%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SWX200+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n001.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 07:05:24 PM UTC 2026
% Result : Theorem 1.92s 2.13s
% Output : Refutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 8 ( 6 unt; 1 nHn; 4 RR)
% Number of literals : 11 ( 1 equ; 3 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
~ le_qNat(s(A),z),
file('SWX200+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ ord(cons(A,cons(B,C)))
| le_qNat(A,B) ),
file('SWX200+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ ord(A)
| ord(B)
| ord(merge(A,B)) ),
file('SWX200+1.p',unknown),
[] ).
cnf(22,axiom,
merge(nil,A) = A,
file('SWX200+1.p',unknown),
[] ).
cnf(26,axiom,
ord(nil),
file('SWX200+1.p',unknown),
[] ).
cnf(28,plain,
ord(A),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[26,12]),22])]),
[iquote('hyper,26,12,demod,22,factor_simp')] ).
cnf(29,plain,
le_qNat(A,B),
inference(hyper,[status(thm)],[28,9]),
[iquote('hyper,28,9')] ).
cnf(30,plain,
$false,
inference(binary,[status(thm)],[29,5]),
[iquote('binary,29.1,5.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWX200+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.18/0.35 % Computer : n001.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue May 5 11:15:33 EDT 2026
% 0.18/0.35 % CPUTime :
% 1.92/2.13 ----- Otter 3.3f, August 2004 -----
% 1.92/2.13 The process was started by sandbox on n001.cluster.edu,
% 1.92/2.13 Tue May 5 11:15:33 2026
% 1.92/2.13 The command was "./otter". The process ID is 13958.
% 1.92/2.13
% 1.92/2.13 set(prolog_style_variables).
% 1.92/2.13 set(auto).
% 1.92/2.13 dependent: set(auto1).
% 1.92/2.13 dependent: set(process_input).
% 1.92/2.13 dependent: clear(print_kept).
% 1.92/2.13 dependent: clear(print_new_demod).
% 1.92/2.13 dependent: clear(print_back_demod).
% 1.92/2.13 dependent: clear(print_back_sub).
% 1.92/2.13 dependent: set(control_memory).
% 1.92/2.13 dependent: assign(max_mem, 12000).
% 1.92/2.13 dependent: assign(pick_given_ratio, 4).
% 1.92/2.13 dependent: assign(stats_level, 1).
% 1.92/2.13 dependent: assign(max_seconds, 10800).
% 1.92/2.13 clear(print_given).
% 1.92/2.13
% 1.92/2.13 formula_list(usable).
% 1.92/2.13 all A (A=A).
% 1.92/2.13 all X X2 (head(cons(X,X2))=X).
% 1.92/2.13 all X X2 (tail(cons(X,X2))=X2).
% 1.92/2.13 all X X2 (nil!=cons(X,X2)).
% 1.92/2.13 all X (proj1S(s(X))=X).
% 1.92/2.13 all X (z!=s(X)).
% 1.92/2.13 all Y le_qNat(z,Y).
% 1.92/2.13 all Z (-le_qNat(s(Z),z)).
% 1.92/2.13 all Z M (le_qNat(s(Z),s(M))<->le_qNat(Z,M)).
% 1.92/2.13 all Y (merge(nil,Y)=Y).
% 1.92/2.13 all Z Xs (merge(cons(Z,Xs),nil)=cons(Z,Xs)).
% 1.92/2.13 all Z Xs Y2 Ys (le_qNat(Z,Y2)->merge(cons(Z,Xs),cons(Y2,Ys))=cons(Z,merge(Xs,cons(Y2,Ys)))).
% 1.92/2.13 all Z Xs Y2 Ys (-le_qNat(Z,Y2)->merge(cons(Z,Xs),cons(Y2,Ys))=cons(Y2,merge(cons(Z,Xs),Ys))).
% 1.92/2.13 ord(nil).
% 1.92/2.13 all Y ord(cons(Y,nil)).
% 1.92/2.13 all Y Y2 Xs (ord(cons(Y,cons(Y2,Xs)))<->le_qNat(Y,Y2)&ord(cons(Y2,Xs))).
% 1.92/2.13 -(exists Xs Ys (-(ord(Xs)-> (-ord(Ys)->ord(merge(Xs,Ys)))))).
% 1.92/2.13 end_of_list.
% 1.92/2.13
% 1.92/2.13 -------> usable clausifies to:
% 1.92/2.13
% 1.92/2.13 list(usable).
% 1.92/2.13 0 [] A=A.
% 1.92/2.13 0 [] head(cons(X,X2))=X.
% 1.92/2.13 0 [] tail(cons(X,X2))=X2.
% 1.92/2.13 0 [] nil!=cons(X,X2).
% 1.92/2.13 0 [] proj1S(s(X))=X.
% 1.92/2.13 0 [] z!=s(X).
% 1.92/2.13 0 [] le_qNat(z,Y).
% 1.92/2.13 0 [] -le_qNat(s(Z),z).
% 1.92/2.13 0 [] -le_qNat(s(Z),s(M))|le_qNat(Z,M).
% 1.92/2.13 0 [] le_qNat(s(Z),s(M))| -le_qNat(Z,M).
% 1.92/2.13 0 [] merge(nil,Y)=Y.
% 1.92/2.13 0 [] merge(cons(Z,Xs),nil)=cons(Z,Xs).
% 1.92/2.13 0 [] -le_qNat(Z,Y2)|merge(cons(Z,Xs),cons(Y2,Ys))=cons(Z,merge(Xs,cons(Y2,Ys))).
% 1.92/2.13 0 [] le_qNat(Z,Y2)|merge(cons(Z,Xs),cons(Y2,Ys))=cons(Y2,merge(cons(Z,Xs),Ys)).
% 1.92/2.13 0 [] ord(nil).
% 1.92/2.13 0 [] ord(cons(Y,nil)).
% 1.92/2.13 0 [] -ord(cons(Y,cons(Y2,Xs)))|le_qNat(Y,Y2).
% 1.92/2.13 0 [] -ord(cons(Y,cons(Y2,Xs)))|ord(cons(Y2,Xs)).
% 1.92/2.13 0 [] ord(cons(Y,cons(Y2,Xs)))| -le_qNat(Y,Y2)| -ord(cons(Y2,Xs)).
% 1.92/2.13 0 [] -ord(Xs)|ord(Ys)|ord(merge(Xs,Ys)).
% 1.92/2.13 end_of_list.
% 1.92/2.13
% 1.92/2.13 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.92/2.13
% 1.92/2.13 This ia a non-Horn set with equality. The strategy will be
% 1.92/2.13 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.92/2.13 deletion, with positive clauses in sos and nonpositive
% 1.92/2.13 clauses in usable.
% 1.92/2.13
% 1.92/2.13 dependent: set(knuth_bendix).
% 1.92/2.13 dependent: set(anl_eq).
% 1.92/2.13 dependent: set(para_from).
% 1.92/2.13 dependent: set(para_into).
% 1.92/2.13 dependent: clear(para_from_right).
% 1.92/2.13 dependent: clear(para_into_right).
% 1.92/2.13 dependent: set(para_from_vars).
% 1.92/2.13 dependent: set(eq_units_both_ways).
% 1.92/2.13 dependent: set(dynamic_demod_all).
% 1.92/2.13 dependent: set(dynamic_demod).
% 1.92/2.13 dependent: set(order_eq).
% 1.92/2.13 dependent: set(back_demod).
% 1.92/2.13 dependent: set(lrpo).
% 1.92/2.13 dependent: set(hyper_res).
% 1.92/2.13 dependent: set(unit_deletion).
% 1.92/2.13 dependent: set(factor).
% 1.92/2.13
% 1.92/2.13 ------------> process usable:
% 1.92/2.13 ** KEPT (pick-wt=5): 2 [copy,1,flip.1] cons(A,B)!=nil.
% 1.92/2.13 ** KEPT (pick-wt=4): 4 [copy,3,flip.1] s(A)!=z.
% 1.92/2.13 ** KEPT (pick-wt=4): 5 [] -le_qNat(s(A),z).
% 1.92/2.13 ** KEPT (pick-wt=8): 6 [] -le_qNat(s(A),s(B))|le_qNat(A,B).
% 1.92/2.13 ** KEPT (pick-wt=8): 7 [] le_qNat(s(A),s(B))| -le_qNat(A,B).
% 1.92/2.13 ** KEPT (pick-wt=18): 8 [] -le_qNat(A,B)|merge(cons(A,C),cons(B,D))=cons(A,merge(C,cons(B,D))).
% 1.92/2.13 ** KEPT (pick-wt=9): 9 [] -ord(cons(A,cons(B,C)))|le_qNat(A,B).
% 1.92/2.13 ** KEPT (pick-wt=10): 10 [] -ord(cons(A,cons(B,C)))|ord(cons(B,C)).
% 1.92/2.13 ** KEPT (pick-wt=13): 11 [] ord(cons(A,cons(B,C)))| -le_qNat(A,B)| -ord(cons(B,C)).
% 1.92/2.13 ** KEPT (pick-wt=8): 12 [] -ord(A)|ord(B)|ord(merge(A,B)).
% 1.92/2.13
% 1.92/2.13 ------------> process sos:
% 1.92/2.13 ** KEPT (pick-wt=3): 13 [] A=A.
% 1.92/2.13 ** KEPT (pick-wt=6): 14 [] head(cons(A,B))=A.
% 1.92/2.13 ---> New Demodulator: 15 [new_demod,14] head(cons(A,B))=A.
% 1.92/2.13 ** KEPT (pick-wt=6): 16 [] tail(cons(A,B))=B.
% 1.92/2.13 ---> New Demodulator: 17 [new_demod,16] tail(cons(A,B))=B.
% 1.92/2.13 ** KEPT (pick-wt=5): 18 [] proj1S(s(A))=A.
% 1.92/2.13 ---> New Demodulator: 19 [new_demod,18] proj1S(s(A))=A.
% 1.92/2.13 ** KEPT (pick-wt=3): 20 [] le_qNat(z,A).
% 1.92/2.13 ** KEPT (pick-wt=5): 21 [] merge(nil,A)=A.
% 1.92/2.13 ---> New Demodulator: 22 [new_demod,21] merge(nil,A)=A.
% 1.92/2.13 ** KEPT (pick-wt=9): 23 [] merge(cons(A,B),nil)=cons(A,B).
% 1.92/2.13 ---> New Demodulator: 24 [new_demod,23] merge(cons(A,B),nil)=cons(A,B).
% 1.92/2.13 ** KEPT (pick-wt=18): 25 [] le_qNat(A,B)|merge(cons(A,C),cons(B,D))=cons(B,merge(cons(A,C),D)).
% 1.92/2.13 ** KEPT (pick-wt=2): 26 [] ord(nil).
% 1.92/2.13 ** KEPT (pick-wt=4): 27 [] ord(cons(A,nil)).
% 1.92/2.13 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 1.92/2.13 >>>> Starting back demodulation with 15.
% 1.92/2.13 >>>> Starting back demodulation with 17.
% 1.92/2.13 >>>> Starting back demodulation with 19.
% 1.92/2.13 >>>> Starting back demodulation with 22.
% 1.92/2.13 >>>> Starting back demodulation with 24.
% 1.92/2.13
% 1.92/2.13 ======= end of input processing =======
% 1.92/2.13
% 1.92/2.13 =========== start of search ===========
% 1.92/2.13
% 1.92/2.13 -------- PROOF --------
% 1.92/2.13
% 1.92/2.13 ----> UNIT CONFLICT at 0.00 sec ----> 30 [binary,29.1,5.1] $F.
% 1.92/2.13
% 1.92/2.13 Length of proof is 2. Level of proof is 2.
% 1.92/2.13
% 1.92/2.13 ---------------- PROOF ----------------
% 1.92/2.13 % SZS status Theorem
% 1.92/2.13 % SZS output start Refutation
% See solution above
% 1.92/2.13 ------------ end of proof -------------
% 1.92/2.13
% 1.92/2.13
% 1.92/2.13 Search stopped by max_proofs option.
% 1.92/2.13
% 1.92/2.13
% 1.92/2.13 Search stopped by max_proofs option.
% 1.92/2.13
% 1.92/2.13 ============ end of search ============
% 1.92/2.13
% 1.92/2.13 -------------- statistics -------------
% 1.92/2.13 clauses given 3
% 1.92/2.13 clauses generated 2
% 1.92/2.13 clauses kept 22
% 1.92/2.13 clauses forward subsumed 1
% 1.92/2.13 clauses back subsumed 5
% 1.92/2.13 Kbytes malloced 976
% 1.92/2.13
% 1.92/2.13 ----------- times (seconds) -----------
% 1.92/2.13 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.92/2.13 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.92/2.13 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.92/2.13
% 1.92/2.13 That finishes the proof of the theorem.
% 1.92/2.13
% 1.92/2.13 Process 13958 finished Tue May 5 11:15:35 2026
% 1.92/2.13 Otter interrupted
% 1.92/2.13 PROOF FOUND
%------------------------------------------------------------------------------