TSTP Solution File: SET863-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET863-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 13:14:26 EDT 2022
% Result : Unsatisfiable 4.43s 4.59s
% Output : Refutation 4.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of clauses : 34 ( 17 unt; 12 nHn; 29 RR)
% Number of literals : 64 ( 0 equ; 17 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_in(A,B,C)
| ~ c_lesse_quals(B,D,tc_set(C))
| c_in(A,D,C) ),
file('SET863-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(c_Main_OsubsetI__1(A,B,C),B,C)
| c_lesse_quals(A,B,tc_set(C)) ),
file('SET863-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(A,B,tc_set(C))
| ~ c_in(D,c_Zorn_Ochain(B,C),tc_set(tc_set(C)))
| c_in(c_Zorn_Ochain__extend__1(D,A,C),D,tc_set(C))
| c_in(c_union(c_insert(A,c_emptyset,tc_set(C)),D,tc_set(C)),c_Zorn_Ochain(B,C),tc_set(tc_set(C))) ),
file('SET863-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_in(A,B,tc_set(C))
| ~ c_in(D,c_Zorn_Ochain(B,C),tc_set(tc_set(C)))
| ~ c_lesse_quals(c_Zorn_Ochain__extend__1(D,A,C),A,tc_set(C))
| c_in(c_union(c_insert(A,c_emptyset,tc_set(C)),D,tc_set(C)),c_Zorn_Ochain(B,C),tc_set(tc_set(C))) ),
file('SET863-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ c_in(A,B,C)
| ~ c_in(D,c_Zorn_Omaxchain(E,C),tc_set(tc_set(C)))
| ~ c_in(c_union(c_insert(B,c_emptyset,tc_set(C)),D,tc_set(C)),c_Zorn_Ochain(E,C),tc_set(tc_set(C)))
| c_in(A,F,C)
| c_in(c_Zorn_Omaxchain__super__lemma__1(D,F,C),D,tc_set(C)) ),
file('SET863-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ c_in(A,B,C)
| ~ c_in(D,c_Zorn_Omaxchain(E,C),tc_set(tc_set(C)))
| ~ c_in(c_union(c_insert(B,c_emptyset,tc_set(C)),D,tc_set(C)),c_Zorn_Ochain(E,C),tc_set(tc_set(C)))
| ~ c_lesse_quals(c_Zorn_Omaxchain__super__lemma__1(D,F,C),F,tc_set(C))
| c_in(A,F,C) ),
file('SET863-2.p',unknown),
[] ).
cnf(7,axiom,
~ c_in(v_xa,v_y,t_a),
file('SET863-2.p',unknown),
[] ).
cnf(8,axiom,
( c_lesse_quals(A,v_y,tc_set(t_a))
| ~ c_in(A,v_c,tc_set(t_a)) ),
file('SET863-2.p',unknown),
[] ).
cnf(9,axiom,
( c_in(c_Main_OsubsetI__1(A,B,C),A,C)
| c_lesse_quals(A,B,tc_set(C)) ),
file('SET863-2.p',unknown),
[] ).
cnf(10,axiom,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('SET863-2.p',unknown),
[] ).
cnf(11,axiom,
c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
file('SET863-2.p',unknown),
[] ).
cnf(12,axiom,
c_in(v_x,v_S,tc_set(t_a)),
file('SET863-2.p',unknown),
[] ).
cnf(13,axiom,
c_lesse_quals(v_y,v_x,tc_set(t_a)),
file('SET863-2.p',unknown),
[] ).
cnf(14,axiom,
c_in(v_xa,v_x,t_a),
file('SET863-2.p',unknown),
[] ).
cnf(18,plain,
( c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,t_a),c_Zorn_Ochain__extend__1(v_c,v_x,t_a),t_a) ),
inference(hyper,[status(thm)],[11,4,12,9]),
[iquote('hyper,11,4,12,9')] ).
cnf(19,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(hyper,[status(thm)],[11,3,12]),
[iquote('hyper,11,3,12')] ).
cnf(89,plain,
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,t_a),c_Zorn_Ochain__extend__1(v_c,v_x,t_a),t_a)
| c_in(v_xa,A,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,A,t_a),v_c,tc_set(t_a)) ),
inference(hyper,[status(thm)],[18,5,14,10]),
[iquote('hyper,18,5,14,10')] ).
cnf(234,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(v_xa,A,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,A,t_a),v_c,tc_set(t_a)) ),
inference(hyper,[status(thm)],[19,5,14,10]),
[iquote('hyper,19,5,14,10')] ).
cnf(255,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,tc_set(t_a)) ),
inference(hyper,[status(thm)],[234,7]),
[iquote('hyper,234,7')] ).
cnf(269,plain,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_lesse_quals(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_y,tc_set(t_a)) ),
inference(hyper,[status(thm)],[255,8]),
[iquote('hyper,255,8')] ).
cnf(328,plain,
c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a)),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[269,6,14,10,19]),7])]),
[iquote('hyper,269,6,14,10,19,unit_del,7,factor_simp')] ).
cnf(348,plain,
c_lesse_quals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_y,tc_set(t_a)),
inference(hyper,[status(thm)],[328,8]),
[iquote('hyper,328,8')] ).
cnf(1567,plain,
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,t_a),c_Zorn_Ochain__extend__1(v_c,v_x,t_a),t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,tc_set(t_a)) ),
inference(hyper,[status(thm)],[89,7]),
[iquote('hyper,89,7')] ).
cnf(2029,plain,
( c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,t_a),c_Zorn_Ochain__extend__1(v_c,v_x,t_a),t_a)
| c_lesse_quals(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_y,tc_set(t_a)) ),
inference(hyper,[status(thm)],[1567,8]),
[iquote('hyper,1567,8')] ).
cnf(3762,plain,
c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,t_a),c_Zorn_Ochain__extend__1(v_c,v_x,t_a),t_a),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[2029,6,14,10,18]),7])]),
[iquote('hyper,2029,6,14,10,18,unit_del,7,factor_simp')] ).
cnf(3763,plain,
c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,t_a),v_y,t_a),
inference(hyper,[status(thm)],[3762,1,348]),
[iquote('hyper,3762,1,348')] ).
cnf(3765,plain,
c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,t_a),v_x,t_a),
inference(hyper,[status(thm)],[3763,1,13]),
[iquote('hyper,3763,1,13')] ).
cnf(3767,plain,
c_lesse_quals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a)),
inference(hyper,[status(thm)],[3765,2]),
[iquote('hyper,3765,2')] ).
cnf(3770,plain,
c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
inference(hyper,[status(thm)],[3767,4,12,11]),
[iquote('hyper,3767,4,12,11')] ).
cnf(3815,plain,
( c_in(v_xa,A,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,A,t_a),v_c,tc_set(t_a)) ),
inference(hyper,[status(thm)],[3770,5,14,10]),
[iquote('hyper,3770,5,14,10')] ).
cnf(3818,plain,
c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,tc_set(t_a)),
inference(hyper,[status(thm)],[3815,7]),
[iquote('hyper,3815,7')] ).
cnf(3824,plain,
c_lesse_quals(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_y,tc_set(t_a)),
inference(hyper,[status(thm)],[3818,8]),
[iquote('hyper,3818,8')] ).
cnf(3898,plain,
c_in(v_xa,v_y,t_a),
inference(hyper,[status(thm)],[3824,6,14,10,3770]),
[iquote('hyper,3824,6,14,10,3770')] ).
cnf(3899,plain,
$false,
inference(binary,[status(thm)],[3898,7]),
[iquote('binary,3898.1,7.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET863-2 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n011.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 10:50:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.98/2.17 ----- Otter 3.3f, August 2004 -----
% 1.98/2.17 The process was started by sandbox on n011.cluster.edu,
% 1.98/2.17 Wed Jul 27 10:50:10 2022
% 1.98/2.17 The command was "./otter". The process ID is 3318.
% 1.98/2.17
% 1.98/2.17 set(prolog_style_variables).
% 1.98/2.17 set(auto).
% 1.98/2.17 dependent: set(auto1).
% 1.98/2.17 dependent: set(process_input).
% 1.98/2.17 dependent: clear(print_kept).
% 1.98/2.17 dependent: clear(print_new_demod).
% 1.98/2.17 dependent: clear(print_back_demod).
% 1.98/2.17 dependent: clear(print_back_sub).
% 1.98/2.17 dependent: set(control_memory).
% 1.98/2.17 dependent: assign(max_mem, 12000).
% 1.98/2.17 dependent: assign(pick_given_ratio, 4).
% 1.98/2.17 dependent: assign(stats_level, 1).
% 1.98/2.17 dependent: assign(max_seconds, 10800).
% 1.98/2.17 clear(print_given).
% 1.98/2.17
% 1.98/2.17 list(usable).
% 1.98/2.17 0 [] -c_in(V_c,V_A,T_a)| -c_lesse_quals(V_A,V_B,tc_set(T_a))|c_in(V_c,V_B,T_a).
% 1.98/2.17 0 [] c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)|c_lesse_quals(V_A,V_B,tc_set(T_a)).
% 1.98/2.17 0 [] -c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)|c_lesse_quals(V_A,V_B,tc_set(T_a)).
% 1.98/2.17 0 [] -c_in(V_z,V_S,tc_set(T_a))| -c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))|c_in(c_Zorn_Ochain__extend__1(V_c,V_z,T_a),V_c,tc_set(T_a))|c_in(c_union(c_insert(V_z,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a))).
% 1.98/2.17 0 [] -c_in(V_z,V_S,tc_set(T_a))| -c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))| -c_lesse_quals(c_Zorn_Ochain__extend__1(V_c,V_z,T_a),V_z,tc_set(T_a))|c_in(c_union(c_insert(V_z,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a))).
% 1.98/2.17 0 [] -c_in(V_z,V_x,T_a)| -c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))| -c_in(c_union(c_insert(V_x,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))|c_in(V_z,V_y,T_a)|c_in(c_Zorn_Omaxchain__super__lemma__1(V_c,V_y,T_a),V_c,tc_set(T_a)).
% 1.98/2.17 0 [] -c_in(V_z,V_x,T_a)| -c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))| -c_in(c_union(c_insert(V_x,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))| -c_lesse_quals(c_Zorn_Omaxchain__super__lemma__1(V_c,V_y,T_a),V_y,tc_set(T_a))|c_in(V_z,V_y,T_a).
% 1.98/2.17 0 [] c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))).
% 1.98/2.17 0 [] c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))).
% 1.98/2.17 0 [] c_in(v_x,v_S,tc_set(t_a)).
% 1.98/2.17 0 [] c_lesse_quals(v_y,v_x,tc_set(t_a)).
% 1.98/2.17 0 [] c_in(v_xa,v_x,t_a).
% 1.98/2.17 0 [] -c_in(v_xa,v_y,t_a).
% 1.98/2.17 0 [] c_lesse_quals(V_U,v_y,tc_set(t_a))| -c_in(V_U,v_c,tc_set(t_a)).
% 1.98/2.17 end_of_list.
% 1.98/2.17
% 1.98/2.17 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=5.
% 1.98/2.17
% 1.98/2.17 This is a non-Horn set without equality. The strategy will
% 1.98/2.17 be ordered hyper_res, unit deletion, and factoring, with
% 1.98/2.17 satellites in sos and with nuclei in usable.
% 1.98/2.17
% 1.98/2.17 dependent: set(hyper_res).
% 1.98/2.17 dependent: set(factor).
% 1.98/2.17 dependent: set(unit_deletion).
% 1.98/2.17
% 1.98/2.17 ------------> process usable:
% 1.98/2.17 ** KEPT (pick-wt=13): 1 [] -c_in(A,B,C)| -c_lesse_quals(B,D,tc_set(C))|c_in(A,D,C).
% 1.98/2.17 ** KEPT (pick-wt=12): 2 [] -c_in(c_Main_OsubsetI__1(A,B,C),B,C)|c_lesse_quals(A,B,tc_set(C)).
% 1.98/2.17 ** KEPT (pick-wt=37): 3 [] -c_in(A,B,tc_set(C))| -c_in(D,c_Zorn_Ochain(B,C),tc_set(tc_set(C)))|c_in(c_Zorn_Ochain__extend__1(D,A,C),D,tc_set(C))|c_in(c_union(c_insert(A,c_emptyset,tc_set(C)),D,tc_set(C)),c_Zorn_Ochain(B,C),tc_set(tc_set(C))).
% 1.98/2.17 ** KEPT (pick-wt=37): 4 [] -c_in(A,B,tc_set(C))| -c_in(D,c_Zorn_Ochain(B,C),tc_set(tc_set(C)))| -c_lesse_quals(c_Zorn_Ochain__extend__1(D,A,C),A,tc_set(C))|c_in(c_union(c_insert(A,c_emptyset,tc_set(C)),D,tc_set(C)),c_Zorn_Ochain(B,C),tc_set(tc_set(C))).
% 1.98/2.17 ** KEPT (pick-wt=40): 5 [] -c_in(A,B,C)| -c_in(D,c_Zorn_Omaxchain(E,C),tc_set(tc_set(C)))| -c_in(c_union(c_insert(B,c_emptyset,tc_set(C)),D,tc_set(C)),c_Zorn_Ochain(E,C),tc_set(tc_set(C)))|c_in(A,F,C)|c_in(c_Zorn_Omaxchain__super__lemma__1(D,F,C),D,tc_set(C)).
% 1.98/2.17 ** KEPT (pick-wt=40): 6 [] -c_in(A,B,C)| -c_in(D,c_Zorn_Omaxchain(E,C),tc_set(tc_set(C)))| -c_in(c_union(c_insert(B,c_emptyset,tc_set(C)),D,tc_set(C)),c_Zorn_Ochain(E,C),tc_set(tc_set(C)))| -c_lesse_quals(c_Zorn_Omaxchain__super__lemma__1(D,F,C),F,tc_set(C))|c_in(A,F,C).
% 1.98/2.17 ** KEPT (pick-wt=4): 7 [] -c_in(v_xa,v_y,t_a).
% 1.98/2.17 ** KEPT (pick-wt=10): 8 [] c_lesse_quals(A,v_y,tc_set(t_a))| -c_in(A,v_c,tc_set(t_a)).
% 1.98/2.17
% 1.98/2.17 ------------> process sos:
% 1.98/2.17 ** KEPT (pick-wt=12): 9 [] c_in(c_Main_OsubsetI__1(A,B,C),A,C)|c_lesse_quals(A,B,tc_set(C)).
% 4.43/4.59 ** KEPT (pick-wt=8): 10 [] c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))).
% 4.43/4.59 ** KEPT (pick-wt=8): 11 [] c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))).
% 4.43/4.59 ** KEPT (pick-wt=5): 12 [] c_in(v_x,v_S,tc_set(t_a)).
% 4.43/4.59 ** KEPT (pick-wt=5): 13 [] c_lesse_quals(v_y,v_x,tc_set(t_a)).
% 4.43/4.59 ** KEPT (pick-wt=4): 14 [] c_in(v_xa,v_x,t_a).
% 4.43/4.59
% 4.43/4.59 ======= end of input processing =======
% 4.43/4.59
% 4.43/4.59 =========== start of search ===========
% 4.43/4.59
% 4.43/4.59
% 4.43/4.59 Resetting weight limit to 31.
% 4.43/4.59
% 4.43/4.59
% 4.43/4.59 Resetting weight limit to 31.
% 4.43/4.59
% 4.43/4.59 sos_size=930
% 4.43/4.59
% 4.43/4.59 -------- PROOF --------
% 4.43/4.59
% 4.43/4.59 ----> UNIT CONFLICT at 2.41 sec ----> 3899 [binary,3898.1,7.1] $F.
% 4.43/4.59
% 4.43/4.59 Length of proof is 19. Level of proof is 14.
% 4.43/4.59
% 4.43/4.59 ---------------- PROOF ----------------
% 4.43/4.59 % SZS status Unsatisfiable
% 4.43/4.59 % SZS output start Refutation
% See solution above
% 4.43/4.59 ------------ end of proof -------------
% 4.43/4.59
% 4.43/4.59
% 4.43/4.59 Search stopped by max_proofs option.
% 4.43/4.59
% 4.43/4.59
% 4.43/4.59 Search stopped by max_proofs option.
% 4.43/4.59
% 4.43/4.59 ============ end of search ============
% 4.43/4.59
% 4.43/4.59 -------------- statistics -------------
% 4.43/4.59 clauses given 78
% 4.43/4.59 clauses generated 17006
% 4.43/4.59 clauses kept 3898
% 4.43/4.59 clauses forward subsumed 7434
% 4.43/4.59 clauses back subsumed 3196
% 4.43/4.59 Kbytes malloced 4882
% 4.43/4.59
% 4.43/4.59 ----------- times (seconds) -----------
% 4.43/4.59 user CPU time 2.41 (0 hr, 0 min, 2 sec)
% 4.43/4.59 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 4.43/4.59 wall-clock time 5 (0 hr, 0 min, 5 sec)
% 4.43/4.59
% 4.43/4.59 That finishes the proof of the theorem.
% 4.43/4.59
% 4.43/4.59 Process 3318 finished Wed Jul 27 10:50:15 2022
% 4.43/4.59 Otter interrupted
% 4.43/4.59 PROOF FOUND
%------------------------------------------------------------------------------