%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : LCL454+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n002.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 11:44:47 AM UTC 2026
% Result : Theorem 10.59s 3.96s
% Output : CNFRefutation 10.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of clauses : 69 ( 40 unt; 0 nHn; 36 RR)
% Number of literals : 108 ( 20 equ; 42 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 : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 78 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_51,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-w1uvs7v7/input.p',i_0_51) ).
cnf(i_0_28,plain,
modus_ponens,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_28) ).
cnf(i_0_6,plain,
( is_a_theorem(implies(X1,implies(X2,and(X1,X2))))
| ~ and_3 ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_6) ).
cnf(i_0_21,plain,
and_3,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_21) ).
cnf(i_0_39,plain,
( is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))
| ~ implies_2 ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_39) ).
cnf(i_0_26,plain,
implies_2,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_26) ).
cnf(i_0_55,plain,
( and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2)
| ~ op_equiv ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_55) ).
cnf(i_0_30,plain,
op_equiv,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_30) ).
cnf(i_0_37,plain,
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ implies_1 ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_37) ).
cnf(i_0_25,plain,
implies_1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_25) ).
cnf(i_0_56,plain,
( not(and(X1,not(X2))) = implies(X1,X2)
| ~ op_implies_and ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_56) ).
cnf(i_0_31,plain,
op_implies_and,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_31) ).
cnf(i_0_81,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_81) ).
cnf(i_0_82,plain,
substitution_of_equivalents,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_82) ).
cnf(i_0_58,plain,
( not(and(not(X1),not(X2))) = or(X1,X2)
| ~ op_or ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_58) ).
cnf(i_0_32,plain,
op_or,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_32) ).
cnf(i_0_2,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ and_1 ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_2) ).
cnf(i_0_19,plain,
and_1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_19) ).
cnf(i_0_57,plain,
( or(not(X1),X2) = implies(X1,X2)
| ~ op_implies_or ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_57) ).
cnf(i_0_67,plain,
op_implies_or,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_67) ).
cnf(i_0_69,plain,
( r1
| ~ is_a_theorem(implies(or(esk43_0,esk43_0),esk43_0)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_69) ).
cnf(i_0_68,negated_conjecture,
~ r1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-w1uvs7v7/input.p',i_0_68) ).
cnf(c_0_105,plain,
( is_a_theorem(X1)
| ~ modus_ponens
| ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(X2,X1)) ),
i_0_51 ).
cnf(c_0_106,plain,
modus_ponens,
i_0_28 ).
cnf(c_0_107,plain,
( is_a_theorem(implies(X1,implies(X2,and(X1,X2))))
| ~ and_3 ),
i_0_6 ).
cnf(c_0_108,plain,
and_3,
i_0_21 ).
cnf(c_0_109,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_105,c_0_106])]) ).
cnf(c_0_110,plain,
is_a_theorem(implies(X1,implies(X2,and(X1,X2)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_108])]) ).
cnf(c_0_111,plain,
( is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))
| ~ implies_2 ),
i_0_39 ).
cnf(c_0_112,plain,
implies_2,
i_0_26 ).
cnf(c_0_113,plain,
( is_a_theorem(implies(X1,and(X2,X1)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_114,plain,
( and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2)
| ~ op_equiv ),
i_0_55 ).
cnf(c_0_115,plain,
op_equiv,
i_0_30 ).
cnf(c_0_116,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_112])]) ).
cnf(c_0_117,plain,
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ implies_1 ),
i_0_37 ).
cnf(c_0_118,plain,
implies_1,
i_0_25 ).
cnf(c_0_119,plain,
( not(and(X1,not(X2))) = implies(X1,X2)
| ~ op_implies_and ),
i_0_56 ).
cnf(c_0_120,plain,
op_implies_and,
i_0_31 ).
cnf(c_0_121,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
i_0_81 ).
cnf(c_0_122,plain,
substitution_of_equivalents,
i_0_82 ).
cnf(c_0_123,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_109,c_0_113]) ).
cnf(c_0_124,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_115])]) ).
cnf(c_0_125,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_109,c_0_116]) ).
cnf(c_0_126,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_118])]) ).
cnf(c_0_127,plain,
( not(and(not(X1),not(X2))) = or(X1,X2)
| ~ op_or ),
i_0_58 ).
cnf(c_0_128,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_120])]) ).
cnf(c_0_129,plain,
op_or,
i_0_32 ).
cnf(c_0_130,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_122])]) ).
cnf(c_0_131,plain,
( is_a_theorem(equiv(X1,X2))
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_132,plain,
( is_a_theorem(implies(and(X1,X2),X1))
| ~ and_1 ),
i_0_2 ).
cnf(c_0_133,plain,
and_1,
i_0_19 ).
cnf(c_0_134,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_135,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_128]),c_0_129])]) ).
cnf(c_0_136,plain,
( or(not(X1),X2) = implies(X1,X2)
| ~ op_implies_or ),
i_0_57 ).
cnf(c_0_137,plain,
op_implies_or,
i_0_67 ).
cnf(c_0_138,plain,
( X1 = X2
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_139,plain,
is_a_theorem(implies(X1,and(X1,X1))),
inference(spm,[status(thm)],[c_0_125,c_0_110]) ).
cnf(c_0_140,plain,
is_a_theorem(implies(and(X1,X2),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_133])]) ).
cnf(c_0_141,plain,
is_a_theorem(or(X1,not(X1))),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_142,plain,
or(not(X1),X2) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_137])]) ).
cnf(c_0_143,plain,
and(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_140])]) ).
cnf(c_0_144,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_145,plain,
( r1
| ~ is_a_theorem(implies(or(esk43_0,esk43_0),esk43_0)) ),
i_0_69 ).
cnf(c_0_146,negated_conjecture,
~ r1,
i_0_68 ).
cnf(c_0_147,plain,
not(not(X1)) = or(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_143]),c_0_135]) ).
cnf(c_0_148,plain,
not(not(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_144]),c_0_135]),c_0_142]),c_0_134])]) ).
cnf(c_0_149,plain,
~ is_a_theorem(implies(or(esk43_0,esk43_0),esk43_0)),
inference(sr,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_150,plain,
or(X1,X1) = X1,
inference(rw,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_151,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_150]),c_0_134])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL454+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : enigmatic-eprover.py %s %d 1
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 21:42:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.46 # ENIGMATIC: Selected SinE mode:
% 0.20/0.46 # Parsing /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.20/0.46 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.20/0.46 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 10.59/3.96 # ENIGMATIC: Solved by G_E___302_C18_F1_URBAN_S5PRR_S0Y:
% 10.59/3.96 # Version: 2.1pre011
% 10.59/3.96 # Preprocessing time : 0.016 s
% 10.59/3.96
% 10.59/3.96 # Proof found!
% 10.59/3.96 # SZS status Theorem
% 10.59/3.96 # SZS output start CNFRefutation
% See solution above
% 10.59/3.96 # Proof object total steps : 69
% 10.59/3.96 # Proof object clause steps : 47
% 10.59/3.96 # Proof object formula steps : 22
% 10.59/3.96 # Proof object conjectures : 2
% 10.59/3.96 # Proof object clause conjectures : 1
% 10.59/3.96 # Proof object formula conjectures : 1
% 10.59/3.96 # Proof object initial clauses used : 22
% 10.59/3.96 # Proof object initial formulas used : 22
% 10.59/3.96 # Proof object generating inferences : 12
% 10.59/3.96 # Proof object simplifying inferences : 33
% 10.59/3.96 # Training examples: 0 positive, 0 negative
% 10.59/3.96 # Parsed axioms : 82
% 10.59/3.96 # Removed by relevancy pruning/SinE : 0
% 10.59/3.96 # Initial clauses : 82
% 10.59/3.96 # Removed in clause preprocessing : 0
% 10.59/3.96 # Initial clauses in saturation : 82
% 10.59/3.96 # Processed clauses : 330
% 10.59/3.96 # ...of these trivial : 36
% 10.59/3.96 # ...subsumed : 82
% 10.59/3.96 # ...remaining for further processing : 212
% 10.59/3.96 # Other redundant clauses eliminated : 0
% 10.59/3.96 # Clauses deleted for lack of memory : 0
% 10.59/3.96 # Backward-subsumed : 4
% 10.59/3.96 # Backward-rewritten : 40
% 10.59/3.96 # Generated clauses : 2259
% 10.59/3.96 # ...of the previous two non-trivial : 1951
% 10.59/3.96 # Contextual simplify-reflections : 12
% 10.59/3.96 # Paramodulations : 2259
% 10.59/3.96 # Factorizations : 0
% 10.59/3.96 # Equation resolutions : 0
% 10.59/3.96 # Propositional unsat checks : 0
% 10.59/3.96 # Propositional unsat check successes : 0
% 10.59/3.96 # Current number of processed clauses : 168
% 10.59/3.96 # Positive orientable unit clauses : 84
% 10.59/3.96 # Positive unorientable unit clauses: 2
% 10.59/3.96 # Negative unit clauses : 4
% 10.59/3.96 # Non-unit-clauses : 78
% 10.59/3.96 # Current number of unprocessed clauses: 1247
% 10.59/3.96 # ...number of literals in the above : 2268
% 10.59/3.96 # Current number of archived formulas : 0
% 10.59/3.96 # Current number of archived clauses : 44
% 10.59/3.96 # Clause-clause subsumption calls (NU) : 2146
% 10.59/3.96 # Rec. Clause-clause subsumption calls : 2092
% 10.59/3.96 # Non-unit clause-clause subsumptions : 93
% 10.59/3.96 # Unit Clause-clause subsumption calls : 516
% 10.59/3.96 # Rewrite failures with RHS unbound : 15
% 10.59/3.96 # BW rewrite match attempts : 437
% 10.59/3.96 # BW rewrite match successes : 38
% 10.59/3.96 # Condensation attempts : 0
% 10.59/3.96 # Condensation successes : 0
% 10.59/3.96 # Termbank termtop insertions : 24770
% 10.59/3.96
% 10.59/3.96 # -------------------------------------------------
% 10.59/3.96 # User time : 0.056 s
% 10.59/3.96 # System time : 0.005 s
% 10.59/3.96 # Total time : 0.061 s
% 10.59/3.96 # ...preprocessing : 0.016 s
% 10.59/3.96 # ...main loop : 0.045 s
% 10.59/3.96 # Maximum resident set size: 8448 pages
% 10.59/3.96
%------------------------------------------------------------------------------