TSTP Solution File: SEU349+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU349+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : Tue Jul 19 14:36:30 EDT 2022
% Result : Theorem 145.35s 145.60s
% Output : Refutation 153.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 43
% Syntax : Number of clauses : 144 ( 34 unt; 67 nHn; 144 RR)
% Number of literals : 484 ( 0 equ; 278 neg)
% Maximal clause size : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 28 ( 27 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
latt_str(skc13),
file('SEU349+1.p',unknown),
[] ).
cnf(2,axiom,
lattice(skc13),
file('SEU349+1.p',unknown),
[] ).
cnf(18,axiom,
~ empty_carrier(skc13),
file('SEU349+1.p',unknown),
[] ).
cnf(24,axiom,
element(skc14,the_carrier(skc13)),
file('SEU349+1.p',unknown),
[] ).
cnf(30,axiom,
( ~ latt_str(u)
| meet_semilatt_str(u) ),
file('SEU349+1.p',unknown),
[] ).
cnf(31,axiom,
( ~ latt_str(u)
| join_semilatt_str(u) ),
file('SEU349+1.p',unknown),
[] ).
cnf(39,axiom,
element(skf8(u,v,w),the_carrier(w)),
file('SEU349+1.p',unknown),
[] ).
cnf(40,axiom,
element(skf9(u,v,w),the_carrier(w)),
file('SEU349+1.p',unknown),
[] ).
cnf(52,axiom,
( ~ relation_of2_as_subset(u,v,w)
| relation_of2(u,v,w) ),
file('SEU349+1.p',unknown),
[] ).
cnf(56,axiom,
( ~ lattice(u)
| ~ latt_str(u)
| empty_carrier(u)
| join_commutative(u) ),
file('SEU349+1.p',unknown),
[] ).
cnf(57,axiom,
( ~ lattice(u)
| ~ latt_str(u)
| empty_carrier(u)
| join_associative(u) ),
file('SEU349+1.p',unknown),
[] ).
cnf(58,axiom,
( ~ lattice(u)
| ~ latt_str(u)
| empty_carrier(u)
| meet_commutative(u) ),
file('SEU349+1.p',unknown),
[] ).
cnf(59,axiom,
( ~ lattice(u)
| ~ latt_str(u)
| empty_carrier(u)
| meet_associative(u) ),
file('SEU349+1.p',unknown),
[] ).
cnf(60,axiom,
( ~ lattice(u)
| ~ latt_str(u)
| empty_carrier(u)
| meet_absorbing(u) ),
file('SEU349+1.p',unknown),
[] ).
cnf(61,axiom,
( ~ lattice(u)
| ~ latt_str(u)
| empty_carrier(u)
| join_absorbing(u) ),
file('SEU349+1.p',unknown),
[] ).
cnf(63,axiom,
( latt_element_smaller(skc13,skc14,skc15)
| relstr_set_smaller(poset_of_lattice(skc13),skc15,cast_to_el_of_LattPOSet(skc13,skc14)) ),
file('SEU349+1.p',unknown),
[] ).
cnf(71,axiom,
( ~ latt_str(u)
| ~ lattice(u)
| empty_carrier(u)
| rel_str(poset_of_lattice(u)) ),
file('SEU349+1.p',unknown),
[] ).
cnf(75,axiom,
( ~ latt_str(u)
| ~ lattice(u)
| empty_carrier(u)
| strict_rel_str(poset_of_lattice(u)) ),
file('SEU349+1.p',unknown),
[] ).
cnf(76,axiom,
( ~ latt_str(u)
| ~ lattice(u)
| empty_carrier(u)
| reflexive_relstr(poset_of_lattice(u)) ),
file('SEU349+1.p',unknown),
[] ).
cnf(77,axiom,
( ~ latt_str(u)
| ~ lattice(u)
| empty_carrier(u)
| transitive_relstr(poset_of_lattice(u)) ),
file('SEU349+1.p',unknown),
[] ).
cnf(78,axiom,
( ~ latt_str(u)
| ~ lattice(u)
| empty_carrier(u)
| antisymmetric_relstr(poset_of_lattice(u)) ),
file('SEU349+1.p',unknown),
[] ).
cnf(80,axiom,
( ~ latt_str(u)
| ~ lattice(u)
| ~ empty_carrier(poset_of_lattice(u))
| empty_carrier(u) ),
file('SEU349+1.p',unknown),
[] ).
cnf(83,axiom,
( ~ latt_element_smaller(skc13,skc14,skc15)
| ~ relstr_set_smaller(poset_of_lattice(skc13),skc15,cast_to_el_of_LattPOSet(skc13,skc14)) ),
file('SEU349+1.p',unknown),
[] ).
cnf(84,axiom,
( ~ strict_rel_str(u)
| ~ rel_str(u)
| equal(rel_str_of(the_carrier(u),the_InternalRel(u)),u) ),
file('SEU349+1.p',unknown),
[] ).
cnf(87,axiom,
( ~ latt_str(u)
| ~ lattice(u)
| empty_carrier(u)
| relation_of2_as_subset(k2_lattice3(u),the_carrier(u),the_carrier(u)) ),
file('SEU349+1.p',unknown),
[] ).
cnf(92,axiom,
( ~ latt_str(u)
| ~ lattice(u)
| empty_carrier(u)
| equal(rel_str_of(the_carrier(u),k2_lattice3(u)),poset_of_lattice(u)) ),
file('SEU349+1.p',unknown),
[] ).
cnf(93,axiom,
( ~ equal(rel_str_of(u,v),rel_str_of(w,x))
| ~ relation_of2(v,u,u)
| equal(u,w) ),
file('SEU349+1.p',unknown),
[] ).
cnf(96,axiom,
( ~ latt_str(u)
| ~ lattice(u)
| ~ element(v,the_carrier(u))
| empty_carrier(u)
| equal(cast_to_el_of_LattPOSet(u,v),v) ),
file('SEU349+1.p',unknown),
[] ).
cnf(97,axiom,
( ~ rel_str(u)
| ~ element(v,the_carrier(u))
| in(skf9(v,w,u),w)
| relstr_set_smaller(u,w,v) ),
file('SEU349+1.p',unknown),
[] ).
cnf(98,axiom,
( ~ latt_str(u)
| ~ lattice(u)
| ~ element(v,the_carrier(poset_of_lattice(u)))
| empty_carrier(u)
| equal(cast_to_el_of_lattice(u,v),v) ),
file('SEU349+1.p',unknown),
[] ).
cnf(100,axiom,
( ~ latt_str(u)
| ~ lattice(u)
| ~ element(v,the_carrier(poset_of_lattice(u)))
| element(cast_to_el_of_lattice(u,v),the_carrier(u))
| empty_carrier(u) ),
file('SEU349+1.p',unknown),
[] ).
cnf(101,axiom,
( ~ latt_str(u)
| ~ lattice(u)
| ~ element(v,the_carrier(u))
| element(cast_to_el_of_LattPOSet(u,v),the_carrier(poset_of_lattice(u)))
| empty_carrier(u) ),
file('SEU349+1.p',unknown),
[] ).
cnf(102,axiom,
( ~ rel_str(u)
| ~ element(v,the_carrier(u))
| ~ related(u,skf9(v,w,u),v)
| relstr_set_smaller(u,w,v) ),
file('SEU349+1.p',unknown),
[] ).
cnf(103,axiom,
( ~ latt_str(u)
| ~ element(v,the_carrier(u))
| empty_carrier(u)
| in(skf8(v,w,u),w)
| latt_element_smaller(u,v,w) ),
file('SEU349+1.p',unknown),
[] ).
cnf(104,axiom,
( ~ latt_str(u)
| ~ element(v,the_carrier(u))
| ~ below(u,skf8(v,w,u),v)
| empty_carrier(u)
| latt_element_smaller(u,v,w) ),
file('SEU349+1.p',unknown),
[] ).
cnf(111,axiom,
( ~ rel_str(u)
| ~ in(v,w)
| ~ element(x,the_carrier(u))
| ~ element(v,the_carrier(u))
| ~ relstr_set_smaller(u,w,x)
| related(u,v,x) ),
file('SEU349+1.p',unknown),
[] ).
cnf(112,axiom,
( ~ rel_str(u)
| ~ reflexive_relstr(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| ~ related(u,v,w)
| empty_carrier(u)
| related_reflexive(u,v,w) ),
file('SEU349+1.p',unknown),
[] ).
cnf(113,axiom,
( ~ rel_str(u)
| ~ reflexive_relstr(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| ~ related_reflexive(u,v,w)
| empty_carrier(u)
| related(u,v,w) ),
file('SEU349+1.p',unknown),
[] ).
cnf(114,axiom,
( ~ latt_str(u)
| ~ in(v,w)
| ~ element(x,the_carrier(u))
| ~ element(v,the_carrier(u))
| ~ latt_element_smaller(u,x,w)
| empty_carrier(u)
| below(u,v,x) ),
file('SEU349+1.p',unknown),
[] ).
cnf(115,axiom,
( ~ lattice(u)
| ~ latt_str(u)
| ~ related_reflexive(poset_of_lattice(u),cast_to_el_of_LattPOSet(u,v),cast_to_el_of_LattPOSet(u,w))
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| below_refl(u,v,w)
| empty_carrier(u) ),
file('SEU349+1.p',unknown),
[] ).
cnf(116,axiom,
( ~ lattice(u)
| ~ latt_str(u)
| ~ below_refl(u,v,w)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| related_reflexive(poset_of_lattice(u),cast_to_el_of_LattPOSet(u,v),cast_to_el_of_LattPOSet(u,w))
| empty_carrier(u) ),
file('SEU349+1.p',unknown),
[] ).
cnf(117,axiom,
( ~ latt_str(u)
| ~ join_absorbing(u)
| ~ meet_absorbing(u)
| ~ meet_commutative(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| ~ below(u,w,v)
| empty_carrier(u)
| below_refl(u,w,v) ),
file('SEU349+1.p',unknown),
[] ).
cnf(118,axiom,
( ~ latt_str(u)
| ~ join_absorbing(u)
| ~ meet_absorbing(u)
| ~ meet_commutative(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| ~ below_refl(u,w,v)
| empty_carrier(u)
| below(u,w,v) ),
file('SEU349+1.p',unknown),
[] ).
cnf(120,plain,
( ~ lattice(u)
| ~ latt_str(u)
| ~ element(v,the_carrier(poset_of_lattice(u)))
| empty_carrier(u)
| element(v,the_carrier(u)) ),
inference(rew,[status(thm),theory(equality)],[98,100]),
[iquote('0:Rew:98.4,100.3')] ).
cnf(121,plain,
( ~ lattice(u)
| ~ latt_str(u)
| ~ element(v,the_carrier(u))
| empty_carrier(u)
| element(v,the_carrier(poset_of_lattice(u))) ),
inference(rew,[status(thm),theory(equality)],[96,101]),
[iquote('0:Rew:96.4,101.3')] ).
cnf(122,plain,
( ~ latt_str(u)
| ~ lattice(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| ~ related_reflexive(poset_of_lattice(u),w,v)
| empty_carrier(u)
| below_refl(u,w,v) ),
inference(rew,[status(thm),theory(equality)],[96,115]),
[iquote('0:Rew:96.4,115.2,96.4,115.2')] ).
cnf(123,plain,
( ~ latt_str(u)
| ~ lattice(u)
| ~ element(v,the_carrier(u))
| ~ element(w,the_carrier(u))
| ~ below_refl(u,w,v)
| empty_carrier(u)
| related_reflexive(poset_of_lattice(u),w,v) ),
inference(rew,[status(thm),theory(equality)],[96,116]),
[iquote('0:Rew:96.4,116.5,96.4,116.5')] ).
cnf(126,plain,
( ~ latt_str(skc13)
| ~ element(u,the_carrier(skc13))
| element(u,the_carrier(poset_of_lattice(skc13)))
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[2,121]),
[iquote('0:Res:2.0,121.1')] ).
cnf(127,plain,
( ~ latt_str(skc13)
| ~ element(u,the_carrier(poset_of_lattice(skc13)))
| element(u,the_carrier(skc13))
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[2,120]),
[iquote('0:Res:2.0,120.1')] ).
cnf(130,plain,
( ~ latt_str(skc13)
| empty_carrier(skc13)
| equal(rel_str_of(the_carrier(skc13),k2_lattice3(skc13)),poset_of_lattice(skc13)) ),
inference(res,[status(thm),theory(equality)],[2,92]),
[iquote('0:Res:2.0,92.0')] ).
cnf(132,plain,
( ~ latt_str(skc13)
| relation_of2_as_subset(k2_lattice3(skc13),the_carrier(skc13),the_carrier(skc13))
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[2,87]),
[iquote('0:Res:2.0,87.0')] ).
cnf(135,plain,
( ~ latt_str(skc13)
| ~ empty_carrier(poset_of_lattice(skc13))
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[2,80]),
[iquote('0:Res:2.0,80.0')] ).
cnf(139,plain,
( ~ latt_str(skc13)
| rel_str(poset_of_lattice(skc13))
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[2,71]),
[iquote('0:Res:2.0,71.0')] ).
cnf(140,plain,
( ~ latt_str(skc13)
| strict_rel_str(poset_of_lattice(skc13))
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[2,75]),
[iquote('0:Res:2.0,75.0')] ).
cnf(141,plain,
( ~ latt_str(skc13)
| reflexive_relstr(poset_of_lattice(skc13))
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[2,76]),
[iquote('0:Res:2.0,76.0')] ).
cnf(142,plain,
( ~ latt_str(skc13)
| transitive_relstr(poset_of_lattice(skc13))
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[2,77]),
[iquote('0:Res:2.0,77.0')] ).
cnf(143,plain,
( ~ latt_str(skc13)
| antisymmetric_relstr(poset_of_lattice(skc13))
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[2,78]),
[iquote('0:Res:2.0,78.0')] ).
cnf(144,plain,
( ~ latt_str(skc13)
| join_commutative(skc13)
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[2,56]),
[iquote('0:Res:2.0,56.1')] ).
cnf(145,plain,
( ~ latt_str(skc13)
| join_associative(skc13)
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[2,57]),
[iquote('0:Res:2.0,57.1')] ).
cnf(146,plain,
( ~ latt_str(skc13)
| meet_commutative(skc13)
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[2,58]),
[iquote('0:Res:2.0,58.1')] ).
cnf(147,plain,
( ~ latt_str(skc13)
| meet_associative(skc13)
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[2,59]),
[iquote('0:Res:2.0,59.1')] ).
cnf(148,plain,
( ~ latt_str(skc13)
| meet_absorbing(skc13)
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[2,60]),
[iquote('0:Res:2.0,60.1')] ).
cnf(149,plain,
( ~ latt_str(skc13)
| join_absorbing(skc13)
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[2,61]),
[iquote('0:Res:2.0,61.1')] ).
cnf(183,plain,
meet_semilatt_str(skc13),
inference(res,[status(thm),theory(equality)],[1,30]),
[iquote('0:Res:1.0,30.0')] ).
cnf(184,plain,
join_semilatt_str(skc13),
inference(res,[status(thm),theory(equality)],[1,31]),
[iquote('0:Res:1.0,31.0')] ).
cnf(232,plain,
( ~ latt_str(skc13)
| ~ below(skc13,skf8(skc14,u,skc13),skc14)
| latt_element_smaller(skc13,skc14,u)
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[24,104]),
[iquote('0:Res:24.0,104.2')] ).
cnf(235,plain,
( ~ latt_str(skc13)
| ~ lattice(skc13)
| element(skc14,the_carrier(poset_of_lattice(skc13)))
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[24,121]),
[iquote('0:Res:24.0,121.2')] ).
cnf(236,plain,
( ~ lattice(skc13)
| ~ latt_str(skc13)
| empty_carrier(skc13)
| equal(cast_to_el_of_LattPOSet(skc13,skc14),skc14) ),
inference(res,[status(thm),theory(equality)],[24,96]),
[iquote('0:Res:24.0,96.2')] ).
cnf(239,plain,
( ~ latt_str(skc13)
| ~ element(u,the_carrier(skc13))
| ~ in(u,v)
| ~ latt_element_smaller(skc13,skc14,v)
| below(skc13,u,skc14)
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[24,114]),
[iquote('0:Res:24.0,114.4')] ).
cnf(241,plain,
( ~ meet_commutative(skc13)
| ~ meet_absorbing(skc13)
| ~ join_absorbing(skc13)
| ~ latt_str(skc13)
| ~ element(u,the_carrier(skc13))
| ~ below_refl(skc13,u,skc14)
| below(skc13,u,skc14)
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[24,118]),
[iquote('0:Res:24.0,118.5')] ).
cnf(242,plain,
( ~ meet_commutative(skc13)
| ~ meet_absorbing(skc13)
| ~ join_absorbing(skc13)
| ~ latt_str(skc13)
| ~ element(u,the_carrier(skc13))
| ~ below(skc13,u,skc14)
| below_refl(skc13,u,skc14)
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[24,117]),
[iquote('0:Res:24.0,117.5')] ).
cnf(243,plain,
( ~ lattice(skc13)
| ~ latt_str(skc13)
| ~ below_refl(skc13,u,skc14)
| ~ element(u,the_carrier(skc13))
| related_reflexive(poset_of_lattice(skc13),u,skc14)
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[24,123]),
[iquote('0:Res:24.0,123.4')] ).
cnf(244,plain,
( ~ lattice(skc13)
| ~ latt_str(skc13)
| ~ related_reflexive(poset_of_lattice(skc13),u,skc14)
| ~ element(u,the_carrier(skc13))
| below_refl(skc13,u,skc14)
| empty_carrier(skc13) ),
inference(res,[status(thm),theory(equality)],[24,122]),
[iquote('0:Res:24.0,122.4')] ).
cnf(248,plain,
join_commutative(skc13),
inference(mrr,[status(thm)],[144,1,18]),
[iquote('0:MRR:144.0,144.2,1.0,18.0')] ).
cnf(249,plain,
join_associative(skc13),
inference(mrr,[status(thm)],[145,1,18]),
[iquote('0:MRR:145.0,145.2,1.0,18.0')] ).
cnf(250,plain,
meet_commutative(skc13),
inference(mrr,[status(thm)],[146,1,18]),
[iquote('0:MRR:146.0,146.2,1.0,18.0')] ).
cnf(251,plain,
meet_associative(skc13),
inference(mrr,[status(thm)],[147,1,18]),
[iquote('0:MRR:147.0,147.2,1.0,18.0')] ).
cnf(252,plain,
meet_absorbing(skc13),
inference(mrr,[status(thm)],[148,1,18]),
[iquote('0:MRR:148.0,148.2,1.0,18.0')] ).
cnf(253,plain,
join_absorbing(skc13),
inference(mrr,[status(thm)],[149,1,18]),
[iquote('0:MRR:149.0,149.2,1.0,18.0')] ).
cnf(258,plain,
rel_str(poset_of_lattice(skc13)),
inference(mrr,[status(thm)],[139,1,18]),
[iquote('0:MRR:139.0,139.2,1.0,18.0')] ).
cnf(259,plain,
strict_rel_str(poset_of_lattice(skc13)),
inference(mrr,[status(thm)],[140,1,18]),
[iquote('0:MRR:140.0,140.2,1.0,18.0')] ).
cnf(260,plain,
reflexive_relstr(poset_of_lattice(skc13)),
inference(mrr,[status(thm)],[141,1,18]),
[iquote('0:MRR:141.0,141.2,1.0,18.0')] ).
cnf(261,plain,
transitive_relstr(poset_of_lattice(skc13)),
inference(mrr,[status(thm)],[142,1,18]),
[iquote('0:MRR:142.0,142.2,1.0,18.0')] ).
cnf(262,plain,
antisymmetric_relstr(poset_of_lattice(skc13)),
inference(mrr,[status(thm)],[143,1,18]),
[iquote('0:MRR:143.0,143.2,1.0,18.0')] ).
cnf(263,plain,
~ empty_carrier(poset_of_lattice(skc13)),
inference(mrr,[status(thm)],[135,1,18]),
[iquote('0:MRR:135.0,135.2,1.0,18.0')] ).
cnf(266,plain,
relation_of2_as_subset(k2_lattice3(skc13),the_carrier(skc13),the_carrier(skc13)),
inference(mrr,[status(thm)],[132,1,18]),
[iquote('0:MRR:132.0,132.2,1.0,18.0')] ).
cnf(268,plain,
equal(rel_str_of(the_carrier(skc13),k2_lattice3(skc13)),poset_of_lattice(skc13)),
inference(mrr,[status(thm)],[130,1,18]),
[iquote('0:MRR:130.0,130.1,1.0,18.0')] ).
cnf(269,plain,
element(skc14,the_carrier(poset_of_lattice(skc13))),
inference(mrr,[status(thm)],[235,1,2,18]),
[iquote('0:MRR:235.0,235.1,235.3,1.0,2.0,18.0')] ).
cnf(270,plain,
equal(cast_to_el_of_LattPOSet(skc13,skc14),skc14),
inference(mrr,[status(thm)],[236,2,1,18]),
[iquote('0:MRR:236.0,236.1,236.2,2.0,1.0,18.0')] ).
cnf(271,plain,
( ~ latt_element_smaller(skc13,skc14,skc15)
| ~ relstr_set_smaller(poset_of_lattice(skc13),skc15,skc14) ),
inference(rew,[status(thm),theory(equality)],[270,83]),
[iquote('0:Rew:270.0,83.1')] ).
cnf(272,plain,
( latt_element_smaller(skc13,skc14,skc15)
| relstr_set_smaller(poset_of_lattice(skc13),skc15,skc14) ),
inference(rew,[status(thm),theory(equality)],[270,63]),
[iquote('0:Rew:270.0,63.1')] ).
cnf(273,plain,
( ~ element(u,the_carrier(skc13))
| element(u,the_carrier(poset_of_lattice(skc13))) ),
inference(mrr,[status(thm)],[126,1,18]),
[iquote('0:MRR:126.0,126.3,1.0,18.0')] ).
cnf(274,plain,
( ~ element(u,the_carrier(poset_of_lattice(skc13)))
| element(u,the_carrier(skc13)) ),
inference(mrr,[status(thm)],[127,1,18]),
[iquote('0:MRR:127.0,127.3,1.0,18.0')] ).
cnf(279,plain,
( ~ below(skc13,skf8(skc14,u,skc13),skc14)
| latt_element_smaller(skc13,skc14,u) ),
inference(mrr,[status(thm)],[232,1,18]),
[iquote('0:MRR:232.0,232.3,1.0,18.0')] ).
cnf(287,plain,
( ~ element(u,the_carrier(skc13))
| ~ related_reflexive(poset_of_lattice(skc13),u,skc14)
| below_refl(skc13,u,skc14) ),
inference(mrr,[status(thm)],[244,2,1,18]),
[iquote('0:MRR:244.0,244.1,244.5,2.0,1.0,18.0')] ).
cnf(288,plain,
( ~ element(u,the_carrier(skc13))
| ~ below_refl(skc13,u,skc14)
| related_reflexive(poset_of_lattice(skc13),u,skc14) ),
inference(mrr,[status(thm)],[243,2,1,18]),
[iquote('0:MRR:243.0,243.1,243.5,2.0,1.0,18.0')] ).
cnf(289,plain,
( ~ in(u,v)
| ~ element(u,the_carrier(skc13))
| ~ latt_element_smaller(skc13,skc14,v)
| below(skc13,u,skc14) ),
inference(mrr,[status(thm)],[239,1,18]),
[iquote('0:MRR:239.0,239.5,1.0,18.0')] ).
cnf(296,plain,
( ~ element(u,the_carrier(skc13))
| ~ below(skc13,u,skc14)
| below_refl(skc13,u,skc14) ),
inference(mrr,[status(thm)],[242,250,252,253,1,18]),
[iquote('0:MRR:242.0,242.1,242.2,242.3,242.7,250.0,252.0,253.0,1.0,18.0')] ).
cnf(297,plain,
( ~ element(u,the_carrier(skc13))
| ~ below_refl(skc13,u,skc14)
| below(skc13,u,skc14) ),
inference(mrr,[status(thm)],[241,250,252,253,1,18]),
[iquote('0:MRR:241.0,241.1,241.2,241.3,241.7,250.0,252.0,253.0,1.0,18.0')] ).
cnf(331,plain,
latt_element_smaller(skc13,skc14,skc15),
inference(spt,[spt(split,[position(s1)])],[272]),
[iquote('1:Spt:272.0')] ).
cnf(332,plain,
~ relstr_set_smaller(poset_of_lattice(skc13),skc15,skc14),
inference(mrr,[status(thm)],[271,331]),
[iquote('1:MRR:271.0,331.0')] ).
cnf(376,plain,
relation_of2(k2_lattice3(skc13),the_carrier(skc13),the_carrier(skc13)),
inference(res,[status(thm),theory(equality)],[266,52]),
[iquote('0:Res:266.0,52.0')] ).
cnf(401,plain,
element(skf9(u,v,poset_of_lattice(skc13)),the_carrier(skc13)),
inference(res,[status(thm),theory(equality)],[40,274]),
[iquote('0:Res:40.0,274.0')] ).
cnf(774,plain,
( ~ equal(rel_str_of(u,v),poset_of_lattice(skc13))
| ~ relation_of2(k2_lattice3(skc13),the_carrier(skc13),the_carrier(skc13))
| equal(the_carrier(skc13),u) ),
inference(spl,[status(thm),theory(equality)],[268,93]),
[iquote('0:SpL:268.0,93.0')] ).
cnf(780,plain,
( ~ equal(rel_str_of(u,v),poset_of_lattice(skc13))
| equal(the_carrier(skc13),u) ),
inference(mrr,[status(thm)],[774,376]),
[iquote('0:MRR:774.1,376.0')] ).
cnf(1053,plain,
( ~ strict_rel_str(u)
| ~ rel_str(u)
| ~ equal(u,poset_of_lattice(skc13))
| equal(the_carrier(skc13),the_carrier(u)) ),
inference(spl,[status(thm),theory(equality)],[84,780]),
[iquote('0:SpL:84.2,780.0')] ).
cnf(1225,plain,
( ~ rel_str(poset_of_lattice(skc13))
| ~ in(u,v)
| ~ element(u,the_carrier(poset_of_lattice(skc13)))
| ~ relstr_set_smaller(poset_of_lattice(skc13),v,skc14)
| related(poset_of_lattice(skc13),u,skc14) ),
inference(res,[status(thm),theory(equality)],[269,111]),
[iquote('0:Res:269.0,111.2')] ).
cnf(1247,plain,
( ~ in(u,v)
| ~ element(u,the_carrier(poset_of_lattice(skc13)))
| ~ relstr_set_smaller(poset_of_lattice(skc13),v,skc14)
| related(poset_of_lattice(skc13),u,skc14) ),
inference(ssi,[status(thm)],[1225,259,262,261,260,258]),
[iquote('0:SSi:1225.0,259.0,262.0,261.0,260.0,258.0')] ).
cnf(1819,plain,
( ~ rel_str(poset_of_lattice(skc13))
| ~ reflexive_relstr(poset_of_lattice(skc13))
| ~ element(u,the_carrier(skc13))
| ~ below_refl(skc13,u,skc14)
| ~ element(u,the_carrier(poset_of_lattice(skc13)))
| ~ element(skc14,the_carrier(poset_of_lattice(skc13)))
| empty_carrier(poset_of_lattice(skc13))
| related(poset_of_lattice(skc13),u,skc14) ),
inference(res,[status(thm),theory(equality)],[288,113]),
[iquote('0:Res:288.2,113.4')] ).
cnf(1821,plain,
( ~ element(u,the_carrier(skc13))
| ~ below_refl(skc13,u,skc14)
| ~ element(u,the_carrier(poset_of_lattice(skc13)))
| ~ element(skc14,the_carrier(poset_of_lattice(skc13)))
| empty_carrier(poset_of_lattice(skc13))
| related(poset_of_lattice(skc13),u,skc14) ),
inference(ssi,[status(thm)],[1819,259,262,261,260,258]),
[iquote('0:SSi:1819.1,1819.0,259.0,262.0,261.0,260.0,258.0,259.0,262.0,261.0,260.0,258.0')] ).
cnf(1822,plain,
( ~ below_refl(skc13,u,skc14)
| ~ element(u,the_carrier(poset_of_lattice(skc13)))
| related(poset_of_lattice(skc13),u,skc14) ),
inference(mrr,[status(thm)],[1821,274,269,263]),
[iquote('0:MRR:1821.0,1821.3,1821.4,274.1,269.0,263.0')] ).
cnf(1905,plain,
( ~ rel_str(poset_of_lattice(skc13))
| ~ reflexive_relstr(poset_of_lattice(skc13))
| ~ element(u,the_carrier(poset_of_lattice(skc13)))
| ~ element(skc14,the_carrier(poset_of_lattice(skc13)))
| ~ related(poset_of_lattice(skc13),u,skc14)
| ~ element(u,the_carrier(skc13))
| empty_carrier(poset_of_lattice(skc13))
| below_refl(skc13,u,skc14) ),
inference(res,[status(thm),theory(equality)],[112,287]),
[iquote('0:Res:112.6,287.1')] ).
cnf(1909,plain,
( ~ element(u,the_carrier(poset_of_lattice(skc13)))
| ~ element(skc14,the_carrier(poset_of_lattice(skc13)))
| ~ related(poset_of_lattice(skc13),u,skc14)
| ~ element(u,the_carrier(skc13))
| empty_carrier(poset_of_lattice(skc13))
| below_refl(skc13,u,skc14) ),
inference(ssi,[status(thm)],[1905,259,262,261,260,258]),
[iquote('0:SSi:1905.1,1905.0,259.0,262.0,261.0,260.0,258.0,259.0,262.0,261.0,260.0,258.0')] ).
cnf(1910,plain,
( ~ related(poset_of_lattice(skc13),u,skc14)
| ~ element(u,the_carrier(skc13))
| below_refl(skc13,u,skc14) ),
inference(mrr,[status(thm)],[1909,273,269,263]),
[iquote('0:MRR:1909.0,1909.1,1909.4,273.1,269.0,263.0')] ).
cnf(2190,plain,
( ~ in(skf9(u,v,poset_of_lattice(skc13)),w)
| ~ latt_element_smaller(skc13,skc14,w)
| below(skc13,skf9(u,v,poset_of_lattice(skc13)),skc14) ),
inference(res,[status(thm),theory(equality)],[401,289]),
[iquote('0:Res:401.0,289.1')] ).
cnf(4204,plain,
( ~ rel_str(poset_of_lattice(skc13))
| ~ below_refl(skc13,skf9(skc14,u,poset_of_lattice(skc13)),skc14)
| ~ element(skf9(skc14,u,poset_of_lattice(skc13)),the_carrier(poset_of_lattice(skc13)))
| ~ element(skc14,the_carrier(poset_of_lattice(skc13)))
| relstr_set_smaller(poset_of_lattice(skc13),u,skc14) ),
inference(res,[status(thm),theory(equality)],[1822,102]),
[iquote('0:Res:1822.2,102.2')] ).
cnf(4208,plain,
( ~ below_refl(skc13,skf9(skc14,u,poset_of_lattice(skc13)),skc14)
| ~ element(skf9(skc14,u,poset_of_lattice(skc13)),the_carrier(poset_of_lattice(skc13)))
| ~ element(skc14,the_carrier(poset_of_lattice(skc13)))
| relstr_set_smaller(poset_of_lattice(skc13),u,skc14) ),
inference(ssi,[status(thm)],[4204,259,262,261,260,258]),
[iquote('0:SSi:4204.0,259.0,262.0,261.0,260.0,258.0')] ).
cnf(4209,plain,
( ~ below_refl(skc13,skf9(skc14,u,poset_of_lattice(skc13)),skc14)
| relstr_set_smaller(poset_of_lattice(skc13),u,skc14) ),
inference(mrr,[status(thm)],[4208,40,269]),
[iquote('0:MRR:4208.1,4208.2,40.0,269.0')] ).
cnf(4210,plain,
( ~ element(skf9(skc14,u,poset_of_lattice(skc13)),the_carrier(skc13))
| ~ below(skc13,skf9(skc14,u,poset_of_lattice(skc13)),skc14)
| relstr_set_smaller(poset_of_lattice(skc13),u,skc14) ),
inference(res,[status(thm),theory(equality)],[296,4209]),
[iquote('0:Res:296.2,4209.0')] ).
cnf(4213,plain,
( ~ below(skc13,skf9(skc14,u,poset_of_lattice(skc13)),skc14)
| relstr_set_smaller(poset_of_lattice(skc13),u,skc14) ),
inference(mrr,[status(thm)],[4210,401]),
[iquote('0:MRR:4210.0,401.0')] ).
cnf(8042,plain,
( ~ element(u,the_carrier(skc13))
| ~ in(u,v)
| ~ relstr_set_smaller(poset_of_lattice(skc13),v,skc14)
| related(poset_of_lattice(skc13),u,skc14) ),
inference(res,[status(thm),theory(equality)],[273,1247]),
[iquote('0:Res:273.1,1247.1')] ).
cnf(13704,plain,
( ~ strict_rel_str(poset_of_lattice(skc13))
| ~ rel_str(poset_of_lattice(skc13))
| equal(the_carrier(poset_of_lattice(skc13)),the_carrier(skc13)) ),
inference(eqr,[status(thm),theory(equality)],[1053]),
[iquote('0:EqR:1053.2')] ).
cnf(13705,plain,
equal(the_carrier(poset_of_lattice(skc13)),the_carrier(skc13)),
inference(ssi,[status(thm)],[13704,259,262,261,260,258]),
[iquote('0:SSi:13704.1,13704.0,259.0,262.0,261.0,260.0,258.0,259.0,262.0,261.0,260.0,258.0')] ).
cnf(18174,plain,
( ~ rel_str(poset_of_lattice(skc13))
| ~ element(u,the_carrier(poset_of_lattice(skc13)))
| ~ latt_element_smaller(skc13,skc14,v)
| relstr_set_smaller(poset_of_lattice(skc13),v,u)
| below(skc13,skf9(u,v,poset_of_lattice(skc13)),skc14) ),
inference(res,[status(thm),theory(equality)],[97,2190]),
[iquote('0:Res:97.2,2190.0')] ).
cnf(18176,plain,
( ~ rel_str(poset_of_lattice(skc13))
| ~ element(u,the_carrier(skc13))
| ~ latt_element_smaller(skc13,skc14,v)
| relstr_set_smaller(poset_of_lattice(skc13),v,u)
| below(skc13,skf9(u,v,poset_of_lattice(skc13)),skc14) ),
inference(rew,[status(thm),theory(equality)],[13705,18174]),
[iquote('0:Rew:13705.0,18174.1')] ).
cnf(18177,plain,
( ~ element(u,the_carrier(skc13))
| ~ latt_element_smaller(skc13,skc14,v)
| relstr_set_smaller(poset_of_lattice(skc13),v,u)
| below(skc13,skf9(u,v,poset_of_lattice(skc13)),skc14) ),
inference(ssi,[status(thm)],[18176,259,262,261,260,258]),
[iquote('0:SSi:18176.0,259.0,262.0,261.0,260.0,258.0')] ).
cnf(53015,plain,
( ~ element(skc14,the_carrier(skc13))
| ~ latt_element_smaller(skc13,skc14,u)
| relstr_set_smaller(poset_of_lattice(skc13),u,skc14)
| relstr_set_smaller(poset_of_lattice(skc13),u,skc14) ),
inference(res,[status(thm),theory(equality)],[18177,4213]),
[iquote('0:Res:18177.3,4213.0')] ).
cnf(53017,plain,
( ~ element(skc14,the_carrier(skc13))
| ~ latt_element_smaller(skc13,skc14,u)
| relstr_set_smaller(poset_of_lattice(skc13),u,skc14) ),
inference(obv,[status(thm),theory(equality)],[53015]),
[iquote('0:Obv:53015.2')] ).
cnf(53018,plain,
( ~ latt_element_smaller(skc13,skc14,u)
| relstr_set_smaller(poset_of_lattice(skc13),u,skc14) ),
inference(mrr,[status(thm)],[53017,24]),
[iquote('0:MRR:53017.0,24.0')] ).
cnf(53107,plain,
~ latt_element_smaller(skc13,skc14,skc15),
inference(res,[status(thm),theory(equality)],[53018,332]),
[iquote('1:Res:53018.1,332.0')] ).
cnf(53129,plain,
$false,
inference(mrr,[status(thm)],[53107,331]),
[iquote('1:MRR:53107.0,331.0')] ).
cnf(53130,plain,
~ latt_element_smaller(skc13,skc14,skc15),
inference(spt,[spt(split,[position(sa)])],[53129,331]),
[iquote('1:Spt:53129.0,272.0,331.0')] ).
cnf(53131,plain,
relstr_set_smaller(poset_of_lattice(skc13),skc15,skc14),
inference(spt,[spt(split,[position(s2)])],[272]),
[iquote('1:Spt:53129.0,272.1')] ).
cnf(53676,plain,
( ~ element(u,the_carrier(skc13))
| ~ in(u,skc15)
| related(poset_of_lattice(skc13),u,skc14) ),
inference(res,[status(thm),theory(equality)],[53131,8042]),
[iquote('1:Res:53131.0,8042.2')] ).
cnf(57092,plain,
( ~ element(u,the_carrier(skc13))
| ~ in(u,skc15)
| ~ element(u,the_carrier(skc13))
| below_refl(skc13,u,skc14) ),
inference(res,[status(thm),theory(equality)],[53676,1910]),
[iquote('1:Res:53676.2,1910.0')] ).
cnf(57095,plain,
( ~ in(u,skc15)
| ~ element(u,the_carrier(skc13))
| below_refl(skc13,u,skc14) ),
inference(obv,[status(thm),theory(equality)],[57092]),
[iquote('1:Obv:57092.0')] ).
cnf(57112,plain,
( ~ in(u,skc15)
| ~ element(u,the_carrier(skc13))
| ~ element(u,the_carrier(skc13))
| below(skc13,u,skc14) ),
inference(res,[status(thm),theory(equality)],[57095,297]),
[iquote('1:Res:57095.2,297.1')] ).
cnf(57119,plain,
( ~ in(u,skc15)
| ~ element(u,the_carrier(skc13))
| below(skc13,u,skc14) ),
inference(obv,[status(thm),theory(equality)],[57112]),
[iquote('1:Obv:57112.1')] ).
cnf(57256,plain,
( ~ in(skf8(skc14,u,skc13),skc15)
| ~ element(skf8(skc14,u,skc13),the_carrier(skc13))
| latt_element_smaller(skc13,skc14,u) ),
inference(res,[status(thm),theory(equality)],[57119,279]),
[iquote('1:Res:57119.2,279.0')] ).
cnf(57260,plain,
( ~ in(skf8(skc14,u,skc13),skc15)
| latt_element_smaller(skc13,skc14,u) ),
inference(mrr,[status(thm)],[57256,39]),
[iquote('1:MRR:57256.1,39.0')] ).
cnf(57270,plain,
( ~ latt_str(skc13)
| ~ element(skc14,the_carrier(skc13))
| empty_carrier(skc13)
| latt_element_smaller(skc13,skc14,skc15)
| latt_element_smaller(skc13,skc14,skc15) ),
inference(res,[status(thm),theory(equality)],[103,57260]),
[iquote('1:Res:103.3,57260.0')] ).
cnf(57295,plain,
( ~ latt_str(skc13)
| ~ element(skc14,the_carrier(skc13))
| empty_carrier(skc13)
| latt_element_smaller(skc13,skc14,skc15) ),
inference(obv,[status(thm),theory(equality)],[57270]),
[iquote('1:Obv:57270.3')] ).
cnf(57296,plain,
( ~ element(skc14,the_carrier(skc13))
| empty_carrier(skc13)
| latt_element_smaller(skc13,skc14,skc15) ),
inference(ssi,[status(thm)],[57295,2,1,251,249,248,184,183,253,252,250]),
[iquote('1:SSi:57295.0,2.0,1.0,251.0,249.0,248.0,184.0,183.0,253.0,252.0,250.0')] ).
cnf(57297,plain,
$false,
inference(mrr,[status(thm)],[57296,24,18,53130]),
[iquote('1:MRR:57296.0,57296.1,57296.2,24.0,18.0,53130.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU349+1 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 20 08:13:22 EDT 2022
% 0.20/0.35 % CPUTime :
% 145.35/145.60
% 145.35/145.60 SPASS V 3.9
% 145.35/145.60 SPASS beiseite: Proof found.
% 145.35/145.60 % SZS status Theorem
% 145.35/145.60 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 145.35/145.60 SPASS derived 43552 clauses, backtracked 4420 clauses, performed 39 splits and kept 22016 clauses.
% 145.35/145.60 SPASS allocated 165489 KBytes.
% 145.35/145.60 SPASS spent 0:2:25.19 on the problem.
% 145.35/145.60 0:00:00.04 for the input.
% 145.35/145.60 0:00:00.04 for the FLOTTER CNF translation.
% 145.35/145.60 0:00:01.50 for inferences.
% 145.35/145.60 0:00:04.03 for the backtracking.
% 145.35/145.60 0:2:17.60 for the reduction.
% 145.35/145.60
% 145.35/145.60
% 145.35/145.60 Here is a proof with depth 8, length 144 :
% 145.35/145.60 % SZS output start Refutation
% See solution above
% 153.25/153.47 Formulae used in the proof : t30_lattice3 dt_l3_lattices d17_lattice3 existence_m1_subset_1 d9_lattice3 redefinition_m2_relset_1 cc1_lattices dt_k3_lattice3 fc4_lattice3 abstractness_v1_orders_2 dt_k2_lattice3 d2_lattice3 free_g1_orders_2 d3_lattice3 d4_lattice3 dt_k5_lattice3 dt_k4_lattice3 redefinition_r3_orders_2 t7_lattice3 redefinition_r3_lattices
% 153.25/153.47
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