TSTP Solution File: SET852-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET852-2 : 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 13:14:24 EDT 2022
% Result : Unsatisfiable 1.69s 1.88s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 5 unt; 6 nHn; 9 RR)
% Number of literals : 21 ( 0 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ c_lesse_quals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('SET852-2.p',unknown),
[] ).
cnf(2,axiom,
~ c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('SET852-2.p',unknown),
[] ).
cnf(3,axiom,
( c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),A,tc_set(tc_set(t_a)))
| c_lesse_quals(A,v_m,tc_set(tc_set(t_a)))
| ~ c_in(A,v_Y,tc_set(tc_set(t_a))) ),
file('SET852-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_lesse_quals(c_Zorn_OUnion__lemma0__1(A,B,C,D),A,tc_set(D))
| c_lesse_quals(B,c_Union(C,D),tc_set(D))
| c_lesse_quals(c_Union(C,D),A,tc_set(D)) ),
file('SET852-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ c_lesse_quals(A,c_Zorn_OUnion__lemma0__1(B,A,C,D),tc_set(D))
| c_lesse_quals(A,c_Union(C,D),tc_set(D))
| c_lesse_quals(c_Union(C,D),B,tc_set(D)) ),
file('SET852-2.p',unknown),
[] ).
cnf(8,axiom,
( c_in(c_Zorn_OUnion__lemma0__1(A,B,C,D),C,tc_set(D))
| c_lesse_quals(B,c_Union(C,D),tc_set(D))
| c_lesse_quals(c_Union(C,D),A,tc_set(D)) ),
file('SET852-2.p',unknown),
[] ).
cnf(15,plain,
( c_in(c_Zorn_OUnion__lemma0__1(v_m,A,v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| c_lesse_quals(A,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(hyper,[status(thm)],[8,1]),
[iquote('hyper,8,1')] ).
cnf(24,plain,
c_in(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))),
inference(hyper,[status(thm)],[15,2]),
[iquote('hyper,15,2')] ).
cnf(25,plain,
( c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lesse_quals(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(hyper,[status(thm)],[24,3]),
[iquote('hyper,24,3')] ).
cnf(31,plain,
c_lesse_quals(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[25,5]),2,1]),
[iquote('hyper,25,5,unit_del,2,1')] ).
cnf(33,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[31,4]),2,1]),
[iquote('hyper,31,4,unit_del,2,1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET852-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 10:31:51 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.69/1.88 ----- Otter 3.3f, August 2004 -----
% 1.69/1.88 The process was started by sandbox2 on n009.cluster.edu,
% 1.69/1.88 Wed Jul 27 10:31:51 2022
% 1.69/1.88 The command was "./otter". The process ID is 17878.
% 1.69/1.88
% 1.69/1.88 set(prolog_style_variables).
% 1.69/1.88 set(auto).
% 1.69/1.88 dependent: set(auto1).
% 1.69/1.88 dependent: set(process_input).
% 1.69/1.88 dependent: clear(print_kept).
% 1.69/1.88 dependent: clear(print_new_demod).
% 1.69/1.88 dependent: clear(print_back_demod).
% 1.69/1.88 dependent: clear(print_back_sub).
% 1.69/1.88 dependent: set(control_memory).
% 1.69/1.88 dependent: assign(max_mem, 12000).
% 1.69/1.88 dependent: assign(pick_given_ratio, 4).
% 1.69/1.88 dependent: assign(stats_level, 1).
% 1.69/1.88 dependent: assign(max_seconds, 10800).
% 1.69/1.88 clear(print_given).
% 1.69/1.88
% 1.69/1.88 list(usable).
% 1.69/1.88 0 [] -c_lesse_quals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))).
% 1.69/1.88 0 [] -c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))).
% 1.69/1.88 0 [] c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a)))|c_lesse_quals(V_U,v_m,tc_set(tc_set(t_a)))| -c_in(V_U,v_Y,tc_set(tc_set(t_a))).
% 1.69/1.88 0 [] c_in(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_C,tc_set(T_a))|c_lesse_quals(V_B,c_Union(V_C,T_a),tc_set(T_a))|c_lesse_quals(c_Union(V_C,T_a),V_A,tc_set(T_a)).
% 1.69/1.88 0 [] -c_lesse_quals(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_A,tc_set(T_a))|c_lesse_quals(V_B,c_Union(V_C,T_a),tc_set(T_a))|c_lesse_quals(c_Union(V_C,T_a),V_A,tc_set(T_a)).
% 1.69/1.88 0 [] -c_lesse_quals(V_B,c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),tc_set(T_a))|c_lesse_quals(V_B,c_Union(V_C,T_a),tc_set(T_a))|c_lesse_quals(c_Union(V_C,T_a),V_A,tc_set(T_a)).
% 1.69/1.88 end_of_list.
% 1.69/1.88
% 1.69/1.88 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.69/1.88
% 1.69/1.88 This is a non-Horn set without equality. The strategy will
% 1.69/1.88 be ordered hyper_res, unit deletion, and factoring, with
% 1.69/1.88 satellites in sos and with nuclei in usable.
% 1.69/1.88
% 1.69/1.88 dependent: set(hyper_res).
% 1.69/1.88 dependent: set(factor).
% 1.69/1.88 dependent: set(unit_deletion).
% 1.69/1.88
% 1.69/1.88 ------------> process usable:
% 1.69/1.88 ** KEPT (pick-wt=9): 1 [] -c_lesse_quals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))).
% 1.69/1.88 ** KEPT (pick-wt=12): 2 [] -c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))).
% 1.69/1.88 ** KEPT (pick-wt=21): 3 [] c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),A,tc_set(tc_set(t_a)))|c_lesse_quals(A,v_m,tc_set(tc_set(t_a)))| -c_in(A,v_Y,tc_set(tc_set(t_a))).
% 1.69/1.88 ** KEPT (pick-wt=23): 4 [] -c_lesse_quals(c_Zorn_OUnion__lemma0__1(A,B,C,D),A,tc_set(D))|c_lesse_quals(B,c_Union(C,D),tc_set(D))|c_lesse_quals(c_Union(C,D),A,tc_set(D)).
% 1.69/1.88 ** KEPT (pick-wt=23): 5 [] -c_lesse_quals(A,c_Zorn_OUnion__lemma0__1(B,A,C,D),tc_set(D))|c_lesse_quals(A,c_Union(C,D),tc_set(D))|c_lesse_quals(c_Union(C,D),B,tc_set(D)).
% 1.69/1.88
% 1.69/1.88 ------------> process sos:
% 1.69/1.88 ** KEPT (pick-wt=23): 8 [] c_in(c_Zorn_OUnion__lemma0__1(A,B,C,D),C,tc_set(D))|c_lesse_quals(B,c_Union(C,D),tc_set(D))|c_lesse_quals(c_Union(C,D),A,tc_set(D)).
% 1.69/1.88
% 1.69/1.88 ======= end of input processing =======
% 1.69/1.88
% 1.69/1.88 =========== start of search ===========
% 1.69/1.88
% 1.69/1.88 -------- PROOF --------
% 1.69/1.88
% 1.69/1.88 -----> EMPTY CLAUSE at 0.00 sec ----> 33 [hyper,31,4,unit_del,2,1] $F.
% 1.69/1.88
% 1.69/1.88 Length of proof is 4. Level of proof is 4.
% 1.69/1.88
% 1.69/1.88 ---------------- PROOF ----------------
% 1.69/1.88 % SZS status Unsatisfiable
% 1.69/1.88 % SZS output start Refutation
% See solution above
% 1.69/1.88 ------------ end of proof -------------
% 1.69/1.88
% 1.69/1.88
% 1.69/1.88 Search stopped by max_proofs option.
% 1.69/1.88
% 1.69/1.88
% 1.69/1.88 Search stopped by max_proofs option.
% 1.69/1.88
% 1.69/1.88 ============ end of search ============
% 1.69/1.88
% 1.69/1.88 -------------- statistics -------------
% 1.69/1.88 clauses given 10
% 1.69/1.88 clauses generated 40
% 1.69/1.88 clauses kept 32
% 1.69/1.88 clauses forward subsumed 13
% 1.69/1.88 clauses back subsumed 1
% 1.69/1.88 Kbytes malloced 976
% 1.69/1.88
% 1.69/1.88 ----------- times (seconds) -----------
% 1.69/1.88 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.88 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.69/1.88
% 1.69/1.88 That finishes the proof of the theorem.
% 1.69/1.88
% 1.69/1.88 Process 17878 finished Wed Jul 27 10:31:52 2022
% 1.69/1.88 Otter interrupted
% 1.69/1.88 PROOF FOUND
%------------------------------------------------------------------------------