%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : LCL373+2 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n013.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 11:44:36 AM UTC 2026
% Result : Theorem 161.18s 22.73s
% Output : CNFRefutation 161.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 3
% Syntax : Number of clauses : 74 ( 34 unt; 0 nHn; 29 RR)
% Number of literals : 119 ( 0 equ; 47 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 270 ( 47 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_1,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(X2,X1)) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-3vqqu6z1/input.p',i_0_1) ).
cnf(i_0_2,plain,
is_a_theorem(implies(implies(implies(implies(implies(X1,implies(X2,X1)),implies(implies(X3,implies(X4,implies(X5,X4))),X6)),X6),implies(implies(implies(implies(implies(implies(implies(X7,X8),implies(implies(X8,X9),implies(X7,X9))),implies(implies(implies(n(X10),X10),X10),X11)),X11),implies(implies(X12,implies(n(X12),X13)),X14)),X14),X15)),X15)),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-3vqqu6z1/input.p',i_0_2) ).
cnf(i_0_3,negated_conjecture,
~ is_a_theorem(implies(implies(implies(x,y),z),implies(implies(x,z),z))),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-3vqqu6z1/input.p',i_0_3) ).
cnf(c_0_7,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(X2,X1)) ),
i_0_1 ).
cnf(c_0_8,plain,
is_a_theorem(implies(implies(implies(implies(implies(X1,implies(X2,X1)),implies(implies(X3,implies(X4,implies(X5,X4))),X6)),X6),implies(implies(implies(implies(implies(implies(implies(X7,X8),implies(implies(X8,X9),implies(X7,X9))),implies(implies(implies(n(X10),X10),X10),X11)),X11),implies(implies(X12,implies(n(X12),X13)),X14)),X14),X15)),X15)),
i_0_2 ).
cnf(c_0_9,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(implies(implies(X2,implies(X3,X2)),implies(implies(X4,implies(X5,implies(X6,X5))),X7)),X7),implies(implies(implies(implies(implies(implies(implies(X8,X9),implies(implies(X9,X10),implies(X8,X10))),implies(implies(implies(n(X11),X11),X11),X12)),X12),implies(implies(X13,implies(n(X13),X14)),X15)),X15),X1))) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_11,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),implies(implies(X3,implies(X4,implies(X5,X4))),X6)),X6)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_10]) ).
cnf(c_0_13,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))),
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_14,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(implies(implies(implies(implies(implies(X2,X3),implies(implies(X3,X4),implies(X2,X4))),implies(implies(implies(n(X5),X5),X5),X6)),X6),implies(implies(X7,implies(n(X7),X8)),X9)),X9),X1)) ),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_15,plain,
is_a_theorem(implies(X1,implies(implies(implies(implies(implies(implies(X2,X3),implies(implies(X3,X4),implies(X2,X4))),implies(implies(implies(n(X5),X5),X5),X6)),X6),implies(implies(X7,implies(n(X7),X8)),X9)),X9))),
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_16,plain,
is_a_theorem(implies(implies(implies(implies(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))),implies(implies(implies(n(X4),X4),X4),X5)),X5),implies(implies(X6,implies(n(X6),X7)),X8)),X8)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(implies(implies(implies(X2,X3),implies(implies(X3,X4),implies(X2,X4))),implies(implies(implies(n(X5),X5),X5),X6)),X6),implies(implies(X7,implies(n(X7),X8)),X1))) ),
inference(spm,[status(thm)],[c_0_7,c_0_16]) ).
cnf(c_0_18,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,implies(X3,X2)),implies(implies(X4,implies(X5,implies(X6,X5))),X1))) ),
inference(spm,[status(thm)],[c_0_7,c_0_11]) ).
cnf(c_0_19,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))),implies(implies(implies(n(X4),X4),X4),X5)),X5)),
inference(spm,[status(thm)],[c_0_17,c_0_10]) ).
cnf(c_0_20,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),X3),implies(X4,X3))),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_22,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_7,c_0_21]) ).
cnf(c_0_23,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X1,X3)) ),
inference(spm,[status(thm)],[c_0_7,c_0_22]) ).
cnf(c_0_24,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(implies(X2,X3),implies(implies(X3,X4),implies(X2,X4))),implies(implies(implies(n(X5),X5),X5),X1))) ),
inference(spm,[status(thm)],[c_0_7,c_0_19]) ).
cnf(c_0_25,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X1,X3)) ),
inference(spm,[status(thm)],[c_0_23,c_0_10]) ).
cnf(c_0_26,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(implies(X2,X3),implies(implies(X3,X4),implies(X2,X4))),X1)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),implies(implies(X3,X1),X4))),
inference(spm,[status(thm)],[c_0_26,c_0_21]) ).
cnf(c_0_28,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))),
inference(spm,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_29,plain,
( is_a_theorem(implies(implies(X1,X2),X3))
| ~ is_a_theorem(implies(implies(implies(X2,X4),implies(X1,X4)),X3)) ),
inference(spm,[status(thm)],[c_0_7,c_0_27]) ).
cnf(c_0_30,plain,
is_a_theorem(implies(implies(implies(implies(n(X1),X1),X1),X2),implies(X3,X2))),
inference(spm,[status(thm)],[c_0_24,c_0_28]) ).
cnf(c_0_31,plain,
is_a_theorem(implies(implies(X1,implies(n(X2),X2)),implies(X3,implies(X1,X2)))),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(implies(n(X2),X2),X2),X1)) ),
inference(spm,[status(thm)],[c_0_24,c_0_12]) ).
cnf(c_0_33,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X3,X1),X2)) ),
inference(spm,[status(thm)],[c_0_7,c_0_28]) ).
cnf(c_0_34,plain,
is_a_theorem(implies(implies(n(X1),X2),implies(X3,implies(implies(X2,X1),X1)))),
inference(spm,[status(thm)],[c_0_29,c_0_31]) ).
cnf(c_0_35,plain,
is_a_theorem(implies(implies(implies(implies(n(X1),X1),X2),X3),implies(implies(X1,X2),X3))),
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
cnf(c_0_36,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(n(X2),X2))) ),
inference(spm,[status(thm)],[c_0_32,c_0_22]) ).
cnf(c_0_37,plain,
is_a_theorem(implies(X1,implies(X2,implies(implies(X1,X3),X3)))),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
is_a_theorem(implies(implies(X1,implies(n(X2),X2)),implies(implies(X2,X3),implies(X1,X3)))),
inference(spm,[status(thm)],[c_0_29,c_0_35]) ).
cnf(c_0_39,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(implies(X3,implies(n(X1),X1))) ),
inference(spm,[status(thm)],[c_0_7,c_0_38]) ).
cnf(c_0_41,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_39]) ).
cnf(c_0_42,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),X2),X3),implies(implies(n(X2),X1),X3))),
inference(spm,[status(thm)],[c_0_40,c_0_34]) ).
cnf(c_0_43,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X2,implies(n(X2),X3)),X1)) ),
inference(spm,[status(thm)],[c_0_17,c_0_12]) ).
cnf(c_0_44,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(X3,X2)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_41]) ).
cnf(c_0_45,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(n(X3),X2),implies(X1,X3)))),
inference(spm,[status(thm)],[c_0_29,c_0_42]) ).
cnf(c_0_46,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,implies(X1,X4))))
| ~ is_a_theorem(implies(X3,implies(X2,X4))) ),
inference(spm,[status(thm)],[c_0_29,c_0_22]) ).
cnf(c_0_47,plain,
is_a_theorem(implies(implies(implies(n(X1),X2),X3),implies(X1,X3))),
inference(spm,[status(thm)],[c_0_43,c_0_21]) ).
cnf(c_0_48,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_32,c_0_28]) ).
cnf(c_0_49,plain,
( is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(X1,X3)))
| ~ is_a_theorem(implies(n(X3),X2)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X1,implies(implies(n(X2),X4),X3))) ),
inference(spm,[status(thm)],[c_0_43,c_0_46]) ).
cnf(c_0_51,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(n(X1),X3),X2)) ),
inference(spm,[status(thm)],[c_0_7,c_0_47]) ).
cnf(c_0_52,plain,
( is_a_theorem(implies(X1,implies(implies(X2,X3),X3)))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_23,c_0_39]) ).
cnf(c_0_53,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(n(X1),X1),X2))),
inference(spm,[status(thm)],[c_0_24,c_0_48]) ).
cnf(c_0_54,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(X3,X2)))
| ~ is_a_theorem(implies(n(X2),X3)) ),
inference(spm,[status(thm)],[c_0_7,c_0_49]) ).
cnf(c_0_55,plain,
is_a_theorem(implies(n(X1),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_50,c_0_39]) ).
cnf(c_0_56,plain,
( is_a_theorem(implies(X1,implies(implies(X2,X3),X3)))
| ~ is_a_theorem(implies(implies(n(X1),X4),X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,plain,
is_a_theorem(implies(implies(n(implies(n(X1),X1)),implies(n(X1),X1)),X1)),
inference(spm,[status(thm)],[c_0_32,c_0_53]) ).
cnf(c_0_58,plain,
( is_a_theorem(implies(n(X1),X2))
| ~ is_a_theorem(implies(n(X2),X1)) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,plain,
is_a_theorem(implies(implies(X1,X2),implies(n(n(X1)),X2))),
inference(spm,[status(thm)],[c_0_40,c_0_55]) ).
cnf(c_0_60,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,implies(X1,X4))))
| ~ is_a_theorem(implies(implies(n(X3),X5),implies(X2,X4))) ),
inference(spm,[status(thm)],[c_0_50,c_0_46]) ).
cnf(c_0_61,plain,
is_a_theorem(implies(implies(n(X1),X1),implies(implies(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,plain,
is_a_theorem(implies(n(implies(X1,X2)),X1)),
inference(spm,[status(thm)],[c_0_58,c_0_55]) ).
cnf(c_0_63,plain,
( is_a_theorem(implies(n(n(X1)),X2))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_7,c_0_59]) ).
cnf(c_0_64,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(X2,implies(X1,X3)))),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,n(implies(X2,X3)))) ),
inference(spm,[status(thm)],[c_0_23,c_0_62]) ).
cnf(c_0_66,plain,
( is_a_theorem(implies(n(X1),n(X2)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_58,c_0_63]) ).
cnf(c_0_67,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X2,implies(X1,X3))) ),
inference(spm,[status(thm)],[c_0_7,c_0_64]) ).
cnf(c_0_68,plain,
( is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X1),X2)))
| ~ is_a_theorem(implies(n(X1),X3)) ),
inference(spm,[status(thm)],[c_0_40,c_0_22]) ).
cnf(c_0_69,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),implies(X3,X2)))),
inference(spm,[status(thm)],[c_0_33,c_0_21]) ).
cnf(c_0_70,plain,
( is_a_theorem(implies(n(X1),X2))
| ~ is_a_theorem(implies(implies(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_71,plain,
( is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),X3)))
| ~ is_a_theorem(implies(n(X2),X1)) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_72,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(n(implies(X2,X3)),implies(X1,X3))) ),
inference(spm,[status(thm)],[c_0_54,c_0_69]) ).
cnf(c_0_73,plain,
( is_a_theorem(implies(n(implies(implies(X1,X2),X2)),X3))
| ~ is_a_theorem(implies(n(X1),X3)) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_74,plain,
( is_a_theorem(implies(X1,implies(implies(X2,X3),X3)))
| ~ is_a_theorem(implies(n(X2),implies(X1,X3))) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_75,negated_conjecture,
~ is_a_theorem(implies(implies(implies(x,y),z),implies(implies(x,z),z))),
i_0_3 ).
cnf(c_0_76,plain,
( is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X2),X2)))
| ~ is_a_theorem(implies(n(X3),X1)) ),
inference(spm,[status(thm)],[c_0_74,c_0_52]) ).
cnf(c_0_77,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_55])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL373+2 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.03 % Command : enigmatic-eprover.py %s %d 1
% 0.07/0.33 % Computer : n013.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Sat Sep 5 06:59:51 UTC 2026
% 0.07/0.33 % CPUTime :
% 0.11/0.43 # ENIGMATIC: Selected complete mode:
% 161.18/22.73 # ENIGMATIC: Solved by Enigma+tptp-cade20-model03-h2e15+lgb-t150-d60-l16000-e0.15+coop-eprover73:
% 161.18/22.73 # ENIGMA: LightGBM model '/export/starexec/sandbox/solver/bin/data/Enigma/tptp-cade20-model03-h2e15/lgb-t150-d60-l16000-e0.15/model.lgb' loaded. (hash_base: 32768; conj_feats: 26; version: 991; iters: 150)
% 161.18/22.73 # Preprocessing time : 4.028 s
% 161.18/22.73 # Presaturation interreduction done
% 161.18/22.73
% 161.18/22.73 # Proof found!
% 161.18/22.73 # SZS status Theorem
% 161.18/22.73 # SZS output start CNFRefutation
% See solution above
% 161.18/22.73 # Training examples: 0 positive, 0 negative
% 161.18/22.73
% 161.18/22.73 # -------------------------------------------------
% 161.18/22.73 # User time : 17.992 s
% 161.18/22.73 # System time : 0.748 s
% 161.18/22.73 # Total time : 18.739 s
% 161.18/22.73 # ...preprocessing : 4.028 s
% 161.18/22.73 # ...main loop : 14.712 s
% 161.18/22.73 # Maximum resident set size: 309444 pages
% 161.18/22.73
%------------------------------------------------------------------------------