TSTP Solution File: SEU369+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SEU369+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 14:36:41 EDT 2022
% Result : Theorem 5.54s 5.76s
% Output : Refutation 5.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 37
% Syntax : Number of clauses : 81 ( 29 unt; 26 nHn; 81 RR)
% Number of literals : 277 ( 0 equ; 180 neg)
% Maximal clause size : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 29 ( 28 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(116,axiom,
latt_str(boole_lattice(u)),
file('SEU369+1.p',unknown),
[] ).
cnf(134,axiom,
complete_latt_str(boole_lattice(u)),
file('SEU369+1.p',unknown),
[] ).
cnf(144,axiom,
strict_latt_str(boole_lattice(u)),
file('SEU369+1.p',unknown),
[] ).
cnf(145,axiom,
join_commutative(boole_lattice(u)),
file('SEU369+1.p',unknown),
[] ).
cnf(146,axiom,
join_associative(boole_lattice(u)),
file('SEU369+1.p',unknown),
[] ).
cnf(147,axiom,
meet_commutative(boole_lattice(u)),
file('SEU369+1.p',unknown),
[] ).
cnf(148,axiom,
meet_associative(boole_lattice(u)),
file('SEU369+1.p',unknown),
[] ).
cnf(149,axiom,
meet_absorbing(boole_lattice(u)),
file('SEU369+1.p',unknown),
[] ).
cnf(150,axiom,
join_absorbing(boole_lattice(u)),
file('SEU369+1.p',unknown),
[] ).
cnf(151,axiom,
lattice(boole_lattice(u)),
file('SEU369+1.p',unknown),
[] ).
cnf(152,axiom,
distributive_lattstr(boole_lattice(u)),
file('SEU369+1.p',unknown),
[] ).
cnf(153,axiom,
modular_lattstr(boole_lattice(u)),
file('SEU369+1.p',unknown),
[] ).
cnf(154,axiom,
lower_bounded_semilattstr(boole_lattice(u)),
file('SEU369+1.p',unknown),
[] ).
cnf(155,axiom,
upper_bounded_semilattstr(boole_lattice(u)),
file('SEU369+1.p',unknown),
[] ).
cnf(156,axiom,
bounded_lattstr(boole_lattice(u)),
file('SEU369+1.p',unknown),
[] ).
cnf(157,axiom,
complemented_lattstr(boole_lattice(u)),
file('SEU369+1.p',unknown),
[] ).
cnf(158,axiom,
boolean_lattstr(boole_lattice(u)),
file('SEU369+1.p',unknown),
[] ).
cnf(194,axiom,
~ empty_carrier(boole_lattice(u)),
file('SEU369+1.p',unknown),
[] ).
cnf(199,axiom,
element(skc26,the_carrier(boole_POSet(skc24))),
file('SEU369+1.p',unknown),
[] ).
cnf(200,axiom,
element(skc25,the_carrier(boole_POSet(skc24))),
file('SEU369+1.p',unknown),
[] ).
cnf(209,axiom,
equal(poset_of_lattice(boole_lattice(u)),boole_POSet(u)),
file('SEU369+1.p',unknown),
[] ).
cnf(221,axiom,
( subset(skc25,skc26)
| related_reflexive(boole_POSet(skc24),skc25,skc26) ),
file('SEU369+1.p',unknown),
[] ).
cnf(235,axiom,
( ~ relation_of2_as_subset(u,v,w)
| relation_of2(u,v,w) ),
file('SEU369+1.p',unknown),
[] ).
cnf(239,axiom,
( ~ subset(skc25,skc26)
| ~ related_reflexive(boole_POSet(skc24),skc25,skc26) ),
file('SEU369+1.p',unknown),
[] ).
cnf(257,axiom,
( ~ rel_str(u)
| relation_of2_as_subset(the_InternalRel(u),the_carrier(u),the_carrier(u)) ),
file('SEU369+1.p',unknown),
[] ).
cnf(266,axiom,
( ~ latt_str(u)
| ~ lattice(u)
| empty_carrier(u)
| rel_str(poset_of_lattice(u)) ),
file('SEU369+1.p',unknown),
[] ).
cnf(276,axiom,
( ~ latt_str(u)
| ~ lattice(u)
| empty_carrier(u)
| strict_rel_str(poset_of_lattice(u)) ),
file('SEU369+1.p',unknown),
[] ).
cnf(287,axiom,
( ~ strict_rel_str(u)
| ~ rel_str(u)
| equal(rel_str_of(the_carrier(u),the_InternalRel(u)),u) ),
file('SEU369+1.p',unknown),
[] ).
cnf(349,axiom,
( ~ latt_str(u)
| ~ lattice(u)
| empty_carrier(u)
| equal(rel_str_of(the_carrier(u),k2_lattice3(u)),poset_of_lattice(u)) ),
file('SEU369+1.p',unknown),
[] ).
cnf(350,axiom,
( ~ equal(rel_str_of(u,v),rel_str_of(w,x))
| ~ relation_of2(v,u,u)
| equal(u,w) ),
file('SEU369+1.p',unknown),
[] ).
cnf(353,axiom,
( ~ latt_str(u)
| ~ lattice(u)
| ~ element(v,the_carrier(u))
| empty_carrier(u)
| equal(cast_to_el_of_LattPOSet(u,v),v) ),
file('SEU369+1.p',unknown),
[] ).
cnf(356,axiom,
( ~ subset(u,v)
| ~ element(v,the_carrier(boole_lattice(w)))
| ~ element(u,the_carrier(boole_lattice(w)))
| below(boole_lattice(w),u,v) ),
file('SEU369+1.p',unknown),
[] ).
cnf(357,axiom,
( ~ element(u,the_carrier(boole_lattice(v)))
| ~ element(w,the_carrier(boole_lattice(v)))
| ~ below(boole_lattice(v),w,u)
| subset(w,u) ),
file('SEU369+1.p',unknown),
[] ).
cnf(368,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('SEU369+1.p',unknown),
[] ).
cnf(369,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('SEU369+1.p',unknown),
[] ).
cnf(370,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('SEU369+1.p',unknown),
[] ).
cnf(371,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('SEU369+1.p',unknown),
[] ).
cnf(382,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)],[353,368]),
[iquote('0:Rew:353.4,368.2,353.4,368.2')] ).
cnf(383,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)],[353,369]),
[iquote('0:Rew:353.4,369.5,353.4,369.5')] ).
cnf(534,plain,
related_reflexive(boole_POSet(skc24),skc25,skc26),
inference(spt,[spt(split,[position(s1)])],[221]),
[iquote('1:Spt:221.1')] ).
cnf(535,plain,
~ subset(skc25,skc26),
inference(mrr,[status(thm)],[239,534]),
[iquote('1:MRR:239.1,534.0')] ).
cnf(661,plain,
( ~ rel_str(u)
| relation_of2(the_InternalRel(u),the_carrier(u),the_carrier(u)) ),
inference(res,[status(thm),theory(equality)],[257,235]),
[iquote('0:Res:257.1,235.0')] ).
cnf(1799,plain,
( ~ strict_rel_str(u)
| ~ rel_str(u)
| ~ equal(u,rel_str_of(v,w))
| ~ relation_of2(the_InternalRel(u),the_carrier(u),the_carrier(u))
| equal(the_carrier(u),v) ),
inference(spl,[status(thm),theory(equality)],[287,350]),
[iquote('0:SpL:287.2,350.0')] ).
cnf(1803,plain,
( ~ strict_rel_str(u)
| ~ rel_str(u)
| ~ equal(u,rel_str_of(v,w))
| equal(the_carrier(u),v) ),
inference(mrr,[status(thm)],[1799,661]),
[iquote('0:MRR:1799.3,661.1')] ).
cnf(2073,plain,
( ~ latt_str(boole_lattice(u))
| ~ lattice(boole_lattice(u))
| ~ element(v,the_carrier(boole_lattice(u)))
| ~ element(w,the_carrier(boole_lattice(u)))
| ~ below_refl(boole_lattice(u),w,v)
| empty_carrier(boole_lattice(u))
| related_reflexive(boole_POSet(u),w,v) ),
inference(spr,[status(thm),theory(equality)],[209,383]),
[iquote('0:SpR:209.0,383.6')] ).
cnf(2075,plain,
( ~ element(u,the_carrier(boole_lattice(v)))
| ~ element(w,the_carrier(boole_lattice(v)))
| ~ below_refl(boole_lattice(v),w,u)
| empty_carrier(boole_lattice(v))
| related_reflexive(boole_POSet(v),w,u) ),
inference(ssi,[status(thm)],[2073,153,157,152,158,148,146,145,134,156,155,154,144,150,149,147,151,116]),
[iquote('0:SSi:2073.1,2073.0,153.0,157.0,152.0,158.0,148.0,146.0,145.0,134.0,156.0,155.0,154.0,144.0,150.0,149.0,147.0,151.0,116.0,153.0,157.0,152.0,158.0,148.0,146.0,145.0,134.0,156.0,155.0,154.0,144.0,150.0,149.0,147.0,151.0,116.0')] ).
cnf(2076,plain,
( ~ element(u,the_carrier(boole_lattice(v)))
| ~ element(w,the_carrier(boole_lattice(v)))
| ~ below_refl(boole_lattice(v),w,u)
| related_reflexive(boole_POSet(v),w,u) ),
inference(mrr,[status(thm)],[2075,194]),
[iquote('0:MRR:2075.3,194.0')] ).
cnf(2098,plain,
( ~ latt_str(boole_lattice(u))
| ~ lattice(boole_lattice(u))
| ~ element(v,the_carrier(boole_lattice(u)))
| ~ element(w,the_carrier(boole_lattice(u)))
| ~ related_reflexive(boole_POSet(u),w,v)
| empty_carrier(boole_lattice(u))
| below_refl(boole_lattice(u),w,v) ),
inference(spl,[status(thm),theory(equality)],[209,382]),
[iquote('0:SpL:209.0,382.4')] ).
cnf(2102,plain,
( ~ element(u,the_carrier(boole_lattice(v)))
| ~ element(w,the_carrier(boole_lattice(v)))
| ~ related_reflexive(boole_POSet(v),w,u)
| empty_carrier(boole_lattice(v))
| below_refl(boole_lattice(v),w,u) ),
inference(ssi,[status(thm)],[2098,153,157,152,158,148,146,145,134,156,155,154,144,150,149,147,151,116]),
[iquote('0:SSi:2098.1,2098.0,153.0,157.0,152.0,158.0,148.0,146.0,145.0,134.0,156.0,155.0,154.0,144.0,150.0,149.0,147.0,151.0,116.0,153.0,157.0,152.0,158.0,148.0,146.0,145.0,134.0,156.0,155.0,154.0,144.0,150.0,149.0,147.0,151.0,116.0')] ).
cnf(2103,plain,
( ~ element(u,the_carrier(boole_lattice(v)))
| ~ element(w,the_carrier(boole_lattice(v)))
| ~ related_reflexive(boole_POSet(v),w,u)
| below_refl(boole_lattice(v),w,u) ),
inference(mrr,[status(thm)],[2102,194]),
[iquote('0:MRR:2102.3,194.0')] ).
cnf(2109,plain,
( ~ latt_str(boole_lattice(u))
| ~ join_absorbing(boole_lattice(u))
| ~ meet_absorbing(boole_lattice(u))
| ~ meet_commutative(boole_lattice(u))
| ~ element(v,the_carrier(boole_lattice(u)))
| ~ element(w,the_carrier(boole_lattice(u)))
| ~ below_refl(boole_lattice(u),w,v)
| ~ element(v,the_carrier(boole_lattice(u)))
| ~ element(w,the_carrier(boole_lattice(u)))
| empty_carrier(boole_lattice(u))
| subset(w,v) ),
inference(res,[status(thm),theory(equality)],[371,357]),
[iquote('0:Res:371.8,357.2')] ).
cnf(2110,plain,
( ~ latt_str(boole_lattice(u))
| ~ join_absorbing(boole_lattice(u))
| ~ meet_absorbing(boole_lattice(u))
| ~ meet_commutative(boole_lattice(u))
| ~ below_refl(boole_lattice(u),v,w)
| ~ element(w,the_carrier(boole_lattice(u)))
| ~ element(v,the_carrier(boole_lattice(u)))
| empty_carrier(boole_lattice(u))
| subset(v,w) ),
inference(obv,[status(thm),theory(equality)],[2109]),
[iquote('0:Obv:2109.5')] ).
cnf(2111,plain,
( ~ below_refl(boole_lattice(u),v,w)
| ~ element(w,the_carrier(boole_lattice(u)))
| ~ element(v,the_carrier(boole_lattice(u)))
| empty_carrier(boole_lattice(u))
| subset(v,w) ),
inference(ssi,[status(thm)],[2110,153,157,152,158,148,146,145,134,156,155,154,144,150,149,147,151,116]),
[iquote('0:SSi:2110.3,2110.2,2110.1,2110.0,153.0,157.0,152.0,158.0,148.0,146.0,145.0,134.0,156.0,155.0,154.0,144.0,150.0,149.0,147.0,151.0,116.0,153.0,157.0,152.0,158.0,148.0,146.0,145.0,134.0,156.0,155.0,154.0,144.0,150.0,149.0,147.0,151.0,116.0,153.0,157.0,152.0,158.0,148.0,146.0,145.0,134.0,156.0,155.0,154.0,144.0,150.0,149.0,147.0,151.0,116.0,153.0,157.0,152.0,158.0,148.0,146.0,145.0,134.0,156.0,155.0,154.0,144.0,150.0,149.0,147.0,151.0,116.0')] ).
cnf(2112,plain,
( ~ below_refl(boole_lattice(u),v,w)
| ~ element(w,the_carrier(boole_lattice(u)))
| ~ element(v,the_carrier(boole_lattice(u)))
| subset(v,w) ),
inference(mrr,[status(thm)],[2111,194]),
[iquote('0:MRR:2111.3,194.0')] ).
cnf(2144,plain,
( ~ latt_str(boole_lattice(u))
| ~ join_absorbing(boole_lattice(u))
| ~ meet_absorbing(boole_lattice(u))
| ~ meet_commutative(boole_lattice(u))
| ~ subset(v,w)
| ~ element(w,the_carrier(boole_lattice(u)))
| ~ element(v,the_carrier(boole_lattice(u)))
| ~ element(w,the_carrier(boole_lattice(u)))
| ~ element(v,the_carrier(boole_lattice(u)))
| empty_carrier(boole_lattice(u))
| below_refl(boole_lattice(u),v,w) ),
inference(res,[status(thm),theory(equality)],[356,370]),
[iquote('0:Res:356.3,370.6')] ).
cnf(2146,plain,
( ~ latt_str(boole_lattice(u))
| ~ join_absorbing(boole_lattice(u))
| ~ meet_absorbing(boole_lattice(u))
| ~ meet_commutative(boole_lattice(u))
| ~ subset(v,w)
| ~ element(w,the_carrier(boole_lattice(u)))
| ~ element(v,the_carrier(boole_lattice(u)))
| empty_carrier(boole_lattice(u))
| below_refl(boole_lattice(u),v,w) ),
inference(obv,[status(thm),theory(equality)],[2144]),
[iquote('0:Obv:2144.6')] ).
cnf(2147,plain,
( ~ subset(u,v)
| ~ element(v,the_carrier(boole_lattice(w)))
| ~ element(u,the_carrier(boole_lattice(w)))
| empty_carrier(boole_lattice(w))
| below_refl(boole_lattice(w),u,v) ),
inference(ssi,[status(thm)],[2146,153,157,152,158,148,146,145,134,156,155,154,144,150,149,147,151,116]),
[iquote('0:SSi:2146.3,2146.2,2146.1,2146.0,153.0,157.0,152.0,158.0,148.0,146.0,145.0,134.0,156.0,155.0,154.0,144.0,150.0,149.0,147.0,151.0,116.0,153.0,157.0,152.0,158.0,148.0,146.0,145.0,134.0,156.0,155.0,154.0,144.0,150.0,149.0,147.0,151.0,116.0,153.0,157.0,152.0,158.0,148.0,146.0,145.0,134.0,156.0,155.0,154.0,144.0,150.0,149.0,147.0,151.0,116.0,153.0,157.0,152.0,158.0,148.0,146.0,145.0,134.0,156.0,155.0,154.0,144.0,150.0,149.0,147.0,151.0,116.0')] ).
cnf(2148,plain,
( ~ subset(u,v)
| ~ element(v,the_carrier(boole_lattice(w)))
| ~ element(u,the_carrier(boole_lattice(w)))
| below_refl(boole_lattice(w),u,v) ),
inference(mrr,[status(thm)],[2147,194]),
[iquote('0:MRR:2147.3,194.0')] ).
cnf(2869,plain,
( ~ latt_str(u)
| ~ lattice(u)
| ~ strict_rel_str(v)
| ~ rel_str(v)
| ~ equal(v,poset_of_lattice(u))
| empty_carrier(u)
| equal(the_carrier(v),the_carrier(u)) ),
inference(spl,[status(thm),theory(equality)],[349,1803]),
[iquote('0:SpL:349.3,1803.2')] ).
cnf(5542,plain,
( ~ element(skc26,the_carrier(boole_lattice(skc24)))
| ~ element(skc25,the_carrier(boole_lattice(skc24)))
| below_refl(boole_lattice(skc24),skc25,skc26) ),
inference(res,[status(thm),theory(equality)],[534,2103]),
[iquote('1:Res:534.0,2103.2')] ).
cnf(11356,plain,
( ~ element(skc26,the_carrier(boole_lattice(skc24)))
| ~ element(skc25,the_carrier(boole_lattice(skc24)))
| ~ element(skc26,the_carrier(boole_lattice(skc24)))
| ~ element(skc25,the_carrier(boole_lattice(skc24)))
| subset(skc25,skc26) ),
inference(res,[status(thm),theory(equality)],[5542,2112]),
[iquote('1:Res:5542.2,2112.0')] ).
cnf(11357,plain,
( ~ element(skc26,the_carrier(boole_lattice(skc24)))
| ~ element(skc25,the_carrier(boole_lattice(skc24)))
| subset(skc25,skc26) ),
inference(obv,[status(thm),theory(equality)],[11356]),
[iquote('1:Obv:11356.1')] ).
cnf(11358,plain,
( ~ element(skc26,the_carrier(boole_lattice(skc24)))
| ~ element(skc25,the_carrier(boole_lattice(skc24))) ),
inference(mrr,[status(thm)],[11357,535]),
[iquote('1:MRR:11357.2,535.0')] ).
cnf(13490,plain,
( ~ latt_str(u)
| ~ lattice(u)
| ~ strict_rel_str(poset_of_lattice(u))
| ~ rel_str(poset_of_lattice(u))
| empty_carrier(u)
| equal(the_carrier(poset_of_lattice(u)),the_carrier(u)) ),
inference(eqr,[status(thm),theory(equality)],[2869]),
[iquote('0:EqR:2869.4')] ).
cnf(13492,plain,
( ~ latt_str(u)
| ~ lattice(u)
| empty_carrier(u)
| equal(the_carrier(poset_of_lattice(u)),the_carrier(u)) ),
inference(mrr,[status(thm)],[13490,276,266]),
[iquote('0:MRR:13490.2,13490.3,276.3,266.3')] ).
cnf(13558,plain,
( ~ latt_str(boole_lattice(u))
| ~ lattice(boole_lattice(u))
| empty_carrier(boole_lattice(u))
| equal(the_carrier(boole_lattice(u)),the_carrier(boole_POSet(u))) ),
inference(spr,[status(thm),theory(equality)],[209,13492]),
[iquote('0:SpR:209.0,13492.3')] ).
cnf(13584,plain,
( empty_carrier(boole_lattice(u))
| equal(the_carrier(boole_lattice(u)),the_carrier(boole_POSet(u))) ),
inference(ssi,[status(thm)],[13558,153,157,152,158,148,146,145,134,156,155,154,144,150,149,147,151,116]),
[iquote('0:SSi:13558.1,13558.0,153.0,157.0,152.0,158.0,148.0,146.0,145.0,134.0,156.0,155.0,154.0,144.0,150.0,149.0,147.0,151.0,116.0,153.0,157.0,152.0,158.0,148.0,146.0,145.0,134.0,156.0,155.0,154.0,144.0,150.0,149.0,147.0,151.0,116.0')] ).
cnf(13585,plain,
equal(the_carrier(boole_lattice(u)),the_carrier(boole_POSet(u))),
inference(mrr,[status(thm)],[13584,194]),
[iquote('0:MRR:13584.0,194.0')] ).
cnf(13586,plain,
( ~ element(skc26,the_carrier(boole_POSet(skc24)))
| ~ element(skc25,the_carrier(boole_lattice(skc24))) ),
inference(rew,[status(thm),theory(equality)],[13585,11358]),
[iquote('1:Rew:13585.0,11358.0')] ).
cnf(13609,plain,
( ~ element(u,the_carrier(boole_POSet(v)))
| ~ element(w,the_carrier(boole_lattice(v)))
| ~ below_refl(boole_lattice(v),w,u)
| related_reflexive(boole_POSet(v),w,u) ),
inference(rew,[status(thm),theory(equality)],[13585,2076]),
[iquote('0:Rew:13585.0,2076.0')] ).
cnf(13614,plain,
( ~ subset(u,v)
| ~ element(v,the_carrier(boole_POSet(w)))
| ~ element(u,the_carrier(boole_lattice(w)))
| below_refl(boole_lattice(w),u,v) ),
inference(rew,[status(thm),theory(equality)],[13585,2148]),
[iquote('0:Rew:13585.0,2148.1')] ).
cnf(13725,plain,
( ~ element(skc26,the_carrier(boole_POSet(skc24)))
| ~ element(skc25,the_carrier(boole_POSet(skc24))) ),
inference(rew,[status(thm),theory(equality)],[13585,13586]),
[iquote('1:Rew:13585.0,13586.1')] ).
cnf(13726,plain,
$false,
inference(mrr,[status(thm)],[13725,199,200]),
[iquote('1:MRR:13725.0,13725.1,199.0,200.0')] ).
cnf(13760,plain,
( ~ subset(u,v)
| ~ element(v,the_carrier(boole_POSet(w)))
| ~ element(u,the_carrier(boole_POSet(w)))
| below_refl(boole_lattice(w),u,v) ),
inference(rew,[status(thm),theory(equality)],[13585,13614]),
[iquote('0:Rew:13585.0,13614.2')] ).
cnf(13805,plain,
( ~ element(u,the_carrier(boole_POSet(v)))
| ~ element(w,the_carrier(boole_POSet(v)))
| ~ below_refl(boole_lattice(v),w,u)
| related_reflexive(boole_POSet(v),w,u) ),
inference(rew,[status(thm),theory(equality)],[13585,13609]),
[iquote('0:Rew:13585.0,13609.1')] ).
cnf(13904,plain,
~ related_reflexive(boole_POSet(skc24),skc25,skc26),
inference(spt,[spt(split,[position(sa)])],[13726,534]),
[iquote('1:Spt:13726.0,221.1,534.0')] ).
cnf(13905,plain,
subset(skc25,skc26),
inference(spt,[spt(split,[position(s2)])],[221]),
[iquote('1:Spt:13726.0,221.0')] ).
cnf(14217,plain,
( ~ element(skc26,the_carrier(boole_POSet(skc24)))
| ~ element(skc25,the_carrier(boole_POSet(skc24)))
| ~ below_refl(boole_lattice(skc24),skc25,skc26) ),
inference(res,[status(thm),theory(equality)],[13805,13904]),
[iquote('1:Res:13805.3,13904.0')] ).
cnf(14224,plain,
~ below_refl(boole_lattice(skc24),skc25,skc26),
inference(mrr,[status(thm)],[14217,199,200]),
[iquote('1:MRR:14217.0,14217.1,199.0,200.0')] ).
cnf(14230,plain,
( ~ subset(skc25,skc26)
| ~ element(skc26,the_carrier(boole_POSet(skc24)))
| ~ element(skc25,the_carrier(boole_POSet(skc24))) ),
inference(res,[status(thm),theory(equality)],[13760,14224]),
[iquote('1:Res:13760.3,14224.0')] ).
cnf(14231,plain,
$false,
inference(mrr,[status(thm)],[14230,13905,199,200]),
[iquote('1:MRR:14230.0,14230.1,14230.2,13905.0,199.0,200.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU369+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 19:53:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 5.54/5.76
% 5.54/5.76 SPASS V 3.9
% 5.54/5.76 SPASS beiseite: Proof found.
% 5.54/5.76 % SZS status Theorem
% 5.54/5.76 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.54/5.76 SPASS derived 10551 clauses, backtracked 61 clauses, performed 2 splits and kept 5254 clauses.
% 5.54/5.76 SPASS allocated 110629 KBytes.
% 5.54/5.76 SPASS spent 0:00:05.41 on the problem.
% 5.54/5.76 0:00:00.04 for the input.
% 5.54/5.76 0:00:00.06 for the FLOTTER CNF translation.
% 5.54/5.76 0:00:00.18 for inferences.
% 5.54/5.76 0:00:00.01 for the backtracking.
% 5.54/5.76 0:00:04.99 for the reduction.
% 5.54/5.76
% 5.54/5.76
% 5.54/5.76 Here is a proof with depth 4, length 81 :
% 5.54/5.76 % SZS output start Refutation
% See solution above
% 5.73/5.90 Formulae used in the proof : dt_k1_lattice3 fc1_knaster fc3_lattice3 t2_yellow_1 d2_yellow_1 redefinition_m2_relset_1 dt_u1_orders_2 dt_k3_lattice3 fc4_lattice3 abstractness_v1_orders_2 d2_lattice3 free_g1_orders_2 d3_lattice3 t2_lattice3 t7_lattice3 redefinition_r3_lattices
% 5.73/5.90
%------------------------------------------------------------------------------