TSTP Solution File: LCL553+1 by Enigma---0.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : LCL553+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n011.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 09:26:45 EDT 2022
% Result : Theorem 10.07s 2.66s
% Output : CNFRefutation 10.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 30
% Syntax : Number of clauses : 173 ( 90 unt; 0 nHn; 81 RR)
% Number of literals : 286 ( 65 equ; 117 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 16 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 282 ( 35 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_4,plain,
( is_a_theorem(and(X1,X2))
| ~ adjunction
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_4) ).
cnf(i_0_105,plain,
adjunction,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_105) ).
cnf(i_0_87,plain,
( and(strict_implies(X1,X2),strict_implies(X2,X1)) = strict_equiv(X1,X2)
| ~ op_strict_equiv ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_87) ).
cnf(i_0_115,plain,
op_strict_equiv,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_115) ).
cnf(i_0_124,plain,
( X1 = X2
| ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_124) ).
cnf(i_0_117,plain,
substitution_strict_equiv,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_117) ).
cnf(i_0_74,plain,
( is_a_theorem(X1)
| ~ modus_ponens_strict_implies
| ~ is_a_theorem(X2)
| ~ is_a_theorem(strict_implies(X2,X1)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_74) ).
cnf(i_0_111,plain,
modus_ponens_strict_implies,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_111) ).
cnf(i_0_30,plain,
( is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))
| ~ axiom_m5 ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_30) ).
cnf(i_0_110,plain,
axiom_m5,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_110) ).
cnf(i_0_22,plain,
( is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))
| ~ axiom_m1 ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_22) ).
cnf(i_0_106,plain,
axiom_m1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_106) ).
cnf(i_0_24,plain,
( is_a_theorem(strict_implies(and(X1,X2),X1))
| ~ axiom_m2 ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_24) ).
cnf(i_0_107,plain,
axiom_m2,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_107) ).
cnf(i_0_82,plain,
( not(and(X1,not(X2))) = implies(X1,X2)
| ~ op_implies_and ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_82) ).
cnf(i_0_61,plain,
op_implies_and,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_61) ).
cnf(i_0_26,plain,
( is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))
| ~ axiom_m3 ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_26) ).
cnf(i_0_108,plain,
axiom_m3,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_108) ).
cnf(i_0_88,plain,
( necessarily(implies(X1,X2)) = strict_implies(X1,X2)
| ~ op_strict_implies ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_88) ).
cnf(i_0_116,plain,
op_strict_implies,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_116) ).
cnf(i_0_85,plain,
( not(and(not(X1),not(X2))) = or(X1,X2)
| ~ op_or ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_85) ).
cnf(i_0_62,plain,
op_or,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_62) ).
cnf(i_0_28,plain,
( is_a_theorem(strict_implies(X1,and(X1,X1)))
| ~ axiom_m4 ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_28) ).
cnf(i_0_109,plain,
axiom_m4,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_109) ).
cnf(i_0_121,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_121) ).
cnf(i_0_118,plain,
substitution_of_equivalents,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_118) ).
cnf(i_0_81,plain,
( and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2)
| ~ op_equiv ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_81) ).
cnf(i_0_60,plain,
op_equiv,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_60) ).
cnf(i_0_63,plain,
( implies_2
| ~ is_a_theorem(implies(implies(esk50_0,implies(esk50_0,esk51_0)),implies(esk50_0,esk51_0))) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_63) ).
cnf(i_0_59,negated_conjecture,
~ implies_2,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-mccxuic8/lgb.p',i_0_59) ).
cnf(c_0_155,plain,
( is_a_theorem(and(X1,X2))
| ~ adjunction
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
i_0_4 ).
cnf(c_0_156,plain,
adjunction,
i_0_105 ).
cnf(c_0_157,plain,
( and(strict_implies(X1,X2),strict_implies(X2,X1)) = strict_equiv(X1,X2)
| ~ op_strict_equiv ),
i_0_87 ).
cnf(c_0_158,plain,
op_strict_equiv,
i_0_115 ).
cnf(c_0_159,plain,
( X1 = X2
| ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
i_0_124 ).
cnf(c_0_160,plain,
substitution_strict_equiv,
i_0_117 ).
cnf(c_0_161,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_156])]) ).
cnf(c_0_162,plain,
and(strict_implies(X1,X2),strict_implies(X2,X1)) = strict_equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_157,c_0_158])]) ).
cnf(c_0_163,plain,
( is_a_theorem(X1)
| ~ modus_ponens_strict_implies
| ~ is_a_theorem(X2)
| ~ is_a_theorem(strict_implies(X2,X1)) ),
i_0_74 ).
cnf(c_0_164,plain,
modus_ponens_strict_implies,
i_0_111 ).
cnf(c_0_165,plain,
( is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))
| ~ axiom_m5 ),
i_0_30 ).
cnf(c_0_166,plain,
axiom_m5,
i_0_110 ).
cnf(c_0_167,plain,
( X1 = X2
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_160])]) ).
cnf(c_0_168,plain,
( is_a_theorem(strict_equiv(X1,X2))
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_161,c_0_162]) ).
cnf(c_0_169,plain,
( is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))
| ~ axiom_m1 ),
i_0_22 ).
cnf(c_0_170,plain,
axiom_m1,
i_0_106 ).
cnf(c_0_171,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_163,c_0_164])]) ).
cnf(c_0_172,plain,
is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_165,c_0_166])]) ).
cnf(c_0_173,plain,
( is_a_theorem(strict_implies(and(X1,X2),X1))
| ~ axiom_m2 ),
i_0_24 ).
cnf(c_0_174,plain,
axiom_m2,
i_0_107 ).
cnf(c_0_175,plain,
( X1 = X2
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_167,c_0_168]) ).
cnf(c_0_176,plain,
is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_169,c_0_170])]) ).
cnf(c_0_177,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(and(strict_implies(X1,X3),strict_implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_171,c_0_172]) ).
cnf(c_0_178,plain,
is_a_theorem(strict_implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_173,c_0_174])]) ).
cnf(c_0_179,plain,
and(X1,X2) = and(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_176])]) ).
cnf(c_0_180,plain,
( not(and(X1,not(X2))) = implies(X1,X2)
| ~ op_implies_and ),
i_0_82 ).
cnf(c_0_181,plain,
op_implies_and,
i_0_61 ).
cnf(c_0_182,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X3,X2))
| ~ is_a_theorem(strict_implies(X1,X3)) ),
inference(spm,[status(thm)],[c_0_177,c_0_161]) ).
cnf(c_0_183,plain,
is_a_theorem(strict_implies(and(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_184,plain,
( is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))
| ~ axiom_m3 ),
i_0_26 ).
cnf(c_0_185,plain,
axiom_m3,
i_0_108 ).
cnf(c_0_186,plain,
( necessarily(implies(X1,X2)) = strict_implies(X1,X2)
| ~ op_strict_implies ),
i_0_88 ).
cnf(c_0_187,plain,
op_strict_implies,
i_0_116 ).
cnf(c_0_188,plain,
( not(and(not(X1),not(X2))) = or(X1,X2)
| ~ op_or ),
i_0_85 ).
cnf(c_0_189,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_180,c_0_181])]) ).
cnf(c_0_190,plain,
op_or,
i_0_62 ).
cnf(c_0_191,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,and(X3,X2))) ),
inference(spm,[status(thm)],[c_0_182,c_0_183]) ).
cnf(c_0_192,plain,
is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_184,c_0_185])]) ).
cnf(c_0_193,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_186,c_0_187])]) ).
cnf(c_0_194,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_188,c_0_189]),c_0_190])]) ).
cnf(c_0_195,plain,
not(and(not(X1),X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_189,c_0_179]) ).
cnf(c_0_196,plain,
( is_a_theorem(strict_implies(X1,and(X1,X1)))
| ~ axiom_m4 ),
i_0_28 ).
cnf(c_0_197,plain,
axiom_m4,
i_0_109 ).
cnf(c_0_198,plain,
is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X2,X3))),
inference(spm,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_199,plain,
necessarily(or(X1,X2)) = strict_implies(not(X1),X2),
inference(spm,[status(thm)],[c_0_193,c_0_194]) ).
cnf(c_0_200,plain,
or(X1,X2) = or(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_195]),c_0_194]),c_0_194]) ).
cnf(c_0_201,plain,
is_a_theorem(strict_implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_197])]) ).
cnf(c_0_202,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(and(and(X3,X1),X2)) ),
inference(spm,[status(thm)],[c_0_171,c_0_198]) ).
cnf(c_0_203,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,and(X2,X3))) ),
inference(spm,[status(thm)],[c_0_182,c_0_178]) ).
cnf(c_0_204,plain,
strict_implies(not(X1),X2) = strict_implies(not(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_200]),c_0_199]) ).
cnf(c_0_205,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_201]),c_0_178])]) ).
cnf(c_0_206,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(and(X3,X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_202,c_0_161]) ).
cnf(c_0_207,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(strict_implies(not(and(X2,X3)),X1)) ),
inference(spm,[status(thm)],[c_0_203,c_0_204]) ).
cnf(c_0_208,plain,
is_a_theorem(strict_implies(X1,X1)),
inference(rw,[status(thm)],[c_0_201,c_0_205]) ).
cnf(c_0_209,plain,
( is_a_theorem(and(strict_implies(X1,X2),X3))
| ~ is_a_theorem(strict_equiv(X2,X1))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_206,c_0_162]) ).
cnf(c_0_210,plain,
strict_equiv(X1,X1) = strict_implies(X1,X1),
inference(spm,[status(thm)],[c_0_162,c_0_205]) ).
cnf(c_0_211,plain,
is_a_theorem(strict_implies(not(X1),not(and(X1,X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_208]),c_0_204]) ).
cnf(c_0_212,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(and(X2,X1)) ),
inference(spm,[status(thm)],[c_0_171,c_0_176]) ).
cnf(c_0_213,plain,
( is_a_theorem(and(strict_implies(X1,X1),X2))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_210]),c_0_208])]) ).
cnf(c_0_214,plain,
is_a_theorem(strict_implies(not(X1),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_211,c_0_189]) ).
cnf(c_0_215,plain,
( X1 = not(X2)
| ~ is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(strict_implies(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_175,c_0_204]) ).
cnf(c_0_216,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(and(strict_implies(X1,not(X3)),strict_implies(not(X2),X3))) ),
inference(spm,[status(thm)],[c_0_177,c_0_204]) ).
cnf(c_0_217,plain,
( is_a_theorem(and(X1,strict_implies(X2,X2)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_212,c_0_213]) ).
cnf(c_0_218,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(strict_implies(not(X2),X1)) ),
inference(spm,[status(thm)],[c_0_207,c_0_205]) ).
cnf(c_0_219,plain,
is_a_theorem(strict_implies(not(not(X1)),or(X1,X2))),
inference(spm,[status(thm)],[c_0_214,c_0_194]) ).
cnf(c_0_220,plain,
( not(not(X1)) = X1
| ~ is_a_theorem(strict_implies(X1,not(not(X1)))) ),
inference(spm,[status(thm)],[c_0_215,c_0_208]) ).
cnf(c_0_221,plain,
not(not(X1)) = or(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_205]),c_0_194]) ).
cnf(c_0_222,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,not(not(X2)))) ),
inference(spm,[status(thm)],[c_0_216,c_0_217]) ).
cnf(c_0_223,plain,
is_a_theorem(strict_implies(not(or(X1,X2)),not(X1))),
inference(spm,[status(thm)],[c_0_218,c_0_219]) ).
cnf(c_0_224,plain,
( or(X1,X1) = X1
| ~ is_a_theorem(strict_implies(X1,or(X1,X1))) ),
inference(spm,[status(thm)],[c_0_220,c_0_221]) ).
cnf(c_0_225,plain,
is_a_theorem(strict_implies(not(X1),or(not(X1),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_223]),c_0_204]) ).
cnf(c_0_226,plain,
or(not(X1),not(X1)) = not(or(X1,X1)),
inference(spm,[status(thm)],[c_0_221,c_0_221]) ).
cnf(c_0_227,plain,
not(or(X1,X1)) = not(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_225]),c_0_226]) ).
cnf(c_0_228,plain,
implies(X1,or(X2,X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_227]),c_0_189]) ).
cnf(c_0_229,plain,
strict_implies(X1,or(X2,X2)) = strict_implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_228]),c_0_193]) ).
cnf(c_0_230,plain,
( and(and(X1,X2),X3) = and(X1,and(X2,X3))
| ~ is_a_theorem(strict_implies(and(X1,and(X2,X3)),and(and(X1,X2),X3))) ),
inference(spm,[status(thm)],[c_0_175,c_0_192]) ).
cnf(c_0_231,plain,
or(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_224,c_0_229]),c_0_208])]) ).
cnf(c_0_232,plain,
not(and(X1,or(X2,X2))) = implies(X1,not(X2)),
inference(spm,[status(thm)],[c_0_189,c_0_221]) ).
cnf(c_0_233,plain,
and(X1,and(X1,X2)) = and(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_205]),c_0_183])]) ).
cnf(c_0_234,plain,
not(not(X1)) = X1,
inference(rw,[status(thm)],[c_0_221,c_0_231]) ).
cnf(c_0_235,plain,
not(and(X1,X2)) = implies(X1,not(X2)),
inference(rw,[status(thm)],[c_0_232,c_0_231]) ).
cnf(c_0_236,plain,
and(X1,and(X2,X1)) = and(X2,X1),
inference(spm,[status(thm)],[c_0_233,c_0_179]) ).
cnf(c_0_237,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(spm,[status(thm)],[c_0_234,c_0_235]) ).
cnf(c_0_238,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(and(strict_implies(not(X3),X1),strict_implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_177,c_0_204]) ).
cnf(c_0_239,plain,
is_a_theorem(strict_implies(or(X1,X1),or(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_221]),c_0_194]) ).
cnf(c_0_240,plain,
implies(and(X1,not(X2)),X2) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_236]),c_0_189]) ).
cnf(c_0_241,plain,
and(X1,not(X2)) = not(implies(X1,X2)),
inference(spm,[status(thm)],[c_0_237,c_0_234]) ).
cnf(c_0_242,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
i_0_121 ).
cnf(c_0_243,plain,
substitution_of_equivalents,
i_0_118 ).
cnf(c_0_244,plain,
( and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2)
| ~ op_equiv ),
i_0_81 ).
cnf(c_0_245,plain,
op_equiv,
i_0_60 ).
cnf(c_0_246,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_171,c_0_204]) ).
cnf(c_0_247,plain,
( is_a_theorem(strict_implies(not(not(X1)),X2))
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_238,c_0_213]) ).
cnf(c_0_248,plain,
is_a_theorem(strict_implies(or(X1,X1),not(not(X1)))),
inference(spm,[status(thm)],[c_0_239,c_0_221]) ).
cnf(c_0_249,plain,
is_a_theorem(strict_implies(not(not(X1)),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_211,c_0_195]) ).
cnf(c_0_250,plain,
implies(or(X1,X1),X2) = or(not(X1),X2),
inference(spm,[status(thm)],[c_0_194,c_0_221]) ).
cnf(c_0_251,plain,
or(X1,implies(X2,X1)) = implies(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_240,c_0_241]),c_0_194]),c_0_200]) ).
cnf(c_0_252,plain,
or(X1,not(X2)) = implies(or(X2,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_232]),c_0_194]) ).
cnf(c_0_253,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_242,c_0_243])]) ).
cnf(c_0_254,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_244,c_0_245])]) ).
cnf(c_0_255,plain,
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_171,c_0_211]) ).
cnf(c_0_256,plain,
not(and(or(X1,X1),X2)) = implies(X2,not(X1)),
inference(spm,[status(thm)],[c_0_195,c_0_221]) ).
cnf(c_0_257,plain,
( is_a_theorem(not(X1))
| ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_246,c_0_247]) ).
cnf(c_0_258,plain,
is_a_theorem(strict_implies(or(X1,X1),X1)),
inference(spm,[status(thm)],[c_0_222,c_0_248]) ).
cnf(c_0_259,plain,
is_a_theorem(strict_implies(not(not(X1)),or(X2,X1))),
inference(spm,[status(thm)],[c_0_249,c_0_194]) ).
cnf(c_0_260,plain,
or(not(X1),X2) = implies(X1,X2),
inference(rw,[status(thm)],[c_0_250,c_0_231]) ).
cnf(c_0_261,plain,
or(X1,or(X2,X1)) = or(X2,X1),
inference(spm,[status(thm)],[c_0_251,c_0_194]) ).
cnf(c_0_262,plain,
or(X1,not(X2)) = implies(X2,X1),
inference(rw,[status(thm)],[c_0_252,c_0_231]) ).
cnf(c_0_263,plain,
( X1 = X2
| ~ is_a_theorem(and(implies(X1,X2),implies(X2,X1))) ),
inference(spm,[status(thm)],[c_0_253,c_0_254]) ).
cnf(c_0_264,plain,
( is_a_theorem(implies(X1,not(X2)))
| ~ is_a_theorem(not(or(X2,X2))) ),
inference(spm,[status(thm)],[c_0_255,c_0_256]) ).
cnf(c_0_265,plain,
( is_a_theorem(not(or(X1,X1)))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_257,c_0_258]) ).
cnf(c_0_266,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(not(not(X2))) ),
inference(spm,[status(thm)],[c_0_171,c_0_259]) ).
cnf(c_0_267,plain,
implies(X1,implies(X1,X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_261]),c_0_262]),c_0_262]) ).
cnf(c_0_268,plain,
( X1 = X2
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_263,c_0_161]) ).
cnf(c_0_269,plain,
( is_a_theorem(implies(X1,not(X2)))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_264,c_0_265]) ).
cnf(c_0_270,plain,
( is_a_theorem(or(X1,not(X2)))
| ~ is_a_theorem(not(or(X2,X2))) ),
inference(spm,[status(thm)],[c_0_266,c_0_221]) ).
cnf(c_0_271,plain,
( is_a_theorem(strict_implies(X1,implies(X2,X3)))
| ~ is_a_theorem(strict_implies(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_182,c_0_214]) ).
cnf(c_0_272,plain,
strict_implies(not(X1),X1) = necessarily(X1),
inference(spm,[status(thm)],[c_0_199,c_0_231]) ).
cnf(c_0_273,plain,
strict_implies(X1,implies(X1,X2)) = strict_implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_267]),c_0_193]) ).
cnf(c_0_274,plain,
( not(X1) = X2
| ~ is_a_theorem(or(X1,X2))
| ~ is_a_theorem(not(X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_268,c_0_269]),c_0_194]) ).
cnf(c_0_275,plain,
( is_a_theorem(or(X1,not(X2)))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_270,c_0_265]) ).
cnf(c_0_276,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(necessarily(not(X1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_271,c_0_272]),c_0_234]),c_0_273]) ).
cnf(c_0_277,plain,
( not(X1) = not(X2)
| ~ is_a_theorem(not(X1))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_274,c_0_275]) ).
cnf(c_0_278,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(necessarily(X1)) ),
inference(spm,[status(thm)],[c_0_276,c_0_234]) ).
cnf(c_0_279,plain,
( X1 = not(X2)
| ~ is_a_theorem(not(X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_277,c_0_234]) ).
cnf(c_0_280,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(and(and(X1,X3),X2)) ),
inference(spm,[status(thm)],[c_0_202,c_0_179]) ).
cnf(c_0_281,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(not(X2))
| ~ is_a_theorem(necessarily(X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_257,c_0_278]),c_0_234]) ).
cnf(c_0_282,plain,
( X1 = X2
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_279,c_0_234]) ).
cnf(c_0_283,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(and(X2,and(X1,X3))) ),
inference(spm,[status(thm)],[c_0_280,c_0_179]) ).
cnf(c_0_284,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_281,c_0_234]) ).
cnf(c_0_285,plain,
( X1 = strict_implies(X2,X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_282,c_0_208]) ).
cnf(c_0_286,plain,
( is_a_theorem(and(X1,strict_implies(X2,X2)))
| ~ is_a_theorem(and(X1,X3)) ),
inference(spm,[status(thm)],[c_0_283,c_0_213]) ).
cnf(c_0_287,plain,
( implies_2
| ~ is_a_theorem(implies(implies(esk50_0,implies(esk50_0,esk51_0)),implies(esk50_0,esk51_0))) ),
i_0_63 ).
cnf(c_0_288,negated_conjecture,
~ implies_2,
i_0_59 ).
cnf(c_0_289,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_284,c_0_193]) ).
cnf(c_0_290,plain,
strict_implies(X1,X1) = strict_implies(X2,X2),
inference(spm,[status(thm)],[c_0_285,c_0_208]) ).
cnf(c_0_291,plain,
( is_a_theorem(and(strict_implies(X1,X1),strict_implies(X2,X2)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_286,c_0_213]) ).
cnf(c_0_292,plain,
~ is_a_theorem(implies(implies(esk50_0,implies(esk50_0,esk51_0)),implies(esk50_0,esk51_0))),
inference(sr,[status(thm)],[c_0_287,c_0_288]) ).
cnf(c_0_293,plain,
( is_a_theorem(implies(X1,X1))
| ~ is_a_theorem(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_289,c_0_290]),c_0_208])]) ).
cnf(c_0_294,plain,
is_a_theorem(and(strict_implies(X1,X1),strict_implies(X2,X2))),
inference(spm,[status(thm)],[c_0_291,c_0_239]) ).
cnf(c_0_295,plain,
~ is_a_theorem(implies(implies(esk50_0,esk51_0),implies(esk50_0,esk51_0))),
inference(rw,[status(thm)],[c_0_292,c_0_267]) ).
cnf(c_0_296,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_293,c_0_294]) ).
cnf(c_0_297,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_295,c_0_296])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL553+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : enigmatic-eprover.py %s %d 1
% 0.12/0.33 % Computer : n011.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 : 600
% 0.12/0.33 % DateTime : Mon Jul 4 18:33:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.44 # ENIGMATIC: Selected SinE mode:
% 0.18/0.45 # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.18/0.45 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.18/0.45 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 10.07/2.66 # ENIGMATIC: Solved by autoschedule-lgb:
% 10.07/2.66 # No SInE strategy applied
% 10.07/2.66 # Trying AutoSched0 for 150 seconds
% 10.07/2.66 # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 10.07/2.66 # and selection function SelectComplexExceptUniqMaxHorn.
% 10.07/2.66 #
% 10.07/2.66 # Preprocessing time : 0.014 s
% 10.07/2.66 # Presaturation interreduction done
% 10.07/2.66
% 10.07/2.66 # Proof found!
% 10.07/2.66 # SZS status Theorem
% 10.07/2.66 # SZS output start CNFRefutation
% See solution above
% 10.07/2.66 # Training examples: 0 positive, 0 negative
% 10.07/2.66
% 10.07/2.66 # -------------------------------------------------
% 10.07/2.66 # User time : 0.372 s
% 10.07/2.66 # System time : 0.028 s
% 10.07/2.66 # Total time : 0.400 s
% 10.07/2.66 # Maximum resident set size: 7120 pages
% 10.07/2.66
%------------------------------------------------------------------------------