TSTP Solution File: SEU358+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU358+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n006.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 : 300s
% DateTime : Thu Aug 31 17:58:28 EDT 2023
% Result : Theorem 112.80s 16.54s
% Output : Refutation 112.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 48
% Syntax : Number of formulae : 499 ( 30 unt; 0 def)
% Number of atoms : 2444 ( 176 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 3304 (1359 ~;1520 |; 301 &)
% ( 50 <=>; 74 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 44 ( 42 usr; 11 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 2 con; 0-3 aty)
% Number of variables : 750 (; 708 !; 42 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f195074,plain,
$false,
inference(avatar_sat_refutation,[],[f747,f2209,f2226,f2230,f190984,f191005,f191022,f191026,f193146,f194053,f195034]) ).
fof(f195034,plain,
( ~ spl29_15
| ~ spl29_16
| ~ spl29_17 ),
inference(avatar_contradiction_clause,[],[f195033]) ).
fof(f195033,plain,
( $false
| ~ spl29_15
| ~ spl29_16
| ~ spl29_17 ),
inference(subsumption_resolution,[],[f195032,f194215]) ).
fof(f194215,plain,
( ~ related(poset_of_lattice(sK0),join_of_latt_set(sK0,sK1),sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))
| ~ spl29_17 ),
inference(subsumption_resolution,[],[f194214,f624]) ).
fof(f624,plain,
! [X64] : latt_element_smaller(sK0,join_of_latt_set(sK0,X64),X64),
inference(subsumption_resolution,[],[f623,f280]) ).
fof(f280,plain,
lattice(sK0),
inference(cnf_transformation,[],[f199]) ).
fof(f199,plain,
( ( meet_of_latt_set(sK0,sK1) != meet_on_relstr(poset_of_lattice(sK0),sK1)
| join_of_latt_set(sK0,sK1) != join_on_relstr(poset_of_lattice(sK0),sK1) )
& latt_str(sK0)
& complete_latt_str(sK0)
& lattice(sK0)
& ~ empty_carrier(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f98,f198,f197]) ).
fof(f197,plain,
( ? [X0] :
( ? [X1] :
( meet_of_latt_set(X0,X1) != meet_on_relstr(poset_of_lattice(X0),X1)
| join_of_latt_set(X0,X1) != join_on_relstr(poset_of_lattice(X0),X1) )
& latt_str(X0)
& complete_latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ( ? [X1] :
( meet_of_latt_set(sK0,X1) != meet_on_relstr(poset_of_lattice(sK0),X1)
| join_of_latt_set(sK0,X1) != join_on_relstr(poset_of_lattice(sK0),X1) )
& latt_str(sK0)
& complete_latt_str(sK0)
& lattice(sK0)
& ~ empty_carrier(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f198,plain,
( ? [X1] :
( meet_of_latt_set(sK0,X1) != meet_on_relstr(poset_of_lattice(sK0),X1)
| join_of_latt_set(sK0,X1) != join_on_relstr(poset_of_lattice(sK0),X1) )
=> ( meet_of_latt_set(sK0,sK1) != meet_on_relstr(poset_of_lattice(sK0),sK1)
| join_of_latt_set(sK0,sK1) != join_on_relstr(poset_of_lattice(sK0),sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( meet_of_latt_set(X0,X1) != meet_on_relstr(poset_of_lattice(X0),X1)
| join_of_latt_set(X0,X1) != join_on_relstr(poset_of_lattice(X0),X1) )
& latt_str(X0)
& complete_latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f97]) ).
fof(f97,plain,
? [X0] :
( ? [X1] :
( meet_of_latt_set(X0,X1) != meet_on_relstr(poset_of_lattice(X0),X1)
| join_of_latt_set(X0,X1) != join_on_relstr(poset_of_lattice(X0),X1) )
& latt_str(X0)
& complete_latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,negated_conjecture,
~ ! [X0] :
( ( latt_str(X0)
& complete_latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( meet_of_latt_set(X0,X1) = meet_on_relstr(poset_of_lattice(X0),X1)
& join_of_latt_set(X0,X1) = join_on_relstr(poset_of_lattice(X0),X1) ) ),
inference(negated_conjecture,[],[f75]) ).
fof(f75,conjecture,
! [X0] :
( ( latt_str(X0)
& complete_latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( meet_of_latt_set(X0,X1) = meet_on_relstr(poset_of_lattice(X0),X1)
& join_of_latt_set(X0,X1) = join_on_relstr(poset_of_lattice(X0),X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',t29_yellow_0) ).
fof(f623,plain,
! [X64] :
( latt_element_smaller(sK0,join_of_latt_set(sK0,X64),X64)
| ~ lattice(sK0) ),
inference(subsumption_resolution,[],[f622,f281]) ).
fof(f281,plain,
complete_latt_str(sK0),
inference(cnf_transformation,[],[f199]) ).
fof(f622,plain,
! [X64] :
( latt_element_smaller(sK0,join_of_latt_set(sK0,X64),X64)
| ~ complete_latt_str(sK0)
| ~ lattice(sK0) ),
inference(subsumption_resolution,[],[f621,f282]) ).
fof(f282,plain,
latt_str(sK0),
inference(cnf_transformation,[],[f199]) ).
fof(f621,plain,
! [X64] :
( latt_element_smaller(sK0,join_of_latt_set(sK0,X64),X64)
| ~ latt_str(sK0)
| ~ complete_latt_str(sK0)
| ~ lattice(sK0) ),
inference(subsumption_resolution,[],[f510,f582]) ).
fof(f582,plain,
! [X31] : element(join_of_latt_set(sK0,X31),the_carrier(sK0)),
inference(subsumption_resolution,[],[f492,f282]) ).
fof(f492,plain,
! [X31] :
( element(join_of_latt_set(sK0,X31),the_carrier(sK0))
| ~ latt_str(sK0) ),
inference(resolution,[],[f279,f389]) ).
fof(f389,plain,
! [X0,X1] :
( element(join_of_latt_set(X0,X1),the_carrier(X0))
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f172,plain,
! [X0,X1] :
( element(join_of_latt_set(X0,X1),the_carrier(X0))
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f171]) ).
fof(f171,plain,
! [X0,X1] :
( element(join_of_latt_set(X0,X1),the_carrier(X0))
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( ( latt_str(X0)
& ~ empty_carrier(X0) )
=> element(join_of_latt_set(X0,X1),the_carrier(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',dt_k15_lattice3) ).
fof(f279,plain,
~ empty_carrier(sK0),
inference(cnf_transformation,[],[f199]) ).
fof(f510,plain,
! [X64] :
( latt_element_smaller(sK0,join_of_latt_set(sK0,X64),X64)
| ~ element(join_of_latt_set(sK0,X64),the_carrier(sK0))
| ~ latt_str(sK0)
| ~ complete_latt_str(sK0)
| ~ lattice(sK0) ),
inference(resolution,[],[f279,f450]) ).
fof(f450,plain,
! [X0,X1] :
( latt_element_smaller(X0,join_of_latt_set(X0,X1),X1)
| ~ element(join_of_latt_set(X0,X1),the_carrier(X0))
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(duplicate_literal_removal,[],[f444]) ).
fof(f444,plain,
! [X0,X1] :
( latt_element_smaller(X0,join_of_latt_set(X0,X1),X1)
| ~ element(join_of_latt_set(X0,X1),the_carrier(X0))
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(equality_resolution,[],[f341]) ).
fof(f341,plain,
! [X2,X0,X1] :
( latt_element_smaller(X0,X2,X1)
| join_of_latt_set(X0,X1) != X2
| ~ element(X2,the_carrier(X0))
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f224]) ).
fof(f224,plain,
! [X0] :
( ! [X1,X2] :
( ( ( join_of_latt_set(X0,X1) = X2
| ( ~ below(X0,X2,sK7(X0,X1,X2))
& latt_element_smaller(X0,sK7(X0,X1,X2),X1)
& element(sK7(X0,X1,X2),the_carrier(X0)) )
| ~ latt_element_smaller(X0,X2,X1) )
& ( ( ! [X4] :
( below(X0,X2,X4)
| ~ latt_element_smaller(X0,X4,X1)
| ~ element(X4,the_carrier(X0)) )
& latt_element_smaller(X0,X2,X1) )
| join_of_latt_set(X0,X1) != X2 ) )
| ~ element(X2,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f222,f223]) ).
fof(f223,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ below(X0,X2,X3)
& latt_element_smaller(X0,X3,X1)
& element(X3,the_carrier(X0)) )
=> ( ~ below(X0,X2,sK7(X0,X1,X2))
& latt_element_smaller(X0,sK7(X0,X1,X2),X1)
& element(sK7(X0,X1,X2),the_carrier(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f222,plain,
! [X0] :
( ! [X1,X2] :
( ( ( join_of_latt_set(X0,X1) = X2
| ? [X3] :
( ~ below(X0,X2,X3)
& latt_element_smaller(X0,X3,X1)
& element(X3,the_carrier(X0)) )
| ~ latt_element_smaller(X0,X2,X1) )
& ( ( ! [X4] :
( below(X0,X2,X4)
| ~ latt_element_smaller(X0,X4,X1)
| ~ element(X4,the_carrier(X0)) )
& latt_element_smaller(X0,X2,X1) )
| join_of_latt_set(X0,X1) != X2 ) )
| ~ element(X2,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(rectify,[],[f221]) ).
fof(f221,plain,
! [X0] :
( ! [X1,X2] :
( ( ( join_of_latt_set(X0,X1) = X2
| ? [X3] :
( ~ below(X0,X2,X3)
& latt_element_smaller(X0,X3,X1)
& element(X3,the_carrier(X0)) )
| ~ latt_element_smaller(X0,X2,X1) )
& ( ( ! [X3] :
( below(X0,X2,X3)
| ~ latt_element_smaller(X0,X3,X1)
| ~ element(X3,the_carrier(X0)) )
& latt_element_smaller(X0,X2,X1) )
| join_of_latt_set(X0,X1) != X2 ) )
| ~ element(X2,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f220]) ).
fof(f220,plain,
! [X0] :
( ! [X1,X2] :
( ( ( join_of_latt_set(X0,X1) = X2
| ? [X3] :
( ~ below(X0,X2,X3)
& latt_element_smaller(X0,X3,X1)
& element(X3,the_carrier(X0)) )
| ~ latt_element_smaller(X0,X2,X1) )
& ( ( ! [X3] :
( below(X0,X2,X3)
| ~ latt_element_smaller(X0,X3,X1)
| ~ element(X3,the_carrier(X0)) )
& latt_element_smaller(X0,X2,X1) )
| join_of_latt_set(X0,X1) != X2 ) )
| ~ element(X2,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0] :
( ! [X1,X2] :
( ( join_of_latt_set(X0,X1) = X2
<=> ( ! [X3] :
( below(X0,X2,X3)
| ~ latt_element_smaller(X0,X3,X1)
| ~ element(X3,the_carrier(X0)) )
& latt_element_smaller(X0,X2,X1) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f135]) ).
fof(f135,plain,
! [X0] :
( ! [X1,X2] :
( ( join_of_latt_set(X0,X1) = X2
<=> ( ! [X3] :
( below(X0,X2,X3)
| ~ latt_element_smaller(X0,X3,X1)
| ~ element(X3,the_carrier(X0)) )
& latt_element_smaller(X0,X2,X1) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ( latt_str(X0)
& ~ empty_carrier(X0) )
=> ( ( latt_str(X0)
& complete_latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ! [X1,X2] :
( element(X2,the_carrier(X0))
=> ( join_of_latt_set(X0,X1) = X2
<=> ( ! [X3] :
( element(X3,the_carrier(X0))
=> ( latt_element_smaller(X0,X3,X1)
=> below(X0,X2,X3) ) )
& latt_element_smaller(X0,X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',d21_lattice3) ).
fof(f194214,plain,
( ~ latt_element_smaller(sK0,join_of_latt_set(sK0,sK1),sK1)
| ~ related(poset_of_lattice(sK0),join_of_latt_set(sK0,sK1),sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))
| ~ spl29_17 ),
inference(forward_literal_rewriting,[],[f194213,f1057]) ).
fof(f1057,plain,
! [X48,X47] :
( ~ latt_element_smaller(sK0,join_of_latt_set(sK0,X48),X47)
| relstr_set_smaller(poset_of_lattice(sK0),X47,join_of_latt_set(sK0,X48)) ),
inference(forward_demodulation,[],[f1056,f1033]) ).
fof(f1033,plain,
! [X21] : join_of_latt_set(sK0,X21) = cast_to_el_of_LattPOSet(sK0,join_of_latt_set(sK0,X21)),
inference(subsumption_resolution,[],[f1032,f279]) ).
fof(f1032,plain,
! [X21] :
( join_of_latt_set(sK0,X21) = cast_to_el_of_LattPOSet(sK0,join_of_latt_set(sK0,X21))
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f1031,f280]) ).
fof(f1031,plain,
! [X21] :
( join_of_latt_set(sK0,X21) = cast_to_el_of_LattPOSet(sK0,join_of_latt_set(sK0,X21))
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f976,f282]) ).
fof(f976,plain,
! [X21] :
( join_of_latt_set(sK0,X21) = cast_to_el_of_LattPOSet(sK0,join_of_latt_set(sK0,X21))
| ~ latt_str(sK0)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(resolution,[],[f582,f337]) ).
fof(f337,plain,
! [X0,X1] :
( cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f129]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( cast_to_el_of_LattPOSet(X0,X1) = X1
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> cast_to_el_of_LattPOSet(X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',d3_lattice3) ).
fof(f1056,plain,
! [X48,X47] :
( relstr_set_smaller(poset_of_lattice(sK0),X47,cast_to_el_of_LattPOSet(sK0,join_of_latt_set(sK0,X48)))
| ~ latt_element_smaller(sK0,join_of_latt_set(sK0,X48),X47) ),
inference(subsumption_resolution,[],[f1055,f279]) ).
fof(f1055,plain,
! [X48,X47] :
( relstr_set_smaller(poset_of_lattice(sK0),X47,cast_to_el_of_LattPOSet(sK0,join_of_latt_set(sK0,X48)))
| ~ latt_element_smaller(sK0,join_of_latt_set(sK0,X48),X47)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f1054,f280]) ).
fof(f1054,plain,
! [X48,X47] :
( relstr_set_smaller(poset_of_lattice(sK0),X47,cast_to_el_of_LattPOSet(sK0,join_of_latt_set(sK0,X48)))
| ~ latt_element_smaller(sK0,join_of_latt_set(sK0,X48),X47)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f990,f282]) ).
fof(f990,plain,
! [X48,X47] :
( relstr_set_smaller(poset_of_lattice(sK0),X47,cast_to_el_of_LattPOSet(sK0,join_of_latt_set(sK0,X48)))
| ~ latt_element_smaller(sK0,join_of_latt_set(sK0,X48),X47)
| ~ latt_str(sK0)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(resolution,[],[f582,f381]) ).
fof(f381,plain,
! [X2,X0,X1] :
( relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| ~ latt_element_smaller(X1,X2,X0)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f239]) ).
fof(f239,plain,
! [X0,X1] :
( ! [X2] :
( ( ( latt_element_smaller(X1,X2,X0)
| ~ relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) )
& ( relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| ~ latt_element_smaller(X1,X2,X0) ) )
| ~ element(X2,the_carrier(X1)) )
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(nnf_transformation,[],[f164]) ).
fof(f164,plain,
! [X0,X1] :
( ! [X2] :
( ( latt_element_smaller(X1,X2,X0)
<=> relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) )
| ~ element(X2,the_carrier(X1)) )
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(flattening,[],[f163]) ).
fof(f163,plain,
! [X0,X1] :
( ! [X2] :
( ( latt_element_smaller(X1,X2,X0)
<=> relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) )
| ~ element(X2,the_carrier(X1)) )
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,axiom,
! [X0,X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( latt_element_smaller(X1,X2,X0)
<=> relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',t30_lattice3) ).
fof(f194213,plain,
( ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1))
| ~ related(poset_of_lattice(sK0),join_of_latt_set(sK0,sK1),sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))
| ~ spl29_17 ),
inference(subsumption_resolution,[],[f194200,f582]) ).
fof(f194200,plain,
( ~ element(join_of_latt_set(sK0,sK1),the_carrier(sK0))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1))
| ~ related(poset_of_lattice(sK0),join_of_latt_set(sK0,sK1),sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))
| ~ spl29_17 ),
inference(equality_resolution,[],[f194164]) ).
fof(f194164,plain,
( ! [X2] :
( join_of_latt_set(sK0,sK1) != X2
| ~ element(X2,the_carrier(sK0))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X2)
| ~ related(poset_of_lattice(sK0),X2,sK5(poset_of_lattice(sK0),sK1,X2)) )
| ~ spl29_17 ),
inference(forward_demodulation,[],[f2229,f3900]) ).
fof(f3900,plain,
the_carrier(sK0) = the_carrier(poset_of_lattice(sK0)),
inference(trivial_inequality_removal,[],[f3899]) ).
fof(f3899,plain,
( poset_of_lattice(sK0) != poset_of_lattice(sK0)
| the_carrier(sK0) = the_carrier(poset_of_lattice(sK0)) ),
inference(superposition,[],[f1374,f837]) ).
fof(f837,plain,
poset_of_lattice(sK0) = rel_str_of(the_carrier(poset_of_lattice(sK0)),the_InternalRel(poset_of_lattice(sK0))),
inference(subsumption_resolution,[],[f836,f552]) ).
fof(f552,plain,
rel_str(poset_of_lattice(sK0)),
inference(subsumption_resolution,[],[f551,f280]) ).
fof(f551,plain,
( rel_str(poset_of_lattice(sK0))
| ~ lattice(sK0) ),
inference(subsumption_resolution,[],[f473,f282]) ).
fof(f473,plain,
( rel_str(poset_of_lattice(sK0))
| ~ latt_str(sK0)
| ~ lattice(sK0) ),
inference(resolution,[],[f279,f336]) ).
fof(f336,plain,
! [X0] :
( rel_str(poset_of_lattice(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0] :
( ( rel_str(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f127]) ).
fof(f127,plain,
! [X0] :
( ( rel_str(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ( rel_str(poset_of_lattice(X0))
& antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',dt_k3_lattice3) ).
fof(f836,plain,
( poset_of_lattice(sK0) = rel_str_of(the_carrier(poset_of_lattice(sK0)),the_InternalRel(poset_of_lattice(sK0)))
| ~ rel_str(poset_of_lattice(sK0)) ),
inference(resolution,[],[f533,f301]) ).
fof(f301,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f108]) ).
fof(f108,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( rel_str(X0)
=> ( strict_rel_str(X0)
=> rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',abstractness_v1_orders_2) ).
fof(f533,plain,
strict_rel_str(poset_of_lattice(sK0)),
inference(subsumption_resolution,[],[f532,f280]) ).
fof(f532,plain,
( strict_rel_str(poset_of_lattice(sK0))
| ~ lattice(sK0) ),
inference(subsumption_resolution,[],[f460,f282]) ).
fof(f460,plain,
( strict_rel_str(poset_of_lattice(sK0))
| ~ latt_str(sK0)
| ~ lattice(sK0) ),
inference(resolution,[],[f279,f323]) ).
fof(f323,plain,
! [X0] :
( strict_rel_str(poset_of_lattice(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0] :
( ( antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0))
& ~ empty_carrier(poset_of_lattice(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f123]) ).
fof(f123,plain,
! [X0] :
( ( antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0))
& ~ empty_carrier(poset_of_lattice(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ( antisymmetric_relstr(poset_of_lattice(X0))
& transitive_relstr(poset_of_lattice(X0))
& reflexive_relstr(poset_of_lattice(X0))
& strict_rel_str(poset_of_lattice(X0))
& ~ empty_carrier(poset_of_lattice(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',fc4_lattice3) ).
fof(f1374,plain,
! [X0,X1] :
( rel_str_of(X0,X1) != poset_of_lattice(sK0)
| the_carrier(sK0) = X0 ),
inference(forward_demodulation,[],[f1363,f529]) ).
fof(f529,plain,
poset_of_lattice(sK0) = rel_str_of(the_carrier(sK0),k2_lattice3(sK0)),
inference(subsumption_resolution,[],[f528,f280]) ).
fof(f528,plain,
( poset_of_lattice(sK0) = rel_str_of(the_carrier(sK0),k2_lattice3(sK0))
| ~ lattice(sK0) ),
inference(subsumption_resolution,[],[f458,f282]) ).
fof(f458,plain,
( poset_of_lattice(sK0) = rel_str_of(the_carrier(sK0),k2_lattice3(sK0))
| ~ latt_str(sK0)
| ~ lattice(sK0) ),
inference(resolution,[],[f279,f321]) ).
fof(f321,plain,
! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f121]) ).
fof(f121,plain,
! [X0] :
( poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> poset_of_lattice(X0) = rel_str_of(the_carrier(X0),k2_lattice3(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',d2_lattice3) ).
fof(f1363,plain,
! [X0,X1] :
( the_carrier(sK0) = X0
| rel_str_of(X0,X1) != rel_str_of(the_carrier(sK0),k2_lattice3(sK0)) ),
inference(resolution,[],[f550,f375]) ).
fof(f375,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| rel_str_of(X0,X1) != rel_str_of(X2,X3)
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( X1 = X3
& X0 = X2 )
| rel_str_of(X0,X1) != rel_str_of(X2,X3) )
| ~ relation_of2(X1,X0,X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0,X1] :
( relation_of2(X1,X0,X0)
=> ! [X2,X3] :
( rel_str_of(X0,X1) = rel_str_of(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',free_g1_orders_2) ).
fof(f550,plain,
relation_of2(k2_lattice3(sK0),the_carrier(sK0),the_carrier(sK0)),
inference(forward_literal_rewriting,[],[f549,f415]) ).
fof(f415,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f256]) ).
fof(f256,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f64,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',redefinition_m2_relset_1) ).
fof(f549,plain,
relation_of2_as_subset(k2_lattice3(sK0),the_carrier(sK0),the_carrier(sK0)),
inference(subsumption_resolution,[],[f548,f280]) ).
fof(f548,plain,
( relation_of2_as_subset(k2_lattice3(sK0),the_carrier(sK0),the_carrier(sK0))
| ~ lattice(sK0) ),
inference(subsumption_resolution,[],[f468,f282]) ).
fof(f468,plain,
( relation_of2_as_subset(k2_lattice3(sK0),the_carrier(sK0),the_carrier(sK0))
| ~ latt_str(sK0)
| ~ lattice(sK0) ),
inference(resolution,[],[f279,f331]) ).
fof(f331,plain,
! [X0] :
( relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0] :
( ( relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
& v1_partfun1(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
& transitive(k2_lattice3(X0))
& antisymmetric(k2_lattice3(X0))
& reflexive(k2_lattice3(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ( relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
& v1_partfun1(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
& transitive(k2_lattice3(X0))
& antisymmetric(k2_lattice3(X0))
& reflexive(k2_lattice3(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ( relation_of2_as_subset(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
& v1_partfun1(k2_lattice3(X0),the_carrier(X0),the_carrier(X0))
& transitive(k2_lattice3(X0))
& antisymmetric(k2_lattice3(X0))
& reflexive(k2_lattice3(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',dt_k2_lattice3) ).
fof(f2229,plain,
( ! [X2] :
( join_of_latt_set(sK0,sK1) != X2
| ~ element(X2,the_carrier(poset_of_lattice(sK0)))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X2)
| ~ related(poset_of_lattice(sK0),X2,sK5(poset_of_lattice(sK0),sK1,X2)) )
| ~ spl29_17 ),
inference(avatar_component_clause,[],[f2228]) ).
fof(f2228,plain,
( spl29_17
<=> ! [X2] :
( join_of_latt_set(sK0,sK1) != X2
| ~ element(X2,the_carrier(poset_of_lattice(sK0)))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X2)
| ~ related(poset_of_lattice(sK0),X2,sK5(poset_of_lattice(sK0),sK1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_17])]) ).
fof(f195032,plain,
( related(poset_of_lattice(sK0),join_of_latt_set(sK0,sK1),sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))
| ~ spl29_15
| ~ spl29_16 ),
inference(forward_literal_rewriting,[],[f195031,f194285]) ).
fof(f194285,plain,
( ! [X37] :
( related(poset_of_lattice(sK0),join_of_latt_set(sK0,X37),sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))
| ~ related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,X37),sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1))) )
| ~ spl29_15 ),
inference(resolution,[],[f194196,f4043]) ).
fof(f4043,plain,
! [X80,X81] :
( ~ element(X81,the_carrier(sK0))
| related(poset_of_lattice(sK0),join_of_latt_set(sK0,X80),X81)
| ~ related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,X80),X81) ),
inference(backward_demodulation,[],[f2412,f3900]) ).
fof(f2412,plain,
! [X80,X81] :
( related(poset_of_lattice(sK0),join_of_latt_set(sK0,X80),X81)
| ~ related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,X80),X81)
| ~ element(X81,the_carrier(poset_of_lattice(sK0))) ),
inference(subsumption_resolution,[],[f2411,f531]) ).
fof(f531,plain,
~ empty_carrier(poset_of_lattice(sK0)),
inference(subsumption_resolution,[],[f530,f280]) ).
fof(f530,plain,
( ~ empty_carrier(poset_of_lattice(sK0))
| ~ lattice(sK0) ),
inference(subsumption_resolution,[],[f459,f282]) ).
fof(f459,plain,
( ~ empty_carrier(poset_of_lattice(sK0))
| ~ latt_str(sK0)
| ~ lattice(sK0) ),
inference(resolution,[],[f279,f322]) ).
fof(f322,plain,
! [X0] :
( ~ empty_carrier(poset_of_lattice(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f2411,plain,
! [X80,X81] :
( related(poset_of_lattice(sK0),join_of_latt_set(sK0,X80),X81)
| ~ related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,X80),X81)
| ~ element(X81,the_carrier(poset_of_lattice(sK0)))
| empty_carrier(poset_of_lattice(sK0)) ),
inference(subsumption_resolution,[],[f2410,f535]) ).
fof(f535,plain,
reflexive_relstr(poset_of_lattice(sK0)),
inference(subsumption_resolution,[],[f534,f280]) ).
fof(f534,plain,
( reflexive_relstr(poset_of_lattice(sK0))
| ~ lattice(sK0) ),
inference(subsumption_resolution,[],[f461,f282]) ).
fof(f461,plain,
( reflexive_relstr(poset_of_lattice(sK0))
| ~ latt_str(sK0)
| ~ lattice(sK0) ),
inference(resolution,[],[f279,f324]) ).
fof(f324,plain,
! [X0] :
( reflexive_relstr(poset_of_lattice(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f2410,plain,
! [X80,X81] :
( related(poset_of_lattice(sK0),join_of_latt_set(sK0,X80),X81)
| ~ related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,X80),X81)
| ~ element(X81,the_carrier(poset_of_lattice(sK0)))
| ~ reflexive_relstr(poset_of_lattice(sK0))
| empty_carrier(poset_of_lattice(sK0)) ),
inference(subsumption_resolution,[],[f2308,f552]) ).
fof(f2308,plain,
! [X80,X81] :
( related(poset_of_lattice(sK0),join_of_latt_set(sK0,X80),X81)
| ~ related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,X80),X81)
| ~ element(X81,the_carrier(poset_of_lattice(sK0)))
| ~ rel_str(poset_of_lattice(sK0))
| ~ reflexive_relstr(poset_of_lattice(sK0))
| empty_carrier(poset_of_lattice(sK0)) ),
inference(resolution,[],[f1053,f412]) ).
fof(f412,plain,
! [X2,X0,X1] :
( related(X0,X1,X2)
| ~ related_reflexive(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f255]) ).
fof(f255,plain,
! [X0,X1,X2] :
( ( ( related_reflexive(X0,X1,X2)
| ~ related(X0,X1,X2) )
& ( related(X0,X1,X2)
| ~ related_reflexive(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f193]) ).
fof(f193,plain,
! [X0,X1,X2] :
( ( related_reflexive(X0,X1,X2)
<=> related(X0,X1,X2) )
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f192]) ).
fof(f192,plain,
! [X0,X1,X2] :
( ( related_reflexive(X0,X1,X2)
<=> related(X0,X1,X2) )
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ rel_str(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X0))
& element(X1,the_carrier(X0))
& rel_str(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( related_reflexive(X0,X1,X2)
<=> related(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',redefinition_r3_orders_2) ).
fof(f1053,plain,
! [X46] : element(join_of_latt_set(sK0,X46),the_carrier(poset_of_lattice(sK0))),
inference(forward_demodulation,[],[f1052,f1033]) ).
fof(f1052,plain,
! [X46] : element(cast_to_el_of_LattPOSet(sK0,join_of_latt_set(sK0,X46)),the_carrier(poset_of_lattice(sK0))),
inference(subsumption_resolution,[],[f1051,f279]) ).
fof(f1051,plain,
! [X46] :
( element(cast_to_el_of_LattPOSet(sK0,join_of_latt_set(sK0,X46)),the_carrier(poset_of_lattice(sK0)))
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f1050,f280]) ).
fof(f1050,plain,
! [X46] :
( element(cast_to_el_of_LattPOSet(sK0,join_of_latt_set(sK0,X46)),the_carrier(poset_of_lattice(sK0)))
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f989,f282]) ).
fof(f989,plain,
! [X46] :
( element(cast_to_el_of_LattPOSet(sK0,join_of_latt_set(sK0,X46)),the_carrier(poset_of_lattice(sK0)))
| ~ latt_str(sK0)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(resolution,[],[f582,f379]) ).
fof(f379,plain,
! [X0,X1] :
( element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
! [X0,X1] :
( element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f159]) ).
fof(f159,plain,
! [X0,X1] :
( element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0)))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0,X1] :
( ( element(X1,the_carrier(X0))
& latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> element(cast_to_el_of_LattPOSet(X0,X1),the_carrier(poset_of_lattice(X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',dt_k4_lattice3) ).
fof(f194196,plain,
( element(sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)),the_carrier(sK0))
| ~ spl29_15 ),
inference(subsumption_resolution,[],[f194195,f624]) ).
fof(f194195,plain,
( ~ latt_element_smaller(sK0,join_of_latt_set(sK0,sK1),sK1)
| element(sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)),the_carrier(sK0))
| ~ spl29_15 ),
inference(forward_literal_rewriting,[],[f194194,f1057]) ).
fof(f194194,plain,
( element(sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)),the_carrier(sK0))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1))
| ~ spl29_15 ),
inference(subsumption_resolution,[],[f194181,f582]) ).
fof(f194181,plain,
( ~ element(join_of_latt_set(sK0,sK1),the_carrier(sK0))
| element(sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)),the_carrier(sK0))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1))
| ~ spl29_15 ),
inference(equality_resolution,[],[f194167]) ).
fof(f194167,plain,
( ! [X0] :
( join_of_latt_set(sK0,sK1) != X0
| ~ element(X0,the_carrier(sK0))
| element(sK5(poset_of_lattice(sK0),sK1,X0),the_carrier(sK0))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X0) )
| ~ spl29_15 ),
inference(forward_demodulation,[],[f194166,f3900]) ).
fof(f194166,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK0))
| join_of_latt_set(sK0,sK1) != X0
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X0)
| element(sK5(poset_of_lattice(sK0),sK1,X0),the_carrier(poset_of_lattice(sK0))) )
| ~ spl29_15 ),
inference(forward_demodulation,[],[f2208,f3900]) ).
fof(f2208,plain,
( ! [X0] :
( join_of_latt_set(sK0,sK1) != X0
| ~ element(X0,the_carrier(poset_of_lattice(sK0)))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X0)
| element(sK5(poset_of_lattice(sK0),sK1,X0),the_carrier(poset_of_lattice(sK0))) )
| ~ spl29_15 ),
inference(avatar_component_clause,[],[f2207]) ).
fof(f2207,plain,
( spl29_15
<=> ! [X0] :
( join_of_latt_set(sK0,sK1) != X0
| ~ element(X0,the_carrier(poset_of_lattice(sK0)))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X0)
| element(sK5(poset_of_lattice(sK0),sK1,X0),the_carrier(poset_of_lattice(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_15])]) ).
fof(f195031,plain,
( related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,sK1),sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))
| ~ spl29_15
| ~ spl29_16 ),
inference(forward_demodulation,[],[f195030,f194235]) ).
fof(f194235,plain,
( sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)) = cast_to_el_of_LattPOSet(sK0,sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))
| ~ spl29_15 ),
inference(resolution,[],[f194196,f554]) ).
fof(f554,plain,
! [X6] :
( ~ element(X6,the_carrier(sK0))
| cast_to_el_of_LattPOSet(sK0,X6) = X6 ),
inference(subsumption_resolution,[],[f553,f280]) ).
fof(f553,plain,
! [X6] :
( cast_to_el_of_LattPOSet(sK0,X6) = X6
| ~ element(X6,the_carrier(sK0))
| ~ lattice(sK0) ),
inference(subsumption_resolution,[],[f474,f282]) ).
fof(f474,plain,
! [X6] :
( cast_to_el_of_LattPOSet(sK0,X6) = X6
| ~ element(X6,the_carrier(sK0))
| ~ latt_str(sK0)
| ~ lattice(sK0) ),
inference(resolution,[],[f279,f337]) ).
fof(f195030,plain,
( related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,sK1),cast_to_el_of_LattPOSet(sK0,sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1))))
| ~ spl29_15
| ~ spl29_16 ),
inference(forward_demodulation,[],[f195029,f194471]) ).
fof(f194471,plain,
( sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)) = cast_to_el_of_lattice(sK0,sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))
| ~ spl29_15 ),
inference(forward_demodulation,[],[f194243,f194235]) ).
fof(f194243,plain,
( cast_to_el_of_LattPOSet(sK0,sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1))) = cast_to_el_of_lattice(sK0,cast_to_el_of_LattPOSet(sK0,sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1))))
| ~ spl29_15 ),
inference(resolution,[],[f194196,f1499]) ).
fof(f1499,plain,
! [X0] :
( ~ element(X0,the_carrier(sK0))
| cast_to_el_of_LattPOSet(sK0,X0) = cast_to_el_of_lattice(sK0,cast_to_el_of_LattPOSet(sK0,X0)) ),
inference(subsumption_resolution,[],[f1498,f279]) ).
fof(f1498,plain,
! [X0] :
( cast_to_el_of_LattPOSet(sK0,X0) = cast_to_el_of_lattice(sK0,cast_to_el_of_LattPOSet(sK0,X0))
| ~ element(X0,the_carrier(sK0))
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f1497,f280]) ).
fof(f1497,plain,
! [X0] :
( cast_to_el_of_LattPOSet(sK0,X0) = cast_to_el_of_lattice(sK0,cast_to_el_of_LattPOSet(sK0,X0))
| ~ element(X0,the_carrier(sK0))
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f1479,f282]) ).
fof(f1479,plain,
! [X0] :
( cast_to_el_of_LattPOSet(sK0,X0) = cast_to_el_of_lattice(sK0,cast_to_el_of_LattPOSet(sK0,X0))
| ~ element(X0,the_carrier(sK0))
| ~ latt_str(sK0)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(resolution,[],[f560,f379]) ).
fof(f560,plain,
! [X11] :
( ~ element(X11,the_carrier(poset_of_lattice(sK0)))
| cast_to_el_of_lattice(sK0,X11) = X11 ),
inference(subsumption_resolution,[],[f559,f280]) ).
fof(f559,plain,
! [X11] :
( cast_to_el_of_lattice(sK0,X11) = X11
| ~ element(X11,the_carrier(poset_of_lattice(sK0)))
| ~ lattice(sK0) ),
inference(subsumption_resolution,[],[f477,f282]) ).
fof(f477,plain,
! [X11] :
( cast_to_el_of_lattice(sK0,X11) = X11
| ~ element(X11,the_carrier(poset_of_lattice(sK0)))
| ~ latt_str(sK0)
| ~ lattice(sK0) ),
inference(resolution,[],[f279,f340]) ).
fof(f340,plain,
! [X0,X1] :
( cast_to_el_of_lattice(X0,X1) = X1
| ~ element(X1,the_carrier(poset_of_lattice(X0)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0] :
( ! [X1] :
( cast_to_el_of_lattice(X0,X1) = X1
| ~ element(X1,the_carrier(poset_of_lattice(X0))) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f133]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( cast_to_el_of_lattice(X0,X1) = X1
| ~ element(X1,the_carrier(poset_of_lattice(X0))) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(poset_of_lattice(X0)))
=> cast_to_el_of_lattice(X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',d4_lattice3) ).
fof(f195029,plain,
( related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,sK1),cast_to_el_of_LattPOSet(sK0,cast_to_el_of_lattice(sK0,sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))))
| ~ spl29_15
| ~ spl29_16 ),
inference(subsumption_resolution,[],[f194890,f194196]) ).
fof(f194890,plain,
( related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,sK1),cast_to_el_of_LattPOSet(sK0,cast_to_el_of_lattice(sK0,sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))))
| ~ element(sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)),the_carrier(sK0))
| ~ spl29_16 ),
inference(resolution,[],[f194234,f14569]) ).
fof(f14569,plain,
! [X8,X7] :
( ~ relstr_set_smaller(poset_of_lattice(sK0),X8,X7)
| related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,X8),cast_to_el_of_LattPOSet(sK0,cast_to_el_of_lattice(sK0,X7)))
| ~ element(X7,the_carrier(sK0)) ),
inference(subsumption_resolution,[],[f14568,f3903]) ).
fof(f3903,plain,
! [X14] :
( ~ element(X14,the_carrier(sK0))
| element(cast_to_el_of_lattice(sK0,X14),the_carrier(sK0)) ),
inference(backward_demodulation,[],[f565,f3900]) ).
fof(f565,plain,
! [X14] :
( ~ element(X14,the_carrier(poset_of_lattice(sK0)))
| element(cast_to_el_of_lattice(sK0,X14),the_carrier(sK0)) ),
inference(subsumption_resolution,[],[f564,f280]) ).
fof(f564,plain,
! [X14] :
( element(cast_to_el_of_lattice(sK0,X14),the_carrier(sK0))
| ~ element(X14,the_carrier(poset_of_lattice(sK0)))
| ~ lattice(sK0) ),
inference(subsumption_resolution,[],[f483,f282]) ).
fof(f483,plain,
! [X14] :
( element(cast_to_el_of_lattice(sK0,X14),the_carrier(sK0))
| ~ element(X14,the_carrier(poset_of_lattice(sK0)))
| ~ latt_str(sK0)
| ~ lattice(sK0) ),
inference(resolution,[],[f279,f380]) ).
fof(f380,plain,
! [X0,X1] :
( element(cast_to_el_of_lattice(X0,X1),the_carrier(X0))
| ~ element(X1,the_carrier(poset_of_lattice(X0)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f162]) ).
fof(f162,plain,
! [X0,X1] :
( element(cast_to_el_of_lattice(X0,X1),the_carrier(X0))
| ~ element(X1,the_carrier(poset_of_lattice(X0)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f161]) ).
fof(f161,plain,
! [X0,X1] :
( element(cast_to_el_of_lattice(X0,X1),the_carrier(X0))
| ~ element(X1,the_carrier(poset_of_lattice(X0)))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1] :
( ( element(X1,the_carrier(poset_of_lattice(X0)))
& latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> element(cast_to_el_of_lattice(X0,X1),the_carrier(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',dt_k5_lattice3) ).
fof(f14568,plain,
! [X8,X7] :
( ~ element(X7,the_carrier(sK0))
| ~ element(cast_to_el_of_lattice(sK0,X7),the_carrier(sK0))
| related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,X8),cast_to_el_of_LattPOSet(sK0,cast_to_el_of_lattice(sK0,X7)))
| ~ relstr_set_smaller(poset_of_lattice(sK0),X8,X7) ),
inference(forward_demodulation,[],[f14567,f3900]) ).
fof(f14567,plain,
! [X8,X7] :
( ~ element(cast_to_el_of_lattice(sK0,X7),the_carrier(sK0))
| related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,X8),cast_to_el_of_LattPOSet(sK0,cast_to_el_of_lattice(sK0,X7)))
| ~ relstr_set_smaller(poset_of_lattice(sK0),X8,X7)
| ~ element(X7,the_carrier(poset_of_lattice(sK0))) ),
inference(subsumption_resolution,[],[f14566,f279]) ).
fof(f14566,plain,
! [X8,X7] :
( ~ element(cast_to_el_of_lattice(sK0,X7),the_carrier(sK0))
| related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,X8),cast_to_el_of_LattPOSet(sK0,cast_to_el_of_lattice(sK0,X7)))
| ~ relstr_set_smaller(poset_of_lattice(sK0),X8,X7)
| ~ element(X7,the_carrier(poset_of_lattice(sK0)))
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f14565,f280]) ).
fof(f14565,plain,
! [X8,X7] :
( ~ element(cast_to_el_of_lattice(sK0,X7),the_carrier(sK0))
| related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,X8),cast_to_el_of_LattPOSet(sK0,cast_to_el_of_lattice(sK0,X7)))
| ~ relstr_set_smaller(poset_of_lattice(sK0),X8,X7)
| ~ element(X7,the_carrier(poset_of_lattice(sK0)))
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f14543,f282]) ).
fof(f14543,plain,
! [X8,X7] :
( ~ element(cast_to_el_of_lattice(sK0,X7),the_carrier(sK0))
| related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,X8),cast_to_el_of_LattPOSet(sK0,cast_to_el_of_lattice(sK0,X7)))
| ~ relstr_set_smaller(poset_of_lattice(sK0),X8,X7)
| ~ element(X7,the_carrier(poset_of_lattice(sK0)))
| ~ latt_str(sK0)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(resolution,[],[f7694,f385]) ).
fof(f385,plain,
! [X2,X0,X1] :
( latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0)
| ~ relstr_set_smaller(poset_of_lattice(X1),X0,X2)
| ~ element(X2,the_carrier(poset_of_lattice(X1)))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f241]) ).
fof(f241,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relstr_set_smaller(poset_of_lattice(X1),X0,X2)
| ~ latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) )
& ( latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0)
| ~ relstr_set_smaller(poset_of_lattice(X1),X0,X2) ) )
| ~ element(X2,the_carrier(poset_of_lattice(X1))) )
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(nnf_transformation,[],[f168]) ).
fof(f168,plain,
! [X0,X1] :
( ! [X2] :
( ( relstr_set_smaller(poset_of_lattice(X1),X0,X2)
<=> latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) )
| ~ element(X2,the_carrier(poset_of_lattice(X1))) )
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(flattening,[],[f167]) ).
fof(f167,plain,
! [X0,X1] :
( ! [X2] :
( ( relstr_set_smaller(poset_of_lattice(X1),X0,X2)
<=> latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) )
| ~ element(X2,the_carrier(poset_of_lattice(X1))) )
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(ennf_transformation,[],[f80]) ).
fof(f80,axiom,
! [X0,X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(poset_of_lattice(X1)))
=> ( relstr_set_smaller(poset_of_lattice(X1),X0,X2)
<=> latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',t31_lattice3) ).
fof(f7694,plain,
! [X2,X1] :
( ~ latt_element_smaller(sK0,X1,X2)
| ~ element(X1,the_carrier(sK0))
| related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,X2),cast_to_el_of_LattPOSet(sK0,X1)) ),
inference(forward_demodulation,[],[f7693,f1033]) ).
fof(f7693,plain,
! [X2,X1] :
( ~ element(X1,the_carrier(sK0))
| related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,join_of_latt_set(sK0,X2)),cast_to_el_of_LattPOSet(sK0,X1))
| ~ latt_element_smaller(sK0,X1,X2) ),
inference(subsumption_resolution,[],[f7692,f279]) ).
fof(f7692,plain,
! [X2,X1] :
( ~ element(X1,the_carrier(sK0))
| related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,join_of_latt_set(sK0,X2)),cast_to_el_of_LattPOSet(sK0,X1))
| ~ latt_element_smaller(sK0,X1,X2)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f7691,f280]) ).
fof(f7691,plain,
! [X2,X1] :
( ~ element(X1,the_carrier(sK0))
| related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,join_of_latt_set(sK0,X2)),cast_to_el_of_LattPOSet(sK0,X1))
| ~ latt_element_smaller(sK0,X1,X2)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f7690,f281]) ).
fof(f7690,plain,
! [X2,X1] :
( ~ element(X1,the_carrier(sK0))
| related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,join_of_latt_set(sK0,X2)),cast_to_el_of_LattPOSet(sK0,X1))
| ~ latt_element_smaller(sK0,X1,X2)
| ~ complete_latt_str(sK0)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f7689,f282]) ).
fof(f7689,plain,
! [X2,X1] :
( ~ element(X1,the_carrier(sK0))
| related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,join_of_latt_set(sK0,X2)),cast_to_el_of_LattPOSet(sK0,X1))
| ~ latt_element_smaller(sK0,X1,X2)
| ~ latt_str(sK0)
| ~ complete_latt_str(sK0)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f7687,f582]) ).
fof(f7687,plain,
! [X2,X1] :
( ~ element(X1,the_carrier(sK0))
| ~ element(join_of_latt_set(sK0,X2),the_carrier(sK0))
| related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,join_of_latt_set(sK0,X2)),cast_to_el_of_LattPOSet(sK0,X1))
| ~ latt_element_smaller(sK0,X1,X2)
| ~ latt_str(sK0)
| ~ complete_latt_str(sK0)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(duplicate_literal_removal,[],[f7684]) ).
fof(f7684,plain,
! [X2,X1] :
( ~ element(X1,the_carrier(sK0))
| ~ element(join_of_latt_set(sK0,X2),the_carrier(sK0))
| related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,join_of_latt_set(sK0,X2)),cast_to_el_of_LattPOSet(sK0,X1))
| ~ latt_element_smaller(sK0,X1,X2)
| ~ element(X1,the_carrier(sK0))
| ~ element(join_of_latt_set(sK0,X2),the_carrier(sK0))
| ~ latt_str(sK0)
| ~ complete_latt_str(sK0)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(resolution,[],[f2156,f449]) ).
fof(f449,plain,
! [X0,X1,X4] :
( below(X0,join_of_latt_set(X0,X1),X4)
| ~ latt_element_smaller(X0,X4,X1)
| ~ element(X4,the_carrier(X0))
| ~ element(join_of_latt_set(X0,X1),the_carrier(X0))
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(duplicate_literal_removal,[],[f443]) ).
fof(f443,plain,
! [X0,X1,X4] :
( below(X0,join_of_latt_set(X0,X1),X4)
| ~ latt_element_smaller(X0,X4,X1)
| ~ element(X4,the_carrier(X0))
| ~ element(join_of_latt_set(X0,X1),the_carrier(X0))
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(equality_resolution,[],[f342]) ).
fof(f342,plain,
! [X2,X0,X1,X4] :
( below(X0,X2,X4)
| ~ latt_element_smaller(X0,X4,X1)
| ~ element(X4,the_carrier(X0))
| join_of_latt_set(X0,X1) != X2
| ~ element(X2,the_carrier(X0))
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f224]) ).
fof(f2156,plain,
! [X2,X3] :
( ~ below(sK0,X2,X3)
| ~ element(X3,the_carrier(sK0))
| ~ element(X2,the_carrier(sK0))
| related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,X2),cast_to_el_of_LattPOSet(sK0,X3)) ),
inference(subsumption_resolution,[],[f2155,f279]) ).
fof(f2155,plain,
! [X2,X3] :
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,X2),cast_to_el_of_LattPOSet(sK0,X3))
| ~ element(X3,the_carrier(sK0))
| ~ element(X2,the_carrier(sK0))
| ~ below(sK0,X2,X3)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f2154,f512]) ).
fof(f512,plain,
meet_commutative(sK0),
inference(subsumption_resolution,[],[f511,f282]) ).
fof(f511,plain,
( meet_commutative(sK0)
| ~ latt_str(sK0) ),
inference(subsumption_resolution,[],[f451,f280]) ).
fof(f451,plain,
( meet_commutative(sK0)
| ~ lattice(sK0)
| ~ latt_str(sK0) ),
inference(resolution,[],[f279,f296]) ).
fof(f296,plain,
! [X0] :
( meet_commutative(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_commutative(X0)
& ~ empty_carrier(X0) )
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f104]) ).
fof(f104,plain,
! [X0] :
( ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_commutative(X0)
& ~ empty_carrier(X0) )
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0] :
( latt_str(X0)
=> ( ( lattice(X0)
& ~ empty_carrier(X0) )
=> ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_commutative(X0)
& ~ empty_carrier(X0) ) ) ),
inference(pure_predicate_removal,[],[f95]) ).
fof(f95,plain,
! [X0] :
( latt_str(X0)
=> ( ( lattice(X0)
& ~ empty_carrier(X0) )
=> ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_commutative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) ) ) ),
inference(pure_predicate_removal,[],[f94]) ).
fof(f94,plain,
! [X0] :
( latt_str(X0)
=> ( ( lattice(X0)
& ~ empty_carrier(X0) )
=> ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) ) ) ),
inference(pure_predicate_removal,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( latt_str(X0)
=> ( ( lattice(X0)
& ~ empty_carrier(X0) )
=> ( join_absorbing(X0)
& meet_absorbing(X0)
& meet_associative(X0)
& meet_commutative(X0)
& join_associative(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',cc1_lattices) ).
fof(f2154,plain,
! [X2,X3] :
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,X2),cast_to_el_of_LattPOSet(sK0,X3))
| ~ element(X3,the_carrier(sK0))
| ~ element(X2,the_carrier(sK0))
| ~ below(sK0,X2,X3)
| ~ meet_commutative(sK0)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f2153,f514]) ).
fof(f514,plain,
meet_absorbing(sK0),
inference(subsumption_resolution,[],[f513,f282]) ).
fof(f513,plain,
( meet_absorbing(sK0)
| ~ latt_str(sK0) ),
inference(subsumption_resolution,[],[f452,f280]) ).
fof(f452,plain,
( meet_absorbing(sK0)
| ~ lattice(sK0)
| ~ latt_str(sK0) ),
inference(resolution,[],[f279,f297]) ).
fof(f297,plain,
! [X0] :
( meet_absorbing(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f2153,plain,
! [X2,X3] :
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,X2),cast_to_el_of_LattPOSet(sK0,X3))
| ~ element(X3,the_carrier(sK0))
| ~ element(X2,the_carrier(sK0))
| ~ below(sK0,X2,X3)
| ~ meet_absorbing(sK0)
| ~ meet_commutative(sK0)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f2152,f516]) ).
fof(f516,plain,
join_absorbing(sK0),
inference(subsumption_resolution,[],[f515,f282]) ).
fof(f515,plain,
( join_absorbing(sK0)
| ~ latt_str(sK0) ),
inference(subsumption_resolution,[],[f453,f280]) ).
fof(f453,plain,
( join_absorbing(sK0)
| ~ lattice(sK0)
| ~ latt_str(sK0) ),
inference(resolution,[],[f279,f298]) ).
fof(f298,plain,
! [X0] :
( join_absorbing(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f2152,plain,
! [X2,X3] :
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,X2),cast_to_el_of_LattPOSet(sK0,X3))
| ~ element(X3,the_carrier(sK0))
| ~ element(X2,the_carrier(sK0))
| ~ below(sK0,X2,X3)
| ~ join_absorbing(sK0)
| ~ meet_absorbing(sK0)
| ~ meet_commutative(sK0)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f2144,f282]) ).
fof(f2144,plain,
! [X2,X3] :
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,X2),cast_to_el_of_LattPOSet(sK0,X3))
| ~ element(X3,the_carrier(sK0))
| ~ element(X2,the_carrier(sK0))
| ~ below(sK0,X2,X3)
| ~ latt_str(sK0)
| ~ join_absorbing(sK0)
| ~ meet_absorbing(sK0)
| ~ meet_commutative(sK0)
| empty_carrier(sK0) ),
inference(duplicate_literal_removal,[],[f2139]) ).
fof(f2139,plain,
! [X2,X3] :
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,X2),cast_to_el_of_LattPOSet(sK0,X3))
| ~ element(X3,the_carrier(sK0))
| ~ element(X2,the_carrier(sK0))
| ~ below(sK0,X2,X3)
| ~ element(X3,the_carrier(sK0))
| ~ element(X2,the_carrier(sK0))
| ~ latt_str(sK0)
| ~ join_absorbing(sK0)
| ~ meet_absorbing(sK0)
| ~ meet_commutative(sK0)
| empty_carrier(sK0) ),
inference(resolution,[],[f556,f406]) ).
fof(f406,plain,
! [X2,X0,X1] :
( below_refl(X0,X1,X2)
| ~ below(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f250]) ).
fof(f250,plain,
! [X0,X1,X2] :
( ( ( below_refl(X0,X1,X2)
| ~ below(X0,X1,X2) )
& ( below(X0,X1,X2)
| ~ below_refl(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f187]) ).
fof(f187,plain,
! [X0,X1,X2] :
( ( below_refl(X0,X1,X2)
<=> below(X0,X1,X2) )
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f186]) ).
fof(f186,plain,
! [X0,X1,X2] :
( ( below_refl(X0,X1,X2)
<=> below(X0,X1,X2) )
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X0))
& element(X1,the_carrier(X0))
& latt_str(X0)
& join_absorbing(X0)
& meet_absorbing(X0)
& meet_commutative(X0)
& ~ empty_carrier(X0) )
=> ( below_refl(X0,X1,X2)
<=> below(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',redefinition_r3_lattices) ).
fof(f556,plain,
! [X8,X7] :
( ~ below_refl(sK0,X7,X8)
| related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,X7),cast_to_el_of_LattPOSet(sK0,X8))
| ~ element(X8,the_carrier(sK0))
| ~ element(X7,the_carrier(sK0)) ),
inference(subsumption_resolution,[],[f555,f280]) ).
fof(f555,plain,
! [X8,X7] :
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,X7),cast_to_el_of_LattPOSet(sK0,X8))
| ~ below_refl(sK0,X7,X8)
| ~ element(X8,the_carrier(sK0))
| ~ element(X7,the_carrier(sK0))
| ~ lattice(sK0) ),
inference(subsumption_resolution,[],[f475,f282]) ).
fof(f475,plain,
! [X8,X7] :
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,X7),cast_to_el_of_LattPOSet(sK0,X8))
| ~ below_refl(sK0,X7,X8)
| ~ element(X8,the_carrier(sK0))
| ~ element(X7,the_carrier(sK0))
| ~ latt_str(sK0)
| ~ lattice(sK0) ),
inference(resolution,[],[f279,f338]) ).
fof(f338,plain,
! [X2,X0,X1] :
( related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| ~ below_refl(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f219]) ).
fof(f219,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( below_refl(X0,X1,X2)
| ~ related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) )
& ( related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2))
| ~ below_refl(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( below_refl(X0,X1,X2)
<=> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f131]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( below_refl(X0,X1,X2)
<=> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f87]) ).
fof(f87,axiom,
! [X0] :
( ( latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( below_refl(X0,X1,X2)
<=> related_reflexive(poset_of_lattice(X0),cast_to_el_of_LattPOSet(X0,X1),cast_to_el_of_LattPOSet(X0,X2)) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',t7_lattice3) ).
fof(f194234,plain,
( relstr_set_smaller(poset_of_lattice(sK0),sK1,sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))
| ~ spl29_16 ),
inference(subsumption_resolution,[],[f194233,f624]) ).
fof(f194233,plain,
( ~ latt_element_smaller(sK0,join_of_latt_set(sK0,sK1),sK1)
| relstr_set_smaller(poset_of_lattice(sK0),sK1,sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))
| ~ spl29_16 ),
inference(forward_literal_rewriting,[],[f194232,f1057]) ).
fof(f194232,plain,
( ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1))
| relstr_set_smaller(poset_of_lattice(sK0),sK1,sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))
| ~ spl29_16 ),
inference(subsumption_resolution,[],[f194219,f582]) ).
fof(f194219,plain,
( ~ element(join_of_latt_set(sK0,sK1),the_carrier(sK0))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1))
| relstr_set_smaller(poset_of_lattice(sK0),sK1,sK5(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))
| ~ spl29_16 ),
inference(equality_resolution,[],[f194165]) ).
fof(f194165,plain,
( ! [X1] :
( join_of_latt_set(sK0,sK1) != X1
| ~ element(X1,the_carrier(sK0))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X1)
| relstr_set_smaller(poset_of_lattice(sK0),sK1,sK5(poset_of_lattice(sK0),sK1,X1)) )
| ~ spl29_16 ),
inference(forward_demodulation,[],[f2225,f3900]) ).
fof(f2225,plain,
( ! [X1] :
( join_of_latt_set(sK0,sK1) != X1
| ~ element(X1,the_carrier(poset_of_lattice(sK0)))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X1)
| relstr_set_smaller(poset_of_lattice(sK0),sK1,sK5(poset_of_lattice(sK0),sK1,X1)) )
| ~ spl29_16 ),
inference(avatar_component_clause,[],[f2224]) ).
fof(f2224,plain,
( spl29_16
<=> ! [X1] :
( join_of_latt_set(sK0,sK1) != X1
| ~ element(X1,the_carrier(poset_of_lattice(sK0)))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X1)
| relstr_set_smaller(poset_of_lattice(sK0),sK1,sK5(poset_of_lattice(sK0),sK1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_16])]) ).
fof(f194053,plain,
( ~ spl29_339
| ~ spl29_340
| ~ spl29_341 ),
inference(avatar_contradiction_clause,[],[f194052]) ).
fof(f194052,plain,
( $false
| ~ spl29_339
| ~ spl29_340
| ~ spl29_341 ),
inference(subsumption_resolution,[],[f194051,f193266]) ).
fof(f193266,plain,
( ~ related(poset_of_lattice(sK0),sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)),meet_of_latt_set(sK0,sK1))
| ~ spl29_341 ),
inference(subsumption_resolution,[],[f193265,f606]) ).
fof(f606,plain,
! [X53] : latt_set_smaller(sK0,meet_of_latt_set(sK0,X53),X53),
inference(subsumption_resolution,[],[f605,f280]) ).
fof(f605,plain,
! [X53] :
( latt_set_smaller(sK0,meet_of_latt_set(sK0,X53),X53)
| ~ lattice(sK0) ),
inference(subsumption_resolution,[],[f604,f281]) ).
fof(f604,plain,
! [X53] :
( latt_set_smaller(sK0,meet_of_latt_set(sK0,X53),X53)
| ~ complete_latt_str(sK0)
| ~ lattice(sK0) ),
inference(subsumption_resolution,[],[f603,f282]) ).
fof(f603,plain,
! [X53] :
( latt_set_smaller(sK0,meet_of_latt_set(sK0,X53),X53)
| ~ latt_str(sK0)
| ~ complete_latt_str(sK0)
| ~ lattice(sK0) ),
inference(subsumption_resolution,[],[f504,f583]) ).
fof(f583,plain,
! [X32] : element(meet_of_latt_set(sK0,X32),the_carrier(sK0)),
inference(subsumption_resolution,[],[f493,f282]) ).
fof(f493,plain,
! [X32] :
( element(meet_of_latt_set(sK0,X32),the_carrier(sK0))
| ~ latt_str(sK0) ),
inference(resolution,[],[f279,f390]) ).
fof(f390,plain,
! [X0,X1] :
( element(meet_of_latt_set(X0,X1),the_carrier(X0))
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f174]) ).
fof(f174,plain,
! [X0,X1] :
( element(meet_of_latt_set(X0,X1),the_carrier(X0))
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f173]) ).
fof(f173,plain,
! [X0,X1] :
( element(meet_of_latt_set(X0,X1),the_carrier(X0))
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( ( latt_str(X0)
& ~ empty_carrier(X0) )
=> element(meet_of_latt_set(X0,X1),the_carrier(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',dt_k16_lattice3) ).
fof(f504,plain,
! [X53] :
( latt_set_smaller(sK0,meet_of_latt_set(sK0,X53),X53)
| ~ element(meet_of_latt_set(sK0,X53),the_carrier(sK0))
| ~ latt_str(sK0)
| ~ complete_latt_str(sK0)
| ~ lattice(sK0) ),
inference(resolution,[],[f279,f442]) ).
fof(f442,plain,
! [X2,X0] :
( latt_set_smaller(X0,meet_of_latt_set(X0,X2),X2)
| ~ element(meet_of_latt_set(X0,X2),the_carrier(X0))
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(equality_resolution,[],[f315]) ).
fof(f315,plain,
! [X2,X0,X1] :
( latt_set_smaller(X0,X1,X2)
| meet_of_latt_set(X0,X2) != X1
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f218]) ).
fof(f218,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( meet_of_latt_set(X0,X2) = X1
| ( ~ below_refl(X0,sK6(X0,X1,X2),X1)
& latt_set_smaller(X0,sK6(X0,X1,X2),X2)
& element(sK6(X0,X1,X2),the_carrier(X0)) )
| ~ latt_set_smaller(X0,X1,X2) )
& ( ( ! [X4] :
( below_refl(X0,X4,X1)
| ~ latt_set_smaller(X0,X4,X2)
| ~ element(X4,the_carrier(X0)) )
& latt_set_smaller(X0,X1,X2) )
| meet_of_latt_set(X0,X2) != X1 ) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f216,f217]) ).
fof(f217,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ below_refl(X0,X3,X1)
& latt_set_smaller(X0,X3,X2)
& element(X3,the_carrier(X0)) )
=> ( ~ below_refl(X0,sK6(X0,X1,X2),X1)
& latt_set_smaller(X0,sK6(X0,X1,X2),X2)
& element(sK6(X0,X1,X2),the_carrier(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f216,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( meet_of_latt_set(X0,X2) = X1
| ? [X3] :
( ~ below_refl(X0,X3,X1)
& latt_set_smaller(X0,X3,X2)
& element(X3,the_carrier(X0)) )
| ~ latt_set_smaller(X0,X1,X2) )
& ( ( ! [X4] :
( below_refl(X0,X4,X1)
| ~ latt_set_smaller(X0,X4,X2)
| ~ element(X4,the_carrier(X0)) )
& latt_set_smaller(X0,X1,X2) )
| meet_of_latt_set(X0,X2) != X1 ) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(rectify,[],[f215]) ).
fof(f215,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( meet_of_latt_set(X0,X2) = X1
| ? [X3] :
( ~ below_refl(X0,X3,X1)
& latt_set_smaller(X0,X3,X2)
& element(X3,the_carrier(X0)) )
| ~ latt_set_smaller(X0,X1,X2) )
& ( ( ! [X3] :
( below_refl(X0,X3,X1)
| ~ latt_set_smaller(X0,X3,X2)
| ~ element(X3,the_carrier(X0)) )
& latt_set_smaller(X0,X1,X2) )
| meet_of_latt_set(X0,X2) != X1 ) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f214]) ).
fof(f214,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( meet_of_latt_set(X0,X2) = X1
| ? [X3] :
( ~ below_refl(X0,X3,X1)
& latt_set_smaller(X0,X3,X2)
& element(X3,the_carrier(X0)) )
| ~ latt_set_smaller(X0,X1,X2) )
& ( ( ! [X3] :
( below_refl(X0,X3,X1)
| ~ latt_set_smaller(X0,X3,X2)
| ~ element(X3,the_carrier(X0)) )
& latt_set_smaller(X0,X1,X2) )
| meet_of_latt_set(X0,X2) != X1 ) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( meet_of_latt_set(X0,X2) = X1
<=> ( ! [X3] :
( below_refl(X0,X3,X1)
| ~ latt_set_smaller(X0,X3,X2)
| ~ element(X3,the_carrier(X0)) )
& latt_set_smaller(X0,X1,X2) ) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f117]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( meet_of_latt_set(X0,X2) = X1
<=> ( ! [X3] :
( below_refl(X0,X3,X1)
| ~ latt_set_smaller(X0,X3,X2)
| ~ element(X3,the_carrier(X0)) )
& latt_set_smaller(X0,X1,X2) ) )
| ~ element(X1,the_carrier(X0)) )
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0] :
( ( latt_str(X0)
& complete_latt_str(X0)
& lattice(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( meet_of_latt_set(X0,X2) = X1
<=> ( ! [X3] :
( element(X3,the_carrier(X0))
=> ( latt_set_smaller(X0,X3,X2)
=> below_refl(X0,X3,X1) ) )
& latt_set_smaller(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',t34_lattice3) ).
fof(f193265,plain,
( ~ latt_set_smaller(sK0,meet_of_latt_set(sK0,sK1),sK1)
| ~ related(poset_of_lattice(sK0),sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)),meet_of_latt_set(sK0,sK1))
| ~ spl29_341 ),
inference(forward_literal_rewriting,[],[f193264,f1232]) ).
fof(f1232,plain,
! [X51,X52] :
( ~ latt_set_smaller(sK0,meet_of_latt_set(sK0,X52),X51)
| relstr_element_smaller(poset_of_lattice(sK0),X51,meet_of_latt_set(sK0,X52)) ),
inference(forward_demodulation,[],[f1231,f1200]) ).
fof(f1200,plain,
! [X21] : meet_of_latt_set(sK0,X21) = cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,X21)),
inference(subsumption_resolution,[],[f1199,f279]) ).
fof(f1199,plain,
! [X21] :
( meet_of_latt_set(sK0,X21) = cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,X21))
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f1198,f280]) ).
fof(f1198,plain,
! [X21] :
( meet_of_latt_set(sK0,X21) = cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,X21))
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f1144,f282]) ).
fof(f1144,plain,
! [X21] :
( meet_of_latt_set(sK0,X21) = cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,X21))
| ~ latt_str(sK0)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(resolution,[],[f583,f337]) ).
fof(f1231,plain,
! [X51,X52] :
( relstr_element_smaller(poset_of_lattice(sK0),X51,cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,X52)))
| ~ latt_set_smaller(sK0,meet_of_latt_set(sK0,X52),X51) ),
inference(subsumption_resolution,[],[f1230,f279]) ).
fof(f1230,plain,
! [X51,X52] :
( relstr_element_smaller(poset_of_lattice(sK0),X51,cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,X52)))
| ~ latt_set_smaller(sK0,meet_of_latt_set(sK0,X52),X51)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f1229,f280]) ).
fof(f1229,plain,
! [X51,X52] :
( relstr_element_smaller(poset_of_lattice(sK0),X51,cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,X52)))
| ~ latt_set_smaller(sK0,meet_of_latt_set(sK0,X52),X51)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f1160,f282]) ).
fof(f1160,plain,
! [X51,X52] :
( relstr_element_smaller(poset_of_lattice(sK0),X51,cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,X52)))
| ~ latt_set_smaller(sK0,meet_of_latt_set(sK0,X52),X51)
| ~ latt_str(sK0)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(resolution,[],[f583,f383]) ).
fof(f383,plain,
! [X2,X0,X1] :
( relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| ~ latt_set_smaller(X1,X2,X0)
| ~ element(X2,the_carrier(X1))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f240,plain,
! [X0,X1] :
( ! [X2] :
( ( ( latt_set_smaller(X1,X2,X0)
| ~ relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) )
& ( relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
| ~ latt_set_smaller(X1,X2,X0) ) )
| ~ element(X2,the_carrier(X1)) )
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(nnf_transformation,[],[f166]) ).
fof(f166,plain,
! [X0,X1] :
( ! [X2] :
( ( latt_set_smaller(X1,X2,X0)
<=> relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) )
| ~ element(X2,the_carrier(X1)) )
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(flattening,[],[f165]) ).
fof(f165,plain,
! [X0,X1] :
( ! [X2] :
( ( latt_set_smaller(X1,X2,X0)
<=> relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) )
| ~ element(X2,the_carrier(X1)) )
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,axiom,
! [X0,X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ( latt_set_smaller(X1,X2,X0)
<=> relstr_element_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',t28_lattice3) ).
fof(f193264,plain,
( ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1))
| ~ related(poset_of_lattice(sK0),sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)),meet_of_latt_set(sK0,sK1))
| ~ spl29_341 ),
inference(subsumption_resolution,[],[f193251,f583]) ).
fof(f193251,plain,
( ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1))
| ~ related(poset_of_lattice(sK0),sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)),meet_of_latt_set(sK0,sK1))
| ~ element(meet_of_latt_set(sK0,sK1),the_carrier(sK0))
| ~ spl29_341 ),
inference(equality_resolution,[],[f191025]) ).
fof(f191025,plain,
( ! [X2] :
( meet_of_latt_set(sK0,sK1) != X2
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X2)
| ~ related(poset_of_lattice(sK0),sK4(poset_of_lattice(sK0),sK1,X2),X2)
| ~ element(X2,the_carrier(sK0)) )
| ~ spl29_341 ),
inference(avatar_component_clause,[],[f191024]) ).
fof(f191024,plain,
( spl29_341
<=> ! [X2] :
( ~ element(X2,the_carrier(sK0))
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X2)
| ~ related(poset_of_lattice(sK0),sK4(poset_of_lattice(sK0),sK1,X2),X2)
| meet_of_latt_set(sK0,sK1) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_341])]) ).
fof(f194051,plain,
( related(poset_of_lattice(sK0),sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)),meet_of_latt_set(sK0,sK1))
| ~ spl29_339
| ~ spl29_340 ),
inference(forward_literal_rewriting,[],[f194050,f193320]) ).
fof(f193320,plain,
( ! [X40] :
( related(poset_of_lattice(sK0),sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)),meet_of_latt_set(sK0,X40))
| ~ related_reflexive(poset_of_lattice(sK0),sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)),meet_of_latt_set(sK0,X40)) )
| ~ spl29_339 ),
inference(resolution,[],[f193228,f4066]) ).
fof(f4066,plain,
! [X78,X79] :
( ~ element(X78,the_carrier(sK0))
| related(poset_of_lattice(sK0),X78,meet_of_latt_set(sK0,X79))
| ~ related_reflexive(poset_of_lattice(sK0),X78,meet_of_latt_set(sK0,X79)) ),
inference(backward_demodulation,[],[f2594,f3900]) ).
fof(f2594,plain,
! [X78,X79] :
( related(poset_of_lattice(sK0),X78,meet_of_latt_set(sK0,X79))
| ~ related_reflexive(poset_of_lattice(sK0),X78,meet_of_latt_set(sK0,X79))
| ~ element(X78,the_carrier(poset_of_lattice(sK0))) ),
inference(subsumption_resolution,[],[f2593,f531]) ).
fof(f2593,plain,
! [X78,X79] :
( related(poset_of_lattice(sK0),X78,meet_of_latt_set(sK0,X79))
| ~ related_reflexive(poset_of_lattice(sK0),X78,meet_of_latt_set(sK0,X79))
| ~ element(X78,the_carrier(poset_of_lattice(sK0)))
| empty_carrier(poset_of_lattice(sK0)) ),
inference(subsumption_resolution,[],[f2592,f535]) ).
fof(f2592,plain,
! [X78,X79] :
( related(poset_of_lattice(sK0),X78,meet_of_latt_set(sK0,X79))
| ~ related_reflexive(poset_of_lattice(sK0),X78,meet_of_latt_set(sK0,X79))
| ~ element(X78,the_carrier(poset_of_lattice(sK0)))
| ~ reflexive_relstr(poset_of_lattice(sK0))
| empty_carrier(poset_of_lattice(sK0)) ),
inference(subsumption_resolution,[],[f2498,f552]) ).
fof(f2498,plain,
! [X78,X79] :
( related(poset_of_lattice(sK0),X78,meet_of_latt_set(sK0,X79))
| ~ related_reflexive(poset_of_lattice(sK0),X78,meet_of_latt_set(sK0,X79))
| ~ element(X78,the_carrier(poset_of_lattice(sK0)))
| ~ rel_str(poset_of_lattice(sK0))
| ~ reflexive_relstr(poset_of_lattice(sK0))
| empty_carrier(poset_of_lattice(sK0)) ),
inference(resolution,[],[f1220,f412]) ).
fof(f1220,plain,
! [X46] : element(meet_of_latt_set(sK0,X46),the_carrier(poset_of_lattice(sK0))),
inference(forward_demodulation,[],[f1219,f1200]) ).
fof(f1219,plain,
! [X46] : element(cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,X46)),the_carrier(poset_of_lattice(sK0))),
inference(subsumption_resolution,[],[f1218,f279]) ).
fof(f1218,plain,
! [X46] :
( element(cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,X46)),the_carrier(poset_of_lattice(sK0)))
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f1217,f280]) ).
fof(f1217,plain,
! [X46] :
( element(cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,X46)),the_carrier(poset_of_lattice(sK0)))
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f1157,f282]) ).
fof(f1157,plain,
! [X46] :
( element(cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,X46)),the_carrier(poset_of_lattice(sK0)))
| ~ latt_str(sK0)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(resolution,[],[f583,f379]) ).
fof(f193228,plain,
( element(sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)),the_carrier(sK0))
| ~ spl29_339 ),
inference(subsumption_resolution,[],[f193227,f606]) ).
fof(f193227,plain,
( ~ latt_set_smaller(sK0,meet_of_latt_set(sK0,sK1),sK1)
| element(sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)),the_carrier(sK0))
| ~ spl29_339 ),
inference(forward_literal_rewriting,[],[f193226,f1232]) ).
fof(f193226,plain,
( ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1))
| element(sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)),the_carrier(sK0))
| ~ spl29_339 ),
inference(subsumption_resolution,[],[f193213,f583]) ).
fof(f193213,plain,
( ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1))
| ~ element(meet_of_latt_set(sK0,sK1),the_carrier(sK0))
| element(sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)),the_carrier(sK0))
| ~ spl29_339 ),
inference(equality_resolution,[],[f191004]) ).
fof(f191004,plain,
( ! [X0] :
( meet_of_latt_set(sK0,sK1) != X0
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X0)
| ~ element(X0,the_carrier(sK0))
| element(sK4(poset_of_lattice(sK0),sK1,X0),the_carrier(sK0)) )
| ~ spl29_339 ),
inference(avatar_component_clause,[],[f191003]) ).
fof(f191003,plain,
( spl29_339
<=> ! [X0] :
( ~ element(X0,the_carrier(sK0))
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X0)
| meet_of_latt_set(sK0,sK1) != X0
| element(sK4(poset_of_lattice(sK0),sK1,X0),the_carrier(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_339])]) ).
fof(f194050,plain,
( related_reflexive(poset_of_lattice(sK0),sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)),meet_of_latt_set(sK0,sK1))
| ~ spl29_339
| ~ spl29_340 ),
inference(forward_demodulation,[],[f194049,f193267]) ).
fof(f193267,plain,
( sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)) = cast_to_el_of_LattPOSet(sK0,sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)))
| ~ spl29_339 ),
inference(resolution,[],[f193228,f554]) ).
fof(f194049,plain,
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1))),meet_of_latt_set(sK0,sK1))
| ~ spl29_339
| ~ spl29_340 ),
inference(forward_demodulation,[],[f194048,f193503]) ).
fof(f193503,plain,
( sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)) = cast_to_el_of_lattice(sK0,sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)))
| ~ spl29_339 ),
inference(forward_demodulation,[],[f193275,f193267]) ).
fof(f193275,plain,
( cast_to_el_of_LattPOSet(sK0,sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1))) = cast_to_el_of_lattice(sK0,cast_to_el_of_LattPOSet(sK0,sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1))))
| ~ spl29_339 ),
inference(resolution,[],[f193228,f1499]) ).
fof(f194048,plain,
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,cast_to_el_of_lattice(sK0,sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)))),meet_of_latt_set(sK0,sK1))
| ~ spl29_339
| ~ spl29_340 ),
inference(subsumption_resolution,[],[f193896,f193228]) ).
fof(f193896,plain,
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,cast_to_el_of_lattice(sK0,sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)))),meet_of_latt_set(sK0,sK1))
| ~ element(sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)),the_carrier(sK0))
| ~ spl29_340 ),
inference(resolution,[],[f193247,f6518]) ).
fof(f6518,plain,
! [X4,X5] :
( ~ relstr_element_smaller(poset_of_lattice(sK0),X5,X4)
| related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,cast_to_el_of_lattice(sK0,X4)),meet_of_latt_set(sK0,X5))
| ~ element(X4,the_carrier(sK0)) ),
inference(subsumption_resolution,[],[f6517,f3903]) ).
fof(f6517,plain,
! [X4,X5] :
( ~ element(X4,the_carrier(sK0))
| ~ element(cast_to_el_of_lattice(sK0,X4),the_carrier(sK0))
| related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,cast_to_el_of_lattice(sK0,X4)),meet_of_latt_set(sK0,X5))
| ~ relstr_element_smaller(poset_of_lattice(sK0),X5,X4) ),
inference(forward_demodulation,[],[f6516,f3900]) ).
fof(f6516,plain,
! [X4,X5] :
( ~ element(cast_to_el_of_lattice(sK0,X4),the_carrier(sK0))
| related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,cast_to_el_of_lattice(sK0,X4)),meet_of_latt_set(sK0,X5))
| ~ relstr_element_smaller(poset_of_lattice(sK0),X5,X4)
| ~ element(X4,the_carrier(poset_of_lattice(sK0))) ),
inference(subsumption_resolution,[],[f6515,f279]) ).
fof(f6515,plain,
! [X4,X5] :
( ~ element(cast_to_el_of_lattice(sK0,X4),the_carrier(sK0))
| related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,cast_to_el_of_lattice(sK0,X4)),meet_of_latt_set(sK0,X5))
| ~ relstr_element_smaller(poset_of_lattice(sK0),X5,X4)
| ~ element(X4,the_carrier(poset_of_lattice(sK0)))
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f6514,f280]) ).
fof(f6514,plain,
! [X4,X5] :
( ~ element(cast_to_el_of_lattice(sK0,X4),the_carrier(sK0))
| related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,cast_to_el_of_lattice(sK0,X4)),meet_of_latt_set(sK0,X5))
| ~ relstr_element_smaller(poset_of_lattice(sK0),X5,X4)
| ~ element(X4,the_carrier(poset_of_lattice(sK0)))
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f6498,f282]) ).
fof(f6498,plain,
! [X4,X5] :
( ~ element(cast_to_el_of_lattice(sK0,X4),the_carrier(sK0))
| related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,cast_to_el_of_lattice(sK0,X4)),meet_of_latt_set(sK0,X5))
| ~ relstr_element_smaller(poset_of_lattice(sK0),X5,X4)
| ~ element(X4,the_carrier(poset_of_lattice(sK0)))
| ~ latt_str(sK0)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(resolution,[],[f2151,f387]) ).
fof(f387,plain,
! [X2,X0,X1] :
( latt_set_smaller(X1,cast_to_el_of_lattice(X1,X2),X0)
| ~ relstr_element_smaller(poset_of_lattice(X1),X0,X2)
| ~ element(X2,the_carrier(poset_of_lattice(X1)))
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f242]) ).
fof(f242,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relstr_element_smaller(poset_of_lattice(X1),X0,X2)
| ~ latt_set_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) )
& ( latt_set_smaller(X1,cast_to_el_of_lattice(X1,X2),X0)
| ~ relstr_element_smaller(poset_of_lattice(X1),X0,X2) ) )
| ~ element(X2,the_carrier(poset_of_lattice(X1))) )
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(nnf_transformation,[],[f170]) ).
fof(f170,plain,
! [X0,X1] :
( ! [X2] :
( ( relstr_element_smaller(poset_of_lattice(X1),X0,X2)
<=> latt_set_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) )
| ~ element(X2,the_carrier(poset_of_lattice(X1))) )
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(flattening,[],[f169]) ).
fof(f169,plain,
! [X0,X1] :
( ! [X2] :
( ( relstr_element_smaller(poset_of_lattice(X1),X0,X2)
<=> latt_set_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) )
| ~ element(X2,the_carrier(poset_of_lattice(X1))) )
| ~ latt_str(X1)
| ~ lattice(X1)
| empty_carrier(X1) ),
inference(ennf_transformation,[],[f74]) ).
fof(f74,axiom,
! [X0,X1] :
( ( latt_str(X1)
& lattice(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(poset_of_lattice(X1)))
=> ( relstr_element_smaller(poset_of_lattice(X1),X0,X2)
<=> latt_set_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',t29_lattice3) ).
fof(f2151,plain,
! [X0,X1] :
( ~ latt_set_smaller(sK0,X0,X1)
| ~ element(X0,the_carrier(sK0))
| related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,X0),meet_of_latt_set(sK0,X1)) ),
inference(forward_demodulation,[],[f2150,f1200]) ).
fof(f2150,plain,
! [X0,X1] :
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,X0),cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,X1)))
| ~ element(X0,the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,X1) ),
inference(subsumption_resolution,[],[f2149,f279]) ).
fof(f2149,plain,
! [X0,X1] :
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,X0),cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,X1)))
| ~ element(X0,the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,X1)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f2148,f280]) ).
fof(f2148,plain,
! [X0,X1] :
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,X0),cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,X1)))
| ~ element(X0,the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,X1)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f2147,f281]) ).
fof(f2147,plain,
! [X0,X1] :
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,X0),cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,X1)))
| ~ element(X0,the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,X1)
| ~ complete_latt_str(sK0)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f2146,f282]) ).
fof(f2146,plain,
! [X0,X1] :
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,X0),cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,X1)))
| ~ element(X0,the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,X1)
| ~ latt_str(sK0)
| ~ complete_latt_str(sK0)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(subsumption_resolution,[],[f2145,f583]) ).
fof(f2145,plain,
! [X0,X1] :
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,X0),cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,X1)))
| ~ element(meet_of_latt_set(sK0,X1),the_carrier(sK0))
| ~ element(X0,the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,X1)
| ~ latt_str(sK0)
| ~ complete_latt_str(sK0)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(duplicate_literal_removal,[],[f2138]) ).
fof(f2138,plain,
! [X0,X1] :
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,X0),cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,X1)))
| ~ element(meet_of_latt_set(sK0,X1),the_carrier(sK0))
| ~ element(X0,the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,X1)
| ~ element(X0,the_carrier(sK0))
| ~ element(meet_of_latt_set(sK0,X1),the_carrier(sK0))
| ~ latt_str(sK0)
| ~ complete_latt_str(sK0)
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(resolution,[],[f556,f441]) ).
fof(f441,plain,
! [X2,X0,X4] :
( below_refl(X0,X4,meet_of_latt_set(X0,X2))
| ~ latt_set_smaller(X0,X4,X2)
| ~ element(X4,the_carrier(X0))
| ~ element(meet_of_latt_set(X0,X2),the_carrier(X0))
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(equality_resolution,[],[f316]) ).
fof(f316,plain,
! [X2,X0,X1,X4] :
( below_refl(X0,X4,X1)
| ~ latt_set_smaller(X0,X4,X2)
| ~ element(X4,the_carrier(X0))
| meet_of_latt_set(X0,X2) != X1
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ complete_latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f218]) ).
fof(f193247,plain,
( relstr_element_smaller(poset_of_lattice(sK0),sK1,sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)))
| ~ spl29_340 ),
inference(subsumption_resolution,[],[f193246,f606]) ).
fof(f193246,plain,
( ~ latt_set_smaller(sK0,meet_of_latt_set(sK0,sK1),sK1)
| relstr_element_smaller(poset_of_lattice(sK0),sK1,sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)))
| ~ spl29_340 ),
inference(forward_literal_rewriting,[],[f193245,f1232]) ).
fof(f193245,plain,
( ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1))
| relstr_element_smaller(poset_of_lattice(sK0),sK1,sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)))
| ~ spl29_340 ),
inference(subsumption_resolution,[],[f193232,f583]) ).
fof(f193232,plain,
( ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1))
| relstr_element_smaller(poset_of_lattice(sK0),sK1,sK4(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)))
| ~ element(meet_of_latt_set(sK0,sK1),the_carrier(sK0))
| ~ spl29_340 ),
inference(equality_resolution,[],[f191021]) ).
fof(f191021,plain,
( ! [X1] :
( meet_of_latt_set(sK0,sK1) != X1
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X1)
| relstr_element_smaller(poset_of_lattice(sK0),sK1,sK4(poset_of_lattice(sK0),sK1,X1))
| ~ element(X1,the_carrier(sK0)) )
| ~ spl29_340 ),
inference(avatar_component_clause,[],[f191020]) ).
fof(f191020,plain,
( spl29_340
<=> ! [X1] :
( ~ element(X1,the_carrier(sK0))
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X1)
| relstr_element_smaller(poset_of_lattice(sK0),sK1,sK4(poset_of_lattice(sK0),sK1,X1))
| meet_of_latt_set(sK0,sK1) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_340])]) ).
fof(f193146,plain,
spl29_338,
inference(avatar_contradiction_clause,[],[f193145]) ).
fof(f193145,plain,
( $false
| spl29_338 ),
inference(subsumption_resolution,[],[f193144,f191688]) ).
fof(f191688,plain,
( ~ related(poset_of_lattice(sK0),sK9(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)),meet_of_latt_set(sK0,sK1))
| spl29_338 ),
inference(forward_demodulation,[],[f191687,f1200]) ).
fof(f191687,plain,
( ~ related(poset_of_lattice(sK0),sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,sK1))),cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,sK1)))
| spl29_338 ),
inference(subsumption_resolution,[],[f191616,f583]) ).
fof(f191616,plain,
( ~ related(poset_of_lattice(sK0),sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,sK1))),cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,sK1)))
| ~ element(meet_of_latt_set(sK0,sK1),the_carrier(sK0))
| spl29_338 ),
inference(resolution,[],[f191147,f606]) ).
fof(f191147,plain,
( ! [X0] :
( ~ latt_set_smaller(sK0,X0,sK1)
| ~ related(poset_of_lattice(sK0),sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,X0)),cast_to_el_of_LattPOSet(sK0,X0))
| ~ element(X0,the_carrier(sK0)) )
| spl29_338 ),
inference(subsumption_resolution,[],[f191146,f3902]) ).
fof(f3902,plain,
! [X13] :
( ~ element(X13,the_carrier(sK0))
| element(cast_to_el_of_LattPOSet(sK0,X13),the_carrier(sK0)) ),
inference(backward_demodulation,[],[f563,f3900]) ).
fof(f563,plain,
! [X13] :
( ~ element(X13,the_carrier(sK0))
| element(cast_to_el_of_LattPOSet(sK0,X13),the_carrier(poset_of_lattice(sK0))) ),
inference(subsumption_resolution,[],[f562,f280]) ).
fof(f562,plain,
! [X13] :
( element(cast_to_el_of_LattPOSet(sK0,X13),the_carrier(poset_of_lattice(sK0)))
| ~ element(X13,the_carrier(sK0))
| ~ lattice(sK0) ),
inference(subsumption_resolution,[],[f482,f282]) ).
fof(f482,plain,
! [X13] :
( element(cast_to_el_of_LattPOSet(sK0,X13),the_carrier(poset_of_lattice(sK0)))
| ~ element(X13,the_carrier(sK0))
| ~ latt_str(sK0)
| ~ lattice(sK0) ),
inference(resolution,[],[f279,f379]) ).
fof(f191146,plain,
( ! [X0] :
( ~ related(poset_of_lattice(sK0),sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,X0)),cast_to_el_of_LattPOSet(sK0,X0))
| ~ element(cast_to_el_of_LattPOSet(sK0,X0),the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,sK1)
| ~ element(X0,the_carrier(sK0)) )
| spl29_338 ),
inference(subsumption_resolution,[],[f191145,f279]) ).
fof(f191145,plain,
( ! [X0] :
( ~ related(poset_of_lattice(sK0),sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,X0)),cast_to_el_of_LattPOSet(sK0,X0))
| ~ element(cast_to_el_of_LattPOSet(sK0,X0),the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,sK1)
| ~ element(X0,the_carrier(sK0))
| empty_carrier(sK0) )
| spl29_338 ),
inference(subsumption_resolution,[],[f191144,f280]) ).
fof(f191144,plain,
( ! [X0] :
( ~ related(poset_of_lattice(sK0),sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,X0)),cast_to_el_of_LattPOSet(sK0,X0))
| ~ element(cast_to_el_of_LattPOSet(sK0,X0),the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,sK1)
| ~ element(X0,the_carrier(sK0))
| ~ lattice(sK0)
| empty_carrier(sK0) )
| spl29_338 ),
inference(subsumption_resolution,[],[f191123,f282]) ).
fof(f191123,plain,
( ! [X0] :
( ~ related(poset_of_lattice(sK0),sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,X0)),cast_to_el_of_LattPOSet(sK0,X0))
| ~ element(cast_to_el_of_LattPOSet(sK0,X0),the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,sK1)
| ~ element(X0,the_carrier(sK0))
| ~ latt_str(sK0)
| ~ lattice(sK0)
| empty_carrier(sK0) )
| spl29_338 ),
inference(resolution,[],[f191018,f383]) ).
fof(f191018,plain,
( ! [X2] :
( ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X2)
| ~ related(poset_of_lattice(sK0),sK9(poset_of_lattice(sK0),sK1,X2),X2)
| ~ element(X2,the_carrier(sK0)) )
| spl29_338 ),
inference(forward_demodulation,[],[f191017,f3900]) ).
fof(f191017,plain,
( ! [X2] :
( ~ related(poset_of_lattice(sK0),sK9(poset_of_lattice(sK0),sK1,X2),X2)
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X2)
| ~ element(X2,the_carrier(poset_of_lattice(sK0))) )
| spl29_338 ),
inference(subsumption_resolution,[],[f191016,f539]) ).
fof(f539,plain,
antisymmetric_relstr(poset_of_lattice(sK0)),
inference(subsumption_resolution,[],[f538,f280]) ).
fof(f538,plain,
( antisymmetric_relstr(poset_of_lattice(sK0))
| ~ lattice(sK0) ),
inference(subsumption_resolution,[],[f463,f282]) ).
fof(f463,plain,
( antisymmetric_relstr(poset_of_lattice(sK0))
| ~ latt_str(sK0)
| ~ lattice(sK0) ),
inference(resolution,[],[f279,f326]) ).
fof(f326,plain,
! [X0] :
( antisymmetric_relstr(poset_of_lattice(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f191016,plain,
( ! [X2] :
( ~ related(poset_of_lattice(sK0),sK9(poset_of_lattice(sK0),sK1,X2),X2)
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X2)
| ~ element(X2,the_carrier(poset_of_lattice(sK0)))
| ~ antisymmetric_relstr(poset_of_lattice(sK0)) )
| spl29_338 ),
inference(subsumption_resolution,[],[f191008,f552]) ).
fof(f191008,plain,
( ! [X2] :
( ~ related(poset_of_lattice(sK0),sK9(poset_of_lattice(sK0),sK1,X2),X2)
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X2)
| ~ element(X2,the_carrier(poset_of_lattice(sK0)))
| ~ rel_str(poset_of_lattice(sK0))
| ~ antisymmetric_relstr(poset_of_lattice(sK0)) )
| spl29_338 ),
inference(resolution,[],[f191001,f359]) ).
fof(f359,plain,
! [X2,X0,X1] :
( ex_inf_of_relstr_set(X0,X1)
| ~ related(X0,sK9(X0,X1,X2),X2)
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(cnf_transformation,[],[f231]) ).
fof(f231,plain,
! [X0] :
( ! [X1] :
( ( ex_inf_of_relstr_set(X0,X1)
| ! [X2] :
( ( ~ related(X0,sK9(X0,X1,X2),X2)
& relstr_element_smaller(X0,X1,sK9(X0,X1,X2))
& element(sK9(X0,X1,X2),the_carrier(X0)) )
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0)) ) )
& ( ( ! [X5] :
( related(X0,X5,sK10(X0,X1))
| ~ relstr_element_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) )
& relstr_element_smaller(X0,X1,sK10(X0,X1))
& element(sK10(X0,X1),the_carrier(X0)) )
| ~ ex_inf_of_relstr_set(X0,X1) ) )
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f228,f230,f229]) ).
fof(f229,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ related(X0,X3,X2)
& relstr_element_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) )
=> ( ~ related(X0,sK9(X0,X1,X2),X2)
& relstr_element_smaller(X0,X1,sK9(X0,X1,X2))
& element(sK9(X0,X1,X2),the_carrier(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f230,plain,
! [X0,X1] :
( ? [X4] :
( ! [X5] :
( related(X0,X5,X4)
| ~ relstr_element_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) )
& relstr_element_smaller(X0,X1,X4)
& element(X4,the_carrier(X0)) )
=> ( ! [X5] :
( related(X0,X5,sK10(X0,X1))
| ~ relstr_element_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) )
& relstr_element_smaller(X0,X1,sK10(X0,X1))
& element(sK10(X0,X1),the_carrier(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f228,plain,
! [X0] :
( ! [X1] :
( ( ex_inf_of_relstr_set(X0,X1)
| ! [X2] :
( ? [X3] :
( ~ related(X0,X3,X2)
& relstr_element_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) )
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0)) ) )
& ( ? [X4] :
( ! [X5] :
( related(X0,X5,X4)
| ~ relstr_element_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) )
& relstr_element_smaller(X0,X1,X4)
& element(X4,the_carrier(X0)) )
| ~ ex_inf_of_relstr_set(X0,X1) ) )
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(rectify,[],[f227]) ).
fof(f227,plain,
! [X0] :
( ! [X1] :
( ( ex_inf_of_relstr_set(X0,X1)
| ! [X2] :
( ? [X3] :
( ~ related(X0,X3,X2)
& relstr_element_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) )
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0)) ) )
& ( ? [X2] :
( ! [X3] :
( related(X0,X3,X2)
| ~ relstr_element_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& relstr_element_smaller(X0,X1,X2)
& element(X2,the_carrier(X0)) )
| ~ ex_inf_of_relstr_set(X0,X1) ) )
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(nnf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0] :
( ! [X1] :
( ex_inf_of_relstr_set(X0,X1)
<=> ? [X2] :
( ! [X3] :
( related(X0,X3,X2)
| ~ relstr_element_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& relstr_element_smaller(X0,X1,X2)
& element(X2,the_carrier(X0)) ) )
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(flattening,[],[f145]) ).
fof(f145,plain,
! [X0] :
( ! [X1] :
( ex_inf_of_relstr_set(X0,X1)
<=> ? [X2] :
( ! [X3] :
( related(X0,X3,X2)
| ~ relstr_element_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& relstr_element_smaller(X0,X1,X2)
& element(X2,the_carrier(X0)) ) )
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0] :
( ( rel_str(X0)
& antisymmetric_relstr(X0) )
=> ! [X1] :
( ex_inf_of_relstr_set(X0,X1)
<=> ? [X2] :
( ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_element_smaller(X0,X1,X3)
=> related(X0,X3,X2) ) )
& relstr_element_smaller(X0,X1,X2)
& element(X2,the_carrier(X0)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',t16_yellow_0) ).
fof(f191001,plain,
( ~ ex_inf_of_relstr_set(poset_of_lattice(sK0),sK1)
| spl29_338 ),
inference(avatar_component_clause,[],[f191000]) ).
fof(f191000,plain,
( spl29_338
<=> ex_inf_of_relstr_set(poset_of_lattice(sK0),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_338])]) ).
fof(f193144,plain,
( related(poset_of_lattice(sK0),sK9(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)),meet_of_latt_set(sK0,sK1))
| spl29_338 ),
inference(forward_literal_rewriting,[],[f193143,f191911]) ).
fof(f191911,plain,
( ! [X40] :
( related(poset_of_lattice(sK0),sK9(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)),meet_of_latt_set(sK0,X40))
| ~ related_reflexive(poset_of_lattice(sK0),sK9(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)),meet_of_latt_set(sK0,X40)) )
| spl29_338 ),
inference(resolution,[],[f191254,f4066]) ).
fof(f191254,plain,
( element(sK9(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)),the_carrier(sK0))
| spl29_338 ),
inference(forward_demodulation,[],[f191253,f1200]) ).
fof(f191253,plain,
( element(sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,sK1))),the_carrier(sK0))
| spl29_338 ),
inference(subsumption_resolution,[],[f191182,f583]) ).
fof(f191182,plain,
( element(sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,sK1))),the_carrier(sK0))
| ~ element(meet_of_latt_set(sK0,sK1),the_carrier(sK0))
| spl29_338 ),
inference(resolution,[],[f191051,f606]) ).
fof(f191051,plain,
( ! [X0] :
( ~ latt_set_smaller(sK0,X0,sK1)
| element(sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,X0)),the_carrier(sK0))
| ~ element(X0,the_carrier(sK0)) )
| spl29_338 ),
inference(subsumption_resolution,[],[f191050,f3902]) ).
fof(f191050,plain,
( ! [X0] :
( element(sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,X0)),the_carrier(sK0))
| ~ element(cast_to_el_of_LattPOSet(sK0,X0),the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,sK1)
| ~ element(X0,the_carrier(sK0)) )
| spl29_338 ),
inference(subsumption_resolution,[],[f191049,f279]) ).
fof(f191049,plain,
( ! [X0] :
( element(sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,X0)),the_carrier(sK0))
| ~ element(cast_to_el_of_LattPOSet(sK0,X0),the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,sK1)
| ~ element(X0,the_carrier(sK0))
| empty_carrier(sK0) )
| spl29_338 ),
inference(subsumption_resolution,[],[f191048,f280]) ).
fof(f191048,plain,
( ! [X0] :
( element(sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,X0)),the_carrier(sK0))
| ~ element(cast_to_el_of_LattPOSet(sK0,X0),the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,sK1)
| ~ element(X0,the_carrier(sK0))
| ~ lattice(sK0)
| empty_carrier(sK0) )
| spl29_338 ),
inference(subsumption_resolution,[],[f191027,f282]) ).
fof(f191027,plain,
( ! [X0] :
( element(sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,X0)),the_carrier(sK0))
| ~ element(cast_to_el_of_LattPOSet(sK0,X0),the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,sK1)
| ~ element(X0,the_carrier(sK0))
| ~ latt_str(sK0)
| ~ lattice(sK0)
| empty_carrier(sK0) )
| spl29_338 ),
inference(resolution,[],[f191012,f383]) ).
fof(f191012,plain,
( ! [X0] :
( ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X0)
| element(sK9(poset_of_lattice(sK0),sK1,X0),the_carrier(sK0))
| ~ element(X0,the_carrier(sK0)) )
| spl29_338 ),
inference(forward_demodulation,[],[f191011,f3900]) ).
fof(f191011,plain,
( ! [X0] :
( element(sK9(poset_of_lattice(sK0),sK1,X0),the_carrier(sK0))
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X0)
| ~ element(X0,the_carrier(poset_of_lattice(sK0))) )
| spl29_338 ),
inference(forward_demodulation,[],[f191010,f3900]) ).
fof(f191010,plain,
( ! [X0] :
( element(sK9(poset_of_lattice(sK0),sK1,X0),the_carrier(poset_of_lattice(sK0)))
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X0)
| ~ element(X0,the_carrier(poset_of_lattice(sK0))) )
| spl29_338 ),
inference(subsumption_resolution,[],[f191009,f539]) ).
fof(f191009,plain,
( ! [X0] :
( element(sK9(poset_of_lattice(sK0),sK1,X0),the_carrier(poset_of_lattice(sK0)))
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X0)
| ~ element(X0,the_carrier(poset_of_lattice(sK0)))
| ~ antisymmetric_relstr(poset_of_lattice(sK0)) )
| spl29_338 ),
inference(subsumption_resolution,[],[f191006,f552]) ).
fof(f191006,plain,
( ! [X0] :
( element(sK9(poset_of_lattice(sK0),sK1,X0),the_carrier(poset_of_lattice(sK0)))
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X0)
| ~ element(X0,the_carrier(poset_of_lattice(sK0)))
| ~ rel_str(poset_of_lattice(sK0))
| ~ antisymmetric_relstr(poset_of_lattice(sK0)) )
| spl29_338 ),
inference(resolution,[],[f191001,f357]) ).
fof(f357,plain,
! [X2,X0,X1] :
( ex_inf_of_relstr_set(X0,X1)
| element(sK9(X0,X1,X2),the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(cnf_transformation,[],[f231]) ).
fof(f193143,plain,
( related_reflexive(poset_of_lattice(sK0),sK9(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)),meet_of_latt_set(sK0,sK1))
| spl29_338 ),
inference(forward_demodulation,[],[f193142,f191858]) ).
fof(f191858,plain,
( sK9(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)) = cast_to_el_of_LattPOSet(sK0,sK9(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)))
| spl29_338 ),
inference(resolution,[],[f191254,f554]) ).
fof(f193142,plain,
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,sK9(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1))),meet_of_latt_set(sK0,sK1))
| spl29_338 ),
inference(forward_demodulation,[],[f193141,f192094]) ).
fof(f192094,plain,
( sK9(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)) = cast_to_el_of_lattice(sK0,sK9(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)))
| spl29_338 ),
inference(forward_demodulation,[],[f191866,f191858]) ).
fof(f191866,plain,
( cast_to_el_of_LattPOSet(sK0,sK9(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1))) = cast_to_el_of_lattice(sK0,cast_to_el_of_LattPOSet(sK0,sK9(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1))))
| spl29_338 ),
inference(resolution,[],[f191254,f1499]) ).
fof(f193141,plain,
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,cast_to_el_of_lattice(sK0,sK9(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)))),meet_of_latt_set(sK0,sK1))
| spl29_338 ),
inference(subsumption_resolution,[],[f193034,f191254]) ).
fof(f193034,plain,
( related_reflexive(poset_of_lattice(sK0),cast_to_el_of_LattPOSet(sK0,cast_to_el_of_lattice(sK0,sK9(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)))),meet_of_latt_set(sK0,sK1))
| ~ element(sK9(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)),the_carrier(sK0))
| spl29_338 ),
inference(resolution,[],[f191429,f6518]) ).
fof(f191429,plain,
( relstr_element_smaller(poset_of_lattice(sK0),sK1,sK9(poset_of_lattice(sK0),sK1,meet_of_latt_set(sK0,sK1)))
| spl29_338 ),
inference(forward_demodulation,[],[f191428,f1200]) ).
fof(f191428,plain,
( relstr_element_smaller(poset_of_lattice(sK0),sK1,sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,sK1))))
| spl29_338 ),
inference(subsumption_resolution,[],[f191357,f583]) ).
fof(f191357,plain,
( relstr_element_smaller(poset_of_lattice(sK0),sK1,sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,meet_of_latt_set(sK0,sK1))))
| ~ element(meet_of_latt_set(sK0,sK1),the_carrier(sK0))
| spl29_338 ),
inference(resolution,[],[f191099,f606]) ).
fof(f191099,plain,
( ! [X0] :
( ~ latt_set_smaller(sK0,X0,sK1)
| relstr_element_smaller(poset_of_lattice(sK0),sK1,sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,X0)))
| ~ element(X0,the_carrier(sK0)) )
| spl29_338 ),
inference(subsumption_resolution,[],[f191098,f3902]) ).
fof(f191098,plain,
( ! [X0] :
( relstr_element_smaller(poset_of_lattice(sK0),sK1,sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,X0)))
| ~ element(cast_to_el_of_LattPOSet(sK0,X0),the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,sK1)
| ~ element(X0,the_carrier(sK0)) )
| spl29_338 ),
inference(subsumption_resolution,[],[f191097,f279]) ).
fof(f191097,plain,
( ! [X0] :
( relstr_element_smaller(poset_of_lattice(sK0),sK1,sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,X0)))
| ~ element(cast_to_el_of_LattPOSet(sK0,X0),the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,sK1)
| ~ element(X0,the_carrier(sK0))
| empty_carrier(sK0) )
| spl29_338 ),
inference(subsumption_resolution,[],[f191096,f280]) ).
fof(f191096,plain,
( ! [X0] :
( relstr_element_smaller(poset_of_lattice(sK0),sK1,sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,X0)))
| ~ element(cast_to_el_of_LattPOSet(sK0,X0),the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,sK1)
| ~ element(X0,the_carrier(sK0))
| ~ lattice(sK0)
| empty_carrier(sK0) )
| spl29_338 ),
inference(subsumption_resolution,[],[f191075,f282]) ).
fof(f191075,plain,
( ! [X0] :
( relstr_element_smaller(poset_of_lattice(sK0),sK1,sK9(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,X0)))
| ~ element(cast_to_el_of_LattPOSet(sK0,X0),the_carrier(sK0))
| ~ latt_set_smaller(sK0,X0,sK1)
| ~ element(X0,the_carrier(sK0))
| ~ latt_str(sK0)
| ~ lattice(sK0)
| empty_carrier(sK0) )
| spl29_338 ),
inference(resolution,[],[f191015,f383]) ).
fof(f191015,plain,
( ! [X1] :
( ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X1)
| relstr_element_smaller(poset_of_lattice(sK0),sK1,sK9(poset_of_lattice(sK0),sK1,X1))
| ~ element(X1,the_carrier(sK0)) )
| spl29_338 ),
inference(forward_demodulation,[],[f191014,f3900]) ).
fof(f191014,plain,
( ! [X1] :
( relstr_element_smaller(poset_of_lattice(sK0),sK1,sK9(poset_of_lattice(sK0),sK1,X1))
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X1)
| ~ element(X1,the_carrier(poset_of_lattice(sK0))) )
| spl29_338 ),
inference(subsumption_resolution,[],[f191013,f539]) ).
fof(f191013,plain,
( ! [X1] :
( relstr_element_smaller(poset_of_lattice(sK0),sK1,sK9(poset_of_lattice(sK0),sK1,X1))
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X1)
| ~ element(X1,the_carrier(poset_of_lattice(sK0)))
| ~ antisymmetric_relstr(poset_of_lattice(sK0)) )
| spl29_338 ),
inference(subsumption_resolution,[],[f191007,f552]) ).
fof(f191007,plain,
( ! [X1] :
( relstr_element_smaller(poset_of_lattice(sK0),sK1,sK9(poset_of_lattice(sK0),sK1,X1))
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X1)
| ~ element(X1,the_carrier(poset_of_lattice(sK0)))
| ~ rel_str(poset_of_lattice(sK0))
| ~ antisymmetric_relstr(poset_of_lattice(sK0)) )
| spl29_338 ),
inference(resolution,[],[f191001,f358]) ).
fof(f358,plain,
! [X2,X0,X1] :
( ex_inf_of_relstr_set(X0,X1)
| relstr_element_smaller(X0,X1,sK9(X0,X1,X2))
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(cnf_transformation,[],[f231]) ).
fof(f191026,plain,
( ~ spl29_338
| spl29_341
| spl29_2 ),
inference(avatar_split_clause,[],[f190998,f745,f191024,f191000]) ).
fof(f745,plain,
( spl29_2
<=> meet_of_latt_set(sK0,sK1) = meet_on_relstr(poset_of_lattice(sK0),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_2])]) ).
fof(f190998,plain,
( ! [X2] :
( ~ element(X2,the_carrier(sK0))
| meet_of_latt_set(sK0,sK1) != X2
| ~ related(poset_of_lattice(sK0),sK4(poset_of_lattice(sK0),sK1,X2),X2)
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X2)
| ~ ex_inf_of_relstr_set(poset_of_lattice(sK0),sK1) )
| spl29_2 ),
inference(forward_demodulation,[],[f190997,f3900]) ).
fof(f190997,plain,
( ! [X2] :
( meet_of_latt_set(sK0,sK1) != X2
| ~ related(poset_of_lattice(sK0),sK4(poset_of_lattice(sK0),sK1,X2),X2)
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X2)
| ~ ex_inf_of_relstr_set(poset_of_lattice(sK0),sK1)
| ~ element(X2,the_carrier(poset_of_lattice(sK0))) )
| spl29_2 ),
inference(subsumption_resolution,[],[f190991,f552]) ).
fof(f190991,plain,
( ! [X2] :
( meet_of_latt_set(sK0,sK1) != X2
| ~ related(poset_of_lattice(sK0),sK4(poset_of_lattice(sK0),sK1,X2),X2)
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X2)
| ~ ex_inf_of_relstr_set(poset_of_lattice(sK0),sK1)
| ~ element(X2,the_carrier(poset_of_lattice(sK0)))
| ~ rel_str(poset_of_lattice(sK0)) )
| spl29_2 ),
inference(superposition,[],[f746,f306]) ).
fof(f306,plain,
! [X2,X0,X1] :
( meet_on_relstr(X0,X1) = X2
| ~ related(X0,sK4(X0,X1,X2),X2)
| ~ relstr_element_smaller(X0,X1,X2)
| ~ ex_inf_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f208,plain,
! [X0] :
( ! [X1,X2] :
( ( ( meet_on_relstr(X0,X1) = X2
| ( ~ related(X0,sK4(X0,X1,X2),X2)
& relstr_element_smaller(X0,X1,sK4(X0,X1,X2))
& element(sK4(X0,X1,X2),the_carrier(X0)) )
| ~ relstr_element_smaller(X0,X1,X2) )
& ( ( ! [X4] :
( related(X0,X4,X2)
| ~ relstr_element_smaller(X0,X1,X4)
| ~ element(X4,the_carrier(X0)) )
& relstr_element_smaller(X0,X1,X2) )
| meet_on_relstr(X0,X1) != X2 ) )
| ~ ex_inf_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f206,f207]) ).
fof(f207,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ related(X0,X3,X2)
& relstr_element_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) )
=> ( ~ related(X0,sK4(X0,X1,X2),X2)
& relstr_element_smaller(X0,X1,sK4(X0,X1,X2))
& element(sK4(X0,X1,X2),the_carrier(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f206,plain,
! [X0] :
( ! [X1,X2] :
( ( ( meet_on_relstr(X0,X1) = X2
| ? [X3] :
( ~ related(X0,X3,X2)
& relstr_element_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) )
| ~ relstr_element_smaller(X0,X1,X2) )
& ( ( ! [X4] :
( related(X0,X4,X2)
| ~ relstr_element_smaller(X0,X1,X4)
| ~ element(X4,the_carrier(X0)) )
& relstr_element_smaller(X0,X1,X2) )
| meet_on_relstr(X0,X1) != X2 ) )
| ~ ex_inf_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(rectify,[],[f205]) ).
fof(f205,plain,
! [X0] :
( ! [X1,X2] :
( ( ( meet_on_relstr(X0,X1) = X2
| ? [X3] :
( ~ related(X0,X3,X2)
& relstr_element_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) )
| ~ relstr_element_smaller(X0,X1,X2) )
& ( ( ! [X3] :
( related(X0,X3,X2)
| ~ relstr_element_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& relstr_element_smaller(X0,X1,X2) )
| meet_on_relstr(X0,X1) != X2 ) )
| ~ ex_inf_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(flattening,[],[f204]) ).
fof(f204,plain,
! [X0] :
( ! [X1,X2] :
( ( ( meet_on_relstr(X0,X1) = X2
| ? [X3] :
( ~ related(X0,X3,X2)
& relstr_element_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) )
| ~ relstr_element_smaller(X0,X1,X2) )
& ( ( ! [X3] :
( related(X0,X3,X2)
| ~ relstr_element_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& relstr_element_smaller(X0,X1,X2) )
| meet_on_relstr(X0,X1) != X2 ) )
| ~ ex_inf_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0] :
( ! [X1,X2] :
( ( meet_on_relstr(X0,X1) = X2
<=> ( ! [X3] :
( related(X0,X3,X2)
| ~ relstr_element_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& relstr_element_smaller(X0,X1,X2) ) )
| ~ ex_inf_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(flattening,[],[f110]) ).
fof(f110,plain,
! [X0] :
( ! [X1,X2] :
( ( meet_on_relstr(X0,X1) = X2
<=> ( ! [X3] :
( related(X0,X3,X2)
| ~ relstr_element_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& relstr_element_smaller(X0,X1,X2) ) )
| ~ ex_inf_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1,X2] :
( element(X2,the_carrier(X0))
=> ( ex_inf_of_relstr_set(X0,X1)
=> ( meet_on_relstr(X0,X1) = X2
<=> ( ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_element_smaller(X0,X1,X3)
=> related(X0,X3,X2) ) )
& relstr_element_smaller(X0,X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',d10_yellow_0) ).
fof(f746,plain,
( meet_of_latt_set(sK0,sK1) != meet_on_relstr(poset_of_lattice(sK0),sK1)
| spl29_2 ),
inference(avatar_component_clause,[],[f745]) ).
fof(f191022,plain,
( ~ spl29_338
| spl29_340
| spl29_2 ),
inference(avatar_split_clause,[],[f190996,f745,f191020,f191000]) ).
fof(f190996,plain,
( ! [X1] :
( ~ element(X1,the_carrier(sK0))
| meet_of_latt_set(sK0,sK1) != X1
| relstr_element_smaller(poset_of_lattice(sK0),sK1,sK4(poset_of_lattice(sK0),sK1,X1))
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X1)
| ~ ex_inf_of_relstr_set(poset_of_lattice(sK0),sK1) )
| spl29_2 ),
inference(forward_demodulation,[],[f190995,f3900]) ).
fof(f190995,plain,
( ! [X1] :
( meet_of_latt_set(sK0,sK1) != X1
| relstr_element_smaller(poset_of_lattice(sK0),sK1,sK4(poset_of_lattice(sK0),sK1,X1))
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X1)
| ~ ex_inf_of_relstr_set(poset_of_lattice(sK0),sK1)
| ~ element(X1,the_carrier(poset_of_lattice(sK0))) )
| spl29_2 ),
inference(subsumption_resolution,[],[f190990,f552]) ).
fof(f190990,plain,
( ! [X1] :
( meet_of_latt_set(sK0,sK1) != X1
| relstr_element_smaller(poset_of_lattice(sK0),sK1,sK4(poset_of_lattice(sK0),sK1,X1))
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X1)
| ~ ex_inf_of_relstr_set(poset_of_lattice(sK0),sK1)
| ~ element(X1,the_carrier(poset_of_lattice(sK0)))
| ~ rel_str(poset_of_lattice(sK0)) )
| spl29_2 ),
inference(superposition,[],[f746,f305]) ).
fof(f305,plain,
! [X2,X0,X1] :
( meet_on_relstr(X0,X1) = X2
| relstr_element_smaller(X0,X1,sK4(X0,X1,X2))
| ~ relstr_element_smaller(X0,X1,X2)
| ~ ex_inf_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f191005,plain,
( ~ spl29_338
| spl29_339
| spl29_2 ),
inference(avatar_split_clause,[],[f190994,f745,f191003,f191000]) ).
fof(f190994,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK0))
| element(sK4(poset_of_lattice(sK0),sK1,X0),the_carrier(sK0))
| meet_of_latt_set(sK0,sK1) != X0
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X0)
| ~ ex_inf_of_relstr_set(poset_of_lattice(sK0),sK1) )
| spl29_2 ),
inference(forward_demodulation,[],[f190993,f3900]) ).
fof(f190993,plain,
( ! [X0] :
( element(sK4(poset_of_lattice(sK0),sK1,X0),the_carrier(sK0))
| meet_of_latt_set(sK0,sK1) != X0
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X0)
| ~ ex_inf_of_relstr_set(poset_of_lattice(sK0),sK1)
| ~ element(X0,the_carrier(poset_of_lattice(sK0))) )
| spl29_2 ),
inference(forward_demodulation,[],[f190992,f3900]) ).
fof(f190992,plain,
( ! [X0] :
( meet_of_latt_set(sK0,sK1) != X0
| element(sK4(poset_of_lattice(sK0),sK1,X0),the_carrier(poset_of_lattice(sK0)))
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X0)
| ~ ex_inf_of_relstr_set(poset_of_lattice(sK0),sK1)
| ~ element(X0,the_carrier(poset_of_lattice(sK0))) )
| spl29_2 ),
inference(subsumption_resolution,[],[f190989,f552]) ).
fof(f190989,plain,
( ! [X0] :
( meet_of_latt_set(sK0,sK1) != X0
| element(sK4(poset_of_lattice(sK0),sK1,X0),the_carrier(poset_of_lattice(sK0)))
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,X0)
| ~ ex_inf_of_relstr_set(poset_of_lattice(sK0),sK1)
| ~ element(X0,the_carrier(poset_of_lattice(sK0)))
| ~ rel_str(poset_of_lattice(sK0)) )
| spl29_2 ),
inference(superposition,[],[f746,f304]) ).
fof(f304,plain,
! [X2,X0,X1] :
( meet_on_relstr(X0,X1) = X2
| element(sK4(X0,X1,X2),the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ~ ex_inf_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f190984,plain,
spl29_14,
inference(avatar_contradiction_clause,[],[f190983]) ).
fof(f190983,plain,
( $false
| spl29_14 ),
inference(subsumption_resolution,[],[f190982,f19858]) ).
fof(f19858,plain,
( ~ related(poset_of_lattice(sK0),join_of_latt_set(sK0,sK1),sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))
| spl29_14 ),
inference(resolution,[],[f7525,f624]) ).
fof(f7525,plain,
( ! [X1] :
( ~ latt_element_smaller(sK0,join_of_latt_set(sK0,X1),sK1)
| ~ related(poset_of_lattice(sK0),join_of_latt_set(sK0,X1),sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,X1))) )
| spl29_14 ),
inference(forward_literal_rewriting,[],[f7504,f1057]) ).
fof(f7504,plain,
( ! [X1] :
( ~ related(poset_of_lattice(sK0),join_of_latt_set(sK0,X1),sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,X1)))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,X1)) )
| spl29_14 ),
inference(resolution,[],[f4024,f582]) ).
fof(f4024,plain,
( ! [X2] :
( ~ element(X2,the_carrier(sK0))
| ~ related(poset_of_lattice(sK0),X2,sK11(poset_of_lattice(sK0),sK1,X2))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X2) )
| spl29_14 ),
inference(backward_demodulation,[],[f2222,f3900]) ).
fof(f2222,plain,
( ! [X2] :
( ~ related(poset_of_lattice(sK0),X2,sK11(poset_of_lattice(sK0),sK1,X2))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X2)
| ~ element(X2,the_carrier(poset_of_lattice(sK0))) )
| spl29_14 ),
inference(subsumption_resolution,[],[f2221,f539]) ).
fof(f2221,plain,
( ! [X2] :
( ~ related(poset_of_lattice(sK0),X2,sK11(poset_of_lattice(sK0),sK1,X2))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X2)
| ~ element(X2,the_carrier(poset_of_lattice(sK0)))
| ~ antisymmetric_relstr(poset_of_lattice(sK0)) )
| spl29_14 ),
inference(subsumption_resolution,[],[f2216,f552]) ).
fof(f2216,plain,
( ! [X2] :
( ~ related(poset_of_lattice(sK0),X2,sK11(poset_of_lattice(sK0),sK1,X2))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X2)
| ~ element(X2,the_carrier(poset_of_lattice(sK0)))
| ~ rel_str(poset_of_lattice(sK0))
| ~ antisymmetric_relstr(poset_of_lattice(sK0)) )
| spl29_14 ),
inference(resolution,[],[f2205,f365]) ).
fof(f365,plain,
! [X2,X0,X1] :
( ex_sup_of_relstr_set(X0,X1)
| ~ related(X0,X2,sK11(X0,X1,X2))
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(cnf_transformation,[],[f236]) ).
fof(f236,plain,
! [X0] :
( ! [X1] :
( ( ex_sup_of_relstr_set(X0,X1)
| ! [X2] :
( ( ~ related(X0,X2,sK11(X0,X1,X2))
& relstr_set_smaller(X0,X1,sK11(X0,X1,X2))
& element(sK11(X0,X1,X2),the_carrier(X0)) )
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0)) ) )
& ( ( ! [X5] :
( related(X0,sK12(X0,X1),X5)
| ~ relstr_set_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) )
& relstr_set_smaller(X0,X1,sK12(X0,X1))
& element(sK12(X0,X1),the_carrier(X0)) )
| ~ ex_sup_of_relstr_set(X0,X1) ) )
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f233,f235,f234]) ).
fof(f234,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ related(X0,X2,X3)
& relstr_set_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) )
=> ( ~ related(X0,X2,sK11(X0,X1,X2))
& relstr_set_smaller(X0,X1,sK11(X0,X1,X2))
& element(sK11(X0,X1,X2),the_carrier(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f235,plain,
! [X0,X1] :
( ? [X4] :
( ! [X5] :
( related(X0,X4,X5)
| ~ relstr_set_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) )
& relstr_set_smaller(X0,X1,X4)
& element(X4,the_carrier(X0)) )
=> ( ! [X5] :
( related(X0,sK12(X0,X1),X5)
| ~ relstr_set_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) )
& relstr_set_smaller(X0,X1,sK12(X0,X1))
& element(sK12(X0,X1),the_carrier(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f233,plain,
! [X0] :
( ! [X1] :
( ( ex_sup_of_relstr_set(X0,X1)
| ! [X2] :
( ? [X3] :
( ~ related(X0,X2,X3)
& relstr_set_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) )
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0)) ) )
& ( ? [X4] :
( ! [X5] :
( related(X0,X4,X5)
| ~ relstr_set_smaller(X0,X1,X5)
| ~ element(X5,the_carrier(X0)) )
& relstr_set_smaller(X0,X1,X4)
& element(X4,the_carrier(X0)) )
| ~ ex_sup_of_relstr_set(X0,X1) ) )
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(rectify,[],[f232]) ).
fof(f232,plain,
! [X0] :
( ! [X1] :
( ( ex_sup_of_relstr_set(X0,X1)
| ! [X2] :
( ? [X3] :
( ~ related(X0,X2,X3)
& relstr_set_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) )
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0)) ) )
& ( ? [X2] :
( ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& relstr_set_smaller(X0,X1,X2)
& element(X2,the_carrier(X0)) )
| ~ ex_sup_of_relstr_set(X0,X1) ) )
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(nnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0] :
( ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& relstr_set_smaller(X0,X1,X2)
& element(X2,the_carrier(X0)) ) )
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(flattening,[],[f147]) ).
fof(f147,plain,
! [X0] :
( ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& relstr_set_smaller(X0,X1,X2)
& element(X2,the_carrier(X0)) ) )
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,axiom,
! [X0] :
( ( rel_str(X0)
& antisymmetric_relstr(X0) )
=> ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X3)
=> related(X0,X2,X3) ) )
& relstr_set_smaller(X0,X1,X2)
& element(X2,the_carrier(X0)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',t15_yellow_0) ).
fof(f2205,plain,
( ~ ex_sup_of_relstr_set(poset_of_lattice(sK0),sK1)
| spl29_14 ),
inference(avatar_component_clause,[],[f2204]) ).
fof(f2204,plain,
( spl29_14
<=> ex_sup_of_relstr_set(poset_of_lattice(sK0),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_14])]) ).
fof(f190982,plain,
( related(poset_of_lattice(sK0),join_of_latt_set(sK0,sK1),sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))
| spl29_14 ),
inference(forward_literal_rewriting,[],[f190981,f97554]) ).
fof(f97554,plain,
( ! [X37] :
( related(poset_of_lattice(sK0),join_of_latt_set(sK0,X37),sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))
| ~ related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,X37),sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1))) )
| spl29_14 ),
inference(resolution,[],[f14156,f4043]) ).
fof(f14156,plain,
( element(sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)),the_carrier(sK0))
| spl29_14 ),
inference(resolution,[],[f6821,f624]) ).
fof(f6821,plain,
( ! [X1] :
( ~ latt_element_smaller(sK0,join_of_latt_set(sK0,X1),sK1)
| element(sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,X1)),the_carrier(sK0)) )
| spl29_14 ),
inference(forward_literal_rewriting,[],[f6800,f1057]) ).
fof(f6800,plain,
( ! [X1] :
( element(sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,X1)),the_carrier(sK0))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,X1)) )
| spl29_14 ),
inference(resolution,[],[f4202,f582]) ).
fof(f4202,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK0))
| element(sK11(poset_of_lattice(sK0),sK1,X0),the_carrier(sK0))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X0) )
| spl29_14 ),
inference(forward_demodulation,[],[f4022,f3900]) ).
fof(f4022,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK0))
| element(sK11(poset_of_lattice(sK0),sK1,X0),the_carrier(poset_of_lattice(sK0)))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X0) )
| spl29_14 ),
inference(backward_demodulation,[],[f2218,f3900]) ).
fof(f2218,plain,
( ! [X0] :
( element(sK11(poset_of_lattice(sK0),sK1,X0),the_carrier(poset_of_lattice(sK0)))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X0)
| ~ element(X0,the_carrier(poset_of_lattice(sK0))) )
| spl29_14 ),
inference(subsumption_resolution,[],[f2217,f539]) ).
fof(f2217,plain,
( ! [X0] :
( element(sK11(poset_of_lattice(sK0),sK1,X0),the_carrier(poset_of_lattice(sK0)))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X0)
| ~ element(X0,the_carrier(poset_of_lattice(sK0)))
| ~ antisymmetric_relstr(poset_of_lattice(sK0)) )
| spl29_14 ),
inference(subsumption_resolution,[],[f2214,f552]) ).
fof(f2214,plain,
( ! [X0] :
( element(sK11(poset_of_lattice(sK0),sK1,X0),the_carrier(poset_of_lattice(sK0)))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X0)
| ~ element(X0,the_carrier(poset_of_lattice(sK0)))
| ~ rel_str(poset_of_lattice(sK0))
| ~ antisymmetric_relstr(poset_of_lattice(sK0)) )
| spl29_14 ),
inference(resolution,[],[f2205,f363]) ).
fof(f363,plain,
! [X2,X0,X1] :
( ex_sup_of_relstr_set(X0,X1)
| element(sK11(X0,X1,X2),the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(cnf_transformation,[],[f236]) ).
fof(f190981,plain,
( related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,sK1),sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))
| spl29_14 ),
inference(forward_demodulation,[],[f190980,f97502]) ).
fof(f97502,plain,
( sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)) = cast_to_el_of_LattPOSet(sK0,sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))
| spl29_14 ),
inference(resolution,[],[f14156,f554]) ).
fof(f190980,plain,
( related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,sK1),cast_to_el_of_LattPOSet(sK0,sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1))))
| spl29_14 ),
inference(forward_demodulation,[],[f190979,f97716]) ).
fof(f97716,plain,
( sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)) = cast_to_el_of_lattice(sK0,sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))
| spl29_14 ),
inference(forward_demodulation,[],[f97510,f97502]) ).
fof(f97510,plain,
( cast_to_el_of_LattPOSet(sK0,sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1))) = cast_to_el_of_lattice(sK0,cast_to_el_of_LattPOSet(sK0,sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1))))
| spl29_14 ),
inference(resolution,[],[f14156,f1499]) ).
fof(f190979,plain,
( related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,sK1),cast_to_el_of_LattPOSet(sK0,cast_to_el_of_lattice(sK0,sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))))
| spl29_14 ),
inference(subsumption_resolution,[],[f190950,f14156]) ).
fof(f190950,plain,
( related_reflexive(poset_of_lattice(sK0),join_of_latt_set(sK0,sK1),cast_to_el_of_LattPOSet(sK0,cast_to_el_of_lattice(sK0,sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))))
| ~ element(sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)),the_carrier(sK0))
| spl29_14 ),
inference(resolution,[],[f14569,f15825]) ).
fof(f15825,plain,
( relstr_set_smaller(poset_of_lattice(sK0),sK1,sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,sK1)))
| spl29_14 ),
inference(resolution,[],[f7479,f624]) ).
fof(f7479,plain,
( ! [X1] :
( ~ latt_element_smaller(sK0,join_of_latt_set(sK0,X1),sK1)
| relstr_set_smaller(poset_of_lattice(sK0),sK1,sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,X1))) )
| spl29_14 ),
inference(forward_literal_rewriting,[],[f7458,f1057]) ).
fof(f7458,plain,
( ! [X1] :
( relstr_set_smaller(poset_of_lattice(sK0),sK1,sK11(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,X1)))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,join_of_latt_set(sK0,X1)) )
| spl29_14 ),
inference(resolution,[],[f4023,f582]) ).
fof(f4023,plain,
( ! [X1] :
( ~ element(X1,the_carrier(sK0))
| relstr_set_smaller(poset_of_lattice(sK0),sK1,sK11(poset_of_lattice(sK0),sK1,X1))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X1) )
| spl29_14 ),
inference(backward_demodulation,[],[f2220,f3900]) ).
fof(f2220,plain,
( ! [X1] :
( relstr_set_smaller(poset_of_lattice(sK0),sK1,sK11(poset_of_lattice(sK0),sK1,X1))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X1)
| ~ element(X1,the_carrier(poset_of_lattice(sK0))) )
| spl29_14 ),
inference(subsumption_resolution,[],[f2219,f539]) ).
fof(f2219,plain,
( ! [X1] :
( relstr_set_smaller(poset_of_lattice(sK0),sK1,sK11(poset_of_lattice(sK0),sK1,X1))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X1)
| ~ element(X1,the_carrier(poset_of_lattice(sK0)))
| ~ antisymmetric_relstr(poset_of_lattice(sK0)) )
| spl29_14 ),
inference(subsumption_resolution,[],[f2215,f552]) ).
fof(f2215,plain,
( ! [X1] :
( relstr_set_smaller(poset_of_lattice(sK0),sK1,sK11(poset_of_lattice(sK0),sK1,X1))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X1)
| ~ element(X1,the_carrier(poset_of_lattice(sK0)))
| ~ rel_str(poset_of_lattice(sK0))
| ~ antisymmetric_relstr(poset_of_lattice(sK0)) )
| spl29_14 ),
inference(resolution,[],[f2205,f364]) ).
fof(f364,plain,
! [X2,X0,X1] :
( ex_sup_of_relstr_set(X0,X1)
| relstr_set_smaller(X0,X1,sK11(X0,X1,X2))
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0)
| ~ antisymmetric_relstr(X0) ),
inference(cnf_transformation,[],[f236]) ).
fof(f2230,plain,
( ~ spl29_14
| spl29_17
| spl29_1 ),
inference(avatar_split_clause,[],[f753,f742,f2228,f2204]) ).
fof(f742,plain,
( spl29_1
<=> join_of_latt_set(sK0,sK1) = join_on_relstr(poset_of_lattice(sK0),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_1])]) ).
fof(f753,plain,
( ! [X2] :
( join_of_latt_set(sK0,sK1) != X2
| ~ related(poset_of_lattice(sK0),X2,sK5(poset_of_lattice(sK0),sK1,X2))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X2)
| ~ ex_sup_of_relstr_set(poset_of_lattice(sK0),sK1)
| ~ element(X2,the_carrier(poset_of_lattice(sK0))) )
| spl29_1 ),
inference(subsumption_resolution,[],[f750,f552]) ).
fof(f750,plain,
( ! [X2] :
( join_of_latt_set(sK0,sK1) != X2
| ~ related(poset_of_lattice(sK0),X2,sK5(poset_of_lattice(sK0),sK1,X2))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X2)
| ~ ex_sup_of_relstr_set(poset_of_lattice(sK0),sK1)
| ~ element(X2,the_carrier(poset_of_lattice(sK0)))
| ~ rel_str(poset_of_lattice(sK0)) )
| spl29_1 ),
inference(superposition,[],[f743,f311]) ).
fof(f311,plain,
! [X2,X0,X1] :
( join_on_relstr(X0,X1) = X2
| ~ related(X0,X2,sK5(X0,X1,X2))
| ~ relstr_set_smaller(X0,X1,X2)
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f213,plain,
! [X0] :
( ! [X1,X2] :
( ( ( join_on_relstr(X0,X1) = X2
| ( ~ related(X0,X2,sK5(X0,X1,X2))
& relstr_set_smaller(X0,X1,sK5(X0,X1,X2))
& element(sK5(X0,X1,X2),the_carrier(X0)) )
| ~ relstr_set_smaller(X0,X1,X2) )
& ( ( ! [X4] :
( related(X0,X2,X4)
| ~ relstr_set_smaller(X0,X1,X4)
| ~ element(X4,the_carrier(X0)) )
& relstr_set_smaller(X0,X1,X2) )
| join_on_relstr(X0,X1) != X2 ) )
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f211,f212]) ).
fof(f212,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ related(X0,X2,X3)
& relstr_set_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) )
=> ( ~ related(X0,X2,sK5(X0,X1,X2))
& relstr_set_smaller(X0,X1,sK5(X0,X1,X2))
& element(sK5(X0,X1,X2),the_carrier(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f211,plain,
! [X0] :
( ! [X1,X2] :
( ( ( join_on_relstr(X0,X1) = X2
| ? [X3] :
( ~ related(X0,X2,X3)
& relstr_set_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) )
| ~ relstr_set_smaller(X0,X1,X2) )
& ( ( ! [X4] :
( related(X0,X2,X4)
| ~ relstr_set_smaller(X0,X1,X4)
| ~ element(X4,the_carrier(X0)) )
& relstr_set_smaller(X0,X1,X2) )
| join_on_relstr(X0,X1) != X2 ) )
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(rectify,[],[f210]) ).
fof(f210,plain,
! [X0] :
( ! [X1,X2] :
( ( ( join_on_relstr(X0,X1) = X2
| ? [X3] :
( ~ related(X0,X2,X3)
& relstr_set_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) )
| ~ relstr_set_smaller(X0,X1,X2) )
& ( ( ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& relstr_set_smaller(X0,X1,X2) )
| join_on_relstr(X0,X1) != X2 ) )
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(flattening,[],[f209]) ).
fof(f209,plain,
! [X0] :
( ! [X1,X2] :
( ( ( join_on_relstr(X0,X1) = X2
| ? [X3] :
( ~ related(X0,X2,X3)
& relstr_set_smaller(X0,X1,X3)
& element(X3,the_carrier(X0)) )
| ~ relstr_set_smaller(X0,X1,X2) )
& ( ( ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& relstr_set_smaller(X0,X1,X2) )
| join_on_relstr(X0,X1) != X2 ) )
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0] :
( ! [X1,X2] :
( ( join_on_relstr(X0,X1) = X2
<=> ( ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& relstr_set_smaller(X0,X1,X2) ) )
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(flattening,[],[f112]) ).
fof(f112,plain,
! [X0] :
( ! [X1,X2] :
( ( join_on_relstr(X0,X1) = X2
<=> ( ! [X3] :
( related(X0,X2,X3)
| ~ relstr_set_smaller(X0,X1,X3)
| ~ element(X3,the_carrier(X0)) )
& relstr_set_smaller(X0,X1,X2) ) )
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1,X2] :
( element(X2,the_carrier(X0))
=> ( ex_sup_of_relstr_set(X0,X1)
=> ( join_on_relstr(X0,X1) = X2
<=> ( ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X3)
=> related(X0,X2,X3) ) )
& relstr_set_smaller(X0,X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672',d9_yellow_0) ).
fof(f743,plain,
( join_of_latt_set(sK0,sK1) != join_on_relstr(poset_of_lattice(sK0),sK1)
| spl29_1 ),
inference(avatar_component_clause,[],[f742]) ).
fof(f2226,plain,
( ~ spl29_14
| spl29_16
| spl29_1 ),
inference(avatar_split_clause,[],[f752,f742,f2224,f2204]) ).
fof(f752,plain,
( ! [X1] :
( join_of_latt_set(sK0,sK1) != X1
| relstr_set_smaller(poset_of_lattice(sK0),sK1,sK5(poset_of_lattice(sK0),sK1,X1))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X1)
| ~ ex_sup_of_relstr_set(poset_of_lattice(sK0),sK1)
| ~ element(X1,the_carrier(poset_of_lattice(sK0))) )
| spl29_1 ),
inference(subsumption_resolution,[],[f749,f552]) ).
fof(f749,plain,
( ! [X1] :
( join_of_latt_set(sK0,sK1) != X1
| relstr_set_smaller(poset_of_lattice(sK0),sK1,sK5(poset_of_lattice(sK0),sK1,X1))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X1)
| ~ ex_sup_of_relstr_set(poset_of_lattice(sK0),sK1)
| ~ element(X1,the_carrier(poset_of_lattice(sK0)))
| ~ rel_str(poset_of_lattice(sK0)) )
| spl29_1 ),
inference(superposition,[],[f743,f310]) ).
fof(f310,plain,
! [X2,X0,X1] :
( join_on_relstr(X0,X1) = X2
| relstr_set_smaller(X0,X1,sK5(X0,X1,X2))
| ~ relstr_set_smaller(X0,X1,X2)
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f2209,plain,
( ~ spl29_14
| spl29_15
| spl29_1 ),
inference(avatar_split_clause,[],[f751,f742,f2207,f2204]) ).
fof(f751,plain,
( ! [X0] :
( join_of_latt_set(sK0,sK1) != X0
| element(sK5(poset_of_lattice(sK0),sK1,X0),the_carrier(poset_of_lattice(sK0)))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X0)
| ~ ex_sup_of_relstr_set(poset_of_lattice(sK0),sK1)
| ~ element(X0,the_carrier(poset_of_lattice(sK0))) )
| spl29_1 ),
inference(subsumption_resolution,[],[f748,f552]) ).
fof(f748,plain,
( ! [X0] :
( join_of_latt_set(sK0,sK1) != X0
| element(sK5(poset_of_lattice(sK0),sK1,X0),the_carrier(poset_of_lattice(sK0)))
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,X0)
| ~ ex_sup_of_relstr_set(poset_of_lattice(sK0),sK1)
| ~ element(X0,the_carrier(poset_of_lattice(sK0)))
| ~ rel_str(poset_of_lattice(sK0)) )
| spl29_1 ),
inference(superposition,[],[f743,f309]) ).
fof(f309,plain,
! [X2,X0,X1] :
( join_on_relstr(X0,X1) = X2
| element(sK5(X0,X1,X2),the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ~ ex_sup_of_relstr_set(X0,X1)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f747,plain,
( ~ spl29_1
| ~ spl29_2 ),
inference(avatar_split_clause,[],[f283,f745,f742]) ).
fof(f283,plain,
( meet_of_latt_set(sK0,sK1) != meet_on_relstr(poset_of_lattice(sK0),sK1)
| join_of_latt_set(sK0,sK1) != join_on_relstr(poset_of_lattice(sK0),sK1) ),
inference(cnf_transformation,[],[f199]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : SEU358+1 : TPTP v8.1.2. Released v3.3.0.
% 0.16/0.16 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.38 % Computer : n006.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Wed Aug 23 14:11:23 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.16/0.38 This is a FOF_THM_RFO_SEQ problem
% 0.22/0.38 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.fw491hogH3/Vampire---4.8_24672
% 0.22/0.38 % (24779)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.45 % (24785)lrs+10_1024_av=off:bsr=on:br=off:ep=RSTC:fsd=off:irw=on:nm=4:nwc=1.1:sims=off:urr=on:stl=125_440 on Vampire---4 for (440ds/0Mi)
% 0.22/0.45 % (24784)ott+11_8:1_aac=none:amm=sco:anc=none:er=known:flr=on:fde=unused:irw=on:nm=0:nwc=1.2:nicw=on:sims=off:sos=all:sac=on_470 on Vampire---4 for (470ds/0Mi)
% 0.22/0.45 % (24781)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.22/0.45 % (24782)lrs+10_4:5_amm=off:bsr=on:bce=on:flr=on:fsd=off:fde=unused:gs=on:gsem=on:lcm=predicate:sos=all:tgt=ground:stl=62_514 on Vampire---4 for (514ds/0Mi)
% 0.22/0.45 % (24783)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.22/0.45 % (24780)lrs+1011_1_bd=preordered:flr=on:fsd=off:fsr=off:irw=on:lcm=reverse:msp=off:nm=2:nwc=10.0:sos=on:sp=reverse_weighted_frequency:tgt=full:stl=62_562 on Vampire---4 for (562ds/0Mi)
% 0.22/0.47 % (24786)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.22/0.47 % (24786)Refutation not found, incomplete strategy% (24786)------------------------------
% 0.22/0.47 % (24786)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.47 % (24786)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.47 % (24786)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.47
% 0.22/0.47 % (24786)Memory used [KB]: 5756
% 0.22/0.47 % (24786)Time elapsed: 0.006 s
% 0.22/0.47 % (24786)------------------------------
% 0.22/0.47 % (24786)------------------------------
% 0.22/0.51 % (24788)lrs-11_32_amm=off:bce=on:cond=on:er=filter:fsd=off:fde=none:gs=on:gsem=on:lcm=reverse:nm=4:nwc=1.1:sos=all:sac=on:sp=frequency:urr=on:stl=125_403 on Vampire---4 for (403ds/0Mi)
% 112.80/16.52 % (24784)First to succeed.
% 112.80/16.54 % (24784)Refutation found. Thanks to Tanya!
% 112.80/16.54 % SZS status Theorem for Vampire---4
% 112.80/16.54 % SZS output start Proof for Vampire---4
% See solution above
% 112.80/16.54 % (24784)------------------------------
% 112.80/16.54 % (24784)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 112.80/16.54 % (24784)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 112.80/16.54 % (24784)Termination reason: Refutation
% 112.80/16.54
% 112.80/16.54 % (24784)Memory used [KB]: 155818
% 112.80/16.54 % (24784)Time elapsed: 16.084 s
% 112.80/16.54 % (24784)------------------------------
% 112.80/16.54 % (24784)------------------------------
% 112.80/16.54 % (24779)Success in time 16.078 s
% 112.80/16.54 % Vampire---4.8 exiting
%------------------------------------------------------------------------------