%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : LCL525+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 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 : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 11:44:56 AM UTC 2026
% Result : Theorem 17.39s 4.57s
% Output : CNFRefutation 17.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 26
% Syntax : Number of clauses : 78 ( 34 unt; 8 nHn; 55 RR)
% Number of literals : 138 ( 23 equ; 55 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_139,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_139) ).
cnf(i_0_143,plain,
substitution_of_equivalents,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_143) ).
cnf(i_0_107,plain,
( and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2)
| ~ op_equiv ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_107) ).
cnf(i_0_70,plain,
op_equiv,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_70) ).
cnf(i_0_108,plain,
( not(and(X1,not(X2))) = implies(X1,X2)
| ~ op_implies_and ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_108) ).
cnf(i_0_71,plain,
op_implies_and,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_71) ).
cnf(i_0_111,plain,
( not(and(not(X1),not(X2))) = or(X1,X2)
| ~ op_or ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_111) ).
cnf(i_0_72,plain,
op_or,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_72) ).
cnf(i_0_96,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-trglk9wb/input.p',i_0_96) ).
cnf(i_0_68,plain,
modus_ponens,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_68) ).
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-trglk9wb/input.p',i_0_10) ).
cnf(i_0_61,plain,
and_3,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_61) ).
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-trglk9wb/input.p',i_0_4) ).
cnf(i_0_20,plain,
( is_a_theorem(implies(necessarily(X1),X1))
| ~ axiom_M ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_20) ).
cnf(i_0_84,plain,
axiom_M,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_84) ).
cnf(i_0_118,plain,
( is_a_theorem(implies(X1,or(X2,X1)))
| ~ or_2 ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_118) ).
cnf(i_0_74,plain,
or_2,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_74) ).
cnf(i_0_1,plain,
( adjunction
| ~ is_a_theorem(and(esk1_0,esk2_0)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_1) ).
cnf(i_0_3,plain,
( adjunction
| is_a_theorem(esk1_0) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_3) ).
cnf(i_0_2,plain,
( adjunction
| is_a_theorem(esk2_0) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_2) ).
cnf(i_0_114,plain,
( necessarily(implies(X1,X2)) = strict_implies(X1,X2)
| ~ op_strict_implies ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_114) ).
cnf(i_0_136,plain,
op_strict_implies,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_136) ).
cnf(i_0_98,plain,
( modus_ponens_strict_implies
| is_a_theorem(strict_implies(esk65_0,esk66_0)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_98) ).
cnf(i_0_131,negated_conjecture,
~ modus_ponens_strict_implies,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_131) ).
cnf(i_0_99,plain,
( modus_ponens_strict_implies
| is_a_theorem(esk65_0) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_99) ).
cnf(i_0_97,plain,
( modus_ponens_strict_implies
| ~ is_a_theorem(esk66_0) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-trglk9wb/input.p',i_0_97) ).
cnf(c_0_170,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
i_0_139 ).
cnf(c_0_171,plain,
substitution_of_equivalents,
i_0_143 ).
cnf(c_0_172,plain,
( and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2)
| ~ op_equiv ),
i_0_107 ).
cnf(c_0_173,plain,
op_equiv,
i_0_70 ).
cnf(c_0_174,plain,
( not(and(X1,not(X2))) = implies(X1,X2)
| ~ op_implies_and ),
i_0_108 ).
cnf(c_0_175,plain,
op_implies_and,
i_0_71 ).
cnf(c_0_176,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_171])]) ).
cnf(c_0_177,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_172,c_0_173])]) ).
cnf(c_0_178,plain,
( not(and(not(X1),not(X2))) = or(X1,X2)
| ~ op_or ),
i_0_111 ).
cnf(c_0_179,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_174,c_0_175])]) ).
cnf(c_0_180,plain,
op_or,
i_0_72 ).
cnf(c_0_181,plain,
( X1 = X2
| ~ is_a_theorem(and(implies(X1,X2),implies(X2,X1))) ),
inference(spm,[status(thm)],[c_0_176,c_0_177]) ).
cnf(c_0_182,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_178,c_0_179]),c_0_180])]) ).
cnf(c_0_183,plain,
( is_a_theorem(X1)
| ~ modus_ponens
| ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(X2,X1)) ),
i_0_96 ).
cnf(c_0_184,plain,
modus_ponens,
i_0_68 ).
cnf(c_0_185,plain,
( is_a_theorem(implies(X1,implies(X2,and(X1,X2))))
| ~ and_3 ),
i_0_10 ).
cnf(c_0_186,plain,
and_3,
i_0_61 ).
cnf(c_0_187,plain,
( X1 = not(X2)
| ~ is_a_theorem(and(implies(X1,not(X2)),or(X2,X1))) ),
inference(spm,[status(thm)],[c_0_181,c_0_182]) ).
cnf(c_0_188,plain,
( is_a_theorem(and(X1,X2))
| ~ adjunction
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
i_0_4 ).
cnf(c_0_189,plain,
( is_a_theorem(implies(necessarily(X1),X1))
| ~ axiom_M ),
i_0_20 ).
cnf(c_0_190,plain,
axiom_M,
i_0_84 ).
cnf(c_0_191,plain,
( is_a_theorem(implies(X1,or(X2,X1)))
| ~ or_2 ),
i_0_118 ).
cnf(c_0_192,plain,
or_2,
i_0_74 ).
cnf(c_0_193,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_183,c_0_184])]) ).
cnf(c_0_194,plain,
is_a_theorem(implies(X1,implies(X2,and(X1,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_185,c_0_186])]) ).
cnf(c_0_195,plain,
( X1 = not(X2)
| ~ is_a_theorem(implies(X1,not(X2)))
| ~ is_a_theorem(or(X2,X1))
| ~ adjunction ),
inference(spm,[status(thm)],[c_0_187,c_0_188]) ).
cnf(c_0_196,plain,
is_a_theorem(implies(necessarily(X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_189,c_0_190])]) ).
cnf(c_0_197,plain,
is_a_theorem(implies(X1,or(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_191,c_0_192])]) ).
cnf(c_0_198,plain,
( is_a_theorem(implies(X1,and(X2,X1)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_193,c_0_194]) ).
cnf(c_0_199,plain,
( necessarily(not(X1)) = not(X1)
| ~ is_a_theorem(or(X1,necessarily(not(X1))))
| ~ adjunction ),
inference(spm,[status(thm)],[c_0_195,c_0_196]) ).
cnf(c_0_200,plain,
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_193,c_0_197]) ).
cnf(c_0_201,plain,
( adjunction
| ~ is_a_theorem(and(esk1_0,esk2_0)) ),
i_0_1 ).
cnf(c_0_202,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_193,c_0_198]) ).
cnf(c_0_203,plain,
( adjunction
| is_a_theorem(esk1_0) ),
i_0_3 ).
cnf(c_0_204,plain,
( adjunction
| is_a_theorem(esk2_0) ),
i_0_2 ).
cnf(c_0_205,plain,
( necessarily(not(X1)) = not(X1)
| ~ is_a_theorem(necessarily(not(X1)))
| ~ adjunction ),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_206,plain,
adjunction,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_203]),c_0_204]) ).
cnf(c_0_207,plain,
( necessarily(implies(X1,X2)) = strict_implies(X1,X2)
| ~ op_strict_implies ),
i_0_114 ).
cnf(c_0_208,plain,
op_strict_implies,
i_0_136 ).
cnf(c_0_209,plain,
( necessarily(not(X1)) = not(X1)
| ~ is_a_theorem(necessarily(not(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_205,c_0_206])]) ).
cnf(c_0_210,plain,
necessarily(implies(X1,X2)) = strict_implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_207,c_0_208])]) ).
cnf(c_0_211,plain,
( modus_ponens_strict_implies
| is_a_theorem(strict_implies(esk65_0,esk66_0)) ),
i_0_98 ).
cnf(c_0_212,negated_conjecture,
~ modus_ponens_strict_implies,
i_0_131 ).
cnf(c_0_213,plain,
( strict_implies(X1,X2) = implies(X1,X2)
| ~ is_a_theorem(strict_implies(X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_179]),c_0_210]),c_0_210]) ).
cnf(c_0_214,plain,
is_a_theorem(strict_implies(esk65_0,esk66_0)),
inference(sr,[status(thm)],[c_0_211,c_0_212]) ).
cnf(c_0_215,plain,
strict_implies(esk65_0,esk66_0) = implies(esk65_0,esk66_0),
inference(spm,[status(thm)],[c_0_213,c_0_214]) ).
cnf(c_0_216,plain,
( modus_ponens_strict_implies
| is_a_theorem(esk65_0) ),
i_0_99 ).
cnf(c_0_217,plain,
( modus_ponens_strict_implies
| ~ is_a_theorem(esk66_0) ),
i_0_97 ).
cnf(c_0_218,plain,
is_a_theorem(implies(esk65_0,esk66_0)),
inference(rw,[status(thm)],[c_0_214,c_0_215]) ).
cnf(c_0_219,plain,
is_a_theorem(esk65_0),
inference(sr,[status(thm)],[c_0_216,c_0_212]) ).
cnf(c_0_220,plain,
~ is_a_theorem(esk66_0),
inference(sr,[status(thm)],[c_0_217,c_0_212]) ).
cnf(c_0_221,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_218]),c_0_219])]),c_0_220]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL525+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : enigmatic-eprover.py %s %d 1
% 0.19/0.43 % Computer : n011.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 5 13:10:00 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.27/0.58 # ENIGMATIC: Selected SinE mode:
% 0.27/0.59 # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.27/0.59 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.27/0.59 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.27/0.59 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 17.39/4.57 # ENIGMATIC: Solved by G_E___302_C18_F1_URBAN_S5PRR_RG_S04BN:
% 17.39/4.57 # Version: 2.1pre011
% 17.39/4.57 # Preprocessing time : 0.017 s
% 17.39/4.57
% 17.39/4.57 # Proof found!
% 17.39/4.57 # SZS status Theorem
% 17.39/4.57 # SZS output start CNFRefutation
% See solution above
% 17.39/4.57 # Proof object total steps : 78
% 17.39/4.57 # Proof object clause steps : 52
% 17.39/4.57 # Proof object formula steps : 26
% 17.39/4.57 # Proof object conjectures : 2
% 17.39/4.57 # Proof object clause conjectures : 1
% 17.39/4.57 # Proof object formula conjectures : 1
% 17.39/4.57 # Proof object initial clauses used : 26
% 17.39/4.57 # Proof object initial formulas used : 26
% 17.39/4.57 # Proof object generating inferences : 12
% 17.39/4.57 # Proof object simplifying inferences : 32
% 17.39/4.57 # Training examples: 0 positive, 0 negative
% 17.39/4.57 # Parsed axioms : 143
% 17.39/4.57 # Removed by relevancy pruning/SinE : 0
% 17.39/4.57 # Initial clauses : 143
% 17.39/4.57 # Removed in clause preprocessing : 0
% 17.39/4.57 # Initial clauses in saturation : 143
% 17.39/4.57 # Processed clauses : 298
% 17.39/4.57 # ...of these trivial : 28
% 17.39/4.57 # ...subsumed : 13
% 17.39/4.57 # ...remaining for further processing : 257
% 17.39/4.57 # Other redundant clauses eliminated : 0
% 17.39/4.57 # Clauses deleted for lack of memory : 0
% 17.39/4.57 # Backward-subsumed : 3
% 17.39/4.57 # Backward-rewritten : 19
% 17.39/4.57 # Generated clauses : 1675
% 17.39/4.57 # ...of the previous two non-trivial : 1609
% 17.39/4.57 # Contextual simplify-reflections : 9
% 17.39/4.57 # Paramodulations : 1675
% 17.39/4.57 # Factorizations : 0
% 17.39/4.57 # Equation resolutions : 0
% 17.39/4.57 # Propositional unsat checks : 0
% 17.39/4.57 # Propositional unsat check successes : 0
% 17.39/4.57 # Current number of processed clauses : 235
% 17.39/4.57 # Positive orientable unit clauses : 68
% 17.39/4.57 # Positive unorientable unit clauses: 1
% 17.39/4.57 # Negative unit clauses : 2
% 17.39/4.57 # Non-unit-clauses : 164
% 17.39/4.57 # Current number of unprocessed clauses: 1323
% 17.39/4.57 # ...number of literals in the above : 3349
% 17.39/4.57 # Current number of archived formulas : 0
% 17.39/4.57 # Current number of archived clauses : 22
% 17.39/4.57 # Clause-clause subsumption calls (NU) : 1458
% 17.39/4.57 # Rec. Clause-clause subsumption calls : 1251
% 17.39/4.57 # Non-unit clause-clause subsumptions : 24
% 17.39/4.57 # Unit Clause-clause subsumption calls : 221
% 17.39/4.57 # Rewrite failures with RHS unbound : 0
% 17.39/4.57 # BW rewrite match attempts : 43
% 17.39/4.57 # BW rewrite match successes : 8
% 17.39/4.57 # Condensation attempts : 0
% 17.39/4.57 # Condensation successes : 0
% 17.39/4.57 # Termbank termtop insertions : 21891
% 17.39/4.57
% 17.39/4.57 # -------------------------------------------------
% 17.39/4.57 # User time : 0.050 s
% 17.39/4.57 # System time : 0.003 s
% 17.39/4.57 # Total time : 0.053 s
% 17.39/4.57 # ...preprocessing : 0.017 s
% 17.39/4.57 # ...main loop : 0.036 s
% 17.39/4.57 # Maximum resident set size: 9216 pages
% 17.39/4.57
%------------------------------------------------------------------------------