%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : SWX199+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n027.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 29.92s 5.39s
% Output : CNFRefutation 29.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of clauses : 53 ( 25 unt; 14 nHn; 13 RR)
% Number of literals : 94 ( 53 equ; 26 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 127 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(i_0_14,negated_conjecture,
( merge(X1,X2) = merge(X2,X1)
| merge(X3,X2) != merge(X2,X3)
| merge(X3,X1) != merge(X1,X3) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-wgyyzcye/input.p',i_0_14) ).
cnf(i_0_11,plain,
merge(cons(X1,X2),nil) = cons(X1,X2),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-wgyyzcye/input.p',i_0_11) ).
cnf(i_0_10,plain,
merge(nil,X1) = X1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-wgyyzcye/input.p',i_0_10) ).
cnf(i_0_13,plain,
( cons(X1,merge(cons(X2,X3),X4)) = merge(cons(X2,X3),cons(X1,X4))
| leqNat(X2,X1) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-wgyyzcye/input.p',i_0_13) ).
cnf(i_0_2,plain,
tail(cons(X1,X2)) = X2,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-wgyyzcye/input.p',i_0_2) ).
cnf(i_0_12,plain,
( cons(X1,merge(X2,cons(X3,X4))) = merge(cons(X1,X2),cons(X3,X4))
| ~ leqNat(X1,X3) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-wgyyzcye/input.p',i_0_12) ).
cnf(i_0_1,plain,
head(cons(X1,X2)) = X1,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-wgyyzcye/input.p',i_0_1) ).
cnf(i_0_6,plain,
leqNat(z,X1),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-wgyyzcye/input.p',i_0_6) ).
cnf(i_0_9,plain,
( leqNat(X1,X2)
| ~ leqNat(s(X1),s(X2)) ),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-wgyyzcye/input.p',i_0_9) ).
cnf(i_0_5,plain,
s(X1) != z,
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-wgyyzcye/input.p',i_0_5) ).
cnf(i_0_7,plain,
~ leqNat(s(X1),z),
file('/export/starexec/sandbox2/tmp/enigma-theBenchmark.p-wgyyzcye/input.p',i_0_7) ).
cnf(c_0_26,negated_conjecture,
( merge(X1,X2) = merge(X2,X1)
| merge(X3,X2) != merge(X2,X3)
| merge(X3,X1) != merge(X1,X3) ),
i_0_14 ).
cnf(c_0_27,plain,
merge(cons(X1,X2),nil) = cons(X1,X2),
i_0_11 ).
cnf(c_0_28,plain,
merge(nil,X1) = X1,
i_0_10 ).
cnf(c_0_29,plain,
( cons(X1,merge(cons(X2,X3),X4)) = merge(cons(X2,X3),cons(X1,X4))
| leqNat(X2,X1) ),
i_0_13 ).
cnf(c_0_30,plain,
( merge(X1,cons(X2,X3)) = merge(cons(X2,X3),X1)
| merge(X1,nil) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_28])]) ).
cnf(c_0_31,plain,
( merge(cons(X1,X2),cons(X3,X4)) = cons(X1,merge(cons(X3,X4),X2))
| leqNat(X3,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_27])]) ).
cnf(c_0_32,plain,
tail(cons(X1,X2)) = X2,
i_0_2 ).
cnf(c_0_33,plain,
( cons(X1,merge(cons(X2,X3),X4)) = cons(X2,merge(cons(X1,X4),X3))
| leqNat(X1,X2)
| leqNat(X2,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_31]) ).
cnf(c_0_34,plain,
( cons(X1,merge(X2,cons(X3,X4))) = merge(cons(X1,X2),cons(X3,X4))
| ~ leqNat(X1,X3) ),
i_0_12 ).
cnf(c_0_35,plain,
( merge(cons(X1,X2),X3) = merge(cons(X4,X3),X2)
| leqNat(X4,X1)
| leqNat(X1,X4) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_32]) ).
cnf(c_0_36,plain,
( merge(cons(X1,X2),cons(X3,X4)) = cons(X3,merge(X4,cons(X1,X2)))
| ~ leqNat(X3,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_30]),c_0_27])]) ).
cnf(c_0_37,plain,
head(cons(X1,X2)) = X1,
i_0_1 ).
cnf(c_0_38,plain,
( merge(cons(X1,nil),X2) = cons(X3,X2)
| leqNat(X3,X1)
| leqNat(X1,X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_35]) ).
cnf(c_0_39,plain,
( cons(X1,merge(X2,cons(X3,X4))) = cons(X3,merge(X4,cons(X1,X2)))
| ~ leqNat(X3,X1)
| ~ leqNat(X1,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_36]) ).
cnf(c_0_40,plain,
( head(merge(cons(X1,nil),X2)) = X3
| leqNat(X3,X1)
| leqNat(X1,X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,plain,
( cons(X1,merge(cons(X2,X3),X4)) = cons(X1,merge(X4,cons(X2,X3)))
| leqNat(X2,X1)
| ~ leqNat(X1,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
cnf(c_0_42,plain,
( X1 = X2
| ~ leqNat(X2,X1)
| ~ leqNat(X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_39]),c_0_37]) ).
cnf(c_0_43,plain,
leqNat(z,X1),
i_0_6 ).
cnf(c_0_44,plain,
( head(merge(cons(X1,nil),X2)) = X1
| leqNat(X1,X1) ),
inference(ef,[status(thm)],[c_0_40]) ).
cnf(c_0_45,plain,
( merge(cons(X1,X2),X3) = merge(X3,cons(X1,X2))
| leqNat(X1,X4)
| ~ leqNat(X4,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_41]),c_0_32]) ).
cnf(c_0_46,plain,
( X1 = z
| ~ leqNat(X1,z) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,plain,
( X1 = X2
| leqNat(X2,X2)
| leqNat(X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_29]),c_0_37]) ).
cnf(c_0_48,plain,
( merge(X1,nil) = X1
| merge(X1,cons(X2,X3)) != merge(cons(X2,X3),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_28])]) ).
cnf(c_0_49,plain,
( merge(cons(X1,X2),X3) = merge(X3,cons(X1,X2))
| leqNat(X1,z) ),
inference(spm,[status(thm)],[c_0_45,c_0_43]) ).
cnf(c_0_50,plain,
( leqNat(X1,X2)
| ~ leqNat(s(X1),s(X2)) ),
i_0_9 ).
cnf(c_0_51,plain,
( X1 = z
| leqNat(X1,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,plain,
s(X1) != z,
i_0_5 ).
cnf(c_0_53,plain,
~ leqNat(s(X1),z),
i_0_7 ).
cnf(c_0_54,plain,
( merge(X1,nil) = X1
| leqNat(X2,z) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,plain,
( merge(X1,cons(X2,X3)) = merge(X3,cons(X4,X1))
| ~ leqNat(X2,X4)
| ~ leqNat(X4,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_39]),c_0_32]) ).
cnf(c_0_56,plain,
leqNat(X1,X1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_57,plain,
( merge(X1,X2) = merge(X2,X1)
| merge(X2,nil) != X2
| merge(X1,nil) != X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_28]),c_0_28]) ).
cnf(c_0_58,plain,
merge(X1,nil) = X1,
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,plain,
merge(X1,cons(X2,X3)) = merge(X3,cons(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_56])]) ).
cnf(c_0_60,plain,
merge(X1,X2) = merge(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58]),c_0_58])]) ).
cnf(c_0_61,plain,
merge(X1,cons(X2,nil)) = cons(X2,X1),
inference(spm,[status(thm)],[c_0_28,c_0_59]) ).
cnf(c_0_62,plain,
merge(cons(X1,X2),X3) = merge(X2,cons(X1,X3)),
inference(spm,[status(thm)],[c_0_60,c_0_59]) ).
cnf(c_0_63,plain,
merge(X1,cons(X2,cons(X3,nil))) = cons(X3,cons(X2,X1)),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_64,plain,
cons(X1,cons(X2,nil)) = cons(X2,cons(X1,nil)),
inference(spm,[status(thm)],[c_0_28,c_0_63]) ).
cnf(c_0_65,plain,
cons(X1,cons(X2,X3)) = cons(X2,cons(X1,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_62,c_0_64]),c_0_62]),c_0_62]),c_0_28]),c_0_62]),c_0_28]) ).
cnf(c_0_66,plain,
X1 = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_65]),c_0_37]) ).
cnf(c_0_67,plain,
$false,
inference(sr,[status(thm)],[c_0_52,c_0_66]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SWX199+1 : TPTP v9.3.0. Released v9.3.0.
% 0.09/0.14 % Command : enigmatic-eprover.py %s %d 1
% 0.16/0.35 % Computer : n027.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue May 5 11:11:51 EDT 2026
% 0.16/0.35 % CPUTime :
% 0.27/0.45 # ENIGMATIC: Selected complete mode:
% 29.92/5.39 # ENIGMATIC: Solved by Enigma+tptp-cade20-model03-h2e15+lgb-t150-d60-l8000-e0.15+coop-eprover73:
% 29.92/5.39 # ENIGMA: LightGBM model '/export/starexec/sandbox2/solver/bin/data/Enigma/tptp-cade20-model03-h2e15/lgb-t150-d60-l8000-e0.15/model.lgb' loaded. (hash_base: 32768; conj_feats: 26; version: 991; iters: 150)
% 29.92/5.39 # Preprocessing time : 1.810 s
% 29.92/5.39 # Presaturation interreduction done
% 29.92/5.39
% 29.92/5.39 # Proof found!
% 29.92/5.39 # SZS status Theorem
% 29.92/5.39 # SZS output start CNFRefutation
% See solution above
% 29.92/5.39 # Training examples: 0 positive, 0 negative
% 29.92/5.39
% 29.92/5.39 # -------------------------------------------------
% 29.92/5.39 # User time : 2.157 s
% 29.92/5.39 # System time : 0.174 s
% 29.92/5.39 # Total time : 2.331 s
% 29.92/5.39 # ...preprocessing : 1.810 s
% 29.92/5.39 # ...main loop : 0.522 s
% 29.92/5.39 # Maximum resident set size: 185556 pages
% 29.92/5.39
%------------------------------------------------------------------------------