TSTP Solution File: LAT313+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LAT313+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 13:02:37 EDT 2022
% Result : Theorem 10.76s 11.00s
% Output : Refutation 10.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 23
% Syntax : Number of clauses : 43 ( 22 unt; 13 nHn; 37 RR)
% Number of literals : 91 ( 10 equ; 40 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ v3_struct_0(dollar_c2),
file('LAT313+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ r1_filter_2(u1_struct_0(dollar_c2),dollar_c1,k17_filter_2(dollar_c2))
| dollar_c1 != u1_struct_0(dollar_c2) ),
file('LAT313+1.p',unknown),
[] ).
cnf(3,plain,
( ~ r1_filter_2(u1_struct_0(dollar_c2),dollar_c1,k17_filter_2(dollar_c2))
| u1_struct_0(dollar_c2) != dollar_c1 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[2])]),
[iquote('copy,2,flip.2')] ).
cnf(13,axiom,
( v3_struct_0(A)
| ~ v10_lattices(A)
| ~ l3_lattices(A)
| k17_filter_2(A) = u1_struct_0(A) ),
file('LAT313+1.p',unknown),
[] ).
cnf(14,plain,
( v3_struct_0(A)
| ~ v10_lattices(A)
| ~ l3_lattices(A)
| u1_struct_0(A) = k17_filter_2(A) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.4')] ).
cnf(19,axiom,
( ~ l2_lattices(A)
| l1_struct_0(A) ),
file('LAT313+1.p',unknown),
[] ).
cnf(21,axiom,
( ~ l3_lattices(A)
| l2_lattices(A) ),
file('LAT313+1.p',unknown),
[] ).
cnf(23,axiom,
( v3_struct_0(A)
| ~ v10_lattices(A)
| ~ l3_lattices(A)
| ~ m2_filter_2(B,A)
| m2_lattice4(B,A) ),
file('LAT313+1.p',unknown),
[] ).
cnf(24,axiom,
( 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))) ),
file('LAT313+1.p',unknown),
[] ).
cnf(27,axiom,
( v3_struct_0(A)
| ~ l1_struct_0(A)
| ~ v1_xboole_0(u1_struct_0(A)) ),
file('LAT313+1.p',unknown),
[] ).
cnf(36,axiom,
( v1_xboole_0(A)
| ~ m1_subset_1(B,k1_zfmisc_1(A))
| ~ m1_subset_1(C,k1_zfmisc_1(A))
| ~ r1_filter_2(A,B,C)
| B = C ),
file('LAT313+1.p',unknown),
[] ).
cnf(38,axiom,
( v1_xboole_0(A)
| ~ m1_subset_1(B,k1_zfmisc_1(A))
| ~ m1_subset_1(C,k1_zfmisc_1(A))
| r1_filter_2(A,B,B) ),
file('LAT313+1.p',unknown),
[] ).
cnf(39,plain,
( v1_xboole_0(A)
| ~ m1_subset_1(B,k1_zfmisc_1(A))
| r1_filter_2(A,B,B) ),
inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[38])]),
[iquote('copy,38,factor_simp')] ).
cnf(42,axiom,
( ~ m1_subset_1(A,B)
| v1_xboole_0(B)
| r2_hidden(A,B) ),
file('LAT313+1.p',unknown),
[] ).
cnf(43,axiom,
( v3_struct_0(A)
| ~ v10_lattices(A)
| ~ l3_lattices(A)
| ~ m2_filter_2(B,A)
| r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),B) ),
file('LAT313+1.p',unknown),
[] ).
cnf(45,axiom,
( m1_subset_1(A,k1_zfmisc_1(B))
| ~ r1_tarski(A,B) ),
file('LAT313+1.p',unknown),
[] ).
cnf(47,axiom,
( v3_struct_0(A)
| ~ v10_lattices(A)
| ~ l3_lattices(A)
| v1_xboole_0(B)
| ~ m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
| ~ v14_lattices(A)
| ~ r2_hidden(k6_lattices(A),B)
| k19_filter_2(A,B) = u1_struct_0(A) ),
file('LAT313+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ r2_hidden(A,B)
| ~ v1_xboole_0(B) ),
file('LAT313+1.p',unknown),
[] ).
cnf(56,axiom,
A = A,
file('LAT313+1.p',unknown),
[] ).
cnf(57,axiom,
v10_lattices(dollar_c2),
file('LAT313+1.p',unknown),
[] ).
cnf(58,axiom,
l3_lattices(dollar_c2),
file('LAT313+1.p',unknown),
[] ).
cnf(59,axiom,
m2_filter_2(dollar_c1,dollar_c2),
file('LAT313+1.p',unknown),
[] ).
cnf(60,axiom,
v14_lattices(dollar_c2),
file('LAT313+1.p',unknown),
[] ).
cnf(61,axiom,
r2_hidden(k6_lattices(dollar_c2),dollar_c1),
file('LAT313+1.p',unknown),
[] ).
cnf(66,axiom,
m1_subset_1(dollar_f1(A),A),
file('LAT313+1.p',unknown),
[] ).
cnf(73,axiom,
r1_tarski(A,A),
file('LAT313+1.p',unknown),
[] ).
cnf(80,plain,
l2_lattices(dollar_c2),
inference(hyper,[status(thm)],[58,21]),
[iquote('hyper,58,21')] ).
cnf(84,plain,
u1_struct_0(dollar_c2) = k17_filter_2(dollar_c2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[58,14,57]),1]),
[iquote('hyper,58,14,57,unit_del,1')] ).
cnf(91,plain,
( ~ r1_filter_2(k17_filter_2(dollar_c2),dollar_c1,k17_filter_2(dollar_c2))
| k17_filter_2(dollar_c2) != dollar_c1 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),84,84]),
[iquote('back_demod,3,demod,84,84')] ).
cnf(102,plain,
r1_filter_2(k17_filter_2(dollar_c2),k19_filter_2(dollar_c2,dollar_c1),dollar_c1),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[59,43,57,58]),84]),1]),
[iquote('hyper,59,43,57,58,demod,84,unit_del,1')] ).
cnf(103,plain,
m2_lattice4(dollar_c1,dollar_c2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[59,23,57,58]),1]),
[iquote('hyper,59,23,57,58,unit_del,1')] ).
cnf(158,plain,
l1_struct_0(dollar_c2),
inference(hyper,[status(thm)],[80,19]),
[iquote('hyper,80,19')] ).
cnf(165,plain,
( v1_xboole_0(A)
| r2_hidden(dollar_f1(A),A) ),
inference(hyper,[status(thm)],[66,42]),
[iquote('hyper,66,42')] ).
cnf(240,plain,
m1_subset_1(A,k1_zfmisc_1(A)),
inference(hyper,[status(thm)],[73,45]),
[iquote('hyper,73,45')] ).
cnf(241,plain,
m1_subset_1(dollar_c1,k1_zfmisc_1(k17_filter_2(dollar_c2))),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[103,24,57,58]),84]),1]),
[iquote('hyper,103,24,57,58,demod,84,unit_del,1')] ).
cnf(314,plain,
~ v1_xboole_0(k17_filter_2(dollar_c2)),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[84,27]),1,158]),
[iquote('para_from,83.1.1,27.3.1,unit_del,1,158')] ).
cnf(353,plain,
( v1_xboole_0(A)
| r1_filter_2(A,A,A) ),
inference(hyper,[status(thm)],[240,39]),
[iquote('hyper,240,39')] ).
cnf(552,plain,
( r1_filter_2(k17_filter_2(dollar_c2),k17_filter_2(dollar_c2),dollar_c1)
| v1_xboole_0(dollar_c1) ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[102,47]),84,84]),1,57,58,241,60,61]),
[iquote('para_into,102.1.2,47.8.1,demod,84,84,unit_del,1,57,58,241,60,61')] ).
cnf(911,plain,
r2_hidden(dollar_f1(dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[165,51,61]),
[iquote('hyper,165,51,61')] ).
cnf(1740,plain,
r1_filter_2(dollar_c1,dollar_c1,dollar_c1),
inference(hyper,[status(thm)],[353,51,911]),
[iquote('hyper,353,51,911')] ).
cnf(2372,plain,
r1_filter_2(k17_filter_2(dollar_c2),k17_filter_2(dollar_c2),dollar_c1),
inference(hyper,[status(thm)],[552,51,911]),
[iquote('hyper,552,51,911')] ).
cnf(2375,plain,
k17_filter_2(dollar_c2) = dollar_c1,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[2372,36,240,241]),314]),
[iquote('hyper,2372,36,240,241,unit_del,314')] ).
cnf(2411,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[91]),2375,2375,2375]),1740,56]),
[iquote('back_demod,91,demod,2375,2375,2375,unit_del,1740,56')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT313+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 08:10:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.06/2.26 ----- Otter 3.3f, August 2004 -----
% 2.06/2.26 The process was started by sandbox on n013.cluster.edu,
% 2.06/2.26 Wed Jul 27 08:10:00 2022
% 2.06/2.26 The command was "./otter". The process ID is 25903.
% 2.06/2.26
% 2.06/2.26 set(prolog_style_variables).
% 2.06/2.26 set(auto).
% 2.06/2.26 dependent: set(auto1).
% 2.06/2.26 dependent: set(process_input).
% 2.06/2.26 dependent: clear(print_kept).
% 2.06/2.26 dependent: clear(print_new_demod).
% 2.06/2.26 dependent: clear(print_back_demod).
% 2.06/2.26 dependent: clear(print_back_sub).
% 2.06/2.26 dependent: set(control_memory).
% 2.06/2.26 dependent: assign(max_mem, 12000).
% 2.06/2.26 dependent: assign(pick_given_ratio, 4).
% 2.06/2.26 dependent: assign(stats_level, 1).
% 2.06/2.26 dependent: assign(max_seconds, 10800).
% 2.06/2.26 clear(print_given).
% 2.06/2.26
% 2.06/2.26 formula_list(usable).
% 2.06/2.26 all A (A=A).
% 2.06/2.26 -(all A (-v3_struct_0(A)&v10_lattices(A)&l3_lattices(A)-> (all B (m2_filter_2(B,A)-> (v14_lattices(A)&r2_hidden(k6_lattices(A),B)->r1_filter_2(u1_struct_0(A),B,k17_filter_2(A))&B=u1_struct_0(A)))))).
% 2.06/2.26 all A B (r2_hidden(A,B)-> -r2_hidden(B,A)).
% 2.06/2.26 all A (v1_xboole_0(A)->v1_funct_1(A)).
% 2.06/2.26 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))).
% 2.06/2.26 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))).
% 2.06/2.26 all A (-v3_struct_0(A)&v10_lattices(A)&l3_lattices(A)->k17_filter_2(A)=u1_struct_0(A)).
% 2.06/2.26 all A (-v3_struct_0(A)&v10_lattices(A)&l3_lattices(A)->m2_filter_2(k17_filter_2(A),A)).
% 2.06/2.26 all A B (-v3_struct_0(A)&v10_lattices(A)&l3_lattices(A)& -v1_xboole_0(B)&m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))->m2_filter_2(k19_filter_2(A,B),A)).
% 2.06/2.26 $T.
% 2.06/2.26 $T.
% 2.06/2.26 all A (-v3_struct_0(A)&l2_lattices(A)->m1_subset_1(k6_lattices(A),u1_struct_0(A))).
% 2.06/2.26 all A (l1_lattices(A)->l1_struct_0(A)).
% 2.06/2.26 $T.
% 2.06/2.26 all A (l2_lattices(A)->l1_struct_0(A)).
% 2.06/2.26 all A (l3_lattices(A)->l1_lattices(A)&l2_lattices(A)).
% 2.06/2.26 $T.
% 2.06/2.26 all A (-v3_struct_0(A)&v10_lattices(A)&l3_lattices(A)-> (all B (m2_filter_2(B,A)-> -v1_xboole_0(B)&m2_lattice4(B,A)))).
% 2.06/2.26 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)))))).
% 2.06/2.26 $T.
% 2.06/2.26 exists A l1_lattices(A).
% 2.06/2.26 exists A l1_struct_0(A).
% 2.06/2.26 exists A l2_lattices(A).
% 2.06/2.26 exists A l3_lattices(A).
% 2.06/2.26 all A exists B m1_subset_1(B,A).
% 2.06/2.26 all A (-v3_struct_0(A)&v10_lattices(A)&l3_lattices(A)-> (exists B m2_filter_2(B,A))).
% 2.06/2.26 all A (-v3_struct_0(A)&v10_lattices(A)&l3_lattices(A)-> (exists B m2_lattice4(B,A))).
% 2.06/2.26 all A (-v3_struct_0(A)&l1_struct_0(A)-> -v1_xboole_0(u1_struct_0(A))).
% 2.06/2.26 all A (-v1_xboole_0(k1_zfmisc_1(A))).
% 2.06/2.26 v1_xboole_0(k1_xboole_0).
% 2.06/2.26 all A (-v3_struct_0(A)&v10_lattices(A)&l3_lattices(A)-> (exists B (m2_lattice4(B,A)& -v1_xboole_0(B)))).
% 2.06/2.26 all A (-v1_xboole_0(A)-> (exists B (m1_subset_1(B,k1_zfmisc_1(A))& -v1_xboole_0(B)))).
% 2.06/2.26 exists A v1_xboole_0(A).
% 2.06/2.26 all A exists B (m1_subset_1(B,k1_zfmisc_1(A))&v1_xboole_0(B)).
% 2.06/2.26 exists A (-v1_xboole_0(A)).
% 2.06/2.26 exists A (l1_struct_0(A)& -v3_struct_0(A)).
% 2.06/2.26 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)))).
% 2.06/2.26 all A B C (-v1_xboole_0(A)&m1_subset_1(B,k1_zfmisc_1(A))&m1_subset_1(C,k1_zfmisc_1(A))-> (r1_filter_2(A,B,C)<->B=C)).
% 2.06/2.26 all A B C (-v1_xboole_0(A)&m1_subset_1(B,k1_zfmisc_1(A))&m1_subset_1(C,k1_zfmisc_1(A))->r1_filter_2(A,B,B)).
% 2.06/2.26 all A B r1_tarski(A,A).
% 2.06/2.26 all A B C (-v1_xboole_0(A)&m1_subset_1(B,k1_zfmisc_1(A))&m1_subset_1(C,k1_zfmisc_1(A))-> (r1_filter_2(A,B,C)->r1_filter_2(A,C,B))).
% 2.06/2.26 all A B (r2_hidden(A,B)->m1_subset_1(A,B)).
% 2.06/2.26 all A B (m1_subset_1(A,B)->v1_xboole_0(B)|r2_hidden(A,B)).
% 2.06/2.26 all A (-v3_struct_0(A)&v10_lattices(A)&l3_lattices(A)-> (all B (m2_filter_2(B,A)->r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),B)))).
% 2.06/2.26 all A B (m1_subset_1(A,k1_zfmisc_1(B))<->r1_tarski(A,B)).
% 2.06/2.26 all A (-v3_struct_0(A)&v10_lattices(A)&l3_lattices(A)-> (all B (-v1_xboole_0(B)&m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))-> (v14_lattices(A)&r2_hidden(k6_lattices(A),B)->r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),k17_filter_2(A))&k19_filter_2(A,B)=u1_struct_0(A))))).
% 2.06/2.26 all A B C (r2_hidden(A,B)&m1_subset_1(B,k1_zfmisc_1(C))->m1_subset_1(A,C)).
% 2.06/2.26 all A B C (-(r2_hidden(A,B)&m1_subset_1(B,k1_zfmisc_1(C))&v1_xboole_0(C))).
% 2.06/2.26 all A (v1_xboole_0(A)->A=k1_xboole_0).
% 2.06/2.26 all A B (-(r2_hidden(A,B)&v1_xboole_0(B))).
% 2.06/2.26 all A B (-(v1_xboole_0(A)&A!=B&v1_xboole_0(B))).
% 2.06/2.26 end_of_list.
% 2.06/2.26
% 2.06/2.26 -------> usable clausifies to:
% 2.06/2.26
% 2.06/2.26 list(usable).
% 2.06/2.26 0 [] A=A.
% 2.06/2.26 0 [] -v3_struct_0($c2).
% 2.06/2.26 0 [] v10_lattices($c2).
% 2.06/2.26 0 [] l3_lattices($c2).
% 2.06/2.26 0 [] m2_filter_2($c1,$c2).
% 2.06/2.26 0 [] v14_lattices($c2).
% 2.06/2.26 0 [] r2_hidden(k6_lattices($c2),$c1).
% 2.06/2.26 0 [] -r1_filter_2(u1_struct_0($c2),$c1,k17_filter_2($c2))|$c1!=u1_struct_0($c2).
% 2.06/2.26 0 [] -r2_hidden(A,B)| -r2_hidden(B,A).
% 2.06/2.26 0 [] -v1_xboole_0(A)|v1_funct_1(A).
% 2.06/2.26 0 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v4_lattices(A).
% 2.06/2.26 0 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v5_lattices(A).
% 2.06/2.26 0 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v6_lattices(A).
% 2.06/2.26 0 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v7_lattices(A).
% 2.06/2.26 0 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v8_lattices(A).
% 2.06/2.26 0 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v9_lattices(A).
% 2.06/2.26 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).
% 2.06/2.26 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)|k17_filter_2(A)=u1_struct_0(A).
% 2.06/2.26 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)|m2_filter_2(k17_filter_2(A),A).
% 2.06/2.26 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)|v1_xboole_0(B)| -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))|m2_filter_2(k19_filter_2(A,B),A).
% 2.06/2.26 0 [] $T.
% 2.06/2.26 0 [] $T.
% 2.06/2.26 0 [] v3_struct_0(A)| -l2_lattices(A)|m1_subset_1(k6_lattices(A),u1_struct_0(A)).
% 2.06/2.26 0 [] -l1_lattices(A)|l1_struct_0(A).
% 2.06/2.26 0 [] $T.
% 2.06/2.26 0 [] -l2_lattices(A)|l1_struct_0(A).
% 2.06/2.26 0 [] -l3_lattices(A)|l1_lattices(A).
% 2.06/2.26 0 [] -l3_lattices(A)|l2_lattices(A).
% 2.06/2.26 0 [] $T.
% 2.06/2.26 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -m2_filter_2(B,A)| -v1_xboole_0(B).
% 2.06/2.26 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -m2_filter_2(B,A)|m2_lattice4(B,A).
% 2.06/2.26 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))).
% 2.06/2.26 0 [] $T.
% 2.06/2.26 0 [] l1_lattices($c3).
% 2.06/2.26 0 [] l1_struct_0($c4).
% 2.06/2.26 0 [] l2_lattices($c5).
% 2.06/2.26 0 [] l3_lattices($c6).
% 2.06/2.26 0 [] m1_subset_1($f1(A),A).
% 2.06/2.26 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)|m2_filter_2($f2(A),A).
% 2.06/2.26 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)|m2_lattice4($f3(A),A).
% 2.06/2.26 0 [] v3_struct_0(A)| -l1_struct_0(A)| -v1_xboole_0(u1_struct_0(A)).
% 2.06/2.26 0 [] -v1_xboole_0(k1_zfmisc_1(A)).
% 2.06/2.26 0 [] v1_xboole_0(k1_xboole_0).
% 2.06/2.26 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)|m2_lattice4($f4(A),A).
% 2.06/2.26 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -v1_xboole_0($f4(A)).
% 2.06/2.26 0 [] v1_xboole_0(A)|m1_subset_1($f5(A),k1_zfmisc_1(A)).
% 2.06/2.26 0 [] v1_xboole_0(A)| -v1_xboole_0($f5(A)).
% 2.06/2.26 0 [] v1_xboole_0($c7).
% 2.06/2.26 0 [] m1_subset_1($f6(A),k1_zfmisc_1(A)).
% 2.06/2.26 0 [] v1_xboole_0($f6(A)).
% 2.06/2.26 0 [] -v1_xboole_0($c8).
% 2.06/2.26 0 [] l1_struct_0($c9).
% 2.06/2.26 0 [] -v3_struct_0($c9).
% 2.06/2.26 0 [] v3_struct_0(A)| -l1_struct_0(A)|m1_subset_1($f7(A),k1_zfmisc_1(u1_struct_0(A))).
% 2.06/2.26 0 [] v3_struct_0(A)| -l1_struct_0(A)| -v1_xboole_0($f7(A)).
% 2.06/2.26 0 [] v1_xboole_0(A)| -m1_subset_1(B,k1_zfmisc_1(A))| -m1_subset_1(C,k1_zfmisc_1(A))| -r1_filter_2(A,B,C)|B=C.
% 2.06/2.26 0 [] v1_xboole_0(A)| -m1_subset_1(B,k1_zfmisc_1(A))| -m1_subset_1(C,k1_zfmisc_1(A))|r1_filter_2(A,B,C)|B!=C.
% 2.06/2.26 0 [] v1_xboole_0(A)| -m1_subset_1(B,k1_zfmisc_1(A))| -m1_subset_1(C,k1_zfmisc_1(A))|r1_filter_2(A,B,B).
% 2.06/2.26 0 [] r1_tarski(A,A).
% 2.06/2.26 0 [] v1_xboole_0(A)| -m1_subset_1(B,k1_zfmisc_1(A))| -m1_subset_1(C,k1_zfmisc_1(A))| -r1_filter_2(A,B,C)|r1_filter_2(A,C,B).
% 2.06/2.26 0 [] -r2_hidden(A,B)|m1_subset_1(A,B).
% 2.06/2.26 0 [] -m1_subset_1(A,B)|v1_xboole_0(B)|r2_hidden(A,B).
% 2.06/2.26 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -m2_filter_2(B,A)|r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),B).
% 2.06/2.26 0 [] -m1_subset_1(A,k1_zfmisc_1(B))|r1_tarski(A,B).
% 2.06/2.26 0 [] m1_subset_1(A,k1_zfmisc_1(B))| -r1_tarski(A,B).
% 2.06/2.26 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)|v1_xboole_0(B)| -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))| -v14_lattices(A)| -r2_hidden(k6_lattices(A),B)|r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),k17_filter_2(A)).
% 2.06/2.26 0 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)|v1_xboole_0(B)| -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))| -v14_lattices(A)| -r2_hidden(k6_lattices(A),B)|k19_filter_2(A,B)=u1_struct_0(A).
% 2.06/2.26 0 [] -r2_hidden(A,B)| -m1_subset_1(B,k1_zfmisc_1(C))|m1_subset_1(A,C).
% 2.06/2.26 0 [] -r2_hidden(A,B)| -m1_subset_1(B,k1_zfmisc_1(C))| -v1_xboole_0(C).
% 2.06/2.26 0 [] -v1_xboole_0(A)|A=k1_xboole_0.
% 2.06/2.26 0 [] -r2_hidden(A,B)| -v1_xboole_0(B).
% 2.06/2.26 0 [] -v1_xboole_0(A)|A=B| -v1_xboole_0(B).
% 2.06/2.26 end_of_list.
% 2.06/2.26
% 2.06/2.26 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=9.
% 2.06/2.26
% 2.06/2.26 This ia a non-Horn set with equality. The strategy will be
% 2.06/2.26 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.06/2.26 deletion, with positive clauses in sos and nonpositive
% 2.06/2.26 clauses in usable.
% 2.06/2.26
% 2.06/2.26 dependent: set(knuth_bendix).
% 2.06/2.26 dependent: set(anl_eq).
% 2.06/2.26 dependent: set(para_from).
% 2.06/2.26 dependent: set(para_into).
% 2.06/2.26 dependent: clear(para_from_right).
% 2.06/2.26 dependent: clear(para_into_right).
% 2.06/2.26 dependent: set(para_from_vars).
% 2.06/2.26 dependent: set(eq_units_both_ways).
% 2.06/2.26 dependent: set(dynamic_demod_all).
% 2.06/2.26 dependent: set(dynamic_demod).
% 2.06/2.26 dependent: set(order_eq).
% 2.06/2.26 dependent: set(back_demod).
% 2.06/2.26 dependent: set(lrpo).
% 2.06/2.26 dependent: set(hyper_res).
% 2.06/2.26 dependent: set(unit_deletion).
% 2.06/2.26 dependent: set(factor).
% 2.06/2.26
% 2.06/2.26 ------------> process usable:
% 2.06/2.26 ** KEPT (pick-wt=2): 1 [] -v3_struct_0($c2).
% 2.06/2.26 ** KEPT (pick-wt=10): 3 [copy,2,flip.2] -r1_filter_2(u1_struct_0($c2),$c1,k17_filter_2($c2))|u1_struct_0($c2)!=$c1.
% 2.06/2.26 ** KEPT (pick-wt=6): 4 [] -r2_hidden(A,B)| -r2_hidden(B,A).
% 2.06/2.26 ** KEPT (pick-wt=4): 5 [] -v1_xboole_0(A)|v1_funct_1(A).
% 2.06/2.26 ** KEPT (pick-wt=8): 6 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v4_lattices(A).
% 2.06/2.26 ** KEPT (pick-wt=8): 7 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v5_lattices(A).
% 2.06/2.26 ** KEPT (pick-wt=8): 8 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v6_lattices(A).
% 2.06/2.26 ** KEPT (pick-wt=8): 9 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v7_lattices(A).
% 2.06/2.26 ** KEPT (pick-wt=8): 10 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v8_lattices(A).
% 2.06/2.26 ** KEPT (pick-wt=8): 11 [] -l3_lattices(A)|v3_struct_0(A)| -v10_lattices(A)|v9_lattices(A).
% 2.06/2.26 ** KEPT (pick-wt=18): 12 [] -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).
% 2.06/2.26 ** KEPT (pick-wt=11): 14 [copy,13,flip.4] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)|u1_struct_0(A)=k17_filter_2(A).
% 2.06/2.26 ** KEPT (pick-wt=10): 15 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)|m2_filter_2(k17_filter_2(A),A).
% 2.06/2.26 ** KEPT (pick-wt=18): 16 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)|v1_xboole_0(B)| -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))|m2_filter_2(k19_filter_2(A,B),A).
% 2.06/2.26 ** KEPT (pick-wt=9): 17 [] v3_struct_0(A)| -l2_lattices(A)|m1_subset_1(k6_lattices(A),u1_struct_0(A)).
% 2.06/2.26 ** KEPT (pick-wt=4): 18 [] -l1_lattices(A)|l1_struct_0(A).
% 2.06/2.26 ** KEPT (pick-wt=4): 19 [] -l2_lattices(A)|l1_struct_0(A).
% 2.06/2.26 ** KEPT (pick-wt=4): 20 [] -l3_lattices(A)|l1_lattices(A).
% 2.06/2.26 ** KEPT (pick-wt=4): 21 [] -l3_lattices(A)|l2_lattices(A).
% 2.06/2.26 ** KEPT (pick-wt=11): 22 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -m2_filter_2(B,A)| -v1_xboole_0(B).
% 2.06/2.26 ** KEPT (pick-wt=12): 23 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -m2_filter_2(B,A)|m2_lattice4(B,A).
% 2.06/2.26 ** KEPT (pick-wt=14): 24 [] 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))).
% 2.06/2.26 ** KEPT (pick-wt=10): 25 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)|m2_filter_2($f2(A),A).
% 2.06/2.26 ** KEPT (pick-wt=10): 26 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)|m2_lattice4($f3(A),A).
% 2.06/2.26 ** KEPT (pick-wt=7): 27 [] v3_struct_0(A)| -l1_struct_0(A)| -v1_xboole_0(u1_struct_0(A)).
% 2.06/2.26 ** KEPT (pick-wt=3): 28 [] -v1_xboole_0(k1_zfmisc_1(A)).
% 2.06/2.26 ** KEPT (pick-wt=10): 29 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)|m2_lattice4($f4(A),A).
% 2.06/2.26 ** KEPT (pick-wt=9): 30 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -v1_xboole_0($f4(A)).
% 2.06/2.26 ** KEPT (pick-wt=5): 31 [] v1_xboole_0(A)| -v1_xboole_0($f5(A)).
% 2.06/2.26 ** KEPT (pick-wt=2): 32 [] -v1_xboole_0($c8).
% 2.06/2.26 ** KEPT (pick-wt=2): 33 [] -v3_struct_0($c9).
% 2.06/2.26 ** KEPT (pick-wt=10): 34 [] v3_struct_0(A)| -l1_struct_0(A)|m1_subset_1($f7(A),k1_zfmisc_1(u1_struct_0(A))).
% 10.76/11.00 ** KEPT (pick-wt=7): 35 [] v3_struct_0(A)| -l1_struct_0(A)| -v1_xboole_0($f7(A)).
% 10.76/11.00 ** KEPT (pick-wt=17): 36 [] v1_xboole_0(A)| -m1_subset_1(B,k1_zfmisc_1(A))| -m1_subset_1(C,k1_zfmisc_1(A))| -r1_filter_2(A,B,C)|B=C.
% 10.76/11.00 ** KEPT (pick-wt=17): 37 [] v1_xboole_0(A)| -m1_subset_1(B,k1_zfmisc_1(A))| -m1_subset_1(C,k1_zfmisc_1(A))|r1_filter_2(A,B,C)|B!=C.
% 10.76/11.00 ** KEPT (pick-wt=10): 39 [copy,38,factor_simp] v1_xboole_0(A)| -m1_subset_1(B,k1_zfmisc_1(A))|r1_filter_2(A,B,B).
% 10.76/11.00 ** KEPT (pick-wt=18): 40 [] v1_xboole_0(A)| -m1_subset_1(B,k1_zfmisc_1(A))| -m1_subset_1(C,k1_zfmisc_1(A))| -r1_filter_2(A,B,C)|r1_filter_2(A,C,B).
% 10.76/11.00 ** KEPT (pick-wt=6): 41 [] -r2_hidden(A,B)|m1_subset_1(A,B).
% 10.76/11.00 ** KEPT (pick-wt=8): 42 [] -m1_subset_1(A,B)|v1_xboole_0(B)|r2_hidden(A,B).
% 10.76/11.00 ** KEPT (pick-wt=16): 43 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)| -m2_filter_2(B,A)|r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),B).
% 10.76/11.00 ** KEPT (pick-wt=7): 44 [] -m1_subset_1(A,k1_zfmisc_1(B))|r1_tarski(A,B).
% 10.76/11.00 ** KEPT (pick-wt=7): 45 [] m1_subset_1(A,k1_zfmisc_1(B))| -r1_tarski(A,B).
% 10.76/11.00 ** KEPT (pick-wt=27): 46 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)|v1_xboole_0(B)| -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))| -v14_lattices(A)| -r2_hidden(k6_lattices(A),B)|r1_filter_2(u1_struct_0(A),k19_filter_2(A,B),k17_filter_2(A)).
% 10.76/11.00 ** KEPT (pick-wt=25): 47 [] v3_struct_0(A)| -v10_lattices(A)| -l3_lattices(A)|v1_xboole_0(B)| -m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))| -v14_lattices(A)| -r2_hidden(k6_lattices(A),B)|k19_filter_2(A,B)=u1_struct_0(A).
% 10.76/11.00 ** KEPT (pick-wt=10): 48 [] -r2_hidden(A,B)| -m1_subset_1(B,k1_zfmisc_1(C))|m1_subset_1(A,C).
% 10.76/11.00 ** KEPT (pick-wt=9): 49 [] -r2_hidden(A,B)| -m1_subset_1(B,k1_zfmisc_1(C))| -v1_xboole_0(C).
% 10.76/11.00 ** KEPT (pick-wt=5): 50 [] -v1_xboole_0(A)|A=k1_xboole_0.
% 10.76/11.00 ** KEPT (pick-wt=5): 51 [] -r2_hidden(A,B)| -v1_xboole_0(B).
% 10.76/11.00 ** KEPT (pick-wt=7): 52 [] -v1_xboole_0(A)|A=B| -v1_xboole_0(B).
% 10.76/11.00
% 10.76/11.00 ------------> process sos:
% 10.76/11.00 ** KEPT (pick-wt=3): 56 [] A=A.
% 10.76/11.00 ** KEPT (pick-wt=2): 57 [] v10_lattices($c2).
% 10.76/11.00 ** KEPT (pick-wt=2): 58 [] l3_lattices($c2).
% 10.76/11.00 ** KEPT (pick-wt=3): 59 [] m2_filter_2($c1,$c2).
% 10.76/11.00 ** KEPT (pick-wt=2): 60 [] v14_lattices($c2).
% 10.76/11.00 ** KEPT (pick-wt=4): 61 [] r2_hidden(k6_lattices($c2),$c1).
% 10.76/11.00 ** KEPT (pick-wt=2): 62 [] l1_lattices($c3).
% 10.76/11.00 ** KEPT (pick-wt=2): 63 [] l1_struct_0($c4).
% 10.76/11.00 ** KEPT (pick-wt=2): 64 [] l2_lattices($c5).
% 10.76/11.00 ** KEPT (pick-wt=2): 65 [] l3_lattices($c6).
% 10.76/11.00 ** KEPT (pick-wt=4): 66 [] m1_subset_1($f1(A),A).
% 10.76/11.00 ** KEPT (pick-wt=2): 67 [] v1_xboole_0(k1_xboole_0).
% 10.76/11.00 ** KEPT (pick-wt=7): 68 [] v1_xboole_0(A)|m1_subset_1($f5(A),k1_zfmisc_1(A)).
% 10.76/11.00 ** KEPT (pick-wt=2): 69 [] v1_xboole_0($c7).
% 10.76/11.00 ** KEPT (pick-wt=5): 70 [] m1_subset_1($f6(A),k1_zfmisc_1(A)).
% 10.76/11.00 ** KEPT (pick-wt=3): 71 [] v1_xboole_0($f6(A)).
% 10.76/11.00 ** KEPT (pick-wt=2): 72 [] l1_struct_0($c9).
% 10.76/11.00 ** KEPT (pick-wt=3): 73 [] r1_tarski(A,A).
% 10.76/11.00 Following clause subsumed by 56 during input processing: 0 [copy,56,flip.1] A=A.
% 10.76/11.00 56 back subsumes 55.
% 10.76/11.00 56 back subsumes 54.
% 10.76/11.00
% 10.76/11.00 ======= end of input processing =======
% 10.76/11.00
% 10.76/11.00 =========== start of search ===========
% 10.76/11.00
% 10.76/11.00
% 10.76/11.00 Resetting weight limit to 6.
% 10.76/11.00
% 10.76/11.00
% 10.76/11.00 Resetting weight limit to 6.
% 10.76/11.00
% 10.76/11.00 sos_size=1986
% 10.76/11.00
% 10.76/11.00 -------- PROOF --------
% 10.76/11.00
% 10.76/11.00 -----> EMPTY CLAUSE at 8.75 sec ----> 2411 [back_demod,91,demod,2375,2375,2375,unit_del,1740,56] $F.
% 10.76/11.00
% 10.76/11.00 Length of proof is 19. Level of proof is 6.
% 10.76/11.00
% 10.76/11.00 ---------------- PROOF ----------------
% 10.76/11.00 % SZS status Theorem
% 10.76/11.00 % SZS output start Refutation
% See solution above
% 10.76/11.00 ------------ end of proof -------------
% 10.76/11.00
% 10.76/11.00
% 10.76/11.00 Search stopped by max_proofs option.
% 10.76/11.00
% 10.76/11.00
% 10.76/11.00 Search stopped by max_proofs option.
% 10.76/11.00
% 10.76/11.00 ============ end of search ============
% 10.76/11.00
% 10.76/11.00 -------------- statistics -------------
% 10.76/11.00 clauses given 559
% 10.76/11.00 clauses generated 68821
% 10.76/11.00 clauses kept 2402
% 10.76/11.00 clauses forward subsumed 3375
% 10.76/11.00 clauses back subsumed 78
% 10.76/11.00 Kbytes malloced 4882
% 10.76/11.00
% 10.76/11.00 ----------- times (seconds) -----------
% 10.76/11.00 user CPU time 8.75 (0 hr, 0 min, 8 sec)
% 10.76/11.00 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 10.76/11.00 wall-clock time 10 (0 hr, 0 min, 10 sec)
% 10.76/11.00
% 10.76/11.00 That finishes the proof of the theorem.
% 10.76/11.00
% 10.76/11.00 Process 25903 finished Wed Jul 27 08:10:10 2022
% 10.76/11.00 Otter interrupted
% 10.76/11.00 PROOF FOUND
%------------------------------------------------------------------------------