%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SWX204+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 1.86s 2.09s
% Output : Refutation 1.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 4 RR)
% Number of literals : 27 ( 26 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 33 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
z != s(A),
file('SWX204+1.p',unknown),
[] ).
cnf(2,plain,
s(A) != z,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(5,axiom,
proj1S(s(A)) = A,
file('SWX204+1.p',unknown),
[] ).
cnf(7,axiom,
x2(z,A) = A,
file('SWX204+1.p',unknown),
[] ).
cnf(8,axiom,
x2(s(A),B) = s(x2(A,B)),
file('SWX204+1.p',unknown),
[] ).
cnf(10,plain,
s(x2(A,B)) = x2(s(A),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[8])]),
[iquote('copy,8,flip.1')] ).
cnf(12,axiom,
x22(z,A) = z,
file('SWX204+1.p',unknown),
[] ).
cnf(14,axiom,
x22(s(A),B) = x2(B,x22(A,B)),
file('SWX204+1.p',unknown),
[] ).
cnf(15,axiom,
x22(A,A) = A,
file('SWX204+1.p',unknown),
[] ).
cnf(17,plain,
s(A) = x2(s(z),A),
inference(para_into,[status(thm),theory(equality)],[10,7]),
[iquote('para_into,9.1.1.1,6.1.1')] ).
cnf(18,plain,
x2(s(z),A) = s(A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[17])]),
[iquote('copy,17,flip.1')] ).
cnf(20,plain,
proj1S(x2(s(A),B)) = x2(A,B),
inference(para_from,[status(thm),theory(equality)],[10,5]),
[iquote('para_from,9.1.1,4.1.1.1')] ).
cnf(21,plain,
x2(s(A),B) != z,
inference(para_from,[status(thm),theory(equality)],[10,2]),
[iquote('para_from,9.1.1,2.1.1')] ).
cnf(23,plain,
x2(s(A),B) = x2(s(z),x2(A,B)),
inference(para_into,[status(thm),theory(equality)],[17,10]),
[iquote('para_into,17.1.1,9.1.1')] ).
cnf(27,plain,
s(s(A)) = x2(s(s(z)),A),
inference(para_from,[status(thm),theory(equality)],[18,10]),
[iquote('para_from,18.1.1,9.1.1.1')] ).
cnf(28,plain,
x2(s(s(z)),A) = s(s(A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[27])]),
[iquote('copy,27,flip.1')] ).
cnf(35,plain,
x2(s(A),x22(A,s(A))) = s(A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,15])]),
[iquote('para_into,13.1.1,15.1.1,flip.1')] ).
cnf(47,plain,
x2(s(s(s(z))),A) = x2(s(s(z)),s(A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[27,27]),10]),
[iquote('para_into,27.1.1.1,27.1.1,demod,10')] ).
cnf(57,plain,
x2(x2(s(z),A),B) = x2(s(z),x2(A,B)),
inference(para_into,[status(thm),theory(equality)],[23,17]),
[iquote('para_into,23.1.1.1,17.1.1')] ).
cnf(62,plain,
s(s(A)) = x2(s(z),x2(s(z),A)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[28,17]),57])]),
[iquote('para_into,28.1.1.1,17.1.1,demod,57,flip.1')] ).
cnf(68,plain,
x2(s(z),x2(s(z),x2(s(z),A))) = x2(s(z),x2(s(z),s(A))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[47]),62,10,62,57,57,7,57,57,57,7,62,57,57,7]),
[iquote('back_demod,47,demod,62,10,62,57,57,7,57,57,57,7,62,57,57,7')] ).
cnf(78,plain,
x2(A,x22(A,s(A))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[35,20]),5])]),
[iquote('para_from,35.1.1,19.1.1.1,demod,5,flip.1')] ).
cnf(80,plain,
x2(A,x22(A,x2(s(z),A))) = A,
inference(para_into,[status(thm),theory(equality)],[78,17]),
[iquote('para_into,78.1.1.2.2,17.1.1')] ).
cnf(114,plain,
x2(s(z),x2(s(z),x2(s(z),A))) = x2(s(z),A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[57,80]),14,12,57,57,57,7])]),
[iquote('para_into,56.1.1.1,80.1.1,demod,14,12,57,57,57,7,flip.1')] ).
cnf(115,plain,
x2(s(z),x2(s(z),s(A))) = x2(s(z),A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[68]),114])]),
[iquote('back_demod,68,demod,114,flip.1')] ).
cnf(131,plain,
x2(s(z),s(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[115,20]),20,7,7])]),
[iquote('para_from,115.1.1,19.1.1.1,demod,20,7,7,flip.1')] ).
cnf(133,plain,
$false,
inference(binary,[status(thm)],[131,21]),
[iquote('binary,131.1,21.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX204+1 : TPTP v9.3.0. Released v9.3.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.16/0.34 % Computer : n008.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 11:28:28 EDT 2026
% 0.16/0.35 % CPUTime :
% 1.86/2.09 ----- Otter 3.3f, August 2004 -----
% 1.86/2.09 The process was started by sandbox2 on n008.cluster.edu,
% 1.86/2.09 Tue May 5 11:28:28 2026
% 1.86/2.09 The command was "./otter". The process ID is 11610.
% 1.86/2.09
% 1.86/2.09 set(prolog_style_variables).
% 1.86/2.09 set(auto).
% 1.86/2.09 dependent: set(auto1).
% 1.86/2.09 dependent: set(process_input).
% 1.86/2.09 dependent: clear(print_kept).
% 1.86/2.09 dependent: clear(print_new_demod).
% 1.86/2.09 dependent: clear(print_back_demod).
% 1.86/2.09 dependent: clear(print_back_sub).
% 1.86/2.09 dependent: set(control_memory).
% 1.86/2.09 dependent: assign(max_mem, 12000).
% 1.86/2.09 dependent: assign(pick_given_ratio, 4).
% 1.86/2.09 dependent: assign(stats_level, 1).
% 1.86/2.09 dependent: assign(max_seconds, 10800).
% 1.86/2.09 clear(print_given).
% 1.86/2.09
% 1.86/2.09 formula_list(usable).
% 1.86/2.09 all A (A=A).
% 1.86/2.09 all X (proj1S(s(X))=X).
% 1.86/2.09 all X (z!=s(X)).
% 1.86/2.09 all Y (x2(z,Y)=Y).
% 1.86/2.09 all Y N (x2(s(N),Y)=s(x2(N,Y))).
% 1.86/2.09 all Y (x22(z,Y)=z).
% 1.86/2.09 all Y N (x22(s(N),Y)=x2(Y,x22(N,Y))).
% 1.86/2.09 -(exists X (x22(X,X)!=X)).
% 1.86/2.09 end_of_list.
% 1.86/2.09
% 1.86/2.09 -------> usable clausifies to:
% 1.86/2.09
% 1.86/2.09 list(usable).
% 1.86/2.09 0 [] A=A.
% 1.86/2.09 0 [] proj1S(s(X))=X.
% 1.86/2.09 0 [] z!=s(X).
% 1.86/2.09 0 [] x2(z,Y)=Y.
% 1.86/2.09 0 [] x2(s(N),Y)=s(x2(N,Y)).
% 1.86/2.09 0 [] x22(z,Y)=z.
% 1.86/2.09 0 [] x22(s(N),Y)=x2(Y,x22(N,Y)).
% 1.86/2.09 0 [] x22(X,X)=X.
% 1.86/2.09 end_of_list.
% 1.86/2.09
% 1.86/2.09 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.86/2.09
% 1.86/2.09 All clauses are units, and equality is present; the
% 1.86/2.09 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.86/2.09
% 1.86/2.09 dependent: set(knuth_bendix).
% 1.86/2.09 dependent: set(anl_eq).
% 1.86/2.09 dependent: set(para_from).
% 1.86/2.09 dependent: set(para_into).
% 1.86/2.09 dependent: clear(para_from_right).
% 1.86/2.09 dependent: clear(para_into_right).
% 1.86/2.09 dependent: set(para_from_vars).
% 1.86/2.09 dependent: set(eq_units_both_ways).
% 1.86/2.09 dependent: set(dynamic_demod_all).
% 1.86/2.09 dependent: set(dynamic_demod).
% 1.86/2.09 dependent: set(order_eq).
% 1.86/2.09 dependent: set(back_demod).
% 1.86/2.09 dependent: set(lrpo).
% 1.86/2.09
% 1.86/2.09 ------------> process usable:
% 1.86/2.09 ** KEPT (pick-wt=4): 2 [copy,1,flip.1] s(A)!=z.
% 1.86/2.09
% 1.86/2.09 ------------> process sos:
% 1.86/2.09 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.86/2.09 ** KEPT (pick-wt=5): 4 [] proj1S(s(A))=A.
% 1.86/2.09 ---> New Demodulator: 5 [new_demod,4] proj1S(s(A))=A.
% 1.86/2.09 ** KEPT (pick-wt=5): 6 [] x2(z,A)=A.
% 1.86/2.09 ---> New Demodulator: 7 [new_demod,6] x2(z,A)=A.
% 1.86/2.09 ** KEPT (pick-wt=9): 9 [copy,8,flip.1] s(x2(A,B))=x2(s(A),B).
% 1.86/2.09 ---> New Demodulator: 10 [new_demod,9] s(x2(A,B))=x2(s(A),B).
% 1.86/2.09 ** KEPT (pick-wt=5): 11 [] x22(z,A)=z.
% 1.86/2.09 ---> New Demodulator: 12 [new_demod,11] x22(z,A)=z.
% 1.86/2.09 ** KEPT (pick-wt=10): 13 [] x22(s(A),B)=x2(B,x22(A,B)).
% 1.86/2.09 ---> New Demodulator: 14 [new_demod,13] x22(s(A),B)=x2(B,x22(A,B)).
% 1.86/2.09 ** KEPT (pick-wt=5): 15 [] x22(A,A)=A.
% 1.86/2.09 ---> New Demodulator: 16 [new_demod,15] x22(A,A)=A.
% 1.86/2.09 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.86/2.09 >>>> Starting back demodulation with 5.
% 1.86/2.09 >>>> Starting back demodulation with 7.
% 1.86/2.09 >>>> Starting back demodulation with 10.
% 1.86/2.09 >>>> Starting back demodulation with 12.
% 1.86/2.09 >>>> Starting back demodulation with 14.
% 1.86/2.09 >>>> Starting back demodulation with 16.
% 1.86/2.09
% 1.86/2.09 ======= end of input processing =======
% 1.86/2.09
% 1.86/2.09 =========== start of search ===========
% 1.86/2.09
% 1.86/2.09 -------- PROOF --------
% 1.86/2.09
% 1.86/2.09 ----> UNIT CONFLICT at 0.01 sec ----> 133 [binary,131.1,21.1] $F.
% 1.86/2.09
% 1.86/2.09 Length of proof is 19. Level of proof is 9.
% 1.86/2.09
% 1.86/2.09 ---------------- PROOF ----------------
% 1.86/2.09 % SZS status Theorem
% 1.86/2.09 % SZS output start Refutation
% See solution above
% 1.86/2.09 ------------ end of proof -------------
% 1.86/2.09
% 1.86/2.09
% 1.86/2.09 Search stopped by max_proofs option.
% 1.86/2.09
% 1.86/2.09
% 1.86/2.09 Search stopped by max_proofs option.
% 1.86/2.09
% 1.86/2.09 ============ end of search ============
% 1.86/2.09
% 1.86/2.09 -------------- statistics -------------
% 1.86/2.09 clauses given 32
% 1.86/2.09 clauses generated 391
% 1.86/2.09 clauses kept 87
% 1.86/2.09 clauses forward subsumed 379
% 1.86/2.09 clauses back subsumed 2
% 1.86/2.09 Kbytes malloced 1953
% 1.86/2.09
% 1.86/2.09 ----------- times (seconds) -----------
% 1.86/2.09 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.86/2.09 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.86/2.09 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.86/2.09
% 1.86/2.09 That finishes the proof of the theorem.
% 1.86/2.09
% 1.86/2.09 Process 11610 finished Tue May 5 11:28:30 2026
% 1.86/2.09 Otter interrupted
% 1.86/2.09 PROOF FOUND
%------------------------------------------------------------------------------