%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SWX206+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% 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 07:05:25 PM UTC 2026
% Result : Theorem 1.93s 2.12s
% Output : Refutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 1
% Number of leaves : 2
% Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 2 RR)
% Number of literals : 3 ( 2 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 2 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
x2(A,A) != A,
file('SWX206+1.p',unknown),
[] ).
cnf(7,axiom,
x2(z,A) = A,
file('SWX206+1.p',unknown),
[] ).
cnf(9,plain,
$false,
inference(binary,[status(thm)],[7,3]),
[iquote('binary,7.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWX206+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.18/0.35 % Computer : n011.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 11:33:02 EDT 2026
% 0.18/0.35 % CPUTime :
% 1.93/2.12
% 1.93/2.12 -------- PROOF --------
% 1.93/2.12 ----- Otter 3.3f, August 2004 -----
% 1.93/2.12 The process was started by sandbox2 on n011.cluster.edu,
% 1.93/2.12 Tue May 5 11:33:02 2026
% 1.93/2.12 The command was "./otter". The process ID is 16821.
% 1.93/2.12
% 1.93/2.12 set(prolog_style_variables).
% 1.93/2.12 set(auto).
% 1.93/2.12 dependent: set(auto1).
% 1.93/2.12 dependent: set(process_input).
% 1.93/2.12 dependent: clear(print_kept).
% 1.93/2.12 dependent: clear(print_new_demod).
% 1.93/2.12 dependent: clear(print_back_demod).
% 1.93/2.12 dependent: clear(print_back_sub).
% 1.93/2.12 dependent: set(control_memory).
% 1.93/2.12 dependent: assign(max_mem, 12000).
% 1.93/2.12 dependent: assign(pick_given_ratio, 4).
% 1.93/2.12 dependent: assign(stats_level, 1).
% 1.93/2.12 dependent: assign(max_seconds, 10800).
% 1.93/2.12 clear(print_given).
% 1.93/2.12
% 1.93/2.12 formula_list(usable).
% 1.93/2.12 all A (A=A).
% 1.93/2.12 all X (proj1S(s(X))=X).
% 1.93/2.12 all X (z!=s(X)).
% 1.93/2.12 all Y (x2(z,Y)=Y).
% 1.93/2.12 all Y N (x2(s(N),Y)=s(x2(N,Y))).
% 1.93/2.12 -(exists X (x2(X,X)=X)).
% 1.93/2.12 end_of_list.
% 1.93/2.12
% 1.93/2.12 -------> usable clausifies to:
% 1.93/2.12
% 1.93/2.12 list(usable).
% 1.93/2.12 0 [] A=A.
% 1.93/2.12 0 [] proj1S(s(X))=X.
% 1.93/2.12 0 [] z!=s(X).
% 1.93/2.12 0 [] x2(z,Y)=Y.
% 1.93/2.12 0 [] x2(s(N),Y)=s(x2(N,Y)).
% 1.93/2.12 0 [] x2(X,X)!=X.
% 1.93/2.12 end_of_list.
% 1.93/2.12
% 1.93/2.12 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.93/2.12
% 1.93/2.12 All clauses are units, and equality is present; the
% 1.93/2.12 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.93/2.12
% 1.93/2.12 dependent: set(knuth_bendix).
% 1.93/2.12 dependent: set(anl_eq).
% 1.93/2.12 dependent: set(para_from).
% 1.93/2.12 dependent: set(para_into).
% 1.93/2.12 dependent: clear(para_from_right).
% 1.93/2.12 dependent: clear(para_into_right).
% 1.93/2.12 dependent: set(para_from_vars).
% 1.93/2.12 dependent: set(eq_units_both_ways).
% 1.93/2.12 dependent: set(dynamic_demod_all).
% 1.93/2.12 dependent: set(dynamic_demod).
% 1.93/2.12 dependent: set(order_eq).
% 1.93/2.12 dependent: set(back_demod).
% 1.93/2.12 dependent: set(lrpo).
% 1.93/2.12
% 1.93/2.12 ------------> process usable:
% 1.93/2.12 ** KEPT (pick-wt=4): 2 [copy,1,flip.1] s(A)!=z.
% 1.93/2.12 ** KEPT (pick-wt=5): 3 [] x2(A,A)!=A.
% 1.93/2.12
% 1.93/2.12 ------------> process sos:
% 1.93/2.12 ** KEPT (pick-wt=3): 4 [] A=A.
% 1.93/2.12 ** KEPT (pick-wt=5): 5 [] proj1S(s(A))=A.
% 1.93/2.12 ---> New Demodulator: 6 [new_demod,5] proj1S(s(A))=A.
% 1.93/2.12 ** KEPT (pick-wt=5): 7 [] x2(z,A)=A.
% 1.93/2.12 ---> New Demodulator: 8 [new_demod,7] x2(z,A)=A.
% 1.93/2.12
% 1.93/2.12 ----> UNIT CONFLICT at 0.00 sec ----> 9 [binary,7.1,3.1] $F.
% 1.93/2.12
% 1.93/2.12 Length of proof is 0. Level of proof is 0.
% 1.93/2.12
% 1.93/2.12 ---------------- PROOF ----------------
% 1.93/2.12 % SZS status Theorem
% 1.93/2.12 % SZS output start Refutation
% See solution above
% 1.93/2.12 ------------ end of proof -------------
% 1.93/2.12
% 1.93/2.12
% 1.93/2.12 Search stopped by max_proofs option.
% 1.93/2.12
% 1.93/2.12
% 1.93/2.12 Search stopped by max_proofs option.
% 1.93/2.12
% 1.93/2.12 ============ end of search ============
% 1.93/2.12
% 1.93/2.12 -------------- statistics -------------
% 1.93/2.12 clauses given 0
% 1.93/2.12 clauses generated 0
% 1.93/2.12 clauses kept 5
% 1.93/2.12 clauses forward subsumed 0
% 1.93/2.12 clauses back subsumed 0
% 1.93/2.12 Kbytes malloced 976
% 1.93/2.12
% 1.93/2.12 ----------- times (seconds) -----------
% 1.93/2.12 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.93/2.12 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.93/2.12 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.93/2.12
% 1.93/2.12 That finishes the proof of the theorem.
% 1.93/2.12
% 1.93/2.12 Process 16821 finished Tue May 5 11:33:04 2026
% 1.93/2.12 Otter interrupted
% 1.93/2.12 PROOF FOUND
%------------------------------------------------------------------------------