%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : LCL895+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 11:48:44 AM UTC 2026
% Result : Theorem 36.77s 6.45s
% Output : CNFRefutation 36.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 50 ( 40 unt; 7 nHn; 13 RR)
% Number of literals : 62 ( 61 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 80 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_1,plain,
'+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kqn32xu3/input.p',i_0_1) ).
cnf(i_0_8,plain,
'+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kqn32xu3/input.p',i_0_8) ).
cnf(i_0_7,plain,
'==>'('+'(X1,X2),X3) = '==>'(X1,'==>'(X2,X3)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kqn32xu3/input.p',i_0_7) ).
cnf(i_0_2,plain,
'+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kqn32xu3/input.p',i_0_2) ).
cnf(i_0_4,plain,
'==>'(X1,X1) = '0',
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kqn32xu3/input.p',i_0_4) ).
cnf(i_0_3,plain,
'+'(X1,'0') = X1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kqn32xu3/input.p',i_0_3) ).
cnf(i_0_10,negated_conjecture,
( '==>'(c,a) = '0'
| '==>'(c,'+'(a,'==>'(a,b))) = '0' ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kqn32xu3/input.p',i_0_10) ).
cnf(i_0_5,plain,
'==>'(X1,'0') = '0',
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kqn32xu3/input.p',i_0_5) ).
cnf(i_0_6,plain,
'==>'('0',X1) = X1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kqn32xu3/input.p',i_0_6) ).
cnf(i_0_9,negated_conjecture,
( '==>'(c,b) = '0'
| '==>'(c,'+'(a,'==>'(a,b))) = '0' ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kqn32xu3/input.p',i_0_9) ).
cnf(i_0_11,negated_conjecture,
( '==>'(c,a) != '0'
| '==>'(c,b) != '0'
| '==>'(c,'+'(a,'==>'(a,b))) != '0' ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-kqn32xu3/input.p',i_0_11) ).
cnf(c_0_23,plain,
'+'('+'(X1,X2),X3) = '+'(X1,'+'(X2,X3)),
i_0_1 ).
cnf(c_0_24,plain,
'+'(X1,'==>'(X1,X2)) = '+'(X2,'==>'(X2,X1)),
i_0_8 ).
cnf(c_0_25,plain,
'==>'('+'(X1,X2),X3) = '==>'(X1,'==>'(X2,X3)),
i_0_7 ).
cnf(c_0_26,plain,
'+'(X1,X2) = '+'(X2,X1),
i_0_2 ).
cnf(c_0_27,plain,
'+'(X1,'==>'(X1,'+'(X2,X3))) = '+'(X2,'+'(X3,'==>'(X2,'==>'(X3,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_28,plain,
'==>'(X1,X1) = '0',
i_0_4 ).
cnf(c_0_29,plain,
'+'(X1,'0') = X1,
i_0_3 ).
cnf(c_0_30,plain,
'==>'(X1,'==>'(X2,X3)) = '==>'(X2,'==>'(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_25]) ).
cnf(c_0_31,plain,
'+'(X1,'==>'(X1,'+'(X2,'==>'(X2,X1)))) = '+'(X2,'==>'(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_26]),c_0_26]) ).
cnf(c_0_32,negated_conjecture,
( '==>'(c,a) = '0'
| '==>'(c,'+'(a,'==>'(a,b))) = '0' ),
i_0_10 ).
cnf(c_0_33,plain,
'+'(X1,'==>'(X2,'==>'(X1,X3))) = '+'('==>'(X2,X3),'==>'('==>'(X2,X3),X1)),
inference(spm,[status(thm)],[c_0_24,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( '+'(b,'==>'(b,'+'(a,'==>'(a,c)))) = c
| '==>'(c,a) = '0' ),
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_31,c_0_32]),c_0_29]),c_0_25]),c_0_23]),c_0_29]),c_0_33]),c_0_30]),c_0_27]) ).
cnf(c_0_35,plain,
'==>'(X1,'==>'('==>'(X1,X2),X2)) = '0',
inference(spm,[status(thm)],[c_0_28,c_0_30]) ).
cnf(c_0_36,plain,
'==>'(X1,'0') = '0',
i_0_5 ).
cnf(c_0_37,plain,
( '+'(a,'==>'(a,c)) = c
| '==>'(c,a) = '0' ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_34]),c_0_25]),c_0_35]),c_0_23]),c_0_29]) ).
cnf(c_0_38,plain,
'==>'(X1,'==>'(X2,X1)) = '0',
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_28]),c_0_36]) ).
cnf(c_0_39,plain,
( '==>'(a,'==>'('==>'(a,c),X1)) = '==>'(c,X1)
| '==>'(c,a) = '0' ),
inference(spm,[status(thm)],[c_0_25,c_0_37]) ).
cnf(c_0_40,plain,
'==>'(X1,'==>'(X2,'==>'(X3,'+'(X1,X2)))) = '0',
inference(spm,[status(thm)],[c_0_25,c_0_38]) ).
cnf(c_0_41,plain,
'==>'(X1,'==>'('==>'(X1,X2),X3)) = '==>'(X2,'==>'('==>'(X2,X1),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_24]),c_0_25]) ).
cnf(c_0_42,plain,
'==>'(c,a) = '0',
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
'==>'('0',X1) = X1,
i_0_6 ).
cnf(c_0_44,plain,
'==>'(X1,'==>'(X2,'==>'('==>'(X1,X3),X3))) = '0',
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_35]),c_0_36]) ).
cnf(c_0_45,plain,
'==>'(X1,'==>'('==>'(X1,X2),'==>'(X3,X2))) = '0',
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_30]),c_0_30]) ).
cnf(c_0_46,plain,
'==>'(X1,'==>'('==>'(X1,'+'(X2,X3)),X4)) = '==>'(X2,'==>'(X3,'==>'('==>'(X2,'==>'(X3,X1)),X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_27]),c_0_25]),c_0_25]) ).
cnf(c_0_47,plain,
'==>'(X1,'==>'(X2,'==>'('==>'(X2,X3),'+'(X1,X3)))) = '0',
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,plain,
'==>'(a,'==>'('==>'(a,c),X1)) = '==>'(c,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_49,plain,
'==>'(X1,'==>'(X2,'==>'(X3,X4))) = '==>'(X2,'==>'(X3,'==>'(X1,X4))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_30]),c_0_25]) ).
cnf(c_0_50,plain,
'==>'(X1,'==>'('==>'(X1,X2),'==>'('==>'(X2,X3),X3))) = '0',
inference(spm,[status(thm)],[c_0_44,c_0_41]) ).
cnf(c_0_51,plain,
'==>'(X1,'==>'('==>'(X1,'+'(X2,'==>'(X2,X3))),X3)) = '0',
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,negated_conjecture,
( '==>'(c,b) = '0'
| '==>'(c,'+'(a,'==>'(a,b))) = '0' ),
i_0_9 ).
cnf(c_0_53,negated_conjecture,
( '==>'(c,a) != '0'
| '==>'(c,b) != '0'
| '==>'(c,'+'(a,'==>'(a,b))) != '0' ),
i_0_11 ).
cnf(c_0_54,plain,
'==>'(c,'==>'('==>'('==>'(a,c),X1),'+'(a,X1))) = '0',
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_55,plain,
'==>'('==>'(X1,X2),'==>'(X3,'==>'('==>'(X3,X1),X2))) = '0',
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,negated_conjecture,
'==>'(c,b) = '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_43])]) ).
cnf(c_0_57,negated_conjecture,
( '==>'(c,'+'(a,'==>'(a,b))) != '0'
| '==>'(c,b) != '0' ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_42])]) ).
cnf(c_0_58,plain,
'==>'(c,'==>'('==>'(c,X1),'+'(X1,'==>'(X1,a)))) = '0',
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_24]),c_0_30]),c_0_48]) ).
cnf(c_0_59,plain,
'==>'(X1,'==>'('==>'(X1,c),b)) = '0',
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_43]) ).
cnf(c_0_60,negated_conjecture,
'==>'(c,'+'(a,'==>'(a,b))) != '0',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_56])]) ).
cnf(c_0_61,plain,
$false,
inference(sr,[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_58,c_0_59]),c_0_28]),c_0_43]),c_0_28]),c_0_43]),c_0_43]),c_0_24]),c_0_60]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL895+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : enigmatic-eprover.py %s %d 1
% 0.09/0.36 % Computer : n010.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 : Fri Sep 4 21:12:54 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.46 # ENIGMATIC: Selected complete mode:
% 36.77/6.45 # ENIGMATIC: Solved by autoschedule:
% 36.77/6.45 # No SInE strategy applied
% 36.77/6.45 # Trying AutoSched0 for 150 seconds
% 36.77/6.45 # AutoSched0-Mode selected heuristic H_____011_C18_F1_PI_SE_SP_S2S
% 36.77/6.45 # and selection function SelectNewComplexAHP.
% 36.77/6.45 #
% 36.77/6.45 # Preprocessing time : 0.023 s
% 36.77/6.45
% 36.77/6.45 # Proof found!
% 36.77/6.45 # SZS status Theorem
% 36.77/6.45 # SZS output start CNFRefutation
% See solution above
% 36.77/6.45 # Training examples: 0 positive, 0 negative
% 36.77/6.45
% 36.77/6.45 # -------------------------------------------------
% 36.77/6.45 # User time : 2.486 s
% 36.77/6.45 # System time : 0.161 s
% 36.77/6.45 # Total time : 2.647 s
% 36.77/6.45 # Maximum resident set size: 3328 pages
% 36.77/6.45
%------------------------------------------------------------------------------