TSTP Solution File: LAT295+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT295+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 : 600s
% DateTime : Sun Jul 17 06:50:18 EDT 2022
% Result : Theorem 2.24s 2.41s
% Output : Refutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 39
% Syntax : Number of clauses : 200 ( 47 unt; 31 nHn; 200 RR)
% Number of literals : 632 ( 0 equ; 426 neg)
% Maximal clause size : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 1 prp; 0-5 aty)
% Number of functors : 21 ( 21 usr; 11 con; 0-6 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
l3_lattices(skc19),
file('LAT295+1.p',unknown),
[] ).
cnf(2,axiom,
l3_lattices(skc20),
file('LAT295+1.p',unknown),
[] ).
cnf(23,axiom,
~ v3_struct_0(skc20),
file('LAT295+1.p',unknown),
[] ).
cnf(24,axiom,
~ v3_struct_0(skc19),
file('LAT295+1.p',unknown),
[] ).
cnf(25,axiom,
equal(skc23,skc21),
file('LAT295+1.p',unknown),
[] ).
cnf(36,axiom,
m1_subset_1(skc23,u1_struct_0(skc20)),
file('LAT295+1.p',unknown),
[] ).
cnf(37,axiom,
m1_subset_1(skc22,u1_struct_0(skc19)),
file('LAT295+1.p',unknown),
[] ).
cnf(38,axiom,
m1_subset_1(skc21,u1_struct_0(skc19)),
file('LAT295+1.p',unknown),
[] ).
cnf(39,axiom,
m1_subset_1(skc22,u1_struct_0(skc20)),
file('LAT295+1.p',unknown),
[] ).
cnf(47,axiom,
( ~ l2_lattices(u)
| l1_struct_0(u) ),
file('LAT295+1.p',unknown),
[] ).
cnf(48,axiom,
( ~ l3_lattices(u)
| l1_lattices(u) ),
file('LAT295+1.p',unknown),
[] ).
cnf(49,axiom,
( ~ l3_lattices(u)
| l2_lattices(u) ),
file('LAT295+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ l1_lattices(u)
| v1_funct_1(u1_lattices(u)) ),
file('LAT295+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ l2_lattices(u)
| v1_funct_1(u2_lattices(u)) ),
file('LAT295+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ v1_xboole_0(u)
| ~ r2_hidden(v,u) ),
file('LAT295+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(k2_zfmisc_1(v,w)))
| v1_relat_1(u) ),
file('LAT295+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ l1_struct_0(u)
| ~ v1_xboole_0(u1_struct_0(u))
| v3_struct_0(u) ),
file('LAT295+1.p',unknown),
[] ).
cnf(70,axiom,
( ~ m2_relset_1(u,v,w)
| m1_relset_1(u,v,w) ),
file('LAT295+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ m1_subset_1(u,v)
| v1_xboole_0(v)
| r2_hidden(u,v) ),
file('LAT295+1.p',unknown),
[] ).
cnf(74,axiom,
( r1_lattices(u,v,w)
| skP0(x,y,w,v,u) ),
file('LAT295+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ r1_lattices(u,v,w)
| skP0(v,u,w,x,y) ),
file('LAT295+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ m2_relset_1(u,v,w)
| m1_subset_1(u,k1_zfmisc_1(k2_zfmisc_1(v,w))) ),
file('LAT295+1.p',unknown),
[] ).
cnf(81,axiom,
( ~ l1_lattices(u)
| v1_funct_2(u1_lattices(u),k2_zfmisc_1(u1_struct_0(u),u1_struct_0(u)),u1_struct_0(u)) ),
file('LAT295+1.p',unknown),
[] ).
cnf(82,axiom,
( ~ l1_lattices(u)
| m2_relset_1(u1_lattices(u),k2_zfmisc_1(u1_struct_0(u),u1_struct_0(u)),u1_struct_0(u)) ),
file('LAT295+1.p',unknown),
[] ).
cnf(83,axiom,
( ~ l2_lattices(u)
| v1_funct_2(u2_lattices(u),k2_zfmisc_1(u1_struct_0(u),u1_struct_0(u)),u1_struct_0(u)) ),
file('LAT295+1.p',unknown),
[] ).
cnf(84,axiom,
( ~ l2_lattices(u)
| m2_relset_1(u2_lattices(u),k2_zfmisc_1(u1_struct_0(u),u1_struct_0(u)),u1_struct_0(u)) ),
file('LAT295+1.p',unknown),
[] ).
cnf(85,axiom,
equal(g3_lattices(u1_struct_0(skc20),u2_lattices(skc20),u1_lattices(skc20)),g3_lattices(u1_struct_0(skc19),u2_lattices(skc19),u1_lattices(skc19))),
file('LAT295+1.p',unknown),
[] ).
cnf(86,axiom,
( ~ v3_lattices(u)
| ~ l3_lattices(u)
| equal(g3_lattices(u1_struct_0(u),u2_lattices(u),u1_lattices(u)),u) ),
file('LAT295+1.p',unknown),
[] ).
cnf(90,axiom,
( ~ l2_lattices(u)
| ~ m1_subset_1(v,u1_struct_0(u))
| ~ m1_subset_1(w,u1_struct_0(u))
| ~ equal(k1_lattices(u,w,v),v)
| v3_struct_0(u)
| r1_lattices(u,w,v) ),
file('LAT295+1.p',unknown),
[] ).
cnf(91,axiom,
( ~ l2_lattices(u)
| ~ m1_subset_1(v,u1_struct_0(u))
| ~ m1_subset_1(w,u1_struct_0(u))
| ~ r1_lattices(u,w,v)
| v3_struct_0(u)
| equal(k1_lattices(u,w,v),v) ),
file('LAT295+1.p',unknown),
[] ).
cnf(92,axiom,
( ~ l1_lattices(u)
| ~ m1_subset_1(v,u1_struct_0(u))
| ~ m1_subset_1(w,u1_struct_0(u))
| v3_struct_0(u)
| equal(k2_binop_1(u1_struct_0(u),u1_struct_0(u),u1_struct_0(u),u1_lattices(u),w,v),k2_lattices(u,w,v)) ),
file('LAT295+1.p',unknown),
[] ).
cnf(93,axiom,
( ~ l2_lattices(u)
| ~ m1_subset_1(v,u1_struct_0(u))
| ~ m1_subset_1(w,u1_struct_0(u))
| v3_struct_0(u)
| equal(k2_binop_1(u1_struct_0(u),u1_struct_0(u),u1_struct_0(u),u2_lattices(u),w,v),k1_lattices(u,w,v)) ),
file('LAT295+1.p',unknown),
[] ).
cnf(94,axiom,
( ~ equal(k1_lattices(skc20,skc23,skc22),k1_lattices(skc19,skc21,skc22))
| ~ equal(k2_lattices(skc20,skc23,skc22),k2_lattices(skc19,skc21,skc22))
| ~ skP0(skc23,skc20,skc22,skc21,skc19)
| ~ skP0(skc21,skc19,skc22,skc23,skc20) ),
file('LAT295+1.p',unknown),
[] ).
cnf(96,axiom,
( ~ v1_funct_1(u)
| ~ v1_funct_1(v)
| ~ m1_relset_1(v,k2_zfmisc_1(w,w),w)
| ~ v1_funct_2(v,k2_zfmisc_1(w,w),w)
| ~ m1_relset_1(u,k2_zfmisc_1(w,w),w)
| ~ v1_funct_2(u,k2_zfmisc_1(w,w),w)
| l3_lattices(g3_lattices(w,v,u)) ),
file('LAT295+1.p',unknown),
[] ).
cnf(97,axiom,
( ~ v1_funct_1(u)
| ~ v1_funct_1(v)
| ~ m1_relset_1(v,k2_zfmisc_1(w,w),w)
| ~ v1_funct_2(v,k2_zfmisc_1(w,w),w)
| ~ m1_relset_1(u,k2_zfmisc_1(w,w),w)
| ~ v1_funct_2(u,k2_zfmisc_1(w,w),w)
| v3_lattices(g3_lattices(w,v,u)) ),
file('LAT295+1.p',unknown),
[] ).
cnf(98,axiom,
( ~ v1_funct_1(u)
| ~ m1_subset_1(v,w)
| ~ m1_subset_1(x,y)
| ~ v1_funct_2(u,k2_zfmisc_1(w,y),z)
| ~ m1_relset_1(u,k2_zfmisc_1(w,y),z)
| v1_xboole_0(y)
| v1_xboole_0(w)
| equal(k2_binop_1(w,y,z,u,v,x),k1_binop_1(u,v,x)) ),
file('LAT295+1.p',unknown),
[] ).
cnf(101,axiom,
( ~ v1_funct_1(u)
| ~ v1_funct_1(v)
| ~ equal(g3_lattices(w,v,u),g3_lattices(x,y,z))
| ~ m1_relset_1(v,k2_zfmisc_1(w,w),w)
| ~ v1_funct_2(v,k2_zfmisc_1(w,w),w)
| ~ m1_relset_1(u,k2_zfmisc_1(w,w),w)
| ~ v1_funct_2(u,k2_zfmisc_1(w,w),w)
| equal(u,z) ),
file('LAT295+1.p',unknown),
[] ).
cnf(102,axiom,
( ~ v1_funct_1(u)
| ~ v1_funct_1(v)
| ~ equal(g3_lattices(w,v,u),g3_lattices(x,y,z))
| ~ m1_relset_1(v,k2_zfmisc_1(w,w),w)
| ~ v1_funct_2(v,k2_zfmisc_1(w,w),w)
| ~ m1_relset_1(u,k2_zfmisc_1(w,w),w)
| ~ v1_funct_2(u,k2_zfmisc_1(w,w),w)
| equal(v,y) ),
file('LAT295+1.p',unknown),
[] ).
cnf(103,axiom,
( ~ v1_funct_1(u)
| ~ v1_funct_1(v)
| ~ equal(g3_lattices(w,v,u),g3_lattices(x,y,z))
| ~ m1_relset_1(v,k2_zfmisc_1(w,w),w)
| ~ v1_funct_2(v,k2_zfmisc_1(w,w),w)
| ~ m1_relset_1(u,k2_zfmisc_1(w,w),w)
| ~ v1_funct_2(u,k2_zfmisc_1(w,w),w)
| equal(w,x) ),
file('LAT295+1.p',unknown),
[] ).
cnf(104,plain,
m1_subset_1(skc21,u1_struct_0(skc20)),
inference(rew,[status(thm),theory(equality)],[25,36]),
[iquote('0:Rew:25.0,36.0')] ).
cnf(107,plain,
( ~ equal(k2_lattices(skc20,skc21,skc22),k2_lattices(skc19,skc21,skc22))
| ~ equal(k1_lattices(skc20,skc21,skc22),k1_lattices(skc19,skc21,skc22))
| ~ skP0(skc21,skc19,skc22,skc21,skc20)
| ~ skP0(skc21,skc20,skc22,skc21,skc19) ),
inference(rew,[status(thm),theory(equality)],[25,94]),
[iquote('0:Rew:25.0,94.3,25.0,94.2,25.0,94.1,25.0,94.0')] ).
cnf(110,plain,
l1_lattices(skc20),
inference(res,[status(thm),theory(equality)],[2,48]),
[iquote('0:Res:2.0,48.0')] ).
cnf(111,plain,
l2_lattices(skc20),
inference(res,[status(thm),theory(equality)],[2,49]),
[iquote('0:Res:2.0,49.0')] ).
cnf(113,plain,
l1_lattices(skc19),
inference(res,[status(thm),theory(equality)],[1,48]),
[iquote('0:Res:1.0,48.0')] ).
cnf(114,plain,
l2_lattices(skc19),
inference(res,[status(thm),theory(equality)],[1,49]),
[iquote('0:Res:1.0,49.0')] ).
cnf(121,plain,
( ~ l1_struct_0(skc19)
| ~ v1_xboole_0(u1_struct_0(skc19)) ),
inference(res,[status(thm),theory(equality)],[67,24]),
[iquote('0:Res:67.2,24.0')] ).
cnf(129,plain,
( ~ l1_struct_0(skc20)
| ~ v1_xboole_0(u1_struct_0(skc20)) ),
inference(res,[status(thm),theory(equality)],[67,23]),
[iquote('0:Res:67.2,23.0')] ).
cnf(137,plain,
( ~ l2_lattices(skc20)
| ~ m1_subset_1(u,u1_struct_0(skc20))
| v3_struct_0(skc20)
| equal(k2_binop_1(u1_struct_0(skc20),u1_struct_0(skc20),u1_struct_0(skc20),u2_lattices(skc20),u,skc22),k1_lattices(skc20,u,skc22)) ),
inference(res,[status(thm),theory(equality)],[39,93]),
[iquote('0:Res:39.0,93.2')] ).
cnf(139,plain,
( ~ l2_lattices(skc20)
| ~ r1_lattices(skc20,u,skc22)
| ~ m1_subset_1(u,u1_struct_0(skc20))
| equal(k1_lattices(skc20,u,skc22),skc22)
| v3_struct_0(skc20) ),
inference(res,[status(thm),theory(equality)],[39,91]),
[iquote('0:Res:39.0,91.3')] ).
cnf(140,plain,
( ~ l2_lattices(skc20)
| ~ equal(k1_lattices(skc20,u,skc22),skc22)
| ~ m1_subset_1(u,u1_struct_0(skc20))
| r1_lattices(skc20,u,skc22)
| v3_struct_0(skc20) ),
inference(res,[status(thm),theory(equality)],[39,90]),
[iquote('0:Res:39.0,90.3')] ).
cnf(149,plain,
( ~ l1_lattices(skc19)
| ~ m1_subset_1(u,u1_struct_0(skc19))
| v3_struct_0(skc19)
| equal(k2_binop_1(u1_struct_0(skc19),u1_struct_0(skc19),u1_struct_0(skc19),u1_lattices(skc19),skc21,u),k2_lattices(skc19,skc21,u)) ),
inference(res,[status(thm),theory(equality)],[38,92]),
[iquote('0:Res:38.0,92.1')] ).
cnf(150,plain,
( ~ l2_lattices(skc19)
| ~ r1_lattices(skc19,skc21,u)
| ~ m1_subset_1(u,u1_struct_0(skc19))
| equal(k1_lattices(skc19,skc21,u),u)
| v3_struct_0(skc19) ),
inference(res,[status(thm),theory(equality)],[38,91]),
[iquote('0:Res:38.0,91.2')] ).
cnf(151,plain,
( ~ l2_lattices(skc19)
| ~ equal(k1_lattices(skc19,skc21,u),u)
| ~ m1_subset_1(u,u1_struct_0(skc19))
| r1_lattices(skc19,skc21,u)
| v3_struct_0(skc19) ),
inference(res,[status(thm),theory(equality)],[38,90]),
[iquote('0:Res:38.0,90.2')] ).
cnf(171,plain,
( ~ l2_lattices(skc19)
| ~ m1_subset_1(u,u1_struct_0(skc19))
| v3_struct_0(skc19)
| equal(k2_binop_1(u1_struct_0(skc19),u1_struct_0(skc19),u1_struct_0(skc19),u2_lattices(skc19),u,skc22),k1_lattices(skc19,u,skc22)) ),
inference(res,[status(thm),theory(equality)],[37,93]),
[iquote('0:Res:37.0,93.2')] ).
cnf(177,plain,
( v1_xboole_0(u1_struct_0(skc19))
| r2_hidden(skc22,u1_struct_0(skc19)) ),
inference(res,[status(thm),theory(equality)],[37,72]),
[iquote('0:Res:37.0,72.0')] ).
cnf(183,plain,
( ~ l1_lattices(skc20)
| ~ m1_subset_1(u,u1_struct_0(skc20))
| v3_struct_0(skc20)
| equal(k2_binop_1(u1_struct_0(skc20),u1_struct_0(skc20),u1_struct_0(skc20),u1_lattices(skc20),skc21,u),k2_lattices(skc20,skc21,u)) ),
inference(res,[status(thm),theory(equality)],[104,92]),
[iquote('0:Res:104.0,92.1')] ).
cnf(184,plain,
( ~ l2_lattices(skc20)
| ~ r1_lattices(skc20,skc21,u)
| ~ m1_subset_1(u,u1_struct_0(skc20))
| equal(k1_lattices(skc20,skc21,u),u)
| v3_struct_0(skc20) ),
inference(res,[status(thm),theory(equality)],[104,91]),
[iquote('0:Res:104.0,91.2')] ).
cnf(194,plain,
( v1_xboole_0(u1_struct_0(skc20))
| r2_hidden(skc21,u1_struct_0(skc20)) ),
inference(res,[status(thm),theory(equality)],[104,72]),
[iquote('0:Res:104.0,72.0')] ).
cnf(199,plain,
( ~ v1_funct_1(u1_lattices(skc20))
| ~ v1_funct_1(u2_lattices(skc20))
| ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ m1_relset_1(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(u1_struct_0(skc20),u1_struct_0(skc19)) ),
inference(res,[status(thm),theory(equality)],[85,103]),
[iquote('0:Res:85.0,103.4')] ).
cnf(200,plain,
( ~ v1_funct_1(u1_lattices(skc20))
| ~ v1_funct_1(u2_lattices(skc20))
| ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ m1_relset_1(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(u2_lattices(skc20),u2_lattices(skc19)) ),
inference(res,[status(thm),theory(equality)],[85,102]),
[iquote('0:Res:85.0,102.4')] ).
cnf(229,plain,
( ~ m1_subset_1(u,u1_struct_0(skc20))
| ~ r1_lattices(skc20,skc21,u)
| equal(k1_lattices(skc20,skc21,u),u) ),
inference(mrr,[status(thm)],[184,111,23]),
[iquote('0:MRR:184.0,184.4,111.0,23.0')] ).
cnf(236,plain,
( ~ m1_subset_1(u,u1_struct_0(skc19))
| ~ equal(k1_lattices(skc19,skc21,u),u)
| r1_lattices(skc19,skc21,u) ),
inference(mrr,[status(thm)],[151,114,24]),
[iquote('0:MRR:151.0,151.4,114.0,24.0')] ).
cnf(237,plain,
( ~ m1_subset_1(u,u1_struct_0(skc19))
| ~ r1_lattices(skc19,skc21,u)
| equal(k1_lattices(skc19,skc21,u),u) ),
inference(mrr,[status(thm)],[150,114,24]),
[iquote('0:MRR:150.0,150.4,114.0,24.0')] ).
cnf(238,plain,
( ~ m1_subset_1(u,u1_struct_0(skc20))
| ~ equal(k1_lattices(skc20,u,skc22),skc22)
| r1_lattices(skc20,u,skc22) ),
inference(mrr,[status(thm)],[140,111,23]),
[iquote('0:MRR:140.0,140.4,111.0,23.0')] ).
cnf(239,plain,
( ~ m1_subset_1(u,u1_struct_0(skc20))
| ~ r1_lattices(skc20,u,skc22)
| equal(k1_lattices(skc20,u,skc22),skc22) ),
inference(mrr,[status(thm)],[139,111,23]),
[iquote('0:MRR:139.0,139.4,111.0,23.0')] ).
cnf(248,plain,
( ~ m1_subset_1(u,u1_struct_0(skc20))
| equal(k2_binop_1(u1_struct_0(skc20),u1_struct_0(skc20),u1_struct_0(skc20),u1_lattices(skc20),skc21,u),k2_lattices(skc20,skc21,u)) ),
inference(mrr,[status(thm)],[183,110,23]),
[iquote('0:MRR:183.0,183.2,110.0,23.0')] ).
cnf(251,plain,
( ~ m1_subset_1(u,u1_struct_0(skc19))
| equal(k2_binop_1(u1_struct_0(skc19),u1_struct_0(skc19),u1_struct_0(skc19),u2_lattices(skc19),u,skc22),k1_lattices(skc19,u,skc22)) ),
inference(mrr,[status(thm)],[171,114,24]),
[iquote('0:MRR:171.0,171.2,114.0,24.0')] ).
cnf(256,plain,
( ~ m1_subset_1(u,u1_struct_0(skc19))
| equal(k2_binop_1(u1_struct_0(skc19),u1_struct_0(skc19),u1_struct_0(skc19),u1_lattices(skc19),skc21,u),k2_lattices(skc19,skc21,u)) ),
inference(mrr,[status(thm)],[149,113,24]),
[iquote('0:MRR:149.0,149.2,113.0,24.0')] ).
cnf(259,plain,
( ~ m1_subset_1(u,u1_struct_0(skc20))
| equal(k2_binop_1(u1_struct_0(skc20),u1_struct_0(skc20),u1_struct_0(skc20),u2_lattices(skc20),u,skc22),k1_lattices(skc20,u,skc22)) ),
inference(mrr,[status(thm)],[137,111,23]),
[iquote('0:MRR:137.0,137.2,111.0,23.0')] ).
cnf(275,plain,
equal(k2_binop_1(u1_struct_0(skc19),u1_struct_0(skc19),u1_struct_0(skc19),u1_lattices(skc19),skc21,skc22),k2_lattices(skc19,skc21,skc22)),
inference(res,[status(thm),theory(equality)],[37,256]),
[iquote('0:Res:37.0,256.0')] ).
cnf(284,plain,
( ~ r1_lattices(skc19,skc21,skc22)
| equal(k1_lattices(skc19,skc21,skc22),skc22) ),
inference(res,[status(thm),theory(equality)],[37,237]),
[iquote('0:Res:37.0,237.1')] ).
cnf(285,plain,
( ~ equal(k1_lattices(skc19,skc21,skc22),skc22)
| r1_lattices(skc19,skc21,skc22) ),
inference(res,[status(thm),theory(equality)],[37,236]),
[iquote('0:Res:37.0,236.1')] ).
cnf(317,plain,
v1_xboole_0(u1_struct_0(skc20)),
inference(spt,[spt(split,[position(s1)])],[194]),
[iquote('1:Spt:194.0')] ).
cnf(318,plain,
~ l1_struct_0(skc20),
inference(mrr,[status(thm)],[129,317]),
[iquote('1:MRR:129.1,317.0')] ).
cnf(319,plain,
$false,
inference(ssi,[status(thm)],[318,47,2,110,111]),
[iquote('1:SSi:318.0,47.0,2.0,110.0,111.1')] ).
cnf(320,plain,
~ v1_xboole_0(u1_struct_0(skc20)),
inference(spt,[spt(split,[position(sa)])],[319,317]),
[iquote('1:Spt:319.0,194.0,317.0')] ).
cnf(321,plain,
r2_hidden(skc21,u1_struct_0(skc20)),
inference(spt,[spt(split,[position(s2)])],[194]),
[iquote('1:Spt:319.0,194.1')] ).
cnf(323,plain,
~ v1_xboole_0(u1_struct_0(skc20)),
inference(res,[status(thm),theory(equality)],[321,62]),
[iquote('1:Res:321.0,62.1')] ).
cnf(331,plain,
v1_xboole_0(u1_struct_0(skc19)),
inference(spt,[spt(split,[position(s2s1)])],[177]),
[iquote('2:Spt:177.0')] ).
cnf(332,plain,
~ l1_struct_0(skc19),
inference(mrr,[status(thm)],[121,331]),
[iquote('2:MRR:121.1,331.0')] ).
cnf(333,plain,
$false,
inference(ssi,[status(thm)],[332,47,1,113,114]),
[iquote('2:SSi:332.0,47.0,1.0,113.0,114.1')] ).
cnf(334,plain,
~ v1_xboole_0(u1_struct_0(skc19)),
inference(spt,[spt(split,[position(s2sa)])],[333,331]),
[iquote('2:Spt:333.0,177.0,331.0')] ).
cnf(335,plain,
r2_hidden(skc22,u1_struct_0(skc19)),
inference(spt,[spt(split,[position(s2s2)])],[177]),
[iquote('2:Spt:333.0,177.1')] ).
cnf(337,plain,
~ v1_xboole_0(u1_struct_0(skc19)),
inference(res,[status(thm),theory(equality)],[335,62]),
[iquote('2:Res:335.0,62.1')] ).
cnf(398,plain,
( ~ m2_relset_1(u,v,w)
| v1_relat_1(u) ),
inference(res,[status(thm),theory(equality)],[78,66]),
[iquote('0:Res:78.1,66.0')] ).
cnf(423,plain,
( ~ l1_lattices(u)
| v1_relat_1(u1_lattices(u)) ),
inference(res,[status(thm),theory(equality)],[82,398]),
[iquote('0:Res:82.1,398.0')] ).
cnf(424,plain,
( ~ l1_lattices(u)
| m1_relset_1(u1_lattices(u),k2_zfmisc_1(u1_struct_0(u),u1_struct_0(u)),u1_struct_0(u)) ),
inference(res,[status(thm),theory(equality)],[82,70]),
[iquote('0:Res:82.1,70.0')] ).
cnf(434,plain,
( ~ l2_lattices(u)
| v1_relat_1(u2_lattices(u)) ),
inference(res,[status(thm),theory(equality)],[84,398]),
[iquote('0:Res:84.1,398.0')] ).
cnf(435,plain,
( ~ l2_lattices(u)
| m1_relset_1(u2_lattices(u),k2_zfmisc_1(u1_struct_0(u),u1_struct_0(u)),u1_struct_0(u)) ),
inference(res,[status(thm),theory(equality)],[84,70]),
[iquote('0:Res:84.1,70.0')] ).
cnf(676,plain,
( ~ equal(k2_lattices(skc20,skc21,skc22),k2_lattices(skc19,skc21,skc22))
| ~ equal(k1_lattices(skc20,skc21,skc22),k1_lattices(skc19,skc21,skc22))
| ~ skP0(skc21,skc19,skc22,skc21,skc20)
| r1_lattices(skc19,skc21,skc22) ),
inference(res,[status(thm),theory(equality)],[74,107]),
[iquote('0:Res:74.1,107.3')] ).
cnf(677,plain,
( ~ r1_lattices(skc20,skc21,skc22)
| ~ equal(k2_lattices(skc20,skc21,skc22),k2_lattices(skc19,skc21,skc22))
| ~ equal(k1_lattices(skc20,skc21,skc22),k1_lattices(skc19,skc21,skc22))
| ~ skP0(skc21,skc19,skc22,skc21,skc20) ),
inference(res,[status(thm),theory(equality)],[76,107]),
[iquote('0:Res:76.1,107.3')] ).
cnf(898,plain,
( ~ v3_lattices(u)
| ~ l3_lattices(u)
| ~ v1_funct_1(v)
| ~ v1_funct_1(w)
| ~ equal(g3_lattices(x,w,v),u)
| ~ m1_relset_1(w,k2_zfmisc_1(x,x),x)
| ~ v1_funct_2(w,k2_zfmisc_1(x,x),x)
| ~ m1_relset_1(v,k2_zfmisc_1(x,x),x)
| ~ v1_funct_2(v,k2_zfmisc_1(x,x),x)
| equal(v,u1_lattices(u)) ),
inference(spl,[status(thm),theory(equality)],[86,101]),
[iquote('0:SpL:86.2,101.2')] ).
cnf(1263,plain,
( ~ v1_funct_1(u1_lattices(skc19))
| ~ m1_subset_1(skc21,u1_struct_0(skc19))
| ~ m1_subset_1(skc22,u1_struct_0(skc19))
| ~ v1_funct_2(u1_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| ~ m1_relset_1(u1_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| v1_xboole_0(u1_struct_0(skc19))
| v1_xboole_0(u1_struct_0(skc19))
| equal(k1_binop_1(u1_lattices(skc19),skc21,skc22),k2_lattices(skc19,skc21,skc22)) ),
inference(spr,[status(thm),theory(equality)],[275,98]),
[iquote('0:SpR:275.0,98.7')] ).
cnf(1264,plain,
( ~ v1_funct_1(u1_lattices(skc19))
| ~ m1_subset_1(skc21,u1_struct_0(skc19))
| ~ m1_subset_1(skc22,u1_struct_0(skc19))
| ~ v1_funct_2(u1_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| ~ m1_relset_1(u1_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| v1_xboole_0(u1_struct_0(skc19))
| equal(k1_binop_1(u1_lattices(skc19),skc21,skc22),k2_lattices(skc19,skc21,skc22)) ),
inference(obv,[status(thm),theory(equality)],[1263]),
[iquote('0:Obv:1263.5')] ).
cnf(1265,plain,
( ~ m1_subset_1(skc21,u1_struct_0(skc19))
| ~ m1_subset_1(skc22,u1_struct_0(skc19))
| ~ v1_funct_2(u1_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| ~ m1_relset_1(u1_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| v1_xboole_0(u1_struct_0(skc19))
| equal(k1_binop_1(u1_lattices(skc19),skc21,skc22),k2_lattices(skc19,skc21,skc22)) ),
inference(ssi,[status(thm)],[1264,53,1,113,114,423]),
[iquote('0:SSi:1264.0,53.0,1.0,113.0,114.1,423.0,1.0,113.0,114.1')] ).
cnf(1266,plain,
( ~ v1_funct_2(u1_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| ~ m1_relset_1(u1_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| equal(k1_binop_1(u1_lattices(skc19),skc21,skc22),k2_lattices(skc19,skc21,skc22)) ),
inference(mrr,[status(thm)],[1265,38,37,337]),
[iquote('2:MRR:1265.0,1265.1,1265.4,38.0,37.0,337.0')] ).
cnf(1665,plain,
( ~ v1_funct_1(u1_lattices(skc20))
| ~ m1_subset_1(u,u1_struct_0(skc20))
| ~ m1_subset_1(skc21,u1_struct_0(skc20))
| ~ m1_subset_1(u,u1_struct_0(skc20))
| ~ v1_funct_2(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ m1_relset_1(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| v1_xboole_0(u1_struct_0(skc20))
| v1_xboole_0(u1_struct_0(skc20))
| equal(k1_binop_1(u1_lattices(skc20),skc21,u),k2_lattices(skc20,skc21,u)) ),
inference(spr,[status(thm),theory(equality)],[248,98]),
[iquote('0:SpR:248.1,98.7')] ).
cnf(1666,plain,
( ~ v1_funct_1(u1_lattices(skc20))
| ~ m1_subset_1(skc21,u1_struct_0(skc20))
| ~ m1_subset_1(u,u1_struct_0(skc20))
| ~ v1_funct_2(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ m1_relset_1(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| v1_xboole_0(u1_struct_0(skc20))
| equal(k1_binop_1(u1_lattices(skc20),skc21,u),k2_lattices(skc20,skc21,u)) ),
inference(obv,[status(thm),theory(equality)],[1665]),
[iquote('0:Obv:1665.6')] ).
cnf(1667,plain,
( ~ m1_subset_1(skc21,u1_struct_0(skc20))
| ~ m1_subset_1(u,u1_struct_0(skc20))
| ~ v1_funct_2(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ m1_relset_1(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| v1_xboole_0(u1_struct_0(skc20))
| equal(k1_binop_1(u1_lattices(skc20),skc21,u),k2_lattices(skc20,skc21,u)) ),
inference(ssi,[status(thm)],[1666,53,2,110,111,423]),
[iquote('0:SSi:1666.0,53.0,2.0,110.0,111.1,423.0,2.0,110.0,111.1')] ).
cnf(1668,plain,
( ~ m1_subset_1(u,u1_struct_0(skc20))
| ~ v1_funct_2(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ m1_relset_1(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(k1_binop_1(u1_lattices(skc20),skc21,u),k2_lattices(skc20,skc21,u)) ),
inference(mrr,[status(thm)],[1667,104,323]),
[iquote('1:MRR:1667.0,1667.4,104.0,323.0')] ).
cnf(1701,plain,
( ~ v1_funct_1(u2_lattices(skc20))
| ~ m1_subset_1(u,u1_struct_0(skc20))
| ~ m1_subset_1(u,u1_struct_0(skc20))
| ~ m1_subset_1(skc22,u1_struct_0(skc20))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| v1_xboole_0(u1_struct_0(skc20))
| v1_xboole_0(u1_struct_0(skc20))
| equal(k1_binop_1(u2_lattices(skc20),u,skc22),k1_lattices(skc20,u,skc22)) ),
inference(spr,[status(thm),theory(equality)],[259,98]),
[iquote('0:SpR:259.1,98.7')] ).
cnf(1702,plain,
( ~ v1_funct_1(u2_lattices(skc20))
| ~ m1_subset_1(u,u1_struct_0(skc20))
| ~ m1_subset_1(skc22,u1_struct_0(skc20))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| v1_xboole_0(u1_struct_0(skc20))
| equal(k1_binop_1(u2_lattices(skc20),u,skc22),k1_lattices(skc20,u,skc22)) ),
inference(obv,[status(thm),theory(equality)],[1701]),
[iquote('0:Obv:1701.6')] ).
cnf(1703,plain,
( ~ m1_subset_1(u,u1_struct_0(skc20))
| ~ m1_subset_1(skc22,u1_struct_0(skc20))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| v1_xboole_0(u1_struct_0(skc20))
| equal(k1_binop_1(u2_lattices(skc20),u,skc22),k1_lattices(skc20,u,skc22)) ),
inference(ssi,[status(thm)],[1702,54,2,110,111,434]),
[iquote('0:SSi:1702.0,54.0,2.0,110.0,111.1,434.0,2.0,110.0,111.1')] ).
cnf(1704,plain,
( ~ m1_subset_1(u,u1_struct_0(skc20))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(k1_binop_1(u2_lattices(skc20),u,skc22),k1_lattices(skc20,u,skc22)) ),
inference(mrr,[status(thm)],[1703,39,323]),
[iquote('1:MRR:1703.1,1703.4,39.0,323.0')] ).
cnf(1835,plain,
( ~ v1_funct_1(u2_lattices(skc19))
| ~ m1_subset_1(u,u1_struct_0(skc19))
| ~ m1_subset_1(u,u1_struct_0(skc19))
| ~ m1_subset_1(skc22,u1_struct_0(skc19))
| ~ v1_funct_2(u2_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| ~ m1_relset_1(u2_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| v1_xboole_0(u1_struct_0(skc19))
| v1_xboole_0(u1_struct_0(skc19))
| equal(k1_binop_1(u2_lattices(skc19),u,skc22),k1_lattices(skc19,u,skc22)) ),
inference(spr,[status(thm),theory(equality)],[251,98]),
[iquote('0:SpR:251.1,98.7')] ).
cnf(1836,plain,
( ~ v1_funct_1(u2_lattices(skc19))
| ~ m1_subset_1(u,u1_struct_0(skc19))
| ~ m1_subset_1(skc22,u1_struct_0(skc19))
| ~ v1_funct_2(u2_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| ~ m1_relset_1(u2_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| v1_xboole_0(u1_struct_0(skc19))
| equal(k1_binop_1(u2_lattices(skc19),u,skc22),k1_lattices(skc19,u,skc22)) ),
inference(obv,[status(thm),theory(equality)],[1835]),
[iquote('0:Obv:1835.6')] ).
cnf(1837,plain,
( ~ m1_subset_1(u,u1_struct_0(skc19))
| ~ m1_subset_1(skc22,u1_struct_0(skc19))
| ~ v1_funct_2(u2_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| ~ m1_relset_1(u2_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| v1_xboole_0(u1_struct_0(skc19))
| equal(k1_binop_1(u2_lattices(skc19),u,skc22),k1_lattices(skc19,u,skc22)) ),
inference(ssi,[status(thm)],[1836,54,1,113,114,434]),
[iquote('0:SSi:1836.0,54.0,1.0,113.0,114.1,434.0,1.0,113.0,114.1')] ).
cnf(1838,plain,
( ~ m1_subset_1(u,u1_struct_0(skc19))
| ~ v1_funct_2(u2_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| ~ m1_relset_1(u2_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| equal(k1_binop_1(u2_lattices(skc19),u,skc22),k1_lattices(skc19,u,skc22)) ),
inference(mrr,[status(thm)],[1837,37,337]),
[iquote('2:MRR:1837.1,1837.4,37.0,337.0')] ).
cnf(2244,plain,
( ~ equal(k2_lattices(skc20,skc21,skc22),k2_lattices(skc19,skc21,skc22))
| ~ equal(k1_lattices(skc20,skc21,skc22),k1_lattices(skc19,skc21,skc22))
| r1_lattices(skc20,skc21,skc22)
| r1_lattices(skc19,skc21,skc22) ),
inference(res,[status(thm),theory(equality)],[74,676]),
[iquote('0:Res:74.1,676.2')] ).
cnf(2266,plain,
( ~ r1_lattices(skc19,skc21,skc22)
| ~ r1_lattices(skc20,skc21,skc22)
| ~ equal(k2_lattices(skc20,skc21,skc22),k2_lattices(skc19,skc21,skc22))
| ~ equal(k1_lattices(skc20,skc21,skc22),k1_lattices(skc19,skc21,skc22)) ),
inference(res,[status(thm),theory(equality)],[76,677]),
[iquote('0:Res:76.1,677.3')] ).
cnf(2267,plain,
( ~ r1_lattices(skc19,skc21,skc22)
| ~ r1_lattices(skc20,skc21,skc22)
| ~ equal(k2_lattices(skc20,skc21,skc22),k2_lattices(skc19,skc21,skc22))
| ~ equal(k1_lattices(skc20,skc21,skc22),skc22) ),
inference(rew,[status(thm),theory(equality)],[284,2266]),
[iquote('0:Rew:284.1,2266.3')] ).
cnf(2681,plain,
( ~ v3_lattices(g3_lattices(u,v,w))
| ~ l3_lattices(g3_lattices(u,v,w))
| ~ v1_funct_1(w)
| ~ v1_funct_1(v)
| ~ m1_relset_1(v,k2_zfmisc_1(u,u),u)
| ~ v1_funct_2(v,k2_zfmisc_1(u,u),u)
| ~ m1_relset_1(w,k2_zfmisc_1(u,u),u)
| ~ v1_funct_2(w,k2_zfmisc_1(u,u),u)
| equal(u1_lattices(g3_lattices(u,v,w)),w) ),
inference(eqr,[status(thm),theory(equality)],[898]),
[iquote('0:EqR:898.4')] ).
cnf(2685,plain,
( ~ v1_funct_1(u)
| ~ v1_funct_1(v)
| ~ m1_relset_1(v,k2_zfmisc_1(w,w),w)
| ~ v1_funct_2(v,k2_zfmisc_1(w,w),w)
| ~ m1_relset_1(u,k2_zfmisc_1(w,w),w)
| ~ v1_funct_2(u,k2_zfmisc_1(w,w),w)
| equal(u1_lattices(g3_lattices(w,v,u)),u) ),
inference(mrr,[status(thm)],[2681,97,96]),
[iquote('0:MRR:2681.0,2681.1,97.6,96.6')] ).
cnf(2691,plain,
( ~ v1_funct_1(u2_lattices(skc20))
| ~ l1_lattices(skc20)
| ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ m1_relset_1(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(u1_struct_0(skc20),u1_struct_0(skc19)) ),
inference(sor,[status(thm)],[199,53]),
[iquote('0:SoR:199.0,53.1')] ).
cnf(2693,plain,
( ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ m1_relset_1(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(u1_struct_0(skc20),u1_struct_0(skc19)) ),
inference(ssi,[status(thm)],[2691,2,110,111,54,434]),
[iquote('0:SSi:2691.1,2691.0,2.0,110.0,111.0,54.1,2.0,110.0,111.0,434.1,2.0,110.0,111.0')] ).
cnf(2697,plain,
( ~ v1_funct_1(u2_lattices(skc20))
| ~ l1_lattices(skc20)
| ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ m1_relset_1(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(u2_lattices(skc20),u2_lattices(skc19)) ),
inference(sor,[status(thm)],[200,53]),
[iquote('0:SoR:200.0,53.1')] ).
cnf(2699,plain,
( ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ m1_relset_1(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(u2_lattices(skc20),u2_lattices(skc19)) ),
inference(ssi,[status(thm)],[2697,2,110,111,54,434]),
[iquote('0:SSi:2697.1,2697.0,2.0,110.0,111.0,54.1,2.0,110.0,111.0,434.1,2.0,110.0,111.0')] ).
cnf(3189,plain,
r1_lattices(skc19,skc21,skc22),
inference(spt,[spt(split,[position(s2s2s1)])],[2244]),
[iquote('3:Spt:2244.3')] ).
cnf(3190,plain,
equal(k1_lattices(skc19,skc21,skc22),skc22),
inference(mrr,[status(thm)],[284,3189]),
[iquote('3:MRR:284.0,3189.0')] ).
cnf(3191,plain,
( ~ r1_lattices(skc20,skc21,skc22)
| ~ equal(k2_lattices(skc20,skc21,skc22),k2_lattices(skc19,skc21,skc22))
| ~ equal(k1_lattices(skc20,skc21,skc22),skc22) ),
inference(mrr,[status(thm)],[2267,3189]),
[iquote('3:MRR:2267.0,3189.0')] ).
cnf(3447,plain,
( ~ l1_lattices(skc20)
| ~ m1_subset_1(u,u1_struct_0(skc20))
| ~ m1_relset_1(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(k1_binop_1(u1_lattices(skc20),skc21,u),k2_lattices(skc20,skc21,u)) ),
inference(res,[status(thm),theory(equality)],[81,1668]),
[iquote('1:Res:81.1,1668.1')] ).
cnf(3448,plain,
( ~ m1_subset_1(u,u1_struct_0(skc20))
| ~ m1_relset_1(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(k1_binop_1(u1_lattices(skc20),skc21,u),k2_lattices(skc20,skc21,u)) ),
inference(ssi,[status(thm)],[3447,2,110,111]),
[iquote('1:SSi:3447.0,2.0,110.0,111.0')] ).
cnf(3452,plain,
( ~ l2_lattices(skc20)
| ~ m1_subset_1(u,u1_struct_0(skc20))
| ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(k1_binop_1(u2_lattices(skc20),u,skc22),k1_lattices(skc20,u,skc22)) ),
inference(res,[status(thm),theory(equality)],[83,1704]),
[iquote('1:Res:83.1,1704.1')] ).
cnf(3453,plain,
( ~ m1_subset_1(u,u1_struct_0(skc20))
| ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(k1_binop_1(u2_lattices(skc20),u,skc22),k1_lattices(skc20,u,skc22)) ),
inference(ssi,[status(thm)],[3452,2,110,111]),
[iquote('1:SSi:3452.0,2.0,110.0,111.0')] ).
cnf(3544,plain,
( ~ l2_lattices(skc19)
| ~ m1_subset_1(u,u1_struct_0(skc19))
| ~ m1_relset_1(u2_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| equal(k1_binop_1(u2_lattices(skc19),u,skc22),k1_lattices(skc19,u,skc22)) ),
inference(res,[status(thm),theory(equality)],[83,1838]),
[iquote('2:Res:83.1,1838.1')] ).
cnf(3545,plain,
( ~ m1_subset_1(u,u1_struct_0(skc19))
| ~ m1_relset_1(u2_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| equal(k1_binop_1(u2_lattices(skc19),u,skc22),k1_lattices(skc19,u,skc22)) ),
inference(ssi,[status(thm)],[3544,1,113,114]),
[iquote('2:SSi:3544.0,1.0,113.0,114.0')] ).
cnf(3724,plain,
( ~ l2_lattices(u)
| ~ v1_funct_1(v)
| ~ v1_funct_1(u2_lattices(u))
| ~ v1_funct_2(u2_lattices(u),k2_zfmisc_1(u1_struct_0(u),u1_struct_0(u)),u1_struct_0(u))
| ~ m1_relset_1(v,k2_zfmisc_1(u1_struct_0(u),u1_struct_0(u)),u1_struct_0(u))
| ~ v1_funct_2(v,k2_zfmisc_1(u1_struct_0(u),u1_struct_0(u)),u1_struct_0(u))
| equal(u1_lattices(g3_lattices(u1_struct_0(u),u2_lattices(u),v)),v) ),
inference(res,[status(thm),theory(equality)],[435,2685]),
[iquote('0:Res:435.1,2685.2')] ).
cnf(3731,plain,
( ~ l2_lattices(u)
| ~ v1_funct_1(v)
| ~ v1_funct_2(u2_lattices(u),k2_zfmisc_1(u1_struct_0(u),u1_struct_0(u)),u1_struct_0(u))
| ~ m1_relset_1(v,k2_zfmisc_1(u1_struct_0(u),u1_struct_0(u)),u1_struct_0(u))
| ~ v1_funct_2(v,k2_zfmisc_1(u1_struct_0(u),u1_struct_0(u)),u1_struct_0(u))
| equal(u1_lattices(g3_lattices(u1_struct_0(u),u2_lattices(u),v)),v) ),
inference(ssi,[status(thm)],[3724,54,434]),
[iquote('0:SSi:3724.2,54.1,434.1')] ).
cnf(3732,plain,
( ~ l2_lattices(u)
| ~ v1_funct_1(v)
| ~ m1_relset_1(v,k2_zfmisc_1(u1_struct_0(u),u1_struct_0(u)),u1_struct_0(u))
| ~ v1_funct_2(v,k2_zfmisc_1(u1_struct_0(u),u1_struct_0(u)),u1_struct_0(u))
| equal(u1_lattices(g3_lattices(u1_struct_0(u),u2_lattices(u),v)),v) ),
inference(mrr,[status(thm)],[3731,83]),
[iquote('0:MRR:3731.2,83.1')] ).
cnf(3982,plain,
( ~ l1_lattices(skc20)
| ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(u1_struct_0(skc20),u1_struct_0(skc19)) ),
inference(res,[status(thm),theory(equality)],[424,2693]),
[iquote('0:Res:424.1,2693.2')] ).
cnf(3983,plain,
( ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(u1_struct_0(skc20),u1_struct_0(skc19)) ),
inference(ssi,[status(thm)],[3982,2,110,111]),
[iquote('0:SSi:3982.0,2.0,110.0,111.0')] ).
cnf(3991,plain,
( ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ m1_relset_1(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| ~ v1_funct_2(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(u2_lattices(skc20),u2_lattices(skc19)) ),
inference(rew,[status(thm),theory(equality)],[3983,2699]),
[iquote('0:Rew:3983.3,2699.2')] ).
cnf(5002,plain,
( ~ l1_lattices(skc20)
| ~ m1_subset_1(u,u1_struct_0(skc20))
| equal(k1_binop_1(u1_lattices(skc20),skc21,u),k2_lattices(skc20,skc21,u)) ),
inference(res,[status(thm),theory(equality)],[424,3448]),
[iquote('1:Res:424.1,3448.1')] ).
cnf(5003,plain,
( ~ m1_subset_1(u,u1_struct_0(skc20))
| equal(k1_binop_1(u1_lattices(skc20),skc21,u),k2_lattices(skc20,skc21,u)) ),
inference(ssi,[status(thm)],[5002,2,110,111]),
[iquote('1:SSi:5002.0,2.0,110.0,111.0')] ).
cnf(5011,plain,
( ~ l2_lattices(skc20)
| ~ m1_subset_1(u,u1_struct_0(skc20))
| equal(k1_binop_1(u2_lattices(skc20),u,skc22),k1_lattices(skc20,u,skc22)) ),
inference(res,[status(thm),theory(equality)],[435,3453]),
[iquote('1:Res:435.1,3453.1')] ).
cnf(5012,plain,
( ~ m1_subset_1(u,u1_struct_0(skc20))
| equal(k1_binop_1(u2_lattices(skc20),u,skc22),k1_lattices(skc20,u,skc22)) ),
inference(ssi,[status(thm)],[5011,2,110,111]),
[iquote('1:SSi:5011.0,2.0,110.0,111.0')] ).
cnf(5072,plain,
( ~ l2_lattices(skc19)
| ~ m1_subset_1(u,u1_struct_0(skc19))
| equal(k1_binop_1(u2_lattices(skc19),u,skc22),k1_lattices(skc19,u,skc22)) ),
inference(res,[status(thm),theory(equality)],[435,3545]),
[iquote('2:Res:435.1,3545.1')] ).
cnf(5073,plain,
( ~ m1_subset_1(u,u1_struct_0(skc19))
| equal(k1_binop_1(u2_lattices(skc19),u,skc22),k1_lattices(skc19,u,skc22)) ),
inference(ssi,[status(thm)],[5072,1,113,114]),
[iquote('2:SSi:5072.0,1.0,113.0,114.0')] ).
cnf(6100,plain,
( ~ l1_lattices(skc19)
| ~ v1_funct_2(u1_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| equal(k1_binop_1(u1_lattices(skc19),skc21,skc22),k2_lattices(skc19,skc21,skc22)) ),
inference(res,[status(thm),theory(equality)],[424,1266]),
[iquote('2:Res:424.1,1266.1')] ).
cnf(6101,plain,
( ~ v1_funct_2(u1_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| equal(k1_binop_1(u1_lattices(skc19),skc21,skc22),k2_lattices(skc19,skc21,skc22)) ),
inference(ssi,[status(thm)],[6100,1,113,114]),
[iquote('2:SSi:6100.0,1.0,113.0,114.0')] ).
cnf(6105,plain,
( ~ l1_lattices(skc19)
| equal(k1_binop_1(u1_lattices(skc19),skc21,skc22),k2_lattices(skc19,skc21,skc22)) ),
inference(res,[status(thm),theory(equality)],[81,6101]),
[iquote('2:Res:81.1,6101.0')] ).
cnf(6106,plain,
equal(k1_binop_1(u1_lattices(skc19),skc21,skc22),k2_lattices(skc19,skc21,skc22)),
inference(ssi,[status(thm)],[6105,1,113,114]),
[iquote('2:SSi:6105.0,1.0,113.0,114.0')] ).
cnf(6585,plain,
( ~ l1_lattices(u)
| ~ l2_lattices(u)
| ~ v1_funct_1(u1_lattices(u))
| ~ v1_funct_2(u1_lattices(u),k2_zfmisc_1(u1_struct_0(u),u1_struct_0(u)),u1_struct_0(u))
| equal(u1_lattices(g3_lattices(u1_struct_0(u),u2_lattices(u),u1_lattices(u))),u1_lattices(u)) ),
inference(res,[status(thm),theory(equality)],[424,3732]),
[iquote('0:Res:424.1,3732.2')] ).
cnf(6590,plain,
( ~ l1_lattices(u)
| ~ l2_lattices(u)
| ~ v1_funct_2(u1_lattices(u),k2_zfmisc_1(u1_struct_0(u),u1_struct_0(u)),u1_struct_0(u))
| equal(u1_lattices(g3_lattices(u1_struct_0(u),u2_lattices(u),u1_lattices(u))),u1_lattices(u)) ),
inference(ssi,[status(thm)],[6585,53,423]),
[iquote('0:SSi:6585.2,53.1,423.1')] ).
cnf(6591,plain,
( ~ l1_lattices(u)
| ~ l2_lattices(u)
| equal(u1_lattices(g3_lattices(u1_struct_0(u),u2_lattices(u),u1_lattices(u))),u1_lattices(u)) ),
inference(mrr,[status(thm)],[6590,81]),
[iquote('0:MRR:6590.2,81.1')] ).
cnf(6689,plain,
( ~ l1_lattices(skc20)
| ~ l2_lattices(skc20)
| equal(u1_lattices(g3_lattices(u1_struct_0(skc19),u2_lattices(skc19),u1_lattices(skc19))),u1_lattices(skc20)) ),
inference(spr,[status(thm),theory(equality)],[85,6591]),
[iquote('0:SpR:85.0,6591.2')] ).
cnf(6696,plain,
equal(u1_lattices(g3_lattices(u1_struct_0(skc19),u2_lattices(skc19),u1_lattices(skc19))),u1_lattices(skc20)),
inference(ssi,[status(thm)],[6689,2,110,111]),
[iquote('0:SSi:6689.1,6689.0,2.0,110.0,111.0,2.0,110.0,111.0')] ).
cnf(6760,plain,
( ~ l1_lattices(skc19)
| ~ l2_lattices(skc19)
| equal(u1_lattices(skc20),u1_lattices(skc19)) ),
inference(spr,[status(thm),theory(equality)],[6696,6591]),
[iquote('0:SpR:6696.0,6591.2')] ).
cnf(6769,plain,
equal(u1_lattices(skc20),u1_lattices(skc19)),
inference(ssi,[status(thm)],[6760,1,113,114]),
[iquote('0:SSi:6760.1,6760.0,1.0,113.0,114.0,1.0,113.0,114.0')] ).
cnf(6781,plain,
( ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ m1_relset_1(u1_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| ~ v1_funct_2(u1_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(u2_lattices(skc20),u2_lattices(skc19)) ),
inference(rew,[status(thm),theory(equality)],[6769,3991]),
[iquote('0:Rew:6769.0,3991.2')] ).
cnf(6786,plain,
( ~ m1_subset_1(u,u1_struct_0(skc20))
| equal(k1_binop_1(u1_lattices(skc19),skc21,u),k2_lattices(skc20,skc21,u)) ),
inference(rew,[status(thm),theory(equality)],[6769,5003]),
[iquote('1:Rew:6769.0,5003.1')] ).
cnf(6796,plain,
( ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u1_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(u1_struct_0(skc20),u1_struct_0(skc19)) ),
inference(rew,[status(thm),theory(equality)],[6769,3983]),
[iquote('0:Rew:6769.0,3983.2')] ).
cnf(6833,plain,
( ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ m1_relset_1(u1_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| ~ v1_funct_2(u1_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(u2_lattices(skc20),u2_lattices(skc19)) ),
inference(rew,[status(thm),theory(equality)],[6769,6781]),
[iquote('0:Rew:6769.0,6781.3')] ).
cnf(6879,plain,
( ~ l1_lattices(skc20)
| v1_funct_2(u1_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20)) ),
inference(spr,[status(thm),theory(equality)],[6769,81]),
[iquote('0:SpR:6769.0,81.1')] ).
cnf(6909,plain,
v1_funct_2(u1_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20)),
inference(ssi,[status(thm)],[6879,2,110,111]),
[iquote('0:SSi:6879.0,2.0,110.0,111.0')] ).
cnf(6910,plain,
( ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(u1_struct_0(skc20),u1_struct_0(skc19)) ),
inference(mrr,[status(thm)],[6796,6909]),
[iquote('0:MRR:6796.2,6909.0')] ).
cnf(6911,plain,
( ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ m1_relset_1(u1_lattices(skc19),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| equal(u2_lattices(skc20),u2_lattices(skc19)) ),
inference(mrr,[status(thm)],[6833,6909]),
[iquote('0:MRR:6833.3,6909.0')] ).
cnf(7166,plain,
( ~ m1_subset_1(skc22,u1_struct_0(skc20))
| equal(k2_lattices(skc20,skc21,skc22),k2_lattices(skc19,skc21,skc22)) ),
inference(spr,[status(thm),theory(equality)],[6786,6106]),
[iquote('2:SpR:6786.1,6106.0')] ).
cnf(7168,plain,
equal(k2_lattices(skc20,skc21,skc22),k2_lattices(skc19,skc21,skc22)),
inference(mrr,[status(thm)],[7166,39]),
[iquote('2:MRR:7166.0,39.0')] ).
cnf(7169,plain,
( ~ r1_lattices(skc20,skc21,skc22)
| ~ equal(k2_lattices(skc19,skc21,skc22),k2_lattices(skc19,skc21,skc22))
| ~ equal(k1_lattices(skc20,skc21,skc22),skc22) ),
inference(rew,[status(thm),theory(equality)],[7168,3191]),
[iquote('3:Rew:7168.0,3191.1')] ).
cnf(7171,plain,
( ~ r1_lattices(skc20,skc21,skc22)
| ~ equal(k1_lattices(skc20,skc21,skc22),skc22) ),
inference(obv,[status(thm),theory(equality)],[7169]),
[iquote('3:Obv:7169.1')] ).
cnf(7193,plain,
( ~ m1_subset_1(skc22,u1_struct_0(skc20))
| ~ r1_lattices(skc20,skc21,skc22)
| ~ r1_lattices(skc20,skc21,skc22)
| ~ equal(skc22,skc22) ),
inference(spl,[status(thm),theory(equality)],[229,7171]),
[iquote('3:SpL:229.2,7171.1')] ).
cnf(7197,plain,
( ~ m1_subset_1(skc22,u1_struct_0(skc20))
| ~ r1_lattices(skc20,skc21,skc22) ),
inference(obv,[status(thm),theory(equality)],[7193]),
[iquote('3:Obv:7193.3')] ).
cnf(7198,plain,
~ r1_lattices(skc20,skc21,skc22),
inference(mrr,[status(thm)],[7197,39]),
[iquote('3:MRR:7197.0,39.0')] ).
cnf(7322,plain,
( ~ l1_lattices(skc19)
| ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(u2_lattices(skc20),u2_lattices(skc19)) ),
inference(res,[status(thm),theory(equality)],[424,6911]),
[iquote('0:Res:424.1,6911.2')] ).
cnf(7323,plain,
( ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(u2_lattices(skc20),u2_lattices(skc19)) ),
inference(ssi,[status(thm)],[7322,1,113,114]),
[iquote('0:SSi:7322.0,1.0,113.0,114.0')] ).
cnf(7566,plain,
( ~ l2_lattices(skc20)
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(u1_struct_0(skc20),u1_struct_0(skc19)) ),
inference(res,[status(thm),theory(equality)],[435,6910]),
[iquote('0:Res:435.1,6910.0')] ).
cnf(7567,plain,
( ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(u1_struct_0(skc20),u1_struct_0(skc19)) ),
inference(ssi,[status(thm)],[7566,2,110,111]),
[iquote('0:SSi:7566.0,2.0,110.0,111.0')] ).
cnf(7574,plain,
( ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc20),u1_struct_0(skc20)),u1_struct_0(skc20))
| equal(u2_lattices(skc20),u2_lattices(skc19)) ),
inference(rew,[status(thm),theory(equality)],[7567,7323]),
[iquote('0:Rew:7567.1,7323.0')] ).
cnf(7578,plain,
( ~ l2_lattices(skc20)
| equal(u1_struct_0(skc20),u1_struct_0(skc19)) ),
inference(res,[status(thm),theory(equality)],[83,7567]),
[iquote('0:Res:83.1,7567.0')] ).
cnf(7579,plain,
equal(u1_struct_0(skc20),u1_struct_0(skc19)),
inference(ssi,[status(thm)],[7578,2,110,111]),
[iquote('0:SSi:7578.0,2.0,110.0,111.0')] ).
cnf(7609,plain,
( ~ m1_subset_1(u,u1_struct_0(skc19))
| equal(k1_binop_1(u2_lattices(skc20),u,skc22),k1_lattices(skc20,u,skc22)) ),
inference(rew,[status(thm),theory(equality)],[7579,5012]),
[iquote('1:Rew:7579.0,5012.0')] ).
cnf(7638,plain,
( ~ m1_subset_1(u,u1_struct_0(skc19))
| ~ r1_lattices(skc20,u,skc22)
| equal(k1_lattices(skc20,u,skc22),skc22) ),
inference(rew,[status(thm),theory(equality)],[7579,239]),
[iquote('0:Rew:7579.0,239.0')] ).
cnf(7640,plain,
( ~ m1_subset_1(u,u1_struct_0(skc19))
| ~ equal(k1_lattices(skc20,u,skc22),skc22)
| r1_lattices(skc20,u,skc22) ),
inference(rew,[status(thm),theory(equality)],[7579,238]),
[iquote('0:Rew:7579.0,238.0')] ).
cnf(7688,plain,
( ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| ~ v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| equal(u2_lattices(skc20),u2_lattices(skc19)) ),
inference(rew,[status(thm),theory(equality)],[7579,7574]),
[iquote('0:Rew:7579.0,7574.1')] ).
cnf(7804,plain,
( ~ l2_lattices(skc20)
| v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19)) ),
inference(spr,[status(thm),theory(equality)],[7579,83]),
[iquote('0:SpR:7579.0,83.1')] ).
cnf(7821,plain,
( ~ l2_lattices(skc20)
| m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19)) ),
inference(spr,[status(thm),theory(equality)],[7579,435]),
[iquote('0:SpR:7579.0,435.1')] ).
cnf(7900,plain,
v1_funct_2(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19)),
inference(ssi,[status(thm)],[7804,2,110,111]),
[iquote('0:SSi:7804.0,2.0,110.0,111.0')] ).
cnf(7901,plain,
( ~ m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19))
| equal(u2_lattices(skc20),u2_lattices(skc19)) ),
inference(mrr,[status(thm)],[7688,7900]),
[iquote('0:MRR:7688.1,7900.0')] ).
cnf(7913,plain,
m1_relset_1(u2_lattices(skc20),k2_zfmisc_1(u1_struct_0(skc19),u1_struct_0(skc19)),u1_struct_0(skc19)),
inference(ssi,[status(thm)],[7821,2,110,111]),
[iquote('0:SSi:7821.0,2.0,110.0,111.0')] ).
cnf(7930,plain,
equal(u2_lattices(skc20),u2_lattices(skc19)),
inference(mrr,[status(thm)],[7901,7913]),
[iquote('0:MRR:7901.0,7913.0')] ).
cnf(7939,plain,
( ~ m1_subset_1(u,u1_struct_0(skc19))
| equal(k1_binop_1(u2_lattices(skc19),u,skc22),k1_lattices(skc20,u,skc22)) ),
inference(rew,[status(thm),theory(equality)],[7930,7609]),
[iquote('1:Rew:7930.0,7609.1')] ).
cnf(7963,plain,
( ~ m1_subset_1(u,u1_struct_0(skc19))
| equal(k1_lattices(skc20,u,skc22),k1_lattices(skc19,u,skc22)) ),
inference(rew,[status(thm),theory(equality)],[5073,7939]),
[iquote('2:Rew:5073.1,7939.1')] ).
cnf(7965,plain,
( ~ m1_subset_1(u,u1_struct_0(skc19))
| ~ equal(k1_lattices(skc19,u,skc22),skc22)
| r1_lattices(skc20,u,skc22) ),
inference(rew,[status(thm),theory(equality)],[7963,7640]),
[iquote('2:Rew:7963.1,7640.1')] ).
cnf(7966,plain,
( ~ m1_subset_1(u,u1_struct_0(skc19))
| ~ r1_lattices(skc20,u,skc22)
| equal(k1_lattices(skc19,u,skc22),skc22) ),
inference(rew,[status(thm),theory(equality)],[7963,7638]),
[iquote('2:Rew:7963.1,7638.2')] ).
cnf(8256,plain,
( ~ m1_subset_1(skc21,u1_struct_0(skc19))
| ~ equal(skc22,skc22)
| r1_lattices(skc20,skc21,skc22) ),
inference(spl,[status(thm),theory(equality)],[3190,7965]),
[iquote('3:SpL:3190.0,7965.1')] ).
cnf(8262,plain,
( ~ m1_subset_1(skc21,u1_struct_0(skc19))
| r1_lattices(skc20,skc21,skc22) ),
inference(obv,[status(thm),theory(equality)],[8256]),
[iquote('3:Obv:8256.1')] ).
cnf(8263,plain,
$false,
inference(mrr,[status(thm)],[8262,38,7198]),
[iquote('3:MRR:8262.0,8262.1,38.0,7198.0')] ).
cnf(8271,plain,
~ r1_lattices(skc19,skc21,skc22),
inference(spt,[spt(split,[position(s2s2sa)])],[8263,3189]),
[iquote('3:Spt:8263.0,2244.3,3189.0')] ).
cnf(8272,plain,
( ~ equal(k2_lattices(skc20,skc21,skc22),k2_lattices(skc19,skc21,skc22))
| ~ equal(k1_lattices(skc20,skc21,skc22),k1_lattices(skc19,skc21,skc22))
| r1_lattices(skc20,skc21,skc22) ),
inference(spt,[spt(split,[position(s2s2s2)])],[2244]),
[iquote('3:Spt:8263.0,2244.0,2244.1,2244.2')] ).
cnf(8273,plain,
~ equal(k1_lattices(skc19,skc21,skc22),skc22),
inference(mrr,[status(thm)],[285,8271]),
[iquote('3:MRR:285.1,8271.0')] ).
cnf(8274,plain,
( ~ equal(k2_lattices(skc19,skc21,skc22),k2_lattices(skc19,skc21,skc22))
| ~ equal(k1_lattices(skc20,skc21,skc22),k1_lattices(skc19,skc21,skc22))
| r1_lattices(skc20,skc21,skc22) ),
inference(rew,[status(thm),theory(equality)],[7168,8272]),
[iquote('3:Rew:7168.0,8272.0')] ).
cnf(8275,plain,
( ~ equal(k1_lattices(skc20,skc21,skc22),k1_lattices(skc19,skc21,skc22))
| r1_lattices(skc20,skc21,skc22) ),
inference(obv,[status(thm),theory(equality)],[8274]),
[iquote('3:Obv:8274.0')] ).
cnf(8315,plain,
( ~ m1_subset_1(skc21,u1_struct_0(skc19))
| ~ r1_lattices(skc20,skc21,skc22)
| ~ equal(skc22,skc22) ),
inference(spl,[status(thm),theory(equality)],[7966,8273]),
[iquote('3:SpL:7966.2,8273.0')] ).
cnf(8327,plain,
( ~ m1_subset_1(skc21,u1_struct_0(skc19))
| ~ r1_lattices(skc20,skc21,skc22) ),
inference(obv,[status(thm),theory(equality)],[8315]),
[iquote('3:Obv:8315.2')] ).
cnf(8328,plain,
~ r1_lattices(skc20,skc21,skc22),
inference(mrr,[status(thm)],[8327,38]),
[iquote('3:MRR:8327.0,38.0')] ).
cnf(8329,plain,
~ equal(k1_lattices(skc20,skc21,skc22),k1_lattices(skc19,skc21,skc22)),
inference(mrr,[status(thm)],[8275,8328]),
[iquote('3:MRR:8275.1,8328.0')] ).
cnf(9052,plain,
( ~ m1_subset_1(skc21,u1_struct_0(skc19))
| ~ equal(k1_lattices(skc19,skc21,skc22),k1_lattices(skc19,skc21,skc22)) ),
inference(spl,[status(thm),theory(equality)],[7963,8329]),
[iquote('3:SpL:7963.1,8329.0')] ).
cnf(9053,plain,
~ m1_subset_1(skc21,u1_struct_0(skc19)),
inference(obv,[status(thm),theory(equality)],[9052]),
[iquote('3:Obv:9052.1')] ).
cnf(9054,plain,
$false,
inference(mrr,[status(thm)],[9053,38]),
[iquote('3:MRR:9053.0,38.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LAT295+1 : TPTP v8.1.0. Released v3.4.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n012.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 : 600
% 0.12/0.33 % DateTime : Wed Jun 29 22:43:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.24/2.41
% 2.24/2.41 SPASS V 3.9
% 2.24/2.41 SPASS beiseite: Proof found.
% 2.24/2.41 % SZS status Theorem
% 2.24/2.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.24/2.41 SPASS derived 6518 clauses, backtracked 20 clauses, performed 4 splits and kept 3109 clauses.
% 2.24/2.41 SPASS allocated 108613 KBytes.
% 2.24/2.41 SPASS spent 0:00:02.07 on the problem.
% 2.24/2.41 0:00:00.02 for the input.
% 2.24/2.41 0:00:00.02 for the FLOTTER CNF translation.
% 2.24/2.41 0:00:00.16 for inferences.
% 2.24/2.41 0:00:00.01 for the backtracking.
% 2.24/2.41 0:00:01.74 for the reduction.
% 2.24/2.41
% 2.24/2.41
% 2.24/2.41 Here is a proof with depth 7, length 200 :
% 2.24/2.41 % SZS output start Refutation
% See solution above
% 2.31/2.48 Formulae used in the proof : t8_filter_2 dt_l2_lattices dt_l3_lattices dt_u1_lattices dt_u2_lattices t7_boole cc1_relset_1 fc1_struct_0 redefinition_m2_relset_1 t2_subset dt_m2_relset_1 abstractness_v3_lattices d3_lattices d2_lattices d1_lattices dt_g3_lattices redefinition_k2_binop_1 free_g3_lattices
% 2.31/2.48
%------------------------------------------------------------------------------