%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : SWX203+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:59:48 PM UTC 2026
% Result : Theorem 9.04s 2.68s
% Output : CNFRefutation 9.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 19
% Syntax : Number of clauses : 76 ( 35 unt; 30 nHn; 50 RR)
% Number of literals : 197 ( 48 equ; 46 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 115 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_28,plain,
append(rev(X1),cons(X2,nil)) = rev(cons(X2,X1)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-v1qqjovi/input.p',i_0_28) ).
cnf(i_0_27,plain,
rev(nil) = nil,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-v1qqjovi/input.p',i_0_27) ).
cnf(i_0_25,plain,
append(nil,X1) = X1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-v1qqjovi/input.p',i_0_25) ).
cnf(i_0_26,plain,
cons(X1,append(X2,X3)) = append(cons(X1,X2),X3),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-v1qqjovi/input.p',i_0_26) ).
cnf(i_0_22,plain,
( elemNat(X1,X2)
| unique(cons(X1,X2))
| ~ unique(X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-v1qqjovi/input.p',i_0_22) ).
cnf(i_0_21,plain,
unique(nil),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-v1qqjovi/input.p',i_0_21) ).
cnf(i_0_17,plain,
~ elemNat(X1,nil),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-v1qqjovi/input.p',i_0_17) ).
cnf(i_0_29,negated_conjecture,
( leqNat(lengthNat(X1),s(s(s(z))))
| ~ unique(X1)
| ~ sorted(rev(X1)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-v1qqjovi/input.p',i_0_29) ).
cnf(i_0_16,plain,
lengthNat(cons(X1,X2)) = s(lengthNat(X2)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-v1qqjovi/input.p',i_0_16) ).
cnf(i_0_15,plain,
lengthNat(nil) = z,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-v1qqjovi/input.p',i_0_15) ).
cnf(i_0_12,plain,
( sorted(cons(X1,cons(X2,X3)))
| ~ leqNat(X1,X2)
| ~ sorted(cons(X2,X3)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-v1qqjovi/input.p',i_0_12) ).
cnf(i_0_11,plain,
sorted(cons(X1,nil)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-v1qqjovi/input.p',i_0_11) ).
cnf(i_0_6,plain,
leqNat(z,X1),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-v1qqjovi/input.p',i_0_6) ).
cnf(i_0_8,plain,
( leqNat(s(X1),s(X2))
| ~ leqNat(X1,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-v1qqjovi/input.p',i_0_8) ).
cnf(i_0_20,plain,
( X1 = X2
| elemNat(X1,X3)
| ~ elemNat(X1,cons(X2,X3)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-v1qqjovi/input.p',i_0_20) ).
cnf(i_0_5,plain,
s(X1) != z,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-v1qqjovi/input.p',i_0_5) ).
cnf(i_0_9,plain,
( leqNat(X1,X2)
| ~ leqNat(s(X1),s(X2)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-v1qqjovi/input.p',i_0_9) ).
cnf(i_0_7,plain,
~ leqNat(s(X1),z),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-v1qqjovi/input.p',i_0_7) ).
cnf(i_0_4,plain,
proj1S(s(X1)) = X1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-v1qqjovi/input.p',i_0_4) ).
cnf(c_0_49,plain,
append(rev(X1),cons(X2,nil)) = rev(cons(X2,X1)),
i_0_28 ).
cnf(c_0_50,plain,
rev(nil) = nil,
i_0_27 ).
cnf(c_0_51,plain,
append(nil,X1) = X1,
i_0_25 ).
cnf(c_0_52,plain,
rev(cons(X1,nil)) = cons(X1,nil),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_53,plain,
cons(X1,append(X2,X3)) = append(cons(X1,X2),X3),
i_0_26 ).
cnf(c_0_54,plain,
( elemNat(X1,X2)
| unique(cons(X1,X2))
| ~ unique(X2) ),
i_0_22 ).
cnf(c_0_55,plain,
unique(nil),
i_0_21 ).
cnf(c_0_56,plain,
~ elemNat(X1,nil),
i_0_17 ).
cnf(c_0_57,plain,
rev(cons(X1,cons(X2,nil))) = cons(X2,cons(X1,nil)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_52]),c_0_53]),c_0_51]) ).
cnf(c_0_58,plain,
unique(cons(X1,nil)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
cnf(c_0_59,negated_conjecture,
( leqNat(lengthNat(X1),s(s(s(z))))
| ~ unique(X1)
| ~ sorted(rev(X1)) ),
i_0_29 ).
cnf(c_0_60,plain,
lengthNat(cons(X1,X2)) = s(lengthNat(X2)),
i_0_16 ).
cnf(c_0_61,plain,
rev(cons(X1,cons(X2,cons(X3,nil)))) = cons(X3,cons(X2,cons(X1,nil))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_57]),c_0_53]),c_0_53]),c_0_51]) ).
cnf(c_0_62,plain,
( elemNat(X1,cons(X2,nil))
| unique(cons(X1,cons(X2,nil))) ),
inference(spm,[status(thm)],[c_0_54,c_0_58]) ).
cnf(c_0_63,negated_conjecture,
( leqNat(s(lengthNat(X1)),s(s(s(z))))
| ~ unique(cons(X2,X1))
| ~ sorted(rev(cons(X2,X1))) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,plain,
rev(cons(X1,cons(X2,cons(X3,cons(X4,nil))))) = cons(X4,cons(X3,cons(X2,cons(X1,nil)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_61]),c_0_53]),c_0_53]),c_0_53]),c_0_51]) ).
cnf(c_0_65,plain,
lengthNat(nil) = z,
i_0_15 ).
cnf(c_0_66,plain,
( elemNat(X1,cons(X2,cons(X3,nil)))
| elemNat(X2,cons(X3,nil))
| unique(cons(X1,cons(X2,cons(X3,nil)))) ),
inference(spm,[status(thm)],[c_0_54,c_0_62]) ).
cnf(c_0_67,negated_conjecture,
( leqNat(s(s(s(s(z)))),s(s(s(z))))
| ~ unique(cons(X1,cons(X2,cons(X3,cons(X4,nil)))))
| ~ sorted(cons(X4,cons(X3,cons(X2,cons(X1,nil))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_60]),c_0_60]),c_0_60]),c_0_65]) ).
cnf(c_0_68,plain,
( elemNat(X1,cons(X2,cons(X3,cons(X4,nil))))
| elemNat(X2,cons(X3,cons(X4,nil)))
| elemNat(X3,cons(X4,nil))
| unique(cons(X1,cons(X2,cons(X3,cons(X4,nil))))) ),
inference(spm,[status(thm)],[c_0_54,c_0_66]) ).
cnf(c_0_69,plain,
( elemNat(X1,cons(X2,cons(X3,cons(X4,nil))))
| elemNat(X2,cons(X3,cons(X4,nil)))
| elemNat(X3,cons(X4,nil))
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| ~ sorted(cons(X4,cons(X3,cons(X2,cons(X1,nil))))) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_70,plain,
( sorted(cons(X1,cons(X2,X3)))
| ~ leqNat(X1,X2)
| ~ sorted(cons(X2,X3)) ),
i_0_12 ).
cnf(c_0_71,plain,
( elemNat(X1,cons(X2,cons(X3,cons(X4,nil))))
| elemNat(X2,cons(X3,cons(X4,nil)))
| elemNat(X3,cons(X4,nil))
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| ~ leqNat(X4,X3)
| ~ sorted(cons(X3,cons(X2,cons(X1,nil)))) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_72,negated_conjecture,
( leqNat(s(s(z)),s(s(s(z))))
| ~ unique(cons(X1,cons(X2,nil)))
| ~ sorted(cons(X2,cons(X1,nil))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_57]),c_0_60]),c_0_65]) ).
cnf(c_0_73,plain,
( elemNat(X1,cons(X2,cons(X3,cons(X4,nil))))
| elemNat(X2,cons(X3,cons(X4,nil)))
| elemNat(X3,cons(X4,nil))
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| ~ leqNat(X4,X3)
| ~ leqNat(X3,X2)
| ~ sorted(cons(X2,cons(X1,nil))) ),
inference(spm,[status(thm)],[c_0_71,c_0_70]) ).
cnf(c_0_74,plain,
sorted(cons(X1,nil)),
i_0_11 ).
cnf(c_0_75,plain,
( elemNat(X1,cons(X2,nil))
| leqNat(s(s(z)),s(s(s(z))))
| ~ sorted(cons(X2,cons(X1,nil))) ),
inference(spm,[status(thm)],[c_0_72,c_0_62]) ).
cnf(c_0_76,plain,
( elemNat(X1,cons(X2,cons(X3,cons(X4,nil))))
| elemNat(X2,cons(X3,cons(X4,nil)))
| elemNat(X3,cons(X4,nil))
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| ~ leqNat(X4,X3)
| ~ leqNat(X3,X2)
| ~ leqNat(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_70]),c_0_74])]) ).
cnf(c_0_77,plain,
leqNat(z,X1),
i_0_6 ).
cnf(c_0_78,plain,
( elemNat(X1,cons(X2,nil))
| leqNat(s(s(z)),s(s(s(z))))
| ~ leqNat(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_70]),c_0_74])]) ).
cnf(c_0_79,plain,
( elemNat(X1,cons(X2,cons(X3,cons(z,nil))))
| elemNat(X2,cons(X3,cons(z,nil)))
| elemNat(X3,cons(z,nil))
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| ~ leqNat(X3,X2)
| ~ leqNat(X2,X1) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_80,plain,
( leqNat(s(X1),s(X2))
| ~ leqNat(X1,X2) ),
i_0_8 ).
cnf(c_0_81,plain,
( X1 = X2
| elemNat(X1,X3)
| ~ elemNat(X1,cons(X2,X3)) ),
i_0_20 ).
cnf(c_0_82,plain,
( elemNat(X1,cons(z,nil))
| leqNat(s(s(z)),s(s(s(z)))) ),
inference(spm,[status(thm)],[c_0_78,c_0_77]) ).
cnf(c_0_83,plain,
( elemNat(X1,cons(s(X2),cons(s(X3),cons(z,nil))))
| elemNat(s(X2),cons(s(X3),cons(z,nil)))
| elemNat(s(X3),cons(z,nil))
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| ~ leqNat(s(X2),X1)
| ~ leqNat(X3,X2) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_84,plain,
s(X1) != z,
i_0_5 ).
cnf(c_0_85,plain,
( X1 = z
| leqNat(s(s(z)),s(s(s(z)))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_56]) ).
cnf(c_0_86,plain,
( elemNat(s(X1),cons(s(X2),cons(s(X3),cons(z,nil))))
| elemNat(s(X2),cons(s(X3),cons(z,nil)))
| elemNat(s(X3),cons(z,nil))
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| ~ leqNat(X3,X2)
| ~ leqNat(X2,X1) ),
inference(spm,[status(thm)],[c_0_83,c_0_80]) ).
cnf(c_0_87,plain,
( leqNat(X1,X2)
| ~ leqNat(s(X1),s(X2)) ),
i_0_9 ).
cnf(c_0_88,plain,
leqNat(s(s(z)),s(s(s(z)))),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_89,plain,
( elemNat(s(X1),cons(s(X2),cons(s(z),cons(z,nil))))
| elemNat(s(X2),cons(s(z),cons(z,nil)))
| elemNat(s(z),cons(z,nil))
| leqNat(s(s(s(s(z)))),s(s(s(z))))
| ~ leqNat(X2,X1) ),
inference(spm,[status(thm)],[c_0_86,c_0_77]) ).
cnf(c_0_90,plain,
leqNat(s(z),s(s(z))),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_91,plain,
( elemNat(s(s(s(z))),cons(s(s(z)),cons(s(z),cons(z,nil))))
| elemNat(s(s(z)),cons(s(z),cons(z,nil)))
| elemNat(s(z),cons(z,nil))
| leqNat(s(s(s(s(z)))),s(s(s(z)))) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_92,plain,
( s(s(s(z))) = s(s(z))
| elemNat(s(s(s(z))),cons(s(z),cons(z,nil)))
| elemNat(s(s(z)),cons(s(z),cons(z,nil)))
| elemNat(s(z),cons(z,nil))
| leqNat(s(s(s(s(z)))),s(s(s(z)))) ),
inference(spm,[status(thm)],[c_0_81,c_0_91]) ).
cnf(c_0_93,plain,
( s(s(s(z))) = s(s(z))
| elemNat(s(s(s(z))),cons(s(z),cons(z,nil)))
| elemNat(s(s(z)),cons(s(z),cons(z,nil)))
| elemNat(s(z),cons(z,nil))
| leqNat(s(s(s(z))),s(s(z))) ),
inference(spm,[status(thm)],[c_0_87,c_0_92]) ).
cnf(c_0_94,plain,
( s(s(s(z))) = s(s(z))
| s(s(s(z))) = s(z)
| elemNat(s(s(z)),cons(s(z),cons(z,nil)))
| elemNat(s(s(s(z))),cons(z,nil))
| elemNat(s(z),cons(z,nil))
| leqNat(s(s(s(z))),s(s(z))) ),
inference(spm,[status(thm)],[c_0_81,c_0_93]) ).
cnf(c_0_95,plain,
( s(s(s(z))) = s(s(z))
| s(s(s(z))) = s(z)
| s(s(z)) = s(z)
| elemNat(s(s(s(z))),cons(z,nil))
| elemNat(s(s(z)),cons(z,nil))
| elemNat(s(z),cons(z,nil))
| leqNat(s(s(s(z))),s(s(z))) ),
inference(spm,[status(thm)],[c_0_81,c_0_94]) ).
cnf(c_0_96,plain,
( s(s(s(z))) = s(s(z))
| s(s(s(z))) = s(z)
| s(s(z)) = s(z)
| elemNat(s(s(s(z))),cons(z,nil))
| elemNat(s(s(z)),cons(z,nil))
| elemNat(s(z),cons(z,nil))
| leqNat(s(s(z)),s(z)) ),
inference(spm,[status(thm)],[c_0_87,c_0_95]) ).
cnf(c_0_97,plain,
( s(s(s(z))) = s(s(z))
| s(s(s(z))) = s(z)
| s(s(z)) = s(z)
| elemNat(s(s(z)),cons(z,nil))
| elemNat(s(z),cons(z,nil))
| leqNat(s(s(z)),s(z)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_96]),c_0_84]),c_0_56]) ).
cnf(c_0_98,plain,
( s(s(s(z))) = s(s(z))
| s(s(s(z))) = s(z)
| s(s(z)) = s(z)
| elemNat(s(z),cons(z,nil))
| leqNat(s(s(z)),s(z)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_97]),c_0_84]),c_0_56]) ).
cnf(c_0_99,plain,
~ leqNat(s(X1),z),
i_0_7 ).
cnf(c_0_100,plain,
( s(s(s(z))) = s(s(z))
| s(s(s(z))) = s(z)
| s(s(z)) = s(z)
| elemNat(s(z),cons(z,nil)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_98]),c_0_99]) ).
cnf(c_0_101,plain,
proj1S(s(X1)) = X1,
i_0_4 ).
cnf(c_0_102,plain,
( s(s(s(z))) = s(s(z))
| s(s(s(z))) = s(z)
| s(s(z)) = s(z) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_100]),c_0_84]),c_0_56]) ).
cnf(c_0_103,plain,
( s(s(s(z))) = s(z)
| s(s(z)) = s(z) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_101])]) ).
cnf(c_0_104,plain,
s(s(z)) = s(z),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_103]),c_0_101]),c_0_84]) ).
cnf(c_0_105,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_104]),c_0_101]),c_0_84]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX203+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : enigmatic-eprover.py %s %d 1
% 0.14/0.33 % Computer : n009.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 11:23:57 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.19/0.44 # ENIGMATIC: Selected complete mode:
% 9.04/2.68 # ENIGMATIC: Solved by autoschedule:
% 9.04/2.68 # No SInE strategy applied
% 9.04/2.68 # Trying AutoSched0 for 150 seconds
% 9.04/2.68 # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 9.04/2.68 # and selection function SelectComplexExceptUniqMaxHorn.
% 9.04/2.68 #
% 9.04/2.68 # Preprocessing time : 0.023 s
% 9.04/2.68 # Presaturation interreduction done
% 9.04/2.68
% 9.04/2.68 # Proof found!
% 9.04/2.68 # SZS status Theorem
% 9.04/2.68 # SZS output start CNFRefutation
% See solution above
% 9.04/2.68 # Training examples: 0 positive, 0 negative
% 9.04/2.68
% 9.04/2.68 # -------------------------------------------------
% 9.04/2.68 # User time : 0.199 s
% 9.04/2.68 # System time : 0.009 s
% 9.04/2.68 # Total time : 0.208 s
% 9.04/2.68 # Maximum resident set size: 7124 pages
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