%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LAT327+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n013.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 13:02:48 EDT 2022
% Result : Theorem 2.16s 2.32s
% Output : Refutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 12
% Syntax : Number of clauses : 23 ( 14 unt; 8 nHn; 23 RR)
% Number of literals : 69 ( 0 equ; 40 neg)
% Maximal clause size : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 18 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ v3_struct_0(dollar_c3),
file('LAT327+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ r2_hidden(dollar_c2,k22_filter_2(dollar_c3,dollar_c2,dollar_c1))
| ~ r2_hidden(dollar_c1,k22_filter_2(dollar_c3,dollar_c2,dollar_c1)) ),
file('LAT327+1.p',unknown),
[] ).
cnf(26,axiom,
( v3_struct_0(A)
| ~ v6_lattices(A)
| ~ v8_lattices(A)
| ~ v9_lattices(A)
| ~ l3_lattices(A)
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(A))
| r3_lattices(A,B,B) ),
file('LAT327+1.p',unknown),
[] ).
cnf(27,plain,
( v3_struct_0(A)
| ~ v6_lattices(A)
| ~ v8_lattices(A)
| ~ v9_lattices(A)
| ~ l3_lattices(A)
| ~ m1_subset_1(B,u1_struct_0(A))
| r3_lattices(A,B,B) ),
inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[26])]),
[iquote('copy,26,factor_simp')] ).
cnf(36,axiom,
( ~ l3_lattices(A)
| v3_struct_0(A)
| ~ v10_lattices(A)
| v6_lattices(A) ),
file('LAT327+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ l3_lattices(A)
| v3_struct_0(A)
| ~ v10_lattices(A)
| v8_lattices(A) ),
file('LAT327+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ l3_lattices(A)
| v3_struct_0(A)
| ~ v10_lattices(A)
| v9_lattices(A) ),
file('LAT327+1.p',unknown),
[] ).
cnf(44,axiom,
( v3_struct_0(A)
| ~ v10_lattices(A)
| ~ l3_lattices(A)
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ m1_subset_1(D,u1_struct_0(A))
| ~ r3_lattices(A,B,C)
| r2_hidden(D,k22_filter_2(A,B,C))
| ~ r3_lattices(A,B,D)
| ~ r3_lattices(A,D,C) ),
file('LAT327+1.p',unknown),
[] ).
cnf(55,plain,
( v3_struct_0(A)
| ~ v10_lattices(A)
| ~ l3_lattices(A)
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ r3_lattices(A,B,C)
| r2_hidden(B,k22_filter_2(A,B,C))
| ~ r3_lattices(A,B,B) ),
inference(factor_simp,[status(thm)],[inference(factor,[status(thm)],[44])]),
[iquote('factor,44.4.6,factor_simp')] ).
cnf(56,plain,
( v3_struct_0(A)
| ~ v10_lattices(A)
| ~ l3_lattices(A)
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ r3_lattices(A,B,C)
| r2_hidden(C,k22_filter_2(A,B,C))
| ~ r3_lattices(A,C,C) ),
inference(factor_simp,[status(thm)],[inference(factor,[status(thm)],[44])]),
[iquote('factor,44.5.6,factor_simp')] ).
cnf(59,axiom,
v10_lattices(dollar_c3),
file('LAT327+1.p',unknown),
[] ).
cnf(60,axiom,
l3_lattices(dollar_c3),
file('LAT327+1.p',unknown),
[] ).
cnf(61,axiom,
m1_subset_1(dollar_c2,u1_struct_0(dollar_c3)),
file('LAT327+1.p',unknown),
[] ).
cnf(62,axiom,
m1_subset_1(dollar_c1,u1_struct_0(dollar_c3)),
file('LAT327+1.p',unknown),
[] ).
cnf(63,axiom,
r3_lattices(dollar_c3,dollar_c2,dollar_c1),
file('LAT327+1.p',unknown),
[] ).
cnf(78,plain,
v9_lattices(dollar_c3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[60,39,59]),1]),
[iquote('hyper,60,39,59,unit_del,1')] ).
cnf(79,plain,
v8_lattices(dollar_c3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[60,38,59]),1]),
[iquote('hyper,60,38,59,unit_del,1')] ).
cnf(81,plain,
v6_lattices(dollar_c3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[60,36,59]),1]),
[iquote('hyper,60,36,59,unit_del,1')] ).
cnf(139,plain,
r3_lattices(dollar_c3,dollar_c1,dollar_c1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[81,27,79,78,60,62]),1]),
[iquote('hyper,81,27,79,78,60,62,unit_del,1')] ).
cnf(140,plain,
r3_lattices(dollar_c3,dollar_c2,dollar_c2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[81,27,79,78,60,61]),1]),
[iquote('hyper,81,27,79,78,60,61,unit_del,1')] ).
cnf(227,plain,
r2_hidden(dollar_c1,k22_filter_2(dollar_c3,dollar_c2,dollar_c1)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[139,56,59,60,61,62,63]),1]),
[iquote('hyper,139,56,59,60,61,62,63,unit_del,1')] ).
cnf(233,plain,
r2_hidden(dollar_c2,k22_filter_2(dollar_c3,dollar_c2,dollar_c1)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[140,55,59,60,61,62,63]),1]),
[iquote('hyper,140,55,59,60,61,62,63,unit_del,1')] ).
cnf(797,plain,
$false,
inference(hyper,[status(thm)],[233,2,227]),
[iquote('hyper,233,2,227')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LAT327+1 : TPTP v8.1.0. Released v3.4.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n013.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 08:16:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.08/2.27 ----- Otter 3.3f, August 2004 -----
% 2.08/2.27 The process was started by sandbox on n013.cluster.edu,
% 2.08/2.27 Wed Jul 27 08:16:15 2022
% 2.08/2.27 The command was "./otter". The process ID is 2053.
% 2.08/2.27
% 2.08/2.27 set(prolog_style_variables).
% 2.08/2.27 set(auto).
% 2.08/2.27 dependent: set(auto1).
% 2.08/2.27 dependent: set(process_input).
% 2.08/2.27 dependent: clear(print_kept).
% 2.08/2.27 dependent: clear(print_new_demod).
% 2.08/2.27 dependent: clear(print_back_demod).
% 2.08/2.27 dependent: clear(print_back_sub).
% 2.08/2.27 dependent: set(control_memory).
% 2.08/2.27 dependent: assign(max_mem, 12000).
% 2.08/2.27 dependent: assign(pick_given_ratio, 4).
% 2.08/2.27 dependent: assign(stats_level, 1).
% 2.08/2.27 dependent: assign(max_seconds, 10800).
% 2.08/2.27 clear(print_given).
% 2.08/2.27
% 2.08/2.27 formula_list(usable).
% 2.08/2.27 all A (A=A).
% 2.08/2.27 -(all A (-v3_struct_0(A)&v10_lattices(A)&l3_lattices(A)-> (all B (m1_subset_1(B,u1_struct_0(A))-> (all C (m1_subset_1(C,u1_struct_0(A))-> (r3_lattices(A,B,C)->r2_hidden(B,k22_filter_2(A,B,C))&r2_hidden(C,k22_filter_2(A,B,C))))))))).
% 2.08/2.27 all A B r1_tarski(A,A).
% 2.08/2.27 $T.
% 2.08/2.27 $T.
% 2.08/2.27 all A (-v1_xboole_0(k1_zfmisc_1(A))).
% 2.08/2.27 v1_xboole_0(k1_xboole_0).
% 2.08/2.27 all A (-v1_xboole_0(A)-> (exists B (m1_subset_1(B,k1_zfmisc_1(A))& -v1_xboole_0(B)))).
% 2.08/2.27 all A exists B (m1_subset_1(B,k1_zfmisc_1(A))&v1_xboole_0(B)).
% 2.08/2.27 all A (-v3_struct_0(A)&l1_struct_0(A)-> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))& -v1_xboole_0(B)))).
% 2.08/2.27 all A B (m1_subset_1(A,k1_zfmisc_1(B))<->r1_tarski(A,B)).
% 2.08/2.27 all A B C (r2_hidden(A,B)&m1_subset_1(B,k1_zfmisc_1(C))->m1_subset_1(A,C)).
% 2.08/2.27 all A B C (-(r2_hidden(A,B)&m1_subset_1(B,k1_zfmisc_1(C))&v1_xboole_0(C))).
% 2.08/2.27 all A B (-(v1_xboole_0(A)&A!=B&v1_xboole_0(B))).
% 2.08/2.27 exists A l1_lattices(A).
% 2.08/2.27 exists A l1_struct_0(A).
% 2.08/2.27 exists A l2_lattices(A).
% 2.08/2.27 all A (-v3_struct_0(A)&v10_lattices(A)&l3_lattices(A)-> (exists B m2_lattice4(B,A))).
% 2.08/2.27 all A (l1_lattices(A)->l1_struct_0(A)).
% 2.08/2.27 $T.
% 2.08/2.27 all A (l2_lattices(A)->l1_struct_0(A)).
% 2.08/2.27 all A (-v3_struct_0(A)&v10_lattices(A)&l3_lattices(A)-> (all B (m2_lattice4(B,A)->m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))))).
% 2.08/2.27 all A (v1_xboole_0(A)->v1_funct_1(A)).
% 2.08/2.27 all A (l3_lattices(A)-> (-v3_struct_0(A)&v4_lattices(A)&v5_lattices(A)&v6_lattices(A)&v7_lattices(A)&v8_lattices(A)&v9_lattices(A)-> -v3_struct_0(A)&v10_lattices(A))).
% 2.08/2.27 all A (-v3_struct_0(A)&l1_struct_0(A)-> -v1_xboole_0(u1_struct_0(A))).
% 2.08/2.27 all A (-v3_struct_0(A)&v10_lattices(A)&l3_lattices(A)-> (exists B (m2_lattice4(B,A)& -v1_xboole_0(B)))).
% 2.08/2.27 exists A v1_xboole_0(A).
% 2.08/2.27 exists A (-v1_xboole_0(A)).
% 2.08/2.27 exists A (l1_struct_0(A)& -v3_struct_0(A)).
% 2.08/2.27 all A B (m1_subset_1(A,B)->v1_xboole_0(B)|r2_hidden(A,B)).
% 2.08/2.27 all A (v1_xboole_0(A)->A=k1_xboole_0).
% 2.08/2.27 all A B (r2_hidden(A,B)-> -r2_hidden(B,A)).
% 2.08/2.27 all A B C (-v3_struct_0(A)&v6_lattices(A)&v8_lattices(A)&v9_lattices(A)&l3_lattices(A)&m1_subset_1(B,u1_struct_0(A))&m1_subset_1(C,u1_struct_0(A))->r3_lattices(A,B,B)).
% 2.08/2.27 exists A l3_lattices(A).
% 2.08/2.27 all A exists B m1_subset_1(B,A).
% 2.08/2.27 all A B C (-v3_struct_0(A)&v6_lattices(A)&v8_lattices(A)&v9_lattices(A)&l3_lattices(A)&m1_subset_1(B,u1_struct_0(A))&m1_subset_1(C,u1_struct_0(A))-> (r3_lattices(A,B,C)<->r1_lattices(A,B,C))).
% 2.08/2.27 all A B C (-v3_struct_0(A)&v10_lattices(A)&l3_lattices(A)&m1_subset_1(B,u1_struct_0(A))&m1_subset_1(C,u1_struct_0(A))-> -v1_xboole_0(k22_filter_2(A,B,C))&m2_lattice4(k22_filter_2(A,B,C),A)).
% 2.08/2.27 all A (l3_lattices(A)->l1_lattices(A)&l2_lattices(A)).
% 2.08/2.27 $T.
% 2.08/2.27 $T.
% 2.08/2.27 all A (l3_lattices(A)-> (-v3_struct_0(A)&v10_lattices(A)-> -v3_struct_0(A)&v4_lattices(A)&v5_lattices(A)&v6_lattices(A)&v7_lattices(A)&v8_lattices(A)&v9_lattices(A))).
% 2.08/2.27 all A B (r2_hidden(A,B)->m1_subset_1(A,B)).
% 2.08/2.27 all A B (-(r2_hidden(A,B)&v1_xboole_0(B))).
% 2.08/2.27 all A (-v3_struct_0(A)&v10_lattices(A)&l3_lattices(A)-> (all B (m1_subset_1(B,u1_struct_0(A))-> (all C (m1_subset_1(C,u1_struct_0(A))-> (all D (m1_subset_1(D,u1_struct_0(A))-> (r3_lattices(A,B,C)-> (r2_hidden(D,k22_filter_2(A,B,C))<->r3_lattices(A,B,D)&r3_lattices(A,D,C)))))))))).
% 2.08/2.27 end_of_list.
% 2.08/2.27
% 2.08/2.27 -------> usable clausifies to:
% 2.08/2.27
% 2.08/2.27 list(usable).
% 2.08/2.27 0 [] A=A.
% 2.08/2.27 0 [] -v3_struct_0($c3).
% 2.08/2.27 0 [] v10_lattices($c3).
% 2.08/2.27 0 [] l3_lattices($c3).
% 2.08/2.27 0 [] m1_subset_1($c2,u1_struct_0($c3)).
% 2.08/2.27 0 [] m1_subset_1($c1,u1_struct_0($c3)).
% 2.08/2.27 0 [] r3_lattices($c3,$c2,$c1).
% 2.08/2.27 0 [] -r2_hidden($c2,k22_filter_2($c3,$c2,$c1))| -r2_hidden($c1,k22_filter_2($c3,$c2,$c1)).
% 2.08/2.27 0 [] r1_tarski(A,A).
% 2.08/2.27 0 [] $T.
% 2.08/2.27 0 [] $T.
% 2.08/2.27 0 [] -v1_xboole_0(k1_zfmisc_1(A)).
% 2.08/2.27 0 [] v1_xboole_0(k1_xboole_0).
% 2.08/2.27 0 [] v1_xboole_0(A)|m1_subset_1($f1(A),k1_zfmisc_1(A)).
% 2.08/2.27 0 [] v1_xboole_0(A)| -v1_xboole_0($f1(A)).
% 2.08/2.27 0 [] m1_subset_1($f2(A),k1_zfmisc_1(A)).
% 2.08/2.27 0 [] v1_xboole_0($f2(A)).
% 2.08/2.27 0 [] v3_struct_0(A)| -l1_struct_0(A)|m1_subset_1($f3(A),k1_zfmisc_1(u1_struct_0(A))).
% 2.08/2.27 0 [] v3_struct_0(A)| -l1_struct_0(A)| -v1_xboole_0($f3(A)).
% 2.08/2.27 0 [] -m1_subset_1(A,k1_zfmisc_1(B))|r1_tarski(A,B).
% 2.08/2.27 0 [] m1_subset_1(A,k1_zfmisc_1(B))| -r1_tarski(A,B).
% 2.08/2.27 0 [] -r2_hidden(A,B)| -m1_subset_1(B,k1_zfmisc_1(C))|m1_subset_1(A,C).
% 2.08/2.27 0 [] -r2_hidden(A,B)| -m1_subset_1(B,k1_zfmisc_1(C))| -v1_xboole_0(C).
% 2.08/2.27 0 [] -v1_xboole_0(A)|A=B| -v1_xboole_0(B).
% 2.08/2.27 0 [] l1_lattices($c4).
% 2.08/2.27 0 [] l1_struct_0($c5).
% 2.08/2.27 0 [] l2_lattices($c6).
% 2.08/2.27 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)|m2_lattice4($f4(A),A).
% 2.08/2.27 0 [] -l1_lattices(A)|l1_struct_0(A).
% 2.08/2.27 0 [] $T.
% 2.08/2.27 0 [] -l2_lattices(A)|l1_struct_0(A).
% 2.08/2.27 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -m2_lattice4(B,A)|m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))).
% 2.08/2.27 0 [] -v1_xboole_0(A)|v1_funct_1(A).
% 2.08/2.27 0 [] -l3_lattices(A)|v3_struct_0(A)| -v4_lattices(A)| -v5_lattices(A)| -v6_lattices(A)| -v7_lattices(A)| -v8_lattices(A)| -v9_lattices(A)|v10_lattices(A).
% 2.08/2.27 0 [] v3_struct_0(A)| -l1_struct_0(A)| -v1_xboole_0(u1_struct_0(A)).
% 2.08/2.27 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)|m2_lattice4($f5(A),A).
% 2.08/2.27 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -v1_xboole_0($f5(A)).
% 2.08/2.27 0 [] v1_xboole_0($c7).
% 2.08/2.27 0 [] -v1_xboole_0($c8).
% 2.08/2.27 0 [] l1_struct_0($c9).
% 2.08/2.27 0 [] -v3_struct_0($c9).
% 2.08/2.27 0 [] -m1_subset_1(A,B)|v1_xboole_0(B)|r2_hidden(A,B).
% 2.08/2.27 0 [] -v1_xboole_0(A)|A=k1_xboole_0.
% 2.08/2.27 0 [] -r2_hidden(A,B)| -r2_hidden(B,A).
% 2.08/2.27 0 [] v3_struct_0(A)| -v6_lattices(A)| -v8_lattices(A)| -v9_lattices(A)| -l3_lattices(A)| -m1_subset_1(B,u1_struct_0(A))| -m1_subset_1(C,u1_struct_0(A))|r3_lattices(A,B,B).
% 2.08/2.27 0 [] l3_lattices($c10).
% 2.08/2.27 0 [] m1_subset_1($f6(A),A).
% 2.08/2.27 0 [] v3_struct_0(A)| -v6_lattices(A)| -v8_lattices(A)| -v9_lattices(A)| -l3_lattices(A)| -m1_subset_1(B,u1_struct_0(A))| -m1_subset_1(C,u1_struct_0(A))| -r3_lattices(A,B,C)|r1_lattices(A,B,C).
% 2.08/2.27 0 [] v3_struct_0(A)| -v6_lattices(A)| -v8_lattices(A)| -v9_lattices(A)| -l3_lattices(A)| -m1_subset_1(B,u1_struct_0(A))| -m1_subset_1(C,u1_struct_0(A))|r3_lattices(A,B,C)| -r1_lattices(A,B,C).
% 2.08/2.27 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -m1_subset_1(B,u1_struct_0(A))| -m1_subset_1(C,u1_struct_0(A))| -v1_xboole_0(k22_filter_2(A,B,C)).
% 2.08/2.27 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -m1_subset_1(B,u1_struct_0(A))| -m1_subset_1(C,u1_struct_0(A))|m2_lattice4(k22_filter_2(A,B,C),A).
% 2.08/2.27 0 [] -l3_lattices(A)|l1_lattices(A).
% 2.08/2.27 0 [] -l3_lattices(A)|l2_lattices(A).
% 2.08/2.27 0 [] $T.
% 2.08/2.27 0 [] $T.
% 2.08/2.27 0 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v4_lattices(A).
% 2.08/2.27 0 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v5_lattices(A).
% 2.08/2.27 0 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v6_lattices(A).
% 2.08/2.27 0 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v7_lattices(A).
% 2.08/2.27 0 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v8_lattices(A).
% 2.08/2.27 0 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v9_lattices(A).
% 2.08/2.27 0 [] -r2_hidden(A,B)|m1_subset_1(A,B).
% 2.08/2.27 0 [] -r2_hidden(A,B)| -v1_xboole_0(B).
% 2.08/2.27 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -m1_subset_1(B,u1_struct_0(A))| -m1_subset_1(C,u1_struct_0(A))| -m1_subset_1(D,u1_struct_0(A))| -r3_lattices(A,B,C)| -r2_hidden(D,k22_filter_2(A,B,C))|r3_lattices(A,B,D).
% 2.08/2.27 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -m1_subset_1(B,u1_struct_0(A))| -m1_subset_1(C,u1_struct_0(A))| -m1_subset_1(D,u1_struct_0(A))| -r3_lattices(A,B,C)| -r2_hidden(D,k22_filter_2(A,B,C))|r3_lattices(A,D,C).
% 2.08/2.27 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -m1_subset_1(B,u1_struct_0(A))| -m1_subset_1(C,u1_struct_0(A))| -m1_subset_1(D,u1_struct_0(A))| -r3_lattices(A,B,C)|r2_hidden(D,k22_filter_2(A,B,C))| -r3_lattices(A,B,D)| -r3_lattices(A,D,C).
% 2.08/2.27 end_of_list.
% 2.08/2.27
% 2.08/2.27 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=10.
% 2.08/2.27
% 2.08/2.27 This ia a non-Horn set with equality. The strategy will be
% 2.08/2.27 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.08/2.27 deletion, with positive clauses in sos and nonpositive
% 2.08/2.28 clauses in usable.
% 2.08/2.28
% 2.08/2.28 dependent: set(knuth_bendix).
% 2.08/2.28 dependent: set(anl_eq).
% 2.08/2.28 dependent: set(para_from).
% 2.08/2.28 dependent: set(para_into).
% 2.08/2.28 dependent: clear(para_from_right).
% 2.08/2.28 dependent: clear(para_into_right).
% 2.08/2.28 dependent: set(para_from_vars).
% 2.08/2.28 dependent: set(eq_units_both_ways).
% 2.08/2.28 dependent: set(dynamic_demod_all).
% 2.08/2.28 dependent: set(dynamic_demod).
% 2.08/2.28 dependent: set(order_eq).
% 2.08/2.28 dependent: set(back_demod).
% 2.08/2.28 dependent: set(lrpo).
% 2.08/2.28 dependent: set(hyper_res).
% 2.08/2.28 dependent: set(unit_deletion).
% 2.08/2.28 dependent: set(factor).
% 2.08/2.28
% 2.08/2.28 ------------> process usable:
% 2.08/2.28 ** KEPT (pick-wt=2): 1 [] -v3_struct_0($c3).
% 2.08/2.28 ** KEPT (pick-wt=12): 2 [] -r2_hidden($c2,k22_filter_2($c3,$c2,$c1))| -r2_hidden($c1,k22_filter_2($c3,$c2,$c1)).
% 2.08/2.28 ** KEPT (pick-wt=3): 3 [] -v1_xboole_0(k1_zfmisc_1(A)).
% 2.08/2.28 ** KEPT (pick-wt=5): 4 [] v1_xboole_0(A)| -v1_xboole_0($f1(A)).
% 2.08/2.28 ** KEPT (pick-wt=10): 5 [] v3_struct_0(A)| -l1_struct_0(A)|m1_subset_1($f3(A),k1_zfmisc_1(u1_struct_0(A))).
% 2.08/2.28 ** KEPT (pick-wt=7): 6 [] v3_struct_0(A)| -l1_struct_0(A)| -v1_xboole_0($f3(A)).
% 2.08/2.28 ** KEPT (pick-wt=7): 7 [] -m1_subset_1(A,k1_zfmisc_1(B))|r1_tarski(A,B).
% 2.08/2.28 ** KEPT (pick-wt=7): 8 [] m1_subset_1(A,k1_zfmisc_1(B))| -r1_tarski(A,B).
% 2.08/2.28 ** KEPT (pick-wt=10): 9 [] -r2_hidden(A,B)| -m1_subset_1(B,k1_zfmisc_1(C))|m1_subset_1(A,C).
% 2.08/2.28 ** KEPT (pick-wt=9): 10 [] -r2_hidden(A,B)| -m1_subset_1(B,k1_zfmisc_1(C))| -v1_xboole_0(C).
% 2.08/2.28 ** KEPT (pick-wt=7): 11 [] -v1_xboole_0(A)|A=B| -v1_xboole_0(B).
% 2.08/2.28 ** KEPT (pick-wt=10): 12 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)|m2_lattice4($f4(A),A).
% 2.08/2.28 ** KEPT (pick-wt=4): 13 [] -l1_lattices(A)|l1_struct_0(A).
% 2.08/2.28 ** KEPT (pick-wt=4): 14 [] -l2_lattices(A)|l1_struct_0(A).
% 2.08/2.28 ** KEPT (pick-wt=14): 15 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -m2_lattice4(B,A)|m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))).
% 2.08/2.28 ** KEPT (pick-wt=4): 16 [] -v1_xboole_0(A)|v1_funct_1(A).
% 2.08/2.28 ** KEPT (pick-wt=18): 17 [] -l3_lattices(A)|v3_struct_0(A)| -v4_lattices(A)| -v5_lattices(A)| -v6_lattices(A)| -v7_lattices(A)| -v8_lattices(A)| -v9_lattices(A)|v10_lattices(A).
% 2.08/2.28 ** KEPT (pick-wt=7): 18 [] v3_struct_0(A)| -l1_struct_0(A)| -v1_xboole_0(u1_struct_0(A)).
% 2.08/2.28 ** KEPT (pick-wt=10): 19 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)|m2_lattice4($f5(A),A).
% 2.08/2.28 ** KEPT (pick-wt=9): 20 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -v1_xboole_0($f5(A)).
% 2.08/2.28 ** KEPT (pick-wt=2): 21 [] -v1_xboole_0($c8).
% 2.08/2.28 ** KEPT (pick-wt=2): 22 [] -v3_struct_0($c9).
% 2.08/2.28 ** KEPT (pick-wt=8): 23 [] -m1_subset_1(A,B)|v1_xboole_0(B)|r2_hidden(A,B).
% 2.08/2.28 ** KEPT (pick-wt=5): 24 [] -v1_xboole_0(A)|A=k1_xboole_0.
% 2.08/2.28 ** KEPT (pick-wt=6): 25 [] -r2_hidden(A,B)| -r2_hidden(B,A).
% 2.08/2.28 ** KEPT (pick-wt=18): 27 [copy,26,factor_simp] v3_struct_0(A)| -v6_lattices(A)| -v8_lattices(A)| -v9_lattices(A)| -l3_lattices(A)| -m1_subset_1(B,u1_struct_0(A))|r3_lattices(A,B,B).
% 2.08/2.28 ** KEPT (pick-wt=26): 28 [] v3_struct_0(A)| -v6_lattices(A)| -v8_lattices(A)| -v9_lattices(A)| -l3_lattices(A)| -m1_subset_1(B,u1_struct_0(A))| -m1_subset_1(C,u1_struct_0(A))| -r3_lattices(A,B,C)|r1_lattices(A,B,C).
% 2.08/2.28 ** KEPT (pick-wt=26): 29 [] v3_struct_0(A)| -v6_lattices(A)| -v8_lattices(A)| -v9_lattices(A)| -l3_lattices(A)| -m1_subset_1(B,u1_struct_0(A))| -m1_subset_1(C,u1_struct_0(A))|r3_lattices(A,B,C)| -r1_lattices(A,B,C).
% 2.08/2.28 ** KEPT (pick-wt=19): 30 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -m1_subset_1(B,u1_struct_0(A))| -m1_subset_1(C,u1_struct_0(A))| -v1_xboole_0(k22_filter_2(A,B,C)).
% 2.08/2.28 ** KEPT (pick-wt=20): 31 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -m1_subset_1(B,u1_struct_0(A))| -m1_subset_1(C,u1_struct_0(A))|m2_lattice4(k22_filter_2(A,B,C),A).
% 2.08/2.28 ** KEPT (pick-wt=4): 32 [] -l3_lattices(A)|l1_lattices(A).
% 2.08/2.28 ** KEPT (pick-wt=4): 33 [] -l3_lattices(A)|l2_lattices(A).
% 2.08/2.28 ** KEPT (pick-wt=8): 34 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v4_lattices(A).
% 2.08/2.28 ** KEPT (pick-wt=8): 35 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v5_lattices(A).
% 2.08/2.28 ** KEPT (pick-wt=8): 36 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v6_lattices(A).
% 2.08/2.28 ** KEPT (pick-wt=8): 37 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v7_lattices(A).
% 2.16/2.32 ** KEPT (pick-wt=8): 38 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v8_lattices(A).
% 2.16/2.32 ** KEPT (pick-wt=8): 39 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v9_lattices(A).
% 2.16/2.32 ** KEPT (pick-wt=6): 40 [] -r2_hidden(A,B)|m1_subset_1(A,B).
% 2.16/2.32 ** KEPT (pick-wt=5): 41 [] -r2_hidden(A,B)| -v1_xboole_0(B).
% 2.16/2.32 ** KEPT (pick-wt=32): 42 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -m1_subset_1(B,u1_struct_0(A))| -m1_subset_1(C,u1_struct_0(A))| -m1_subset_1(D,u1_struct_0(A))| -r3_lattices(A,B,C)| -r2_hidden(D,k22_filter_2(A,B,C))|r3_lattices(A,B,D).
% 2.16/2.32 ** KEPT (pick-wt=32): 43 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -m1_subset_1(B,u1_struct_0(A))| -m1_subset_1(C,u1_struct_0(A))| -m1_subset_1(D,u1_struct_0(A))| -r3_lattices(A,B,C)| -r2_hidden(D,k22_filter_2(A,B,C))|r3_lattices(A,D,C).
% 2.16/2.32 ** KEPT (pick-wt=36): 44 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -m1_subset_1(B,u1_struct_0(A))| -m1_subset_1(C,u1_struct_0(A))| -m1_subset_1(D,u1_struct_0(A))| -r3_lattices(A,B,C)|r2_hidden(D,k22_filter_2(A,B,C))| -r3_lattices(A,B,D)| -r3_lattices(A,D,C).
% 2.16/2.32
% 2.16/2.32 ------------> process sos:
% 2.16/2.32 ** KEPT (pick-wt=3): 58 [] A=A.
% 2.16/2.32 ** KEPT (pick-wt=2): 59 [] v10_lattices($c3).
% 2.16/2.32 ** KEPT (pick-wt=2): 60 [] l3_lattices($c3).
% 2.16/2.32 ** KEPT (pick-wt=4): 61 [] m1_subset_1($c2,u1_struct_0($c3)).
% 2.16/2.32 ** KEPT (pick-wt=4): 62 [] m1_subset_1($c1,u1_struct_0($c3)).
% 2.16/2.32 ** KEPT (pick-wt=4): 63 [] r3_lattices($c3,$c2,$c1).
% 2.16/2.32 ** KEPT (pick-wt=3): 64 [] r1_tarski(A,A).
% 2.16/2.32 ** KEPT (pick-wt=2): 65 [] v1_xboole_0(k1_xboole_0).
% 2.16/2.32 ** KEPT (pick-wt=7): 66 [] v1_xboole_0(A)|m1_subset_1($f1(A),k1_zfmisc_1(A)).
% 2.16/2.32 ** KEPT (pick-wt=5): 67 [] m1_subset_1($f2(A),k1_zfmisc_1(A)).
% 2.16/2.32 ** KEPT (pick-wt=3): 68 [] v1_xboole_0($f2(A)).
% 2.16/2.32 ** KEPT (pick-wt=2): 69 [] l1_lattices($c4).
% 2.16/2.32 ** KEPT (pick-wt=2): 70 [] l1_struct_0($c5).
% 2.16/2.32 ** KEPT (pick-wt=2): 71 [] l2_lattices($c6).
% 2.16/2.32 ** KEPT (pick-wt=2): 72 [] v1_xboole_0($c7).
% 2.16/2.32 ** KEPT (pick-wt=2): 73 [] l1_struct_0($c9).
% 2.16/2.32 ** KEPT (pick-wt=2): 74 [] l3_lattices($c10).
% 2.16/2.32 ** KEPT (pick-wt=4): 75 [] m1_subset_1($f6(A),A).
% 2.16/2.32 Following clause subsumed by 58 during input processing: 0 [copy,58,flip.1] A=A.
% 2.16/2.32 58 back subsumes 45.
% 2.16/2.32
% 2.16/2.32 ======= end of input processing =======
% 2.16/2.32
% 2.16/2.32 =========== start of search ===========
% 2.16/2.32
% 2.16/2.32 -------- PROOF --------
% 2.16/2.32
% 2.16/2.32 -----> EMPTY CLAUSE at 0.05 sec ----> 797 [hyper,233,2,227] $F.
% 2.16/2.32
% 2.16/2.32 Length of proof is 10. Level of proof is 3.
% 2.16/2.32
% 2.16/2.32 ---------------- PROOF ----------------
% 2.16/2.32 % SZS status Theorem
% 2.16/2.32 % SZS output start Refutation
% See solution above
% 2.16/2.32 ------------ end of proof -------------
% 2.16/2.32
% 2.16/2.32
% 2.16/2.32 Search stopped by max_proofs option.
% 2.16/2.32
% 2.16/2.32
% 2.16/2.32 Search stopped by max_proofs option.
% 2.16/2.32
% 2.16/2.32 ============ end of search ============
% 2.16/2.32
% 2.16/2.32 -------------- statistics -------------
% 2.16/2.32 clauses given 133
% 2.16/2.32 clauses generated 1583
% 2.16/2.32 clauses kept 793
% 2.16/2.32 clauses forward subsumed 857
% 2.16/2.32 clauses back subsumed 28
% 2.16/2.32 Kbytes malloced 2929
% 2.16/2.32
% 2.16/2.32 ----------- times (seconds) -----------
% 2.16/2.32 user CPU time 0.05 (0 hr, 0 min, 0 sec)
% 2.16/2.32 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.16/2.32 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.16/2.32
% 2.16/2.32 That finishes the proof of the theorem.
% 2.16/2.32
% 2.16/2.32 Process 2053 finished Wed Jul 27 08:16:17 2022
% 2.16/2.32 Otter interrupted
% 2.16/2.32 PROOF FOUND
%------------------------------------------------------------------------------