%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : SWX187+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n011.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 06:59:46 PM UTC 2026
% Result : Theorem 14.39s 3.12s
% Output : CNFRefutation 14.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of clauses : 41 ( 28 unt; 7 nHn; 16 RR)
% Number of literals : 74 ( 54 equ; 28 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 104 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_18,negated_conjecture,
( X1 = X2
| rotate(s(z),X3) = X3
| X3 != X4
| rotate(X1,X3) != rotate(X2,X4)
| ~ x2(X2,length(X4))
| ~ x2(X1,length(X3)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-01zmwyfc/input.p',i_0_18) ).
cnf(i_0_7,plain,
length(cons(X1,X2)) = s(length(X2)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-01zmwyfc/input.p',i_0_7) ).
cnf(i_0_14,plain,
cons(X1,x(X2,X3)) = x(cons(X1,X2),X3),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-01zmwyfc/input.p',i_0_14) ).
cnf(i_0_13,plain,
x(nil,X1) = X1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-01zmwyfc/input.p',i_0_13) ).
cnf(i_0_11,plain,
x2(z,s(X1)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-01zmwyfc/input.p',i_0_11) ).
cnf(i_0_17,plain,
rotate(z,X1) = X1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-01zmwyfc/input.p',i_0_17) ).
cnf(i_0_16,plain,
rotate(X1,x(X2,cons(X3,nil))) = rotate(s(X1),cons(X3,X2)),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-01zmwyfc/input.p',i_0_16) ).
cnf(i_0_8,plain,
( x2(s(X1),s(X2))
| ~ x2(X1,X2) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-01zmwyfc/input.p',i_0_8) ).
cnf(i_0_5,plain,
s(X1) != z,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-01zmwyfc/input.p',i_0_5) ).
cnf(i_0_1,plain,
head(cons(X1,X2)) = X1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-01zmwyfc/input.p',i_0_1) ).
cnf(c_0_29,negated_conjecture,
( X1 = X2
| rotate(s(z),X3) = X3
| X3 != X4
| rotate(X1,X3) != rotate(X2,X4)
| ~ x2(X2,length(X4))
| ~ x2(X1,length(X3)) ),
i_0_18 ).
cnf(c_0_30,negated_conjecture,
( rotate(s(z),X1) = X1
| X2 = X3
| rotate(X2,X1) != rotate(X3,X1)
| ~ x2(X3,length(X1))
| ~ x2(X2,length(X1)) ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_31,plain,
length(cons(X1,X2)) = s(length(X2)),
i_0_7 ).
cnf(c_0_32,plain,
cons(X1,x(X2,X3)) = x(cons(X1,X2),X3),
i_0_14 ).
cnf(c_0_33,plain,
x(nil,X1) = X1,
i_0_13 ).
cnf(c_0_34,plain,
( rotate(s(z),cons(X1,X2)) = cons(X1,X2)
| X3 = X4
| rotate(X3,cons(X1,X2)) != rotate(X4,cons(X1,X2))
| ~ x2(X4,s(length(X2)))
| ~ x2(X3,s(length(X2))) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
x2(z,s(X1)),
i_0_11 ).
cnf(c_0_36,plain,
rotate(z,X1) = X1,
i_0_17 ).
cnf(c_0_37,plain,
rotate(X1,x(X2,cons(X3,nil))) = rotate(s(X1),cons(X3,X2)),
i_0_16 ).
cnf(c_0_38,plain,
cons(X1,X2) = x(cons(X1,nil),X2),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
( rotate(s(z),cons(X1,X2)) = cons(X1,X2)
| X3 = z
| rotate(X3,cons(X1,X2)) != cons(X1,X2)
| ~ x2(X3,s(length(X2))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_40,plain,
rotate(s(X1),x(cons(X2,nil),X3)) = rotate(X1,x(X3,cons(X2,nil))),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,plain,
x(cons(X1,nil),x(X2,X3)) = x(cons(X1,X2),X3),
inference(rw,[status(thm)],[c_0_32,c_0_38]) ).
cnf(c_0_42,plain,
( x2(s(X1),s(X2))
| ~ x2(X1,X2) ),
i_0_8 ).
cnf(c_0_43,plain,
( x(cons(X1,X2),cons(X3,nil)) = x(cons(X3,nil),cons(X1,X2))
| X4 = z
| rotate(X4,x(cons(X3,nil),cons(X1,X2))) != x(cons(X3,nil),cons(X1,X2))
| ~ x2(X4,s(s(length(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(spm,[status(thm)],[c_0_39,c_0_31]),c_0_38]),c_0_40]),c_0_36]),c_0_38]),c_0_38]),c_0_38]) ).
cnf(c_0_44,plain,
x(x(cons(X1,nil),X2),X3) = x(cons(X1,nil),x(X2,X3)),
inference(spm,[status(thm)],[c_0_41,c_0_38]) ).
cnf(c_0_45,plain,
x2(s(z),s(s(X1))),
inference(spm,[status(thm)],[c_0_42,c_0_35]) ).
cnf(c_0_46,plain,
( x(cons(X1,nil),x(cons(X2,X3),cons(X4,nil))) = x(cons(X4,nil),x(cons(X1,nil),cons(X2,X3)))
| X5 = z
| rotate(X5,x(cons(X4,nil),x(cons(X1,nil),cons(X2,X3)))) != x(cons(X4,nil),x(cons(X1,nil),cons(X2,X3)))
| ~ x2(X5,s(s(s(length(X3))))) ),
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_43,c_0_31]),c_0_38]),c_0_44]),c_0_38]),c_0_38]),c_0_38]) ).
cnf(c_0_47,plain,
x2(s(s(z)),s(s(s(X1)))),
inference(spm,[status(thm)],[c_0_42,c_0_45]) ).
cnf(c_0_48,plain,
s(X1) != z,
i_0_5 ).
cnf(c_0_49,plain,
rotate(s(X1),x(cons(X2,X3),X4)) = rotate(X1,x(x(X3,X4),cons(X2,nil))),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_50,plain,
( x(cons(X1,nil),x(cons(X2,X3),cons(X4,nil))) = x(cons(X4,nil),x(cons(X1,nil),cons(X2,X3)))
| x(x(cons(X2,X3),cons(X4,nil)),cons(X1,nil)) != x(cons(X4,nil),x(cons(X1,nil),cons(X2,X3))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_49]),c_0_33]),c_0_44]),c_0_40]),c_0_36]) ).
cnf(c_0_51,plain,
x(x(cons(X1,X2),X3),X4) = x(cons(X1,nil),x(x(X2,X3),X4)),
inference(spm,[status(thm)],[c_0_44,c_0_41]) ).
cnf(c_0_52,plain,
( x(cons(X1,nil),x(cons(X2,X3),cons(X4,nil))) = x(cons(X4,nil),x(cons(X1,nil),cons(X2,X3)))
| x(cons(X2,nil),x(x(X3,cons(X4,nil)),cons(X1,nil))) != x(cons(X4,nil),x(cons(X1,nil),cons(X2,X3))) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_53,plain,
( x(cons(X1,nil),x(cons(X2,nil),x(cons(X3,X4),cons(X5,nil)))) = x(cons(X5,nil),x(cons(X1,nil),x(cons(X2,nil),cons(X3,X4))))
| x(cons(X2,nil),x(cons(X3,nil),x(x(X4,cons(X5,nil)),cons(X1,nil)))) != x(cons(X5,nil),x(cons(X1,nil),x(cons(X2,nil),cons(X3,X4)))) ),
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_52,c_0_41]),c_0_38]),c_0_51]),c_0_33]),c_0_38]),c_0_51]),c_0_33]),c_0_38]) ).
cnf(c_0_54,plain,
head(cons(X1,X2)) = X1,
i_0_1 ).
cnf(c_0_55,plain,
( x(cons(X1,nil),x(cons(X2,nil),x(cons(X3,nil),cons(X4,nil)))) = x(cons(X4,nil),x(cons(X1,nil),x(cons(X2,nil),cons(X3,nil))))
| x(cons(X2,nil),x(cons(X3,nil),x(cons(X4,nil),cons(X1,nil)))) != x(cons(X4,nil),x(cons(X1,nil),x(cons(X2,nil),cons(X3,nil)))) ),
inference(spm,[status(thm)],[c_0_53,c_0_33]) ).
cnf(c_0_56,plain,
head(x(cons(X1,X2),X3)) = X1,
inference(spm,[status(thm)],[c_0_54,c_0_32]) ).
cnf(c_0_57,plain,
x(cons(X1,nil),x(cons(X2,nil),x(cons(X1,nil),cons(X2,nil)))) = x(cons(X2,nil),x(cons(X1,nil),x(cons(X2,nil),cons(X1,nil)))),
inference(er,[status(thm)],[c_0_55]) ).
cnf(c_0_58,plain,
X1 = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_56]) ).
cnf(c_0_59,plain,
$false,
inference(sr,[status(thm)],[c_0_48,c_0_58]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX187+1 : TPTP v9.3.0. Released v9.3.0.
% 0.11/0.13 % Command : enigmatic-eprover.py %s %d 1
% 0.16/0.34 % Computer : n011.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 09:39:19 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.28/0.45 # ENIGMATIC: Selected complete mode:
% 14.39/3.12 # ENIGMATIC: Solved by autoschedule:
% 14.39/3.12 # No SInE strategy applied
% 14.39/3.12 # Trying AutoSched0 for 150 seconds
% 14.39/3.12 # AutoSched0-Mode selected heuristic G_E___200_B02_F1_SE_CS_SP_PI_S0S
% 14.39/3.12 # and selection function SelectComplexG.
% 14.39/3.12 #
% 14.39/3.12 # Preprocessing time : 0.023 s
% 14.39/3.12
% 14.39/3.12 # Proof found!
% 14.39/3.12 # SZS status Theorem
% 14.39/3.12 # SZS output start CNFRefutation
% See solution above
% 14.39/3.12 # Training examples: 0 positive, 0 negative
% 14.39/3.12
% 14.39/3.12 # -------------------------------------------------
% 14.39/3.12 # User time : 0.772 s
% 14.39/3.12 # System time : 0.029 s
% 14.39/3.12 # Total time : 0.801 s
% 14.39/3.12 # Maximum resident set size: 7120 pages
% 14.39/3.12
%------------------------------------------------------------------------------