TSTP Solution File: GRP642+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP642+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 12:57:30 EDT 2022
% Result : Theorem 2.10s 2.28s
% Output : Refutation 2.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 19
% Syntax : Number of clauses : 30 ( 21 unt; 5 nHn; 29 RR)
% Number of literals : 65 ( 8 equ; 31 neg)
% Maximal clause size : 11 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ v3_struct_0(dollar_c2),
file('GRP642+1.p',unknown),
[] ).
cnf(9,axiom,
( v3_struct_0(A)
| ~ v3_group_1(A)
| ~ v4_group_1(A)
| ~ l1_group_1(A)
| ~ v1_funct_1(B)
| ~ v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| B != k1_latsubgr(A)
| ~ v1_group_1(C)
| ~ m1_group_2(C,A)
| k1_funct_1(B,C) = u1_struct_0(C) ),
file('GRP642+1.p',unknown),
[] ).
cnf(16,axiom,
( v3_struct_0(A)
| ~ v3_group_1(A)
| ~ v4_group_1(A)
| ~ l1_group_1(A)
| v1_funct_1(k1_latsubgr(A)) ),
file('GRP642+1.p',unknown),
[] ).
cnf(17,axiom,
( 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))) ),
file('GRP642+1.p',unknown),
[] ).
cnf(18,axiom,
( 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))) ),
file('GRP642+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ l1_group_1(A)
| l1_struct_0(A) ),
file('GRP642+1.p',unknown),
[] ).
cnf(20,axiom,
( v3_struct_0(A)
| ~ v3_group_1(A)
| ~ l1_group_1(A)
| ~ m1_group_2(B,A)
| ~ v3_struct_0(B) ),
file('GRP642+1.p',unknown),
[] ).
cnf(22,axiom,
( v3_struct_0(A)
| ~ v3_group_1(A)
| ~ l1_group_1(A)
| ~ m1_group_2(B,A)
| l1_group_1(B) ),
file('GRP642+1.p',unknown),
[] ).
cnf(29,axiom,
( v3_struct_0(A)
| ~ l1_struct_0(A)
| ~ v1_xboole_0(u1_struct_0(A)) ),
file('GRP642+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ v1_xboole_0(A)
| A = B
| ~ v1_xboole_0(B) ),
file('GRP642+1.p',unknown),
[] ).
cnf(54,axiom,
A = A,
file('GRP642+1.p',unknown),
[] ).
cnf(55,axiom,
v3_group_1(dollar_c2),
file('GRP642+1.p',unknown),
[] ).
cnf(56,axiom,
v4_group_1(dollar_c2),
file('GRP642+1.p',unknown),
[] ).
cnf(57,axiom,
l1_group_1(dollar_c2),
file('GRP642+1.p',unknown),
[] ).
cnf(58,axiom,
v1_group_1(dollar_c1),
file('GRP642+1.p',unknown),
[] ).
cnf(59,axiom,
m1_group_2(dollar_c1,dollar_c2),
file('GRP642+1.p',unknown),
[] ).
cnf(60,axiom,
k1_funct_1(k1_latsubgr(dollar_c2),dollar_c1) = k1_xboole_0,
file('GRP642+1.p',unknown),
[] ).
cnf(67,axiom,
v1_xboole_0(k1_xboole_0),
file('GRP642+1.p',unknown),
[] ).
cnf(73,axiom,
v1_xboole_0(dollar_c5),
file('GRP642+1.p',unknown),
[] ).
cnf(100,plain,
m2_relset_1(k1_latsubgr(dollar_c2),k1_group_3(dollar_c2),k1_zfmisc_1(u1_struct_0(dollar_c2))),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[57,18,55,56]),1]),
[iquote('hyper,57,18,55,56,unit_del,1')] ).
cnf(101,plain,
v1_funct_2(k1_latsubgr(dollar_c2),k1_group_3(dollar_c2),k1_zfmisc_1(u1_struct_0(dollar_c2))),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[57,17,55,56]),1]),
[iquote('hyper,57,17,55,56,unit_del,1')] ).
cnf(102,plain,
v1_funct_1(k1_latsubgr(dollar_c2)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[57,16,55,56]),1]),
[iquote('hyper,57,16,55,56,unit_del,1')] ).
cnf(117,plain,
l1_group_1(dollar_c1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[59,22,55,57]),1]),
[iquote('hyper,59,22,55,57,unit_del,1')] ).
cnf(158,plain,
k1_xboole_0 = dollar_c5,
inference(hyper,[status(thm)],[73,49,67]),
[iquote('hyper,73,49,67')] ).
cnf(173,plain,
k1_funct_1(k1_latsubgr(dollar_c2),dollar_c1) = dollar_c5,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[60]),158]),
[iquote('back_demod,60,demod,158')] ).
cnf(199,plain,
l1_struct_0(dollar_c1),
inference(hyper,[status(thm)],[117,19]),
[iquote('hyper,117,19')] ).
cnf(676,plain,
u1_struct_0(dollar_c1) = dollar_c5,
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[101,9,55,56,57,102,100,54,58,59]),173]),1])]),
[iquote('hyper,101,9,55,56,57,102,100,54,58,59,demod,173,unit_del,1,flip.1')] ).
cnf(681,plain,
v3_struct_0(dollar_c1),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[676,29]),199,73]),
[iquote('para_from,676.1.1,29.3.1,unit_del,199,73')] ).
cnf(682,plain,
v3_struct_0(dollar_c2),
inference(hyper,[status(thm)],[681,20,55,57,59]),
[iquote('hyper,681,20,55,57,59')] ).
cnf(683,plain,
$false,
inference(binary,[status(thm)],[682,1]),
[iquote('binary,682.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP642+1 : TPTP v8.1.0. Released v3.4.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n018.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 05:12:16 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.96/2.11 ----- Otter 3.3f, August 2004 -----
% 1.96/2.11 The process was started by sandbox2 on n018.cluster.edu,
% 1.96/2.11 Wed Jul 27 05:12:16 2022
% 1.96/2.11 The command was "./otter". The process ID is 564.
% 1.96/2.11
% 1.96/2.11 set(prolog_style_variables).
% 1.96/2.11 set(auto).
% 1.96/2.11 dependent: set(auto1).
% 1.96/2.11 dependent: set(process_input).
% 1.96/2.11 dependent: clear(print_kept).
% 1.96/2.11 dependent: clear(print_new_demod).
% 1.96/2.11 dependent: clear(print_back_demod).
% 1.96/2.11 dependent: clear(print_back_sub).
% 1.96/2.11 dependent: set(control_memory).
% 1.96/2.11 dependent: assign(max_mem, 12000).
% 1.96/2.11 dependent: assign(pick_given_ratio, 4).
% 1.96/2.11 dependent: assign(stats_level, 1).
% 1.96/2.11 dependent: assign(max_seconds, 10800).
% 1.96/2.11 clear(print_given).
% 1.96/2.11
% 1.96/2.11 formula_list(usable).
% 1.96/2.11 all A (A=A).
% 1.96/2.11 -(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)->k1_funct_1(k1_latsubgr(A),B)!=k1_xboole_0)))).
% 1.96/2.11 all A (l1_group_1(A)-> (v1_group_1(A)->A=g1_group_1(u1_struct_0(A),u1_group_1(A)))).
% 1.96/2.11 all A B (r2_hidden(A,B)-> -r2_hidden(B,A)).
% 1.96/2.11 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))).
% 1.96/2.11 all A B C (m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))->v1_relat_1(C)).
% 1.96/2.11 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))))).
% 1.96/2.11 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))))).
% 1.96/2.11 all A (-v3_struct_0(A)&v3_group_1(A)&v4_group_1(A)&l1_group_1(A)-> (all B (v1_funct_1(B)&v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))&m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))-> (B=k1_latsubgr(A)<-> (all C (v1_group_1(C)&m1_group_2(C,A)->k1_funct_1(B,C)=u1_struct_0(C))))))).
% 1.96/2.11 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))).
% 1.96/2.11 $T.
% 1.96/2.11 $T.
% 1.96/2.11 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)))).
% 1.96/2.11 $T.
% 1.96/2.11 $T.
% 1.96/2.11 $T.
% 1.96/2.11 all A (l1_group_1(A)->l1_struct_0(A)).
% 1.96/2.11 $T.
% 1.96/2.11 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)))).
% 1.96/2.11 $T.
% 1.96/2.11 $T.
% 1.96/2.11 all A B C (m2_relset_1(C,A,B)->m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))).
% 1.96/2.11 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))).
% 1.96/2.11 $T.
% 1.96/2.11 exists A l1_group_1(A).
% 1.96/2.11 exists A l1_struct_0(A).
% 1.96/2.11 all A (-v3_struct_0(A)&v3_group_1(A)&l1_group_1(A)-> (exists B m1_group_2(B,A))).
% 1.96/2.11 all A B exists C m1_relset_1(C,A,B).
% 1.96/2.11 all A exists B m1_subset_1(B,A).
% 1.96/2.11 all A B exists C m2_relset_1(C,A,B).
% 1.96/2.11 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))).
% 1.96/2.11 all A (-v3_struct_0(A)&l1_struct_0(A)-> -v1_xboole_0(u1_struct_0(A))).
% 1.96/2.11 all A (-v1_xboole_0(k1_zfmisc_1(A))).
% 1.96/2.11 v1_xboole_0(k1_xboole_0).
% 1.96/2.11 all A B (-v1_xboole_0(A)& -v1_xboole_0(B)-> -v1_xboole_0(k2_zfmisc_1(A,B))).
% 1.96/2.11 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))).
% 1.96/2.11 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)).
% 1.96/2.11 all A (-v1_xboole_0(A)-> (exists B (m1_subset_1(B,k1_zfmisc_1(A))& -v1_xboole_0(B)))).
% 1.96/2.11 exists A v1_xboole_0(A).
% 1.96/2.11 all A B exists C (m1_relset_1(C,A,B)&v1_relat_1(C)&v1_funct_1(C)).
% 1.96/2.11 all A exists B (m1_subset_1(B,k1_zfmisc_1(A))&v1_xboole_0(B)).
% 1.96/2.11 exists A (-v1_xboole_0(A)).
% 1.96/2.11 exists A (l1_struct_0(A)& -v3_struct_0(A)).
% 1.96/2.11 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)))).
% 1.96/2.11 all A B C (m2_relset_1(C,A,B)<->m1_relset_1(C,A,B)).
% 1.96/2.11 all A B r1_tarski(A,A).
% 1.96/2.11 all A B (r2_hidden(A,B)->m1_subset_1(A,B)).
% 1.96/2.11 all A B (m1_subset_1(A,B)->v1_xboole_0(B)|r2_hidden(A,B)).
% 1.96/2.11 all A B (m1_subset_1(A,k1_zfmisc_1(B))<->r1_tarski(A,B)).
% 1.96/2.11 all A B C (r2_hidden(A,B)&m1_subset_1(B,k1_zfmisc_1(C))->m1_subset_1(A,C)).
% 1.96/2.12 all A B C (-(r2_hidden(A,B)&m1_subset_1(B,k1_zfmisc_1(C))&v1_xboole_0(C))).
% 1.96/2.12 all A (v1_xboole_0(A)->A=k1_xboole_0).
% 1.96/2.12 all A B (-(r2_hidden(A,B)&v1_xboole_0(B))).
% 1.96/2.12 all A B (-(v1_xboole_0(A)&A!=B&v1_xboole_0(B))).
% 1.96/2.12 end_of_list.
% 1.96/2.12
% 1.96/2.12 -------> usable clausifies to:
% 1.96/2.12
% 1.96/2.12 list(usable).
% 1.96/2.12 0 [] A=A.
% 1.96/2.12 0 [] -v3_struct_0($c2).
% 1.96/2.12 0 [] v3_group_1($c2).
% 1.96/2.12 0 [] v4_group_1($c2).
% 1.96/2.12 0 [] l1_group_1($c2).
% 1.96/2.12 0 [] v1_group_1($c1).
% 1.96/2.12 0 [] m1_group_2($c1,$c2).
% 1.96/2.12 0 [] k1_funct_1(k1_latsubgr($c2),$c1)=k1_xboole_0.
% 1.96/2.12 0 [] -l1_group_1(A)| -v1_group_1(A)|A=g1_group_1(u1_struct_0(A),u1_group_1(A)).
% 1.96/2.12 0 [] -r2_hidden(A,B)| -r2_hidden(B,A).
% 1.96/2.12 0 [] -m1_relset_1(C,A,B)| -v1_funct_1(C)| -v1_partfun1(C,A,B)|v1_funct_2(C,A,B).
% 1.96/2.12 0 [] -m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))|v1_relat_1(C).
% 1.96/2.12 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).
% 1.96/2.12 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).
% 1.96/2.12 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).
% 1.96/2.12 0 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)| -v1_funct_1(B)| -v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))| -m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))|B!=k1_latsubgr(A)| -v1_group_1(C)| -m1_group_2(C,A)|k1_funct_1(B,C)=u1_struct_0(C).
% 1.96/2.12 0 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)| -v1_funct_1(B)| -v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))| -m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))|B=k1_latsubgr(A)|v1_group_1($f1(A,B)).
% 1.96/2.12 0 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)| -v1_funct_1(B)| -v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))| -m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))|B=k1_latsubgr(A)|m1_group_2($f1(A,B),A).
% 1.96/2.12 0 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)| -v1_funct_1(B)| -v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))| -m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))|B=k1_latsubgr(A)|k1_funct_1(B,$f1(A,B))!=u1_struct_0($f1(A,B)).
% 1.96/2.12 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)).
% 1.96/2.12 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)).
% 1.96/2.12 0 [] $T.
% 1.96/2.12 0 [] $T.
% 1.96/2.12 0 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)|v1_funct_1(k1_latsubgr(A)).
% 1.96/2.12 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))).
% 1.96/2.12 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))).
% 1.96/2.12 0 [] $T.
% 1.96/2.12 0 [] $T.
% 1.96/2.12 0 [] $T.
% 1.96/2.12 0 [] -l1_group_1(A)|l1_struct_0(A).
% 1.96/2.12 0 [] $T.
% 1.96/2.12 0 [] v3_struct_0(A)| -v3_group_1(A)| -l1_group_1(A)| -m1_group_2(B,A)| -v3_struct_0(B).
% 1.96/2.12 0 [] v3_struct_0(A)| -v3_group_1(A)| -l1_group_1(A)| -m1_group_2(B,A)|v3_group_1(B).
% 1.96/2.12 0 [] v3_struct_0(A)| -v3_group_1(A)| -l1_group_1(A)| -m1_group_2(B,A)|l1_group_1(B).
% 1.96/2.12 0 [] $T.
% 1.96/2.12 0 [] $T.
% 1.96/2.12 0 [] -m2_relset_1(C,A,B)|m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))).
% 1.96/2.12 0 [] -l1_group_1(A)|v1_funct_1(u1_group_1(A)).
% 1.96/2.12 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)).
% 1.96/2.12 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)).
% 1.96/2.12 0 [] $T.
% 1.96/2.12 0 [] l1_group_1($c3).
% 1.96/2.12 0 [] l1_struct_0($c4).
% 1.96/2.12 0 [] v3_struct_0(A)| -v3_group_1(A)| -l1_group_1(A)|m1_group_2($f2(A),A).
% 1.96/2.12 0 [] m1_relset_1($f3(A,B),A,B).
% 1.96/2.12 0 [] m1_subset_1($f4(A),A).
% 1.96/2.12 0 [] m2_relset_1($f5(A,B),A,B).
% 1.96/2.12 0 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)| -v1_xboole_0(k1_group_3(A)).
% 1.96/2.12 0 [] v3_struct_0(A)| -l1_struct_0(A)| -v1_xboole_0(u1_struct_0(A)).
% 1.96/2.12 0 [] -v1_xboole_0(k1_zfmisc_1(A)).
% 1.96/2.12 0 [] v1_xboole_0(k1_xboole_0).
% 1.96/2.12 0 [] v1_xboole_0(A)|v1_xboole_0(B)| -v1_xboole_0(k2_zfmisc_1(A,B)).
% 1.96/2.12 0 [] -v1_funct_1(B)| -v1_funct_2(B,k2_zfmisc_1(A,A),A)| -m1_relset_1(B,k2_zfmisc_1(A,A),A)|g1_group_1(A,B)!=g1_group_1(C,D)|A=C.
% 1.96/2.12 0 [] -v1_funct_1(B)| -v1_funct_2(B,k2_zfmisc_1(A,A),A)| -m1_relset_1(B,k2_zfmisc_1(A,A),A)|g1_group_1(A,B)!=g1_group_1(C,D)|B=D.
% 1.96/2.12 0 [] m1_relset_1($f6(A,B),A,B).
% 1.96/2.12 0 [] v1_relat_1($f6(A,B)).
% 1.96/2.12 0 [] v1_funct_1($f6(A,B)).
% 1.96/2.12 0 [] v1_funct_2($f6(A,B),A,B).
% 1.96/2.12 0 [] v1_xboole_0(A)|m1_subset_1($f7(A),k1_zfmisc_1(A)).
% 1.96/2.12 0 [] v1_xboole_0(A)| -v1_xboole_0($f7(A)).
% 1.96/2.12 0 [] v1_xboole_0($c5).
% 1.96/2.12 0 [] m1_relset_1($f8(A,B),A,B).
% 1.96/2.12 0 [] v1_relat_1($f8(A,B)).
% 1.96/2.12 0 [] v1_funct_1($f8(A,B)).
% 1.96/2.12 0 [] m1_subset_1($f9(A),k1_zfmisc_1(A)).
% 1.96/2.12 0 [] v1_xboole_0($f9(A)).
% 1.96/2.12 0 [] -v1_xboole_0($c6).
% 1.96/2.12 0 [] l1_struct_0($c7).
% 1.96/2.12 0 [] -v3_struct_0($c7).
% 1.96/2.12 0 [] v3_struct_0(A)| -l1_struct_0(A)|m1_subset_1($f10(A),k1_zfmisc_1(u1_struct_0(A))).
% 1.96/2.12 0 [] v3_struct_0(A)| -l1_struct_0(A)| -v1_xboole_0($f10(A)).
% 1.96/2.12 0 [] -m2_relset_1(C,A,B)|m1_relset_1(C,A,B).
% 1.96/2.12 0 [] m2_relset_1(C,A,B)| -m1_relset_1(C,A,B).
% 1.96/2.12 0 [] r1_tarski(A,A).
% 1.96/2.12 0 [] -r2_hidden(A,B)|m1_subset_1(A,B).
% 1.96/2.12 0 [] -m1_subset_1(A,B)|v1_xboole_0(B)|r2_hidden(A,B).
% 1.96/2.12 0 [] -m1_subset_1(A,k1_zfmisc_1(B))|r1_tarski(A,B).
% 1.96/2.12 0 [] m1_subset_1(A,k1_zfmisc_1(B))| -r1_tarski(A,B).
% 1.96/2.12 0 [] -r2_hidden(A,B)| -m1_subset_1(B,k1_zfmisc_1(C))|m1_subset_1(A,C).
% 1.96/2.12 0 [] -r2_hidden(A,B)| -m1_subset_1(B,k1_zfmisc_1(C))| -v1_xboole_0(C).
% 1.96/2.12 0 [] -v1_xboole_0(A)|A=k1_xboole_0.
% 1.96/2.12 0 [] -r2_hidden(A,B)| -v1_xboole_0(B).
% 1.96/2.12 0 [] -v1_xboole_0(A)|A=B| -v1_xboole_0(B).
% 1.96/2.12 end_of_list.
% 1.96/2.12
% 1.96/2.12 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=11.
% 1.96/2.12
% 1.96/2.12 This ia a non-Horn set with equality. The strategy will be
% 1.96/2.12 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.96/2.12 deletion, with positive clauses in sos and nonpositive
% 1.96/2.12 clauses in usable.
% 1.96/2.12
% 1.96/2.12 dependent: set(knuth_bendix).
% 1.96/2.12 dependent: set(anl_eq).
% 1.96/2.12 dependent: set(para_from).
% 1.96/2.12 dependent: set(para_into).
% 1.96/2.12 dependent: clear(para_from_right).
% 1.96/2.12 dependent: clear(para_into_right).
% 1.96/2.12 dependent: set(para_from_vars).
% 1.96/2.12 dependent: set(eq_units_both_ways).
% 1.96/2.12 dependent: set(dynamic_demod_all).
% 1.96/2.12 dependent: set(dynamic_demod).
% 1.96/2.12 dependent: set(order_eq).
% 1.96/2.12 dependent: set(back_demod).
% 1.96/2.12 dependent: set(lrpo).
% 1.96/2.12 dependent: set(hyper_res).
% 1.96/2.12 dependent: set(unit_deletion).
% 1.96/2.12 dependent: set(factor).
% 1.96/2.12
% 1.96/2.12 ------------> process usable:
% 1.96/2.12 ** KEPT (pick-wt=2): 1 [] -v3_struct_0($c2).
% 1.96/2.12 ** KEPT (pick-wt=11): 3 [copy,2,flip.3] -l1_group_1(A)| -v1_group_1(A)|g1_group_1(u1_struct_0(A),u1_group_1(A))=A.
% 1.96/2.12 ** KEPT (pick-wt=6): 4 [] -r2_hidden(A,B)| -r2_hidden(B,A).
% 1.96/2.12 ** KEPT (pick-wt=14): 5 [] -m1_relset_1(A,B,C)| -v1_funct_1(A)| -v1_partfun1(A,B,C)|v1_funct_2(A,B,C).
% 1.96/2.12 ** KEPT (pick-wt=8): 6 [] -m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C)))|v1_relat_1(A).
% 1.96/2.12 ** KEPT (pick-wt=16): 7 [] v1_xboole_0(A)| -m1_relset_1(B,C,A)| -v1_funct_1(B)| -v1_funct_2(B,C,A)|v1_partfun1(B,C,A).
% 1.96/2.12 ** KEPT (pick-wt=16): 8 [] v1_xboole_0(A)|v1_xboole_0(B)| -m1_relset_1(C,A,B)| -v1_funct_1(C)| -v1_funct_2(C,A,B)| -v1_xboole_0(C).
% 1.96/2.12 Following clause subsumed by 7 during input processing: 0 [] v1_xboole_0(A)|v1_xboole_0(B)| -m1_relset_1(C,A,B)| -v1_funct_1(C)| -v1_funct_2(C,A,B)|v1_partfun1(C,A,B).
% 1.96/2.12 ** KEPT (pick-wt=39): 9 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)| -v1_funct_1(B)| -v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))| -m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))|B!=k1_latsubgr(A)| -v1_group_1(C)| -m1_group_2(C,A)|k1_funct_1(B,C)=u1_struct_0(C).
% 1.96/2.12 ** KEPT (pick-wt=32): 10 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)| -v1_funct_1(B)| -v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))| -m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))|B=k1_latsubgr(A)|v1_group_1($f1(A,B)).
% 1.96/2.12 ** KEPT (pick-wt=33): 11 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)| -v1_funct_1(B)| -v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))| -m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))|B=k1_latsubgr(A)|m1_group_2($f1(A,B),A).
% 1.96/2.12 ** KEPT (pick-wt=38): 13 [copy,12,flip.9] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)| -v1_funct_1(B)| -v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))| -m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))|B=k1_latsubgr(A)|u1_struct_0($f1(A,B))!=k1_funct_1(B,$f1(A,B)).
% 1.96/2.12 ** KEPT (pick-wt=18): 14 [] -v1_funct_1(A)| -v1_funct_2(A,k2_zfmisc_1(B,B),B)| -m1_relset_1(A,k2_zfmisc_1(B,B),B)|v1_group_1(g1_group_1(B,A)).
% 1.96/2.12 ** KEPT (pick-wt=18): 15 [] -v1_funct_1(A)| -v1_funct_2(A,k2_zfmisc_1(B,B),B)| -m1_relset_1(A,k2_zfmisc_1(B,B),B)|l1_group_1(g1_group_1(B,A)).
% 1.96/2.12 ** KEPT (pick-wt=11): 16 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)|v1_funct_1(k1_latsubgr(A)).
% 1.96/2.12 ** KEPT (pick-wt=16): 17 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)|v1_funct_2(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))).
% 1.96/2.12 ** KEPT (pick-wt=16): 18 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)|m2_relset_1(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))).
% 1.96/2.12 ** KEPT (pick-wt=4): 19 [] -l1_group_1(A)|l1_struct_0(A).
% 1.96/2.12 ** KEPT (pick-wt=11): 20 [] v3_struct_0(A)| -v3_group_1(A)| -l1_group_1(A)| -m1_group_2(B,A)| -v3_struct_0(B).
% 1.96/2.12 ** KEPT (pick-wt=11): 21 [] v3_struct_0(A)| -v3_group_1(A)| -l1_group_1(A)| -m1_group_2(B,A)|v3_group_1(B).
% 1.96/2.12 ** KEPT (pick-wt=11): 22 [] v3_struct_0(A)| -v3_group_1(A)| -l1_group_1(A)| -m1_group_2(B,A)|l1_group_1(B).
% 1.96/2.12 ** KEPT (pick-wt=10): 23 [] -m2_relset_1(A,B,C)|m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,C))).
% 1.96/2.12 ** KEPT (pick-wt=5): 24 [] -l1_group_1(A)|v1_funct_1(u1_group_1(A)).
% 1.96/2.12 ** KEPT (pick-wt=12): 25 [] -l1_group_1(A)|v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)).
% 1.96/2.12 ** KEPT (pick-wt=12): 26 [] -l1_group_1(A)|m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)).
% 1.96/2.12 ** KEPT (pick-wt=10): 27 [] v3_struct_0(A)| -v3_group_1(A)| -l1_group_1(A)|m1_group_2($f2(A),A).
% 1.96/2.12 ** KEPT (pick-wt=11): 28 [] v3_struct_0(A)| -v3_group_1(A)| -v4_group_1(A)| -l1_group_1(A)| -v1_xboole_0(k1_group_3(A)).
% 1.96/2.12 ** KEPT (pick-wt=7): 29 [] v3_struct_0(A)| -l1_struct_0(A)| -v1_xboole_0(u1_struct_0(A)).
% 1.96/2.12 ** KEPT (pick-wt=3): 30 [] -v1_xboole_0(k1_zfmisc_1(A)).
% 1.96/2.12 ** KEPT (pick-wt=8): 31 [] v1_xboole_0(A)|v1_xboole_0(B)| -v1_xboole_0(k2_zfmisc_1(A,B)).
% 1.96/2.12 ** KEPT (pick-wt=24): 32 [] -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.
% 1.96/2.12 ** KEPT (pick-wt=24): 33 [] -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.
% 1.96/2.12 ** KEPT (pick-wt=5): 34 [] v1_xboole_0(A)| -v1_xboole_0($f7(A)).
% 1.96/2.12 ** KEPT (pick-wt=2): 35 [] -v1_xboole_0($c6).
% 1.96/2.12 ** KEPT (pick-wt=2): 36 [] -v3_struct_0($c7).
% 1.96/2.12 ** KEPT (pick-wt=10): 37 [] v3_struct_0(A)| -l1_struct_0(A)|m1_subset_1($f10(A),k1_zfmisc_1(u1_struct_0(A))).
% 1.96/2.12 ** KEPT (pick-wt=7): 38 [] v3_struct_0(A)| -l1_struct_0(A)| -v1_xboole_0($f10(A)).
% 1.96/2.12 ** KEPT (pick-wt=8): 39 [] -m2_relset_1(A,B,C)|m1_relset_1(A,B,C).
% 1.96/2.12 ** KEPT (pick-wt=8): 40 [] m2_relset_1(A,B,C)| -m1_relset_1(A,B,C).
% 1.96/2.12 ** KEPT (pick-wt=6): 41 [] -r2_hidden(A,B)|m1_subset_1(A,B).
% 1.96/2.12 ** KEPT (pick-wt=8): 42 [] -m1_subset_1(A,B)|v1_xboole_0(B)|r2_hidden(A,B).
% 1.96/2.12 ** KEPT (pick-wt=7): 43 [] -m1_subset_1(A,k1_zfmisc_1(B))|r1_tarski(A,B).
% 1.96/2.12 ** KEPT (pick-wt=7): 44 [] m1_subset_1(A,k1_zfmisc_1(B))| -r1_tarski(A,B).
% 1.96/2.12 ** KEPT (pick-wt=10): 45 [] -r2_hidden(A,B)| -m1_subset_1(B,k1_zfmisc_1(C))|m1_subset_1(A,C).
% 1.96/2.12 ** KEPT (pick-wt=9): 46 [] -r2_hidden(A,B)| -m1_subset_1(B,k1_zfmisc_1(C))| -v1_xboole_0(C).
% 1.96/2.12 ** KEPT (pick-wt=5): 47 [] -v1_xboole_0(A)|A=k1_xboole_0.
% 1.96/2.12 ** KEPT (pick-wt=5): 48 [] -r2_hidden(A,B)| -v1_xboole_0(B).
% 1.96/2.12 ** KEPT (pick-wt=7): 49 [] -v1_xboole_0(A)|A=B| -v1_xboole_0(B).
% 1.96/2.12
% 1.96/2.12 ------------> process sos:
% 1.96/2.12 ** KEPT (pick-wt=3): 54 [] A=A.
% 1.96/2.12 ** KEPT (pick-wt=2): 55 [] v3_group_1($c2).
% 1.96/2.12 ** KEPT (pick-wt=2): 56 [] v4_group_1($c2).
% 1.96/2.12 ** KEPT (pick-wt=2): 57 [] l1_group_1($c2).
% 1.96/2.12 ** KEPT (pick-wt=2): 58 [] v1_group_1($c1).
% 1.96/2.12 ** KEPT (pick-wt=3): 59 [] m1_group_2($c1,$c2).
% 1.96/2.12 ** KEPT (pick-wt=6): 60 [] k1_funct_1(k1_latsubgr($c2),$c1)=k1_xboole_0.
% 1.96/2.12 ---> New Demodulator: 61 [new_demod,60] k1_funct_1(k1_latsubgr($c2),$c1)=k1_xboole_0.
% 1.96/2.12 ** KEPT (pick-wt=2): 62 [] l1_group_1($c3).
% 1.96/2.12 ** KEPT (pick-wt=2): 63 [] l1_struct_0($c4).
% 1.96/2.12 ** KEPT (pick-wt=6): 64 [] m1_relset_1($f3(A,B),A,B).
% 1.96/2.12 ** KEPT (pick-wt=4): 65 [] m1_subset_1($f4(A),A).
% 1.96/2.12 ** KEPT (pick-wt=6): 66 [] m2_relset_1($f5(A,B),A,B).
% 2.10/2.28 ** KEPT (pick-wt=2): 67 [] v1_xboole_0(k1_xboole_0).
% 2.10/2.28 ** KEPT (pick-wt=6): 68 [] m1_relset_1($f6(A,B),A,B).
% 2.10/2.28 ** KEPT (pick-wt=4): 69 [] v1_relat_1($f6(A,B)).
% 2.10/2.28 ** KEPT (pick-wt=4): 70 [] v1_funct_1($f6(A,B)).
% 2.10/2.28 ** KEPT (pick-wt=6): 71 [] v1_funct_2($f6(A,B),A,B).
% 2.10/2.28 ** KEPT (pick-wt=7): 72 [] v1_xboole_0(A)|m1_subset_1($f7(A),k1_zfmisc_1(A)).
% 2.10/2.28 ** KEPT (pick-wt=2): 73 [] v1_xboole_0($c5).
% 2.10/2.28 ** KEPT (pick-wt=6): 74 [] m1_relset_1($f8(A,B),A,B).
% 2.10/2.28 ** KEPT (pick-wt=4): 75 [] v1_relat_1($f8(A,B)).
% 2.10/2.28 ** KEPT (pick-wt=4): 76 [] v1_funct_1($f8(A,B)).
% 2.10/2.28 ** KEPT (pick-wt=5): 77 [] m1_subset_1($f9(A),k1_zfmisc_1(A)).
% 2.10/2.28 ** KEPT (pick-wt=3): 78 [] v1_xboole_0($f9(A)).
% 2.10/2.28 ** KEPT (pick-wt=2): 79 [] l1_struct_0($c7).
% 2.10/2.28 ** KEPT (pick-wt=3): 80 [] r1_tarski(A,A).
% 2.10/2.28 Following clause subsumed by 54 during input processing: 0 [copy,54,flip.1] A=A.
% 2.10/2.28 54 back subsumes 53.
% 2.10/2.28 >>>> Starting back demodulation with 61.
% 2.10/2.28
% 2.10/2.28 ======= end of input processing =======
% 2.10/2.28
% 2.10/2.28 =========== start of search ===========
% 2.10/2.28
% 2.10/2.28
% 2.10/2.28 Resetting weight limit to 6.
% 2.10/2.28
% 2.10/2.28
% 2.10/2.28 Resetting weight limit to 6.
% 2.10/2.28
% 2.10/2.28 sos_size=485
% 2.10/2.28
% 2.10/2.28 -------- PROOF --------
% 2.10/2.28
% 2.10/2.28 ----> UNIT CONFLICT at 0.17 sec ----> 683 [binary,682.1,1.1] $F.
% 2.10/2.28
% 2.10/2.28 Length of proof is 10. Level of proof is 5.
% 2.10/2.28
% 2.10/2.28 ---------------- PROOF ----------------
% 2.10/2.28 % SZS status Theorem
% 2.10/2.28 % SZS output start Refutation
% See solution above
% 2.10/2.28 ------------ end of proof -------------
% 2.10/2.28
% 2.10/2.28
% 2.10/2.28 Search stopped by max_proofs option.
% 2.10/2.28
% 2.10/2.28
% 2.10/2.28 Search stopped by max_proofs option.
% 2.10/2.28
% 2.10/2.28 ============ end of search ============
% 2.10/2.28
% 2.10/2.28 -------------- statistics -------------
% 2.10/2.28 clauses given 123
% 2.10/2.28 clauses generated 2783
% 2.10/2.28 clauses kept 673
% 2.10/2.28 clauses forward subsumed 349
% 2.10/2.28 clauses back subsumed 7
% 2.10/2.28 Kbytes malloced 4882
% 2.10/2.28
% 2.10/2.28 ----------- times (seconds) -----------
% 2.10/2.28 user CPU time 0.17 (0 hr, 0 min, 0 sec)
% 2.10/2.28 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.10/2.28 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.10/2.28
% 2.10/2.28 That finishes the proof of the theorem.
% 2.10/2.28
% 2.10/2.28 Process 564 finished Wed Jul 27 05:12:18 2022
% 2.10/2.28 Otter interrupted
% 2.10/2.28 PROOF FOUND
%------------------------------------------------------------------------------