%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : LCL888+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n005.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 11:48:43 AM UTC 2026
% Result : Theorem 41.14s 7.65s
% Output : CNFRefutation 41.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of clauses : 66 ( 39 unt; 0 nHn; 36 RR)
% Number of literals : 100 ( 31 equ; 37 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 109 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_3,plain,
'+'(X1,'0') = X1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-dx77sy_s/input.p',i_0_3) ).
cnf(i_0_2,plain,
'+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-dx77sy_s/input.p',i_0_2) ).
cnf(i_0_6,plain,
( X1 = X2
| ~ '>='(X2,X1)
| ~ '>='(X1,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-dx77sy_s/input.p',i_0_6) ).
cnf(i_0_9,plain,
'>='(X1,'0'),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-dx77sy_s/input.p',i_0_9) ).
cnf(i_0_13,plain,
'+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-dx77sy_s/input.p',i_0_13) ).
cnf(i_0_8,plain,
( '>='(X1,'==>'(X2,X3))
| ~ '>='('+'(X2,X1),X3) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-dx77sy_s/input.p',i_0_8) ).
cnf(i_0_11,plain,
( '>='('==>'(X1,X2),'==>'(X3,X2))
| ~ '>='(X3,X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-dx77sy_s/input.p',i_0_11) ).
cnf(i_0_15,negated_conjecture,
'==>'(esk3_0,esk2_0) = esk3_0,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-dx77sy_s/input.p',i_0_15) ).
cnf(i_0_7,plain,
( '>='('+'(X1,X2),X3)
| ~ '>='(X2,'==>'(X1,X3)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-dx77sy_s/input.p',i_0_7) ).
cnf(i_0_4,plain,
'>='(X1,X1),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-dx77sy_s/input.p',i_0_4) ).
cnf(i_0_5,plain,
( '>='(X1,X2)
| ~ '>='(X3,X2)
| ~ '>='(X1,X3) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-dx77sy_s/input.p',i_0_5) ).
cnf(i_0_16,negated_conjecture,
'==>'(esk1_0,esk2_0) = esk1_0,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-dx77sy_s/input.p',i_0_16) ).
cnf(i_0_1,plain,
'+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-dx77sy_s/input.p',i_0_1) ).
cnf(i_0_10,plain,
( '>='('+'(X1,X2),'+'(X3,X2))
| ~ '>='(X1,X3) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-dx77sy_s/input.p',i_0_10) ).
cnf(i_0_14,negated_conjecture,
esk3_0 != esk1_0,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-dx77sy_s/input.p',i_0_14) ).
cnf(c_0_32,plain,
'+'(X1,'0') = X1,
i_0_3 ).
cnf(c_0_33,plain,
'+'(X1,X2) = '+'(X2,X1),
i_0_2 ).
cnf(c_0_34,plain,
( X1 = X2
| ~ '>='(X2,X1)
| ~ '>='(X1,X2) ),
i_0_6 ).
cnf(c_0_35,plain,
'>='(X1,'0'),
i_0_9 ).
cnf(c_0_36,plain,
'+'('0',X1) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
'+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
i_0_13 ).
cnf(c_0_38,plain,
( '0' = X1
| ~ '>='('0',X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
( '>='(X1,'==>'(X2,X3))
| ~ '>='('+'(X2,X1),X3) ),
i_0_8 ).
cnf(c_0_40,plain,
'+'(X1,'==>'(X1,'0')) = '==>'('0',X1),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
( '==>'(X1,X2) = '0'
| ~ '>='(X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_32]) ).
cnf(c_0_42,plain,
( '>='('==>'(X1,X2),'==>'(X3,X2))
| ~ '>='(X3,X1) ),
i_0_11 ).
cnf(c_0_43,plain,
'==>'('0',X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_32]),c_0_35])]) ).
cnf(c_0_44,plain,
'>='(X1,'==>'(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_35])]) ).
cnf(c_0_45,negated_conjecture,
'==>'(esk3_0,esk2_0) = esk3_0,
i_0_15 ).
cnf(c_0_46,plain,
( '>='('+'(X1,X2),X3)
| ~ '>='(X2,'==>'(X1,X3)) ),
i_0_7 ).
cnf(c_0_47,plain,
'>='(X1,X1),
i_0_4 ).
cnf(c_0_48,plain,
( '>='(X1,X2)
| ~ '>='(X3,X2)
| ~ '>='(X1,X3) ),
i_0_5 ).
cnf(c_0_49,negated_conjecture,
'==>'(esk1_0,esk2_0) = esk1_0,
i_0_16 ).
cnf(c_0_50,plain,
'+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
i_0_1 ).
cnf(c_0_51,plain,
( '+'(X1,'==>'(X1,X2)) = X2
| ~ '>='(X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_41]),c_0_32]) ).
cnf(c_0_52,negated_conjecture,
'>='(esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_53,plain,
'>='('+'(X1,'==>'(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_54,plain,
( '>='(X1,'==>'(X2,X3))
| ~ '>='('+'(X2,X4),X3)
| ~ '>='(X1,X4) ),
inference(spm,[status(thm)],[c_0_48,c_0_39]) ).
cnf(c_0_55,negated_conjecture,
( '>='(X1,esk1_0)
| ~ '>='('+'(esk1_0,X1),esk2_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_49]) ).
cnf(c_0_56,plain,
'+'(X1,'+'('==>'(X1,X2),X3)) = '+'(X2,'+'('==>'(X2,X1),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_37]),c_0_50]) ).
cnf(c_0_57,plain,
'+'(X1,'+'(X2,X3)) = '+'(X2,'+'(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_33]),c_0_50]) ).
cnf(c_0_58,negated_conjecture,
'+'(esk3_0,esk3_0) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_45]),c_0_52])]) ).
cnf(c_0_59,plain,
( '>='('+'(X1,X2),'+'(X3,X2))
| ~ '>='(X1,X3) ),
i_0_10 ).
cnf(c_0_60,negated_conjecture,
( '>='(X1,esk3_0)
| ~ '>='('+'(esk3_0,X1),esk2_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_45]) ).
cnf(c_0_61,plain,
'>='('+'(X1,'+'(X2,'==>'(X2,'==>'(X1,X3)))),X3),
inference(spm,[status(thm)],[c_0_46,c_0_53]) ).
cnf(c_0_62,plain,
( '>='(X1,'==>'(X2,'==>'(X3,'+'(X2,X4))))
| ~ '>='(X1,X4) ),
inference(spm,[status(thm)],[c_0_54,c_0_44]) ).
cnf(c_0_63,plain,
( '==>'(X1,X2) = X3
| ~ '>='('==>'(X1,X2),X3)
| ~ '>='('+'(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_39]) ).
cnf(c_0_64,plain,
( '>='('+'('==>'(esk1_0,X1),X2),esk1_0)
| ~ '>='('+'(X1,'+'('==>'(X1,esk1_0),X2)),esk2_0) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_65,plain,
'+'(esk3_0,'+'(X1,esk3_0)) = '+'(X1,esk2_0),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_66,plain,
'>='('+'(X1,X2),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_36]),c_0_35])]) ).
cnf(c_0_67,plain,
( '>='('+'(X1,X2),esk3_0)
| ~ '>='('+'(X1,'+'(esk3_0,X2)),esk2_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_57]) ).
cnf(c_0_68,negated_conjecture,
'>='('+'(esk1_0,'+'(X1,'==>'(X1,esk1_0))),esk2_0),
inference(spm,[status(thm)],[c_0_61,c_0_49]) ).
cnf(c_0_69,plain,
'>='(X1,'==>'(X2,'==>'(X3,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_32]),c_0_35])]) ).
cnf(c_0_70,plain,
( '==>'(X1,X2) = '==>'(X3,X4)
| ~ '>='('+'(X1,'==>'(X3,X4)),X2)
| ~ '>='('+'(X3,'==>'(X1,X2)),X4) ),
inference(spm,[status(thm)],[c_0_63,c_0_39]) ).
cnf(c_0_71,plain,
'>='('+'(esk3_0,'==>'(esk1_0,esk3_0)),esk1_0),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66])]),c_0_33]) ).
cnf(c_0_72,negated_conjecture,
'>='('+'(esk1_0,'==>'(esk3_0,esk1_0)),esk3_0),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,plain,
( '>='(X1,esk1_0)
| ~ '>='('+'(X1,esk1_0),esk2_0) ),
inference(spm,[status(thm)],[c_0_55,c_0_33]) ).
cnf(c_0_74,negated_conjecture,
( '>='('+'(esk3_0,X1),esk2_0)
| ~ '>='(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_46,c_0_45]) ).
cnf(c_0_75,plain,
'==>'(X1,'==>'(X2,X1)) = '0',
inference(spm,[status(thm)],[c_0_38,c_0_69]) ).
cnf(c_0_76,plain,
'==>'(esk3_0,esk1_0) = '==>'(esk1_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72])]) ).
cnf(c_0_77,negated_conjecture,
( '>='(esk3_0,esk1_0)
| ~ '>='(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_78,negated_conjecture,
esk3_0 != esk1_0,
i_0_14 ).
cnf(c_0_79,plain,
( '>='('+'('==>'(esk3_0,X1),X2),esk3_0)
| ~ '>='('+'(X1,'+'('==>'(X1,esk3_0),X2)),esk2_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_56]) ).
cnf(c_0_80,plain,
'==>'(esk1_0,'==>'(esk1_0,esk3_0)) = '0',
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_81,plain,
~ '>='(esk1_0,esk3_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_77]),c_0_78]) ).
cnf(c_0_82,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_68]),c_0_76]),c_0_37]),c_0_80]),c_0_32]),c_0_81]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL888+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.03 % Command : enigmatic-eprover.py %s %d 1
% 0.10/0.36 % Computer : n005.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 : Sat Sep 5 20:47:52 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.12/0.46 # ENIGMATIC: Selected complete mode:
% 41.14/7.65 # ENIGMATIC: Solved by Enigma+tptp-cade20-model03-h2e15+lgb-t150-d60-l8000-e0.15+coop-eprover73:
% 41.14/7.65 # ENIGMA: LightGBM model '/export/starexec/sandbox2/solver/bin/data/Enigma/tptp-cade20-model03-h2e15/lgb-t150-d60-l8000-e0.15/model.lgb' loaded. (hash_base: 32768; conj_feats: 25; version: 991; iters: 150)
% 41.14/7.65 # Preprocessing time : 2.367 s
% 41.14/7.65 # Presaturation interreduction done
% 41.14/7.65
% 41.14/7.65 # Proof found!
% 41.14/7.65 # SZS status Theorem
% 41.14/7.65 # SZS output start CNFRefutation
% See solution above
% 41.14/7.65 # Training examples: 0 positive, 0 negative
% 41.14/7.65
% 41.14/7.65 # -------------------------------------------------
% 41.14/7.65 # User time : 2.857 s
% 41.14/7.65 # System time : 0.364 s
% 41.14/7.65 # Total time : 3.221 s
% 41.14/7.65 # ...preprocessing : 2.367 s
% 41.14/7.65 # ...main loop : 0.854 s
% 41.14/7.65 # Maximum resident set size: 186804 pages
% 41.14/7.65
%------------------------------------------------------------------------------