TSTP Solution File: SET845-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET845-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 1.63s 1.86s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 13 ( 10 unt; 0 nHn; 12 RR)
% Number of literals : 17 ( 6 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 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 : 12 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_in(A,B,tc_set(C))
| c_lesse_quals(A,c_Union(B,C),tc_set(C)) ),
file('SET845-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_lesse_quals(A,B,tc_set(C))
| ~ c_lesse_quals(B,A,tc_set(C))
| B = A ),
file('SET845-2.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('SET845-2.p',unknown),
[] ).
cnf(4,axiom,
v_m != c_Zorn_Osucc(v_S,v_m,t_a),
file('SET845-2.p',unknown),
[] ).
cnf(5,plain,
c_Zorn_Osucc(v_S,v_m,t_a) != v_m,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.1')] ).
cnf(7,axiom,
c_lesse_quals(A,c_Zorn_Osucc(B,A,C),tc_set(tc_set(C))),
file('SET845-2.p',unknown),
[] ).
cnf(8,axiom,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('SET845-2.p',unknown),
[] ).
cnf(9,axiom,
v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
file('SET845-2.p',unknown),
[] ).
cnf(11,plain,
c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9])]),
[iquote('copy,9,flip.1')] ).
cnf(12,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)],[8,3]),
[iquote('hyper,8,3')] ).
cnf(36,plain,
c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[12,1]),11]),
[iquote('hyper,12,1,demod,11')] ).
cnf(47,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = v_m,
inference(hyper,[status(thm)],[36,2,7]),
[iquote('hyper,36,2,7')] ).
cnf(49,plain,
$false,
inference(binary,[status(thm)],[47,5]),
[iquote('binary,47.1,5.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET845-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.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 10:53:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.63/1.86 ----- Otter 3.3f, August 2004 -----
% 1.63/1.86 The process was started by sandbox on n012.cluster.edu,
% 1.63/1.86 Wed Jul 27 10:53:35 2022
% 1.63/1.86 The command was "./otter". The process ID is 14152.
% 1.63/1.86
% 1.63/1.86 set(prolog_style_variables).
% 1.63/1.86 set(auto).
% 1.63/1.86 dependent: set(auto1).
% 1.63/1.86 dependent: set(process_input).
% 1.63/1.86 dependent: clear(print_kept).
% 1.63/1.86 dependent: clear(print_new_demod).
% 1.63/1.86 dependent: clear(print_back_demod).
% 1.63/1.86 dependent: clear(print_back_sub).
% 1.63/1.86 dependent: set(control_memory).
% 1.63/1.86 dependent: assign(max_mem, 12000).
% 1.63/1.86 dependent: assign(pick_given_ratio, 4).
% 1.63/1.86 dependent: assign(stats_level, 1).
% 1.63/1.86 dependent: assign(max_seconds, 10800).
% 1.63/1.86 clear(print_given).
% 1.63/1.86
% 1.63/1.86 list(usable).
% 1.63/1.86 0 [] A=A.
% 1.63/1.86 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)).
% 1.63/1.86 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.
% 1.63/1.86 0 [] c_lesse_quals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))).
% 1.63/1.86 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))).
% 1.63/1.86 0 [] c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))).
% 1.63/1.86 0 [] v_m=c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)).
% 1.63/1.86 0 [] v_m!=c_Zorn_Osucc(v_S,v_m,t_a).
% 1.63/1.86 end_of_list.
% 1.63/1.86
% 1.63/1.86 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.63/1.86
% 1.63/1.86 This is a Horn set with equality. The strategy will be
% 1.63/1.86 Knuth-Bendix and hyper_res, with positive clauses in
% 1.63/1.86 sos and nonpositive clauses in usable.
% 1.63/1.86
% 1.63/1.86 dependent: set(knuth_bendix).
% 1.63/1.86 dependent: set(anl_eq).
% 1.63/1.86 dependent: set(para_from).
% 1.63/1.86 dependent: set(para_into).
% 1.63/1.86 dependent: clear(para_from_right).
% 1.63/1.86 dependent: clear(para_into_right).
% 1.63/1.86 dependent: set(para_from_vars).
% 1.63/1.86 dependent: set(eq_units_both_ways).
% 1.63/1.86 dependent: set(dynamic_demod_all).
% 1.63/1.86 dependent: set(dynamic_demod).
% 1.63/1.86 dependent: set(order_eq).
% 1.63/1.86 dependent: set(back_demod).
% 1.63/1.86 dependent: set(lrpo).
% 1.63/1.86 dependent: set(hyper_res).
% 1.63/1.86 dependent: clear(order_hyper).
% 1.63/1.86
% 1.63/1.86 ------------> process usable:
% 1.63/1.86 ** KEPT (pick-wt=12): 1 [] -c_in(A,B,tc_set(C))|c_lesse_quals(A,c_Union(B,C),tc_set(C)).
% 1.63/1.86 ** KEPT (pick-wt=13): 2 [] -c_lesse_quals(A,B,tc_set(C))| -c_lesse_quals(B,A,tc_set(C))|B=A.
% 1.63/1.86 ** 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))).
% 1.63/1.86 ** KEPT (pick-wt=6): 5 [copy,4,flip.1] c_Zorn_Osucc(v_S,v_m,t_a)!=v_m.
% 1.63/1.86
% 1.63/1.86 ------------> process sos:
% 1.63/1.86 ** KEPT (pick-wt=3): 6 [] A=A.
% 1.63/1.86 ** KEPT (pick-wt=9): 7 [] c_lesse_quals(A,c_Zorn_Osucc(B,A,C),tc_set(tc_set(C))).
% 1.63/1.86 ** KEPT (pick-wt=8): 8 [] c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))).
% 1.63/1.86 ** KEPT (pick-wt=8): 10 [copy,9,flip.1] c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))=v_m.
% 1.63/1.86 ---> New Demodulator: 11 [new_demod,10] c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))=v_m.
% 1.63/1.86 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 1.63/1.86 >>>> Starting back demodulation with 11.
% 1.63/1.86
% 1.63/1.86 ======= end of input processing =======
% 1.63/1.86
% 1.63/1.86 =========== start of search ===========
% 1.63/1.86
% 1.63/1.86 -------- PROOF --------
% 1.63/1.86
% 1.63/1.86 ----> UNIT CONFLICT at 0.00 sec ----> 49 [binary,47.1,5.1] $F.
% 1.63/1.86
% 1.63/1.86 Length of proof is 5. Level of proof is 3.
% 1.63/1.86
% 1.63/1.86 ---------------- PROOF ----------------
% 1.63/1.86 % SZS status Unsatisfiable
% 1.63/1.86 % SZS output start Refutation
% See solution above
% 1.63/1.86 ------------ end of proof -------------
% 1.63/1.86
% 1.63/1.86
% 1.63/1.86 Search stopped by max_proofs option.
% 1.63/1.86
% 1.63/1.86
% 1.63/1.86 Search stopped by max_proofs option.
% 1.63/1.86
% 1.63/1.86 ============ end of search ============
% 1.63/1.86
% 1.63/1.86 -------------- statistics -------------
% 1.63/1.86 clauses given 7
% 1.63/1.86 clauses generated 41
% 1.63/1.86 clauses kept 44
% 1.63/1.86 clauses forward subsumed 6
% 1.63/1.86 clauses back subsumed 0
% 1.63/1.86 Kbytes malloced 976
% 1.63/1.86
% 1.63/1.86 ----------- times (seconds) -----------
% 1.63/1.86 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.63/1.86 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.63/1.86 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.63/1.86
% 1.63/1.86 That finishes the proof of the theorem.
% 1.63/1.86
% 1.63/1.86 Process 14152 finished Wed Jul 27 10:53:37 2022
% 1.63/1.86 Otter interrupted
% 1.63/1.86 PROOF FOUND
%------------------------------------------------------------------------------