%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : LCL562+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n006.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 11:45:01 AM UTC 2026
% Result : Theorem 19.76s 4.10s
% Output : CNFRefutation 19.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 28
% Syntax : Number of clauses : 149 ( 81 unt; 0 nHn; 71 RR)
% Number of literals : 240 ( 54 equ; 95 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 17 ( 15 usr; 15 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 244 ( 27 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_121,plain,
( X1 = X2
| ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_121) ).
cnf(i_0_115,plain,
substitution_strict_equiv,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_115) ).
cnf(i_0_85,plain,
( and(strict_implies(X1,X2),strict_implies(X2,X1)) = strict_equiv(X1,X2)
| ~ op_strict_equiv ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_85) ).
cnf(i_0_113,plain,
op_strict_equiv,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_113) ).
cnf(i_0_72,plain,
( is_a_theorem(X1)
| ~ modus_ponens_strict_implies
| ~ is_a_theorem(X2)
| ~ is_a_theorem(strict_implies(X2,X1)) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_72) ).
cnf(i_0_109,plain,
modus_ponens_strict_implies,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_109) ).
cnf(i_0_32,plain,
( is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))
| ~ axiom_m5 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_32) ).
cnf(i_0_108,plain,
axiom_m5,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_108) ).
cnf(i_0_4,plain,
( is_a_theorem(and(X1,X2))
| ~ adjunction
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_4) ).
cnf(i_0_103,plain,
adjunction,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_103) ).
cnf(i_0_22,plain,
( is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))
| ~ axiom_m1 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_22) ).
cnf(i_0_104,plain,
axiom_m1,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_104) ).
cnf(i_0_26,plain,
( is_a_theorem(strict_implies(and(X1,X2),X1))
| ~ axiom_m2 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_26) ).
cnf(i_0_105,plain,
axiom_m2,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_105) ).
cnf(i_0_80,plain,
( not(and(X1,not(X2))) = implies(X1,X2)
| ~ op_implies_and ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_80) ).
cnf(i_0_61,plain,
op_implies_and,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_61) ).
cnf(i_0_28,plain,
( is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X1,and(X2,X3))))
| ~ axiom_m3 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_28) ).
cnf(i_0_106,plain,
axiom_m3,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_106) ).
cnf(i_0_86,plain,
( necessarily(implies(X1,X2)) = strict_implies(X1,X2)
| ~ op_strict_implies ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_86) ).
cnf(i_0_114,plain,
op_strict_implies,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_114) ).
cnf(i_0_83,plain,
( not(and(not(X1),not(X2))) = or(X1,X2)
| ~ op_or ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_83) ).
cnf(i_0_62,plain,
op_or,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_62) ).
cnf(i_0_30,plain,
( is_a_theorem(strict_implies(X1,and(X1,X1)))
| ~ axiom_m4 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_30) ).
cnf(i_0_107,plain,
axiom_m4,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_107) ).
cnf(i_0_79,plain,
( and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2)
| ~ op_equiv ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_79) ).
cnf(i_0_60,plain,
op_equiv,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_60) ).
cnf(i_0_55,plain,
( equivalence_2
| ~ is_a_theorem(implies(equiv(esk46_0,esk47_0),implies(esk47_0,esk46_0))) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_55) ).
cnf(i_0_59,negated_conjecture,
~ equivalence_2,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-etvb2nd8/lgb.p',i_0_59) ).
cnf(c_0_150,plain,
( X1 = X2
| ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
i_0_121 ).
cnf(c_0_151,plain,
substitution_strict_equiv,
i_0_115 ).
cnf(c_0_152,plain,
( and(strict_implies(X1,X2),strict_implies(X2,X1)) = strict_equiv(X1,X2)
| ~ op_strict_equiv ),
i_0_85 ).
cnf(c_0_153,plain,
op_strict_equiv,
i_0_113 ).
cnf(c_0_154,plain,
( is_a_theorem(X1)
| ~ modus_ponens_strict_implies
| ~ is_a_theorem(X2)
| ~ is_a_theorem(strict_implies(X2,X1)) ),
i_0_72 ).
cnf(c_0_155,plain,
modus_ponens_strict_implies,
i_0_109 ).
cnf(c_0_156,plain,
( is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))
| ~ axiom_m5 ),
i_0_32 ).
cnf(c_0_157,plain,
axiom_m5,
i_0_108 ).
cnf(c_0_158,plain,
( X1 = X2
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_151])]) ).
cnf(c_0_159,plain,
and(strict_implies(X1,X2),strict_implies(X2,X1)) = strict_equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_152,c_0_153])]) ).
cnf(c_0_160,plain,
( is_a_theorem(and(X1,X2))
| ~ adjunction
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
i_0_4 ).
cnf(c_0_161,plain,
adjunction,
i_0_103 ).
cnf(c_0_162,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_154,c_0_155])]) ).
cnf(c_0_163,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_156,c_0_157])]) ).
cnf(c_0_164,plain,
( X1 = X2
| ~ is_a_theorem(and(strict_implies(X1,X2),strict_implies(X2,X1))) ),
inference(spm,[status(thm)],[c_0_158,c_0_159]) ).
cnf(c_0_165,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_160,c_0_161])]) ).
cnf(c_0_166,plain,
( is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))
| ~ axiom_m1 ),
i_0_22 ).
cnf(c_0_167,plain,
axiom_m1,
i_0_104 ).
cnf(c_0_168,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_162,c_0_163]) ).
cnf(c_0_169,plain,
( is_a_theorem(strict_implies(and(X1,X2),X1))
| ~ axiom_m2 ),
i_0_26 ).
cnf(c_0_170,plain,
axiom_m2,
i_0_105 ).
cnf(c_0_171,plain,
( not(and(X1,not(X2))) = implies(X1,X2)
| ~ op_implies_and ),
i_0_80 ).
cnf(c_0_172,plain,
op_implies_and,
i_0_61 ).
cnf(c_0_173,plain,
( X1 = X2
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_174,plain,
is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_166,c_0_167])]) ).
cnf(c_0_175,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_168,c_0_165]) ).
cnf(c_0_176,plain,
is_a_theorem(strict_implies(and(X1,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(and(and(X1,X2),X3),and(X1,and(X2,X3))))
| ~ axiom_m3 ),
i_0_28 ).
cnf(c_0_178,plain,
axiom_m3,
i_0_106 ).
cnf(c_0_179,plain,
( necessarily(implies(X1,X2)) = strict_implies(X1,X2)
| ~ op_strict_implies ),
i_0_86 ).
cnf(c_0_180,plain,
op_strict_implies,
i_0_114 ).
cnf(c_0_181,plain,
( not(and(not(X1),not(X2))) = or(X1,X2)
| ~ op_or ),
i_0_83 ).
cnf(c_0_182,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_171,c_0_172])]) ).
cnf(c_0_183,plain,
op_or,
i_0_62 ).
cnf(c_0_184,plain,
and(X1,X2) = and(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_174])]) ).
cnf(c_0_185,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,and(X2,X3))) ),
inference(spm,[status(thm)],[c_0_175,c_0_176]) ).
cnf(c_0_186,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_177,c_0_178])]) ).
cnf(c_0_187,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_179,c_0_180])]) ).
cnf(c_0_188,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_181,c_0_182]),c_0_183])]) ).
cnf(c_0_189,plain,
not(and(not(X1),X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_182,c_0_184]) ).
cnf(c_0_190,plain,
is_a_theorem(strict_implies(and(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_185,c_0_174]) ).
cnf(c_0_191,plain,
( is_a_theorem(and(X1,and(X2,X3)))
| ~ is_a_theorem(and(and(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_162,c_0_186]) ).
cnf(c_0_192,plain,
( is_a_theorem(strict_implies(X1,and(X1,X1)))
| ~ axiom_m4 ),
i_0_30 ).
cnf(c_0_193,plain,
axiom_m4,
i_0_107 ).
cnf(c_0_194,plain,
necessarily(or(X1,X2)) = strict_implies(not(X1),X2),
inference(spm,[status(thm)],[c_0_187,c_0_188]) ).
cnf(c_0_195,plain,
or(X1,X2) = or(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_189]),c_0_188]),c_0_188]) ).
cnf(c_0_196,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(and(X2,X1)) ),
inference(spm,[status(thm)],[c_0_162,c_0_190]) ).
cnf(c_0_197,plain,
( is_a_theorem(and(X1,and(X2,X3)))
| ~ is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_191,c_0_165]) ).
cnf(c_0_198,plain,
is_a_theorem(strict_implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_192,c_0_193])]) ).
cnf(c_0_199,plain,
strict_implies(not(X1),X2) = strict_implies(not(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_195]),c_0_194]) ).
cnf(c_0_200,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(and(X3,X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_196,c_0_197]) ).
cnf(c_0_201,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_198]),c_0_176])]) ).
cnf(c_0_202,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_185,c_0_199]) ).
cnf(c_0_203,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_200,c_0_159]) ).
cnf(c_0_204,plain,
strict_equiv(X1,X1) = strict_implies(X1,X1),
inference(spm,[status(thm)],[c_0_159,c_0_201]) ).
cnf(c_0_205,plain,
is_a_theorem(strict_implies(X1,X1)),
inference(spm,[status(thm)],[c_0_185,c_0_198]) ).
cnf(c_0_206,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(strict_implies(implies(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_202,c_0_182]) ).
cnf(c_0_207,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(and(X2,X1)) ),
inference(spm,[status(thm)],[c_0_162,c_0_174]) ).
cnf(c_0_208,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_203,c_0_204]),c_0_205])]) ).
cnf(c_0_209,plain,
is_a_theorem(strict_implies(not(X1),implies(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_205]),c_0_199]) ).
cnf(c_0_210,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_173,c_0_199]) ).
cnf(c_0_211,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_168,c_0_199]) ).
cnf(c_0_212,plain,
( is_a_theorem(and(X1,strict_implies(X2,X2)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_207,c_0_208]) ).
cnf(c_0_213,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(strict_implies(not(X2),X1)) ),
inference(spm,[status(thm)],[c_0_202,c_0_201]) ).
cnf(c_0_214,plain,
is_a_theorem(strict_implies(not(not(X1)),or(X1,X2))),
inference(spm,[status(thm)],[c_0_209,c_0_188]) ).
cnf(c_0_215,plain,
( not(not(X1)) = X1
| ~ is_a_theorem(strict_implies(X1,not(not(X1)))) ),
inference(spm,[status(thm)],[c_0_210,c_0_205]) ).
cnf(c_0_216,plain,
not(not(X1)) = or(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_201]),c_0_188]) ).
cnf(c_0_217,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,not(not(X2)))) ),
inference(spm,[status(thm)],[c_0_211,c_0_212]) ).
cnf(c_0_218,plain,
is_a_theorem(strict_implies(not(or(X1,X2)),not(X1))),
inference(spm,[status(thm)],[c_0_213,c_0_214]) ).
cnf(c_0_219,plain,
( or(X1,X1) = X1
| ~ is_a_theorem(strict_implies(X1,or(X1,X1))) ),
inference(spm,[status(thm)],[c_0_215,c_0_216]) ).
cnf(c_0_220,plain,
is_a_theorem(strict_implies(not(X1),or(not(X1),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_218]),c_0_199]) ).
cnf(c_0_221,plain,
or(not(X1),not(X1)) = not(or(X1,X1)),
inference(spm,[status(thm)],[c_0_216,c_0_216]) ).
cnf(c_0_222,plain,
not(or(X1,X1)) = not(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219,c_0_220]),c_0_221]) ).
cnf(c_0_223,plain,
implies(X1,or(X2,X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_222]),c_0_182]) ).
cnf(c_0_224,plain,
strict_implies(X1,or(X2,X2)) = strict_implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_223]),c_0_187]) ).
cnf(c_0_225,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_173,c_0_186]) ).
cnf(c_0_226,plain,
or(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_219,c_0_224]),c_0_205])]) ).
cnf(c_0_227,plain,
not(and(X1,or(X2,X2))) = implies(X1,not(X2)),
inference(spm,[status(thm)],[c_0_182,c_0_216]) ).
cnf(c_0_228,plain,
and(X1,and(X1,X2)) = and(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_201]),c_0_190])]) ).
cnf(c_0_229,plain,
not(not(X1)) = X1,
inference(rw,[status(thm)],[c_0_216,c_0_226]) ).
cnf(c_0_230,plain,
not(and(X1,X2)) = implies(X1,not(X2)),
inference(rw,[status(thm)],[c_0_227,c_0_226]) ).
cnf(c_0_231,plain,
and(X1,and(X2,X1)) = and(X2,X1),
inference(spm,[status(thm)],[c_0_228,c_0_184]) ).
cnf(c_0_232,plain,
not(implies(X1,not(X2))) = and(X1,X2),
inference(spm,[status(thm)],[c_0_229,c_0_230]) ).
cnf(c_0_233,plain,
implies(and(X1,not(X2)),X2) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_231]),c_0_182]) ).
cnf(c_0_234,plain,
and(X1,not(X2)) = not(implies(X1,X2)),
inference(spm,[status(thm)],[c_0_232,c_0_229]) ).
cnf(c_0_235,plain,
implies(or(X1,X1),X2) = or(not(X1),X2),
inference(spm,[status(thm)],[c_0_188,c_0_216]) ).
cnf(c_0_236,plain,
or(X1,implies(X2,X1)) = implies(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_233,c_0_234]),c_0_188]),c_0_195]) ).
cnf(c_0_237,plain,
or(X1,not(X2)) = implies(or(X2,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_227]),c_0_188]) ).
cnf(c_0_238,plain,
or(not(X1),X2) = implies(X1,X2),
inference(rw,[status(thm)],[c_0_235,c_0_226]) ).
cnf(c_0_239,plain,
or(X1,or(X2,X1)) = or(X2,X1),
inference(spm,[status(thm)],[c_0_236,c_0_188]) ).
cnf(c_0_240,plain,
or(X1,not(X2)) = implies(X2,X1),
inference(rw,[status(thm)],[c_0_237,c_0_226]) ).
cnf(c_0_241,plain,
implies(X1,implies(X1,X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_239]),c_0_240]),c_0_240]) ).
cnf(c_0_242,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_168,c_0_199]) ).
cnf(c_0_243,plain,
( is_a_theorem(strict_implies(X1,implies(X2,X3)))
| ~ is_a_theorem(strict_implies(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_175,c_0_209]) ).
cnf(c_0_244,plain,
strict_implies(not(X1),X1) = necessarily(X1),
inference(spm,[status(thm)],[c_0_194,c_0_226]) ).
cnf(c_0_245,plain,
strict_implies(X1,implies(X1,X2)) = strict_implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_241]),c_0_187]) ).
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_162,c_0_199]) ).
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_242,c_0_208]) ).
cnf(c_0_248,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_243,c_0_244]),c_0_229]),c_0_245]) ).
cnf(c_0_249,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,and(X3,X2))) ),
inference(spm,[status(thm)],[c_0_175,c_0_190]) ).
cnf(c_0_250,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_251,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(necessarily(X1)) ),
inference(spm,[status(thm)],[c_0_248,c_0_229]) ).
cnf(c_0_252,plain,
is_a_theorem(strict_implies(and(and(X1,X2),X3),and(X2,X3))),
inference(spm,[status(thm)],[c_0_249,c_0_186]) ).
cnf(c_0_253,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_250,c_0_251]),c_0_229]) ).
cnf(c_0_254,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(and(and(X3,X1),X2)) ),
inference(spm,[status(thm)],[c_0_162,c_0_252]) ).
cnf(c_0_255,plain,
( and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2)
| ~ op_equiv ),
i_0_79 ).
cnf(c_0_256,plain,
op_equiv,
i_0_60 ).
cnf(c_0_257,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_253,c_0_229]) ).
cnf(c_0_258,plain,
( is_a_theorem(and(X1,strict_implies(X2,X2)))
| ~ is_a_theorem(and(X3,X1)) ),
inference(spm,[status(thm)],[c_0_254,c_0_212]) ).
cnf(c_0_259,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_255,c_0_256])]) ).
cnf(c_0_260,plain,
( equivalence_2
| ~ is_a_theorem(implies(equiv(esk46_0,esk47_0),implies(esk47_0,esk46_0))) ),
i_0_55 ).
cnf(c_0_261,negated_conjecture,
~ equivalence_2,
i_0_59 ).
cnf(c_0_262,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_257,c_0_187]) ).
cnf(c_0_263,plain,
( is_a_theorem(and(strict_implies(X1,X1),strict_implies(X2,X2)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_258,c_0_212]) ).
cnf(c_0_264,plain,
is_a_theorem(strict_implies(equiv(X1,X2),and(implies(X2,X1),implies(X1,X2)))),
inference(spm,[status(thm)],[c_0_174,c_0_259]) ).
cnf(c_0_265,plain,
~ is_a_theorem(implies(equiv(esk46_0,esk47_0),implies(esk47_0,esk46_0))),
inference(sr,[status(thm)],[c_0_260,c_0_261]) ).
cnf(c_0_266,plain,
( is_a_theorem(implies(and(X1,X2),X2))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_262,c_0_190]) ).
cnf(c_0_267,plain,
is_a_theorem(and(strict_implies(X1,X1),strict_implies(X2,X2))),
inference(spm,[status(thm)],[c_0_263,c_0_264]) ).
cnf(c_0_268,plain,
~ is_a_theorem(implies(and(implies(esk46_0,esk47_0),implies(esk47_0,esk46_0)),implies(esk47_0,esk46_0))),
inference(rw,[status(thm)],[c_0_265,c_0_259]) ).
cnf(c_0_269,plain,
is_a_theorem(implies(and(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_266,c_0_267]) ).
cnf(c_0_270,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_268,c_0_269])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL562+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 : n006.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 : Sun Sep 6 01:09:33 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.45 # ENIGMATIC: Selected SinE mode:
% 0.12/0.45 # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.45 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.12/0.45 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.12/0.45 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 19.76/4.10 # ENIGMATIC: Solved by autoschedule-lgb:
% 19.76/4.10 # No SInE strategy applied
% 19.76/4.10 # Trying AutoSched0 for 150 seconds
% 19.76/4.10 # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 19.76/4.10 # and selection function SelectComplexExceptUniqMaxHorn.
% 19.76/4.10 #
% 19.76/4.10 # Preprocessing time : 0.014 s
% 19.76/4.10 # Presaturation interreduction done
% 19.76/4.10
% 19.76/4.10 # Proof found!
% 19.76/4.10 # SZS status Theorem
% 19.76/4.10 # SZS output start CNFRefutation
% See solution above
% 19.76/4.10 # Training examples: 0 positive, 0 negative
% 19.76/4.10
% 19.76/4.10 # -------------------------------------------------
% 19.76/4.10 # User time : 0.466 s
% 19.76/4.10 # System time : 0.030 s
% 19.76/4.10 # Total time : 0.496 s
% 19.76/4.10 # Maximum resident set size: 3584 pages
% 19.76/4.10
%------------------------------------------------------------------------------