%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : LCL539+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n019.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 11:44:58 AM UTC 2026
% Result : Theorem 14.69s 3.87s
% Output : CNFRefutation 14.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of clauses : 68 ( 34 unt; 2 nHn; 46 RR)
% Number of literals : 111 ( 17 equ; 44 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 11 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 70 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_97,plain,
( is_a_theorem(X1)
| ~ modus_ponens
| ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(X2,X1)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-2_9iehek/lgb.p',i_0_97) ).
cnf(i_0_68,plain,
modus_ponens,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-2_9iehek/lgb.p',i_0_68) ).
cnf(i_0_8,plain,
( is_a_theorem(implies(and(X1,X2),X2))
| ~ and_2 ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-2_9iehek/lgb.p',i_0_8) ).
cnf(i_0_60,plain,
and_2,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-2_9iehek/lgb.p',i_0_60) ).
cnf(i_0_6,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ and_1 ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-2_9iehek/lgb.p',i_0_6) ).
cnf(i_0_59,plain,
and_1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-2_9iehek/lgb.p',i_0_59) ).
cnf(i_0_10,plain,
( is_a_theorem(implies(X1,implies(X2,and(X1,X2))))
| ~ and_3 ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-2_9iehek/lgb.p',i_0_10) ).
cnf(i_0_61,plain,
and_3,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-2_9iehek/lgb.p',i_0_61) ).
cnf(i_0_20,plain,
( is_a_theorem(implies(necessarily(X1),X1))
| ~ axiom_M ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-2_9iehek/lgb.p',i_0_20) ).
cnf(i_0_85,plain,
axiom_M,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-2_9iehek/lgb.p',i_0_85) ).
cnf(i_0_114,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-2_9iehek/lgb.p',i_0_114) ).
cnf(i_0_135,plain,
op_strict_equiv,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-2_9iehek/lgb.p',i_0_135) ).
cnf(i_0_140,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-2_9iehek/lgb.p',i_0_140) ).
cnf(i_0_144,plain,
substitution_of_equivalents,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-2_9iehek/lgb.p',i_0_144) ).
cnf(i_0_108,plain,
( and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2)
| ~ op_equiv ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-2_9iehek/lgb.p',i_0_108) ).
cnf(i_0_70,plain,
op_equiv,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-2_9iehek/lgb.p',i_0_70) ).
cnf(i_0_115,plain,
( necessarily(implies(X1,X2)) = strict_implies(X1,X2)
| ~ op_strict_implies ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-2_9iehek/lgb.p',i_0_115) ).
cnf(i_0_136,plain,
op_strict_implies,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-2_9iehek/lgb.p',i_0_136) ).
cnf(i_0_142,plain,
( substitution_strict_equiv
| is_a_theorem(strict_equiv(esk90_0,esk91_0)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-2_9iehek/lgb.p',i_0_142) ).
cnf(i_0_137,negated_conjecture,
~ substitution_strict_equiv,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-2_9iehek/lgb.p',i_0_137) ).
cnf(i_0_141,plain,
( substitution_strict_equiv
| esk91_0 != esk90_0 ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-2_9iehek/lgb.p',i_0_141) ).
cnf(c_0_166,plain,
( is_a_theorem(X1)
| ~ modus_ponens
| ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(X2,X1)) ),
i_0_97 ).
cnf(c_0_167,plain,
modus_ponens,
i_0_68 ).
cnf(c_0_168,plain,
( is_a_theorem(implies(and(X1,X2),X2))
| ~ and_2 ),
i_0_8 ).
cnf(c_0_169,plain,
and_2,
i_0_60 ).
cnf(c_0_170,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ and_1 ),
i_0_6 ).
cnf(c_0_171,plain,
and_1,
i_0_59 ).
cnf(c_0_172,plain,
( is_a_theorem(implies(X1,implies(X2,and(X1,X2))))
| ~ and_3 ),
i_0_10 ).
cnf(c_0_173,plain,
and_3,
i_0_61 ).
cnf(c_0_174,plain,
( is_a_theorem(implies(necessarily(X1),X1))
| ~ axiom_M ),
i_0_20 ).
cnf(c_0_175,plain,
axiom_M,
i_0_85 ).
cnf(c_0_176,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_166,c_0_167])]) ).
cnf(c_0_177,plain,
is_a_theorem(implies(and(X1,X2),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_168,c_0_169])]) ).
cnf(c_0_178,plain,
( and(strict_implies(X1,X2),strict_implies(X2,X1)) = strict_equiv(X1,X2)
| ~ op_strict_equiv ),
i_0_114 ).
cnf(c_0_179,plain,
op_strict_equiv,
i_0_135 ).
cnf(c_0_180,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_171])]) ).
cnf(c_0_181,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
i_0_140 ).
cnf(c_0_182,plain,
substitution_of_equivalents,
i_0_144 ).
cnf(c_0_183,plain,
( and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2)
| ~ op_equiv ),
i_0_108 ).
cnf(c_0_184,plain,
op_equiv,
i_0_70 ).
cnf(c_0_185,plain,
is_a_theorem(implies(X1,implies(X2,and(X1,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_172,c_0_173])]) ).
cnf(c_0_186,plain,
is_a_theorem(implies(necessarily(X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_174,c_0_175])]) ).
cnf(c_0_187,plain,
( necessarily(implies(X1,X2)) = strict_implies(X1,X2)
| ~ op_strict_implies ),
i_0_115 ).
cnf(c_0_188,plain,
op_strict_implies,
i_0_136 ).
cnf(c_0_189,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(and(X2,X1)) ),
inference(spm,[status(thm)],[c_0_176,c_0_177]) ).
cnf(c_0_190,plain,
and(strict_implies(X1,X2),strict_implies(X2,X1)) = strict_equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_178,c_0_179])]) ).
cnf(c_0_191,plain,
( substitution_strict_equiv
| is_a_theorem(strict_equiv(esk90_0,esk91_0)) ),
i_0_142 ).
cnf(c_0_192,negated_conjecture,
~ substitution_strict_equiv,
i_0_137 ).
cnf(c_0_193,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(and(X1,X2)) ),
inference(spm,[status(thm)],[c_0_176,c_0_180]) ).
cnf(c_0_194,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_181,c_0_182])]) ).
cnf(c_0_195,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_183,c_0_184])]) ).
cnf(c_0_196,plain,
( is_a_theorem(implies(X1,and(X2,X1)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_176,c_0_185]) ).
cnf(c_0_197,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(necessarily(X1)) ),
inference(spm,[status(thm)],[c_0_176,c_0_186]) ).
cnf(c_0_198,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_187,c_0_188])]) ).
cnf(c_0_199,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_equiv(X2,X1)) ),
inference(spm,[status(thm)],[c_0_189,c_0_190]) ).
cnf(c_0_200,plain,
is_a_theorem(strict_equiv(esk90_0,esk91_0)),
inference(sr,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_201,plain,
( is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(strict_equiv(X1,X2)) ),
inference(spm,[status(thm)],[c_0_193,c_0_190]) ).
cnf(c_0_202,plain,
( X1 = X2
| ~ is_a_theorem(and(implies(X1,X2),implies(X2,X1))) ),
inference(spm,[status(thm)],[c_0_194,c_0_195]) ).
cnf(c_0_203,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_176,c_0_196]) ).
cnf(c_0_204,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_197,c_0_198]) ).
cnf(c_0_205,plain,
is_a_theorem(strict_implies(esk91_0,esk90_0)),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_206,plain,
is_a_theorem(strict_implies(esk90_0,esk91_0)),
inference(spm,[status(thm)],[c_0_201,c_0_200]) ).
cnf(c_0_207,plain,
( substitution_strict_equiv
| esk91_0 != esk90_0 ),
i_0_141 ).
cnf(c_0_208,plain,
( X1 = X2
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_202,c_0_203]) ).
cnf(c_0_209,plain,
is_a_theorem(implies(esk91_0,esk90_0)),
inference(spm,[status(thm)],[c_0_204,c_0_205]) ).
cnf(c_0_210,plain,
is_a_theorem(implies(esk90_0,esk91_0)),
inference(spm,[status(thm)],[c_0_204,c_0_206]) ).
cnf(c_0_211,plain,
esk91_0 != esk90_0,
inference(sr,[status(thm)],[c_0_207,c_0_192]) ).
cnf(c_0_212,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_209]),c_0_210])]),c_0_211]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL539+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : enigmatic-eprover.py %s %d 1
% 0.08/0.34 % Computer : n019.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 5 14:54:55 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.44 # ENIGMATIC: Selected SinE mode:
% 0.12/0.45 # Parsing /export/starexec/sandbox2/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
% 14.69/3.87 # ENIGMATIC: Solved by autoschedule-lgb:
% 14.69/3.87 # No SInE strategy applied
% 14.69/3.87 # Trying AutoSched0 for 150 seconds
% 14.69/3.87 # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AI
% 14.69/3.87 # and selection function SelectComplexExceptUniqMaxHorn.
% 14.69/3.87 #
% 14.69/3.87 # Preprocessing time : 0.025 s
% 14.69/3.87 # Presaturation interreduction done
% 14.69/3.87
% 14.69/3.87 # Proof found!
% 14.69/3.87 # SZS status Theorem
% 14.69/3.87 # SZS output start CNFRefutation
% See solution above
% 14.69/3.87 # Training examples: 0 positive, 0 negative
% 14.69/3.87
% 14.69/3.87 # -------------------------------------------------
% 14.69/3.87 # User time : 0.098 s
% 14.69/3.87 # System time : 0.011 s
% 14.69/3.87 # Total time : 0.110 s
% 14.69/3.87 # Maximum resident set size: 3584 pages
% 14.69/3.87
%------------------------------------------------------------------------------