TSTP Solution File: GRP644+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP644+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.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 12:57:31 EDT 2022
% Result : Theorem 2.04s 2.22s
% Output : Refutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 13
% Syntax : Number of clauses : 17 ( 13 unt; 4 nHn; 17 RR)
% Number of literals : 45 ( 0 equ; 26 neg)
% Maximal clause size : 9 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ v3_struct_0(dollar_c3),
file('GRP644+1.p',unknown),
[] ).
cnf(2,axiom,
~ r2_hidden(k3_group_1(dollar_c3,dollar_c1),k1_funct_1(k1_latsubgr(dollar_c3),dollar_c2)),
file('GRP644+1.p',unknown),
[] ).
cnf(15,axiom,
( v3_struct_0(A)
| ~ v3_group_1(A)
| ~ v4_group_1(A)
| ~ l1_group_1(A)
| ~ m1_subset_1(B,u1_struct_0(A))
| m1_subset_1(k3_group_1(A,B),u1_struct_0(A)) ),
file('GRP644+1.p',unknown),
[] ).
cnf(38,axiom,
( v3_struct_0(A)
| ~ v3_group_1(A)
| ~ v4_group_1(A)
| ~ l1_group_1(A)
| ~ v1_group_1(B)
| ~ m1_group_2(B,A)
| ~ m1_subset_1(C,u1_struct_0(A))
| ~ r2_hidden(C,k1_funct_1(k1_latsubgr(A),B))
| r1_rlvect_1(B,C) ),
file('GRP644+1.p',unknown),
[] ).
cnf(39,axiom,
( v3_struct_0(A)
| ~ v3_group_1(A)
| ~ v4_group_1(A)
| ~ l1_group_1(A)
| ~ v1_group_1(B)
| ~ m1_group_2(B,A)
| ~ m1_subset_1(C,u1_struct_0(A))
| r2_hidden(C,k1_funct_1(k1_latsubgr(A),B))
| ~ r1_rlvect_1(B,C) ),
file('GRP644+1.p',unknown),
[] ).
cnf(46,axiom,
( v3_struct_0(A)
| ~ v3_group_1(A)
| ~ v4_group_1(A)
| ~ l1_group_1(A)
| ~ m1_subset_1(B,u1_struct_0(A))
| ~ m1_group_2(C,A)
| ~ r1_rlvect_1(C,B)
| r1_rlvect_1(C,k3_group_1(A,B)) ),
file('GRP644+1.p',unknown),
[] ).
cnf(55,axiom,
v3_group_1(dollar_c3),
file('GRP644+1.p',unknown),
[] ).
cnf(56,axiom,
v4_group_1(dollar_c3),
file('GRP644+1.p',unknown),
[] ).
cnf(57,axiom,
l1_group_1(dollar_c3),
file('GRP644+1.p',unknown),
[] ).
cnf(58,axiom,
v1_group_1(dollar_c2),
file('GRP644+1.p',unknown),
[] ).
cnf(59,axiom,
m1_group_2(dollar_c2,dollar_c3),
file('GRP644+1.p',unknown),
[] ).
cnf(60,axiom,
m1_subset_1(dollar_c1,u1_struct_0(dollar_c3)),
file('GRP644+1.p',unknown),
[] ).
cnf(61,axiom,
r2_hidden(dollar_c1,k1_funct_1(k1_latsubgr(dollar_c3),dollar_c2)),
file('GRP644+1.p',unknown),
[] ).
cnf(144,plain,
m1_subset_1(k3_group_1(dollar_c3,dollar_c1),u1_struct_0(dollar_c3)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[60,15,55,56,57]),1]),
[iquote('hyper,60,15,55,56,57,unit_del,1')] ).
cnf(176,plain,
r1_rlvect_1(dollar_c2,dollar_c1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[61,38,55,56,57,58,59,60]),1]),
[iquote('hyper,61,38,55,56,57,58,59,60,unit_del,1')] ).
cnf(242,plain,
r1_rlvect_1(dollar_c2,k3_group_1(dollar_c3,dollar_c1)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[176,46,55,56,57,60,59]),1]),
[iquote('hyper,176,46,55,56,57,60,59,unit_del,1')] ).
cnf(695,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[144,39,55,56,57,58,59,242]),1,2]),
[iquote('hyper,144,39,55,56,57,58,59,242,unit_del,1,2')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP644+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 05:00:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.93/2.14 ----- Otter 3.3f, August 2004 -----
% 1.93/2.14 The process was started by sandbox2 on n024.cluster.edu,
% 1.93/2.14 Wed Jul 27 05:00:25 2022
% 1.93/2.14 The command was "./otter". The process ID is 6849.
% 1.93/2.14
% 1.93/2.14 set(prolog_style_variables).
% 1.93/2.14 set(auto).
% 1.93/2.14 dependent: set(auto1).
% 1.93/2.14 dependent: set(process_input).
% 1.93/2.14 dependent: clear(print_kept).
% 1.93/2.14 dependent: clear(print_new_demod).
% 1.93/2.14 dependent: clear(print_back_demod).
% 1.93/2.14 dependent: clear(print_back_sub).
% 1.93/2.14 dependent: set(control_memory).
% 1.93/2.14 dependent: assign(max_mem, 12000).
% 1.93/2.14 dependent: assign(pick_given_ratio, 4).
% 1.93/2.14 dependent: assign(stats_level, 1).
% 1.93/2.14 dependent: assign(max_seconds, 10800).
% 1.93/2.14 clear(print_given).
% 1.93/2.14
% 1.93/2.14 formula_list(usable).
% 1.93/2.14 all A (A=A).
% 1.93/2.14 -(all A (-v3_struct_0(A)&v3_group_1(A)&v4_group_1(A)&l1_group_1(A)-> (all B (v1_group_1(B)&m1_group_2(B,A)-> (all C (m1_subset_1(C,u1_struct_0(A))-> (r2_hidden(C,k1_funct_1(k1_latsubgr(A),B))->r2_hidden(k3_group_1(A,C),k1_funct_1(k1_latsubgr(A),B))))))))).
% 1.93/2.14 all A (l1_group_1(A)-> (v1_group_1(A)->A=g1_group_1(u1_struct_0(A),u1_group_1(A)))).
% 1.93/2.14 all A B (r2_hidden(A,B)-> -r2_hidden(B,A)).
% 1.93/2.14 all A B C (m1_relset_1(C,A,B)-> (v1_funct_1(C)&v1_partfun1(C,A,B)->v1_funct_1(C)&v1_funct_2(C,A,B))).
% 1.93/2.14 all A B C (m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))->v1_relat_1(C)).
% 1.93/2.14 all A B (-v1_xboole_0(B)-> (all C (m1_relset_1(C,A,B)-> (v1_funct_1(C)&v1_funct_2(C,A,B)->v1_funct_1(C)&v1_partfun1(C,A,B)&v1_funct_2(C,A,B))))).
% 1.93/2.14 all A B (-v1_xboole_0(A)& -v1_xboole_0(B)-> (all C (m1_relset_1(C,A,B)-> (v1_funct_1(C)&v1_funct_2(C,A,B)->v1_funct_1(C)& -v1_xboole_0(C)&v1_partfun1(C,A,B)&v1_funct_2(C,A,B))))).
% 1.93/2.14 all A B (v1_funct_1(B)&v1_funct_2(B,k2_zfmisc_1(A,A),A)&m1_relset_1(B,k2_zfmisc_1(A,A),A)->v1_group_1(g1_group_1(A,B))&l1_group_1(g1_group_1(A,B))).
% 1.93/2.14 $T.
% 1.93/2.14 $T.
% 1.93/2.14 all A (-v3_struct_0(A)&v3_group_1(A)&v4_group_1(A)&l1_group_1(A)->v1_funct_1(k1_latsubgr(A))&v1_funct_2(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))&m2_relset_1(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))).
% 1.93/2.14 $T.
% 1.93/2.14 $T.
% 1.93/2.14 $T.
% 1.93/2.14 all A B (-v3_struct_0(A)&v3_group_1(A)&v4_group_1(A)&l1_group_1(A)&m1_subset_1(B,u1_struct_0(A))->m1_subset_1(k3_group_1(A,B),u1_struct_0(A))).
% 1.93/2.14 all A (l1_group_1(A)->l1_struct_0(A)).
% 1.93/2.14 $T.
% 1.93/2.14 all A (-v3_struct_0(A)&v3_group_1(A)&l1_group_1(A)-> (all B (m1_group_2(B,A)-> -v3_struct_0(B)&v3_group_1(B)&l1_group_1(B)))).
% 1.93/2.14 $T.
% 1.93/2.14 $T.
% 1.93/2.14 all A B C (m2_relset_1(C,A,B)->m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))).
% 1.93/2.14 all A (l1_group_1(A)->v1_funct_1(u1_group_1(A))&v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))&m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))).
% 1.93/2.14 $T.
% 1.93/2.14 exists A l1_group_1(A).
% 1.93/2.14 exists A l1_struct_0(A).
% 1.93/2.14 all A (-v3_struct_0(A)&v3_group_1(A)&l1_group_1(A)-> (exists B m1_group_2(B,A))).
% 1.93/2.14 all A B exists C m1_relset_1(C,A,B).
% 1.93/2.14 all A exists B m1_subset_1(B,A).
% 1.93/2.14 all A B exists C m2_relset_1(C,A,B).
% 1.93/2.14 all A (-v3_struct_0(A)&v3_group_1(A)&v4_group_1(A)&l1_group_1(A)-> -v1_xboole_0(k1_group_3(A))).
% 1.93/2.14 all A (-v3_struct_0(A)&l1_struct_0(A)-> -v1_xboole_0(u1_struct_0(A))).
% 1.93/2.14 all A (-v1_xboole_0(k1_zfmisc_1(A))).
% 1.93/2.14 v1_xboole_0(k1_xboole_0).
% 1.93/2.14 all A B (-v1_xboole_0(A)& -v1_xboole_0(B)-> -v1_xboole_0(k2_zfmisc_1(A,B))).
% 1.93/2.14 all A B (v1_funct_1(B)&v1_funct_2(B,k2_zfmisc_1(A,A),A)&m1_relset_1(B,k2_zfmisc_1(A,A),A)-> (all C D (g1_group_1(A,B)=g1_group_1(C,D)->A=C&B=D))).
% 1.93/2.14 all A B exists C (m1_relset_1(C,A,B)&v1_relat_1(C)&v1_funct_1(C)&v1_funct_2(C,A,B)).
% 1.93/2.14 all A (-v1_xboole_0(A)-> (exists B (m1_subset_1(B,k1_zfmisc_1(A))& -v1_xboole_0(B)))).
% 1.93/2.14 exists A v1_xboole_0(A).
% 1.93/2.14 all A B exists C (m1_relset_1(C,A,B)&v1_relat_1(C)&v1_funct_1(C)).
% 1.93/2.14 all A exists B (m1_subset_1(B,k1_zfmisc_1(A))&v1_xboole_0(B)).
% 1.93/2.14 exists A (-v1_xboole_0(A)).
% 1.93/2.14 exists A (l1_struct_0(A)& -v3_struct_0(A)).
% 1.93/2.14 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)))).
% 1.93/2.14 all A B C (m2_relset_1(C,A,B)<->m1_relset_1(C,A,B)).
% 1.93/2.14 all A B r1_tarski(A,A).
% 1.93/2.14 all A (-v3_struct_0(A)&v3_group_1(A)&v4_group_1(A)&l1_group_1(A)-> (all B (v1_group_1(B)&m1_group_2(B,A)-> (all C (m1_subset_1(C,u1_struct_0(A))-> (r2_hidden(C,k1_funct_1(k1_latsubgr(A),B))<->r1_rlvect_1(B,C))))))).
% 1.93/2.14 all A B (r2_hidden(A,B)->m1_subset_1(A,B)).
% 1.93/2.14 all A B (m1_subset_1(A,B)->v1_xboole_0(B)|r2_hidden(A,B)).
% 1.93/2.14 all A B (m1_subset_1(A,k1_zfmisc_1(B))<->r1_tarski(A,B)).
% 1.93/2.14 all A B C (r2_hidden(A,B)&m1_subset_1(B,k1_zfmisc_1(C))->m1_subset_1(A,C)).
% 1.93/2.14 all A B C (-(r2_hidden(A,B)&m1_subset_1(B,k1_zfmisc_1(C))&v1_xboole_0(C))).
% 1.93/2.14 all A (-v3_struct_0(A)&v3_group_1(A)&v4_group_1(A)&l1_group_1(A)-> (all B (m1_subset_1(B,u1_struct_0(A))-> (all C (m1_group_2(C,A)-> (r1_rlvect_1(C,B)->r1_rlvect_1(C,k3_group_1(A,B)))))))).
% 1.93/2.14 all A (v1_xboole_0(A)->A=k1_xboole_0).
% 1.93/2.14 all A B (-(r2_hidden(A,B)&v1_xboole_0(B))).
% 1.93/2.14 all A B (-(v1_xboole_0(A)&A!=B&v1_xboole_0(B))).
% 1.93/2.14 end_of_list.
% 1.93/2.14
% 1.93/2.14 -------> usable clausifies to:
% 1.93/2.14
% 1.93/2.14 list(usable).
% 1.93/2.14 0 [] A=A.
% 1.93/2.14 0 [] -v3_struct_0($c3).
% 1.93/2.14 0 [] v3_group_1($c3).
% 1.93/2.14 0 [] v4_group_1($c3).
% 1.93/2.14 0 [] l1_group_1($c3).
% 1.93/2.14 0 [] v1_group_1($c2).
% 1.93/2.14 0 [] m1_group_2($c2,$c3).
% 1.93/2.14 0 [] m1_subset_1($c1,u1_struct_0($c3)).
% 1.93/2.14 0 [] r2_hidden($c1,k1_funct_1(k1_latsubgr($c3),$c2)).
% 1.93/2.14 0 [] -r2_hidden(k3_group_1($c3,$c1),k1_funct_1(k1_latsubgr($c3),$c2)).
% 1.93/2.14 0 [] -l1_group_1(A)| -v1_group_1(A)|A=g1_group_1(u1_struct_0(A),u1_group_1(A)).
% 1.93/2.15 0 [] -r2_hidden(A,B)| -r2_hidden(B,A).
% 1.93/2.15 0 [] -m1_relset_1(C,A,B)| -v1_funct_1(C)| -v1_partfun1(C,A,B)|v1_funct_2(C,A,B).
% 1.93/2.15 0 [] -m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))|v1_relat_1(C).
% 1.93/2.15 0 [] v1_xboole_0(B)| -m1_relset_1(C,A,B)| -v1_funct_1(C)| -v1_funct_2(C,A,B)|v1_partfun1(C,A,B).
% 1.93/2.15 0 [] v1_xboole_0(A)|v1_xboole_0(B)| -m1_relset_1(C,A,B)| -v1_funct_1(C)| -v1_funct_2(C,A,B)| -v1_xboole_0(C).
% 1.93/2.15 0 [] v1_xboole_0(A)|v1_xboole_0(B)| -m1_relset_1(C,A,B)| -v1_funct_1(C)| -v1_funct_2(C,A,B)|v1_partfun1(C,A,B).
% 1.93/2.15 0 [] -v1_funct_1(B)| -v1_funct_2(B,k2_zfmisc_1(A,A),A)| -m1_relset_1(B,k2_zfmisc_1(A,A),A)|v1_group_1(g1_group_1(A,B)).
% 1.93/2.15 0 [] -v1_funct_1(B)| -v1_funct_2(B,k2_zfmisc_1(A,A),A)| -m1_relset_1(B,k2_zfmisc_1(A,A),A)|l1_group_1(g1_group_1(A,B)).
% 1.93/2.15 0 [] $T.
% 1.93/2.15 0 [] $T.
% 1.93/2.15 0 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)|v1_funct_1(k1_latsubgr(A)).
% 1.93/2.15 0 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)|v1_funct_2(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))).
% 1.93/2.15 0 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)|m2_relset_1(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))).
% 1.93/2.15 0 [] $T.
% 1.93/2.15 0 [] $T.
% 1.93/2.15 0 [] $T.
% 1.93/2.15 0 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)| -m1_subset_1(B,u1_struct_0(A))|m1_subset_1(k3_group_1(A,B),u1_struct_0(A)).
% 1.93/2.15 0 [] -l1_group_1(A)|l1_struct_0(A).
% 1.93/2.15 0 [] $T.
% 1.93/2.15 0 [] v3_struct_0(A)| -v3_group_1(A)| -l1_group_1(A)| -m1_group_2(B,A)| -v3_struct_0(B).
% 1.93/2.15 0 [] v3_struct_0(A)| -v3_group_1(A)| -l1_group_1(A)| -m1_group_2(B,A)|v3_group_1(B).
% 1.93/2.15 0 [] v3_struct_0(A)| -v3_group_1(A)| -l1_group_1(A)| -m1_group_2(B,A)|l1_group_1(B).
% 1.93/2.15 0 [] $T.
% 1.93/2.15 0 [] $T.
% 1.93/2.15 0 [] -m2_relset_1(C,A,B)|m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))).
% 1.93/2.15 0 [] -l1_group_1(A)|v1_funct_1(u1_group_1(A)).
% 1.93/2.15 0 [] -l1_group_1(A)|v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)).
% 1.93/2.15 0 [] -l1_group_1(A)|m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)).
% 1.93/2.15 0 [] $T.
% 1.93/2.15 0 [] l1_group_1($c4).
% 1.93/2.15 0 [] l1_struct_0($c5).
% 1.93/2.15 0 [] v3_struct_0(A)| -v3_group_1(A)| -l1_group_1(A)|m1_group_2($f1(A),A).
% 1.93/2.15 0 [] m1_relset_1($f2(A,B),A,B).
% 1.93/2.15 0 [] m1_subset_1($f3(A),A).
% 1.93/2.15 0 [] m2_relset_1($f4(A,B),A,B).
% 1.93/2.15 0 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)| -v1_xboole_0(k1_group_3(A)).
% 1.93/2.15 0 [] v3_struct_0(A)| -l1_struct_0(A)| -v1_xboole_0(u1_struct_0(A)).
% 1.93/2.15 0 [] -v1_xboole_0(k1_zfmisc_1(A)).
% 1.93/2.15 0 [] v1_xboole_0(k1_xboole_0).
% 1.93/2.15 0 [] v1_xboole_0(A)|v1_xboole_0(B)| -v1_xboole_0(k2_zfmisc_1(A,B)).
% 1.93/2.15 0 [] -v1_funct_1(B)| -v1_funct_2(B,k2_zfmisc_1(A,A),A)| -m1_relset_1(B,k2_zfmisc_1(A,A),A)|g1_group_1(A,B)!=g1_group_1(C,D)|A=C.
% 1.93/2.15 0 [] -v1_funct_1(B)| -v1_funct_2(B,k2_zfmisc_1(A,A),A)| -m1_relset_1(B,k2_zfmisc_1(A,A),A)|g1_group_1(A,B)!=g1_group_1(C,D)|B=D.
% 1.93/2.15 0 [] m1_relset_1($f5(A,B),A,B).
% 1.93/2.15 0 [] v1_relat_1($f5(A,B)).
% 1.93/2.15 0 [] v1_funct_1($f5(A,B)).
% 1.93/2.15 0 [] v1_funct_2($f5(A,B),A,B).
% 1.93/2.15 0 [] v1_xboole_0(A)|m1_subset_1($f6(A),k1_zfmisc_1(A)).
% 1.93/2.15 0 [] v1_xboole_0(A)| -v1_xboole_0($f6(A)).
% 1.93/2.15 0 [] v1_xboole_0($c6).
% 1.93/2.15 0 [] m1_relset_1($f7(A,B),A,B).
% 1.93/2.15 0 [] v1_relat_1($f7(A,B)).
% 1.93/2.15 0 [] v1_funct_1($f7(A,B)).
% 1.93/2.15 0 [] m1_subset_1($f8(A),k1_zfmisc_1(A)).
% 1.93/2.15 0 [] v1_xboole_0($f8(A)).
% 1.93/2.15 0 [] -v1_xboole_0($c7).
% 1.93/2.15 0 [] l1_struct_0($c8).
% 1.93/2.15 0 [] -v3_struct_0($c8).
% 1.93/2.15 0 [] v3_struct_0(A)| -l1_struct_0(A)|m1_subset_1($f9(A),k1_zfmisc_1(u1_struct_0(A))).
% 1.93/2.15 0 [] v3_struct_0(A)| -l1_struct_0(A)| -v1_xboole_0($f9(A)).
% 1.93/2.15 0 [] -m2_relset_1(C,A,B)|m1_relset_1(C,A,B).
% 1.93/2.15 0 [] m2_relset_1(C,A,B)| -m1_relset_1(C,A,B).
% 1.93/2.15 0 [] r1_tarski(A,A).
% 1.93/2.15 0 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)| -v1_group_1(B)| -m1_group_2(B,A)| -m1_subset_1(C,u1_struct_0(A))| -r2_hidden(C,k1_funct_1(k1_latsubgr(A),B))|r1_rlvect_1(B,C).
% 1.93/2.15 0 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)| -v1_group_1(B)| -m1_group_2(B,A)| -m1_subset_1(C,u1_struct_0(A))|r2_hidden(C,k1_funct_1(k1_latsubgr(A),B))| -r1_rlvect_1(B,C).
% 1.93/2.15 0 [] -r2_hidden(A,B)|m1_subset_1(A,B).
% 1.93/2.15 0 [] -m1_subset_1(A,B)|v1_xboole_0(B)|r2_hidden(A,B).
% 1.93/2.15 0 [] -m1_subset_1(A,k1_zfmisc_1(B))|r1_tarski(A,B).
% 1.93/2.15 0 [] m1_subset_1(A,k1_zfmisc_1(B))| -r1_tarski(A,B).
% 1.93/2.15 0 [] -r2_hidden(A,B)| -m1_subset_1(B,k1_zfmisc_1(C))|m1_subset_1(A,C).
% 1.93/2.15 0 [] -r2_hidden(A,B)| -m1_subset_1(B,k1_zfmisc_1(C))| -v1_xboole_0(C).
% 1.93/2.15 0 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)| -m1_subset_1(B,u1_struct_0(A))| -m1_group_2(C,A)| -r1_rlvect_1(C,B)|r1_rlvect_1(C,k3_group_1(A,B)).
% 1.93/2.15 0 [] -v1_xboole_0(A)|A=k1_xboole_0.
% 1.93/2.15 0 [] -r2_hidden(A,B)| -v1_xboole_0(B).
% 1.93/2.15 0 [] -v1_xboole_0(A)|A=B| -v1_xboole_0(B).
% 1.93/2.15 end_of_list.
% 1.93/2.15
% 1.93/2.15 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=9.
% 1.93/2.15
% 1.93/2.15 This ia a non-Horn set with equality. The strategy will be
% 1.93/2.15 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.93/2.15 deletion, with positive clauses in sos and nonpositive
% 1.93/2.15 clauses in usable.
% 1.93/2.15
% 1.93/2.15 dependent: set(knuth_bendix).
% 1.93/2.15 dependent: set(anl_eq).
% 1.93/2.15 dependent: set(para_from).
% 1.93/2.15 dependent: set(para_into).
% 1.93/2.15 dependent: clear(para_from_right).
% 1.93/2.15 dependent: clear(para_into_right).
% 1.93/2.15 dependent: set(para_from_vars).
% 1.93/2.15 dependent: set(eq_units_both_ways).
% 1.93/2.15 dependent: set(dynamic_demod_all).
% 1.93/2.15 dependent: set(dynamic_demod).
% 1.93/2.15 dependent: set(order_eq).
% 1.93/2.15 dependent: set(back_demod).
% 1.93/2.15 dependent: set(lrpo).
% 1.93/2.15 dependent: set(hyper_res).
% 1.93/2.15 dependent: set(unit_deletion).
% 1.93/2.15 dependent: set(factor).
% 1.93/2.15
% 1.93/2.15 ------------> process usable:
% 1.93/2.15 ** KEPT (pick-wt=2): 1 [] -v3_struct_0($c3).
% 1.93/2.15 ** KEPT (pick-wt=8): 2 [] -r2_hidden(k3_group_1($c3,$c1),k1_funct_1(k1_latsubgr($c3),$c2)).
% 1.93/2.15 ** KEPT (pick-wt=11): 4 [copy,3,flip.3] -l1_group_1(A)| -v1_group_1(A)|g1_group_1(u1_struct_0(A),u1_group_1(A))=A.
% 1.93/2.15 ** KEPT (pick-wt=6): 5 [] -r2_hidden(A,B)| -r2_hidden(B,A).
% 1.93/2.15 ** KEPT (pick-wt=14): 6 [] -m1_relset_1(A,B,C)| -v1_funct_1(A)| -v1_partfun1(A,B,C)|v1_funct_2(A,B,C).
% 1.93/2.15 ** KEPT (pick-wt=8): 7 [] -m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C)))|v1_relat_1(A).
% 1.93/2.15 ** KEPT (pick-wt=16): 8 [] v1_xboole_0(A)| -m1_relset_1(B,C,A)| -v1_funct_1(B)| -v1_funct_2(B,C,A)|v1_partfun1(B,C,A).
% 1.93/2.15 ** KEPT (pick-wt=16): 9 [] v1_xboole_0(A)|v1_xboole_0(B)| -m1_relset_1(C,A,B)| -v1_funct_1(C)| -v1_funct_2(C,A,B)| -v1_xboole_0(C).
% 1.93/2.15 Following clause subsumed by 8 during input processing: 0 [] v1_xboole_0(A)|v1_xboole_0(B)| -m1_relset_1(C,A,B)| -v1_funct_1(C)| -v1_funct_2(C,A,B)|v1_partfun1(C,A,B).
% 1.93/2.15 ** KEPT (pick-wt=18): 10 [] -v1_funct_1(A)| -v1_funct_2(A,k2_zfmisc_1(B,B),B)| -m1_relset_1(A,k2_zfmisc_1(B,B),B)|v1_group_1(g1_group_1(B,A)).
% 1.93/2.15 ** KEPT (pick-wt=18): 11 [] -v1_funct_1(A)| -v1_funct_2(A,k2_zfmisc_1(B,B),B)| -m1_relset_1(A,k2_zfmisc_1(B,B),B)|l1_group_1(g1_group_1(B,A)).
% 1.93/2.15 ** KEPT (pick-wt=11): 12 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)|v1_funct_1(k1_latsubgr(A)).
% 1.93/2.15 ** KEPT (pick-wt=16): 13 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)|v1_funct_2(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))).
% 1.93/2.15 ** KEPT (pick-wt=16): 14 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)|m2_relset_1(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))).
% 1.93/2.15 ** KEPT (pick-wt=18): 15 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)| -m1_subset_1(B,u1_struct_0(A))|m1_subset_1(k3_group_1(A,B),u1_struct_0(A)).
% 1.93/2.15 ** KEPT (pick-wt=4): 16 [] -l1_group_1(A)|l1_struct_0(A).
% 1.93/2.15 ** KEPT (pick-wt=11): 17 [] v3_struct_0(A)| -v3_group_1(A)| -l1_group_1(A)| -m1_group_2(B,A)| -v3_struct_0(B).
% 1.93/2.15 ** KEPT (pick-wt=11): 18 [] v3_struct_0(A)| -v3_group_1(A)| -l1_group_1(A)| -m1_group_2(B,A)|v3_group_1(B).
% 1.93/2.15 ** KEPT (pick-wt=11): 19 [] v3_struct_0(A)| -v3_group_1(A)| -l1_group_1(A)| -m1_group_2(B,A)|l1_group_1(B).
% 1.93/2.15 ** KEPT (pick-wt=10): 20 [] -m2_relset_1(A,B,C)|m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C))).
% 1.93/2.15 ** KEPT (pick-wt=5): 21 [] -l1_group_1(A)|v1_funct_1(u1_group_1(A)).
% 1.93/2.15 ** KEPT (pick-wt=12): 22 [] -l1_group_1(A)|v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)).
% 1.93/2.15 ** KEPT (pick-wt=12): 23 [] -l1_group_1(A)|m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)).
% 1.93/2.15 ** KEPT (pick-wt=10): 24 [] v3_struct_0(A)| -v3_group_1(A)| -l1_group_1(A)|m1_group_2($f1(A),A).
% 1.93/2.15 ** KEPT (pick-wt=11): 25 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)| -v1_xboole_0(k1_group_3(A)).
% 1.93/2.15 ** KEPT (pick-wt=7): 26 [] v3_struct_0(A)| -l1_struct_0(A)| -v1_xboole_0(u1_struct_0(A)).
% 1.93/2.15 ** KEPT (pick-wt=3): 27 [] -v1_xboole_0(k1_zfmisc_1(A)).
% 1.93/2.15 ** KEPT (pick-wt=8): 28 [] v1_xboole_0(A)|v1_xboole_0(B)| -v1_xboole_0(k2_zfmisc_1(A,B)).
% 1.93/2.15 ** KEPT (pick-wt=24): 29 [] -v1_funct_1(A)| -v1_funct_2(A,k2_zfmisc_1(B,B),B)| -m1_relset_1(A,k2_zfmisc_1(B,B),B)|g1_group_1(B,A)!=g1_group_1(C,D)|B=C.
% 1.93/2.15 ** KEPT (pick-wt=24): 30 [] -v1_funct_1(A)| -v1_funct_2(A,k2_zfmisc_1(B,B),B)| -m1_relset_1(A,k2_zfmisc_1(B,B),B)|g1_group_1(B,A)!=g1_group_1(C,D)|A=D.
% 1.93/2.15 ** KEPT (pick-wt=5): 31 [] v1_xboole_0(A)| -v1_xboole_0($f6(A)).
% 1.93/2.15 ** KEPT (pick-wt=2): 32 [] -v1_xboole_0($c7).
% 1.93/2.15 ** KEPT (pick-wt=2): 33 [] -v3_struct_0($c8).
% 1.93/2.15 ** KEPT (pick-wt=10): 34 [] v3_struct_0(A)| -l1_struct_0(A)|m1_subset_1($f9(A),k1_zfmisc_1(u1_struct_0(A))).
% 1.93/2.15 ** KEPT (pick-wt=7): 35 [] v3_struct_0(A)| -l1_struct_0(A)| -v1_xboole_0($f9(A)).
% 1.93/2.15 ** KEPT (pick-wt=8): 36 [] -m2_relset_1(A,B,C)|m1_relset_1(A,B,C).
% 1.93/2.15 ** KEPT (pick-wt=8): 37 [] m2_relset_1(A,B,C)| -m1_relset_1(A,B,C).
% 1.93/2.15 ** KEPT (pick-wt=26): 38 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)| -v1_group_1(B)| -m1_group_2(B,A)| -m1_subset_1(C,u1_struct_0(A))| -r2_hidden(C,k1_funct_1(k1_latsubgr(A),B))|r1_rlvect_1(B,C).
% 1.93/2.15 ** KEPT (pick-wt=26): 39 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)| -v1_group_1(B)| -m1_group_2(B,A)| -m1_subset_1(C,u1_struct_0(A))|r2_hidden(C,k1_funct_1(k1_latsubgr(A),B))| -r1_rlvect_1(B,C).
% 1.93/2.15 ** KEPT (pick-wt=6): 40 [] -r2_hidden(A,B)|m1_subset_1(A,B).
% 1.93/2.15 ** KEPT (pick-wt=8): 41 [] -m1_subset_1(A,B)|v1_xboole_0(B)|r2_hidden(A,B).
% 1.93/2.15 ** KEPT (pick-wt=7): 42 [] -m1_subset_1(A,k1_zfmisc_1(B))|r1_tarski(A,B).
% 1.93/2.15 ** KEPT (pick-wt=7): 43 [] m1_subset_1(A,k1_zfmisc_1(B))| -r1_tarski(A,B).
% 1.93/2.15 ** KEPT (pick-wt=10): 44 [] -r2_hidden(A,B)| -m1_subset_1(B,k1_zfmisc_1(C))|m1_subset_1(A,C).
% 1.93/2.15 ** KEPT (pick-wt=9): 45 [] -r2_hidden(A,B)| -m1_subset_1(B,k1_zfmisc_1(C))| -v1_xboole_0(C).
% 1.93/2.15 ** KEPT (pick-wt=23): 46 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)| -m1_subset_1(B,u1_struct_0(A))| -m1_group_2(C,A)| -r1_rlvect_1(C,B)|r1_rlvect_1(C,k3_group_1(A,B)).
% 1.93/2.15 ** KEPT (pick-wt=5): 47 [] -v1_xboole_0(A)|A=k1_xboole_0.
% 1.93/2.15 ** KEPT (pick-wt=5): 48 [] -r2_hidden(A,B)| -v1_xboole_0(B).
% 1.93/2.15 ** KEPT (pick-wt=7): 49 [] -v1_xboole_0(A)|A=B| -v1_xboole_0(B).
% 1.93/2.15
% 1.93/2.15 ------------> process sos:
% 1.93/2.15 ** KEPT (pick-wt=3): 54 [] A=A.
% 1.93/2.15 ** KEPT (pick-wt=2): 55 [] v3_group_1($c3).
% 1.93/2.15 ** KEPT (pick-wt=2): 56 [] v4_group_1($c3).
% 1.93/2.15 ** KEPT (pick-wt=2): 57 [] l1_group_1($c3).
% 1.93/2.15 ** KEPT (pick-wt=2): 58 [] v1_group_1($c2).
% 1.93/2.15 ** KEPT (pick-wt=3): 59 [] m1_group_2($c2,$c3).
% 1.93/2.15 ** KEPT (pick-wt=4): 60 [] m1_subset_1($c1,u1_struct_0($c3)).
% 1.93/2.15 ** KEPT (pick-wt=6): 61 [] r2_hidden($c1,k1_funct_1(k1_latsubgr($c3),$c2)).
% 1.93/2.15 ** KEPT (pick-wt=2): 62 [] l1_group_1($c4).
% 1.93/2.15 ** KEPT (pick-wt=2): 63 [] l1_struct_0($c5).
% 1.93/2.15 ** KEPT (pick-wt=6): 64 [] m1_relset_1($f2(A,B),A,B).
% 1.93/2.15 ** KEPT (pick-wt=4): 65 [] m1_subset_1($f3(A),A).
% 1.93/2.15 ** KEPT (pick-wt=6): 66 [] m2_relset_1($f4(A,B),A,B).
% 1.93/2.15 ** KEPT (pick-wt=2): 67 [] v1_xboole_0(k1_xboole_0).
% 1.93/2.15 ** KEPT (pick-wt=6): 68 [] m1_relset_1($f5(A,B),A,B).
% 2.04/2.22 ** KEPT (pick-wt=4): 69 [] v1_relat_1($f5(A,B)).
% 2.04/2.22 ** KEPT (pick-wt=4): 70 [] v1_funct_1($f5(A,B)).
% 2.04/2.22 ** KEPT (pick-wt=6): 71 [] v1_funct_2($f5(A,B),A,B).
% 2.04/2.22 ** KEPT (pick-wt=7): 72 [] v1_xboole_0(A)|m1_subset_1($f6(A),k1_zfmisc_1(A)).
% 2.04/2.22 ** KEPT (pick-wt=2): 73 [] v1_xboole_0($c6).
% 2.04/2.22 ** KEPT (pick-wt=6): 74 [] m1_relset_1($f7(A,B),A,B).
% 2.04/2.22 ** KEPT (pick-wt=4): 75 [] v1_relat_1($f7(A,B)).
% 2.04/2.22 ** KEPT (pick-wt=4): 76 [] v1_funct_1($f7(A,B)).
% 2.04/2.22 ** KEPT (pick-wt=5): 77 [] m1_subset_1($f8(A),k1_zfmisc_1(A)).
% 2.04/2.22 ** KEPT (pick-wt=3): 78 [] v1_xboole_0($f8(A)).
% 2.04/2.22 ** KEPT (pick-wt=2): 79 [] l1_struct_0($c8).
% 2.04/2.22 ** KEPT (pick-wt=3): 80 [] r1_tarski(A,A).
% 2.04/2.22 Following clause subsumed by 54 during input processing: 0 [copy,54,flip.1] A=A.
% 2.04/2.22 54 back subsumes 53.
% 2.04/2.22
% 2.04/2.22 ======= end of input processing =======
% 2.04/2.22
% 2.04/2.22 =========== start of search ===========
% 2.04/2.22
% 2.04/2.22
% 2.04/2.22 Resetting weight limit to 6.
% 2.04/2.22
% 2.04/2.22
% 2.04/2.22 Resetting weight limit to 6.
% 2.04/2.22
% 2.04/2.22 sos_size=547
% 2.04/2.22
% 2.04/2.22 -------- PROOF --------
% 2.04/2.22
% 2.04/2.22 -----> EMPTY CLAUSE at 0.08 sec ----> 695 [hyper,144,39,55,56,57,58,59,242,unit_del,1,2] $F.
% 2.04/2.22
% 2.04/2.22 Length of proof is 3. Level of proof is 2.
% 2.04/2.22
% 2.04/2.22 ---------------- PROOF ----------------
% 2.04/2.22 % SZS status Theorem
% 2.04/2.22 % SZS output start Refutation
% See solution above
% 2.04/2.22 ------------ end of proof -------------
% 2.04/2.22
% 2.04/2.22
% 2.04/2.22 Search stopped by max_proofs option.
% 2.04/2.22
% 2.04/2.22
% 2.04/2.22 Search stopped by max_proofs option.
% 2.04/2.22
% 2.04/2.22 ============ end of search ============
% 2.04/2.22
% 2.04/2.22 -------------- statistics -------------
% 2.04/2.22 clauses given 105
% 2.04/2.22 clauses generated 1471
% 2.04/2.22 clauses kept 690
% 2.04/2.22 clauses forward subsumed 449
% 2.04/2.22 clauses back subsumed 3
% 2.04/2.22 Kbytes malloced 4882
% 2.04/2.22
% 2.04/2.22 ----------- times (seconds) -----------
% 2.04/2.22 user CPU time 0.08 (0 hr, 0 min, 0 sec)
% 2.04/2.22 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.04/2.22 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.04/2.22
% 2.04/2.22 That finishes the proof of the theorem.
% 2.04/2.22
% 2.04/2.22 Process 6849 finished Wed Jul 27 05:00:27 2022
% 2.04/2.22 Otter interrupted
% 2.04/2.22 PROOF FOUND
%------------------------------------------------------------------------------