TSTP Solution File: SET847-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET847-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 21.51s 21.68s
% Output : Refutation 21.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of clauses : 20 ( 9 unt; 4 nHn; 9 RR)
% Number of literals : 34 ( 7 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 48 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_in(A,B,C)
| c_in(A,D,C)
| c_in(A,c_minus(B,D,tc_set(C)),C) ),
file('SET847-2.p',unknown),
[] ).
cnf(2,axiom,
~ c_in(A,c_emptyset,B),
file('SET847-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_lesse_quals(A,B,tc_set(C))
| ~ c_lesse_quals(B,A,tc_set(C))
| B = A ),
file('SET847-2.p',unknown),
[] ).
cnf(4,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('SET847-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
| c_in(A,c_Zorn_Ochain(B,C),tc_set(tc_set(C))) ),
file('SET847-2.p',unknown),
[] ).
cnf(6,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('SET847-2.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)))
| 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)],[6])]),
[iquote('copy,6,flip.2')] ).
cnf(8,axiom,
( ~ c_in(A,c_minus(c_Zorn_Ochain(B,C),c_Zorn_Omaxchain(B,C),tc_set(tc_set(tc_set(C)))),tc_set(tc_set(C)))
| c_Zorn_Osucc(B,A,C) != A ),
file('SET847-2.p',unknown),
[] ).
cnf(9,axiom,
~ c_in(A,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('SET847-2.p',unknown),
[] ).
cnf(12,axiom,
c_lesse_quals(c_emptyset,A,tc_set(B)),
file('SET847-2.p',unknown),
[] ).
cnf(13,axiom,
( c_in(c_Main_OsubsetI__1(A,B,C),A,C)
| c_lesse_quals(A,B,tc_set(C)) ),
file('SET847-2.p',unknown),
[] ).
cnf(14,axiom,
c_lesse_quals(A,A,tc_set(B)),
file('SET847-2.p',unknown),
[] ).
cnf(18,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)],[14,4]),
[iquote('hyper,14,4')] ).
cnf(35,plain,
( c_in(c_Main_OsubsetI__1(A,c_emptyset,B),A,B)
| A = c_emptyset ),
inference(hyper,[status(thm)],[13,3,12]),
[iquote('hyper,13,3,12')] ).
cnf(55,plain,
( ~ c_in(A,c_minus(c_Zorn_Ochain(B,C),c_emptyset,tc_set(tc_set(tc_set(C)))),tc_set(tc_set(C)))
| c_Zorn_Osucc(B,A,C) != A
| c_in(c_Main_OsubsetI__1(c_Zorn_Omaxchain(B,C),c_emptyset,D),c_Zorn_Omaxchain(B,C),D) ),
inference(para_from,[status(thm),theory(equality)],[35,8]),
[iquote('para_from,35.2.1,8.1.2.2')] ).
cnf(161,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)],[18,7]),
[iquote('hyper,18,7')] ).
cnf(163,plain,
c_in(c_Union(c_Zorn_OTFin(A,B),tc_set(B)),c_Zorn_Ochain(A,B),tc_set(tc_set(B))),
inference(hyper,[status(thm)],[18,5]),
[iquote('hyper,18,5')] ).
cnf(200,plain,
( c_in(c_Union(c_Zorn_OTFin(A,B),tc_set(B)),C,tc_set(tc_set(B)))
| c_in(c_Union(c_Zorn_OTFin(A,B),tc_set(B)),c_minus(c_Zorn_Ochain(A,B),C,tc_set(tc_set(tc_set(B)))),tc_set(tc_set(B))) ),
inference(hyper,[status(thm)],[163,1]),
[iquote('hyper,163,1')] ).
cnf(3440,plain,
c_in(c_Main_OsubsetI__1(c_Zorn_Omaxchain(A,B),c_emptyset,C),c_Zorn_Omaxchain(A,B),C),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[200,55,161]),2]),
[iquote('hyper,200,55,161,unit_del,2')] ).
cnf(3441,plain,
$false,
inference(binary,[status(thm)],[3440,9]),
[iquote('binary,3440.1,9.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET847-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.14/0.33 % Computer : n009.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Wed Jul 27 10:25:21 EDT 2022
% 0.14/0.33 % CPUTime :
% 21.51/21.68 ----- Otter 3.3f, August 2004 -----
% 21.51/21.68 The process was started by sandbox2 on n009.cluster.edu,
% 21.51/21.68 Wed Jul 27 10:25:21 2022
% 21.51/21.68 The command was "./otter". The process ID is 12738.
% 21.51/21.68
% 21.51/21.68 set(prolog_style_variables).
% 21.51/21.68 set(auto).
% 21.51/21.68 dependent: set(auto1).
% 21.51/21.68 dependent: set(process_input).
% 21.51/21.68 dependent: clear(print_kept).
% 21.51/21.68 dependent: clear(print_new_demod).
% 21.51/21.68 dependent: clear(print_back_demod).
% 21.51/21.68 dependent: clear(print_back_sub).
% 21.51/21.68 dependent: set(control_memory).
% 21.51/21.68 dependent: assign(max_mem, 12000).
% 21.51/21.68 dependent: assign(pick_given_ratio, 4).
% 21.51/21.68 dependent: assign(stats_level, 1).
% 21.51/21.68 dependent: assign(max_seconds, 10800).
% 21.51/21.68 clear(print_given).
% 21.51/21.68
% 21.51/21.68 list(usable).
% 21.51/21.68 0 [] A=A.
% 21.51/21.68 0 [] -c_in(V_c,V_A,T_a)|c_in(V_c,V_B,T_a)|c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a).
% 21.51/21.68 0 [] -c_in(V_a,c_emptyset,T_a).
% 21.51/21.68 0 [] c_lesse_quals(c_emptyset,V_A,tc_set(T_a)).
% 21.51/21.68 0 [] c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)|c_lesse_quals(V_A,V_B,tc_set(T_a)).
% 21.51/21.68 0 [] -c_lesse_quals(V_B,V_A,tc_set(T_a))| -c_lesse_quals(V_A,V_B,tc_set(T_a))|V_A=V_B.
% 21.51/21.68 0 [] c_lesse_quals(V_A,V_A,tc_set(T_a)).
% 21.51/21.68 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))).
% 21.51/21.68 0 [] -c_in(V_c,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))|c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a))).
% 21.51/21.68 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).
% 21.51/21.68 0 [] -c_in(V_c,c_minus(c_Zorn_Ochain(V_S,T_a),c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(tc_set(T_a)))),tc_set(tc_set(T_a)))|c_Zorn_Osucc(V_S,V_c,T_a)!=V_c.
% 21.51/21.68 0 [] -c_in(V_U,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))).
% 21.51/21.68 end_of_list.
% 21.51/21.68
% 21.51/21.68 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 21.51/21.68
% 21.51/21.68 This ia a non-Horn set with equality. The strategy will be
% 21.51/21.68 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 21.51/21.68 deletion, with positive clauses in sos and nonpositive
% 21.51/21.68 clauses in usable.
% 21.51/21.68
% 21.51/21.68 dependent: set(knuth_bendix).
% 21.51/21.68 dependent: set(anl_eq).
% 21.51/21.68 dependent: set(para_from).
% 21.51/21.68 dependent: set(para_into).
% 21.51/21.68 dependent: clear(para_from_right).
% 21.51/21.68 dependent: clear(para_into_right).
% 21.51/21.68 dependent: set(para_from_vars).
% 21.51/21.68 dependent: set(eq_units_both_ways).
% 21.51/21.68 dependent: set(dynamic_demod_all).
% 21.51/21.68 dependent: set(dynamic_demod).
% 21.51/21.68 dependent: set(order_eq).
% 21.51/21.68 dependent: set(back_demod).
% 21.51/21.68 dependent: set(lrpo).
% 21.51/21.68 dependent: set(hyper_res).
% 21.51/21.68 dependent: set(unit_deletion).
% 21.51/21.68 dependent: set(factor).
% 21.51/21.68
% 21.51/21.68 ------------> process usable:
% 21.51/21.68 ** KEPT (pick-wt=16): 1 [] -c_in(A,B,C)|c_in(A,D,C)|c_in(A,c_minus(B,D,tc_set(C)),C).
% 21.51/21.68 ** KEPT (pick-wt=4): 2 [] -c_in(A,c_emptyset,B).
% 21.51/21.68 ** KEPT (pick-wt=13): 3 [] -c_lesse_quals(A,B,tc_set(C))| -c_lesse_quals(B,A,tc_set(C))|B=A.
% 21.51/21.68 ** KEPT (pick-wt=20): 4 [] -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))).
% 21.51/21.68 ** KEPT (pick-wt=16): 5 [] -c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))|c_in(A,c_Zorn_Ochain(B,C),tc_set(tc_set(C))).
% 21.51/21.68 ** KEPT (pick-wt=29): 7 [copy,6,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)).
% 21.51/21.68 ** KEPT (pick-wt=22): 8 [] -c_in(A,c_minus(c_Zorn_Ochain(B,C),c_Zorn_Omaxchain(B,C),tc_set(tc_set(tc_set(C)))),tc_set(tc_set(C)))|c_Zorn_Osucc(B,A,C)!=A.
% 21.51/21.68 ** KEPT (pick-wt=8): 9 [] -c_in(A,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))).
% 21.51/21.68
% 21.51/21.68 ------------> process sos:
% 21.51/21.68 ** KEPT (pick-wt=3): 11 [] A=A.
% 21.51/21.68 ** KEPT (pick-wt=5): 12 [] c_lesse_quals(c_emptyset,A,tc_set(B)).
% 21.51/21.68 ** KEPT (pick-wt=12): 13 [] c_in(c_Main_OsubsetI__1(A,B,C),A,C)|c_lesse_quals(A,B,tc_set(C)).
% 21.51/21.68 ** KEPT (pick-wt=5): 14 [] c_lesse_quals(A,A,tc_set(B)).
% 21.51/21.68 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] A=A.
% 21.51/21.68 11 back subsumes 10.
% 21.51/21.68
% 21.51/21.68 ======= end of input processing =======
% 21.51/21.68
% 21.51/21.68 =========== start of search ===========
% 21.51/21.68
% 21.51/21.68
% 21.51/21.68 Resetting weight limit to 18.
% 21.51/21.68
% 21.51/21.68
% 21.51/21.68 Resetting weight limit to 18.
% 21.51/21.68
% 21.51/21.68 sos_size=3051
% 21.51/21.68
% 21.51/21.68 -- HEY sandbox2, WE HAVE A PROOF!! --
% 21.51/21.68
% 21.51/21.68 ----> UNIT CONFLICT at 19.77 sec ----> 3441 [binary,3440.1,9.1] $F.
% 21.51/21.68
% 21.51/21.68 Length of proof is 8. Level of proof is 4.
% 21.51/21.68
% 21.51/21.68 ---------------- PROOF ----------------
% 21.51/21.68 % SZS status Unsatisfiable
% 21.51/21.68 % SZS output start Refutation
% See solution above
% 21.51/21.68 ------------ end of proof -------------
% 21.51/21.68
% 21.51/21.68
% 21.51/21.68 Search stopped by max_proofs option.
% 21.51/21.68
% 21.51/21.68
% 21.51/21.68 Search stopped by max_proofs option.
% 21.51/21.68
% 21.51/21.68 ============ end of search ============
% 21.51/21.68
% 21.51/21.68 -------------- statistics -------------
% 21.51/21.68 clauses given 586
% 21.51/21.68 clauses generated 446359
% 21.51/21.68 clauses kept 3438
% 21.51/21.68 clauses forward subsumed 20089
% 21.51/21.68 clauses back subsumed 148
% 21.51/21.68 Kbytes malloced 4882
% 21.51/21.68
% 21.51/21.68 ----------- times (seconds) -----------
% 21.51/21.68 user CPU time 19.77 (0 hr, 0 min, 19 sec)
% 21.51/21.68 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 21.51/21.68 wall-clock time 21 (0 hr, 0 min, 21 sec)
% 21.51/21.68
% 21.51/21.68 That finishes the proof of the theorem.
% 21.51/21.68
% 21.51/21.68 Process 12738 finished Wed Jul 27 10:25:42 2022
% 21.51/21.68 Otter interrupted
% 21.51/21.68 PROOF FOUND
%------------------------------------------------------------------------------