TSTP Solution File: SET843-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET843-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n007.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 13:14:22 EDT 2022
% Result : Unsatisfiable 1.69s 1.90s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 25 ( 14 unt; 3 nHn; 21 RR)
% Number of literals : 41 ( 16 equ; 16 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 : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 28 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_in(A,B,tc_set(C))
| c_lesse_quals(A,c_Union(B,C),tc_set(C)) ),
file('SET843-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_lesse_quals(A,B,tc_set(C))
| ~ c_lesse_quals(B,A,tc_set(C))
| B = A ),
file('SET843-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
| c_in(c_Zorn_Osucc(B,A,C),c_Zorn_OTFin(B,C),tc_set(tc_set(C))) ),
file('SET843-2.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('SET843-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
| ~ c_in(D,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
| A != c_Zorn_Osucc(B,A,C)
| c_lesse_quals(D,A,tc_set(tc_set(C))) ),
file('SET843-2.p',unknown),
[] ).
cnf(6,plain,
( ~ c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
| ~ c_in(D,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
| c_Zorn_Osucc(B,A,C) != A
| c_lesse_quals(D,A,tc_set(tc_set(C))) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
[iquote('copy,5,flip.3')] ).
cnf(7,axiom,
( v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| v_m != c_Zorn_Osucc(v_S,v_m,t_a) ),
file('SET843-2.p',unknown),
[] ).
cnf(8,plain,
( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) != v_m
| c_Zorn_Osucc(v_S,v_m,t_a) != v_m ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])])]),
[iquote('copy,7,flip.1,flip.2')] ).
cnf(11,axiom,
A = A,
file('SET843-2.p',unknown),
[] ).
cnf(12,axiom,
c_lesse_quals(A,A,tc_set(B)),
file('SET843-2.p',unknown),
[] ).
cnf(13,axiom,
c_lesse_quals(A,c_Zorn_Osucc(B,A,C),tc_set(tc_set(C))),
file('SET843-2.p',unknown),
[] ).
cnf(14,axiom,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('SET843-2.p',unknown),
[] ).
cnf(15,axiom,
( v_m = c_Zorn_Osucc(v_S,v_m,t_a)
| v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
file('SET843-2.p',unknown),
[] ).
cnf(16,plain,
( c_Zorn_Osucc(v_S,v_m,t_a) = v_m
| c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])])]),
[iquote('copy,15,flip.1,flip.2')] ).
cnf(17,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)],[12,4]),
[iquote('hyper,12,4')] ).
cnf(19,plain,
c_in(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(hyper,[status(thm)],[14,3]),
[iquote('hyper,14,3')] ).
cnf(20,plain,
c_lesse_quals(v_m,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),
inference(hyper,[status(thm)],[14,1]),
[iquote('hyper,14,1')] ).
cnf(32,plain,
c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),tc_set(tc_set(t_a))),
inference(hyper,[status(thm)],[19,1]),
[iquote('hyper,19,1')] ).
cnf(102,plain,
( c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a)))
| c_Zorn_Osucc(v_S,v_m,t_a) = v_m ),
inference(para_into,[status(thm),theory(equality)],[32,16]),
[iquote('para_into,32.1.2,16.2.1')] ).
cnf(112,plain,
c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[102,6,14,19])]),
[iquote('hyper,102,6,14,19,factor_simp')] ).
cnf(114,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = v_m,
inference(hyper,[status(thm)],[112,2,13]),
[iquote('hyper,112,2,13')] ).
cnf(115,plain,
c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) != v_m,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[8]),114]),11]),
[iquote('back_demod,8,demod,114,unit_del,11')] ).
cnf(116,plain,
c_lesse_quals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(hyper,[status(thm)],[114,6,14,17]),
[iquote('hyper,113,6,14,17')] ).
cnf(143,plain,
c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m,
inference(hyper,[status(thm)],[116,2,20]),
[iquote('hyper,116,2,20')] ).
cnf(145,plain,
$false,
inference(binary,[status(thm)],[143,115]),
[iquote('binary,143.1,115.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET843-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n007.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 10:36:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.69/1.90 ----- Otter 3.3f, August 2004 -----
% 1.69/1.90 The process was started by sandbox on n007.cluster.edu,
% 1.69/1.90 Wed Jul 27 10:36:01 2022
% 1.69/1.90 The command was "./otter". The process ID is 32641.
% 1.69/1.90
% 1.69/1.90 set(prolog_style_variables).
% 1.69/1.90 set(auto).
% 1.69/1.90 dependent: set(auto1).
% 1.69/1.90 dependent: set(process_input).
% 1.69/1.90 dependent: clear(print_kept).
% 1.69/1.90 dependent: clear(print_new_demod).
% 1.69/1.90 dependent: clear(print_back_demod).
% 1.69/1.90 dependent: clear(print_back_sub).
% 1.69/1.90 dependent: set(control_memory).
% 1.69/1.90 dependent: assign(max_mem, 12000).
% 1.69/1.90 dependent: assign(pick_given_ratio, 4).
% 1.69/1.90 dependent: assign(stats_level, 1).
% 1.69/1.90 dependent: assign(max_seconds, 10800).
% 1.69/1.90 clear(print_given).
% 1.69/1.90
% 1.69/1.90 list(usable).
% 1.69/1.90 0 [] A=A.
% 1.69/1.90 0 [] -c_in(V_B,V_A,tc_set(T_a))|c_lesse_quals(V_B,c_Union(V_A,T_a),tc_set(T_a)).
% 1.69/1.90 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.
% 1.69/1.90 0 [] c_lesse_quals(V_A,V_A,tc_set(T_a)).
% 1.69/1.90 0 [] c_lesse_quals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))).
% 1.69/1.90 0 [] -c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))|c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))).
% 1.69/1.90 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))).
% 1.69/1.90 0 [] -c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))| -c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))|V_m!=c_Zorn_Osucc(V_S,V_m,T_a)|c_lesse_quals(V_n,V_m,tc_set(tc_set(T_a))).
% 1.69/1.90 0 [] c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))).
% 1.69/1.90 0 [] v_m!=c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))|v_m!=c_Zorn_Osucc(v_S,v_m,t_a).
% 1.69/1.90 0 [] v_m=c_Zorn_Osucc(v_S,v_m,t_a)|v_m=c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)).
% 1.69/1.90 end_of_list.
% 1.69/1.90
% 1.69/1.90 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.69/1.90
% 1.69/1.90 This ia a non-Horn set with equality. The strategy will be
% 1.69/1.90 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.69/1.90 deletion, with positive clauses in sos and nonpositive
% 1.69/1.90 clauses in usable.
% 1.69/1.90
% 1.69/1.90 dependent: set(knuth_bendix).
% 1.69/1.90 dependent: set(anl_eq).
% 1.69/1.90 dependent: set(para_from).
% 1.69/1.90 dependent: set(para_into).
% 1.69/1.90 dependent: clear(para_from_right).
% 1.69/1.90 dependent: clear(para_into_right).
% 1.69/1.90 dependent: set(para_from_vars).
% 1.69/1.90 dependent: set(eq_units_both_ways).
% 1.69/1.90 dependent: set(dynamic_demod_all).
% 1.69/1.90 dependent: set(dynamic_demod).
% 1.69/1.90 dependent: set(order_eq).
% 1.69/1.90 dependent: set(back_demod).
% 1.69/1.90 dependent: set(lrpo).
% 1.69/1.90 dependent: set(hyper_res).
% 1.69/1.90 dependent: set(unit_deletion).
% 1.69/1.90 dependent: set(factor).
% 1.69/1.90
% 1.69/1.90 ------------> process usable:
% 1.69/1.90 ** KEPT (pick-wt=12): 1 [] -c_in(A,B,tc_set(C))|c_lesse_quals(A,c_Union(B,C),tc_set(C)).
% 1.69/1.90 ** KEPT (pick-wt=13): 2 [] -c_lesse_quals(A,B,tc_set(C))| -c_lesse_quals(B,A,tc_set(C))|B=A.
% 1.69/1.90 ** KEPT (pick-wt=19): 3 [] -c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))|c_in(c_Zorn_Osucc(B,A,C),c_Zorn_OTFin(B,C),tc_set(tc_set(C))).
% 1.69/1.90 ** 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))).
% 1.69/1.90 ** KEPT (pick-wt=28): 6 [copy,5,flip.3] -c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))| -c_in(D,c_Zorn_OTFin(B,C),tc_set(tc_set(C)))|c_Zorn_Osucc(B,A,C)!=A|c_lesse_quals(D,A,tc_set(tc_set(C))).
% 1.69/1.90 ** KEPT (pick-wt=14): 8 [copy,7,flip.1,flip.2] c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))!=v_m|c_Zorn_Osucc(v_S,v_m,t_a)!=v_m.
% 1.69/1.90
% 1.69/1.90 ------------> process sos:
% 1.69/1.90 ** KEPT (pick-wt=3): 11 [] A=A.
% 1.69/1.90 ** KEPT (pick-wt=5): 12 [] c_lesse_quals(A,A,tc_set(B)).
% 1.69/1.90 ** KEPT (pick-wt=9): 13 [] c_lesse_quals(A,c_Zorn_Osucc(B,A,C),tc_set(tc_set(C))).
% 1.69/1.90 ** KEPT (pick-wt=8): 14 [] c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))).
% 1.69/1.90 ** KEPT (pick-wt=14): 16 [copy,15,flip.1,flip.2] c_Zorn_Osucc(v_S,v_m,t_a)=v_m|c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))=v_m.
% 1.69/1.90 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] A=A.
% 1.69/1.90 11 back subsumes 9.
% 1.69/1.90 12 back subsumes 10.
% 1.69/1.90
% 1.69/1.90 ======= end of input processing =======
% 1.69/1.90
% 1.69/1.90 =========== start of search ===========
% 1.69/1.90
% 1.69/1.90 -------- PROOF --------
% 1.69/1.90
% 1.69/1.90 ----> UNIT CONFLICT at 0.01 sec ----> 145 [binary,143.1,115.1] $F.
% 1.69/1.90
% 1.69/1.90 Length of proof is 13. Level of proof is 7.
% 1.69/1.90
% 1.69/1.90 ---------------- PROOF ----------------
% 1.69/1.90 % SZS status Unsatisfiable
% 1.69/1.90 % SZS output start Refutation
% See solution above
% 1.69/1.90 ------------ end of proof -------------
% 1.69/1.90
% 1.69/1.90
% 1.69/1.90 Search stopped by max_proofs option.
% 1.69/1.90
% 1.69/1.90
% 1.69/1.90 Search stopped by max_proofs option.
% 1.69/1.90
% 1.69/1.90 ============ end of search ============
% 1.69/1.90
% 1.69/1.90 -------------- statistics -------------
% 1.69/1.90 clauses given 17
% 1.69/1.90 clauses generated 301
% 1.69/1.90 clauses kept 139
% 1.69/1.90 clauses forward subsumed 219
% 1.69/1.90 clauses back subsumed 10
% 1.69/1.90 Kbytes malloced 976
% 1.69/1.90
% 1.69/1.90 ----------- times (seconds) -----------
% 1.69/1.90 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.69/1.90 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.90 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.69/1.90
% 1.69/1.90 That finishes the proof of the theorem.
% 1.69/1.90
% 1.69/1.90 Process 32641 finished Wed Jul 27 10:36:02 2022
% 1.69/1.90 Otter interrupted
% 1.69/1.90 PROOF FOUND
%------------------------------------------------------------------------------