%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : LCL535+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 11:44:57 AM UTC 2026
% Result : Theorem 13.46s 3.95s
% Output : CNFRefutation 13.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 34
% Syntax : Number of clauses : 109 ( 64 unt; 0 nHn; 55 RR)
% Number of literals : 165 ( 29 equ; 60 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 18 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 114 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_96,plain,
( is_a_theorem(X1)
| ~ modus_ponens
| ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(X2,X1)) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_96) ).
cnf(i_0_68,plain,
modus_ponens,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_68) ).
cnf(i_0_10,plain,
( is_a_theorem(implies(X1,implies(X2,and(X1,X2))))
| ~ and_3 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_10) ).
cnf(i_0_61,plain,
and_3,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_61) ).
cnf(i_0_139,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_139) ).
cnf(i_0_143,plain,
substitution_of_equivalents,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_143) ).
cnf(i_0_107,plain,
( and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2)
| ~ op_equiv ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_107) ).
cnf(i_0_70,plain,
op_equiv,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_70) ).
cnf(i_0_79,plain,
( is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))
| ~ implies_2 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_79) ).
cnf(i_0_66,plain,
implies_2,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_66) ).
cnf(i_0_6,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ and_1 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_6) ).
cnf(i_0_59,plain,
and_1,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_59) ).
cnf(i_0_108,plain,
( not(and(X1,not(X2))) = implies(X1,X2)
| ~ op_implies_and ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_108) ).
cnf(i_0_71,plain,
op_implies_and,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_71) ).
cnf(i_0_111,plain,
( not(and(not(X1),not(X2))) = or(X1,X2)
| ~ op_or ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_111) ).
cnf(i_0_72,plain,
op_or,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_72) ).
cnf(i_0_116,plain,
( is_a_theorem(implies(X1,or(X1,X2)))
| ~ or_1 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_116) ).
cnf(i_0_73,plain,
or_1,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_73) ).
cnf(i_0_112,plain,
( not(necessarily(not(X1))) = possibly(X1)
| ~ op_possibly ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_112) ).
cnf(i_0_86,plain,
op_possibly,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_86) ).
cnf(i_0_14,plain,
( is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))
| ~ axiom_5 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_14) ).
cnf(i_0_82,plain,
axiom_5,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_82) ).
cnf(i_0_20,plain,
( is_a_theorem(implies(necessarily(X1),X1))
| ~ axiom_M ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_20) ).
cnf(i_0_84,plain,
axiom_M,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_84) ).
cnf(i_0_102,plain,
( is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))
| ~ modus_tollens ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_102) ).
cnf(i_0_69,plain,
modus_tollens,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_69) ).
cnf(i_0_105,plain,
( is_a_theorem(necessarily(X1))
| ~ necessitation
| ~ is_a_theorem(X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_105) ).
cnf(i_0_85,plain,
necessitation,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_85) ).
cnf(i_0_114,plain,
( necessarily(implies(X1,X2)) = strict_implies(X1,X2)
| ~ op_strict_implies ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_114) ).
cnf(i_0_136,plain,
op_strict_implies,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_136) ).
cnf(i_0_39,plain,
( axiom_m9
| ~ is_a_theorem(strict_implies(possibly(possibly(esk32_0)),possibly(esk32_0))) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_39) ).
cnf(i_0_131,negated_conjecture,
~ axiom_m9,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_131) ).
cnf(i_0_77,plain,
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ implies_1 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_77) ).
cnf(i_0_65,plain,
implies_1,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-ztvcceuv/lgb.p',i_0_65) ).
cnf(c_0_178,plain,
( is_a_theorem(X1)
| ~ modus_ponens
| ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(X2,X1)) ),
i_0_96 ).
cnf(c_0_179,plain,
modus_ponens,
i_0_68 ).
cnf(c_0_180,plain,
( is_a_theorem(implies(X1,implies(X2,and(X1,X2))))
| ~ and_3 ),
i_0_10 ).
cnf(c_0_181,plain,
and_3,
i_0_61 ).
cnf(c_0_182,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
i_0_139 ).
cnf(c_0_183,plain,
substitution_of_equivalents,
i_0_143 ).
cnf(c_0_184,plain,
( and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2)
| ~ op_equiv ),
i_0_107 ).
cnf(c_0_185,plain,
op_equiv,
i_0_70 ).
cnf(c_0_186,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_178,c_0_179])]) ).
cnf(c_0_187,plain,
is_a_theorem(implies(X1,implies(X2,and(X1,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_180,c_0_181])]) ).
cnf(c_0_188,plain,
( is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))
| ~ implies_2 ),
i_0_79 ).
cnf(c_0_189,plain,
implies_2,
i_0_66 ).
cnf(c_0_190,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_182,c_0_183])]) ).
cnf(c_0_191,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_184,c_0_185])]) ).
cnf(c_0_192,plain,
( is_a_theorem(implies(X1,and(X2,X1)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_186,c_0_187]) ).
cnf(c_0_193,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_188,c_0_189])]) ).
cnf(c_0_194,plain,
( X1 = X2
| ~ is_a_theorem(and(implies(X1,X2),implies(X2,X1))) ),
inference(spm,[status(thm)],[c_0_190,c_0_191]) ).
cnf(c_0_195,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_186,c_0_192]) ).
cnf(c_0_196,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_186,c_0_193]) ).
cnf(c_0_197,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ and_1 ),
i_0_6 ).
cnf(c_0_198,plain,
and_1,
i_0_59 ).
cnf(c_0_199,plain,
( not(and(X1,not(X2))) = implies(X1,X2)
| ~ op_implies_and ),
i_0_108 ).
cnf(c_0_200,plain,
op_implies_and,
i_0_71 ).
cnf(c_0_201,plain,
( X1 = X2
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_194,c_0_195]) ).
cnf(c_0_202,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(spm,[status(thm)],[c_0_196,c_0_187]) ).
cnf(c_0_203,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_197,c_0_198])]) ).
cnf(c_0_204,plain,
( not(and(not(X1),not(X2))) = or(X1,X2)
| ~ op_or ),
i_0_111 ).
cnf(c_0_205,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_199,c_0_200])]) ).
cnf(c_0_206,plain,
op_or,
i_0_72 ).
cnf(c_0_207,plain,
( is_a_theorem(implies(X1,or(X1,X2)))
| ~ or_1 ),
i_0_116 ).
cnf(c_0_208,plain,
or_1,
i_0_73 ).
cnf(c_0_209,plain,
( not(necessarily(not(X1))) = possibly(X1)
| ~ op_possibly ),
i_0_112 ).
cnf(c_0_210,plain,
op_possibly,
i_0_86 ).
cnf(c_0_211,plain,
( is_a_theorem(implies(possibly(X1),necessarily(possibly(X1))))
| ~ axiom_5 ),
i_0_14 ).
cnf(c_0_212,plain,
axiom_5,
i_0_82 ).
cnf(c_0_213,plain,
( is_a_theorem(implies(necessarily(X1),X1))
| ~ axiom_M ),
i_0_20 ).
cnf(c_0_214,plain,
axiom_M,
i_0_84 ).
cnf(c_0_215,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_203])]) ).
cnf(c_0_216,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_204,c_0_205]),c_0_206])]) ).
cnf(c_0_217,plain,
( is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))
| ~ modus_tollens ),
i_0_102 ).
cnf(c_0_218,plain,
modus_tollens,
i_0_69 ).
cnf(c_0_219,plain,
is_a_theorem(implies(X1,or(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_207,c_0_208])]) ).
cnf(c_0_220,plain,
not(necessarily(not(X1))) = possibly(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_209,c_0_210])]) ).
cnf(c_0_221,plain,
is_a_theorem(implies(possibly(X1),necessarily(possibly(X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_211,c_0_212])]) ).
cnf(c_0_222,plain,
is_a_theorem(implies(necessarily(X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_213,c_0_214])]) ).
cnf(c_0_223,plain,
not(not(X1)) = or(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_215]),c_0_216]) ).
cnf(c_0_224,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_217,c_0_216]),c_0_218])]) ).
cnf(c_0_225,plain,
is_a_theorem(or(X1,or(not(X1),X2))),
inference(spm,[status(thm)],[c_0_219,c_0_216]) ).
cnf(c_0_226,plain,
( is_a_theorem(necessarily(X1))
| ~ necessitation
| ~ is_a_theorem(X1) ),
i_0_105 ).
cnf(c_0_227,plain,
necessitation,
i_0_85 ).
cnf(c_0_228,plain,
( necessarily(implies(X1,X2)) = strict_implies(X1,X2)
| ~ op_strict_implies ),
i_0_114 ).
cnf(c_0_229,plain,
op_strict_implies,
i_0_136 ).
cnf(c_0_230,plain,
possibly(necessarily(not(X1))) = not(necessarily(possibly(X1))),
inference(spm,[status(thm)],[c_0_220,c_0_220]) ).
cnf(c_0_231,plain,
necessarily(possibly(X1)) = possibly(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_221]),c_0_222])]) ).
cnf(c_0_232,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_219,c_0_223]) ).
cnf(c_0_233,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_186,c_0_224]) ).
cnf(c_0_234,plain,
is_a_theorem(or(X1,not(not(not(X1))))),
inference(spm,[status(thm)],[c_0_225,c_0_223]) ).
cnf(c_0_235,plain,
( axiom_m9
| ~ is_a_theorem(strict_implies(possibly(possibly(esk32_0)),possibly(esk32_0))) ),
i_0_39 ).
cnf(c_0_236,negated_conjecture,
~ axiom_m9,
i_0_131 ).
cnf(c_0_237,plain,
( is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_226,c_0_227])]) ).
cnf(c_0_238,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_228,c_0_229])]) ).
cnf(c_0_239,plain,
possibly(necessarily(not(X1))) = not(possibly(X1)),
inference(rw,[status(thm)],[c_0_230,c_0_231]) ).
cnf(c_0_240,plain,
( not(not(X1)) = X1
| ~ is_a_theorem(or(not(X1),X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_232]),c_0_216]) ).
cnf(c_0_241,plain,
is_a_theorem(or(not(X1),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_234]),c_0_216]) ).
cnf(c_0_242,plain,
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ implies_1 ),
i_0_77 ).
cnf(c_0_243,plain,
implies_1,
i_0_65 ).
cnf(c_0_244,plain,
~ is_a_theorem(strict_implies(possibly(possibly(esk32_0)),possibly(esk32_0))),
inference(sr,[status(thm)],[c_0_235,c_0_236]) ).
cnf(c_0_245,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_237,c_0_238]) ).
cnf(c_0_246,plain,
not(not(possibly(X1))) = possibly(possibly(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_220]),c_0_231]),c_0_230]),c_0_231]) ).
cnf(c_0_247,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_240,c_0_241])]) ).
cnf(c_0_248,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_242,c_0_243])]) ).
cnf(c_0_249,plain,
~ is_a_theorem(implies(possibly(possibly(esk32_0)),possibly(esk32_0))),
inference(spm,[status(thm)],[c_0_244,c_0_245]) ).
cnf(c_0_250,plain,
possibly(possibly(X1)) = possibly(X1),
inference(rw,[status(thm)],[c_0_246,c_0_247]) ).
cnf(c_0_251,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_196,c_0_248]) ).
cnf(c_0_252,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_249,c_0_250]),c_0_251])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL535+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : enigmatic-eprover.py %s %d 1
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 5 11:54:12 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.44 # ENIGMATIC: Selected SinE mode:
% 0.13/0.45 # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.45 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.13/0.45 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.13/0.45 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 13.46/3.95 # ENIGMATIC: Solved by autoschedule-lgb:
% 13.46/3.95 # No SInE strategy applied
% 13.46/3.95 # Trying AutoSched0 for 150 seconds
% 13.46/3.95 # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 13.46/3.95 # and selection function SelectComplexExceptUniqMaxHorn.
% 13.46/3.95 #
% 13.46/3.95 # Preprocessing time : 0.026 s
% 13.46/3.95 # Presaturation interreduction done
% 13.46/3.95
% 13.46/3.95 # Proof found!
% 13.46/3.95 # SZS status Theorem
% 13.46/3.95 # SZS output start CNFRefutation
% See solution above
% 13.46/3.95 # Training examples: 0 positive, 0 negative
% 13.46/3.95
% 13.46/3.95 # -------------------------------------------------
% 13.46/3.95 # User time : 0.218 s
% 13.46/3.95 # System time : 0.017 s
% 13.46/3.95 # Total time : 0.236 s
% 13.46/3.95 # Maximum resident set size: 3584 pages
% 13.46/3.95
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