).
tff(decl_117,type,
esk27_0: $i ).
tff(decl_118,type,
esk28_0: $i ).
tff(decl_119,type,
esk29_0: $i ).
tff(decl_120,type,
esk30_0: $i ).
tff(decl_121,type,
esk31_0: $i ).
tff(decl_122,type,
esk32_0: $i ).
tff(decl_123,type,
esk33_0: $i ).
tff(decl_124,type,
esk34_0: $i ).
tff(decl_125,type,
esk35_0: $i ).
tff(decl_126,type,
esk36_0: $i ).
tff(decl_127,type,
esk37_0: $i ).
tff(decl_128,type,
esk38_0: $i ).
tff(decl_129,type,
esk39_0: $i ).
tff(decl_130,type,
esk40_0: $i ).
tff(decl_131,type,
esk41_0: $i ).
tff(decl_132,type,
esk42_0: $i ).
tff(decl_133,type,
esk43_0: $i ).
tff(decl_134,type,
esk44_0: $i ).
tff(decl_135,type,
esk45_0: $i ).
tff(decl_136,type,
esk46_0: $i ).
tff(decl_137,type,
esk47_0: $i ).
tff(decl_138,type,
esk48_0: $i ).
tff(decl_139,type,
esk49_0: $i ).
tff(decl_140,type,
esk50_0: $i ).
tff(decl_141,type,
esk51_0: $i ).
tff(decl_142,type,
esk52_0: $i ).
tff(decl_143,type,
esk53_0: $i ).
tff(decl_144,type,
esk54_0: $i ).
tff(decl_145,type,
esk55_0: $i ).
tff(decl_146,type,
esk56_0: $i ).
tff(decl_147,type,
esk57_0: $i ).
tff(decl_148,type,
esk58_0: $i ).
tff(decl_149,type,
esk59_0: $i ).
tff(decl_150,type,
esk60_0: $i ).
tff(decl_151,type,
esk61_0: $i ).
tff(decl_152,type,
esk62_0: $i ).
tff(decl_153,type,
esk63_0: $i ).
tff(decl_154,type,
esk64_0: $i ).
tff(decl_155,type,
esk65_0: $i ).
tff(decl_156,type,
esk66_0: $i ).
tff(decl_157,type,
esk67_0: $i ).
tff(decl_158,type,
esk68_0: $i ).
tff(decl_159,type,
esk69_0: $i ).
tff(decl_160,type,
esk70_0: $i ).
tff(decl_161,type,
esk71_0: $i ).
tff(decl_162,type,
esk72_0: $i ).
tff(decl_163,type,
esk73_0: $i ).
tff(decl_164,type,
esk74_0: $i ).
tff(decl_165,type,
esk75_0: $i ).
tff(decl_166,type,
esk76_0: $i ).
tff(decl_167,type,
esk77_0: $i ).
tff(decl_168,type,
esk78_0: $i ).
tff(decl_169,type,
esk79_0: $i ).
tff(decl_170,type,
esk80_0: $i ).
tff(decl_171,type,
esk81_0: $i ).
tff(decl_172,type,
esk82_0: $i ).
tff(decl_173,type,
esk83_0: $i ).
tff(decl_174,type,
esk84_0: $i ).
tff(decl_175,type,
esk85_0: $i ).
tff(decl_176,type,
esk86_0: $i ).
tff(decl_177,type,
esk87_0: $i ).
tff(decl_178,type,
esk88_0: $i ).
tff(decl_179,type,
esk89_0: $i ).
tff(decl_180,type,
esk90_0: $i ).
tff(decl_181,type,
esk91_0: $i ).
tff(decl_182,type,
esk92_0: $i ).
tff(decl_183,type,
esk93_0: $i ).
tff(decl_184,type,
esk94_0: $i ).
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(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(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(hilbert_implies_2,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
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(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(hilbert_and_1,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_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(hilbert_op_implies_and,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
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_op_or,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_op_or) ).
fof(modus_tollens,axiom,
( modus_tollens
<=> ! [X1,X2] : is_a_theorem(implies(implies(not(X2),not(X1)),implies(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
fof(hilbert_or_1,axiom,
or_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_or_1) ).
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(hilbert_modus_tollens,axiom,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_tollens) ).
fof(hilbert_implies_1,axiom,
implies_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_1) ).
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(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(hilbert_and_2,axiom,
and_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_2) ).
fof(necessitation,axiom,
( necessitation
<=> ! [X1] :
( is_a_theorem(X1)
=> is_a_theorem(necessarily(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',necessitation) ).
fof(km5_axiom_M,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_axiom_M) ).
fof(km5_necessitation,axiom,
necessitation,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_necessitation) ).
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(op_strict_implies,axiom,
( op_strict_implies
=> ! [X1,X2] : strict_implies(X1,X2) = necessarily(implies(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
fof(km5_axiom_5,axiom,
axiom_5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax',km5_axiom_5) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(implies_3,axiom,
( implies_3
<=> ! [X1,X2,X3] : is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_3) ).
fof(hilbert_implies_3,axiom,
implies_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_3) ).
fof(axiom_m1,axiom,
( axiom_m1
<=> ! [X1,X2] : is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax',axiom_m1) ).
fof(s1_0_axiom_m1,conjecture,
axiom_m1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m1) ).
fof(c_0_36,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_37,plain,
! [X41,X42] :
( ( ~ and_3
| is_a_theorem(implies(X41,implies(X42,and(X41,X42)))) )
& ( ~ 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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_3])])])]) ).
fof(c_0_38,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])])])])]) ).
fof(c_0_39,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_40,plain,
( is_a_theorem(X2)
| ~ modus_ponens
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,plain,
modus_ponens,
inference(split_conjunct,[status(thm)],[hilbert_modus_ponens]) ).
cnf(c_0_42,plain,
( is_a_theorem(implies(X1,implies(X2,and(X1,X2))))
| ~ and_3 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,plain,
and_3,
inference(split_conjunct,[status(thm)],[hilbert_and_3]) ).
fof(c_0_44,plain,
! [X23,X24] :
( ( ~ implies_2
| is_a_theorem(implies(implies(X23,implies(X23,X24)),implies(X23,X24))) )
& ( ~ 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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_2])])])]) ).
cnf(c_0_45,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
substitution_of_equivalents,
inference(split_conjunct,[status(thm)],[substitution_of_equivalents]) ).
cnf(c_0_47,plain,
( equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1))
| ~ op_equiv ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,plain,
op_equiv,
inference(split_conjunct,[status(thm)],[hilbert_op_equiv]) ).
cnf(c_0_49,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_40,c_0_41])]) ).
cnf(c_0_50,plain,
is_a_theorem(implies(X1,implies(X2,and(X1,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).
cnf(c_0_51,plain,
( is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))
| ~ implies_2 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,plain,
implies_2,
inference(split_conjunct,[status(thm)],[hilbert_implies_2]) ).
cnf(c_0_53,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
cnf(c_0_54,plain,
equiv(X1,X2) = and(implies(X1,X2),implies(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
cnf(c_0_55,plain,
( is_a_theorem(implies(X1,and(X2,X1)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
fof(c_0_57,plain,
! [X33,X34] :
( ( ~ and_1
| is_a_theorem(implies(and(X33,X34),X33)) )
& ( ~ is_a_theorem(implies(and(esk14_0,esk15_0),esk14_0))
| and_1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_1])])])]) ).
fof(c_0_58,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_59,plain,
( X1 = X2
| ~ is_a_theorem(and(implies(X1,X2),implies(X2,X1))) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_55]) ).
cnf(c_0_61,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_49,c_0_56]) ).
cnf(c_0_62,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ and_1 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_63,plain,
and_1,
inference(split_conjunct,[status(thm)],[hilbert_and_1]) ).
fof(c_0_64,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_65,plain,
( implies(X1,X2) = not(and(X1,not(X2)))
| ~ op_implies_and ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_66,plain,
op_implies_and,
inference(split_conjunct,[status(thm)],[hilbert_op_implies_and]) ).
fof(c_0_67,plain,
! [X45,X46] :
( ( ~ or_1
| is_a_theorem(implies(X45,or(X45,X46))) )
& ( ~ is_a_theorem(implies(esk20_0,or(esk20_0,esk21_0)))
| or_1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[or_1])])])]) ).
cnf(c_0_68,plain,
( X1 = X2
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_69,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(spm,[status(thm)],[c_0_61,c_0_50]) ).
cnf(c_0_70,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]) ).
cnf(c_0_71,plain,
( or(X1,X2) = not(and(not(X1),not(X2)))
| ~ op_or ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_72,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66])]) ).
cnf(c_0_73,plain,
op_or,
inference(split_conjunct,[status(thm)],[hilbert_op_or]) ).
fof(c_0_74,plain,
! [X15,X16] :
( ( ~ modus_tollens
| is_a_theorem(implies(implies(not(X16),not(X15)),implies(X15,X16))) )
& ( ~ is_a_theorem(implies(implies(not(esk6_0),not(esk5_0)),implies(esk5_0,esk6_0)))
| modus_tollens ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_tollens])])])]) ).
cnf(c_0_75,plain,
( is_a_theorem(implies(X1,or(X1,X2)))
| ~ or_1 ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_76,plain,
or_1,
inference(split_conjunct,[status(thm)],[hilbert_or_1]) ).
fof(c_0_77,plain,
! [X19,X20] :
( ( ~ implies_1
| is_a_theorem(implies(X19,implies(X20,X19))) )
& ( ~ is_a_theorem(implies(esk7_0,implies(esk8_0,esk7_0)))
| implies_1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_1])])])]) ).
cnf(c_0_78,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70])]) ).
cnf(c_0_79,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).
cnf(c_0_80,plain,
( is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))
| ~ modus_tollens ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_81,plain,
modus_tollens,
inference(split_conjunct,[status(thm)],[hilbert_modus_tollens]) ).
cnf(c_0_82,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76])]) ).
cnf(c_0_83,plain,
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ implies_1 ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_84,plain,
implies_1,
inference(split_conjunct,[status(thm)],[hilbert_implies_1]) ).
cnf(c_0_85,plain,
not(not(X1)) = or(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_78]),c_0_79]) ).
cnf(c_0_86,plain,
is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_79]),c_0_81])]) ).
cnf(c_0_87,plain,
is_a_theorem(or(X1,or(not(X1),X2))),
inference(spm,[status(thm)],[c_0_82,c_0_79]) ).
fof(c_0_88,plain,
! [X37,X38] :
( ( ~ and_2
| is_a_theorem(implies(and(X37,X38),X38)) )
& ( ~ is_a_theorem(implies(and(esk16_0,esk17_0),esk17_0))
| and_2 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_2])])])]) ).
cnf(c_0_89,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84])]) ).
fof(c_0_90,plain,
! [X145] :
( ( ~ axiom_M
| is_a_theorem(implies(necessarily(X145),X145)) )
& ( ~ is_a_theorem(implies(necessarily(esk65_0),esk65_0))
| axiom_M ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_M])])])]) ).
cnf(c_0_91,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_82,c_0_85]) ).
cnf(c_0_92,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_49,c_0_86]) ).
cnf(c_0_93,plain,
is_a_theorem(or(X1,not(not(not(X1))))),
inference(spm,[status(thm)],[c_0_87,c_0_85]) ).
cnf(c_0_94,plain,
( is_a_theorem(implies(and(X1,X2),X2))
| ~ and_2 ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_95,plain,
and_2,
inference(split_conjunct,[status(thm)],[hilbert_and_2]) ).
cnf(c_0_96,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_89]) ).
fof(c_0_97,plain,
! [X127] :
( ( ~ necessitation
| ~ is_a_theorem(X127)
| is_a_theorem(necessarily(X127)) )
& ( is_a_theorem(esk56_0)
| necessitation )
& ( ~ is_a_theorem(necessarily(esk56_0))
| necessitation ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[necessitation])])])])]) ).
cnf(c_0_98,plain,
( is_a_theorem(implies(necessarily(X1),X1))
| ~ axiom_M ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_99,plain,
axiom_M,
inference(split_conjunct,[status(thm)],[km5_axiom_M]) ).
cnf(c_0_100,plain,
( not(not(X1)) = X1
| ~ is_a_theorem(or(not(X1),X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_91]),c_0_79]) ).
cnf(c_0_101,plain,
is_a_theorem(or(not(X1),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_79]) ).
cnf(c_0_102,plain,
is_a_theorem(implies(and(X1,X2),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95])]) ).
cnf(c_0_103,plain,
( X1 = X2
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_96]) ).
cnf(c_0_104,plain,
( is_a_theorem(necessarily(X1))
| ~ necessitation
| ~ is_a_theorem(X1) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_105,plain,
necessitation,
inference(split_conjunct,[status(thm)],[km5_necessitation]) ).
fof(c_0_106,plain,
! [X151] :
( ( ~ axiom_5
| is_a_theorem(implies(possibly(X151),necessarily(possibly(X151)))) )
& ( ~ is_a_theorem(implies(possibly(esk68_0),necessarily(possibly(esk68_0))))
| axiom_5 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_5])])])]) ).
cnf(c_0_107,plain,
is_a_theorem(implies(necessarily(X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_99])]) ).
fof(c_0_108,plain,
! [X207,X208] :
( ~ op_strict_implies
| strict_implies(X207,X208) = necessarily(implies(X207,X208)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_implies])])]) ).
cnf(c_0_109,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_101])]) ).
cnf(c_0_110,plain,
( and(X1,X2) = X2
| ~ is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_55]),c_0_102])]) ).
cnf(c_0_111,plain,
( X1 = X2
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_103,c_0_96]) ).
cnf(c_0_112,plain,
( is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_104,c_0_105])]) ).
cnf(c_0_113,plain,
( is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))
| ~ axiom_5 ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_114,plain,
axiom_5,
inference(split_conjunct,[status(thm)],[km5_axiom_5]) ).
cnf(c_0_115,plain,
( necessarily(X1) = X1
| ~ is_a_theorem(necessarily(X1)) ),
inference(spm,[status(thm)],[c_0_103,c_0_107]) ).
cnf(c_0_116,plain,
( strict_implies(X1,X2) = necessarily(implies(X1,X2))
| ~ op_strict_implies ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_117,plain,
op_strict_implies,
inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(c_0_118,plain,
not(and(X1,X2)) = implies(X1,not(X2)),
inference(spm,[status(thm)],[c_0_72,c_0_109]) ).
cnf(c_0_119,plain,
and(implies(X1,X1),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_69]),c_0_78]) ).
cnf(c_0_120,plain,
( necessarily(X1) = X2
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_121,plain,
is_a_theorem(implies(possibly(X1),necessarily(possibly(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114])]) ).
cnf(c_0_122,plain,
( implies(X1,X1) = X2
| ~ is_a_theorem(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_69]),c_0_78]) ).
cnf(c_0_123,plain,
( necessarily(X1) = X1
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_115,c_0_112]) ).
cnf(c_0_124,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_117])]) ).
fof(c_0_125,plain,
! [X27,X28,X29] :
( ( ~ implies_3
| is_a_theorem(implies(implies(X27,X28),implies(implies(X28,X29),implies(X27,X29)))) )
& ( ~ is_a_theorem(implies(implies(esk11_0,esk12_0),implies(implies(esk12_0,esk13_0),implies(esk11_0,esk13_0))))
| implies_3 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_3])])])]) ).
cnf(c_0_126,plain,
implies(implies(X1,X1),not(X2)) = not(X2),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_127,plain,
( necessarily(X1) = implies(and(X2,X3),X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_120,c_0_70]) ).
cnf(c_0_128,plain,
necessarily(possibly(X1)) = possibly(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_121]),c_0_107])]) ).
cnf(c_0_129,plain,
implies(X1,X1) = implies(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_69]),c_0_78]) ).
cnf(c_0_130,plain,
strict_implies(X1,X1) = implies(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_69]),c_0_78]),c_0_124]),c_0_78]) ).
cnf(c_0_131,plain,
( is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))))
| ~ implies_3 ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_132,plain,
implies_3,
inference(split_conjunct,[status(thm)],[hilbert_implies_3]) ).
cnf(c_0_133,plain,
( implies(X1,and(X2,X1)) = X2
| ~ is_a_theorem(implies(implies(X1,and(X2,X1)),X2)) ),
inference(spm,[status(thm)],[c_0_68,c_0_50]) ).
cnf(c_0_134,plain,
implies(implies(X1,X1),X2) = X2,
inference(spm,[status(thm)],[c_0_126,c_0_109]) ).
cnf(c_0_135,plain,
implies(and(X1,X2),X1) = implies(esk1_0,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_121]),c_0_128]),c_0_129]),c_0_124]),c_0_130]) ).
cnf(c_0_136,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_61,c_0_89]) ).
cnf(c_0_137,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_131,c_0_132])]) ).
cnf(c_0_138,plain,
and(X1,implies(X2,X2)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135]),c_0_136])]) ).
cnf(c_0_139,plain,
( implies(implies(X1,X2),implies(X3,X2)) = implies(X3,X1)
| ~ is_a_theorem(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X3,X1))) ),
inference(spm,[status(thm)],[c_0_68,c_0_137]) ).
cnf(c_0_140,plain,
implies(X1,not(implies(X2,X2))) = not(X1),
inference(spm,[status(thm)],[c_0_118,c_0_138]) ).
fof(c_0_141,plain,
! [X169,X170] :
( ( ~ axiom_m1
| is_a_theorem(strict_implies(and(X169,X170),and(X170,X169))) )
& ( ~ is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0)))
| axiom_m1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m1])])])]) ).
fof(c_0_142,negated_conjecture,
~ axiom_m1,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[s1_0_axiom_m1])]) ).
cnf(c_0_143,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(spm,[status(thm)],[c_0_109,c_0_118]) ).
cnf(c_0_144,plain,
or(X1,not(X2)) = implies(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_140]),c_0_79]),c_0_140]),c_0_79]),c_0_86])]) ).
cnf(c_0_145,plain,
( axiom_m1
| ~ is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0))) ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_146,negated_conjecture,
~ axiom_m1,
inference(split_conjunct,[status(thm)],[c_0_142]) ).
cnf(c_0_147,plain,
and(not(X1),X2) = not(implies(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_79]),c_0_144]) ).
cnf(c_0_148,plain,
~ is_a_theorem(strict_implies(and(esk77_0,esk78_0),and(esk78_0,esk77_0))),
inference(sr,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_149,plain,
and(X1,X2) = and(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_109]),c_0_143]) ).
cnf(c_0_150,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_130]),c_0_136])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL528+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Aug 24 19:12:40 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.56 start to proof: theBenchmark
% 1.19/1.27 % Version : CSE_E---1.5
% 1.19/1.27 % Problem : theBenchmark.p
% 1.19/1.27 % Proof found
% 1.19/1.27 % SZS status Theorem for theBenchmark.p
% 1.19/1.27 % SZS output start Proof
% See solution above
% 1.19/1.28 % Total time : 0.693000 s
% 1.19/1.28 % SZS output end Proof
% 1.19/1.28 % Total time : 0.698000 s
%------------------------------------------------------------------------------