TSTP Solution File: SET848-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET848-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 1.91s 2.11s
% Output : Refutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 14 ( 9 unt; 2 nHn; 8 RR)
% Number of literals : 20 ( 3 equ; 7 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 : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 23 ( 1 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('SET848-2.p',unknown),
[] ).
cnf(2,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('SET848-2.p',unknown),
[] ).
cnf(3,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('SET848-2.p',unknown),
[] ).
cnf(4,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('SET848-2.p',unknown),
[] ).
cnf(5,axiom,
~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('SET848-2.p',unknown),
[] ).
cnf(6,axiom,
A = A,
file('SET848-2.p',unknown),
[] ).
cnf(7,axiom,
c_lesse_quals(A,A,tc_set(B)),
file('SET848-2.p',unknown),
[] ).
cnf(8,axiom,
c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a) = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
file('SET848-2.p',unknown),
[] ).
cnf(10,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)],[7,2]),
[iquote('hyper,7,2')] ).
cnf(11,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)],[10,3]),
[iquote('hyper,10,3')] ).
cnf(13,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)],[11,1]),
[iquote('hyper,11,1')] ).
cnf(14,plain,
~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),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))),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[8,4]),6]),
[iquote('para_from,8.1.1,4.2.1,unit_del,6')] ).
cnf(25,plain,
c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),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))),
inference(hyper,[status(thm)],[13,5]),
[iquote('hyper,13,5')] ).
cnf(26,plain,
$false,
inference(binary,[status(thm)],[25,14]),
[iquote('binary,25.1,14.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET848-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n020.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 10:37:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.91/2.11 ----- Otter 3.3f, August 2004 -----
% 1.91/2.11 The process was started by sandbox2 on n020.cluster.edu,
% 1.91/2.11 Wed Jul 27 10:37:53 2022
% 1.91/2.11 The command was "./otter". The process ID is 11478.
% 1.91/2.11
% 1.91/2.11 set(prolog_style_variables).
% 1.91/2.11 set(auto).
% 1.91/2.11 dependent: set(auto1).
% 1.91/2.11 dependent: set(process_input).
% 1.91/2.11 dependent: clear(print_kept).
% 1.91/2.11 dependent: clear(print_new_demod).
% 1.91/2.11 dependent: clear(print_back_demod).
% 1.91/2.11 dependent: clear(print_back_sub).
% 1.91/2.11 dependent: set(control_memory).
% 1.91/2.11 dependent: assign(max_mem, 12000).
% 1.91/2.11 dependent: assign(pick_given_ratio, 4).
% 1.91/2.11 dependent: assign(stats_level, 1).
% 1.91/2.11 dependent: assign(max_seconds, 10800).
% 1.91/2.11 clear(print_given).
% 1.91/2.11
% 1.91/2.11 list(usable).
% 1.91/2.11 0 [] A=A.
% 1.91/2.11 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).
% 1.91/2.11 0 [] c_lesse_quals(V_A,V_A,tc_set(T_a)).
% 1.91/2.11 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))).
% 1.91/2.11 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))).
% 1.91/2.11 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.
% 1.91/2.11 0 [] -c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))).
% 1.91/2.11 0 [] c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a)=c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)).
% 1.91/2.11 end_of_list.
% 1.91/2.11
% 1.91/2.11 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.91/2.11
% 1.91/2.11 This ia a non-Horn set with equality. The strategy will be
% 1.91/2.11 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.91/2.11 deletion, with positive clauses in sos and nonpositive
% 1.91/2.11 clauses in usable.
% 1.91/2.11
% 1.91/2.11 dependent: set(knuth_bendix).
% 1.91/2.11 dependent: set(anl_eq).
% 1.91/2.11 dependent: set(para_from).
% 1.91/2.11 dependent: set(para_into).
% 1.91/2.11 dependent: clear(para_from_right).
% 1.91/2.11 dependent: clear(para_into_right).
% 1.91/2.11 dependent: set(para_from_vars).
% 1.91/2.11 dependent: set(eq_units_both_ways).
% 1.91/2.11 dependent: set(dynamic_demod_all).
% 1.91/2.11 dependent: set(dynamic_demod).
% 1.91/2.11 dependent: set(order_eq).
% 1.91/2.11 dependent: set(back_demod).
% 1.91/2.11 dependent: set(lrpo).
% 1.91/2.11 dependent: set(hyper_res).
% 1.91/2.11 dependent: set(unit_deletion).
% 1.91/2.11 dependent: set(factor).
% 1.91/2.11
% 1.91/2.11 ------------> process usable:
% 1.91/2.11 ** 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).
% 1.91/2.11 ** KEPT (pick-wt=20): 2 [] -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))).
% 1.91/2.11 ** KEPT (pick-wt=16): 3 [] -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))).
% 1.91/2.11 ** KEPT (pick-wt=22): 4 [] -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.
% 1.91/2.11 ** KEPT (pick-wt=13): 5 [] -c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))).
% 1.91/2.11
% 1.91/2.11 ------------> process sos:
% 1.91/2.11 ** KEPT (pick-wt=3): 6 [] A=A.
% 1.91/2.11 ** KEPT (pick-wt=5): 7 [] c_lesse_quals(A,A,tc_set(B)).
% 1.91/2.11 ** KEPT (pick-wt=16): 8 [] c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a)=c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)).
% 1.91/2.11 ---> New Demodulator: 9 [new_demod,8] c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a)=c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)).
% 1.91/2.11 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 1.91/2.11 >>>> Starting back demodulation with 9.
% 1.91/2.11
% 1.91/2.11 ======= end of input processing =======
% 1.91/2.11
% 1.91/2.11 =========== start of search ===========
% 1.91/2.11
% 1.91/2.11 -------- PROOF --------
% 1.91/2.11
% 1.91/2.11 ----> UNIT CONFLICT at 0.00 sec ----> 26 [binary,25.1,14.1] $F.
% 1.91/2.11
% 1.91/2.11 Length of proof is 5. Level of proof is 4.
% 1.91/2.11
% 1.91/2.11 ---------------- PROOF ----------------
% 1.91/2.11 % SZS status Unsatisfiable
% 1.91/2.11 % SZS output start Refutation
% See solution above
% 1.91/2.11 ------------ end of proof -------------
% 1.91/2.11
% 1.91/2.11
% 1.91/2.11 Search stopped by max_proofs option.
% 1.91/2.11
% 1.91/2.11
% 1.91/2.11 Search stopped by max_proofs option.
% 1.91/2.11
% 1.91/2.11 ============ end of search ============
% 1.91/2.11
% 1.91/2.11 -------------- statistics -------------
% 1.91/2.11 clauses given 10
% 1.91/2.11 clauses generated 20
% 1.91/2.11 clauses kept 24
% 1.91/2.11 clauses forward subsumed 5
% 1.91/2.11 clauses back subsumed 0
% 1.91/2.11 Kbytes malloced 1953
% 1.91/2.11
% 1.91/2.11 ----------- times (seconds) -----------
% 1.91/2.11 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.91/2.11 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.91/2.11 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.91/2.11
% 1.91/2.11 That finishes the proof of the theorem.
% 1.91/2.11
% 1.91/2.11 Process 11478 finished Wed Jul 27 10:37:55 2022
% 1.91/2.11 Otter interrupted
% 1.96/2.11 PROOF FOUND
%------------------------------------------------------------------------------