%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SWX233-1 : 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 07:05:28 PM UTC 2026
% Result : Unsatisfiable 1.96s 2.15s
% Output : Refutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 9 ( 9 unt; 0 nHn; 6 RR)
% Number of literals : 9 ( 8 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 5 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
e_q(prop1(A),bfalse) != btrue,
file('SWX233-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('SWX233-1.p',unknown),
[] ).
cnf(15,axiom,
f(nil) = btrue,
file('SWX233-1.p',unknown),
[] ).
cnf(20,axiom,
prop1(A) = e_q(f(A),bfalse),
file('SWX233-1.p',unknown),
[] ).
cnf(24,axiom,
e_q(btrue,bfalse) = bfalse,
file('SWX233-1.p',unknown),
[] ).
cnf(26,axiom,
e_q(A,A) = btrue,
file('SWX233-1.p',unknown),
[] ).
cnf(27,plain,
e_q(e_q(f(A),bfalse),bfalse) != btrue,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),20]),
[iquote('back_demod,1,demod,20')] ).
cnf(28,plain,
btrue != btrue,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[27,15]),24,26]),
[iquote('para_into,27.1.1.1.1,15.1.1,demod,24,26')] ).
cnf(29,plain,
$false,
inference(binary,[status(thm)],[28,2]),
[iquote('binary,28.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX233-1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.17/0.34 % Computer : n031.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 13:08:54 EDT 2026
% 0.17/0.34 % CPUTime :
% 1.96/2.15 ----- Otter 3.3f, August 2004 -----
% 1.96/2.15 The process was started by sandbox on n031.cluster.edu,
% 1.96/2.15 Tue May 5 13:08:54 2026
% 1.96/2.15 The command was "./otter". The process ID is 5488.
% 1.96/2.15
% 1.96/2.15 set(prolog_style_variables).
% 1.96/2.15 set(auto).
% 1.96/2.15 dependent: set(auto1).
% 1.96/2.15 dependent: set(process_input).
% 1.96/2.15 dependent: clear(print_kept).
% 1.96/2.15 dependent: clear(print_new_demod).
% 1.96/2.15 dependent: clear(print_back_demod).
% 1.96/2.15 dependent: clear(print_back_sub).
% 1.96/2.15 dependent: set(control_memory).
% 1.96/2.15 dependent: assign(max_mem, 12000).
% 1.96/2.15 dependent: assign(pick_given_ratio, 4).
% 1.96/2.15 dependent: assign(stats_level, 1).
% 1.96/2.15 dependent: assign(max_seconds, 10800).
% 1.96/2.15 clear(print_given).
% 1.96/2.15
% 1.96/2.15 list(usable).
% 1.96/2.15 0 [] A=A.
% 1.96/2.15 0 [] aux(Z,btrue)=bfalse.
% 1.96/2.15 0 [] aux(Z,bfalse)=btrue.
% 1.96/2.15 0 [] h(nil)=nil.
% 1.96/2.15 0 [] h(cons(Y,Xs))=Xs.
% 1.96/2.15 0 [] g(btrue)=bfalse.
% 1.96/2.15 0 [] g(bfalse)=btrue.
% 1.96/2.15 0 [] f(nil)=btrue.
% 1.96/2.15 0 [] f(cons(Y,Z))=aux(Z,f(Z)).
% 1.96/2.15 0 [] prop1(X)=e_q(f(X),bfalse).
% 1.96/2.15 0 [] e_q(bfalse,btrue)=bfalse.
% 1.96/2.15 0 [] e_q(btrue,bfalse)=bfalse.
% 1.96/2.15 0 [] e_q(X,X)=btrue.
% 1.96/2.15 0 [] e_q(prop1(X),bfalse)!=btrue.
% 1.96/2.15 end_of_list.
% 1.96/2.15
% 1.96/2.15 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.96/2.15
% 1.96/2.15 All clauses are units, and equality is present; the
% 1.96/2.15 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.96/2.15
% 1.96/2.15 dependent: set(knuth_bendix).
% 1.96/2.15 dependent: set(anl_eq).
% 1.96/2.15 dependent: set(para_from).
% 1.96/2.15 dependent: set(para_into).
% 1.96/2.15 dependent: clear(para_from_right).
% 1.96/2.15 dependent: clear(para_into_right).
% 1.96/2.15 dependent: set(para_from_vars).
% 1.96/2.15 dependent: set(eq_units_both_ways).
% 1.96/2.15 dependent: set(dynamic_demod_all).
% 1.96/2.15 dependent: set(dynamic_demod).
% 1.96/2.15 dependent: set(order_eq).
% 1.96/2.15 dependent: set(back_demod).
% 1.96/2.15 dependent: set(lrpo).
% 1.96/2.15
% 1.96/2.15 ------------> process usable:
% 1.96/2.15 ** KEPT (pick-wt=6): 1 [] e_q(prop1(A),bfalse)!=btrue.
% 1.96/2.15
% 1.96/2.15 ------------> process sos:
% 1.96/2.15 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.96/2.15 ** KEPT (pick-wt=5): 3 [] aux(A,btrue)=bfalse.
% 1.96/2.15 ---> New Demodulator: 4 [new_demod,3] aux(A,btrue)=bfalse.
% 1.96/2.15 ** KEPT (pick-wt=5): 5 [] aux(A,bfalse)=btrue.
% 1.96/2.15 ---> New Demodulator: 6 [new_demod,5] aux(A,bfalse)=btrue.
% 1.96/2.15 ** KEPT (pick-wt=4): 7 [] h(nil)=nil.
% 1.96/2.15 ---> New Demodulator: 8 [new_demod,7] h(nil)=nil.
% 1.96/2.15 ** KEPT (pick-wt=6): 9 [] h(cons(A,B))=B.
% 1.96/2.15 ---> New Demodulator: 10 [new_demod,9] h(cons(A,B))=B.
% 1.96/2.15 ** KEPT (pick-wt=4): 11 [] g(btrue)=bfalse.
% 1.96/2.15 ---> New Demodulator: 12 [new_demod,11] g(btrue)=bfalse.
% 1.96/2.15 ** KEPT (pick-wt=4): 13 [] g(bfalse)=btrue.
% 1.96/2.15 ---> New Demodulator: 14 [new_demod,13] g(bfalse)=btrue.
% 1.96/2.15 ** KEPT (pick-wt=4): 15 [] f(nil)=btrue.
% 1.96/2.15 ---> New Demodulator: 16 [new_demod,15] f(nil)=btrue.
% 1.96/2.15 ** KEPT (pick-wt=9): 17 [] f(cons(A,B))=aux(B,f(B)).
% 1.96/2.15 ---> New Demodulator: 18 [new_demod,17] f(cons(A,B))=aux(B,f(B)).
% 1.96/2.15 ** KEPT (pick-wt=7): 19 [] prop1(A)=e_q(f(A),bfalse).
% 1.96/2.15 ---> New Demodulator: 20 [new_demod,19] prop1(A)=e_q(f(A),bfalse).
% 1.96/2.15 ** KEPT (pick-wt=5): 21 [] e_q(bfalse,btrue)=bfalse.
% 1.96/2.15 ---> New Demodulator: 22 [new_demod,21] e_q(bfalse,btrue)=bfalse.
% 1.96/2.15 ** KEPT (pick-wt=5): 23 [] e_q(btrue,bfalse)=bfalse.
% 1.96/2.15 ---> New Demodulator: 24 [new_demod,23] e_q(btrue,bfalse)=bfalse.
% 1.96/2.15 ** KEPT (pick-wt=5): 25 [] e_q(A,A)=btrue.
% 1.96/2.15 ---> New Demodulator: 26 [new_demod,25] e_q(A,A)=btrue.
% 1.96/2.15 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.96/2.15 >>>> Starting back demodulation with 4.
% 1.96/2.15 >>>> Starting back demodulation with 6.
% 1.96/2.15 >>>> Starting back demodulation with 8.
% 1.96/2.15 >>>> Starting back demodulation with 10.
% 1.96/2.15 >>>> Starting back demodulation with 12.
% 1.96/2.15 >>>> Starting back demodulation with 14.
% 1.96/2.15 >>>> Starting back demodulation with 16.
% 1.96/2.15 >>>> Starting back demodulation with 18.
% 1.96/2.15 >>>> Starting back demodulation with 20.
% 1.96/2.15 >> back demodulating 1 with 20.
% 1.96/2.15 >>>> Starting back demodulation with 22.
% 1.96/2.15 >>>> Starting back demodulation with 24.
% 1.96/2.15 >>>> Starting back demodulation with 26.
% 1.96/2.15
% 1.96/2.15 ======= end of input processing =======
% 1.96/2.15
% 1.96/2.15 =========== start of search ===========
% 1.96/2.15
% 1.96/2.15 -------- PROOF --------
% 1.96/2.15
% 1.96/2.15 ----> UNIT CONFLICT at 0.00 sec ----> 29 [binary,28.1,2.1] $F.
% 1.96/2.15
% 1.96/2.15 Length of proof is 2. Level of proof is 2.
% 1.96/2.15
% 1.96/2.15 ---------------- PROOF ----------------
% 1.96/2.15 % SZS status Unsatisfiable
% 1.96/2.15 % SZS output start Refutation
% See solution above
% 1.96/2.15 ------------ end of proof -------------
% 1.96/2.15
% 1.96/2.15
% 1.96/2.15 Search stopped by max_proofs option.
% 1.96/2.15
% 1.96/2.15
% 1.96/2.15 Search stopped by max_proofs option.
% 1.96/2.15
% 1.96/2.15 ============ end of search ============
% 1.96/2.15
% 1.96/2.15 -------------- statistics -------------
% 1.96/2.15 clauses given 13
% 1.96/2.15 clauses generated 23
% 1.96/2.15 clauses kept 16
% 1.96/2.15 clauses forward subsumed 23
% 1.96/2.15 clauses back subsumed 0
% 1.96/2.15 Kbytes malloced 976
% 1.96/2.15
% 1.96/2.15 ----------- times (seconds) -----------
% 1.96/2.15 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.96/2.15 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.96/2.15 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.96/2.15
% 1.96/2.15 That finishes the proof of the theorem.
% 1.96/2.15
% 1.96/2.15 Process 5488 finished Tue May 5 13:08:55 2026
% 1.96/2.15 Otter interrupted
% 1.96/2.15 PROOF FOUND
%------------------------------------------------------------------------------