TSTP Solution File: LAT345+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LAT345+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 06:51:10 EDT 2022
% Result : Theorem 11.24s 11.41s
% Output : Refutation 12.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 37
% Syntax : Number of clauses : 149 ( 42 unt; 42 nHn; 149 RR)
% Number of literals : 404 ( 0 equ; 210 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
v4_conlat_1(skc8),
file('LAT345+1.p',unknown),
[] ).
cnf(2,axiom,
l2_conlat_1(skc8),
file('LAT345+1.p',unknown),
[] ).
cnf(11,axiom,
v6_conlat_1(skc9,skc8),
file('LAT345+1.p',unknown),
[] ).
cnf(12,axiom,
~ v3_conlat_1(skc8),
file('LAT345+1.p',unknown),
[] ).
cnf(13,axiom,
v9_conlat_1(skc9,skc8),
file('LAT345+1.p',unknown),
[] ).
cnf(14,axiom,
l3_conlat_1(skc9,skc8),
file('LAT345+1.p',unknown),
[] ).
cnf(19,axiom,
~ v7_conlat_1(skc9,skc8),
file('LAT345+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ l2_conlat_1(u)
| l1_conlat_1(u) ),
file('LAT345+1.p',unknown),
[] ).
cnf(38,axiom,
( ~ l2_conlat_1(u)
| v3_conlat_1(u)
| v4_conlat_1(k7_conlat_2(u)) ),
file('LAT345+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ l2_conlat_1(u)
| v3_conlat_1(u)
| l2_conlat_1(k7_conlat_2(u)) ),
file('LAT345+1.p',unknown),
[] ).
cnf(40,axiom,
( ~ v1_relat_1(u)
| equal(k4_relat_1(k4_relat_1(u)),u) ),
file('LAT345+1.p',unknown),
[] ).
cnf(43,axiom,
~ equal(k9_conlat_2(k7_conlat_2(skc8),k9_conlat_2(skc8,skc9)),skc9),
file('LAT345+1.p',unknown),
[] ).
cnf(44,axiom,
( ~ m1_subset_1(u,k1_zfmisc_1(k2_zfmisc_1(v,w)))
| v1_relat_1(u) ),
file('LAT345+1.p',unknown),
[] ).
cnf(45,axiom,
( ~ l2_conlat_1(u)
| ~ v3_conlat_1(k7_conlat_2(u))
| v3_conlat_1(u) ),
file('LAT345+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ m2_relset_1(u,v,w)
| m1_relset_1(u,v,w) ),
file('LAT345+1.p',unknown),
[] ).
cnf(62,axiom,
( ~ m1_relset_1(u,v,w)
| m2_relset_1(u,v,w) ),
file('LAT345+1.p',unknown),
[] ).
cnf(65,axiom,
( ~ m1_relset_1(u,v,w)
| v4_conlat_1(g2_conlat_1(v,w,u)) ),
file('LAT345+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ m1_relset_1(u,v,w)
| l2_conlat_1(g2_conlat_1(v,w,u)) ),
file('LAT345+1.p',unknown),
[] ).
cnf(67,axiom,
( ~ l2_conlat_1(u)
| m2_relset_1(u3_conlat_1(u),u1_conlat_1(u),u2_conlat_1(u)) ),
file('LAT345+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ m2_relset_1(u,v,w)
| m1_subset_1(u,k1_zfmisc_1(k2_zfmisc_1(v,w))) ),
file('LAT345+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ m1_relset_1(u,v,w)
| m2_relset_1(k6_relset_1(v,w,u),w,v) ),
file('LAT345+1.p',unknown),
[] ).
cnf(73,axiom,
( ~ m1_relset_1(u,v,w)
| equal(k6_relset_1(v,w,u),k4_relat_1(u)) ),
file('LAT345+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ m1_relset_1(u,v,w)
| equal(k6_relset_1(v,w,k6_relset_1(v,w,u)),u) ),
file('LAT345+1.p',unknown),
[] ).
cnf(80,axiom,
( ~ v4_conlat_1(u)
| ~ l2_conlat_1(u)
| equal(g2_conlat_1(u1_conlat_1(u),u2_conlat_1(u),u3_conlat_1(u)),u) ),
file('LAT345+1.p',unknown),
[] ).
cnf(81,axiom,
( ~ l2_conlat_1(u)
| ~ l3_conlat_1(v,u)
| v3_conlat_1(u)
| v6_conlat_1(k8_conlat_2(u,v),k7_conlat_2(u)) ),
file('LAT345+1.p',unknown),
[] ).
cnf(82,axiom,
( ~ l2_conlat_1(u)
| ~ l3_conlat_1(v,u)
| v3_conlat_1(u)
| l3_conlat_1(k8_conlat_2(u,v),k7_conlat_2(u)) ),
file('LAT345+1.p',unknown),
[] ).
cnf(83,axiom,
( ~ equal(g2_conlat_1(u,v,w),g2_conlat_1(x,y,z))
| ~ m1_relset_1(w,u,v)
| equal(u,x) ),
file('LAT345+1.p',unknown),
[] ).
cnf(84,axiom,
( ~ equal(g2_conlat_1(u,v,w),g2_conlat_1(x,y,z))
| ~ m1_relset_1(w,u,v)
| equal(v,y) ),
file('LAT345+1.p',unknown),
[] ).
cnf(85,axiom,
( ~ equal(g2_conlat_1(u,v,w),g2_conlat_1(x,y,z))
| ~ m1_relset_1(w,u,v)
| equal(w,z) ),
file('LAT345+1.p',unknown),
[] ).
cnf(86,axiom,
( ~ l2_conlat_1(u)
| v3_conlat_1(u)
| equal(g2_conlat_1(u2_conlat_1(u),u1_conlat_1(u),k6_relset_1(u1_conlat_1(u),u2_conlat_1(u),u3_conlat_1(u))),k7_conlat_2(u)) ),
file('LAT345+1.p',unknown),
[] ).
cnf(89,axiom,
( ~ l1_conlat_1(u)
| ~ l3_conlat_1(v,u)
| ~ v6_conlat_1(v,u)
| equal(g3_conlat_1(u,u4_conlat_1(u,v),u5_conlat_1(u,v)),v) ),
file('LAT345+1.p',unknown),
[] ).
cnf(90,axiom,
( ~ l2_conlat_1(u)
| ~ v9_conlat_1(v,u)
| ~ l3_conlat_1(v,u)
| v3_conlat_1(u)
| v7_conlat_1(v,u)
| l3_conlat_1(k9_conlat_2(u,v),k7_conlat_2(u)) ),
file('LAT345+1.p',unknown),
[] ).
cnf(91,axiom,
( ~ l2_conlat_1(u)
| ~ v9_conlat_1(v,u)
| ~ l3_conlat_1(v,u)
| v3_conlat_1(u)
| v7_conlat_1(v,u)
| v9_conlat_1(k9_conlat_2(u,v),k7_conlat_2(u)) ),
file('LAT345+1.p',unknown),
[] ).
cnf(93,axiom,
( ~ l2_conlat_1(u)
| ~ v9_conlat_1(v,u)
| ~ l3_conlat_1(v,u)
| v3_conlat_1(u)
| v7_conlat_1(v,u)
| equal(k8_conlat_2(u,v),k9_conlat_2(u,v)) ),
file('LAT345+1.p',unknown),
[] ).
cnf(94,axiom,
( ~ l2_conlat_1(u)
| ~ l3_conlat_1(v,u)
| ~ v9_conlat_1(v,u)
| ~ v7_conlat_1(k9_conlat_2(u,v),k7_conlat_2(u))
| v3_conlat_1(u)
| v7_conlat_1(v,u) ),
file('LAT345+1.p',unknown),
[] ).
cnf(98,axiom,
( ~ l2_conlat_1(u)
| ~ l3_conlat_1(v,u)
| ~ l3_conlat_1(w,k7_conlat_2(u))
| ~ v6_conlat_1(w,k7_conlat_2(u))
| ~ equal(w,k8_conlat_2(u,v))
| v3_conlat_1(u)
| equal(u5_conlat_1(k7_conlat_2(u),w),u4_conlat_1(u,v)) ),
file('LAT345+1.p',unknown),
[] ).
cnf(99,axiom,
( ~ l2_conlat_1(u)
| ~ l3_conlat_1(v,u)
| ~ l3_conlat_1(w,k7_conlat_2(u))
| ~ v6_conlat_1(w,k7_conlat_2(u))
| ~ equal(w,k8_conlat_2(u,v))
| v3_conlat_1(u)
| equal(u4_conlat_1(k7_conlat_2(u),w),u5_conlat_1(u,v)) ),
file('LAT345+1.p',unknown),
[] ).
cnf(101,plain,
( ~ m1_relset_1(u,v,w)
| m2_relset_1(k4_relat_1(u),w,v) ),
inference(rew,[status(thm),theory(equality)],[73,72]),
[iquote('0:Rew:73.1,72.1')] ).
cnf(102,plain,
( ~ m1_relset_1(u,v,w)
| equal(k6_relset_1(v,w,k4_relat_1(u)),u) ),
inference(rew,[status(thm),theory(equality)],[73,79]),
[iquote('0:Rew:73.1,79.1')] ).
cnf(104,plain,
( ~ equal(u,k8_conlat_2(skc8,v))
| ~ l3_conlat_1(v,skc8)
| ~ v6_conlat_1(u,k7_conlat_2(skc8))
| ~ l3_conlat_1(u,k7_conlat_2(skc8))
| equal(u4_conlat_1(k7_conlat_2(skc8),u),u5_conlat_1(skc8,v))
| v3_conlat_1(skc8) ),
inference(res,[status(thm),theory(equality)],[2,99]),
[iquote('0:Res:2.0,99.0')] ).
cnf(105,plain,
( ~ equal(u,k8_conlat_2(skc8,v))
| ~ l3_conlat_1(v,skc8)
| ~ v6_conlat_1(u,k7_conlat_2(skc8))
| ~ l3_conlat_1(u,k7_conlat_2(skc8))
| equal(u5_conlat_1(k7_conlat_2(skc8),u),u4_conlat_1(skc8,v))
| v3_conlat_1(skc8) ),
inference(res,[status(thm),theory(equality)],[2,98]),
[iquote('0:Res:2.0,98.0')] ).
cnf(111,plain,
( v3_conlat_1(skc8)
| equal(g2_conlat_1(u2_conlat_1(skc8),u1_conlat_1(skc8),k6_relset_1(u1_conlat_1(skc8),u2_conlat_1(skc8),u3_conlat_1(skc8))),k7_conlat_2(skc8)) ),
inference(res,[status(thm),theory(equality)],[2,86]),
[iquote('0:Res:2.0,86.0')] ).
cnf(112,plain,
( ~ v4_conlat_1(skc8)
| equal(g2_conlat_1(u1_conlat_1(skc8),u2_conlat_1(skc8),u3_conlat_1(skc8)),skc8) ),
inference(res,[status(thm),theory(equality)],[2,80]),
[iquote('0:Res:2.0,80.0')] ).
cnf(113,plain,
( ~ l3_conlat_1(u,skc8)
| v6_conlat_1(k8_conlat_2(skc8,u),k7_conlat_2(skc8))
| v3_conlat_1(skc8) ),
inference(res,[status(thm),theory(equality)],[2,81]),
[iquote('0:Res:2.0,81.0')] ).
cnf(114,plain,
( ~ l3_conlat_1(u,skc8)
| l3_conlat_1(k8_conlat_2(skc8,u),k7_conlat_2(skc8))
| v3_conlat_1(skc8) ),
inference(res,[status(thm),theory(equality)],[2,82]),
[iquote('0:Res:2.0,82.0')] ).
cnf(115,plain,
m2_relset_1(u3_conlat_1(skc8),u1_conlat_1(skc8),u2_conlat_1(skc8)),
inference(res,[status(thm),theory(equality)],[2,67]),
[iquote('0:Res:2.0,67.0')] ).
cnf(118,plain,
( ~ v3_conlat_1(k7_conlat_2(skc8))
| v3_conlat_1(skc8) ),
inference(res,[status(thm),theory(equality)],[2,45]),
[iquote('0:Res:2.0,45.0')] ).
cnf(124,plain,
( v4_conlat_1(k7_conlat_2(skc8))
| v3_conlat_1(skc8) ),
inference(res,[status(thm),theory(equality)],[2,38]),
[iquote('0:Res:2.0,38.0')] ).
cnf(125,plain,
( l2_conlat_1(k7_conlat_2(skc8))
| v3_conlat_1(skc8) ),
inference(res,[status(thm),theory(equality)],[2,39]),
[iquote('0:Res:2.0,39.0')] ).
cnf(126,plain,
l1_conlat_1(skc8),
inference(res,[status(thm),theory(equality)],[2,22]),
[iquote('0:Res:2.0,22.0')] ).
cnf(128,plain,
( ~ l2_conlat_1(skc8)
| ~ v9_conlat_1(skc9,skc8)
| ~ v7_conlat_1(k9_conlat_2(skc8,skc9),k7_conlat_2(skc8))
| v7_conlat_1(skc9,skc8)
| v3_conlat_1(skc8) ),
inference(res,[status(thm),theory(equality)],[14,94]),
[iquote('0:Res:14.0,94.2')] ).
cnf(129,plain,
( ~ l2_conlat_1(skc8)
| ~ v9_conlat_1(skc9,skc8)
| v7_conlat_1(skc9,skc8)
| equal(k8_conlat_2(skc8,skc9),k9_conlat_2(skc8,skc9))
| v3_conlat_1(skc8) ),
inference(res,[status(thm),theory(equality)],[14,93]),
[iquote('0:Res:14.0,93.1')] ).
cnf(131,plain,
( ~ l2_conlat_1(skc8)
| ~ v9_conlat_1(skc9,skc8)
| v9_conlat_1(k9_conlat_2(skc8,skc9),k7_conlat_2(skc8))
| v7_conlat_1(skc9,skc8)
| v3_conlat_1(skc8) ),
inference(res,[status(thm),theory(equality)],[14,91]),
[iquote('0:Res:14.0,91.1')] ).
cnf(132,plain,
( ~ l2_conlat_1(skc8)
| ~ v9_conlat_1(skc9,skc8)
| l3_conlat_1(k9_conlat_2(skc8,skc9),k7_conlat_2(skc8))
| v7_conlat_1(skc9,skc8)
| v3_conlat_1(skc8) ),
inference(res,[status(thm),theory(equality)],[14,90]),
[iquote('0:Res:14.0,90.1')] ).
cnf(133,plain,
( ~ l1_conlat_1(skc8)
| ~ v6_conlat_1(skc9,skc8)
| equal(g3_conlat_1(skc8,u4_conlat_1(skc8,skc9),u5_conlat_1(skc8,skc9)),skc9) ),
inference(res,[status(thm),theory(equality)],[14,89]),
[iquote('0:Res:14.0,89.2')] ).
cnf(198,plain,
v4_conlat_1(k7_conlat_2(skc8)),
inference(mrr,[status(thm)],[124,12]),
[iquote('0:MRR:124.1,12.0')] ).
cnf(199,plain,
l2_conlat_1(k7_conlat_2(skc8)),
inference(mrr,[status(thm)],[125,12]),
[iquote('0:MRR:125.1,12.0')] ).
cnf(200,plain,
~ v3_conlat_1(k7_conlat_2(skc8)),
inference(mrr,[status(thm)],[118,12]),
[iquote('0:MRR:118.1,12.0')] ).
cnf(223,plain,
equal(g2_conlat_1(u1_conlat_1(skc8),u2_conlat_1(skc8),u3_conlat_1(skc8)),skc8),
inference(mrr,[status(thm)],[112,1]),
[iquote('0:MRR:112.0,1.0')] ).
cnf(224,plain,
( ~ l3_conlat_1(u,skc8)
| v6_conlat_1(k8_conlat_2(skc8,u),k7_conlat_2(skc8)) ),
inference(mrr,[status(thm)],[113,12]),
[iquote('0:MRR:113.2,12.0')] ).
cnf(225,plain,
( ~ l3_conlat_1(u,skc8)
| l3_conlat_1(k8_conlat_2(skc8,u),k7_conlat_2(skc8)) ),
inference(mrr,[status(thm)],[114,12]),
[iquote('0:MRR:114.2,12.0')] ).
cnf(226,plain,
equal(g2_conlat_1(u2_conlat_1(skc8),u1_conlat_1(skc8),k6_relset_1(u1_conlat_1(skc8),u2_conlat_1(skc8),u3_conlat_1(skc8))),k7_conlat_2(skc8)),
inference(mrr,[status(thm)],[111,12]),
[iquote('0:MRR:111.0,12.0')] ).
cnf(227,plain,
equal(g3_conlat_1(skc8,u4_conlat_1(skc8,skc9),u5_conlat_1(skc8,skc9)),skc9),
inference(mrr,[status(thm)],[133,126,11]),
[iquote('0:MRR:133.0,133.1,126.0,11.0')] ).
cnf(229,plain,
v9_conlat_1(k9_conlat_2(skc8,skc9),k7_conlat_2(skc8)),
inference(mrr,[status(thm)],[131,2,13,19,12]),
[iquote('0:MRR:131.0,131.1,131.3,131.4,2.0,13.0,19.0,12.0')] ).
cnf(230,plain,
l3_conlat_1(k9_conlat_2(skc8,skc9),k7_conlat_2(skc8)),
inference(mrr,[status(thm)],[132,2,13,19,12]),
[iquote('0:MRR:132.0,132.1,132.3,132.4,2.0,13.0,19.0,12.0')] ).
cnf(234,plain,
~ v7_conlat_1(k9_conlat_2(skc8,skc9),k7_conlat_2(skc8)),
inference(mrr,[status(thm)],[128,2,13,19,12]),
[iquote('0:MRR:128.0,128.1,128.3,128.4,2.0,13.0,19.0,12.0')] ).
cnf(235,plain,
equal(k8_conlat_2(skc8,skc9),k9_conlat_2(skc8,skc9)),
inference(mrr,[status(thm)],[129,2,13,19,12]),
[iquote('0:MRR:129.0,129.1,129.2,129.4,2.0,13.0,19.0,12.0')] ).
cnf(244,plain,
( ~ l3_conlat_1(u,skc8)
| ~ l3_conlat_1(v,k7_conlat_2(skc8))
| ~ v6_conlat_1(v,k7_conlat_2(skc8))
| ~ equal(v,k8_conlat_2(skc8,u))
| equal(u5_conlat_1(k7_conlat_2(skc8),v),u4_conlat_1(skc8,u)) ),
inference(mrr,[status(thm)],[105,12]),
[iquote('0:MRR:105.5,12.0')] ).
cnf(245,plain,
( ~ l3_conlat_1(u,skc8)
| ~ l3_conlat_1(v,k7_conlat_2(skc8))
| ~ v6_conlat_1(v,k7_conlat_2(skc8))
| ~ equal(v,k8_conlat_2(skc8,u))
| equal(u4_conlat_1(k7_conlat_2(skc8),v),u5_conlat_1(skc8,u)) ),
inference(mrr,[status(thm)],[104,12]),
[iquote('0:MRR:104.5,12.0')] ).
cnf(332,plain,
m1_relset_1(u3_conlat_1(skc8),u1_conlat_1(skc8),u2_conlat_1(skc8)),
inference(res,[status(thm),theory(equality)],[115,61]),
[iquote('0:Res:115.0,61.0')] ).
cnf(339,plain,
( ~ l2_conlat_1(u)
| m1_relset_1(u3_conlat_1(u),u1_conlat_1(u),u2_conlat_1(u)) ),
inference(res,[status(thm),theory(equality)],[67,61]),
[iquote('0:Res:67.1,61.0')] ).
cnf(359,plain,
( ~ m1_relset_1(u,v,w)
| m1_relset_1(k4_relat_1(u),w,v) ),
inference(res,[status(thm),theory(equality)],[101,61]),
[iquote('0:Res:101.1,61.0')] ).
cnf(364,plain,
( ~ m2_relset_1(u,v,w)
| v1_relat_1(u) ),
inference(res,[status(thm),theory(equality)],[71,44]),
[iquote('0:Res:71.1,44.0')] ).
cnf(368,plain,
( ~ m1_relset_1(u,v,w)
| v1_relat_1(u) ),
inference(res,[status(thm),theory(equality)],[62,364]),
[iquote('0:Res:62.1,364.0')] ).
cnf(421,plain,
( ~ v1_relat_1(u)
| ~ m1_relset_1(k4_relat_1(u),v,w)
| equal(k6_relset_1(v,w,u),k4_relat_1(u)) ),
inference(spr,[status(thm),theory(equality)],[40,102]),
[iquote('0:SpR:40.1,102.1')] ).
cnf(539,plain,
( ~ v4_conlat_1(u)
| ~ l2_conlat_1(u)
| ~ equal(u,g2_conlat_1(v,w,x))
| ~ m1_relset_1(u3_conlat_1(u),u1_conlat_1(u),u2_conlat_1(u))
| equal(u2_conlat_1(u),w) ),
inference(spl,[status(thm),theory(equality)],[80,84]),
[iquote('0:SpL:80.2,84.0')] ).
cnf(543,plain,
( ~ v4_conlat_1(u)
| ~ l2_conlat_1(u)
| ~ equal(u,g2_conlat_1(v,w,x))
| equal(u2_conlat_1(u),w) ),
inference(mrr,[status(thm)],[539,339]),
[iquote('0:MRR:539.3,339.1')] ).
cnf(579,plain,
( ~ v4_conlat_1(u)
| ~ l2_conlat_1(u)
| ~ equal(u,g2_conlat_1(v,w,x))
| ~ m1_relset_1(u3_conlat_1(u),u1_conlat_1(u),u2_conlat_1(u))
| equal(u1_conlat_1(u),v) ),
inference(spl,[status(thm),theory(equality)],[80,83]),
[iquote('0:SpL:80.2,83.0')] ).
cnf(583,plain,
( ~ v4_conlat_1(u)
| ~ l2_conlat_1(u)
| ~ equal(u,g2_conlat_1(v,w,x))
| equal(u1_conlat_1(u),v) ),
inference(mrr,[status(thm)],[579,339]),
[iquote('0:MRR:579.3,339.1')] ).
cnf(597,plain,
( ~ l2_conlat_1(u)
| ~ m1_relset_1(u3_conlat_1(u),u1_conlat_1(u),u2_conlat_1(u))
| v3_conlat_1(u)
| equal(g2_conlat_1(u2_conlat_1(u),u1_conlat_1(u),k4_relat_1(u3_conlat_1(u))),k7_conlat_2(u)) ),
inference(spr,[status(thm),theory(equality)],[73,86]),
[iquote('0:SpR:73.1,86.2')] ).
cnf(604,plain,
( ~ l2_conlat_1(u)
| v3_conlat_1(u)
| equal(g2_conlat_1(u2_conlat_1(u),u1_conlat_1(u),k4_relat_1(u3_conlat_1(u))),k7_conlat_2(u)) ),
inference(mrr,[status(thm)],[597,339]),
[iquote('0:MRR:597.1,339.1')] ).
cnf(797,plain,
( ~ l2_conlat_1(u)
| ~ l3_conlat_1(v,u)
| ~ l3_conlat_1(k8_conlat_2(u,v),k7_conlat_2(u))
| ~ v6_conlat_1(k8_conlat_2(u,v),k7_conlat_2(u))
| v3_conlat_1(u)
| equal(u4_conlat_1(k7_conlat_2(u),k8_conlat_2(u,v)),u5_conlat_1(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[99]),
[iquote('0:EqR:99.4')] ).
cnf(801,plain,
( ~ l2_conlat_1(u)
| ~ l3_conlat_1(v,u)
| v3_conlat_1(u)
| equal(u4_conlat_1(k7_conlat_2(u),k8_conlat_2(u,v)),u5_conlat_1(u,v)) ),
inference(mrr,[status(thm)],[797,82,81]),
[iquote('0:MRR:797.2,797.3,82.3,81.3')] ).
cnf(818,plain,
( ~ l2_conlat_1(u)
| ~ l3_conlat_1(v,u)
| ~ l3_conlat_1(k8_conlat_2(u,v),k7_conlat_2(u))
| ~ v6_conlat_1(k8_conlat_2(u,v),k7_conlat_2(u))
| v3_conlat_1(u)
| equal(u5_conlat_1(k7_conlat_2(u),k8_conlat_2(u,v)),u4_conlat_1(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[98]),
[iquote('0:EqR:98.4')] ).
cnf(822,plain,
( ~ l2_conlat_1(u)
| ~ l3_conlat_1(v,u)
| v3_conlat_1(u)
| equal(u5_conlat_1(k7_conlat_2(u),k8_conlat_2(u,v)),u4_conlat_1(u,v)) ),
inference(mrr,[status(thm)],[818,82,81]),
[iquote('0:MRR:818.2,818.3,82.3,81.3')] ).
cnf(1157,plain,
( ~ m1_relset_1(u3_conlat_1(skc8),u1_conlat_1(skc8),u2_conlat_1(skc8))
| equal(g2_conlat_1(u2_conlat_1(skc8),u1_conlat_1(skc8),k4_relat_1(u3_conlat_1(skc8))),k7_conlat_2(skc8)) ),
inference(spr,[status(thm),theory(equality)],[73,226]),
[iquote('0:SpR:73.1,226.0')] ).
cnf(1158,plain,
( ~ equal(g2_conlat_1(u,v,w),k7_conlat_2(skc8))
| ~ m1_relset_1(w,u,v)
| equal(u,u2_conlat_1(skc8)) ),
inference(spl,[status(thm),theory(equality)],[226,83]),
[iquote('0:SpL:226.0,83.0')] ).
cnf(1160,plain,
( ~ equal(g2_conlat_1(u,v,w),k7_conlat_2(skc8))
| ~ m1_relset_1(w,u,v)
| equal(w,k6_relset_1(u1_conlat_1(skc8),u2_conlat_1(skc8),u3_conlat_1(skc8))) ),
inference(spl,[status(thm),theory(equality)],[226,85]),
[iquote('0:SpL:226.0,85.0')] ).
cnf(1168,plain,
equal(g2_conlat_1(u2_conlat_1(skc8),u1_conlat_1(skc8),k4_relat_1(u3_conlat_1(skc8))),k7_conlat_2(skc8)),
inference(mrr,[status(thm)],[1157,332]),
[iquote('0:MRR:1157.0,332.0')] ).
cnf(1259,plain,
( ~ v1_relat_1(u)
| ~ m1_relset_1(u,v,w)
| equal(k6_relset_1(w,v,u),k4_relat_1(u)) ),
inference(res,[status(thm),theory(equality)],[359,421]),
[iquote('0:Res:359.1,421.1')] ).
cnf(1260,plain,
( ~ m1_relset_1(u,v,w)
| equal(k6_relset_1(w,v,u),k4_relat_1(u)) ),
inference(mrr,[status(thm)],[1259,368]),
[iquote('0:MRR:1259.0,368.1')] ).
cnf(1322,plain,
( ~ m1_relset_1(k4_relat_1(u),v,w)
| ~ m1_relset_1(u,w,v)
| equal(k4_relat_1(k4_relat_1(u)),u) ),
inference(spr,[status(thm),theory(equality)],[1260,102]),
[iquote('0:SpR:1260.1,102.1')] ).
cnf(1327,plain,
( ~ m1_relset_1(u,v,w)
| equal(k4_relat_1(k4_relat_1(u)),u) ),
inference(mrr,[status(thm)],[1322,359]),
[iquote('0:MRR:1322.0,359.1')] ).
cnf(1338,plain,
equal(k4_relat_1(k4_relat_1(u3_conlat_1(skc8))),u3_conlat_1(skc8)),
inference(res,[status(thm),theory(equality)],[332,1327]),
[iquote('0:Res:332.0,1327.0')] ).
cnf(1523,plain,
( ~ v4_conlat_1(g2_conlat_1(u,v,w))
| ~ l2_conlat_1(g2_conlat_1(u,v,w))
| equal(u2_conlat_1(g2_conlat_1(u,v,w)),v) ),
inference(eqr,[status(thm),theory(equality)],[543]),
[iquote('0:EqR:543.2')] ).
cnf(1539,plain,
( ~ v4_conlat_1(u)
| ~ l2_conlat_1(u)
| ~ equal(u,k7_conlat_2(skc8))
| equal(u1_conlat_1(u),u2_conlat_1(skc8)) ),
inference(spl,[status(thm),theory(equality)],[226,583]),
[iquote('0:SpL:226.0,583.2')] ).
cnf(1629,plain,
( ~ l2_conlat_1(u)
| ~ l1_conlat_1(k7_conlat_2(u))
| ~ l3_conlat_1(v,u)
| ~ l3_conlat_1(k8_conlat_2(u,v),k7_conlat_2(u))
| ~ v6_conlat_1(k8_conlat_2(u,v),k7_conlat_2(u))
| v3_conlat_1(u)
| equal(g3_conlat_1(k7_conlat_2(u),u5_conlat_1(u,v),u5_conlat_1(k7_conlat_2(u),k8_conlat_2(u,v))),k8_conlat_2(u,v)) ),
inference(spr,[status(thm),theory(equality)],[801,89]),
[iquote('0:SpR:801.3,89.3')] ).
cnf(1649,plain,
( ~ l2_conlat_1(u)
| ~ l1_conlat_1(k7_conlat_2(u))
| ~ l3_conlat_1(v,u)
| ~ l3_conlat_1(k8_conlat_2(u,v),k7_conlat_2(u))
| ~ v6_conlat_1(k8_conlat_2(u,v),k7_conlat_2(u))
| v3_conlat_1(u)
| equal(g3_conlat_1(k7_conlat_2(u),u5_conlat_1(u,v),u4_conlat_1(u,v)),k8_conlat_2(u,v)) ),
inference(rew,[status(thm),theory(equality)],[822,1629]),
[iquote('0:Rew:822.3,1629.6')] ).
cnf(1650,plain,
( ~ l2_conlat_1(u)
| ~ l1_conlat_1(k7_conlat_2(u))
| ~ l3_conlat_1(v,u)
| v3_conlat_1(u)
| equal(g3_conlat_1(k7_conlat_2(u),u5_conlat_1(u,v),u4_conlat_1(u,v)),k8_conlat_2(u,v)) ),
inference(mrr,[status(thm)],[1649,82,81]),
[iquote('0:MRR:1649.3,1649.4,82.3,81.3')] ).
cnf(1937,plain,
( ~ l3_conlat_1(u,skc8)
| ~ l3_conlat_1(k8_conlat_2(skc8,u),k7_conlat_2(skc8))
| ~ v6_conlat_1(k8_conlat_2(skc8,u),k7_conlat_2(skc8))
| equal(u4_conlat_1(k7_conlat_2(skc8),k8_conlat_2(skc8,u)),u5_conlat_1(skc8,u)) ),
inference(eqr,[status(thm),theory(equality)],[245]),
[iquote('0:EqR:245.3')] ).
cnf(1942,plain,
( ~ l3_conlat_1(u,skc8)
| equal(u4_conlat_1(k7_conlat_2(skc8),k8_conlat_2(skc8,u)),u5_conlat_1(skc8,u)) ),
inference(mrr,[status(thm)],[1937,225,224]),
[iquote('0:MRR:1937.1,1937.2,225.1,224.1')] ).
cnf(1945,plain,
( ~ l3_conlat_1(u,skc8)
| ~ l3_conlat_1(k8_conlat_2(skc8,u),k7_conlat_2(skc8))
| ~ v6_conlat_1(k8_conlat_2(skc8,u),k7_conlat_2(skc8))
| equal(u5_conlat_1(k7_conlat_2(skc8),k8_conlat_2(skc8,u)),u4_conlat_1(skc8,u)) ),
inference(eqr,[status(thm),theory(equality)],[244]),
[iquote('0:EqR:244.3')] ).
cnf(1950,plain,
( ~ l3_conlat_1(u,skc8)
| equal(u5_conlat_1(k7_conlat_2(skc8),k8_conlat_2(skc8,u)),u4_conlat_1(skc8,u)) ),
inference(mrr,[status(thm)],[1945,225,224]),
[iquote('0:MRR:1945.1,1945.2,225.1,224.1')] ).
cnf(2295,plain,
( ~ l3_conlat_1(skc9,skc8)
| equal(u4_conlat_1(k7_conlat_2(skc8),k9_conlat_2(skc8,skc9)),u5_conlat_1(skc8,skc9)) ),
inference(spr,[status(thm),theory(equality)],[235,1942]),
[iquote('0:SpR:235.0,1942.1')] ).
cnf(2360,plain,
( ~ l3_conlat_1(skc9,skc8)
| equal(u5_conlat_1(k7_conlat_2(skc8),k9_conlat_2(skc8,skc9)),u4_conlat_1(skc8,skc9)) ),
inference(spr,[status(thm),theory(equality)],[235,1950]),
[iquote('0:SpR:235.0,1950.1')] ).
cnf(3042,plain,
( ~ m1_relset_1(u,v,w)
| ~ m1_relset_1(u,v,w)
| equal(u2_conlat_1(g2_conlat_1(v,w,u)),w) ),
inference(sor,[status(thm)],[1523,65,66]),
[iquote('0:SoR:1523.0,1523.1,65.1,66.1')] ).
cnf(3043,plain,
( ~ m1_relset_1(u,v,w)
| equal(u2_conlat_1(g2_conlat_1(v,w,u)),w) ),
inference(obv,[status(thm),theory(equality)],[3042]),
[iquote('0:Obv:3042.0')] ).
cnf(3081,plain,
( ~ m1_relset_1(k4_relat_1(u3_conlat_1(skc8)),u2_conlat_1(skc8),u1_conlat_1(skc8))
| equal(u2_conlat_1(k7_conlat_2(skc8)),u1_conlat_1(skc8)) ),
inference(spr,[status(thm),theory(equality)],[1168,3043]),
[iquote('0:SpR:1168.0,3043.1')] ).
cnf(3266,plain,
( ~ m1_relset_1(u3_conlat_1(skc8),u1_conlat_1(skc8),u2_conlat_1(skc8))
| equal(u2_conlat_1(k7_conlat_2(skc8)),u1_conlat_1(skc8)) ),
inference(res,[status(thm),theory(equality)],[359,3081]),
[iquote('0:Res:359.1,3081.0')] ).
cnf(3267,plain,
equal(u2_conlat_1(k7_conlat_2(skc8)),u1_conlat_1(skc8)),
inference(mrr,[status(thm)],[3266,332]),
[iquote('0:MRR:3266.0,332.0')] ).
cnf(3283,plain,
( ~ l2_conlat_1(k7_conlat_2(skc8))
| m2_relset_1(u3_conlat_1(k7_conlat_2(skc8)),u1_conlat_1(k7_conlat_2(skc8)),u1_conlat_1(skc8)) ),
inference(spr,[status(thm),theory(equality)],[3267,67]),
[iquote('0:SpR:3267.0,67.1')] ).
cnf(3284,plain,
( ~ l2_conlat_1(k7_conlat_2(skc8))
| m1_relset_1(u3_conlat_1(k7_conlat_2(skc8)),u1_conlat_1(k7_conlat_2(skc8)),u1_conlat_1(skc8)) ),
inference(spr,[status(thm),theory(equality)],[3267,339]),
[iquote('0:SpR:3267.0,339.1')] ).
cnf(3285,plain,
( ~ v4_conlat_1(k7_conlat_2(skc8))
| ~ l2_conlat_1(k7_conlat_2(skc8))
| equal(g2_conlat_1(u1_conlat_1(k7_conlat_2(skc8)),u1_conlat_1(skc8),u3_conlat_1(k7_conlat_2(skc8))),k7_conlat_2(skc8)) ),
inference(spr,[status(thm),theory(equality)],[3267,80]),
[iquote('0:SpR:3267.0,80.2')] ).
cnf(3292,plain,
( ~ l2_conlat_1(k7_conlat_2(skc8))
| v3_conlat_1(k7_conlat_2(skc8))
| equal(g2_conlat_1(u1_conlat_1(skc8),u1_conlat_1(k7_conlat_2(skc8)),k4_relat_1(u3_conlat_1(k7_conlat_2(skc8)))),k7_conlat_2(k7_conlat_2(skc8))) ),
inference(spr,[status(thm),theory(equality)],[3267,604]),
[iquote('0:SpR:3267.0,604.2')] ).
cnf(3311,plain,
m2_relset_1(u3_conlat_1(k7_conlat_2(skc8)),u1_conlat_1(k7_conlat_2(skc8)),u1_conlat_1(skc8)),
inference(ssi,[status(thm)],[3283,198,199]),
[iquote('0:SSi:3283.0,198.0,199.0')] ).
cnf(3312,plain,
m1_relset_1(u3_conlat_1(k7_conlat_2(skc8)),u1_conlat_1(k7_conlat_2(skc8)),u1_conlat_1(skc8)),
inference(ssi,[status(thm)],[3284,198,199]),
[iquote('0:SSi:3284.0,198.0,199.0')] ).
cnf(3318,plain,
equal(g2_conlat_1(u1_conlat_1(k7_conlat_2(skc8)),u1_conlat_1(skc8),u3_conlat_1(k7_conlat_2(skc8))),k7_conlat_2(skc8)),
inference(ssi,[status(thm)],[3285,198,199]),
[iquote('0:SSi:3285.1,3285.0,198.0,199.0,198.0,199.0')] ).
cnf(3319,plain,
( v3_conlat_1(k7_conlat_2(skc8))
| equal(g2_conlat_1(u1_conlat_1(skc8),u1_conlat_1(k7_conlat_2(skc8)),k4_relat_1(u3_conlat_1(k7_conlat_2(skc8)))),k7_conlat_2(k7_conlat_2(skc8))) ),
inference(ssi,[status(thm)],[3292,198,199]),
[iquote('0:SSi:3292.0,198.0,199.0')] ).
cnf(3320,plain,
equal(g2_conlat_1(u1_conlat_1(skc8),u1_conlat_1(k7_conlat_2(skc8)),k4_relat_1(u3_conlat_1(k7_conlat_2(skc8)))),k7_conlat_2(k7_conlat_2(skc8))),
inference(mrr,[status(thm)],[3319,200]),
[iquote('0:MRR:3319.0,200.0')] ).
cnf(3351,plain,
( ~ v4_conlat_1(k7_conlat_2(skc8))
| ~ l2_conlat_1(k7_conlat_2(skc8))
| ~ equal(k7_conlat_2(skc8),k7_conlat_2(skc8))
| m2_relset_1(u3_conlat_1(k7_conlat_2(skc8)),u2_conlat_1(skc8),u1_conlat_1(skc8)) ),
inference(spr,[status(thm),theory(equality)],[1539,3311]),
[iquote('0:SpR:1539.3,3311.0')] ).
cnf(3355,plain,
( ~ v4_conlat_1(k7_conlat_2(skc8))
| ~ l2_conlat_1(k7_conlat_2(skc8))
| m2_relset_1(u3_conlat_1(k7_conlat_2(skc8)),u2_conlat_1(skc8),u1_conlat_1(skc8)) ),
inference(obv,[status(thm),theory(equality)],[3351]),
[iquote('0:Obv:3351.2')] ).
cnf(3356,plain,
m2_relset_1(u3_conlat_1(k7_conlat_2(skc8)),u2_conlat_1(skc8),u1_conlat_1(skc8)),
inference(ssi,[status(thm)],[3355,198,199]),
[iquote('0:SSi:3355.1,3355.0,198.0,199.0,198.0,199.0')] ).
cnf(3362,plain,
m1_relset_1(u3_conlat_1(k7_conlat_2(skc8)),u2_conlat_1(skc8),u1_conlat_1(skc8)),
inference(res,[status(thm),theory(equality)],[3356,61]),
[iquote('0:Res:3356.0,61.0')] ).
cnf(4524,plain,
( ~ equal(k7_conlat_2(skc8),k7_conlat_2(skc8))
| ~ m1_relset_1(u3_conlat_1(k7_conlat_2(skc8)),u1_conlat_1(k7_conlat_2(skc8)),u1_conlat_1(skc8))
| equal(u1_conlat_1(k7_conlat_2(skc8)),u2_conlat_1(skc8)) ),
inference(spl,[status(thm),theory(equality)],[3318,1158]),
[iquote('0:SpL:3318.0,1158.0')] ).
cnf(4528,plain,
( ~ m1_relset_1(u3_conlat_1(k7_conlat_2(skc8)),u1_conlat_1(k7_conlat_2(skc8)),u1_conlat_1(skc8))
| equal(u1_conlat_1(k7_conlat_2(skc8)),u2_conlat_1(skc8)) ),
inference(obv,[status(thm),theory(equality)],[4524]),
[iquote('0:Obv:4524.0')] ).
cnf(4529,plain,
equal(u1_conlat_1(k7_conlat_2(skc8)),u2_conlat_1(skc8)),
inference(mrr,[status(thm)],[4528,3312]),
[iquote('0:MRR:4528.0,3312.0')] ).
cnf(4536,plain,
equal(g2_conlat_1(u2_conlat_1(skc8),u1_conlat_1(skc8),u3_conlat_1(k7_conlat_2(skc8))),k7_conlat_2(skc8)),
inference(rew,[status(thm),theory(equality)],[4529,3318]),
[iquote('0:Rew:4529.0,3318.0')] ).
cnf(4544,plain,
equal(g2_conlat_1(u1_conlat_1(skc8),u2_conlat_1(skc8),k4_relat_1(u3_conlat_1(k7_conlat_2(skc8)))),k7_conlat_2(k7_conlat_2(skc8))),
inference(rew,[status(thm),theory(equality)],[4529,3320]),
[iquote('0:Rew:4529.0,3320.0')] ).
cnf(4942,plain,
( ~ equal(k7_conlat_2(skc8),k7_conlat_2(skc8))
| ~ m1_relset_1(u3_conlat_1(k7_conlat_2(skc8)),u2_conlat_1(skc8),u1_conlat_1(skc8))
| equal(k6_relset_1(u1_conlat_1(skc8),u2_conlat_1(skc8),u3_conlat_1(skc8)),u3_conlat_1(k7_conlat_2(skc8))) ),
inference(spl,[status(thm),theory(equality)],[4536,1160]),
[iquote('0:SpL:4536.0,1160.0')] ).
cnf(4945,plain,
( ~ m1_relset_1(u3_conlat_1(k7_conlat_2(skc8)),u2_conlat_1(skc8),u1_conlat_1(skc8))
| equal(k6_relset_1(u1_conlat_1(skc8),u2_conlat_1(skc8),u3_conlat_1(skc8)),u3_conlat_1(k7_conlat_2(skc8))) ),
inference(obv,[status(thm),theory(equality)],[4942]),
[iquote('0:Obv:4942.0')] ).
cnf(4946,plain,
equal(k6_relset_1(u1_conlat_1(skc8),u2_conlat_1(skc8),u3_conlat_1(skc8)),u3_conlat_1(k7_conlat_2(skc8))),
inference(mrr,[status(thm)],[4945,3362]),
[iquote('0:MRR:4945.0,3362.0')] ).
cnf(5252,plain,
( ~ m1_relset_1(u3_conlat_1(skc8),u1_conlat_1(skc8),u2_conlat_1(skc8))
| equal(k4_relat_1(u3_conlat_1(skc8)),u3_conlat_1(k7_conlat_2(skc8))) ),
inference(spr,[status(thm),theory(equality)],[4946,73]),
[iquote('0:SpR:4946.0,73.1')] ).
cnf(5270,plain,
equal(k4_relat_1(u3_conlat_1(skc8)),u3_conlat_1(k7_conlat_2(skc8))),
inference(mrr,[status(thm)],[5252,332]),
[iquote('0:MRR:5252.0,332.0')] ).
cnf(5274,plain,
equal(k4_relat_1(u3_conlat_1(k7_conlat_2(skc8))),u3_conlat_1(skc8)),
inference(rew,[status(thm),theory(equality)],[5270,1338]),
[iquote('0:Rew:5270.0,1338.0')] ).
cnf(5296,plain,
equal(g2_conlat_1(u1_conlat_1(skc8),u2_conlat_1(skc8),u3_conlat_1(skc8)),k7_conlat_2(k7_conlat_2(skc8))),
inference(rew,[status(thm),theory(equality)],[5274,4544]),
[iquote('0:Rew:5274.0,4544.0')] ).
cnf(5298,plain,
equal(k7_conlat_2(k7_conlat_2(skc8)),skc8),
inference(rew,[status(thm),theory(equality)],[223,5296]),
[iquote('0:Rew:223.0,5296.0')] ).
cnf(5779,plain,
( ~ l2_conlat_1(u)
| ~ l2_conlat_1(k7_conlat_2(u))
| ~ l3_conlat_1(v,u)
| v3_conlat_1(u)
| equal(g3_conlat_1(k7_conlat_2(u),u5_conlat_1(u,v),u4_conlat_1(u,v)),k8_conlat_2(u,v)) ),
inference(sor,[status(thm)],[1650,22]),
[iquote('0:SoR:1650.1,22.1')] ).
cnf(5780,plain,
( ~ l2_conlat_1(u)
| ~ l3_conlat_1(v,u)
| v3_conlat_1(u)
| equal(g3_conlat_1(k7_conlat_2(u),u5_conlat_1(u,v),u4_conlat_1(u,v)),k8_conlat_2(u,v)) ),
inference(mrr,[status(thm)],[5779,39]),
[iquote('0:MRR:5779.1,39.2')] ).
cnf(20165,plain,
equal(u5_conlat_1(k7_conlat_2(skc8),k9_conlat_2(skc8,skc9)),u4_conlat_1(skc8,skc9)),
inference(mrr,[status(thm)],[2360,14]),
[iquote('0:MRR:2360.0,14.0')] ).
cnf(20630,plain,
equal(u4_conlat_1(k7_conlat_2(skc8),k9_conlat_2(skc8,skc9)),u5_conlat_1(skc8,skc9)),
inference(mrr,[status(thm)],[2295,14]),
[iquote('0:MRR:2295.0,14.0')] ).
cnf(21135,plain,
( ~ l2_conlat_1(k7_conlat_2(skc8))
| ~ l3_conlat_1(k9_conlat_2(skc8,skc9),k7_conlat_2(skc8))
| v3_conlat_1(k7_conlat_2(skc8))
| equal(g3_conlat_1(k7_conlat_2(k7_conlat_2(skc8)),u4_conlat_1(skc8,skc9),u4_conlat_1(k7_conlat_2(skc8),k9_conlat_2(skc8,skc9))),k8_conlat_2(k7_conlat_2(skc8),k9_conlat_2(skc8,skc9))) ),
inference(spr,[status(thm),theory(equality)],[20165,5780]),
[iquote('0:SpR:20165.0,5780.3')] ).
cnf(21174,plain,
( ~ l2_conlat_1(k7_conlat_2(skc8))
| ~ l3_conlat_1(k9_conlat_2(skc8,skc9),k7_conlat_2(skc8))
| v3_conlat_1(k7_conlat_2(skc8))
| equal(g3_conlat_1(skc8,u4_conlat_1(skc8,skc9),u4_conlat_1(k7_conlat_2(skc8),k9_conlat_2(skc8,skc9))),k8_conlat_2(k7_conlat_2(skc8),k9_conlat_2(skc8,skc9))) ),
inference(rew,[status(thm),theory(equality)],[5298,21135]),
[iquote('0:Rew:5298.0,21135.3')] ).
cnf(21175,plain,
( ~ l2_conlat_1(k7_conlat_2(skc8))
| ~ l3_conlat_1(k9_conlat_2(skc8,skc9),k7_conlat_2(skc8))
| v3_conlat_1(k7_conlat_2(skc8))
| equal(g3_conlat_1(skc8,u4_conlat_1(skc8,skc9),u5_conlat_1(skc8,skc9)),k8_conlat_2(k7_conlat_2(skc8),k9_conlat_2(skc8,skc9))) ),
inference(rew,[status(thm),theory(equality)],[20630,21174]),
[iquote('0:Rew:20630.0,21174.3')] ).
cnf(21176,plain,
( ~ l2_conlat_1(k7_conlat_2(skc8))
| ~ l3_conlat_1(k9_conlat_2(skc8,skc9),k7_conlat_2(skc8))
| v3_conlat_1(k7_conlat_2(skc8))
| equal(k8_conlat_2(k7_conlat_2(skc8),k9_conlat_2(skc8,skc9)),skc9) ),
inference(rew,[status(thm),theory(equality)],[227,21175]),
[iquote('0:Rew:227.0,21175.3')] ).
cnf(21177,plain,
( ~ l3_conlat_1(k9_conlat_2(skc8,skc9),k7_conlat_2(skc8))
| v3_conlat_1(k7_conlat_2(skc8))
| equal(k8_conlat_2(k7_conlat_2(skc8),k9_conlat_2(skc8,skc9)),skc9) ),
inference(ssi,[status(thm)],[21176,198,199]),
[iquote('0:SSi:21176.0,198.0,199.0')] ).
cnf(21178,plain,
equal(k8_conlat_2(k7_conlat_2(skc8),k9_conlat_2(skc8,skc9)),skc9),
inference(mrr,[status(thm)],[21177,230,200]),
[iquote('0:MRR:21177.0,21177.1,230.0,200.0')] ).
cnf(21199,plain,
( ~ l2_conlat_1(k7_conlat_2(skc8))
| ~ v9_conlat_1(k9_conlat_2(skc8,skc9),k7_conlat_2(skc8))
| ~ l3_conlat_1(k9_conlat_2(skc8,skc9),k7_conlat_2(skc8))
| v3_conlat_1(k7_conlat_2(skc8))
| v7_conlat_1(k9_conlat_2(skc8,skc9),k7_conlat_2(skc8))
| equal(k9_conlat_2(k7_conlat_2(skc8),k9_conlat_2(skc8,skc9)),skc9) ),
inference(spr,[status(thm),theory(equality)],[21178,93]),
[iquote('0:SpR:21178.0,93.5')] ).
cnf(21219,plain,
( ~ v9_conlat_1(k9_conlat_2(skc8,skc9),k7_conlat_2(skc8))
| ~ l3_conlat_1(k9_conlat_2(skc8,skc9),k7_conlat_2(skc8))
| v3_conlat_1(k7_conlat_2(skc8))
| v7_conlat_1(k9_conlat_2(skc8,skc9),k7_conlat_2(skc8))
| equal(k9_conlat_2(k7_conlat_2(skc8),k9_conlat_2(skc8,skc9)),skc9) ),
inference(ssi,[status(thm)],[21199,198,199]),
[iquote('0:SSi:21199.0,198.0,199.0')] ).
cnf(21220,plain,
$false,
inference(mrr,[status(thm)],[21219,229,230,200,234,43]),
[iquote('0:MRR:21219.0,21219.1,21219.2,21219.3,21219.4,229.0,230.0,200.0,234.0,43.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LAT345+1 : TPTP v8.1.0. Released v3.4.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Wed Jun 29 07:19:34 EDT 2022
% 0.11/0.33 % CPUTime :
% 11.24/11.41
% 11.24/11.41 SPASS V 3.9
% 11.24/11.41 SPASS beiseite: Proof found.
% 11.24/11.41 % SZS status Theorem
% 11.24/11.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.24/11.41 SPASS derived 14115 clauses, backtracked 447 clauses, performed 11 splits and kept 6101 clauses.
% 11.24/11.41 SPASS allocated 119252 KBytes.
% 11.24/11.41 SPASS spent 0:0:11.07 on the problem.
% 11.24/11.41 0:00:00.04 for the input.
% 11.24/11.41 0:00:00.05 for the FLOTTER CNF translation.
% 11.24/11.41 0:00:00.28 for inferences.
% 11.24/11.41 0:00:00.12 for the backtracking.
% 11.24/11.41 0:0:10.38 for the reduction.
% 11.24/11.41
% 11.24/11.41
% 11.24/11.41 Here is a proof with depth 8, length 149 :
% 11.24/11.41 % SZS output start Refutation
% See solution above
% 12.86/13.04 Formulae used in the proof : t20_conlat_2 dt_l2_conlat_1 dt_k7_conlat_2 involutiveness_k4_relat_1 cc1_relset_1 redefinition_m2_relset_1 dt_g2_conlat_1 dt_u3_conlat_1 dt_m2_relset_1 dt_k6_relset_1 redefinition_k6_relset_1 involutiveness_k6_relset_1 abstractness_v4_conlat_1 dt_k8_conlat_2 free_g2_conlat_1 d7_conlat_2 abstractness_v6_conlat_1 dt_k9_conlat_2 redefinition_k9_conlat_2 d8_conlat_2
% 12.86/13.04
%------------------------------------------------------------------------------