TSTP Solution File: SET865-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET865-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 13:14:26 EDT 2022
% Result : Unsatisfiable 1.82s 2.04s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 15 ( 8 unt; 0 nHn; 12 RR)
% Number of literals : 25 ( 4 equ; 12 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( c_in(c_Union(A,t_a),v_S,tc_set(t_a))
| ~ c_in(A,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
file('SET865-2.p',unknown),
[] ).
cnf(2,axiom,
( c_in(v_x(A),v_S,tc_set(t_a))
| ~ c_in(A,v_S,tc_set(t_a)) ),
file('SET865-2.p',unknown),
[] ).
cnf(3,axiom,
( c_lesse_quals(A,v_x(A),tc_set(t_a))
| ~ c_in(A,v_S,tc_set(t_a)) ),
file('SET865-2.p',unknown),
[] ).
cnf(4,axiom,
( A != v_x(A)
| ~ c_in(A,v_S,tc_set(t_a)) ),
file('SET865-2.p',unknown),
[] ).
cnf(5,plain,
( v_x(A) != A
| ~ c_in(A,v_S,tc_set(t_a)) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.1')] ).
cnf(6,axiom,
( ~ c_in(A,B,C)
| ~ c_lesse_quals(B,D,tc_set(C))
| c_in(A,D,C) ),
file('SET865-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ c_in(A,B,tc_set(C))
| ~ c_in(D,c_Zorn_Omaxchain(B,C),tc_set(tc_set(C)))
| ~ c_lesse_quals(c_Union(D,C),A,tc_set(C))
| c_Union(D,C) = A ),
file('SET865-2.p',unknown),
[] ).
cnf(9,axiom,
c_in(c_Zorn_OHausdorff__1(A,B),c_Zorn_Omaxchain(A,B),tc_set(tc_set(B))),
file('SET865-2.p',unknown),
[] ).
cnf(10,axiom,
c_lesse_quals(c_Zorn_Omaxchain(A,B),c_Zorn_Ochain(A,B),tc_set(tc_set(tc_set(B)))),
file('SET865-2.p',unknown),
[] ).
cnf(11,plain,
c_in(c_Zorn_OHausdorff__1(A,B),c_Zorn_Ochain(A,B),tc_set(tc_set(B))),
inference(hyper,[status(thm)],[10,6,9]),
[iquote('hyper,10,6,9')] ).
cnf(12,plain,
c_in(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_S,tc_set(t_a)),
inference(hyper,[status(thm)],[11,1]),
[iquote('hyper,11,1')] ).
cnf(13,plain,
c_lesse_quals(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),tc_set(t_a)),
inference(hyper,[status(thm)],[12,3]),
[iquote('hyper,12,3')] ).
cnf(14,plain,
c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),v_S,tc_set(t_a)),
inference(hyper,[status(thm)],[12,2]),
[iquote('hyper,12,2')] ).
cnf(18,plain,
v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)) = c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[14,7,9,13])]),
[iquote('hyper,14,7,9,13,flip.1')] ).
cnf(22,plain,
$false,
inference(hyper,[status(thm)],[18,5,12]),
[iquote('hyper,18,5,12')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET865-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n011.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 10:22:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.82/2.04 ----- Otter 3.3f, August 2004 -----
% 1.82/2.04 The process was started by sandbox on n011.cluster.edu,
% 1.82/2.04 Wed Jul 27 10:22:25 2022
% 1.82/2.04 The command was "./otter". The process ID is 14541.
% 1.82/2.04
% 1.82/2.04 set(prolog_style_variables).
% 1.82/2.04 set(auto).
% 1.82/2.04 dependent: set(auto1).
% 1.82/2.04 dependent: set(process_input).
% 1.82/2.04 dependent: clear(print_kept).
% 1.82/2.04 dependent: clear(print_new_demod).
% 1.82/2.04 dependent: clear(print_back_demod).
% 1.82/2.04 dependent: clear(print_back_sub).
% 1.82/2.04 dependent: set(control_memory).
% 1.82/2.04 dependent: assign(max_mem, 12000).
% 1.82/2.04 dependent: assign(pick_given_ratio, 4).
% 1.82/2.04 dependent: assign(stats_level, 1).
% 1.82/2.04 dependent: assign(max_seconds, 10800).
% 1.82/2.04 clear(print_given).
% 1.82/2.04
% 1.82/2.04 list(usable).
% 1.82/2.04 0 [] A=A.
% 1.82/2.04 0 [] c_in(c_Union(V_U,t_a),v_S,tc_set(t_a))| -c_in(V_U,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))).
% 1.82/2.04 0 [] c_in(v_x(V_U),v_S,tc_set(t_a))| -c_in(V_U,v_S,tc_set(t_a)).
% 1.82/2.04 0 [] c_lesse_quals(V_U,v_x(V_U),tc_set(t_a))| -c_in(V_U,v_S,tc_set(t_a)).
% 1.82/2.04 0 [] V_U!=v_x(V_U)| -c_in(V_U,v_S,tc_set(t_a)).
% 1.82/2.04 0 [] -c_in(V_c,V_A,T_a)| -c_lesse_quals(V_A,V_B,tc_set(T_a))|c_in(V_c,V_B,T_a).
% 1.82/2.04 0 [] c_in(c_Zorn_OHausdorff__1(V_S,T_a),c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a))).
% 1.82/2.04 0 [] -c_in(V_u,V_S,tc_set(T_a))| -c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))| -c_lesse_quals(c_Union(V_c,T_a),V_u,tc_set(T_a))|c_Union(V_c,T_a)=V_u.
% 1.82/2.04 0 [] c_lesse_quals(c_Zorn_Omaxchain(V_S,T_a),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(tc_set(T_a)))).
% 1.82/2.04 end_of_list.
% 1.82/2.04
% 1.82/2.04 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.82/2.04
% 1.82/2.04 This is a Horn set with equality. The strategy will be
% 1.82/2.04 Knuth-Bendix and hyper_res, with positive clauses in
% 1.82/2.04 sos and nonpositive clauses in usable.
% 1.82/2.04
% 1.82/2.04 dependent: set(knuth_bendix).
% 1.82/2.04 dependent: set(anl_eq).
% 1.82/2.04 dependent: set(para_from).
% 1.82/2.04 dependent: set(para_into).
% 1.82/2.04 dependent: clear(para_from_right).
% 1.82/2.04 dependent: clear(para_into_right).
% 1.82/2.04 dependent: set(para_from_vars).
% 1.82/2.04 dependent: set(eq_units_both_ways).
% 1.82/2.04 dependent: set(dynamic_demod_all).
% 1.82/2.04 dependent: set(dynamic_demod).
% 1.82/2.04 dependent: set(order_eq).
% 1.82/2.04 dependent: set(back_demod).
% 1.82/2.04 dependent: set(lrpo).
% 1.82/2.04 dependent: set(hyper_res).
% 1.82/2.04 dependent: clear(order_hyper).
% 1.82/2.04
% 1.82/2.04 ------------> process usable:
% 1.82/2.04 ** KEPT (pick-wt=15): 1 [] c_in(c_Union(A,t_a),v_S,tc_set(t_a))| -c_in(A,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))).
% 1.82/2.04 ** KEPT (pick-wt=11): 2 [] c_in(v_x(A),v_S,tc_set(t_a))| -c_in(A,v_S,tc_set(t_a)).
% 1.82/2.04 ** KEPT (pick-wt=11): 3 [] c_lesse_quals(A,v_x(A),tc_set(t_a))| -c_in(A,v_S,tc_set(t_a)).
% 1.82/2.04 ** KEPT (pick-wt=9): 5 [copy,4,flip.1] v_x(A)!=A| -c_in(A,v_S,tc_set(t_a)).
% 1.82/2.04 ** KEPT (pick-wt=13): 6 [] -c_in(A,B,C)| -c_lesse_quals(B,D,tc_set(C))|c_in(A,D,C).
% 1.82/2.04 ** KEPT (pick-wt=25): 7 [] -c_in(A,B,tc_set(C))| -c_in(D,c_Zorn_Omaxchain(B,C),tc_set(tc_set(C)))| -c_lesse_quals(c_Union(D,C),A,tc_set(C))|c_Union(D,C)=A.
% 1.82/2.04
% 1.82/2.04 ------------> process sos:
% 1.82/2.04 ** KEPT (pick-wt=3): 8 [] A=A.
% 1.82/2.04 ** KEPT (pick-wt=10): 9 [] c_in(c_Zorn_OHausdorff__1(A,B),c_Zorn_Omaxchain(A,B),tc_set(tc_set(B))).
% 1.82/2.04 ** KEPT (pick-wt=11): 10 [] c_lesse_quals(c_Zorn_Omaxchain(A,B),c_Zorn_Ochain(A,B),tc_set(tc_set(tc_set(B)))).
% 1.82/2.04 Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] A=A.
% 1.82/2.04
% 1.82/2.04 ======= end of input processing =======
% 1.82/2.04
% 1.82/2.04 =========== start of search ===========
% 1.82/2.04
% 1.82/2.04 -------- PROOF --------
% 1.82/2.04
% 1.82/2.04 -----> EMPTY CLAUSE at 0.00 sec ----> 22 [hyper,18,5,12] $F.
% 1.82/2.04
% 1.82/2.04 Length of proof is 6. Level of proof is 4.
% 1.82/2.04
% 1.82/2.04 ---------------- PROOF ----------------
% 1.82/2.04 % SZS status Unsatisfiable
% 1.82/2.04 % SZS output start Refutation
% See solution above
% 1.82/2.04 ------------ end of proof -------------
% 1.82/2.04
% 1.82/2.04
% 1.82/2.04 Search stopped by max_proofs option.
% 1.82/2.04
% 1.82/2.04
% 1.82/2.04 Search stopped by max_proofs option.
% 1.82/2.04
% 1.82/2.04 ============ end of search ============
% 1.82/2.04
% 1.82/2.04 -------------- statistics -------------
% 1.82/2.04 clauses given 8
% 1.82/2.04 clauses generated 11
% 1.82/2.04 clauses kept 19
% 1.82/2.04 clauses forward subsumed 4
% 1.82/2.04 clauses back subsumed 0
% 1.82/2.04 Kbytes malloced 976
% 1.82/2.04
% 1.82/2.04 ----------- times (seconds) -----------
% 1.82/2.04 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.82/2.04 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.82/2.04 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.82/2.04
% 1.82/2.04 That finishes the proof of the theorem.
% 1.82/2.04
% 1.82/2.04 Process 14541 finished Wed Jul 27 10:22:27 2022
% 1.82/2.04 Otter interrupted
% 1.82/2.04 PROOF FOUND
%------------------------------------------------------------------------------