%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : LCL900+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n010.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 11:48:45 AM UTC 2026
% Result : Theorem 31.14s 5.73s
% Output : CNFRefutation 31.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 12
% Syntax : Number of clauses : 87 ( 72 unt; 0 nHn; 15 RR)
% Number of literals : 104 ( 53 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 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 : 169 ( 27 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_8,plain,
( '>='(X1,'==>'(X2,X3))
| ~ '>='('+'(X2,X1),X3) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tnvs275o/input.p',i_0_8) ).
cnf(i_0_3,plain,
'+'(X1,'0') = X1,
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tnvs275o/input.p',i_0_3) ).
cnf(i_0_4,plain,
'>='(X1,X1),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tnvs275o/input.p',i_0_4) ).
cnf(i_0_6,plain,
( X1 = X2
| ~ '>='(X2,X1)
| ~ '>='(X1,X2) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tnvs275o/input.p',i_0_6) ).
cnf(i_0_9,plain,
'>='(X1,'0'),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tnvs275o/input.p',i_0_9) ).
cnf(i_0_7,plain,
( '>='('+'(X1,X2),X3)
| ~ '>='(X2,'==>'(X1,X3)) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tnvs275o/input.p',i_0_7) ).
cnf(i_0_13,plain,
'+'(X1,'1') = '1',
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tnvs275o/input.p',i_0_13) ).
cnf(i_0_2,plain,
'+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tnvs275o/input.p',i_0_2) ).
cnf(i_0_14,plain,
'==>'('==>'(X1,X2),X2) = '==>'('==>'(X2,X1),X1),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tnvs275o/input.p',i_0_14) ).
cnf(i_0_1,plain,
'+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tnvs275o/input.p',i_0_1) ).
cnf(i_0_12,plain,
( '>='('==>'(X1,X2),'==>'(X1,X3))
| ~ '>='(X2,X3) ),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tnvs275o/input.p',i_0_12) ).
cnf(i_0_15,negated_conjecture,
'+'(esk1_0,'==>'(esk1_0,esk2_0)) != '+'(esk2_0,'==>'(esk2_0,esk1_0)),
file('/export/starexec/sandbox/tmp/enigma-theBenchmark.p-tnvs275o/input.p',i_0_15) ).
cnf(c_0_28,plain,
( '>='(X1,'==>'(X2,X3))
| ~ '>='('+'(X2,X1),X3) ),
i_0_8 ).
cnf(c_0_29,plain,
'+'(X1,'0') = X1,
i_0_3 ).
cnf(c_0_30,plain,
( '>='('0','==>'(X1,X2))
| ~ '>='(X1,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_31,plain,
'>='(X1,X1),
i_0_4 ).
cnf(c_0_32,plain,
( X1 = X2
| ~ '>='(X2,X1)
| ~ '>='(X1,X2) ),
i_0_6 ).
cnf(c_0_33,plain,
'>='('0','==>'(X1,X1)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,plain,
'>='(X1,'0'),
i_0_9 ).
cnf(c_0_35,plain,
( '>='('+'(X1,X2),X3)
| ~ '>='(X2,'==>'(X1,X3)) ),
i_0_7 ).
cnf(c_0_36,plain,
'==>'(X1,X1) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_37,plain,
'>='('+'(X1,X2),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_34])]) ).
cnf(c_0_38,plain,
'+'(X1,'1') = '1',
i_0_13 ).
cnf(c_0_39,plain,
'>='('1',X1),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,plain,
'+'(X1,X2) = '+'(X2,X1),
i_0_2 ).
cnf(c_0_41,plain,
( X1 = '1'
| ~ '>='(X1,'1') ),
inference(spm,[status(thm)],[c_0_32,c_0_39]) ).
cnf(c_0_42,plain,
'>='('+'(X1,'==>'(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_35,c_0_31]) ).
cnf(c_0_43,plain,
( '0' = X1
| ~ '>='('0',X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_34]) ).
cnf(c_0_44,plain,
'>='(X1,'==>'(X2,'0')),
inference(spm,[status(thm)],[c_0_28,c_0_34]) ).
cnf(c_0_45,plain,
( '>='(X1,'==>'(X2,X3))
| ~ '>='('+'(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_28,c_0_40]) ).
cnf(c_0_46,plain,
'+'(X1,'==>'(X1,'1')) = '1',
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,plain,
'==>'(X1,'0') = '0',
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,plain,
'==>'('==>'(X1,X2),X2) = '==>'('==>'(X2,X1),X1),
i_0_14 ).
cnf(c_0_49,plain,
'>='(X1,'==>'(X2,'+'(X2,X1))),
inference(spm,[status(thm)],[c_0_28,c_0_31]) ).
cnf(c_0_50,plain,
'+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
i_0_1 ).
cnf(c_0_51,plain,
'>='(X1,'==>'('==>'(X1,'1'),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_39])]) ).
cnf(c_0_52,plain,
'==>'('==>'('0',X1),X1) = '0',
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,plain,
'>='(X1,'==>'(X2,X1)),
inference(spm,[status(thm)],[c_0_45,c_0_37]) ).
cnf(c_0_54,plain,
'>='(X1,'==>'(X2,'==>'(X3,'+'(X3,'+'(X2,X1))))),
inference(spm,[status(thm)],[c_0_28,c_0_49]) ).
cnf(c_0_55,plain,
'+'(X1,'+'(X2,'==>'('+'(X1,X2),'1'))) = '1',
inference(spm,[status(thm)],[c_0_50,c_0_46]) ).
cnf(c_0_56,plain,
( '>='(X1,'==>'('+'(X2,X3),X4))
| ~ '>='('+'(X2,'+'(X3,X1)),X4) ),
inference(spm,[status(thm)],[c_0_28,c_0_50]) ).
cnf(c_0_57,plain,
'>='('+'(X1,'+'(X2,'==>'(X2,'==>'(X1,X3)))),X3),
inference(spm,[status(thm)],[c_0_35,c_0_42]) ).
cnf(c_0_58,plain,
'>='('0','==>'(X1,'==>'('==>'(X1,'1'),X2))),
inference(spm,[status(thm)],[c_0_30,c_0_51]) ).
cnf(c_0_59,plain,
'>='('==>'('0',X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_52]),c_0_29]) ).
cnf(c_0_60,plain,
'+'('1',X1) = '1',
inference(spm,[status(thm)],[c_0_38,c_0_40]) ).
cnf(c_0_61,plain,
'>='('0','==>'(X1,'==>'(X2,X1))),
inference(spm,[status(thm)],[c_0_30,c_0_53]) ).
cnf(c_0_62,plain,
'>='('==>'('+'(X1,X2),'1'),'==>'(X2,'==>'(X1,'1'))),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_63,plain,
'>='('==>'(X1,'==>'(X2,X3)),'==>'('+'(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_64,plain,
'==>'(X1,'==>'('==>'(X1,'1'),X2)) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_58]),c_0_34])]) ).
cnf(c_0_65,plain,
'==>'('0',X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_59]),c_0_53])]) ).
cnf(c_0_66,plain,
( '>='('==>'(X1,X2),'==>'(X1,X3))
| ~ '>='(X2,X3) ),
i_0_12 ).
cnf(c_0_67,plain,
( '>='(X1,'==>'('1',X2))
| ~ '>='('1',X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_60]) ).
cnf(c_0_68,plain,
'==>'(X1,'==>'(X2,X1)) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_61]),c_0_34])]) ).
cnf(c_0_69,plain,
'==>'(X1,'==>'(X2,'1')) = '==>'('+'(X2,X1),'1'),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_62]),c_0_63])]) ).
cnf(c_0_70,plain,
'==>'('==>'('==>'('==>'(X1,'1'),X2),X1),X1) = '==>'('==>'(X1,'1'),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_64]),c_0_65]) ).
cnf(c_0_71,plain,
( '==>'(X1,'+'(X1,X2)) = X2
| ~ '>='('==>'(X1,'+'(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_49]) ).
cnf(c_0_72,plain,
'>='('==>'(X1,'+'(X2,'==>'(X2,X3))),'==>'(X1,X3)),
inference(spm,[status(thm)],[c_0_66,c_0_42]) ).
cnf(c_0_73,plain,
'>='('0','==>'('+'(X1,X2),X1)),
inference(spm,[status(thm)],[c_0_30,c_0_37]) ).
cnf(c_0_74,plain,
'>='(X1,'==>'('1',X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_39])]) ).
cnf(c_0_75,plain,
'==>'('==>'('==>'(X1,X2),X2),X2) = '==>'(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_68]),c_0_65]) ).
cnf(c_0_76,plain,
'==>'('+'('==>'(X1,'1'),X2),'1') = '==>'(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_36]),c_0_65]),c_0_36]),c_0_65]) ).
cnf(c_0_77,plain,
'==>'(X1,'+'(X1,'==>'(X1,X2))) = '==>'(X1,X2),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_78,plain,
'==>'('+'(X1,X2),X1) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_73]),c_0_34])]) ).
cnf(c_0_79,plain,
'+'(X1,'+'(X2,'==>'(X2,'==>'(X1,'1')))) = '1',
inference(spm,[status(thm)],[c_0_41,c_0_57]) ).
cnf(c_0_80,plain,
'==>'('1',X1) = '0',
inference(spm,[status(thm)],[c_0_43,c_0_74]) ).
cnf(c_0_81,plain,
'==>'('==>'('==>'(X1,X2),X2),X1) = '==>'(X2,X1),
inference(spm,[status(thm)],[c_0_75,c_0_48]) ).
cnf(c_0_82,plain,
'==>'(X1,'==>'(X2,X3)) = '==>'('+'(X2,X1),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_76]),c_0_50]),c_0_76]) ).
cnf(c_0_83,plain,
'==>'('+'('==>'(X1,X2),X3),'1') = '==>'(X3,'+'('==>'(X2,'1'),X1)),
inference(spm,[status(thm)],[c_0_76,c_0_76]) ).
cnf(c_0_84,plain,
'==>'('==>'(X1,X2),'+'(X1,'==>'(X1,X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_77]),c_0_78]),c_0_65]) ).
cnf(c_0_85,plain,
'+'('==>'(X1,'1'),'+'(X2,'==>'(X2,X1))) = '1',
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_48]),c_0_80]),c_0_65]) ).
cnf(c_0_86,plain,
'==>'('==>'('+'(X1,'==>'('+'(X1,X2),X3)),X3),X2) = '==>'('==>'(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_82]) ).
cnf(c_0_87,plain,
'==>'('+'(X1,'==>'(X2,X3)),'1') = '==>'(X1,'+'('==>'(X3,'1'),X2)),
inference(spm,[status(thm)],[c_0_83,c_0_40]) ).
cnf(c_0_88,plain,
'+'('0',X1) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_40]) ).
cnf(c_0_89,plain,
'==>'('==>'(X1,X2),'1') = '+'('==>'(X2,'1'),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_76]),c_0_50]),c_0_85]) ).
cnf(c_0_90,plain,
'==>'('==>'(X1,'+'(X1,X2)),X2) = '==>'('==>'(X1,'1'),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_36]),c_0_88]) ).
cnf(c_0_91,plain,
'==>'('+'('==>'('==>'(X1,X2),X2),X3),X2) = '==>'('+'(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_75]),c_0_82]) ).
cnf(c_0_92,plain,
'+'('==>'(X1,'1'),'==>'(X2,'+'(X2,X1))) = '+'('==>'(X1,'1'),'==>'(X2,'1')),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_89]) ).
cnf(c_0_93,plain,
'>='('0','==>'('+'(X1,'==>'(X1,X2)),X2)),
inference(spm,[status(thm)],[c_0_30,c_0_42]) ).
cnf(c_0_94,plain,
'==>'('+'(X1,X2),X2) = '0',
inference(spm,[status(thm)],[c_0_78,c_0_40]) ).
cnf(c_0_95,plain,
'==>'(X1,'+'(X2,'==>'(X2,X1))) = '==>'(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_89]),c_0_36]),c_0_88]),c_0_87]),c_0_36]),c_0_88]),c_0_87]),c_0_87]),c_0_36]),c_0_88]),c_0_40]) ).
cnf(c_0_96,plain,
'==>'('+'(X1,'==>'(X1,X2)),X2) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_93]),c_0_34])]) ).
cnf(c_0_97,plain,
'==>'('+'(X1,'+'(X2,X3)),X3) = '0',
inference(spm,[status(thm)],[c_0_94,c_0_50]) ).
cnf(c_0_98,plain,
'==>'('==>'(X1,X2),'+'(X2,'==>'(X2,X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_95]),c_0_96]),c_0_65]) ).
cnf(c_0_99,plain,
'==>'('+'(X1,'+'(X2,X3)),X2) = '0',
inference(spm,[status(thm)],[c_0_97,c_0_40]) ).
cnf(c_0_100,negated_conjecture,
'+'(esk1_0,'==>'(esk1_0,esk2_0)) != '+'(esk2_0,'==>'(esk2_0,esk1_0)),
i_0_15 ).
cnf(c_0_101,plain,
'+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_98]),c_0_82]),c_0_99]),c_0_40]),c_0_65]) ).
cnf(c_0_102,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_101])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL900+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.03 % Command : enigmatic-eprover.py %s %d 1
% 0.09/0.34 % Computer : n010.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 5 19:39:40 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.40 # ENIGMATIC: Selected complete mode:
% 31.14/5.73 # ENIGMATIC: Solved by autoschedule:
% 31.14/5.73 # No SInE strategy applied
% 31.14/5.73 # Trying AutoSched0 for 150 seconds
% 31.14/5.73 # AutoSched0-Mode selected heuristic H_____047_C18_F1_AE_R8_CS_SP_S2S
% 31.14/5.73 # and selection function SelectNewComplexAHP.
% 31.14/5.73 #
% 31.14/5.73 # Preprocessing time : 0.012 s
% 31.14/5.73
% 31.14/5.73 # Proof found!
% 31.14/5.73 # SZS status Theorem
% 31.14/5.73 # SZS output start CNFRefutation
% See solution above
% 31.14/5.73 # Training examples: 0 positive, 0 negative
% 31.14/5.73
% 31.14/5.73 # -------------------------------------------------
% 31.14/5.73 # User time : 1.800 s
% 31.14/5.73 # System time : 0.098 s
% 31.14/5.73 # Total time : 1.898 s
% 31.14/5.73 # Maximum resident set size: 3328 pages
% 31.14/5.73
%------------------------------------------------------------------------------