%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : LCL456+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n027.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 15.86s 4.34s
% Output : CNFRefutation 15.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 22
% Syntax : Number of clauses : 67 ( 38 unt; 0 nHn; 36 RR)
% Number of literals : 106 ( 17 equ; 42 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 78 ( 3 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/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/input.p',i_0_51) ).
cnf(i_0_28,plain,
modus_ponens,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/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/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/input.p',i_0_6) ).
cnf(i_0_21,plain,
and_3,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/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/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/input.p',i_0_39) ).
cnf(i_0_26,plain,
implies_2,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/input.p',i_0_26) ).
cnf(i_0_37,plain,
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ implies_1 ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/input.p',i_0_37) ).
cnf(i_0_25,plain,
implies_1,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/input.p',i_0_25) ).
cnf(i_0_56,plain,
( not(and(X1,not(X2))) = implies(X1,X2)
| ~ op_implies_and ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/input.p',i_0_56) ).
cnf(i_0_31,plain,
op_implies_and,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/input.p',i_0_31) ).
cnf(i_0_55,plain,
( and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2)
| ~ op_equiv ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/input.p',i_0_55) ).
cnf(i_0_30,plain,
op_equiv,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/input.p',i_0_30) ).
cnf(i_0_58,plain,
( not(and(not(X1),not(X2))) = or(X1,X2)
| ~ op_or ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/input.p',i_0_58) ).
cnf(i_0_32,plain,
op_or,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/input.p',i_0_32) ).
cnf(i_0_81,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/input.p',i_0_81) ).
cnf(i_0_82,plain,
substitution_of_equivalents,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/input.p',i_0_82) ).
cnf(i_0_57,plain,
( or(not(X1),X2) = implies(X1,X2)
| ~ op_implies_or ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/input.p',i_0_57) ).
cnf(i_0_67,plain,
op_implies_or,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/input.p',i_0_67) ).
cnf(i_0_53,plain,
( is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))
| ~ modus_tollens ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/input.p',i_0_53) ).
cnf(i_0_29,plain,
modus_tollens,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/input.p',i_0_29) ).
cnf(i_0_73,plain,
( r3
| ~ is_a_theorem(implies(or(esk46_0,esk47_0),or(esk47_0,esk46_0))) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/input.p',i_0_73) ).
cnf(i_0_68,negated_conjecture,
~ r3,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-9uz7hl6f/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(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))
| ~ implies_2 ),
i_0_39 ).
cnf(c_0_110,plain,
implies_2,
i_0_26 ).
cnf(c_0_111,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_112,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_113,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110])]) ).
cnf(c_0_114,plain,
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ implies_1 ),
i_0_37 ).
cnf(c_0_115,plain,
implies_1,
i_0_25 ).
cnf(c_0_116,plain,
( not(and(X1,not(X2))) = implies(X1,X2)
| ~ op_implies_and ),
i_0_56 ).
cnf(c_0_117,plain,
op_implies_and,
i_0_31 ).
cnf(c_0_118,plain,
( is_a_theorem(implies(X1,and(X2,X1)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_119,plain,
( and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2)
| ~ op_equiv ),
i_0_55 ).
cnf(c_0_120,plain,
op_equiv,
i_0_30 ).
cnf(c_0_121,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(X1,X2))) ),
inference(spm,[status(thm)],[c_0_111,c_0_113]) ).
cnf(c_0_122,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_115])]) ).
cnf(c_0_123,plain,
( not(and(not(X1),not(X2))) = or(X1,X2)
| ~ op_or ),
i_0_58 ).
cnf(c_0_124,plain,
not(and(X1,not(X2))) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_117])]) ).
cnf(c_0_125,plain,
op_or,
i_0_32 ).
cnf(c_0_126,plain,
( X1 = X2
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X1,X2)) ),
i_0_81 ).
cnf(c_0_127,plain,
substitution_of_equivalents,
i_0_82 ).
cnf(c_0_128,plain,
( is_a_theorem(and(X1,X2))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_111,c_0_118]) ).
cnf(c_0_129,plain,
and(implies(X1,X2),implies(X2,X1)) = equiv(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_120])]) ).
cnf(c_0_130,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_131,plain,
implies(not(X1),X2) = or(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_124]),c_0_125])]) ).
cnf(c_0_132,plain,
( or(not(X1),X2) = implies(X1,X2)
| ~ op_implies_or ),
i_0_57 ).
cnf(c_0_133,plain,
op_implies_or,
i_0_67 ).
cnf(c_0_134,plain,
( is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1)))
| ~ modus_tollens ),
i_0_53 ).
cnf(c_0_135,plain,
modus_tollens,
i_0_29 ).
cnf(c_0_136,plain,
( X1 = X2
| ~ is_a_theorem(equiv(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_126,c_0_127])]) ).
cnf(c_0_137,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_128,c_0_129]) ).
cnf(c_0_138,plain,
is_a_theorem(or(X1,not(X1))),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_139,plain,
or(not(X1),X2) = implies(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_133])]) ).
cnf(c_0_140,plain,
is_a_theorem(implies(or(X1,not(X2)),implies(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_131]),c_0_135])]) ).
cnf(c_0_141,plain,
( X1 = X2
| ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_142,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_143,plain,
( r3
| ~ is_a_theorem(implies(or(esk46_0,esk47_0),or(esk47_0,esk46_0))) ),
i_0_73 ).
cnf(c_0_144,negated_conjecture,
~ r3,
i_0_68 ).
cnf(c_0_145,plain,
is_a_theorem(implies(or(X1,not(not(X2))),or(X2,X1))),
inference(spm,[status(thm)],[c_0_140,c_0_131]) ).
cnf(c_0_146,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_141,c_0_142]),c_0_131]),c_0_139]),c_0_130])]) ).
cnf(c_0_147,plain,
~ is_a_theorem(implies(or(esk46_0,esk47_0),or(esk47_0,esk46_0))),
inference(sr,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_148,plain,
is_a_theorem(implies(or(X1,X2),or(X2,X1))),
inference(rw,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_149,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_148])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL456+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : enigmatic-eprover.py %s %d 1
% 0.10/0.36 % Computer : n027.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 4 18:44:59 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.45 # ENIGMATIC: Selected SinE mode:
% 0.22/0.46 # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.46 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.22/0.46 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.22/0.46 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 15.86/4.34 # ENIGMATIC: Solved by G_E___302_C18_F1_URBAN_S5PRR_RG_S0Y:
% 15.86/4.34 # Version: 2.1pre011
% 15.86/4.34 # Preprocessing time : 0.016 s
% 15.86/4.34
% 15.86/4.34 # Proof found!
% 15.86/4.34 # SZS status Theorem
% 15.86/4.34 # SZS output start CNFRefutation
% See solution above
% 15.86/4.35 # Proof object total steps : 67
% 15.86/4.35 # Proof object clause steps : 45
% 15.86/4.35 # Proof object formula steps : 22
% 15.86/4.35 # Proof object conjectures : 2
% 15.86/4.35 # Proof object clause conjectures : 1
% 15.86/4.35 # Proof object formula conjectures : 1
% 15.86/4.35 # Proof object initial clauses used : 22
% 15.86/4.35 # Proof object initial formulas used : 22
% 15.86/4.35 # Proof object generating inferences : 10
% 15.86/4.35 # Proof object simplifying inferences : 30
% 15.86/4.35 # Training examples: 0 positive, 0 negative
% 15.86/4.35 # Parsed axioms : 82
% 15.86/4.35 # Removed by relevancy pruning/SinE : 0
% 15.86/4.35 # Initial clauses : 82
% 15.86/4.35 # Removed in clause preprocessing : 0
% 15.86/4.35 # Initial clauses in saturation : 82
% 15.86/4.35 # Processed clauses : 400
% 15.86/4.35 # ...of these trivial : 53
% 15.86/4.35 # ...subsumed : 105
% 15.86/4.35 # ...remaining for further processing : 242
% 15.86/4.35 # Other redundant clauses eliminated : 0
% 15.86/4.35 # Clauses deleted for lack of memory : 0
% 15.86/4.35 # Backward-subsumed : 7
% 15.86/4.35 # Backward-rewritten : 36
% 15.86/4.35 # Generated clauses : 4699
% 15.86/4.35 # ...of the previous two non-trivial : 4330
% 15.86/4.35 # Contextual simplify-reflections : 14
% 15.86/4.35 # Paramodulations : 4699
% 15.86/4.35 # Factorizations : 0
% 15.86/4.35 # Equation resolutions : 0
% 15.86/4.35 # Propositional unsat checks : 0
% 15.86/4.35 # Propositional unsat check successes : 0
% 15.86/4.35 # Current number of processed clauses : 199
% 15.86/4.35 # Positive orientable unit clauses : 92
% 15.86/4.35 # Positive unorientable unit clauses: 2
% 15.86/4.35 # Negative unit clauses : 4
% 15.86/4.35 # Non-unit-clauses : 101
% 15.86/4.35 # Current number of unprocessed clauses: 2890
% 15.86/4.35 # ...number of literals in the above : 5367
% 15.86/4.35 # Current number of archived formulas : 0
% 15.86/4.35 # Current number of archived clauses : 43
% 15.86/4.35 # Clause-clause subsumption calls (NU) : 3096
% 15.86/4.35 # Rec. Clause-clause subsumption calls : 2893
% 15.86/4.35 # Non-unit clause-clause subsumptions : 114
% 15.86/4.35 # Unit Clause-clause subsumption calls : 520
% 15.86/4.35 # Rewrite failures with RHS unbound : 0
% 15.86/4.35 # BW rewrite match attempts : 560
% 15.86/4.35 # BW rewrite match successes : 21
% 15.86/4.35 # Condensation attempts : 0
% 15.86/4.35 # Condensation successes : 0
% 15.86/4.35 # Termbank termtop insertions : 49183
% 15.86/4.35
% 15.86/4.35 # -------------------------------------------------
% 15.86/4.35 # User time : 0.096 s
% 15.86/4.35 # System time : 0.002 s
% 15.86/4.35 # Total time : 0.098 s
% 15.86/4.35 # ...preprocessing : 0.016 s
% 15.86/4.35 # ...main loop : 0.083 s
% 15.86/4.35 # Maximum resident set size: 9984 pages
% 15.86/4.35
%------------------------------------------------------------------------------