%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : LCL568+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n001.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 21.77s 5.03s
% Output : CNFRefutation 21.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 30
% Syntax : Number of clauses : 127 ( 75 unt; 0 nHn; 63 RR)
% Number of literals : 199 ( 45 equ; 76 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 : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 164 ( 11 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/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_4) ).
cnf(i_0_63,plain,
adjunction,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_63) ).
cnf(i_0_61,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-p06lasxd/lgb.p',i_0_61) ).
cnf(i_0_76,plain,
op_strict_equiv,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_76) ).
cnf(i_0_81,plain,
( X1 = X2
| ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_81) ).
cnf(i_0_78,plain,
substitution_strict_equiv,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_78) ).
cnf(i_0_16,plain,
( is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))
| ~ axiom_m1 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_16) ).
cnf(i_0_64,plain,
axiom_m1,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_64) ).
cnf(i_0_50,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-p06lasxd/lgb.p',i_0_50) ).
cnf(i_0_72,plain,
modus_ponens_strict_implies,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_72) ).
cnf(i_0_26,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-p06lasxd/lgb.p',i_0_26) ).
cnf(i_0_68,plain,
axiom_m5,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_68) ).
cnf(i_0_56,plain,
( not(and(X1,not(X2))) = implies(X1,X2)
| ~ op_implies_and ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_56) ).
cnf(i_0_44,plain,
op_implies_and,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_44) ).
cnf(i_0_62,plain,
( necessarily(implies(X1,X2)) = strict_implies(X1,X2)
| ~ op_strict_implies ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_62) ).
cnf(i_0_77,plain,
op_strict_implies,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_77) ).
cnf(i_0_59,plain,
( not(and(not(X1),not(X2))) = or(X1,X2)
| ~ op_or ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_59) ).
cnf(i_0_74,plain,
op_or,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_74) ).
cnf(i_0_20,plain,
( is_a_theorem(strict_implies(and(X1,X2),X1))
| ~ axiom_m2 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_20) ).
cnf(i_0_65,plain,
axiom_m2,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_65) ).
cnf(i_0_24,plain,
( is_a_theorem(strict_implies(X1,and(X1,X1)))
| ~ axiom_m4 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_24) ).
cnf(i_0_67,plain,
axiom_m4,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_67) ).
cnf(i_0_60,plain,
( not(necessarily(not(X1))) = possibly(X1)
| ~ op_possibly ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_60) ).
cnf(i_0_75,plain,
op_possibly,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_75) ).
cnf(i_0_28,plain,
( is_a_theorem(strict_implies(X1,possibly(X1)))
| ~ axiom_m6 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_28) ).
cnf(i_0_69,plain,
axiom_m6,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_69) ).
cnf(i_0_34,plain,
( is_a_theorem(strict_implies(possibly(possibly(X1)),possibly(X1)))
| ~ axiom_m9 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_34) ).
cnf(i_0_70,plain,
axiom_m9,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_70) ).
cnf(i_0_5,plain,
( axiom_4
| ~ is_a_theorem(implies(necessarily(esk3_0),necessarily(necessarily(esk3_0)))) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_5) ).
cnf(i_0_46,negated_conjecture,
~ axiom_4,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-p06lasxd/lgb.p',i_0_46) ).
cnf(c_0_112,plain,
( is_a_theorem(and(X1,X2))
| ~ adjunction
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
i_0_4 ).
cnf(c_0_113,plain,
adjunction,
i_0_63 ).
cnf(c_0_114,plain,
( and(strict_implies(X1,X2),strict_implies(X2,X1)) = strict_equiv(X1,X2)
| ~ op_strict_equiv ),
i_0_61 ).
cnf(c_0_115,plain,
op_strict_equiv,
i_0_76 ).
cnf(c_0_116,plain,
( X1 = X2
| ~ substitution_strict_equiv
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
i_0_81 ).
cnf(c_0_117,plain,
substitution_strict_equiv,
i_0_78 ).
cnf(c_0_118,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_112,c_0_113])]) ).
cnf(c_0_119,plain,
and(strict_implies(X1,X2),strict_implies(X2,X1)) = strict_equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_115])]) ).
cnf(c_0_120,plain,
( X1 = X2
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_117])]) ).
cnf(c_0_121,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_118,c_0_119]) ).
cnf(c_0_122,plain,
( is_a_theorem(strict_implies(and(X1,X2),and(X2,X1)))
| ~ axiom_m1 ),
i_0_16 ).
cnf(c_0_123,plain,
axiom_m1,
i_0_64 ).
cnf(c_0_124,plain,
( is_a_theorem(X1)
| ~ modus_ponens_strict_implies
| ~ is_a_theorem(X2)
| ~ is_a_theorem(strict_implies(X2,X1)) ),
i_0_50 ).
cnf(c_0_125,plain,
modus_ponens_strict_implies,
i_0_72 ).
cnf(c_0_126,plain,
( is_a_theorem(strict_implies(and(strict_implies(X1,X2),strict_implies(X2,X3)),strict_implies(X1,X3)))
| ~ axiom_m5 ),
i_0_26 ).
cnf(c_0_127,plain,
axiom_m5,
i_0_68 ).
cnf(c_0_128,plain,
( not(and(X1,not(X2))) = implies(X1,X2)
| ~ op_implies_and ),
i_0_56 ).
cnf(c_0_129,plain,
op_implies_and,
i_0_44 ).
cnf(c_0_130,plain,
( X1 = X2
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_131,plain,
is_a_theorem(strict_implies(and(X1,X2),and(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_123])]) ).
cnf(c_0_132,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_124,c_0_125])]) ).
cnf(c_0_133,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_126,c_0_127])]) ).
cnf(c_0_134,plain,
( necessarily(implies(X1,X2)) = strict_implies(X1,X2)
| ~ op_strict_implies ),
i_0_62 ).
cnf(c_0_135,plain,
op_strict_implies,
i_0_77 ).
cnf(c_0_136,plain,
( not(and(not(X1),not(X2))) = or(X1,X2)
| ~ op_or ),
i_0_59 ).
cnf(c_0_137,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_129])]) ).
cnf(c_0_138,plain,
op_or,
i_0_74 ).
cnf(c_0_139,plain,
and(X1,X2) = and(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_131])]) ).
cnf(c_0_140,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_132,c_0_133]) ).
cnf(c_0_141,plain,
( is_a_theorem(strict_implies(and(X1,X2),X1))
| ~ axiom_m2 ),
i_0_20 ).
cnf(c_0_142,plain,
axiom_m2,
i_0_65 ).
cnf(c_0_143,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_135])]) ).
cnf(c_0_144,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_137]),c_0_138])]) ).
cnf(c_0_145,plain,
not(and(not(X1),X2)) = implies(X2,X1),
inference(spm,[status(thm)],[c_0_137,c_0_139]) ).
cnf(c_0_146,plain,
( is_a_theorem(strict_implies(X1,and(X1,X1)))
| ~ axiom_m4 ),
i_0_24 ).
cnf(c_0_147,plain,
axiom_m4,
i_0_67 ).
cnf(c_0_148,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_140,c_0_118]) ).
cnf(c_0_149,plain,
is_a_theorem(strict_implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_142])]) ).
cnf(c_0_150,plain,
necessarily(or(X1,X2)) = strict_implies(not(X1),X2),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_151,plain,
or(X1,X2) = or(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_145]),c_0_144]),c_0_144]) ).
cnf(c_0_152,plain,
is_a_theorem(strict_implies(X1,and(X1,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_146,c_0_147])]) ).
cnf(c_0_153,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,and(X2,X3))) ),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_154,plain,
strict_implies(not(X1),X2) = strict_implies(not(X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_150]) ).
cnf(c_0_155,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_152]),c_0_149])]) ).
cnf(c_0_156,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_153,c_0_154]) ).
cnf(c_0_157,plain,
is_a_theorem(strict_implies(X1,X1)),
inference(rw,[status(thm)],[c_0_152,c_0_155]) ).
cnf(c_0_158,plain,
is_a_theorem(strict_implies(not(X1),not(and(X1,X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_154]) ).
cnf(c_0_159,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(not(X2),X3))
| ~ is_a_theorem(strict_implies(X1,not(X3))) ),
inference(spm,[status(thm)],[c_0_148,c_0_154]) ).
cnf(c_0_160,plain,
( is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(strict_implies(not(X2),X1)) ),
inference(spm,[status(thm)],[c_0_156,c_0_155]) ).
cnf(c_0_161,plain,
is_a_theorem(strict_implies(not(not(X1)),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_158,c_0_145]) ).
cnf(c_0_162,plain,
not(not(X1)) = or(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_155]),c_0_144]) ).
cnf(c_0_163,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,not(not(X2)))) ),
inference(spm,[status(thm)],[c_0_159,c_0_157]) ).
cnf(c_0_164,plain,
is_a_theorem(strict_implies(not(implies(X1,X2)),not(X2))),
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_165,plain,
not(and(X1,or(X2,X2))) = implies(X1,not(X2)),
inference(spm,[status(thm)],[c_0_137,c_0_162]) ).
cnf(c_0_166,plain,
is_a_theorem(strict_implies(not(X1),implies(X2,not(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_154]) ).
cnf(c_0_167,plain,
implies(or(X1,X1),not(X1)) = not(or(X1,X1)),
inference(spm,[status(thm)],[c_0_165,c_0_155]) ).
cnf(c_0_168,plain,
is_a_theorem(strict_implies(not(X1),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_158,c_0_137]) ).
cnf(c_0_169,plain,
is_a_theorem(strict_implies(not(X1),not(or(X1,X1)))),
inference(spm,[status(thm)],[c_0_166,c_0_167]) ).
cnf(c_0_170,plain,
is_a_theorem(strict_implies(not(not(X1)),or(X1,X2))),
inference(spm,[status(thm)],[c_0_168,c_0_144]) ).
cnf(c_0_171,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_130,c_0_154]) ).
cnf(c_0_172,plain,
not(or(X1,X1)) = not(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_169]),c_0_154]),c_0_170])]) ).
cnf(c_0_173,plain,
( not(necessarily(not(X1))) = possibly(X1)
| ~ op_possibly ),
i_0_60 ).
cnf(c_0_174,plain,
op_possibly,
i_0_75 ).
cnf(c_0_175,plain,
( is_a_theorem(strict_implies(X1,possibly(X1)))
| ~ axiom_m6 ),
i_0_28 ).
cnf(c_0_176,plain,
axiom_m6,
i_0_69 ).
cnf(c_0_177,plain,
( not(not(X1)) = X1
| ~ is_a_theorem(strict_implies(X1,not(not(X1)))) ),
inference(spm,[status(thm)],[c_0_171,c_0_157]) ).
cnf(c_0_178,plain,
implies(X1,or(X2,X2)) = implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_172]),c_0_137]) ).
cnf(c_0_179,plain,
not(necessarily(not(X1))) = possibly(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_173,c_0_174])]) ).
cnf(c_0_180,plain,
is_a_theorem(strict_implies(X1,possibly(X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_175,c_0_176])]) ).
cnf(c_0_181,plain,
( or(X1,X1) = X1
| ~ is_a_theorem(strict_implies(X1,or(X1,X1))) ),
inference(spm,[status(thm)],[c_0_177,c_0_162]) ).
cnf(c_0_182,plain,
strict_implies(X1,or(X2,X2)) = strict_implies(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_178]),c_0_143]) ).
cnf(c_0_183,plain,
not(and(X1,possibly(X2))) = implies(X1,necessarily(not(X2))),
inference(spm,[status(thm)],[c_0_137,c_0_179]) ).
cnf(c_0_184,plain,
( is_a_theorem(strict_implies(possibly(possibly(X1)),possibly(X1)))
| ~ axiom_m9 ),
i_0_34 ).
cnf(c_0_185,plain,
axiom_m9,
i_0_70 ).
cnf(c_0_186,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(not(X2)) ),
inference(spm,[status(thm)],[c_0_132,c_0_154]) ).
cnf(c_0_187,plain,
( is_a_theorem(strict_implies(X1,possibly(X2)))
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_148,c_0_180]) ).
cnf(c_0_188,plain,
or(necessarily(not(X1)),X2) = implies(possibly(X1),X2),
inference(spm,[status(thm)],[c_0_144,c_0_179]) ).
cnf(c_0_189,plain,
or(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_181,c_0_182]),c_0_157])]) ).
cnf(c_0_190,plain,
implies(possibly(X1),necessarily(not(X1))) = not(possibly(X1)),
inference(spm,[status(thm)],[c_0_183,c_0_155]) ).
cnf(c_0_191,plain,
is_a_theorem(strict_implies(possibly(possibly(X1)),possibly(X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_184,c_0_185])]) ).
cnf(c_0_192,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(not(X1),X2))
| ~ is_a_theorem(not(possibly(X2))) ),
inference(spm,[status(thm)],[c_0_186,c_0_187]) ).
cnf(c_0_193,plain,
not(possibly(X1)) = necessarily(not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_189]),c_0_190]) ).
cnf(c_0_194,plain,
possibly(possibly(X1)) = possibly(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_191]),c_0_180])]) ).
cnf(c_0_195,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(not(X2),X1))
| ~ is_a_theorem(not(possibly(X2))) ),
inference(spm,[status(thm)],[c_0_192,c_0_154]) ).
cnf(c_0_196,plain,
possibly(and(X1,not(X2))) = not(strict_implies(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_137]),c_0_143]) ).
cnf(c_0_197,plain,
( axiom_4
| ~ is_a_theorem(implies(necessarily(esk3_0),necessarily(necessarily(esk3_0)))) ),
i_0_5 ).
cnf(c_0_198,negated_conjecture,
~ axiom_4,
i_0_46 ).
cnf(c_0_199,plain,
necessarily(necessarily(not(X1))) = necessarily(not(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_194]),c_0_193]),c_0_193]) ).
cnf(c_0_200,plain,
not(not(X1)) = X1,
inference(rw,[status(thm)],[c_0_162,c_0_189]) ).
cnf(c_0_201,plain,
( is_a_theorem(not(X1))
| ~ is_a_theorem(not(possibly(X1))) ),
inference(spm,[status(thm)],[c_0_195,c_0_157]) ).
cnf(c_0_202,plain,
possibly(and(not(X1),X2)) = not(strict_implies(X2,X1)),
inference(spm,[status(thm)],[c_0_196,c_0_139]) ).
cnf(c_0_203,plain,
~ is_a_theorem(implies(necessarily(esk3_0),necessarily(necessarily(esk3_0)))),
inference(sr,[status(thm)],[c_0_197,c_0_198]) ).
cnf(c_0_204,plain,
necessarily(necessarily(X1)) = necessarily(X1),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_205,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(not(strict_implies(X1,X2)))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_145]) ).
cnf(c_0_206,plain,
~ is_a_theorem(implies(necessarily(esk3_0),necessarily(esk3_0))),
inference(rw,[status(thm)],[c_0_203,c_0_204]) ).
cnf(c_0_207,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(rw,[status(thm)],[c_0_205,c_0_200]) ).
cnf(c_0_208,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_207]),c_0_157])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL568+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : enigmatic-eprover.py %s %d 1
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 5 04:29:17 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.23/0.46 # ENIGMATIC: Selected SinE mode:
% 0.23/0.47 # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.47 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.23/0.47 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.23/0.47 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 21.77/5.03 # ENIGMATIC: Solved by autoschedule-lgb:
% 21.77/5.03 # No SInE strategy applied
% 21.77/5.03 # Trying AutoSched0 for 150 seconds
% 21.77/5.03 # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 21.77/5.03 # and selection function SelectComplexExceptUniqMaxHorn.
% 21.77/5.03 #
% 21.77/5.03 # Preprocessing time : 0.024 s
% 21.77/5.03 # Presaturation interreduction done
% 21.77/5.03
% 21.77/5.03 # Proof found!
% 21.77/5.03 # SZS status Theorem
% 21.77/5.03 # SZS output start CNFRefutation
% See solution above
% 21.77/5.03 # Training examples: 0 positive, 0 negative
% 21.77/5.03
% 21.77/5.03 # -------------------------------------------------
% 21.77/5.03 # User time : 0.432 s
% 21.77/5.03 # System time : 0.022 s
% 21.77/5.03 # Total time : 0.454 s
% 21.77/5.03 # Maximum resident set size: 3584 pages
% 21.77/5.03
%------------------------------------------------------------------------------