TSTP Solution File: SET849-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET849-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 : Wed Jul 27 13:14:23 EDT 2022
% Result : Unsatisfiable 1.89s 2.09s
% Output : Refutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 8 ( 5 unt; 0 nHn; 5 RR)
% Number of literals : 11 ( 4 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 13 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_lesse_quals(A,c_Zorn_OTFin(B,C),tc_set(tc_set(tc_set(C))))
| c_in(c_Union(A,tc_set(C)),c_Zorn_OTFin(B,C),tc_set(tc_set(C))) ),
file('SET849-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(c_Union(c_Zorn_OTFin(A,B),tc_set(B)),c_Zorn_OTFin(A,B),tc_set(tc_set(B)))
| c_Union(c_Zorn_OTFin(A,B),tc_set(B)) = c_Zorn_Osucc(A,c_Union(c_Zorn_OTFin(A,B),tc_set(B)),B) ),
file('SET849-2.p',unknown),
[] ).
cnf(3,plain,
( ~ c_in(c_Union(c_Zorn_OTFin(A,B),tc_set(B)),c_Zorn_OTFin(A,B),tc_set(tc_set(B)))
| c_Zorn_Osucc(A,c_Union(c_Zorn_OTFin(A,B),tc_set(B)),B) = c_Union(c_Zorn_OTFin(A,B),tc_set(B)) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[2])]),
[iquote('copy,2,flip.2')] ).
cnf(4,axiom,
c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a) != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
file('SET849-2.p',unknown),
[] ).
cnf(6,axiom,
c_lesse_quals(A,A,tc_set(B)),
file('SET849-2.p',unknown),
[] ).
cnf(7,plain,
c_in(c_Union(c_Zorn_OTFin(A,B),tc_set(B)),c_Zorn_OTFin(A,B),tc_set(tc_set(B))),
inference(hyper,[status(thm)],[6,1]),
[iquote('hyper,6,1')] ).
cnf(8,plain,
c_Zorn_Osucc(A,c_Union(c_Zorn_OTFin(A,B),tc_set(B)),B) = c_Union(c_Zorn_OTFin(A,B),tc_set(B)),
inference(hyper,[status(thm)],[7,3]),
[iquote('hyper,7,3')] ).
cnf(10,plain,
$false,
inference(binary,[status(thm)],[8,4]),
[iquote('binary,8.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET849-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 11:02:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.89/2.09 ----- Otter 3.3f, August 2004 -----
% 1.89/2.09 The process was started by sandbox on n023.cluster.edu,
% 1.89/2.09 Wed Jul 27 11:02:33 2022
% 1.89/2.09 The command was "./otter". The process ID is 20880.
% 1.89/2.09
% 1.89/2.09 set(prolog_style_variables).
% 1.89/2.09 set(auto).
% 1.89/2.09 dependent: set(auto1).
% 1.89/2.09 dependent: set(process_input).
% 1.89/2.09 dependent: clear(print_kept).
% 1.89/2.09 dependent: clear(print_new_demod).
% 1.89/2.09 dependent: clear(print_back_demod).
% 1.89/2.09 dependent: clear(print_back_sub).
% 1.89/2.09 dependent: set(control_memory).
% 1.89/2.09 dependent: assign(max_mem, 12000).
% 1.89/2.09 dependent: assign(pick_given_ratio, 4).
% 1.89/2.09 dependent: assign(stats_level, 1).
% 1.89/2.09 dependent: assign(max_seconds, 10800).
% 1.89/2.09 clear(print_given).
% 1.89/2.09
% 1.89/2.09 list(usable).
% 1.89/2.09 0 [] A=A.
% 1.89/2.09 0 [] c_lesse_quals(V_A,V_A,tc_set(T_a)).
% 1.89/2.09 0 [] -c_lesse_quals(V_Y,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(tc_set(T_a))))|c_in(c_Union(V_Y,tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))).
% 1.89/2.09 0 [] -c_in(c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))|c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a))=c_Zorn_Osucc(V_S,c_Union(c_Zorn_OTFin(V_S,T_a),tc_set(T_a)),T_a).
% 1.89/2.09 0 [] c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a)!=c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)).
% 1.89/2.09 end_of_list.
% 1.89/2.09
% 1.89/2.09 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.89/2.09
% 1.89/2.09 This is a Horn set with equality. The strategy will be
% 1.89/2.09 Knuth-Bendix and hyper_res, with positive clauses in
% 1.89/2.09 sos and nonpositive clauses in usable.
% 1.89/2.09
% 1.89/2.09 dependent: set(knuth_bendix).
% 1.89/2.09 dependent: set(anl_eq).
% 1.89/2.09 dependent: set(para_from).
% 1.89/2.09 dependent: set(para_into).
% 1.89/2.09 dependent: clear(para_from_right).
% 1.89/2.09 dependent: clear(para_into_right).
% 1.89/2.09 dependent: set(para_from_vars).
% 1.89/2.09 dependent: set(eq_units_both_ways).
% 1.89/2.09 dependent: set(dynamic_demod_all).
% 1.89/2.09 dependent: set(dynamic_demod).
% 1.89/2.09 dependent: set(order_eq).
% 1.89/2.09 dependent: set(back_demod).
% 1.89/2.09 dependent: set(lrpo).
% 1.89/2.09 dependent: set(hyper_res).
% 1.89/2.09 dependent: clear(order_hyper).
% 1.89/2.09
% 1.89/2.09 ------------> process usable:
% 1.89/2.09 ** KEPT (pick-wt=20): 1 [] -c_lesse_quals(A,c_Zorn_OTFin(B,C),tc_set(tc_set(tc_set(C))))|c_in(c_Union(A,tc_set(C)),c_Zorn_OTFin(B,C),tc_set(tc_set(C))).
% 1.89/2.09 ** KEPT (pick-wt=29): 3 [copy,2,flip.2] -c_in(c_Union(c_Zorn_OTFin(A,B),tc_set(B)),c_Zorn_OTFin(A,B),tc_set(tc_set(B)))|c_Zorn_Osucc(A,c_Union(c_Zorn_OTFin(A,B),tc_set(B)),B)=c_Union(c_Zorn_OTFin(A,B),tc_set(B)).
% 1.89/2.09 ** KEPT (pick-wt=16): 4 [] c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a)!=c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)).
% 1.89/2.09
% 1.89/2.09 ------------> process sos:
% 1.89/2.09 ** KEPT (pick-wt=3): 5 [] A=A.
% 1.89/2.09 ** KEPT (pick-wt=5): 6 [] c_lesse_quals(A,A,tc_set(B)).
% 1.89/2.09 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 1.89/2.09
% 1.89/2.09 ======= end of input processing =======
% 1.89/2.09
% 1.89/2.09 =========== start of search ===========
% 1.89/2.09
% 1.89/2.09 -------- PROOF --------
% 1.89/2.09
% 1.89/2.09 ----> UNIT CONFLICT at 0.00 sec ----> 10 [binary,8.1,4.1] $F.
% 1.89/2.09
% 1.89/2.09 Length of proof is 3. Level of proof is 2.
% 1.89/2.09
% 1.89/2.09 ---------------- PROOF ----------------
% 1.89/2.09 % SZS status Unsatisfiable
% 1.89/2.09 % SZS output start Refutation
% See solution above
% 1.89/2.09 ------------ end of proof -------------
% 1.89/2.09
% 1.89/2.09
% 1.89/2.09 Search stopped by max_proofs option.
% 1.89/2.09
% 1.89/2.09
% 1.89/2.09 Search stopped by max_proofs option.
% 1.89/2.09
% 1.89/2.09 ============ end of search ============
% 1.89/2.09
% 1.89/2.09 -------------- statistics -------------
% 1.89/2.09 clauses given 3
% 1.89/2.09 clauses generated 2
% 1.89/2.09 clauses kept 7
% 1.89/2.09 clauses forward subsumed 1
% 1.89/2.09 clauses back subsumed 0
% 1.89/2.09 Kbytes malloced 976
% 1.89/2.09
% 1.89/2.09 ----------- times (seconds) -----------
% 1.89/2.09 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.89/2.09 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.89/2.09 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.89/2.09
% 1.89/2.09 That finishes the proof of the theorem.
% 1.89/2.09
% 1.89/2.09 Process 20880 finished Wed Jul 27 11:02:34 2022
% 1.89/2.09 Otter interrupted
% 1.89/2.09 PROOF FOUND
%------------------------------------------------------------------------------