TSTP Solution File: SEU352+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU352+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 : Tue Jul 19 14:36:32 EDT 2022
% Result : Theorem 1.53s 1.76s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 37
% Syntax : Number of clauses : 140 ( 30 unt; 72 nHn; 140 RR)
% Number of literals : 614 ( 0 equ; 405 neg)
% Maximal clause size : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
lattice(skc8),
file('SEU352+1.p',unknown),
[] ).
cnf(2,axiom,
complete_latt_str(skc8),
file('SEU352+1.p',unknown),
[] ).
cnf(3,axiom,
latt_str(skc8),
file('SEU352+1.p',unknown),
[] ).
cnf(8,axiom,
empty(empty_set),
file('SEU352+1.p',unknown),
[] ).
cnf(11,axiom,
~ empty_carrier(skc8),
file('SEU352+1.p',unknown),
[] ).
cnf(12,axiom,
empty(skf20(u)),
file('SEU352+1.p',unknown),
[] ).
cnf(19,axiom,
element(skf11(u),the_carrier(u)),
file('SEU352+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ latt_str(u)
| meet_semilatt_str(u) ),
file('SEU352+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ latt_str(u)
| join_semilatt_str(u) ),
file('SEU352+1.p',unknown),
[] ).
cnf(26,axiom,
element(skf20(u),powerset(u)),
file('SEU352+1.p',unknown),
[] ).
cnf(27,axiom,
element(skf12(u,v),the_carrier(v)),
file('SEU352+1.p',unknown),
[] ).
cnf(28,axiom,
element(skf13(u,v),the_carrier(v)),
file('SEU352+1.p',unknown),
[] ).
cnf(34,axiom,
( ~ empty(u)
| equal(u,empty_set) ),
file('SEU352+1.p',unknown),
[] ).
cnf(37,axiom,
element(skf15(u,v,w),the_carrier(w)),
file('SEU352+1.p',unknown),
[] ).
cnf(39,axiom,
( ~ empty(u)
| ~ in(v,u) ),
file('SEU352+1.p',unknown),
[] ).
cnf(51,axiom,
( ~ lattice(u)
| ~ latt_str(u)
| empty_carrier(u)
| join_commutative(u) ),
file('SEU352+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ lattice(u)
| ~ latt_str(u)
| empty_carrier(u)
| join_associative(u) ),
file('SEU352+1.p',unknown),
[] ).
cnf(53,axiom,
( ~ lattice(u)
| ~ latt_str(u)
| empty_carrier(u)
| meet_commutative(u) ),
file('SEU352+1.p',unknown),
[] ).
cnf(54,axiom,
( ~ lattice(u)
| ~ latt_str(u)
| empty_carrier(u)
| meet_associative(u) ),
file('SEU352+1.p',unknown),
[] ).
cnf(55,axiom,
( ~ lattice(u)
| ~ latt_str(u)
| empty_carrier(u)
| meet_absorbing(u) ),
file('SEU352+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ lattice(u)
| ~ latt_str(u)
| empty_carrier(u)
| join_absorbing(u) ),
file('SEU352+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ meet_semilatt_str(u)
| empty_carrier(u)
| element(bottom_of_semilattstr(u),the_carrier(u)) ),
file('SEU352+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ latt_str(u)
| empty_carrier(u)
| element(join_of_latt_set(u,v),the_carrier(u)) ),
file('SEU352+1.p',unknown),
[] ).
cnf(66,axiom,
( ~ empty(u)
| ~ in(v,w)
| ~ element(w,powerset(u)) ),
file('SEU352+1.p',unknown),
[] ).
cnf(72,axiom,
( ~ lattice(skc8)
| ~ lower_bounded_semilattstr(skc8)
| ~ latt_str(skc8)
| ~ equal(join_of_latt_set(skc8,empty_set),bottom_of_semilattstr(skc8))
| empty_carrier(skc8) ),
file('SEU352+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ latt_str(u)
| ~ element(v,the_carrier(u))
| empty_carrier(u)
| in(skf14(v,w,u),w)
| latt_element_smaller(u,v,w) ),
file('SEU352+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ meet_semilatt_str(u)
| ~ lower_bounded_semilattstr(u)
| ~ element(v,the_carrier(u))
| empty_carrier(u)
| equal(meet(u,v,skf11(u)),skf11(u)) ),
file('SEU352+1.p',unknown),
[] ).
cnf(79,axiom,
( ~ meet_semilatt_str(u)
| ~ lower_bounded_semilattstr(u)
| ~ element(v,the_carrier(u))
| empty_carrier(u)
| equal(meet(u,skf11(u),v),skf11(u)) ),
file('SEU352+1.p',unknown),
[] ).
cnf(83,axiom,
( ~ meet_semilatt_str(u)
| ~ meet_commutative(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| empty_carrier(u)
| element(meet_commut(u,w,v),the_carrier(u)) ),
file('SEU352+1.p',unknown),
[] ).
cnf(86,axiom,
( ~ meet_semilatt_str(u)
| ~ meet_commutative(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| empty_carrier(u)
| equal(meet(u,w,v),meet_commut(u,w,v)) ),
file('SEU352+1.p',unknown),
[] ).
cnf(87,axiom,
( ~ meet_semilatt_str(u)
| ~ meet_commutative(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| empty_carrier(u)
| equal(meet_commut(u,w,v),meet_commut(u,v,w)) ),
file('SEU352+1.p',unknown),
[] ).
cnf(88,axiom,
( ~ latt_str(u)
| ~ meet_absorbing(u)
| ~ meet_commutative(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| empty_carrier(u)
| below(u,meet_commut(u,w,v),w) ),
file('SEU352+1.p',unknown),
[] ).
cnf(92,axiom,
( ~ meet_semilatt_str(u)
| ~ element(v,the_carrier(u))
| ~ equal(meet(u,v,skf12(v,u)),v)
| ~ equal(meet(u,skf12(v,u),v),v)
| empty_carrier(u)
| lower_bounded_semilattstr(u) ),
file('SEU352+1.p',unknown),
[] ).
cnf(93,axiom,
( ~ join_semilatt_str(u)
| ~ join_commutative(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| ~ below(u,v,w)
| ~ below(u,w,v)
| empty_carrier(u)
| equal(w,v) ),
file('SEU352+1.p',unknown),
[] ).
cnf(98,axiom,
( ~ complete_latt_str(u)
| ~ lattice(u)
| ~ latt_str(u)
| ~ element(v,the_carrier(u))
| ~ latt_element_smaller(u,v,w)
| ~ below(u,v,skf15(v,w,u))
| empty_carrier(u)
| equal(v,join_of_latt_set(u,w)) ),
file('SEU352+1.p',unknown),
[] ).
cnf(99,axiom,
( ~ lower_bounded_semilattstr(u)
| ~ meet_semilatt_str(u)
| ~ element(v,the_carrier(u))
| ~ equal(meet(u,v,skf13(v,u)),v)
| ~ equal(meet(u,skf13(v,u),v),v)
| empty_carrier(u)
| equal(v,bottom_of_semilattstr(u)) ),
file('SEU352+1.p',unknown),
[] ).
cnf(100,axiom,
( ~ complete_latt_str(u)
| ~ lattice(u)
| ~ latt_str(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| ~ equal(v,join_of_latt_set(u,x))
| ~ latt_element_smaller(u,w,x)
| empty_carrier(u)
| below(u,v,w) ),
file('SEU352+1.p',unknown),
[] ).
cnf(104,plain,
( ~ lower_bounded_semilattstr(skc8)
| ~ equal(join_of_latt_set(skc8,empty_set),bottom_of_semilattstr(skc8)) ),
inference(mrr,[status(thm)],[72,1,3,11]),
[iquote('0:MRR:72.0,72.2,72.4,1.0,3.0,11.0')] ).
cnf(112,plain,
( ~ meet_commutative(skc8)
| ~ meet_absorbing(skc8)
| ~ element(u,the_carrier(skc8))
| ~ element(v,the_carrier(skc8))
| empty_carrier(skc8)
| below(skc8,meet_commut(skc8,u,v),u) ),
inference(res,[status(thm),theory(equality)],[3,88]),
[iquote('0:Res:3.0,88.2')] ).
cnf(117,plain,
( ~ element(u,the_carrier(skc8))
| in(skf14(u,v,skc8),v)
| latt_element_smaller(skc8,u,v)
| empty_carrier(skc8) ),
inference(res,[status(thm),theory(equality)],[3,77]),
[iquote('0:Res:3.0,77.0')] ).
cnf(118,plain,
( element(join_of_latt_set(skc8,u),the_carrier(skc8))
| empty_carrier(skc8) ),
inference(res,[status(thm),theory(equality)],[3,59]),
[iquote('0:Res:3.0,59.0')] ).
cnf(119,plain,
( ~ lattice(skc8)
| join_commutative(skc8)
| empty_carrier(skc8) ),
inference(res,[status(thm),theory(equality)],[3,51]),
[iquote('0:Res:3.0,51.0')] ).
cnf(120,plain,
( ~ lattice(skc8)
| join_associative(skc8)
| empty_carrier(skc8) ),
inference(res,[status(thm),theory(equality)],[3,52]),
[iquote('0:Res:3.0,52.0')] ).
cnf(121,plain,
( ~ lattice(skc8)
| meet_commutative(skc8)
| empty_carrier(skc8) ),
inference(res,[status(thm),theory(equality)],[3,53]),
[iquote('0:Res:3.0,53.0')] ).
cnf(122,plain,
( ~ lattice(skc8)
| meet_associative(skc8)
| empty_carrier(skc8) ),
inference(res,[status(thm),theory(equality)],[3,54]),
[iquote('0:Res:3.0,54.0')] ).
cnf(123,plain,
( ~ lattice(skc8)
| meet_absorbing(skc8)
| empty_carrier(skc8) ),
inference(res,[status(thm),theory(equality)],[3,55]),
[iquote('0:Res:3.0,55.0')] ).
cnf(124,plain,
( ~ lattice(skc8)
| join_absorbing(skc8)
| empty_carrier(skc8) ),
inference(res,[status(thm),theory(equality)],[3,56]),
[iquote('0:Res:3.0,56.0')] ).
cnf(125,plain,
meet_semilatt_str(skc8),
inference(res,[status(thm),theory(equality)],[3,22]),
[iquote('0:Res:3.0,22.0')] ).
cnf(126,plain,
join_semilatt_str(skc8),
inference(res,[status(thm),theory(equality)],[3,23]),
[iquote('0:Res:3.0,23.0')] ).
cnf(131,plain,
( ~ latt_str(skc8)
| ~ complete_latt_str(skc8)
| ~ element(u,the_carrier(skc8))
| ~ latt_element_smaller(skc8,u,v)
| ~ equal(w,join_of_latt_set(skc8,v))
| ~ element(w,the_carrier(skc8))
| below(skc8,w,u)
| empty_carrier(skc8) ),
inference(res,[status(thm),theory(equality)],[1,100]),
[iquote('0:Res:1.0,100.1')] ).
cnf(132,plain,
( ~ latt_str(skc8)
| ~ complete_latt_str(skc8)
| ~ latt_element_smaller(skc8,u,v)
| ~ below(skc8,u,skf15(u,v,skc8))
| ~ element(u,the_carrier(skc8))
| equal(u,join_of_latt_set(skc8,v))
| empty_carrier(skc8) ),
inference(res,[status(thm),theory(equality)],[1,98]),
[iquote('0:Res:1.0,98.1')] ).
cnf(154,plain,
( ~ meet_commutative(skc8)
| ~ meet_semilatt_str(skc8)
| ~ element(u,the_carrier(skc8))
| ~ element(v,the_carrier(skc8))
| equal(meet_commut(skc8,u,v),meet_commut(skc8,v,u)) ),
inference(res,[status(thm),theory(equality)],[87,11]),
[iquote('0:Res:87.5,11.0')] ).
cnf(155,plain,
( ~ meet_commutative(skc8)
| ~ meet_semilatt_str(skc8)
| ~ element(u,the_carrier(skc8))
| ~ element(v,the_carrier(skc8))
| equal(meet(skc8,u,v),meet_commut(skc8,u,v)) ),
inference(res,[status(thm),theory(equality)],[86,11]),
[iquote('0:Res:86.5,11.0')] ).
cnf(158,plain,
( ~ meet_commutative(skc8)
| ~ meet_semilatt_str(skc8)
| ~ element(u,the_carrier(skc8))
| ~ element(v,the_carrier(skc8))
| element(meet_commut(skc8,u,v),the_carrier(skc8)) ),
inference(res,[status(thm),theory(equality)],[83,11]),
[iquote('0:Res:83.5,11.0')] ).
cnf(178,plain,
( ~ meet_semilatt_str(skc8)
| element(bottom_of_semilattstr(skc8),the_carrier(skc8)) ),
inference(res,[status(thm),theory(equality)],[58,11]),
[iquote('0:Res:58.1,11.0')] ).
cnf(181,plain,
join_commutative(skc8),
inference(mrr,[status(thm)],[119,1,11]),
[iquote('0:MRR:119.0,119.2,1.0,11.0')] ).
cnf(182,plain,
join_associative(skc8),
inference(mrr,[status(thm)],[120,1,11]),
[iquote('0:MRR:120.0,120.2,1.0,11.0')] ).
cnf(183,plain,
meet_commutative(skc8),
inference(mrr,[status(thm)],[121,1,11]),
[iquote('0:MRR:121.0,121.2,1.0,11.0')] ).
cnf(184,plain,
meet_associative(skc8),
inference(mrr,[status(thm)],[122,1,11]),
[iquote('0:MRR:122.0,122.2,1.0,11.0')] ).
cnf(185,plain,
meet_absorbing(skc8),
inference(mrr,[status(thm)],[123,1,11]),
[iquote('0:MRR:123.0,123.2,1.0,11.0')] ).
cnf(186,plain,
join_absorbing(skc8),
inference(mrr,[status(thm)],[124,1,11]),
[iquote('0:MRR:124.0,124.2,1.0,11.0')] ).
cnf(187,plain,
element(join_of_latt_set(skc8,u),the_carrier(skc8)),
inference(mrr,[status(thm)],[118,11]),
[iquote('0:MRR:118.1,11.0')] ).
cnf(188,plain,
element(bottom_of_semilattstr(skc8),the_carrier(skc8)),
inference(mrr,[status(thm)],[178,125]),
[iquote('0:MRR:178.0,125.0')] ).
cnf(193,plain,
( ~ element(u,the_carrier(skc8))
| in(skf14(u,v,skc8),v)
| latt_element_smaller(skc8,u,v) ),
inference(mrr,[status(thm)],[117,11]),
[iquote('0:MRR:117.3,11.0')] ).
cnf(199,plain,
( ~ element(u,the_carrier(skc8))
| ~ element(v,the_carrier(skc8))
| element(meet_commut(skc8,v,u),the_carrier(skc8)) ),
inference(mrr,[status(thm)],[158,183,125]),
[iquote('0:MRR:158.0,158.1,183.0,125.0')] ).
cnf(201,plain,
( ~ element(u,the_carrier(skc8))
| ~ element(v,the_carrier(skc8))
| equal(meet(skc8,v,u),meet_commut(skc8,v,u)) ),
inference(mrr,[status(thm)],[155,183,125]),
[iquote('0:MRR:155.0,155.1,183.0,125.0')] ).
cnf(203,plain,
( ~ element(u,the_carrier(skc8))
| ~ element(v,the_carrier(skc8))
| equal(meet_commut(skc8,v,u),meet_commut(skc8,u,v)) ),
inference(mrr,[status(thm)],[154,183,125]),
[iquote('0:MRR:154.0,154.1,183.0,125.0')] ).
cnf(204,plain,
( ~ element(u,the_carrier(skc8))
| ~ element(v,the_carrier(skc8))
| below(skc8,meet_commut(skc8,v,u),v) ),
inference(mrr,[status(thm)],[112,183,185,11]),
[iquote('0:MRR:112.0,112.1,112.4,183.0,185.0,11.0')] ).
cnf(217,plain,
( ~ element(u,the_carrier(skc8))
| ~ latt_element_smaller(skc8,u,v)
| ~ below(skc8,u,skf15(u,v,skc8))
| equal(u,join_of_latt_set(skc8,v)) ),
inference(mrr,[status(thm)],[132,3,2,11]),
[iquote('0:MRR:132.0,132.1,132.6,3.0,2.0,11.0')] ).
cnf(219,plain,
( ~ element(u,the_carrier(skc8))
| ~ element(v,the_carrier(skc8))
| ~ equal(u,join_of_latt_set(skc8,w))
| ~ latt_element_smaller(skc8,v,w)
| below(skc8,u,v) ),
inference(mrr,[status(thm)],[131,3,2,11]),
[iquote('0:MRR:131.0,131.1,131.7,3.0,2.0,11.0')] ).
cnf(220,plain,
~ lower_bounded_semilattstr(skc8),
inference(spt,[spt(split,[position(s1)])],[104]),
[iquote('1:Spt:104.0')] ).
cnf(222,plain,
equal(skf20(u),empty_set),
inference(ems,[status(thm)],[34,12]),
[iquote('0:EmS:34.0,12.0')] ).
cnf(227,plain,
element(empty_set,powerset(u)),
inference(rew,[status(thm),theory(equality)],[222,26]),
[iquote('0:Rew:222.0,26.0')] ).
cnf(354,plain,
( ~ empty(u)
| ~ in(v,empty_set) ),
inference(res,[status(thm),theory(equality)],[227,66]),
[iquote('0:Res:227.0,66.2')] ).
cnf(359,plain,
~ in(u,empty_set),
inference(ems,[status(thm)],[354,8]),
[iquote('0:EmS:354.0,8.0')] ).
cnf(677,plain,
( ~ meet_semilatt_str(u)
| ~ meet_commutative(u)
| ~ meet_semilatt_str(u)
| ~ lower_bounded_semilattstr(u)
| ~ element(v,the_carrier(u))
| ~ element(skf11(u),the_carrier(u))
| ~ element(v,the_carrier(u))
| empty_carrier(u)
| empty_carrier(u)
| equal(meet_commut(u,skf11(u),v),skf11(u)) ),
inference(spr,[status(thm),theory(equality)],[86,79]),
[iquote('0:SpR:86.5,79.4')] ).
cnf(684,plain,
( ~ meet_commutative(u)
| ~ meet_semilatt_str(u)
| ~ lower_bounded_semilattstr(u)
| ~ element(skf11(u),the_carrier(u))
| ~ element(v,the_carrier(u))
| empty_carrier(u)
| equal(meet_commut(u,skf11(u),v),skf11(u)) ),
inference(obv,[status(thm),theory(equality)],[677]),
[iquote('0:Obv:677.7')] ).
cnf(685,plain,
( ~ meet_commutative(u)
| ~ meet_semilatt_str(u)
| ~ lower_bounded_semilattstr(u)
| ~ element(v,the_carrier(u))
| empty_carrier(u)
| equal(meet_commut(u,skf11(u),v),skf11(u)) ),
inference(mrr,[status(thm)],[684,19]),
[iquote('0:MRR:684.3,19.0')] ).
cnf(829,plain,
( ~ meet_semilatt_str(u)
| ~ meet_commutative(u)
| ~ meet_semilatt_str(u)
| ~ element(v,the_carrier(u))
| ~ element(skf12(v,u),the_carrier(u))
| ~ element(v,the_carrier(u))
| ~ equal(meet(u,v,skf12(v,u)),v)
| ~ equal(meet_commut(u,skf12(v,u),v),v)
| empty_carrier(u)
| empty_carrier(u)
| lower_bounded_semilattstr(u) ),
inference(spl,[status(thm),theory(equality)],[86,92]),
[iquote('0:SpL:86.5,92.3')] ).
cnf(832,plain,
( ~ meet_commutative(u)
| ~ meet_semilatt_str(u)
| ~ element(skf12(v,u),the_carrier(u))
| ~ element(v,the_carrier(u))
| ~ equal(meet(u,v,skf12(v,u)),v)
| ~ equal(meet_commut(u,skf12(v,u),v),v)
| empty_carrier(u)
| lower_bounded_semilattstr(u) ),
inference(obv,[status(thm),theory(equality)],[829]),
[iquote('0:Obv:829.8')] ).
cnf(833,plain,
( ~ meet_commutative(u)
| ~ meet_semilatt_str(u)
| ~ element(skf12(v,u),the_carrier(u))
| ~ element(v,the_carrier(u))
| ~ equal(meet_commut(u,v,skf12(v,u)),v)
| ~ equal(meet_commut(u,v,skf12(v,u)),v)
| empty_carrier(u)
| lower_bounded_semilattstr(u) ),
inference(rew,[status(thm),theory(equality)],[87,832,86]),
[iquote('0:Rew:87.5,832.5,86.5,832.4')] ).
cnf(834,plain,
( ~ meet_commutative(u)
| ~ meet_semilatt_str(u)
| ~ element(skf12(v,u),the_carrier(u))
| ~ element(v,the_carrier(u))
| ~ equal(meet_commut(u,v,skf12(v,u)),v)
| empty_carrier(u)
| lower_bounded_semilattstr(u) ),
inference(obv,[status(thm),theory(equality)],[833]),
[iquote('0:Obv:833.4')] ).
cnf(835,plain,
( ~ meet_commutative(u)
| ~ meet_semilatt_str(u)
| ~ element(v,the_carrier(u))
| ~ equal(meet_commut(u,v,skf12(v,u)),v)
| empty_carrier(u)
| lower_bounded_semilattstr(u) ),
inference(mrr,[status(thm)],[834,27]),
[iquote('0:MRR:834.2,27.0')] ).
cnf(915,plain,
( ~ meet_semilatt_str(u)
| ~ meet_commutative(u)
| ~ join_semilatt_str(u)
| ~ join_commutative(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| ~ element(x,the_carrier(u))
| ~ below(u,meet_commut(u,w,v),x)
| ~ below(u,x,meet_commut(u,w,v))
| empty_carrier(u)
| empty_carrier(u)
| equal(x,meet_commut(u,w,v)) ),
inference(res,[status(thm),theory(equality)],[83,93]),
[iquote('0:Res:83.5,93.2')] ).
cnf(930,plain,
( ~ meet_semilatt_str(u)
| ~ meet_commutative(u)
| ~ join_semilatt_str(u)
| ~ join_commutative(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| ~ element(x,the_carrier(u))
| ~ below(u,meet_commut(u,w,v),x)
| ~ below(u,x,meet_commut(u,w,v))
| empty_carrier(u)
| equal(x,meet_commut(u,w,v)) ),
inference(obv,[status(thm),theory(equality)],[915]),
[iquote('0:Obv:915.9')] ).
cnf(1023,plain,
( ~ meet_semilatt_str(u)
| ~ meet_commutative(u)
| ~ lower_bounded_semilattstr(u)
| ~ meet_semilatt_str(u)
| ~ element(v,the_carrier(u))
| ~ element(skf13(v,u),the_carrier(u))
| ~ element(v,the_carrier(u))
| ~ equal(meet(u,v,skf13(v,u)),v)
| ~ equal(meet_commut(u,skf13(v,u),v),v)
| empty_carrier(u)
| empty_carrier(u)
| equal(v,bottom_of_semilattstr(u)) ),
inference(spl,[status(thm),theory(equality)],[86,99]),
[iquote('0:SpL:86.5,99.4')] ).
cnf(1024,plain,
( ~ meet_semilatt_str(u)
| ~ lower_bounded_semilattstr(u)
| ~ lower_bounded_semilattstr(u)
| ~ meet_semilatt_str(u)
| ~ element(skf13(skf11(u),u),the_carrier(u))
| ~ element(skf11(u),the_carrier(u))
| ~ equal(meet(u,skf11(u),skf13(skf11(u),u)),skf11(u))
| ~ equal(skf11(u),skf11(u))
| empty_carrier(u)
| empty_carrier(u)
| equal(skf11(u),bottom_of_semilattstr(u)) ),
inference(spl,[status(thm),theory(equality)],[78,99]),
[iquote('0:SpL:78.4,99.4')] ).
cnf(1026,plain,
( ~ lower_bounded_semilattstr(u)
| ~ meet_semilatt_str(u)
| ~ element(skf13(skf11(u),u),the_carrier(u))
| ~ element(skf11(u),the_carrier(u))
| ~ equal(meet(u,skf11(u),skf13(skf11(u),u)),skf11(u))
| empty_carrier(u)
| equal(skf11(u),bottom_of_semilattstr(u)) ),
inference(obv,[status(thm),theory(equality)],[1024]),
[iquote('0:Obv:1024.8')] ).
cnf(1027,plain,
( ~ lower_bounded_semilattstr(u)
| ~ meet_semilatt_str(u)
| ~ element(skf13(skf11(u),u),the_carrier(u))
| ~ element(skf11(u),the_carrier(u))
| ~ equal(skf11(u),skf11(u))
| empty_carrier(u)
| equal(skf11(u),bottom_of_semilattstr(u)) ),
inference(rew,[status(thm),theory(equality)],[79,1026]),
[iquote('0:Rew:79.4,1026.4')] ).
cnf(1028,plain,
( ~ lower_bounded_semilattstr(u)
| ~ meet_semilatt_str(u)
| ~ element(skf13(skf11(u),u),the_carrier(u))
| ~ element(skf11(u),the_carrier(u))
| empty_carrier(u)
| equal(skf11(u),bottom_of_semilattstr(u)) ),
inference(obv,[status(thm),theory(equality)],[1027]),
[iquote('0:Obv:1027.4')] ).
cnf(1029,plain,
( ~ lower_bounded_semilattstr(u)
| ~ meet_semilatt_str(u)
| empty_carrier(u)
| equal(skf11(u),bottom_of_semilattstr(u)) ),
inference(mrr,[status(thm)],[1028,28,19]),
[iquote('0:MRR:1028.2,1028.3,28.0,19.0')] ).
cnf(1033,plain,
( ~ meet_commutative(u)
| ~ meet_semilatt_str(u)
| ~ lower_bounded_semilattstr(u)
| ~ element(v,the_carrier(u))
| empty_carrier(u)
| equal(meet_commut(u,bottom_of_semilattstr(u),v),bottom_of_semilattstr(u)) ),
inference(rew,[status(thm),theory(equality)],[1029,685]),
[iquote('0:Rew:1029.3,685.5')] ).
cnf(1035,plain,
( ~ meet_commutative(u)
| ~ lower_bounded_semilattstr(u)
| ~ meet_semilatt_str(u)
| ~ element(skf13(v,u),the_carrier(u))
| ~ element(v,the_carrier(u))
| ~ equal(meet(u,v,skf13(v,u)),v)
| ~ equal(meet_commut(u,skf13(v,u),v),v)
| empty_carrier(u)
| equal(v,bottom_of_semilattstr(u)) ),
inference(obv,[status(thm),theory(equality)],[1023]),
[iquote('0:Obv:1023.9')] ).
cnf(1036,plain,
( ~ meet_commutative(u)
| ~ lower_bounded_semilattstr(u)
| ~ meet_semilatt_str(u)
| ~ element(skf13(v,u),the_carrier(u))
| ~ element(v,the_carrier(u))
| ~ equal(meet_commut(u,v,skf13(v,u)),v)
| ~ equal(meet_commut(u,v,skf13(v,u)),v)
| empty_carrier(u)
| equal(v,bottom_of_semilattstr(u)) ),
inference(rew,[status(thm),theory(equality)],[87,1035,86]),
[iquote('0:Rew:87.5,1035.6,86.5,1035.5')] ).
cnf(1037,plain,
( ~ meet_commutative(u)
| ~ lower_bounded_semilattstr(u)
| ~ meet_semilatt_str(u)
| ~ element(skf13(v,u),the_carrier(u))
| ~ element(v,the_carrier(u))
| ~ equal(meet_commut(u,v,skf13(v,u)),v)
| empty_carrier(u)
| equal(v,bottom_of_semilattstr(u)) ),
inference(obv,[status(thm),theory(equality)],[1036]),
[iquote('0:Obv:1036.5')] ).
cnf(1038,plain,
( ~ meet_commutative(u)
| ~ lower_bounded_semilattstr(u)
| ~ meet_semilatt_str(u)
| ~ element(v,the_carrier(u))
| ~ equal(meet_commut(u,v,skf13(v,u)),v)
| empty_carrier(u)
| equal(v,bottom_of_semilattstr(u)) ),
inference(mrr,[status(thm)],[1037,28]),
[iquote('0:MRR:1037.3,28.0')] ).
cnf(1153,plain,
( ~ complete_latt_str(u)
| ~ lattice(u)
| ~ latt_str(u)
| ~ element(join_of_latt_set(u,v),the_carrier(u))
| ~ element(w,the_carrier(u))
| ~ latt_element_smaller(u,w,v)
| empty_carrier(u)
| below(u,join_of_latt_set(u,v),w) ),
inference(eqr,[status(thm),theory(equality)],[100]),
[iquote('0:EqR:100.5')] ).
cnf(1154,plain,
( ~ complete_latt_str(u)
| ~ lattice(u)
| ~ latt_str(u)
| ~ element(v,the_carrier(u))
| ~ latt_element_smaller(u,v,w)
| empty_carrier(u)
| below(u,join_of_latt_set(u,w),v) ),
inference(mrr,[status(thm)],[1153,59]),
[iquote('0:MRR:1153.3,59.2')] ).
cnf(1323,plain,
( ~ empty(u)
| ~ element(v,the_carrier(skc8))
| latt_element_smaller(skc8,v,u) ),
inference(res,[status(thm),theory(equality)],[193,39]),
[iquote('0:Res:193.1,39.1')] ).
cnf(1332,plain,
( ~ element(u,the_carrier(skc8))
| latt_element_smaller(skc8,u,empty_set) ),
inference(res,[status(thm),theory(equality)],[193,359]),
[iquote('0:Res:193.1,359.0')] ).
cnf(1508,plain,
( ~ meet_semilatt_str(skc8)
| ~ element(u,the_carrier(skc8))
| ~ element(skf12(u,skc8),the_carrier(skc8))
| ~ element(u,the_carrier(skc8))
| ~ equal(meet(skc8,u,skf12(u,skc8)),u)
| ~ equal(meet_commut(skc8,skf12(u,skc8),u),u)
| empty_carrier(skc8)
| lower_bounded_semilattstr(skc8) ),
inference(spl,[status(thm),theory(equality)],[201,92]),
[iquote('0:SpL:201.2,92.3')] ).
cnf(1519,plain,
( ~ meet_semilatt_str(skc8)
| ~ element(skf12(u,skc8),the_carrier(skc8))
| ~ element(u,the_carrier(skc8))
| ~ equal(meet(skc8,u,skf12(u,skc8)),u)
| ~ equal(meet_commut(skc8,skf12(u,skc8),u),u)
| empty_carrier(skc8)
| lower_bounded_semilattstr(skc8) ),
inference(obv,[status(thm),theory(equality)],[1508]),
[iquote('0:Obv:1508.1')] ).
cnf(1520,plain,
( ~ meet_semilatt_str(skc8)
| ~ element(skf12(u,skc8),the_carrier(skc8))
| ~ element(u,the_carrier(skc8))
| ~ equal(meet_commut(skc8,u,skf12(u,skc8)),u)
| ~ equal(meet_commut(skc8,skf12(u,skc8),u),u)
| empty_carrier(skc8)
| lower_bounded_semilattstr(skc8) ),
inference(rew,[status(thm),theory(equality)],[201,1519]),
[iquote('0:Rew:201.2,1519.3')] ).
cnf(1521,plain,
( ~ meet_semilatt_str(skc8)
| ~ element(skf12(u,skc8),the_carrier(skc8))
| ~ element(u,the_carrier(skc8))
| ~ equal(meet_commut(skc8,u,skf12(u,skc8)),u)
| ~ equal(meet_commut(skc8,u,skf12(u,skc8)),u)
| empty_carrier(skc8)
| lower_bounded_semilattstr(skc8) ),
inference(rew,[status(thm),theory(equality)],[203,1520]),
[iquote('0:Rew:203.2,1520.4')] ).
cnf(1522,plain,
( ~ meet_semilatt_str(skc8)
| ~ element(skf12(u,skc8),the_carrier(skc8))
| ~ element(u,the_carrier(skc8))
| ~ equal(meet_commut(skc8,u,skf12(u,skc8)),u)
| empty_carrier(skc8)
| lower_bounded_semilattstr(skc8) ),
inference(obv,[status(thm),theory(equality)],[1521]),
[iquote('0:Obv:1521.3')] ).
cnf(1523,plain,
( ~ element(skf12(u,skc8),the_carrier(skc8))
| ~ element(u,the_carrier(skc8))
| ~ equal(meet_commut(skc8,u,skf12(u,skc8)),u)
| empty_carrier(skc8)
| lower_bounded_semilattstr(skc8) ),
inference(ssi,[status(thm)],[1522,2,1,3,182,181,126,186,184,185,183,125]),
[iquote('0:SSi:1522.0,2.0,1.0,3.0,182.0,181.0,126.0,186.0,184.0,185.0,183.0,125.0')] ).
cnf(1524,plain,
( ~ element(u,the_carrier(skc8))
| ~ equal(meet_commut(skc8,u,skf12(u,skc8)),u) ),
inference(mrr,[status(thm)],[1523,27,11,220]),
[iquote('1:MRR:1523.0,1523.3,1523.4,27.0,11.0,220.0')] ).
cnf(1927,plain,
( ~ meet_commutative(skc8)
| ~ meet_semilatt_str(skc8)
| ~ lower_bounded_semilattstr(skc8)
| ~ element(skf12(bottom_of_semilattstr(skc8),skc8),the_carrier(skc8))
| ~ element(bottom_of_semilattstr(skc8),the_carrier(skc8))
| ~ equal(bottom_of_semilattstr(skc8),bottom_of_semilattstr(skc8))
| empty_carrier(skc8) ),
inference(spl,[status(thm),theory(equality)],[1033,1524]),
[iquote('1:SpL:1033.5,1524.1')] ).
cnf(1928,plain,
( ~ meet_commutative(skc8)
| ~ meet_semilatt_str(skc8)
| ~ lower_bounded_semilattstr(skc8)
| ~ element(skf12(bottom_of_semilattstr(skc8),skc8),the_carrier(skc8))
| ~ element(bottom_of_semilattstr(skc8),the_carrier(skc8))
| empty_carrier(skc8) ),
inference(obv,[status(thm),theory(equality)],[1927]),
[iquote('1:Obv:1927.5')] ).
cnf(1929,plain,
( ~ lower_bounded_semilattstr(skc8)
| ~ element(skf12(bottom_of_semilattstr(skc8),skc8),the_carrier(skc8))
| ~ element(bottom_of_semilattstr(skc8),the_carrier(skc8))
| empty_carrier(skc8) ),
inference(ssi,[status(thm)],[1928,2,1,3,182,181,126,186,184,185,183,125]),
[iquote('1:SSi:1928.1,1928.0,2.0,1.0,3.0,182.0,181.0,126.0,186.0,184.0,185.0,183.0,125.0,2.0,1.0,3.0,182.0,181.0,126.0,186.0,184.0,185.0,183.0,125.0')] ).
cnf(1930,plain,
~ lower_bounded_semilattstr(skc8),
inference(mrr,[status(thm)],[1929,27,188,11]),
[iquote('1:MRR:1929.1,1929.2,1929.3,27.0,188.0,11.0')] ).
cnf(2020,plain,
( ~ element(join_of_latt_set(skc8,u),the_carrier(skc8))
| ~ element(v,the_carrier(skc8))
| ~ latt_element_smaller(skc8,v,u)
| below(skc8,join_of_latt_set(skc8,u),v) ),
inference(eqr,[status(thm),theory(equality)],[219]),
[iquote('0:EqR:219.2')] ).
cnf(2021,plain,
( ~ element(u,the_carrier(skc8))
| ~ latt_element_smaller(skc8,u,v)
| below(skc8,join_of_latt_set(skc8,v),u) ),
inference(mrr,[status(thm)],[2020,187]),
[iquote('0:MRR:2020.0,187.0')] ).
cnf(2283,plain,
( ~ complete_latt_str(skc8)
| ~ lattice(skc8)
| ~ latt_str(skc8)
| ~ element(skf15(join_of_latt_set(skc8,u),v,skc8),the_carrier(skc8))
| ~ latt_element_smaller(skc8,skf15(join_of_latt_set(skc8,u),v,skc8),u)
| ~ element(join_of_latt_set(skc8,u),the_carrier(skc8))
| ~ latt_element_smaller(skc8,join_of_latt_set(skc8,u),v)
| empty_carrier(skc8)
| equal(join_of_latt_set(skc8,u),join_of_latt_set(skc8,v)) ),
inference(res,[status(thm),theory(equality)],[1154,217]),
[iquote('0:Res:1154.6,217.2')] ).
cnf(2284,plain,
( ~ element(skf15(join_of_latt_set(skc8,u),v,skc8),the_carrier(skc8))
| ~ latt_element_smaller(skc8,skf15(join_of_latt_set(skc8,u),v,skc8),u)
| ~ element(join_of_latt_set(skc8,u),the_carrier(skc8))
| ~ latt_element_smaller(skc8,join_of_latt_set(skc8,u),v)
| empty_carrier(skc8)
| equal(join_of_latt_set(skc8,u),join_of_latt_set(skc8,v)) ),
inference(ssi,[status(thm)],[2283,2,1,3,182,181,126,186,184,185,183,125]),
[iquote('0:SSi:2283.2,2283.1,2283.0,2.0,1.0,3.0,182.0,181.0,126.0,186.0,184.0,185.0,183.0,125.0,2.0,1.0,3.0,182.0,181.0,126.0,186.0,184.0,185.0,183.0,125.0,2.0,1.0,3.0,182.0,181.0,126.0,186.0,184.0,185.0,183.0,125.0')] ).
cnf(2285,plain,
( ~ latt_element_smaller(skc8,skf15(join_of_latt_set(skc8,u),v,skc8),u)
| ~ latt_element_smaller(skc8,join_of_latt_set(skc8,u),v)
| equal(join_of_latt_set(skc8,u),join_of_latt_set(skc8,v)) ),
inference(mrr,[status(thm)],[2284,37,187,11]),
[iquote('0:MRR:2284.0,2284.2,2284.4,37.0,187.0,11.0')] ).
cnf(3262,plain,
( ~ meet_semilatt_str(skc8)
| ~ meet_commutative(skc8)
| ~ join_semilatt_str(skc8)
| ~ join_commutative(skc8)
| ~ element(u,the_carrier(skc8))
| ~ element(v,the_carrier(skc8))
| ~ element(u,the_carrier(skc8))
| ~ element(v,the_carrier(skc8))
| ~ element(v,the_carrier(skc8))
| ~ below(skc8,v,meet_commut(skc8,v,u))
| empty_carrier(skc8)
| equal(meet_commut(skc8,v,u),v) ),
inference(res,[status(thm),theory(equality)],[204,930]),
[iquote('0:Res:204.2,930.7')] ).
cnf(3263,plain,
( ~ meet_semilatt_str(skc8)
| ~ meet_commutative(skc8)
| ~ join_semilatt_str(skc8)
| ~ join_commutative(skc8)
| ~ element(u,the_carrier(skc8))
| ~ element(v,the_carrier(skc8))
| ~ below(skc8,v,meet_commut(skc8,v,u))
| empty_carrier(skc8)
| equal(meet_commut(skc8,v,u),v) ),
inference(obv,[status(thm),theory(equality)],[3262]),
[iquote('0:Obv:3262.7')] ).
cnf(3264,plain,
( ~ element(u,the_carrier(skc8))
| ~ element(v,the_carrier(skc8))
| ~ below(skc8,v,meet_commut(skc8,v,u))
| empty_carrier(skc8)
| equal(meet_commut(skc8,v,u),v) ),
inference(ssi,[status(thm)],[3263,2,1,3,182,181,126,186,184,185,183,125]),
[iquote('0:SSi:3263.3,3263.2,3263.1,3263.0,2.0,1.0,3.0,182.0,181.0,126.0,186.0,184.0,185.0,183.0,125.0,2.0,1.0,3.0,182.0,181.0,126.0,186.0,184.0,185.0,183.0,125.0,2.0,1.0,3.0,182.0,181.0,126.0,186.0,184.0,185.0,183.0,125.0,2.0,1.0,3.0,182.0,181.0,126.0,186.0,184.0,185.0,183.0,125.0')] ).
cnf(3265,plain,
( ~ element(u,the_carrier(skc8))
| ~ element(v,the_carrier(skc8))
| ~ below(skc8,v,meet_commut(skc8,v,u))
| equal(meet_commut(skc8,v,u),v) ),
inference(mrr,[status(thm)],[3264,11]),
[iquote('0:MRR:3264.3,11.0')] ).
cnf(4771,plain,
( ~ element(skf15(join_of_latt_set(skc8,empty_set),u,skc8),the_carrier(skc8))
| ~ latt_element_smaller(skc8,join_of_latt_set(skc8,empty_set),u)
| equal(join_of_latt_set(skc8,empty_set),join_of_latt_set(skc8,u)) ),
inference(res,[status(thm),theory(equality)],[1332,2285]),
[iquote('0:Res:1332.1,2285.0')] ).
cnf(4774,plain,
( ~ latt_element_smaller(skc8,join_of_latt_set(skc8,empty_set),u)
| equal(join_of_latt_set(skc8,empty_set),join_of_latt_set(skc8,u)) ),
inference(mrr,[status(thm)],[4771,37]),
[iquote('0:MRR:4771.0,37.0')] ).
cnf(4782,plain,
( ~ empty(u)
| ~ element(join_of_latt_set(skc8,empty_set),the_carrier(skc8))
| equal(join_of_latt_set(skc8,empty_set),join_of_latt_set(skc8,u)) ),
inference(res,[status(thm),theory(equality)],[1323,4774]),
[iquote('0:Res:1323.2,4774.0')] ).
cnf(4784,plain,
( ~ empty(u)
| equal(join_of_latt_set(skc8,empty_set),join_of_latt_set(skc8,u)) ),
inference(mrr,[status(thm)],[4782,187]),
[iquote('0:MRR:4782.1,187.0')] ).
cnf(4801,plain,
( ~ empty(u)
| ~ element(v,the_carrier(skc8))
| ~ latt_element_smaller(skc8,v,u)
| below(skc8,join_of_latt_set(skc8,empty_set),v) ),
inference(spr,[status(thm),theory(equality)],[4784,2021]),
[iquote('0:SpR:4784.1,2021.2')] ).
cnf(4853,plain,
( ~ empty(u)
| ~ element(v,the_carrier(skc8))
| below(skc8,join_of_latt_set(skc8,empty_set),v) ),
inference(mrr,[status(thm)],[4801,1323]),
[iquote('0:MRR:4801.2,1323.2')] ).
cnf(5019,plain,
( ~ element(u,the_carrier(skc8))
| below(skc8,join_of_latt_set(skc8,empty_set),u) ),
inference(ems,[status(thm)],[4853,8]),
[iquote('0:EmS:4853.0,8.0')] ).
cnf(5028,plain,
( ~ element(meet_commut(skc8,join_of_latt_set(skc8,empty_set),u),the_carrier(skc8))
| ~ element(u,the_carrier(skc8))
| ~ element(join_of_latt_set(skc8,empty_set),the_carrier(skc8))
| equal(meet_commut(skc8,join_of_latt_set(skc8,empty_set),u),join_of_latt_set(skc8,empty_set)) ),
inference(res,[status(thm),theory(equality)],[5019,3265]),
[iquote('0:Res:5019.1,3265.2')] ).
cnf(5031,plain,
( ~ element(u,the_carrier(skc8))
| equal(meet_commut(skc8,join_of_latt_set(skc8,empty_set),u),join_of_latt_set(skc8,empty_set)) ),
inference(mrr,[status(thm)],[5028,199,187]),
[iquote('0:MRR:5028.0,5028.2,199.2,187.0')] ).
cnf(5079,plain,
( ~ meet_commutative(skc8)
| ~ meet_semilatt_str(skc8)
| ~ element(skf12(join_of_latt_set(skc8,empty_set),skc8),the_carrier(skc8))
| ~ element(join_of_latt_set(skc8,empty_set),the_carrier(skc8))
| ~ equal(join_of_latt_set(skc8,empty_set),join_of_latt_set(skc8,empty_set))
| empty_carrier(skc8)
| lower_bounded_semilattstr(skc8) ),
inference(spl,[status(thm),theory(equality)],[5031,835]),
[iquote('0:SpL:5031.1,835.3')] ).
cnf(5080,plain,
( ~ meet_commutative(skc8)
| ~ lower_bounded_semilattstr(skc8)
| ~ meet_semilatt_str(skc8)
| ~ element(skf13(join_of_latt_set(skc8,empty_set),skc8),the_carrier(skc8))
| ~ element(join_of_latt_set(skc8,empty_set),the_carrier(skc8))
| ~ equal(join_of_latt_set(skc8,empty_set),join_of_latt_set(skc8,empty_set))
| empty_carrier(skc8)
| equal(join_of_latt_set(skc8,empty_set),bottom_of_semilattstr(skc8)) ),
inference(spl,[status(thm),theory(equality)],[5031,1038]),
[iquote('0:SpL:5031.1,1038.4')] ).
cnf(5093,plain,
( ~ meet_commutative(skc8)
| ~ meet_semilatt_str(skc8)
| ~ element(skf12(join_of_latt_set(skc8,empty_set),skc8),the_carrier(skc8))
| ~ element(join_of_latt_set(skc8,empty_set),the_carrier(skc8))
| empty_carrier(skc8)
| lower_bounded_semilattstr(skc8) ),
inference(obv,[status(thm),theory(equality)],[5079]),
[iquote('0:Obv:5079.4')] ).
cnf(5094,plain,
( ~ element(skf12(join_of_latt_set(skc8,empty_set),skc8),the_carrier(skc8))
| ~ element(join_of_latt_set(skc8,empty_set),the_carrier(skc8))
| empty_carrier(skc8)
| lower_bounded_semilattstr(skc8) ),
inference(ssi,[status(thm)],[5093,2,1,3,182,181,126,186,184,185,183,125]),
[iquote('0:SSi:5093.1,5093.0,2.0,1.0,3.0,182.0,181.0,126.0,186.0,184.0,185.0,183.0,125.0,2.0,1.0,3.0,182.0,181.0,126.0,186.0,184.0,185.0,183.0,125.0')] ).
cnf(5095,plain,
$false,
inference(mrr,[status(thm)],[5094,27,187,11,1930]),
[iquote('1:MRR:5094.0,5094.1,5094.2,5094.3,27.0,187.0,11.0,1930.0')] ).
cnf(5105,plain,
( ~ meet_commutative(skc8)
| ~ lower_bounded_semilattstr(skc8)
| ~ meet_semilatt_str(skc8)
| ~ element(skf13(join_of_latt_set(skc8,empty_set),skc8),the_carrier(skc8))
| ~ element(join_of_latt_set(skc8,empty_set),the_carrier(skc8))
| empty_carrier(skc8)
| equal(join_of_latt_set(skc8,empty_set),bottom_of_semilattstr(skc8)) ),
inference(obv,[status(thm),theory(equality)],[5080]),
[iquote('0:Obv:5080.5')] ).
cnf(5112,plain,
lower_bounded_semilattstr(skc8),
inference(spt,[spt(split,[position(sa)])],[5095,220]),
[iquote('1:Spt:5095.0,104.0,220.0')] ).
cnf(5113,plain,
~ equal(join_of_latt_set(skc8,empty_set),bottom_of_semilattstr(skc8)),
inference(spt,[spt(split,[position(s2)])],[104]),
[iquote('1:Spt:5095.0,104.1')] ).
cnf(5137,plain,
( ~ lower_bounded_semilattstr(skc8)
| ~ element(skf13(join_of_latt_set(skc8,empty_set),skc8),the_carrier(skc8))
| ~ element(join_of_latt_set(skc8,empty_set),the_carrier(skc8))
| empty_carrier(skc8)
| equal(join_of_latt_set(skc8,empty_set),bottom_of_semilattstr(skc8)) ),
inference(ssi,[status(thm)],[5105,2,1,3,182,181,126,186,184,185,183,125]),
[iquote('0:SSi:5105.2,5105.0,2.0,1.0,3.0,182.0,181.0,126.0,186.0,184.0,185.0,183.0,125.0,2.0,1.0,3.0,182.0,181.0,126.0,186.0,184.0,185.0,183.0,125.0')] ).
cnf(5138,plain,
( ~ lower_bounded_semilattstr(skc8)
| equal(join_of_latt_set(skc8,empty_set),bottom_of_semilattstr(skc8)) ),
inference(mrr,[status(thm)],[5137,28,187,11]),
[iquote('0:MRR:5137.1,5137.2,5137.3,28.0,187.0,11.0')] ).
cnf(5139,plain,
$false,
inference(mrr,[status(thm)],[5138,5112,5113]),
[iquote('1:MRR:5138.0,5138.1,5112.0,5113.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU352+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.11 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n021.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 : Sun Jun 19 17:07:48 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.53/1.76
% 1.53/1.76 SPASS V 3.9
% 1.53/1.76 SPASS beiseite: Proof found.
% 1.53/1.76 % SZS status Theorem
% 1.53/1.76 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.53/1.76 SPASS derived 4096 clauses, backtracked 46 clauses, performed 1 splits and kept 2166 clauses.
% 1.53/1.76 SPASS allocated 103577 KBytes.
% 1.53/1.76 SPASS spent 0:00:01.42 on the problem.
% 1.53/1.76 0:00:00.04 for the input.
% 1.53/1.76 0:00:00.04 for the FLOTTER CNF translation.
% 1.53/1.76 0:00:00.09 for inferences.
% 1.53/1.76 0:00:00.00 for the backtracking.
% 1.53/1.76 0:00:01.16 for the reduction.
% 1.53/1.76
% 1.53/1.76
% 1.53/1.76 Here is a proof with depth 9, length 140 :
% 1.53/1.76 % SZS output start Refutation
% See solution above
% 1.61/1.81 Formulae used in the proof : t50_lattice3 fc1_xboole_0 rc2_subset_1 d13_lattices existence_m1_subset_1 dt_l3_lattices d16_lattices t6_boole d21_lattice3 t7_boole cc1_lattices dt_k5_lattices dt_k15_lattice3 t5_subset d17_lattice3 dt_k4_lattices redefinition_k4_lattices commutativity_k4_lattices t23_lattices t26_lattices
% 1.61/1.81
%------------------------------------------------------------------------------