%------------------------------------------------------------------------------
% 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 : n031.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 : Unsatisfiable 1.92s 2.13s
% Output : Refutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 5 RR)
% Number of literals : 25 ( 24 equ; 4 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
e_q2(mul_idem(A),bfalse) != btrue,
file('SWX204-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('SWX204-1.p',unknown),
[] ).
cnf(4,axiom,
x2(z,A) = A,
file('SWX204-1.p',unknown),
[] ).
cnf(5,axiom,
x2(s(A),B) = s(x2(A,B)),
file('SWX204-1.p',unknown),
[] ).
cnf(7,plain,
s(x2(A,B)) = x2(s(A),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
[iquote('copy,5,flip.1')] ).
cnf(9,axiom,
x22(z,A) = z,
file('SWX204-1.p',unknown),
[] ).
cnf(11,axiom,
x22(s(A),B) = x2(B,x22(A,B)),
file('SWX204-1.p',unknown),
[] ).
cnf(13,axiom,
mul_idem(A) = e_q(x22(A,A),A),
file('SWX204-1.p',unknown),
[] ).
cnf(18,axiom,
e_q(s(A),s(B)) = e_q(A,B),
file('SWX204-1.p',unknown),
[] ).
cnf(22,axiom,
e_q(s(A),z) = bfalse,
file('SWX204-1.p',unknown),
[] ).
cnf(27,axiom,
e_q2(A,A) = btrue,
file('SWX204-1.p',unknown),
[] ).
cnf(28,plain,
e_q2(e_q(x22(A,A),A),bfalse) != btrue,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),13]),
[iquote('back_demod,1,demod,13')] ).
cnf(29,plain,
s(A) = x2(s(z),A),
inference(para_into,[status(thm),theory(equality)],[7,4]),
[iquote('para_into,6.1.1.1,3.1.1')] ).
cnf(30,plain,
x2(s(z),A) = s(A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[29])]),
[iquote('copy,29,flip.1')] ).
cnf(34,plain,
e_q(x2(s(A),B),z) = bfalse,
inference(para_into,[status(thm),theory(equality)],[22,7]),
[iquote('para_into,22.1.1.1,6.1.1')] ).
cnf(37,plain,
x2(s(A),B) = x2(s(z),x2(A,B)),
inference(para_into,[status(thm),theory(equality)],[29,7]),
[iquote('para_into,29.1.1,6.1.1')] ).
cnf(41,plain,
s(s(A)) = x2(s(s(z)),A),
inference(para_from,[status(thm),theory(equality)],[30,7]),
[iquote('para_from,30.1.1,6.1.1.1')] ).
cnf(42,plain,
x2(s(s(z)),A) = s(s(A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[41])]),
[iquote('copy,41,flip.1')] ).
cnf(50,plain,
e_q(x2(s(A),B),s(C)) = e_q(x2(A,B),C),
inference(para_into,[status(thm),theory(equality)],[18,7]),
[iquote('para_into,18.1.1.1,6.1.1')] ).
cnf(59,plain,
e_q2(e_q(x2(A,x22(A,s(A))),A),bfalse) != btrue,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[28,11]),50]),
[iquote('para_into,28.1.1.1.1,10.1.1,demod,50')] ).
cnf(82,plain,
s(s(A)) = x2(x2(s(z),s(z)),A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[42,29])]),
[iquote('para_into,42.1.1.1,29.1.1,flip.1')] ).
cnf(105,plain,
x2(x2(s(z),A),B) = x2(s(z),x2(A,B)),
inference(para_into,[status(thm),theory(equality)],[37,29]),
[iquote('para_into,37.1.1.1,29.1.1')] ).
cnf(112,plain,
s(s(A)) = x2(s(z),x2(s(z),A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[82]),105]),
[iquote('back_demod,82,demod,105')] ).
cnf(136,plain,
btrue != btrue,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[59,30]),112,11,9,105,105,4,7,112,105,105,4,50,4,34,27]),
[iquote('para_into,59.1.1.1.1,30.1.1,demod,112,11,9,105,105,4,7,112,105,105,4,50,4,34,27')] ).
cnf(137,plain,
$false,
inference(binary,[status(thm)],[136,2]),
[iquote('binary,136.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX204-1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.16/0.34 % Computer : n031.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 11:31:53 EDT 2026
% 0.16/0.34 % CPUTime :
% 1.92/2.13 ----- Otter 3.3f, August 2004 -----
% 1.92/2.13 The process was started by sandbox on n031.cluster.edu,
% 1.92/2.13 Tue May 5 11:31:54 2026
% 1.92/2.13 The command was "./otter". The process ID is 12588.
% 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 list(usable).
% 1.92/2.13 0 [] A=A.
% 1.92/2.13 0 [] x2(z,Y)=Y.
% 1.92/2.13 0 [] x2(s(N),Y)=s(x2(N,Y)).
% 1.92/2.13 0 [] x22(z,Y)=z.
% 1.92/2.13 0 [] x22(s(N),Y)=x2(Y,x22(N,Y)).
% 1.92/2.13 0 [] mul_idem(X)=e_q(x22(X,X),X).
% 1.92/2.13 0 [] e_q2(bfalse,btrue)=bfalse.
% 1.92/2.13 0 [] e_q2(btrue,bfalse)=bfalse.
% 1.92/2.13 0 [] e_q(s(X),s(Y))=e_q(X,Y).
% 1.92/2.13 0 [] e_q(z,s(X))=bfalse.
% 1.92/2.13 0 [] e_q(s(X),z)=bfalse.
% 1.92/2.13 0 [] e_q(X,X)=btrue.
% 1.92/2.13 0 [] e_q2(X,X)=btrue.
% 1.92/2.13 0 [] e_q2(mul_idem(X),bfalse)!=btrue.
% 1.92/2.13 end_of_list.
% 1.92/2.13
% 1.92/2.13 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.92/2.13
% 1.92/2.13 All clauses are units, and equality is present; the
% 1.92/2.13 strategy will be Knuth-Bendix with positive clauses in sos.
% 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
% 1.92/2.13 ------------> process usable:
% 1.92/2.13 ** KEPT (pick-wt=6): 1 [] e_q2(mul_idem(A),bfalse)!=btrue.
% 1.92/2.13
% 1.92/2.13 ------------> process sos:
% 1.92/2.13 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.92/2.13 ** KEPT (pick-wt=5): 3 [] x2(z,A)=A.
% 1.92/2.13 ---> New Demodulator: 4 [new_demod,3] x2(z,A)=A.
% 1.92/2.13 ** KEPT (pick-wt=9): 6 [copy,5,flip.1] s(x2(A,B))=x2(s(A),B).
% 1.92/2.13 ---> New Demodulator: 7 [new_demod,6] s(x2(A,B))=x2(s(A),B).
% 1.92/2.13 ** KEPT (pick-wt=5): 8 [] x22(z,A)=z.
% 1.92/2.13 ---> New Demodulator: 9 [new_demod,8] x22(z,A)=z.
% 1.92/2.13 ** KEPT (pick-wt=10): 10 [] x22(s(A),B)=x2(B,x22(A,B)).
% 1.92/2.13 ---> New Demodulator: 11 [new_demod,10] x22(s(A),B)=x2(B,x22(A,B)).
% 1.92/2.13 ** KEPT (pick-wt=8): 12 [] mul_idem(A)=e_q(x22(A,A),A).
% 1.92/2.13 ---> New Demodulator: 13 [new_demod,12] mul_idem(A)=e_q(x22(A,A),A).
% 1.92/2.13 ** KEPT (pick-wt=5): 14 [] e_q2(bfalse,btrue)=bfalse.
% 1.92/2.13 ---> New Demodulator: 15 [new_demod,14] e_q2(bfalse,btrue)=bfalse.
% 1.92/2.13 ** KEPT (pick-wt=5): 16 [] e_q2(btrue,bfalse)=bfalse.
% 1.92/2.13 ---> New Demodulator: 17 [new_demod,16] e_q2(btrue,bfalse)=bfalse.
% 1.92/2.13 ** KEPT (pick-wt=9): 18 [] e_q(s(A),s(B))=e_q(A,B).
% 1.92/2.13 ---> New Demodulator: 19 [new_demod,18] e_q(s(A),s(B))=e_q(A,B).
% 1.92/2.13 ** KEPT (pick-wt=6): 20 [] e_q(z,s(A))=bfalse.
% 1.92/2.13 ---> New Demodulator: 21 [new_demod,20] e_q(z,s(A))=bfalse.
% 1.92/2.13 ** KEPT (pick-wt=6): 22 [] e_q(s(A),z)=bfalse.
% 1.92/2.13 ---> New Demodulator: 23 [new_demod,22] e_q(s(A),z)=bfalse.
% 1.92/2.13 ** KEPT (pick-wt=5): 24 [] e_q(A,A)=btrue.
% 1.92/2.13 ---> New Demodulator: 25 [new_demod,24] e_q(A,A)=btrue.
% 1.92/2.13 ** KEPT (pick-wt=5): 26 [] e_q2(A,A)=btrue.
% 1.92/2.13 ---> New Demodulator: 27 [new_demod,26] e_q2(A,A)=btrue.
% 1.92/2.13 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.92/2.13 >>>> Starting back demodulation with 4.
% 1.92/2.13 >>>> Starting back demodulation with 7.
% 1.92/2.13 >>>> Starting back demodulation with 9.
% 1.92/2.13 >>>> Starting back demodulation with 11.
% 1.92/2.13 >>>> Starting back demodulation with 13.
% 1.92/2.13 >> back demodulating 1 with 13.
% 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 21.
% 1.92/2.13 >>>> Starting back demodulation with 23.
% 1.92/2.13 >>>> Starting back demodulation with 25.
% 1.92/2.13 >>>> Starting back demodulation with 27.
% 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 ----> 137 [binary,136.1,2.1] $F.
% 1.92/2.13
% 1.92/2.13 Length of proof is 14. Level of proof is 8.
% 1.92/2.13
% 1.92/2.13 ---------------- PROOF ----------------
% 1.92/2.13 % SZS status Unsatisfiable
% 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 35
% 1.92/2.13 clauses generated 225
% 1.92/2.13 clauses kept 97
% 1.92/2.13 clauses forward subsumed 228
% 1.92/2.13 clauses back subsumed 0
% 1.92/2.13 Kbytes malloced 1953
% 1.92/2.13
% 1.92/2.13 ----------- times (seconds) -----------
% 1.92/2.13 user CPU time 0.01 (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 1 (0 hr, 0 min, 1 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 12588 finished Tue May 5 11:31:55 2026
% 1.92/2.13 Otter interrupted
% 1.92/2.13 PROOF FOUND
%------------------------------------------------------------------------------