%------------------------------------------------------------------------------
% 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 : n010.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 : Unsatisfiable 1.85s 2.08s
% Output : Refutation 1.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of clauses : 28 ( 28 unt; 0 nHn; 5 RR)
% Number of literals : 28 ( 27 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-5 aty)
% Number of variables : 66 ( 25 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
e_q2(prop_merge_ord_not3(A,B),bfalse) != btrue,
file('SWX200-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('SWX200-1.p',unknown),
[] ).
cnf(3,axiom,
aux(A,B,C,D,btrue) = cons(A,merge(B,cons(C,D))),
file('SWX200-1.p',unknown),
[] ).
cnf(4,plain,
cons(A,merge(B,cons(C,D))) = aux(A,B,C,D,btrue),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3])]),
[iquote('copy,3,flip.1')] ).
cnf(6,axiom,
aux(A,B,C,D,bfalse) = cons(C,merge(cons(A,B),D)),
file('SWX200-1.p',unknown),
[] ).
cnf(7,plain,
cons(A,merge(cons(B,C),D)) = aux(B,C,A,D,bfalse),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(9,axiom,
aux2(A,B,C,btrue) = ord(cons(B,C)),
file('SWX200-1.p',unknown),
[] ).
cnf(11,axiom,
aux2(A,B,C,bfalse) = bfalse,
file('SWX200-1.p',unknown),
[] ).
cnf(14,axiom,
le_qNat(s(A),z) = bfalse,
file('SWX200-1.p',unknown),
[] ).
cnf(19,axiom,
merge(nil,A) = A,
file('SWX200-1.p',unknown),
[] ).
cnf(24,axiom,
ord(nil) = btrue,
file('SWX200-1.p',unknown),
[] ).
cnf(28,axiom,
ord(cons(A,cons(B,C))) = aux2(A,B,C,le_qNat(A,B)),
file('SWX200-1.p',unknown),
[] ).
cnf(31,axiom,
impl(btrue,A) = A,
file('SWX200-1.p',unknown),
[] ).
cnf(34,axiom,
prop_merge_ord_not3(A,B) = impl(e_q2(ord(A),btrue),impl(e_q2(ord(B),bfalse),e_q2(ord(merge(A,B)),btrue))),
file('SWX200-1.p',unknown),
[] ).
cnf(35,plain,
impl(e_q2(ord(A),btrue),impl(e_q2(ord(B),bfalse),e_q2(ord(merge(A,B)),btrue))) = prop_merge_ord_not3(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[34])]),
[iquote('copy,34,flip.1')] ).
cnf(38,axiom,
e_q2(bfalse,btrue) = bfalse,
file('SWX200-1.p',unknown),
[] ).
cnf(50,axiom,
e_q2(A,A) = btrue,
file('SWX200-1.p',unknown),
[] ).
cnf(51,plain,
ord(cons(A,B)) = aux2(C,A,B,btrue),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9])]),
[iquote('copy,9,flip.1')] ).
cnf(54,plain,
cons(A,cons(B,C)) = aux(A,nil,B,C,btrue),
inference(para_into,[status(thm),theory(equality)],[4,19]),
[iquote('para_into,4.1.1.2,18.1.1')] ).
cnf(57,plain,
ord(aux(A,nil,B,C,btrue)) = aux2(A,B,C,le_qNat(A,B)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[28]),54]),
[iquote('back_demod,28,demod,54')] ).
cnf(95,plain,
impl(e_q2(ord(A),bfalse),e_q2(ord(A),btrue)) = prop_merge_ord_not3(nil,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[35,24]),50,19,31]),
[iquote('para_into,35.1.1.1.1,24.1.1,demod,50,19,31')] ).
cnf(129,plain,
aux2(A,B,C,le_qNat(A,B)) = aux2(D,A,cons(B,C),btrue),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[54,51]),57]),
[iquote('para_from,53.1.1,51.1.1.1,demod,57')] ).
cnf(196,plain,
aux2(A,s(B),cons(z,C),btrue) = bfalse,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[129,14]),11])]),
[iquote('para_into,129.1.1.4,14.1.1,demod,11,flip.1')] ).
cnf(231,plain,
aux2(A,s(B),aux(C,D,z,E,bfalse),btrue) = bfalse,
inference(para_into,[status(thm),theory(equality)],[196,7]),
[iquote('para_into,196.1.1.3,7.1.1')] ).
cnf(248,plain,
ord(cons(s(A),aux(B,C,z,D,bfalse))) = bfalse,
inference(para_into,[status(thm),theory(equality)],[231,9]),
[iquote('para_into,231.1.1,9.1.1')] ).
cnf(251,plain,
prop_merge_ord_not3(nil,cons(s(A),aux(B,C,z,D,bfalse))) = bfalse,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[248,95]),50,248,38,31])]),
[iquote('para_from,247.1.1,95.1.1.1.1,demod,50,248,38,31,flip.1')] ).
cnf(259,plain,
btrue != btrue,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[251,1]),50]),
[iquote('para_from,251.1.1,1.1.1.1,demod,50')] ).
cnf(260,plain,
$false,
inference(binary,[status(thm)],[259,2]),
[iquote('binary,259.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWX200-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : otter-tptp-script %s
% 0.16/0.33 % Computer : n010.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 11:15:51 EDT 2026
% 0.16/0.33 % CPUTime :
% 1.85/2.07 ----- Otter 3.3f, August 2004 -----
% 1.85/2.07 The process was started by sandbox2 on n010.cluster.edu,
% 1.85/2.07 Tue May 5 11:15:51 2026
% 1.85/2.07 The command was "./otter". The process ID is 16922.
% 1.85/2.07
% 1.85/2.07 set(prolog_style_variables).
% 1.85/2.07 set(auto).
% 1.85/2.07 dependent: set(auto1).
% 1.85/2.07 dependent: set(process_input).
% 1.85/2.07 dependent: clear(print_kept).
% 1.85/2.07 dependent: clear(print_new_demod).
% 1.85/2.07 dependent: clear(print_back_demod).
% 1.85/2.07 dependent: clear(print_back_sub).
% 1.85/2.07 dependent: set(control_memory).
% 1.85/2.07 dependent: assign(max_mem, 12000).
% 1.85/2.07 dependent: assign(pick_given_ratio, 4).
% 1.85/2.07 dependent: assign(stats_level, 1).
% 1.85/2.07 dependent: assign(max_seconds, 10800).
% 1.85/2.07 clear(print_given).
% 1.85/2.07
% 1.85/2.07 list(usable).
% 1.85/2.07 0 [] A=A.
% 1.85/2.07 0 [] aux(Z,Xs,Y2,Ys,btrue)=cons(Z,merge(Xs,cons(Y2,Ys))).
% 1.85/2.07 0 [] aux(Z,Xs,Y2,Ys,bfalse)=cons(Y2,merge(cons(Z,Xs),Ys)).
% 1.85/2.07 0 [] aux2(Y,Y2,Xs,btrue)=ord(cons(Y2,Xs)).
% 1.85/2.07 0 [] aux2(Y,Y2,Xs,bfalse)=bfalse.
% 1.85/2.07 0 [] le_qNat(z,Y)=btrue.
% 1.85/2.07 0 [] le_qNat(s(Z),z)=bfalse.
% 1.85/2.07 0 [] le_qNat(s(Z),s(M))=le_qNat(Z,M).
% 1.85/2.07 0 [] merge(nil,Y)=Y.
% 1.85/2.07 0 [] merge(cons(Z,Xs),nil)=cons(Z,Xs).
% 1.85/2.07 0 [] merge(cons(Z,Xs),cons(Y2,Ys))=aux(Z,Xs,Y2,Ys,le_qNat(Z,Y2)).
% 1.85/2.07 0 [] ord(nil)=btrue.
% 1.85/2.07 0 [] ord(cons(Y,nil))=btrue.
% 1.85/2.07 0 [] ord(cons(Y,cons(Y2,Xs)))=aux2(Y,Y2,Xs,le_qNat(Y,Y2)).
% 1.85/2.07 0 [] impl(btrue,Q)=Q.
% 1.85/2.07 0 [] impl(bfalse,Q)=btrue.
% 1.85/2.07 0 [] prop_merge_ord_not3(X,Y)=impl(e_q2(ord(X),btrue),impl(e_q2(ord(Y),bfalse),e_q2(ord(merge(X,Y)),btrue))).
% 1.85/2.07 0 [] e_q2(bfalse,btrue)=bfalse.
% 1.85/2.07 0 [] e_q2(btrue,bfalse)=bfalse.
% 1.85/2.07 0 [] e_q(s(X),s(Y))=e_q(X,Y).
% 1.85/2.07 0 [] e_q(z,s(X))=bfalse.
% 1.85/2.07 0 [] e_q(s(X),z)=bfalse.
% 1.85/2.07 0 [] e_q(X,X)=btrue.
% 1.85/2.07 0 [] e_q2(X,X)=btrue.
% 1.85/2.07 0 [] e_q2(prop_merge_ord_not3(X,Y),bfalse)!=btrue.
% 1.85/2.07 end_of_list.
% 1.85/2.07
% 1.85/2.07 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.85/2.07
% 1.85/2.07 All clauses are units, and equality is present; the
% 1.85/2.07 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.85/2.07
% 1.85/2.07 dependent: set(knuth_bendix).
% 1.85/2.07 dependent: set(anl_eq).
% 1.85/2.07 dependent: set(para_from).
% 1.85/2.07 dependent: set(para_into).
% 1.85/2.07 dependent: clear(para_from_right).
% 1.85/2.07 dependent: clear(para_into_right).
% 1.85/2.07 dependent: set(para_from_vars).
% 1.85/2.07 dependent: set(eq_units_both_ways).
% 1.85/2.07 dependent: set(dynamic_demod_all).
% 1.85/2.07 dependent: set(dynamic_demod).
% 1.85/2.07 dependent: set(order_eq).
% 1.85/2.07 dependent: set(back_demod).
% 1.85/2.07 dependent: set(lrpo).
% 1.85/2.07
% 1.85/2.07 ------------> process usable:
% 1.85/2.07 ** KEPT (pick-wt=7): 1 [] e_q2(prop_merge_ord_not3(A,B),bfalse)!=btrue.
% 1.85/2.07
% 1.85/2.07 ------------> process sos:
% 1.85/2.07 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.85/2.07 ** KEPT (pick-wt=14): 4 [copy,3,flip.1] cons(A,merge(B,cons(C,D)))=aux(A,B,C,D,btrue).
% 1.85/2.07 ---> New Demodulator: 5 [new_demod,4] cons(A,merge(B,cons(C,D)))=aux(A,B,C,D,btrue).
% 1.85/2.07 ** KEPT (pick-wt=14): 7 [copy,6,flip.1] cons(A,merge(cons(B,C),D))=aux(B,C,A,D,bfalse).
% 1.85/2.07 ---> New Demodulator: 8 [new_demod,7] cons(A,merge(cons(B,C),D))=aux(B,C,A,D,bfalse).
% 1.85/2.07 ** KEPT (pick-wt=10): 9 [] aux2(A,B,C,btrue)=ord(cons(B,C)).
% 1.85/2.07 ** KEPT (pick-wt=7): 10 [] aux2(A,B,C,bfalse)=bfalse.
% 1.85/2.07 ---> New Demodulator: 11 [new_demod,10] aux2(A,B,C,bfalse)=bfalse.
% 1.85/2.07 ** KEPT (pick-wt=5): 12 [] le_qNat(z,A)=btrue.
% 1.85/2.07 ---> New Demodulator: 13 [new_demod,12] le_qNat(z,A)=btrue.
% 1.85/2.07 ** KEPT (pick-wt=6): 14 [] le_qNat(s(A),z)=bfalse.
% 1.85/2.07 ---> New Demodulator: 15 [new_demod,14] le_qNat(s(A),z)=bfalse.
% 1.85/2.07 ** KEPT (pick-wt=9): 16 [] le_qNat(s(A),s(B))=le_qNat(A,B).
% 1.85/2.07 ---> New Demodulator: 17 [new_demod,16] le_qNat(s(A),s(B))=le_qNat(A,B).
% 1.85/2.07 ** KEPT (pick-wt=5): 18 [] merge(nil,A)=A.
% 1.85/2.07 ---> New Demodulator: 19 [new_demod,18] merge(nil,A)=A.
% 1.85/2.07 ** KEPT (pick-wt=9): 20 [] merge(cons(A,B),nil)=cons(A,B).
% 1.85/2.07 ---> New Demodulator: 21 [new_demod,20] merge(cons(A,B),nil)=cons(A,B).
% 1.85/2.07 ** KEPT (pick-wt=16): 22 [] merge(cons(A,B),cons(C,D))=aux(A,B,C,D,le_qNat(A,C)).
% 1.85/2.07 ---> New Demodulator: 23 [new_demod,22] merge(cons(A,B),cons(C,D))=aux(A,B,C,D,le_qNat(A,C)).
% 1.85/2.07 ** KEPT (pick-wt=4): 24 [] ord(nil)=btrue.
% 1.85/2.07 ---> New Demodulator: 25 [new_demod,24] ord(nil)=btrue.
% 1.85/2.07 ** KEPT (pick-wt=6): 26 [] ord(cons(A,nil))=btrue.
% 1.85/2.07 ---> New Demodulator: 27 [new_demod,26] ord(cons(A,nil))=btrue.
% 1.85/2.07 ** KEPT (pick-wt=14): 28 [] ord(cons(A,cons(B,C)))=aux2(A,B,C,le_qNat(A,B)).
% 1.85/2.07 ---> New Demodulator: 29 [new_demod,28] ord(cons(A,cons(B,C)))=aux2(A,B,C,le_qNat(A,B)).
% 1.85/2.07 ** KEPT (pick-wt=5): 30 [] impl(btrue,A)=A.
% 1.85/2.07 ---> New Demodulator: 31 [new_demod,30] impl(btrue,A)=A.
% 1.85/2.08 ** KEPT (pick-wt=5): 32 [] impl(bfalse,A)=btrue.
% 1.85/2.08 ---> New Demodulator: 33 [new_demod,32] impl(bfalse,A)=btrue.
% 1.85/2.08 ** KEPT (pick-wt=20): 35 [copy,34,flip.1] impl(e_q2(ord(A),btrue),impl(e_q2(ord(B),bfalse),e_q2(ord(merge(A,B)),btrue)))=prop_merge_ord_not3(A,B).
% 1.85/2.08 ---> New Demodulator: 36 [new_demod,35] impl(e_q2(ord(A),btrue),impl(e_q2(ord(B),bfalse),e_q2(ord(merge(A,B)),btrue)))=prop_merge_ord_not3(A,B).
% 1.85/2.08 ** KEPT (pick-wt=5): 37 [] e_q2(bfalse,btrue)=bfalse.
% 1.85/2.08 ---> New Demodulator: 38 [new_demod,37] e_q2(bfalse,btrue)=bfalse.
% 1.85/2.08 ** KEPT (pick-wt=5): 39 [] e_q2(btrue,bfalse)=bfalse.
% 1.85/2.08 ---> New Demodulator: 40 [new_demod,39] e_q2(btrue,bfalse)=bfalse.
% 1.85/2.08 ** KEPT (pick-wt=9): 41 [] e_q(s(A),s(B))=e_q(A,B).
% 1.85/2.08 ---> New Demodulator: 42 [new_demod,41] e_q(s(A),s(B))=e_q(A,B).
% 1.85/2.08 ** KEPT (pick-wt=6): 43 [] e_q(z,s(A))=bfalse.
% 1.85/2.08 ---> New Demodulator: 44 [new_demod,43] e_q(z,s(A))=bfalse.
% 1.85/2.08 ** KEPT (pick-wt=6): 45 [] e_q(s(A),z)=bfalse.
% 1.85/2.08 ---> New Demodulator: 46 [new_demod,45] e_q(s(A),z)=bfalse.
% 1.85/2.08 ** KEPT (pick-wt=5): 47 [] e_q(A,A)=btrue.
% 1.85/2.08 ---> New Demodulator: 48 [new_demod,47] e_q(A,A)=btrue.
% 1.85/2.08 ** KEPT (pick-wt=5): 49 [] e_q2(A,A)=btrue.
% 1.85/2.08 ---> New Demodulator: 50 [new_demod,49] e_q2(A,A)=btrue.
% 1.85/2.08 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.85/2.08 >>>> Starting back demodulation with 5.
% 1.85/2.08 >>>> Starting back demodulation with 8.
% 1.85/2.08 ** KEPT (pick-wt=10): 51 [copy,9,flip.1] ord(cons(A,B))=aux2(C,A,B,btrue).
% 1.85/2.08 >>>> Starting back demodulation with 11.
% 1.85/2.08 >>>> Starting back demodulation with 13.
% 1.85/2.08 >>>> Starting back demodulation with 15.
% 1.85/2.08 >>>> Starting back demodulation with 17.
% 1.85/2.08 >>>> Starting back demodulation with 19.
% 1.85/2.08 >>>> Starting back demodulation with 21.
% 1.85/2.08 >>>> Starting back demodulation with 23.
% 1.85/2.08 >>>> Starting back demodulation with 25.
% 1.85/2.08 >>>> Starting back demodulation with 27.
% 1.85/2.08 >>>> Starting back demodulation with 29.
% 1.85/2.08 >>>> Starting back demodulation with 31.
% 1.85/2.08 >>>> Starting back demodulation with 33.
% 1.85/2.08 >>>> Starting back demodulation with 36.
% 1.85/2.08 >>>> Starting back demodulation with 38.
% 1.85/2.08 >>>> Starting back demodulation with 40.
% 1.85/2.08 >>>> Starting back demodulation with 42.
% 1.85/2.08 >>>> Starting back demodulation with 44.
% 1.85/2.08 >>>> Starting back demodulation with 46.
% 1.85/2.08 >>>> Starting back demodulation with 48.
% 1.85/2.08 >>>> Starting back demodulation with 50.
% 1.85/2.08 Following clause subsumed by 9 during input processing: 0 [copy,51,flip.1] aux2(A,B,C,btrue)=ord(cons(B,C)).
% 1.85/2.08
% 1.85/2.08 ======= end of input processing =======
% 1.85/2.08
% 1.85/2.08 =========== start of search ===========
% 1.85/2.08
% 1.85/2.08
% 1.85/2.08 Resetting weight limit to 17.
% 1.85/2.08
% 1.85/2.08
% 1.85/2.08 Resetting weight limit to 17.
% 1.85/2.08
% 1.85/2.08 sos_size=127
% 1.85/2.08
% 1.85/2.08 -------- PROOF --------
% 1.85/2.08
% 1.85/2.08 ----> UNIT CONFLICT at 0.01 sec ----> 260 [binary,259.1,2.1] $F.
% 1.85/2.08
% 1.85/2.08 Length of proof is 13. Level of proof is 9.
% 1.85/2.08
% 1.85/2.08 ---------------- PROOF ----------------
% 1.85/2.08 % SZS status Unsatisfiable
% 1.85/2.08 % SZS output start Refutation
% See solution above
% 1.85/2.08 ------------ end of proof -------------
% 1.85/2.08
% 1.85/2.08
% 1.85/2.08 Search stopped by max_proofs option.
% 1.85/2.08
% 1.85/2.08
% 1.85/2.08 Search stopped by max_proofs option.
% 1.85/2.08
% 1.85/2.08 ============ end of search ============
% 1.85/2.08
% 1.85/2.08 -------------- statistics -------------
% 1.85/2.08 clauses given 53
% 1.85/2.08 clauses generated 302
% 1.85/2.08 clauses kept 189
% 1.85/2.08 clauses forward subsumed 252
% 1.85/2.08 clauses back subsumed 0
% 1.85/2.08 Kbytes malloced 4882
% 1.85/2.08
% 1.85/2.08 ----------- times (seconds) -----------
% 1.85/2.08 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.85/2.08 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.85/2.08 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.85/2.08
% 1.85/2.08 That finishes the proof of the theorem.
% 1.85/2.08
% 1.85/2.08 Process 16922 finished Tue May 5 11:15:52 2026
% 1.85/2.08 Otter interrupted
% 1.85/2.08 PROOF FOUND
%------------------------------------------------------------------------------