%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : SWX217+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n007.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 06:59:50 PM UTC 2026
% Result : Theorem 8.40s 2.49s
% Output : CNFRefutation 8.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of clauses : 77 ( 54 unt; 11 nHn; 49 RR)
% Number of literals : 100 ( 65 equ; 19 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_22,plain,
suc(addNat(rd(X1),rd(X1))) = rd(cons(i,X1)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-excvzz0d/input.p',i_0_22) ).
cnf(i_0_23,plain,
addNat(rd(X1),rd(X1)) = rd(cons(o,X1)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-excvzz0d/input.p',i_0_23) ).
cnf(i_0_21,plain,
rd(nil) = zero,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-excvzz0d/input.p',i_0_21) ).
cnf(i_0_18,plain,
addNat(zero,X1) = X1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-excvzz0d/input.p',i_0_18) ).
cnf(i_0_12,plain,
( ~ evenNat(X1)
| ~ evenNat(suc(X1)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-excvzz0d/input.p',i_0_12) ).
cnf(i_0_10,plain,
evenNat(zero),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-excvzz0d/input.p',i_0_10) ).
cnf(i_0_15,plain,
( cons(i,shw(half(suc(X1)))) = shw(suc(X1))
| evenNat(suc(X1)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-excvzz0d/input.p',i_0_15) ).
cnf(i_0_8,plain,
half(suc(zero)) = zero,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-excvzz0d/input.p',i_0_8) ).
cnf(i_0_13,plain,
shw(zero) = nil,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-excvzz0d/input.p',i_0_13) ).
cnf(i_0_14,plain,
( cons(o,shw(half(suc(X1)))) = shw(suc(X1))
| ~ evenNat(suc(X1)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-excvzz0d/input.p',i_0_14) ).
cnf(i_0_9,plain,
half(suc(suc(X1))) = suc(half(X1)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-excvzz0d/input.p',i_0_9) ).
cnf(i_0_19,plain,
suc(addNat(X1,X2)) = addNat(suc(X1),X2),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-excvzz0d/input.p',i_0_19) ).
cnf(i_0_11,plain,
( evenNat(X1)
| evenNat(suc(X1)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-excvzz0d/input.p',i_0_11) ).
cnf(i_0_7,plain,
half(zero) = zero,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-excvzz0d/input.p',i_0_7) ).
cnf(i_0_17,plain,
cons(X1,append(X2,X3)) = append(cons(X1,X2),X3),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-excvzz0d/input.p',i_0_17) ).
cnf(i_0_16,plain,
append(nil,X1) = X1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-excvzz0d/input.p',i_0_16) ).
cnf(i_0_25,negated_conjecture,
rd(append(shw(X1),shw(X2))) = rd(append(shw(X2),shw(X1))),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-excvzz0d/input.p',i_0_25) ).
cnf(i_0_1,plain,
head(cons(X1,X2)) = X1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-excvzz0d/input.p',i_0_1) ).
cnf(i_0_6,plain,
i != o,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-excvzz0d/input.p',i_0_6) ).
cnf(c_0_45,plain,
suc(addNat(rd(X1),rd(X1))) = rd(cons(i,X1)),
i_0_22 ).
cnf(c_0_46,plain,
addNat(rd(X1),rd(X1)) = rd(cons(o,X1)),
i_0_23 ).
cnf(c_0_47,plain,
rd(nil) = zero,
i_0_21 ).
cnf(c_0_48,plain,
addNat(zero,X1) = X1,
i_0_18 ).
cnf(c_0_49,plain,
( ~ evenNat(X1)
| ~ evenNat(suc(X1)) ),
i_0_12 ).
cnf(c_0_50,plain,
suc(rd(cons(o,X1))) = rd(cons(i,X1)),
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,plain,
rd(cons(o,nil)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_52,plain,
( ~ evenNat(rd(cons(i,X1)))
| ~ evenNat(rd(cons(o,X1))) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_53,plain,
rd(cons(i,nil)) = suc(zero),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,plain,
evenNat(zero),
i_0_10 ).
cnf(c_0_55,plain,
( cons(i,shw(half(suc(X1)))) = shw(suc(X1))
| evenNat(suc(X1)) ),
i_0_15 ).
cnf(c_0_56,plain,
half(suc(zero)) = zero,
i_0_8 ).
cnf(c_0_57,plain,
shw(zero) = nil,
i_0_13 ).
cnf(c_0_58,plain,
~ evenNat(suc(zero)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_51]),c_0_54])]) ).
cnf(c_0_59,plain,
( cons(o,shw(half(suc(X1)))) = shw(suc(X1))
| ~ evenNat(suc(X1)) ),
i_0_14 ).
cnf(c_0_60,plain,
half(suc(suc(X1))) = suc(half(X1)),
i_0_9 ).
cnf(c_0_61,plain,
cons(i,nil) = shw(suc(zero)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_58]) ).
cnf(c_0_62,plain,
( cons(o,shw(suc(half(X1)))) = shw(suc(suc(X1)))
| ~ evenNat(suc(suc(X1))) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_63,plain,
rd(shw(suc(zero))) = suc(zero),
inference(rw,[status(thm)],[c_0_53,c_0_61]) ).
cnf(c_0_64,plain,
suc(addNat(X1,X2)) = addNat(suc(X1),X2),
i_0_19 ).
cnf(c_0_65,plain,
( cons(o,shw(suc(zero))) = shw(suc(suc(suc(zero))))
| ~ evenNat(suc(suc(suc(zero)))) ),
inference(spm,[status(thm)],[c_0_62,c_0_56]) ).
cnf(c_0_66,plain,
( evenNat(X1)
| evenNat(suc(X1)) ),
i_0_11 ).
cnf(c_0_67,plain,
rd(cons(o,shw(suc(zero)))) = suc(suc(zero)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_63]),c_0_64]),c_0_48]) ).
cnf(c_0_68,plain,
( cons(o,shw(suc(zero))) = shw(suc(suc(suc(zero))))
| evenNat(suc(suc(zero))) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_69,plain,
rd(cons(i,shw(suc(zero)))) = suc(suc(suc(zero))),
inference(spm,[status(thm)],[c_0_50,c_0_67]) ).
cnf(c_0_70,plain,
( suc(rd(shw(suc(suc(suc(zero)))))) = suc(suc(suc(zero)))
| evenNat(suc(suc(zero))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_68]),c_0_69]) ).
cnf(c_0_71,plain,
half(zero) = zero,
i_0_7 ).
cnf(c_0_72,plain,
( suc(half(rd(shw(suc(suc(suc(zero))))))) = suc(suc(zero))
| evenNat(suc(suc(zero))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_70]),c_0_60]),c_0_60]),c_0_71]) ).
cnf(c_0_73,plain,
cons(X1,append(X2,X3)) = append(cons(X1,X2),X3),
i_0_17 ).
cnf(c_0_74,plain,
append(nil,X1) = X1,
i_0_16 ).
cnf(c_0_75,plain,
( cons(i,shw(half(rd(cons(i,X1))))) = shw(rd(cons(i,X1)))
| evenNat(rd(cons(i,X1))) ),
inference(spm,[status(thm)],[c_0_55,c_0_50]) ).
cnf(c_0_76,plain,
( evenNat(half(rd(shw(suc(suc(suc(zero)))))))
| evenNat(suc(suc(zero))) ),
inference(spm,[status(thm)],[c_0_66,c_0_72]) ).
cnf(c_0_77,plain,
( rd(shw(suc(suc(suc(zero))))) = suc(suc(zero))
| evenNat(suc(suc(zero))) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_78,plain,
( cons(o,shw(suc(zero))) = shw(suc(suc(zero)))
| ~ evenNat(suc(suc(zero))) ),
inference(spm,[status(thm)],[c_0_62,c_0_71]) ).
cnf(c_0_79,plain,
append(shw(suc(zero)),X1) = cons(i,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_61]),c_0_74]) ).
cnf(c_0_80,plain,
( cons(i,shw(suc(zero))) = shw(suc(suc(suc(zero))))
| evenNat(suc(suc(suc(zero)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_69]),c_0_60]),c_0_56]) ).
cnf(c_0_81,plain,
rd(cons(o,cons(o,shw(suc(zero))))) = suc(suc(suc(suc(zero)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_67]),c_0_64]),c_0_64]),c_0_48]) ).
cnf(c_0_82,plain,
evenNat(suc(suc(zero))),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_60]),c_0_71]),c_0_58]) ).
cnf(c_0_83,negated_conjecture,
rd(append(shw(X1),shw(X2))) = rd(append(shw(X2),shw(X1))),
i_0_25 ).
cnf(c_0_84,plain,
( append(shw(suc(suc(zero))),X1) = cons(o,cons(i,X1))
| ~ evenNat(suc(suc(zero))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_78]),c_0_79]) ).
cnf(c_0_85,plain,
( cons(i,shw(suc(zero))) = shw(suc(suc(suc(zero))))
| ~ evenNat(suc(suc(zero))) ),
inference(spm,[status(thm)],[c_0_49,c_0_80]) ).
cnf(c_0_86,plain,
rd(cons(i,cons(o,shw(suc(zero))))) = suc(suc(suc(suc(suc(zero))))),
inference(spm,[status(thm)],[c_0_50,c_0_81]) ).
cnf(c_0_87,plain,
cons(o,shw(suc(zero))) = shw(suc(suc(zero))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_82])]) ).
cnf(c_0_88,plain,
head(cons(X1,X2)) = X1,
i_0_1 ).
cnf(c_0_89,negated_conjecture,
rd(append(shw(X1),shw(suc(zero)))) = rd(cons(i,shw(X1))),
inference(spm,[status(thm)],[c_0_83,c_0_79]) ).
cnf(c_0_90,plain,
append(shw(suc(suc(zero))),X1) = cons(o,cons(i,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_82])]) ).
cnf(c_0_91,plain,
cons(i,shw(suc(zero))) = shw(suc(suc(suc(zero)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_82])]) ).
cnf(c_0_92,plain,
rd(cons(i,shw(suc(suc(zero))))) = suc(suc(suc(suc(suc(zero))))),
inference(rw,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_93,plain,
( head(shw(suc(suc(suc(zero))))) = i
| ~ evenNat(suc(suc(zero))) ),
inference(spm,[status(thm)],[c_0_88,c_0_85]) ).
cnf(c_0_94,plain,
rd(cons(o,cons(i,shw(suc(zero))))) = suc(suc(suc(suc(suc(suc(zero)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_69]),c_0_64]),c_0_64]),c_0_64]),c_0_48]) ).
cnf(c_0_95,negated_conjecture,
rd(cons(o,shw(suc(suc(suc(zero)))))) = suc(suc(suc(suc(suc(zero))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]),c_0_92]) ).
cnf(c_0_96,plain,
( head(shw(suc(X1))) = o
| ~ evenNat(suc(X1)) ),
inference(spm,[status(thm)],[c_0_88,c_0_59]) ).
cnf(c_0_97,plain,
head(shw(suc(suc(suc(zero))))) = i,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_82])]) ).
cnf(c_0_98,plain,
i != o,
i_0_6 ).
cnf(c_0_99,plain,
suc(suc(suc(suc(suc(suc(zero)))))) = suc(suc(suc(suc(suc(zero))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_91]),c_0_95]) ).
cnf(c_0_100,plain,
~ evenNat(suc(suc(suc(zero)))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98]) ).
cnf(c_0_101,plain,
suc(suc(suc(zero))) = suc(suc(zero)),
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_60,c_0_99]),c_0_60]),c_0_60]),c_0_56]),c_0_60]),c_0_60]),c_0_71]) ).
cnf(c_0_102,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_101]),c_0_82])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX217+1 : TPTP v9.3.0. Released v9.3.0.
% 0.13/0.13 % Command : enigmatic-eprover.py %s %d 1
% 0.17/0.34 % Computer : n007.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 12:13:25 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.21/0.45 # ENIGMATIC: Selected complete mode:
% 8.40/2.49 # ENIGMATIC: Solved by autoschedule:
% 8.40/2.49 # No SInE strategy applied
% 8.40/2.49 # Trying AutoSched0 for 150 seconds
% 8.40/2.49 # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 8.40/2.49 # and selection function SelectComplexExceptUniqMaxHorn.
% 8.40/2.49 #
% 8.40/2.49 # Preprocessing time : 0.023 s
% 8.40/2.49 # Presaturation interreduction done
% 8.40/2.49
% 8.40/2.49 # Proof found!
% 8.40/2.49 # SZS status Theorem
% 8.40/2.49 # SZS output start CNFRefutation
% See solution above
% 8.40/2.49 # Training examples: 0 positive, 0 negative
% 8.40/2.49
% 8.40/2.49 # -------------------------------------------------
% 8.40/2.49 # User time : 0.233 s
% 8.40/2.49 # System time : 0.007 s
% 8.40/2.49 # Total time : 0.240 s
% 8.40/2.49 # Maximum resident set size: 7124 pages
% 8.40/2.49
%------------------------------------------------------------------------------