%------------------------------------------------------------------------------
% 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 : n002.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 1.99s 2.17s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 5 RR)
% Number of literals : 11 ( 10 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 8 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
e_q2(plus_not_idem(A),bfalse) != btrue,
file('SWX206-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('SWX206-1.p',unknown),
[] ).
cnf(4,axiom,
impl(btrue,A) = A,
file('SWX206-1.p',unknown),
[] ).
cnf(7,axiom,
x2(z,A) = A,
file('SWX206-1.p',unknown),
[] ).
cnf(13,axiom,
plus_not_idem(A) = impl(e_q(x2(A,A),A),e_q2(btrue,bfalse)),
file('SWX206-1.p',unknown),
[] ).
cnf(17,axiom,
e_q2(btrue,bfalse) = bfalse,
file('SWX206-1.p',unknown),
[] ).
cnf(25,axiom,
e_q(A,A) = btrue,
file('SWX206-1.p',unknown),
[] ).
cnf(27,axiom,
e_q2(A,A) = btrue,
file('SWX206-1.p',unknown),
[] ).
cnf(28,plain,
e_q2(impl(e_q(x2(A,A),A),bfalse),bfalse) != btrue,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),13,17]),
[iquote('back_demod,1,demod,13,17')] ).
cnf(52,plain,
btrue != btrue,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[28,7]),25,4,27]),
[iquote('para_into,28.1.1.1.1.1,7.1.1,demod,25,4,27')] ).
cnf(53,plain,
$false,
inference(binary,[status(thm)],[52,2]),
[iquote('binary,52.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX206-1 : TPTP v9.3.0. Released v9.3.0.
% 0.13/0.13 % Command : otter-tptp-script %s
% 0.19/0.34 % Computer : n002.cluster.edu
% 0.19/0.34 % Model : x86_64 x86_64
% 0.19/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.34 % Memory : 8042.1875MB
% 0.19/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Tue May 5 11:34:46 EDT 2026
% 0.19/0.34 % CPUTime :
% 1.99/2.17 ----- Otter 3.3f, August 2004 -----
% 1.99/2.17 The process was started by sandbox2 on n002.cluster.edu,
% 1.99/2.17 Tue May 5 11:34:46 2026
% 1.99/2.17 The command was "./otter". The process ID is 22331.
% 1.99/2.17
% 1.99/2.17 set(prolog_style_variables).
% 1.99/2.17 set(auto).
% 1.99/2.17 dependent: set(auto1).
% 1.99/2.17 dependent: set(process_input).
% 1.99/2.17 dependent: clear(print_kept).
% 1.99/2.17 dependent: clear(print_new_demod).
% 1.99/2.17 dependent: clear(print_back_demod).
% 1.99/2.17 dependent: clear(print_back_sub).
% 1.99/2.17 dependent: set(control_memory).
% 1.99/2.17 dependent: assign(max_mem, 12000).
% 1.99/2.17 dependent: assign(pick_given_ratio, 4).
% 1.99/2.17 dependent: assign(stats_level, 1).
% 1.99/2.17 dependent: assign(max_seconds, 10800).
% 1.99/2.17 clear(print_given).
% 1.99/2.17
% 1.99/2.17 list(usable).
% 1.99/2.17 0 [] A=A.
% 1.99/2.17 0 [] impl(btrue,Q)=Q.
% 1.99/2.17 0 [] impl(bfalse,Q)=btrue.
% 1.99/2.17 0 [] x2(z,Y)=Y.
% 1.99/2.17 0 [] x2(s(N),Y)=s(x2(N,Y)).
% 1.99/2.17 0 [] plus_not_idem(X)=impl(e_q(x2(X,X),X),e_q2(btrue,bfalse)).
% 1.99/2.17 0 [] e_q2(bfalse,btrue)=bfalse.
% 1.99/2.17 0 [] e_q2(btrue,bfalse)=bfalse.
% 1.99/2.17 0 [] e_q(s(X),s(Y))=e_q(X,Y).
% 1.99/2.17 0 [] e_q(z,s(X))=bfalse.
% 1.99/2.17 0 [] e_q(s(X),z)=bfalse.
% 1.99/2.17 0 [] e_q(X,X)=btrue.
% 1.99/2.17 0 [] e_q2(X,X)=btrue.
% 1.99/2.17 0 [] e_q2(plus_not_idem(X),bfalse)!=btrue.
% 1.99/2.17 end_of_list.
% 1.99/2.17
% 1.99/2.17 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.99/2.17
% 1.99/2.17 All clauses are units, and equality is present; the
% 1.99/2.17 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.99/2.17
% 1.99/2.17 dependent: set(knuth_bendix).
% 1.99/2.17 dependent: set(anl_eq).
% 1.99/2.17 dependent: set(para_from).
% 1.99/2.17 dependent: set(para_into).
% 1.99/2.17 dependent: clear(para_from_right).
% 1.99/2.17 dependent: clear(para_into_right).
% 1.99/2.17 dependent: set(para_from_vars).
% 1.99/2.17 dependent: set(eq_units_both_ways).
% 1.99/2.17 dependent: set(dynamic_demod_all).
% 1.99/2.17 dependent: set(dynamic_demod).
% 1.99/2.17 dependent: set(order_eq).
% 1.99/2.17 dependent: set(back_demod).
% 1.99/2.17 dependent: set(lrpo).
% 1.99/2.17
% 1.99/2.17 ------------> process usable:
% 1.99/2.17 ** KEPT (pick-wt=6): 1 [] e_q2(plus_not_idem(A),bfalse)!=btrue.
% 1.99/2.17
% 1.99/2.17 ------------> process sos:
% 1.99/2.17 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.99/2.17 ** KEPT (pick-wt=5): 3 [] impl(btrue,A)=A.
% 1.99/2.17 ---> New Demodulator: 4 [new_demod,3] impl(btrue,A)=A.
% 1.99/2.17 ** KEPT (pick-wt=5): 5 [] impl(bfalse,A)=btrue.
% 1.99/2.17 ---> New Demodulator: 6 [new_demod,5] impl(bfalse,A)=btrue.
% 1.99/2.17 ** KEPT (pick-wt=5): 7 [] x2(z,A)=A.
% 1.99/2.17 ---> New Demodulator: 8 [new_demod,7] x2(z,A)=A.
% 1.99/2.17 ** KEPT (pick-wt=9): 10 [copy,9,flip.1] s(x2(A,B))=x2(s(A),B).
% 1.99/2.17 ---> New Demodulator: 11 [new_demod,10] s(x2(A,B))=x2(s(A),B).
% 1.99/2.17 ** KEPT (pick-wt=12): 12 [] plus_not_idem(A)=impl(e_q(x2(A,A),A),e_q2(btrue,bfalse)).
% 1.99/2.17 ---> New Demodulator: 13 [new_demod,12] plus_not_idem(A)=impl(e_q(x2(A,A),A),e_q2(btrue,bfalse)).
% 1.99/2.17 ** KEPT (pick-wt=5): 14 [] e_q2(bfalse,btrue)=bfalse.
% 1.99/2.17 ---> New Demodulator: 15 [new_demod,14] e_q2(bfalse,btrue)=bfalse.
% 1.99/2.17 ** KEPT (pick-wt=5): 16 [] e_q2(btrue,bfalse)=bfalse.
% 1.99/2.17 ---> New Demodulator: 17 [new_demod,16] e_q2(btrue,bfalse)=bfalse.
% 1.99/2.17 ** KEPT (pick-wt=9): 18 [] e_q(s(A),s(B))=e_q(A,B).
% 1.99/2.17 ---> New Demodulator: 19 [new_demod,18] e_q(s(A),s(B))=e_q(A,B).
% 1.99/2.17 ** KEPT (pick-wt=6): 20 [] e_q(z,s(A))=bfalse.
% 1.99/2.17 ---> New Demodulator: 21 [new_demod,20] e_q(z,s(A))=bfalse.
% 1.99/2.17 ** KEPT (pick-wt=6): 22 [] e_q(s(A),z)=bfalse.
% 1.99/2.17 ---> New Demodulator: 23 [new_demod,22] e_q(s(A),z)=bfalse.
% 1.99/2.17 ** KEPT (pick-wt=5): 24 [] e_q(A,A)=btrue.
% 1.99/2.17 ---> New Demodulator: 25 [new_demod,24] e_q(A,A)=btrue.
% 1.99/2.17 ** KEPT (pick-wt=5): 26 [] e_q2(A,A)=btrue.
% 1.99/2.17 ---> New Demodulator: 27 [new_demod,26] e_q2(A,A)=btrue.
% 1.99/2.17 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.99/2.17 >>>> Starting back demodulation with 4.
% 1.99/2.17 >>>> Starting back demodulation with 6.
% 1.99/2.17 >>>> Starting back demodulation with 8.
% 1.99/2.17 >>>> Starting back demodulation with 11.
% 1.99/2.17 >>>> Starting back demodulation with 13.
% 1.99/2.17 >> back demodulating 1 with 13.
% 1.99/2.17 >>>> Starting back demodulation with 15.
% 1.99/2.17 >>>> Starting back demodulation with 17.
% 1.99/2.17 >> back demodulating 12 with 17.
% 1.99/2.17 >>>> Starting back demodulation with 19.
% 1.99/2.17 >>>> Starting back demodulation with 21.
% 1.99/2.17 >>>> Starting back demodulation with 23.
% 1.99/2.17 >>>> Starting back demodulation with 25.
% 1.99/2.17 >>>> Starting back demodulation with 27.
% 1.99/2.17 >>>> Starting back demodulation with 30.
% 1.99/2.17
% 1.99/2.17 ======= end of input processing =======
% 1.99/2.17
% 1.99/2.17 =========== start of search ===========
% 1.99/2.17
% 1.99/2.17 -------- PROOF --------
% 1.99/2.17
% 1.99/2.17 ----> UNIT CONFLICT at 0.00 sec ----> 53 [binary,52.1,2.1] $F.
% 1.99/2.17
% 1.99/2.17 Length of proof is 2. Level of proof is 2.
% 1.99/2.17
% 1.99/2.17 ---------------- PROOF ----------------
% 1.99/2.17 % SZS status Unsatisfiable
% 1.99/2.17 % SZS output start Refutation
% See solution above
% 1.99/2.17 ------------ end of proof -------------
% 1.99/2.17
% 1.99/2.17
% 1.99/2.17 Search stopped by max_proofs option.
% 1.99/2.17
% 1.99/2.17
% 1.99/2.17 Search stopped by max_proofs option.
% 1.99/2.17
% 1.99/2.17 ============ end of search ============
% 1.99/2.17
% 1.99/2.17 -------------- statistics -------------
% 1.99/2.17 clauses given 16
% 1.99/2.17 clauses generated 48
% 1.99/2.17 clauses kept 32
% 1.99/2.17 clauses forward subsumed 42
% 1.99/2.17 clauses back subsumed 0
% 1.99/2.17 Kbytes malloced 976
% 1.99/2.17
% 1.99/2.17 ----------- times (seconds) -----------
% 1.99/2.17 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.99/2.17 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.99/2.17 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.99/2.17
% 1.99/2.17 That finishes the proof of the theorem.
% 1.99/2.17
% 1.99/2.17 Process 22331 finished Tue May 5 11:34:48 2026
% 1.99/2.17 Otter interrupted
% 1.99/2.17 PROOF FOUND
%------------------------------------------------------------------------------