TSTP Solution File: SET858-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET858-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 13:14:25 EDT 2022
% Result : Unsatisfiable 1.94s 2.14s
% Output : Refutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 20 ( 10 unt; 9 nHn; 19 RR)
% Number of literals : 46 ( 3 equ; 17 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 27 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ c_lesse_quals(v_n,v_m,tc_set(tc_set(t_a))),
file('SET858-2.p',unknown),
[] ).
cnf(2,axiom,
~ c_lesse_quals(v_m,v_n,tc_set(tc_set(t_a))),
file('SET858-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_lesse_quals(A,B,tc_set(C))
| ~ c_lesse_quals(D,A,tc_set(C))
| c_lesse_quals(D,B,tc_set(C)) ),
file('SET858-2.p',unknown),
[] ).
cnf(4,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)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(B,A,C),c_Zorn_OTFin(B,C),tc_set(tc_set(C)))
| c_lesse_quals(D,A,tc_set(tc_set(C)))
| c_lesse_quals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C))) ),
file('SET858-2.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)))
| c_lesse_quals(D,A,tc_set(tc_set(C)))
| c_lesse_quals(c_Zorn_OTFin__linear__lemma1__1(B,A,C),A,tc_set(tc_set(C)))
| c_lesse_quals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C))) ),
file('SET858-2.p',unknown),
[] ).
cnf(6,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)))
| c_Zorn_OTFin__linear__lemma1__1(B,A,C) != A
| c_lesse_quals(D,A,tc_set(tc_set(C)))
| c_lesse_quals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C))) ),
file('SET858-2.p',unknown),
[] ).
cnf(7,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)))
| ~ c_lesse_quals(c_Zorn_Osucc(B,c_Zorn_OTFin__linear__lemma1__1(B,A,C),C),A,tc_set(tc_set(C)))
| c_lesse_quals(D,A,tc_set(tc_set(C)))
| c_lesse_quals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C))) ),
file('SET858-2.p',unknown),
[] ).
cnf(8,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)))
| ~ c_lesse_quals(A,D,tc_set(tc_set(C)))
| c_lesse_quals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C)))
| A = D ),
file('SET858-2.p',unknown),
[] ).
cnf(16,axiom,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('SET858-2.p',unknown),
[] ).
cnf(17,axiom,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('SET858-2.p',unknown),
[] ).
cnf(18,axiom,
c_lesse_quals(A,c_Zorn_Osucc(B,A,C),tc_set(tc_set(C))),
file('SET858-2.p',unknown),
[] ).
cnf(30,plain,
( c_lesse_quals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a)))
| c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[17,5,16]),1]),
[iquote('hyper,17,5,16,unit_del,1')] ).
cnf(32,plain,
( c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[17,4,16]),1]),
[iquote('hyper,17,4,16,unit_del,1')] ).
cnf(87,plain,
c_lesse_quals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a))),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[30,3,18]),2]),
[iquote('hyper,30,3,18,unit_del,2')] ).
cnf(376,plain,
c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[32,3,18]),2]),
[iquote('hyper,32,3,18,unit_del,2')] ).
cnf(379,plain,
( c_lesse_quals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),t_a),v_m,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) = v_m ),
inference(hyper,[status(thm)],[376,8,16,87]),
[iquote('hyper,376,8,16,87')] ).
cnf(459,plain,
( c_lesse_quals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),t_a),v_m,tc_set(tc_set(t_a)))
| c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[379,6,16,17]),1]),
[iquote('hyper,379,6,16,17,unit_del,1')] ).
cnf(856,plain,
c_lesse_quals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[459,7,16,17]),1])]),
[iquote('hyper,459,7,16,17,unit_del,1,factor_simp')] ).
cnf(870,plain,
c_lesse_quals(v_m,v_n,tc_set(tc_set(t_a))),
inference(hyper,[status(thm)],[856,3,18]),
[iquote('hyper,856,3,18')] ).
cnf(871,plain,
$false,
inference(binary,[status(thm)],[870,2]),
[iquote('binary,870.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET858-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.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 10:52:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.71/1.92 ----- Otter 3.3f, August 2004 -----
% 1.71/1.92 The process was started by sandbox on n018.cluster.edu,
% 1.71/1.92 Wed Jul 27 10:52:46 2022
% 1.71/1.92 The command was "./otter". The process ID is 13437.
% 1.71/1.92
% 1.71/1.92 set(prolog_style_variables).
% 1.71/1.92 set(auto).
% 1.71/1.92 dependent: set(auto1).
% 1.71/1.92 dependent: set(process_input).
% 1.71/1.92 dependent: clear(print_kept).
% 1.71/1.92 dependent: clear(print_new_demod).
% 1.71/1.92 dependent: clear(print_back_demod).
% 1.71/1.92 dependent: clear(print_back_sub).
% 1.71/1.92 dependent: set(control_memory).
% 1.71/1.92 dependent: assign(max_mem, 12000).
% 1.71/1.92 dependent: assign(pick_given_ratio, 4).
% 1.71/1.92 dependent: assign(stats_level, 1).
% 1.71/1.92 dependent: assign(max_seconds, 10800).
% 1.71/1.92 clear(print_given).
% 1.71/1.92
% 1.71/1.92 list(usable).
% 1.71/1.92 0 [] A=A.
% 1.71/1.92 0 [] c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))).
% 1.71/1.92 0 [] c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))).
% 1.71/1.92 0 [] -c_lesse_quals(v_n,v_m,tc_set(tc_set(t_a))).
% 1.71/1.92 0 [] -c_lesse_quals(v_m,v_n,tc_set(tc_set(t_a))).
% 1.71/1.92 0 [] -c_lesse_quals(V_B,V_C,tc_set(T_a))| -c_lesse_quals(V_A,V_B,tc_set(T_a))|c_lesse_quals(V_A,V_C,tc_set(T_a)).
% 1.71/1.92 0 [] c_lesse_quals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))).
% 1.71/1.92 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)))|c_in(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))|c_lesse_quals(V_n,V_m,tc_set(tc_set(T_a)))|c_lesse_quals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))).
% 1.71/1.92 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)))|c_lesse_quals(V_n,V_m,tc_set(tc_set(T_a)))|c_lesse_quals(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),V_m,tc_set(tc_set(T_a)))|c_lesse_quals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))).
% 1.71/1.92 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)))|c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a)!=V_m|c_lesse_quals(V_n,V_m,tc_set(tc_set(T_a)))|c_lesse_quals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))).
% 1.71/1.92 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)))| -c_lesse_quals(c_Zorn_Osucc(V_S,c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),T_a),V_m,tc_set(tc_set(T_a)))|c_lesse_quals(V_n,V_m,tc_set(tc_set(T_a)))|c_lesse_quals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))).
% 1.71/1.92 0 [] -c_in(V_U,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))| -c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))| -c_lesse_quals(V_U,V_m,tc_set(tc_set(T_a)))|c_lesse_quals(c_Zorn_Osucc(V_S,V_U,T_a),V_m,tc_set(tc_set(T_a)))|V_U=V_m.
% 1.71/1.92 end_of_list.
% 1.71/1.92
% 1.71/1.92 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.71/1.92
% 1.71/1.92 This ia a non-Horn set with equality. The strategy will be
% 1.71/1.92 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.71/1.92 deletion, with positive clauses in sos and nonpositive
% 1.71/1.92 clauses in usable.
% 1.71/1.92
% 1.71/1.92 dependent: set(knuth_bendix).
% 1.71/1.92 dependent: set(anl_eq).
% 1.71/1.92 dependent: set(para_from).
% 1.71/1.92 dependent: set(para_into).
% 1.71/1.92 dependent: clear(para_from_right).
% 1.71/1.92 dependent: clear(para_into_right).
% 1.71/1.92 dependent: set(para_from_vars).
% 1.71/1.92 dependent: set(eq_units_both_ways).
% 1.71/1.92 dependent: set(dynamic_demod_all).
% 1.71/1.92 dependent: set(dynamic_demod).
% 1.71/1.92 dependent: set(order_eq).
% 1.71/1.92 dependent: set(back_demod).
% 1.71/1.92 dependent: set(lrpo).
% 1.71/1.92 dependent: set(hyper_res).
% 1.71/1.92 dependent: set(unit_deletion).
% 1.71/1.92 dependent: set(factor).
% 1.71/1.92
% 1.71/1.92 ------------> process usable:
% 1.71/1.92 ** KEPT (pick-wt=6): 1 [] -c_lesse_quals(v_n,v_m,tc_set(tc_set(t_a))).
% 1.71/1.92 ** KEPT (pick-wt=6): 2 [] -c_lesse_quals(v_m,v_n,tc_set(tc_set(t_a))).
% 1.71/1.92 ** KEPT (pick-wt=15): 3 [] -c_lesse_quals(A,B,tc_set(C))| -c_lesse_quals(D,A,tc_set(C))|c_lesse_quals(D,B,tc_set(C)).
% 1.71/1.92 ** KEPT (pick-wt=42): 4 [] -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_in(c_Zorn_OTFin__linear__lemma1__1(B,A,C),c_Zorn_OTFin(B,C),tc_set(tc_set(C)))|c_lesse_quals(D,A,tc_set(tc_set(C)))|c_lesse_quals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C))).
% 1.71/1.92 ** KEPT (pick-wt=40): 5 [] -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_lesse_quals(D,A,tc_set(tc_set(C)))|c_lesse_quals(c_Zorn_OTFin__linear__lemma1__1(B,A,C),A,tc_set(tc_set(C)))|c_lesse_quals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C))).
% 1.94/2.14 ** KEPT (pick-wt=37): 6 [] -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_OTFin__linear__lemma1__1(B,A,C)!=A|c_lesse_quals(D,A,tc_set(tc_set(C)))|c_lesse_quals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C))).
% 1.94/2.14 ** KEPT (pick-wt=43): 7 [] -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_lesse_quals(c_Zorn_Osucc(B,c_Zorn_OTFin__linear__lemma1__1(B,A,C),C),A,tc_set(tc_set(C)))|c_lesse_quals(D,A,tc_set(tc_set(C)))|c_lesse_quals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C))).
% 1.94/2.14 ** KEPT (pick-wt=34): 8 [] -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_lesse_quals(A,D,tc_set(tc_set(C)))|c_lesse_quals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C)))|A=D.
% 1.94/2.14
% 1.94/2.14 ------------> process sos:
% 1.94/2.14 ** KEPT (pick-wt=3): 15 [] A=A.
% 1.94/2.14 ** KEPT (pick-wt=8): 16 [] c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))).
% 1.94/2.14 ** KEPT (pick-wt=8): 17 [] c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))).
% 1.94/2.14 ** KEPT (pick-wt=9): 18 [] c_lesse_quals(A,c_Zorn_Osucc(B,A,C),tc_set(tc_set(C))).
% 1.94/2.14 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] A=A.
% 1.94/2.14 15 back subsumes 14.
% 1.94/2.14
% 1.94/2.14 ======= end of input processing =======
% 1.94/2.14
% 1.94/2.14 =========== start of search ===========
% 1.94/2.14
% 1.94/2.14 -------- PROOF --------
% 1.94/2.14
% 1.94/2.14 ----> UNIT CONFLICT at 0.21 sec ----> 871 [binary,870.1,2.1] $F.
% 1.94/2.14
% 1.94/2.14 Length of proof is 8. Level of proof is 6.
% 1.94/2.14
% 1.94/2.14 ---------------- PROOF ----------------
% 1.94/2.14 % SZS status Unsatisfiable
% 1.94/2.14 % SZS output start Refutation
% See solution above
% 1.94/2.14 ------------ end of proof -------------
% 1.94/2.14
% 1.94/2.14
% 1.94/2.14 Search stopped by max_proofs option.
% 1.94/2.14
% 1.94/2.14
% 1.94/2.14 Search stopped by max_proofs option.
% 1.94/2.14
% 1.94/2.14 ============ end of search ============
% 1.94/2.14
% 1.94/2.14 -------------- statistics -------------
% 1.94/2.14 clauses given 44
% 1.94/2.14 clauses generated 2255
% 1.94/2.14 clauses kept 870
% 1.94/2.14 clauses forward subsumed 1371
% 1.94/2.14 clauses back subsumed 155
% 1.94/2.14 Kbytes malloced 2929
% 1.94/2.14
% 1.94/2.14 ----------- times (seconds) -----------
% 1.94/2.14 user CPU time 0.21 (0 hr, 0 min, 0 sec)
% 1.94/2.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.94/2.14 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.94/2.14
% 1.94/2.14 That finishes the proof of the theorem.
% 1.94/2.14
% 1.94/2.14 Process 13437 finished Wed Jul 27 10:52:48 2022
% 1.94/2.14 Otter interrupted
% 1.94/2.14 PROOF FOUND
%------------------------------------------------------------------------------