%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP180^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:07:05 AM UTC 2026
% Result : Theorem 37.67s 11.18s
% Output : Refutation 38.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 278
% Syntax : Number of formulae : 558 ( 243 unt; 0 typ; 0 def)
% Number of atoms : 2190 ( 556 equ; 0 cnn)
% Maximal formula atoms : 38 ( 3 avg)
% Number of connectives : 10832 ( 128 ~; 22 |; 80 &;10164 @)
% ( 0 <=>; 438 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 168 ( 168 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 60 usr; 13 con; 0-8 aty)
% Number of variables : 2234 ( 92 ^;2118 !; 24 ?;2234 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(v_type,type,
v: $tType ).
thf(v2_type,type,
v2: $tType ).
thf(bounded_lattice_decl,type,
bounded_lattice:
!>[TA: $tType] : $o ).
thf(bot_decl,type,
bot:
!>[TA: $tType] : $o ).
thf(lattice_decl,type,
lattice:
!>[TA: $tType] : $o ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(semilattice_sup_decl,type,
semilattice_sup:
!>[TA: $tType] : $o ).
thf(bounde1808546759up_bot_decl,type,
bounde1808546759up_bot:
!>[TA: $tType] : $o ).
thf(bNF_Gr_decl,type,
bNF_Gr:
!>[TA: $tType,TB: $tType] : ( ( set @ TB ) > ( TB > TA ) > ( set @ ( product_prod @ TB @ TA ) ) ) ).
thf(comp_decl,type,
comp:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB ) > ( TA > TC ) > TA > TB ) ).
thf(standard_S_Bot_decl,type,
standard_S_Bot:
!>[TA: $tType] : ( standard_Constant @ TA ) ).
thf(standard_S_Const_decl,type,
standard_S_Const:
!>[TA: $tType] : ( TA > ( standard_Constant @ TA ) ) ).
thf(standard_S_Top_decl,type,
standard_S_Top:
!>[TA: $tType] : ( standard_Constant @ TA ) ).
thf(getRel_decl,type,
getRel:
!>[TA: $tType,TB: $tType] : ( TB > ( labeled_graph @ TB @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) ) ).
thf(semantics_decl,type,
semantics:
!>[TA: $tType,TB: $tType] : ( ( labeled_graph @ TB @ TA ) > ( allegorical_term @ TB ) > ( set @ ( product_prod @ TA @ TA ) ) ) ).
thf(edge_preserving_decl,type,
edge_preserving:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( set @ ( product_prod @ TC @ TB ) ) > ( set @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ) ) > ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) > $o ) ).
thf(graph_homomorphism_decl,type,
graph_homomorphism:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( labeled_graph @ TC @ TB ) > ( labeled_graph @ TC @ TA ) > ( set @ ( product_prod @ TB @ TA ) ) > $o ) ).
thf(graph_union_decl,type,
graph_union:
!>[TA: $tType,TB: $tType] : ( ( labeled_graph @ TB @ TA ) > ( labeled_graph @ TB @ TA ) > ( labeled_graph @ TB @ TA ) ) ).
thf(labeled_LG_decl,type,
labeled_LG:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ) ) > ( set @ TA ) > ( labeled_graph @ TB @ TA ) ) ).
thf(labele1974067554_graph_decl,type,
labele1974067554_graph:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( ( set @ ( product_prod @ TC @ ( product_prod @ TB @ TB ) ) ) > ( set @ TB ) > TA ) > ( labeled_graph @ TC @ TB ) > TA ) ).
thf(labeled_edges_decl,type,
labeled_edges:
!>[TA: $tType,TB: $tType] : ( ( labeled_graph @ TB @ TA ) > ( set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ) ) ) ).
thf(labeled_vertices_decl,type,
labeled_vertices:
!>[TA: $tType,TB: $tType] : ( ( labeled_graph @ TB @ TA ) > ( set @ TA ) ) ).
thf(map_graph_decl,type,
map_graph:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( set @ ( product_prod @ TC @ TB ) ) > ( labeled_graph @ TA @ TC ) > ( labeled_graph @ TA @ TB ) ) ).
thf(restrict_decl,type,
restrict:
!>[TA: $tType,TB: $tType] : ( ( labeled_graph @ TB @ TA ) > ( labeled_graph @ TB @ TA ) ) ).
thf(sup_sup_decl,type,
sup_sup:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(product_rec_prod_decl,type,
product_rec_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(field_decl,type,
field:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > ( set @ TA ) ) ).
thf(id_on_decl,type,
id_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) ) ).
thf(total_on_decl,type,
total_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(agree_on_decl,type,
agree_on:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( labeled_graph @ TC @ TB ) > ( set @ ( product_prod @ TB @ TA ) ) > ( set @ ( product_prod @ TB @ TA ) ) > $o ) ).
thf(consequence_graph_decl,type,
consequence_graph:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( set @ ( product_prod @ ( labeled_graph @ TC @ TB ) @ ( labeled_graph @ TC @ TB ) ) ) > ( labeled_graph @ TC @ TA ) > $o ) ).
thf(extensible_decl,type,
extensible:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( product_prod @ ( labeled_graph @ TC @ TB ) @ ( labeled_graph @ TC @ TB ) ) > ( labeled_graph @ TC @ TA ) > ( set @ ( product_prod @ TB @ TA ) ) > $o ) ).
thf(least_decl,type,
least:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( itself @ TD ) > ( set @ ( product_prod @ ( labeled_graph @ TC @ TB ) @ ( labeled_graph @ TC @ TB ) ) ) > ( labeled_graph @ TC @ TA ) > ( labeled_graph @ TC @ TA ) > $o ) ).
thf(least_559130134_graph_decl,type,
least_559130134_graph:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( itself @ TD ) > ( set @ ( product_prod @ ( labeled_graph @ TC @ TB ) @ ( labeled_graph @ TC @ TB ) ) ) > ( labeled_graph @ TC @ TA ) > ( labeled_graph @ TC @ TA ) > $o ) ).
thf(maintained_decl,type,
maintained:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( product_prod @ ( labeled_graph @ TC @ TB ) @ ( labeled_graph @ TC @ TB ) ) > ( labeled_graph @ TC @ TA ) > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(is_singleton_decl,type,
is_singleton:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(the_elem_decl,type,
the_elem:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(standa1138209853_rules_decl,type,
standa1138209853_rules:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) ) ) ) ).
thf(standa2002409347_rules_decl,type,
standa2002409347_rules:
!>[TA: $tType] : ( ( set @ ( standard_Constant @ TA ) ) > ( set @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) ) ) ) ).
thf(standa244753842y_rule_decl,type,
standa244753842y_rule:
!>[TA: $tType] : ( product_prod @ ( labeled_graph @ TA @ nat ) @ ( labeled_graph @ TA @ nat ) ) ).
thf(standa438229444_rules_decl,type,
standa438229444_rules:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( standard_Constant @ TA ) ) > ( set @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) ) ) ) ).
thf(standa400804411p_rule_decl,type,
standa400804411p_rule:
!>[TA: $tType] : ( TA > ( product_prod @ ( labeled_graph @ TA @ nat ) @ ( labeled_graph @ TA @ nat ) ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(c_decl,type,
c: set @ v2 ).
thf(g_decl,type,
g: labeled_graph @ ( standard_Constant @ v2 ) @ v ).
thf(l_decl,type,
l: set @ ( standard_Constant @ v2 ) ).
thf(h_decl,type,
h: v > v ).
thf(m_decl,type,
m: v2 > v ).
thf(x_decl,type,
x: v ).
thf(xa_decl,type,
xa: v2 ).
thf(y_decl,type,
y: v2 ).
thf(139,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) )] : ( edge_preserving @ TB @ TB @ TA @ ( id_on @ TB @ A ) @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_edge__preserving__Id) ).
thf(645,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) )] : ( edge_preserving @ TB @ TB @ TA @ ( id_on @ TB @ A ) @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(269,axiom,
( ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Bot @ v2 ) @ g )
= ( bot_bot @ ( set @ ( product_prod @ v @ v ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_cf) ).
thf(1036,plain,
( ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Bot @ v2 ) @ g )
= ( bot_bot @ ( set @ ( product_prod @ v @ v ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(35,axiom,
! [TA: $tType] : ( semilattice_sup @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Osemilattice__sup_8) ).
thf(365,plain,
! [TA: $tType] : ( semilattice_sup @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(177,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: labeled_graph @ TA @ TB,C: TB,D: TA,E: TB > TC,F: TC,G: TC] :
( ( member @ TB @ A @ ( labeled_vertices @ TA @ TB @ B ) )
=> ( ( member @ TB @ C @ ( labeled_vertices @ TA @ TB @ B ) )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ A @ C ) @ ( getRel @ TA @ TB @ D @ B ) )
=> ( ( ( E @ A )
= F )
=> ( ( ( E @ C )
= G )
=> ( member @ ( product_prod @ TC @ TC ) @ ( product_Pair @ TC @ TC @ F @ G ) @ ( getRel @ TA @ TC @ D @ ( map_graph @ TB @ TC @ TA @ ( bNF_Gr @ TB @ TC @ ( labeled_vertices @ TA @ TB @ B ) @ E ) @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_getRel__map__fn) ).
thf(760,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: labeled_graph @ TA @ TB,C: TB,D: TA,E: TB > TC,F: TC,G: TC] :
( ( member @ TB @ A @ ( labeled_vertices @ TA @ TB @ B ) )
=> ( ( member @ TB @ C @ ( labeled_vertices @ TA @ TB @ B ) )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ A @ C ) @ ( getRel @ TA @ TB @ D @ B ) )
=> ( ( ( E @ A )
= F )
=> ( ( ( E @ C )
= G )
=> ( member @ ( product_prod @ TC @ TC ) @ ( product_Pair @ TC @ TC @ F @ G ) @ ( getRel @ TA @ TC @ D @ ( map_graph @ TB @ TC @ TA @ ( bNF_Gr @ TB @ TC @ ( labeled_vertices @ TA @ TB @ B ) @ E ) @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(267,axiom,
! [A: v2] :
( ( member @ v2 @ A @ c )
=> ? [B: v] : ( member @ ( product_prod @ v @ v ) @ ( product_Pair @ v @ v @ B @ B ) @ ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Const @ v2 @ A ) @ ( map_graph @ v @ v @ ( standard_Constant @ v2 ) @ ( bNF_Gr @ v @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) @ h ) @ g ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15__092_060open_062_092_060And_062c_O_Ac_A_092_060in_062_AC_A_092_060Longrightarrow_062_A_092_060exists_062v_O_A_Iv_M_Av_J_A_092_060in_062_AgetRel_A_IS__Const_Ac_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062) ).
thf(1031,plain,
! [A: v2] :
( ( member @ v2 @ A @ c )
=> ? [B: v] : ( member @ ( product_prod @ v @ v ) @ ( product_Pair @ v @ v @ B @ B ) @ ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Const @ v2 @ A ) @ ( map_graph @ v @ v @ ( standard_Constant @ v2 ) @ ( bNF_Gr @ v @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) @ h ) @ g ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(147,axiom,
member @ v2 @ y @ c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__C1_C_I2_J) ).
thf(666,plain,
member @ v2 @ y @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TB @ TA] :
~ ! [B: set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ),C: set @ TA] :
( A
!= ( labeled_LG @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_labeled__graph_Oexhaust) ).
thf(408,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TB @ TA] :
~ ! [B: set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ),C: set @ TA] :
( A
!= ( labeled_LG @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(94,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_singleton__insert__inj__eq) ).
thf(523,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(255,axiom,
maintained @ ( standard_Constant @ v2 ) @ nat @ v @ ( standa244753842y_rule @ ( standard_Constant @ v2 ) ) @ g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_ne) ).
thf(994,plain,
maintained @ ( standard_Constant @ v2 ) @ nat @ v @ ( standa244753842y_rule @ ( standard_Constant @ v2 ) ) @ g,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice_2) ).
thf(308,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(210,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_insert__iff) ).
thf(873,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(271,axiom,
! [TA: $tType,A: TA] : ( total_on @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) @ ( insert @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_total__on__singleton) ).
thf(1041,plain,
! [TA: $tType,A: TA] : ( total_on @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) @ ( insert @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(63,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_le__supI1) ).
thf(440,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(90,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_Un__empty__left) ).
thf(511,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(164,axiom,
! [TA: $tType,TB: $tType] :
( ( graph_union @ TA @ TB )
= ( ^ [A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] : ( labeled_LG @ TA @ TB @ ( sup_sup @ ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) @ ( labeled_edges @ TA @ TB @ A ) @ ( labeled_edges @ TA @ TB @ B ) ) @ ( sup_sup @ ( set @ TB ) @ ( labeled_vertices @ TA @ TB @ A ) @ ( labeled_vertices @ TA @ TB @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_graph__union__def) ).
thf(715,plain,
! [TA: $tType,TB: $tType] :
( ( graph_union @ TA @ TB )
= ( ^ [A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] : ( labeled_LG @ TA @ TB @ ( sup_sup @ ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) @ ( labeled_edges @ TA @ TB @ A ) @ ( labeled_edges @ TA @ TB @ B ) ) @ ( sup_sup @ ( set @ TB ) @ ( labeled_vertices @ TA @ TB @ A ) @ ( labeled_vertices @ TA @ TB @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(75,axiom,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_is__singleton__the__elem) ).
thf(472,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(158,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_prod__cases5) ).
thf(698,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(231,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TC,B: labeled_graph @ TA @ TB] : ( maintained @ TA @ TC @ TB @ ( product_Pair @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC ) @ A @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_maintained__refl) ).
thf(930,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TC,B: labeled_graph @ TA @ TB] : ( maintained @ TA @ TC @ TB @ ( product_Pair @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC ) @ A @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(149,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_empty__iff) ).
thf(670,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(215,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TC,B: TC,C: TC,D: allegorical_term @ TA,E: TC > TB] :
( ( A
= ( restrict @ TA @ TC @ A ) )
=> ( ( member @ ( product_prod @ TC @ TC ) @ ( product_Pair @ TC @ TC @ B @ C ) @ ( semantics @ TA @ TC @ A @ D ) )
=> ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ ( E @ B ) @ ( E @ C ) ) @ ( semantics @ TA @ TB @ ( map_graph @ TC @ TB @ TA @ ( bNF_Gr @ TC @ TB @ ( labeled_vertices @ TA @ TC @ A ) @ E ) @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_map__graph__in) ).
thf(885,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TC,B: TC,C: TC,D: allegorical_term @ TA,E: TC > TB] :
( ( A
= ( restrict @ TA @ TC @ A ) )
=> ( ( member @ ( product_prod @ TC @ TC ) @ ( product_Pair @ TC @ TC @ B @ C ) @ ( semantics @ TA @ TC @ A @ D ) )
=> ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ ( E @ B ) @ ( E @ C ) ) @ ( semantics @ TA @ TB @ ( map_graph @ TC @ TB @ TA @ ( bNF_Gr @ TC @ TB @ ( labeled_vertices @ TA @ TC @ A ) @ E ) @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( ( labeled_vertices @ TA @ TB @ ( restrict @ TA @ TB @ A ) )
= ( labeled_vertices @ TA @ TB @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_vertices__restrict) ).
thf(565,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( ( labeled_vertices @ TA @ TB @ ( restrict @ TA @ TB @ A ) )
= ( labeled_vertices @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(142,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_Collect__empty__eq__bot) ).
thf(651,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(44,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_subset__antisym) ).
thf(389,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(111,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
=> ~ ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_le__supE) ).
thf(570,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
=> ~ ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( lattice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Olattice) ).
thf(344,plain,
! [TA: $tType,TB: $tType] :
( ( lattice @ TA )
=> ( lattice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(277,axiom,
! [A: product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat )] :
( ( member @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) ) @ A @ ( standa2002409347_rules @ v2 @ l ) )
=> ( maintained @ ( standard_Constant @ v2 ) @ nat @ v @ A @ g ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86__092_060open_062maintainedA_A_Iidentity__rules_AL_J_AG_H_092_060close_062) ).
thf(1055,plain,
! [A: product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat )] :
( ( member @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) ) @ A @ ( standa2002409347_rules @ v2 @ l ) )
=> ( maintained @ ( standard_Constant @ v2 ) @ nat @ v @ A @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(167,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: TB,C: TB,D: TA] :
( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ B @ C ) @ ( getRel @ TA @ TB @ D @ A ) )
=> ( member @ TB @ B @ ( labeled_vertices @ TA @ TB @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_getRel__dom_I1_J) ).
thf(724,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: TB,C: TB,D: TA] :
( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ B @ C ) @ ( getRel @ TA @ TB @ D @ A ) )
=> ( member @ TB @ B @ ( labeled_vertices @ TA @ TB @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(116,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_inf__sup__ord_I3_J) ).
thf(587,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(129,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ),B: set @ TA,C: set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ),D: set @ TA] :
( ( ( labeled_LG @ TB @ TA @ A @ B )
= ( labeled_LG @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_labeled__graph_Oinject) ).
thf(619,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ),B: set @ TA,C: set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ),D: set @ TA] :
( ( ( labeled_LG @ TB @ TA @ A @ B )
= ( labeled_LG @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TB @ TA] :
( ( A
= ( restrict @ TB @ TA @ A ) )
=> ( ( maintained @ TB @ nat @ TA @ ( standa244753842y_rule @ TB ) @ A )
= ( ( labeled_vertices @ TB @ TA @ A )
!= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_nonempty__rule) ).
thf(542,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TB @ TA] :
( ( A
= ( restrict @ TB @ TA @ A ) )
=> ( ( maintained @ TB @ nat @ TA @ ( standa244753842y_rule @ TB ) @ A )
= ( ( labeled_vertices @ TB @ TA @ A )
!= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( A
= ( labeled_LG @ TA @ TB @ ( labeled_edges @ TA @ TB @ A ) @ ( labeled_vertices @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_labeled__graph_Oexhaust__sel) ).
thf(460,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( A
= ( labeled_LG @ TA @ TB @ ( labeled_edges @ TA @ TB @ A ) @ ( labeled_vertices @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(221,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TB,B: set @ ( product_prod @ TC @ TB )] :
( ( graph_homomorphism @ TA @ TC @ TB @ ( labeled_LG @ TA @ TC @ ( bot_bot @ ( set @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ) ) ) @ ( bot_bot @ ( set @ TC ) ) ) @ A @ B )
= ( ( B
= ( bot_bot @ ( set @ ( product_prod @ TC @ TB ) ) ) )
& ( A
= ( restrict @ TA @ TB @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_graph__homomorphism__empty) ).
thf(902,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TB,B: set @ ( product_prod @ TC @ TB )] :
( ( graph_homomorphism @ TA @ TC @ TB @ ( labeled_LG @ TA @ TC @ ( bot_bot @ ( set @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ) ) ) @ ( bot_bot @ ( set @ TC ) ) ) @ A @ B )
= ( ( B
= ( bot_bot @ ( set @ ( product_prod @ TC @ TB ) ) ) )
& ( A
= ( restrict @ TA @ TB @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ! [E: TA] :
( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_comp__eq__elim) ).
thf(559,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ! [E: TA] :
( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(136,axiom,
lattice @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Olattice_5) ).
thf(638,plain,
lattice @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(209,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_prod__cases3) ).
thf(870,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(124,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_singleton__inject) ).
thf(606,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(54,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_Un__absorb) ).
thf(416,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(16,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_sup_Oassoc) ).
thf(316,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_sup_Oleft__idem) ).
thf(284,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(181,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_mk__disjoint__insert) ).
thf(770,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(76,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_sup__ge2) ).
thf(475,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(18,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_inf__sup__aci_I5_J) ).
thf(321,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,A: ( labeled_graph @ TA @ TB ) > $o,B: labeled_graph @ TA @ TB] :
( ! [C: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ),D: set @ TB] : ( A @ ( labeled_LG @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_labeled__graph_Oinduct) ).
thf(376,plain,
! [TA: $tType,TB: $tType,A: ( labeled_graph @ TA @ TB ) > $o,B: labeled_graph @ TA @ TB] :
( ! [C: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ),D: set @ TB] : ( A @ ( labeled_LG @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(200,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_insert__subset) ).
thf(834,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC ) ),B: labeled_graph @ TA @ TB] :
( ( consequence_graph @ TA @ TC @ TB @ A @ B )
=> ( B
= ( restrict @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_consequence__graphD_I3_J) ).
thf(514,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC ) ),B: labeled_graph @ TA @ TB] :
( ( consequence_graph @ TA @ TC @ TB @ A @ B )
=> ( B
= ( restrict @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(234,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_old_Oprod_Oexhaust) ).
thf(937,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(191,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_prod__induct4) ).
thf(806,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(244,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TC @ TA,B: labeled_graph @ TC @ TA,C: labeled_graph @ TC @ TB,D: set @ ( product_prod @ TA @ TB )] :
( ( maintained @ TC @ TA @ TB @ ( product_Pair @ ( labeled_graph @ TC @ TA ) @ ( labeled_graph @ TC @ TA ) @ A @ B ) @ C )
=> ( ( graph_homomorphism @ TC @ TA @ TB @ A @ C @ D )
=> ( extensible @ TC @ TA @ TB @ ( product_Pair @ ( labeled_graph @ TC @ TA ) @ ( labeled_graph @ TC @ TA ) @ A @ B ) @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_maintainedD) ).
thf(966,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TC @ TA,B: labeled_graph @ TC @ TA,C: labeled_graph @ TC @ TB,D: set @ ( product_prod @ TA @ TB )] :
( ( maintained @ TC @ TA @ TB @ ( product_Pair @ ( labeled_graph @ TC @ TA ) @ ( labeled_graph @ TC @ TA ) @ A @ B ) @ C )
=> ( ( graph_homomorphism @ TC @ TA @ TB @ A @ C @ D )
=> ( extensible @ TC @ TA @ TB @ ( product_Pair @ ( labeled_graph @ TC @ TA ) @ ( labeled_graph @ TC @ TA ) @ A @ B ) @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(29,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_sup__assoc) ).
thf(348,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: TA > TB,D: TA] :
( ( ( comp @ TC @ TB @ TA @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_comp__eq__dest__lhs) ).
thf(574,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: TA > TB,D: TA] :
( ( ( comp @ TC @ TB @ TA @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(222,axiom,
( g
= ( restrict @ ( standard_Constant @ v2 ) @ v @ g ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_gr_I1_J) ).
thf(905,plain,
( g
= ( restrict @ ( standard_Constant @ v2 ) @ v @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(78,axiom,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_Un__commute) ).
thf(480,plain,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(179,axiom,
maintained @ ( standard_Constant @ v2 ) @ nat @ v @ ( standa400804411p_rule @ ( standard_Constant @ v2 ) @ ( standard_S_Top @ v2 ) ) @ g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_tr) ).
thf(766,plain,
maintained @ ( standard_Constant @ v2 ) @ nat @ v @ ( standa400804411p_rule @ ( standard_Constant @ v2 ) @ ( standard_S_Top @ v2 ) ) @ g,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(1,conjecture,
member @ ( product_prod @ v @ v ) @ ( product_Pair @ v @ v @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Const @ v2 @ y ) @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( member @ ( product_prod @ v @ v ) @ ( product_Pair @ v @ v @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Const @ v2 @ y ) @ g ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(280,plain,
~ ( member @ ( product_prod @ v @ v ) @ ( product_Pair @ v @ v @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Const @ v2 @ y ) @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_sup__left__commute) ).
thf(293,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(68,axiom,
preorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_14) ).
thf(453,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(145,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( ( ord_less_eq @ TA @ A @ C )
& ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_le__sup__iff) ).
thf(660,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( ( ord_less_eq @ TA @ A @ C )
& ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(257,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC ) ),B: labeled_graph @ TA @ TB,C: product_prod @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC )] :
( ( consequence_graph @ TA @ TC @ TB @ A @ B )
=> ( ( member @ ( product_prod @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC ) ) @ C @ A )
=> ( maintained @ TA @ TC @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_consequence__graphD_I1_J) ).
thf(998,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC ) ),B: labeled_graph @ TA @ TB,C: product_prod @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC )] :
( ( consequence_graph @ TA @ TC @ TB @ A @ B )
=> ( ( member @ ( product_prod @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC ) ) @ C @ A )
=> ( maintained @ TA @ TC @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(52,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( bot_bot @ TA )
= ( sup_sup @ TA @ A @ B ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_sup__bot_Oneutr__eq__iff) ).
thf(411,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( bot_bot @ TA )
= ( sup_sup @ TA @ A @ B ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(47,axiom,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_is__singleton__def) ).
thf(397,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(155,axiom,
! [TA: $tType] :
( ( standa1138209853_rules @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_constant__rules__empty) ).
thf(687,plain,
! [TA: $tType] :
( ( standa1138209853_rules @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(212,axiom,
( ( comp @ v @ v @ v @ h @ h )
= h ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_h_I1_J) ).
thf(877,plain,
( ( comp @ v @ v @ v @ h @ h )
= h ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(157,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TC,B: TC > TB,C: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) )] :
( ! [D: TA,E: TC,F: TC] :
( ( member @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ) @ ( product_Pair @ TA @ ( product_prod @ TC @ TC ) @ D @ ( product_Pair @ TC @ TC @ E @ F ) ) @ ( labeled_edges @ TA @ TC @ A ) )
=> ( ( member @ TC @ E @ ( labeled_vertices @ TA @ TC @ A ) )
=> ( ( member @ TC @ F @ ( labeled_vertices @ TA @ TC @ A ) )
=> ( member @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ TB ) @ D @ ( product_Pair @ TB @ TB @ ( B @ E ) @ ( B @ F ) ) ) @ C ) ) ) )
=> ( edge_preserving @ TC @ TB @ TA @ ( bNF_Gr @ TC @ TB @ ( labeled_vertices @ TA @ TC @ A ) @ B ) @ ( labeled_edges @ TA @ TC @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_edge__preserving__on__graphI) ).
thf(692,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TC,B: TC > TB,C: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) )] :
( ! [D: TA,E: TC,F: TC] :
( ( member @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ) @ ( product_Pair @ TA @ ( product_prod @ TC @ TC ) @ D @ ( product_Pair @ TC @ TC @ E @ F ) ) @ ( labeled_edges @ TA @ TC @ A ) )
=> ( ( member @ TC @ E @ ( labeled_vertices @ TA @ TC @ A ) )
=> ( ( member @ TC @ F @ ( labeled_vertices @ TA @ TC @ A ) )
=> ( member @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ TB ) @ D @ ( product_Pair @ TB @ TB @ ( B @ E ) @ ( B @ F ) ) ) @ C ) ) ) )
=> ( edge_preserving @ TC @ TB @ TA @ ( bNF_Gr @ TC @ TB @ ( labeled_vertices @ TA @ TC @ A ) @ B ) @ ( labeled_edges @ TA @ TC @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] : ( graph_homomorphism @ TA @ TB @ TB @ ( restrict @ TA @ TB @ A ) @ ( restrict @ TA @ TB @ A ) @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_graph__homomorphism__Id) ).
thf(380,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] : ( graph_homomorphism @ TA @ TB @ TB @ ( restrict @ TA @ TB @ A ) @ ( restrict @ TA @ TB @ A ) @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ ( product_prod @ TC @ ( product_prod @ TA @ TA ) ) ) > ( set @ TA ) > TB,B: set @ ( product_prod @ TC @ ( product_prod @ TA @ TA ) ),C: set @ TA] :
( ( labele1974067554_graph @ TC @ TA @ TB @ A @ ( labeled_LG @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_labeled__graph_Ocase) ).
thf(529,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ ( product_prod @ TC @ ( product_prod @ TA @ TA ) ) ) > ( set @ TA ) > TB,B: set @ ( product_prod @ TC @ ( product_prod @ TA @ TA ) ),C: set @ TA] :
( ( labele1974067554_graph @ TC @ TA @ TB @ A @ ( labeled_LG @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(229,axiom,
! [TA: $tType,TB: $tType,A: set @ TA] :
( ( labeled_LG @ TB @ TA @ ( bot_bot @ ( set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ) ) ) @ A )
= ( restrict @ TB @ TA @ ( labeled_LG @ TB @ TA @ ( bot_bot @ ( set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_graph__empty__e) ).
thf(925,plain,
! [TA: $tType,TB: $tType,A: set @ TA] :
( ( labeled_LG @ TB @ TA @ ( bot_bot @ ( set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ) ) ) @ A )
= ( restrict @ TB @ TA @ ( labeled_LG @ TB @ TA @ ( bot_bot @ ( set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(192,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TC @ TA,B: labeled_graph @ TC @ TB,C: set @ ( product_prod @ TA @ TB ),D: labeled_graph @ TC @ TA,E: set @ ( product_prod @ TA @ TB )] :
( ( graph_homomorphism @ TC @ TA @ TB @ A @ B @ C )
=> ( ( agree_on @ TC @ TA @ TB @ D @ E @ C )
=> ( extensible @ TC @ TA @ TB @ ( product_Pair @ ( labeled_graph @ TC @ TA ) @ ( labeled_graph @ TC @ TA ) @ D @ A ) @ B @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_extensibleI) ).
thf(810,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TC @ TA,B: labeled_graph @ TC @ TB,C: set @ ( product_prod @ TA @ TB ),D: labeled_graph @ TC @ TA,E: set @ ( product_prod @ TA @ TB )] :
( ( graph_homomorphism @ TC @ TA @ TB @ A @ B @ C )
=> ( ( agree_on @ TC @ TA @ TB @ D @ E @ C )
=> ( extensible @ TC @ TA @ TB @ ( product_Pair @ ( labeled_graph @ TC @ TA ) @ ( labeled_graph @ TC @ TA ) @ D @ A ) @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(278,axiom,
member @ v2 @ xa @ c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__C1_C_I1_J) ).
thf(1057,plain,
member @ v2 @ xa @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(224,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_singletonI) ).
thf(910,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(218,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_old_Oprod_Orec) ).
thf(894,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(174,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: TB,C: TB,D: TA] :
( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ B @ C ) @ ( getRel @ TA @ TB @ D @ A ) )
=> ( member @ TB @ C @ ( labeled_vertices @ TA @ TB @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_getRel__dom_I2_J) ).
thf(746,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: TB,C: TB,D: TA] :
( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ B @ C ) @ ( getRel @ TA @ TB @ D @ A ) )
=> ( member @ TB @ C @ ( labeled_vertices @ TA @ TB @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_bot__apply) ).
thf(302,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(208,axiom,
! [TA: $tType,A: set @ TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [B: TA,C: TA] :
( ( member @ TA @ B @ A )
=> ( ( member @ TA @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_is__singletonI_H) ).
thf(862,plain,
! [TA: $tType,A: set @ TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [B: TA,C: TA] :
( ( member @ TA @ B @ A )
=> ( ( member @ TA @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(120,axiom,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_subset__empty) ).
thf(598,plain,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(45,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_order__refl) ).
thf(392,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(133,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] :
( ( ( ( labeled_edges @ TA @ TB @ A )
= ( labeled_edges @ TA @ TB @ B ) )
& ( ( labeled_vertices @ TA @ TB @ A )
= ( labeled_vertices @ TA @ TB @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_labeled__graph_Oexpand) ).
thf(630,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] :
( ( ( ( labeled_edges @ TA @ TB @ A )
= ( labeled_edges @ TA @ TB @ B ) )
& ( ( labeled_vertices @ TA @ TB @ A )
= ( labeled_vertices @ TA @ TB @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(169,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: set @ ( product_prod @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC ) ),B: labeled_graph @ TA @ TB,C: labeled_graph @ TA @ TB,D: itself @ TD] :
( ( consequence_graph @ TA @ TC @ TB @ A @ B )
=> ( ( graph_homomorphism @ TA @ TB @ TB @ C @ B @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ C ) ) )
=> ( ! [E: labeled_graph @ TA @ TD] :
( ( consequence_graph @ TA @ TC @ TD @ A @ E )
=> ( maintained @ TA @ TB @ TD @ ( product_Pair @ ( labeled_graph @ TA @ TB ) @ ( labeled_graph @ TA @ TB ) @ C @ B ) @ E ) )
=> ( least_559130134_graph @ TD @ TA @ TC @ TB @ D @ A @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_least__consequence__graphI) ).
thf(729,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: set @ ( product_prod @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC ) ),B: labeled_graph @ TA @ TB,C: labeled_graph @ TA @ TB,D: itself @ TD] :
( ( consequence_graph @ TA @ TC @ TB @ A @ B )
=> ( ( graph_homomorphism @ TA @ TB @ TB @ C @ B @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ C ) ) )
=> ( ! [E: labeled_graph @ TA @ TD] :
( ( consequence_graph @ TA @ TC @ TD @ A @ E )
=> ( maintained @ TA @ TB @ TD @ ( product_Pair @ ( labeled_graph @ TA @ TB ) @ ( labeled_graph @ TA @ TB ) @ C @ B ) @ E ) )
=> ( least_559130134_graph @ TD @ TA @ TC @ TB @ D @ A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(264,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB,D: TB] :
( ( ~ ( member @ TA @ A @ B )
| ( ( C @ A )
!= D ) )
=> ~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ D ) @ ( bNF_Gr @ TA @ TB @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_Gr__not__in) ).
thf(1021,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB,D: TB] :
( ( ~ ( member @ TA @ A @ B )
| ( ( C @ A )
!= D ) )
=> ~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ D ) @ ( bNF_Gr @ TA @ TB @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(183,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TC @ TB ),B: set @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ),C: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ),D: TC,E: TB,F: TC,G: TB,H: TA] :
( ( edge_preserving @ TC @ TB @ TA @ A @ B @ C )
=> ( ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ D @ E ) @ A )
=> ( ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ F @ G ) @ A )
=> ( ( member @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ) @ ( product_Pair @ TA @ ( product_prod @ TC @ TC ) @ H @ ( product_Pair @ TC @ TC @ D @ F ) ) @ B )
=> ( member @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ TB ) @ H @ ( product_Pair @ TB @ TB @ E @ G ) ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_edge__preserving__atomic) ).
thf(778,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TC @ TB ),B: set @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ),C: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ),D: TC,E: TB,F: TC,G: TB,H: TA] :
( ( edge_preserving @ TC @ TB @ TA @ A @ B @ C )
=> ( ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ D @ E ) @ A )
=> ( ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ F @ G ) @ A )
=> ( ( member @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ) @ ( product_Pair @ TA @ ( product_prod @ TC @ TC ) @ H @ ( product_Pair @ TC @ TC @ D @ F ) ) @ B )
=> ( member @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ TB ) @ H @ ( product_Pair @ TB @ TB @ E @ G ) ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(80,axiom,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_the__elem__eq) ).
thf(484,plain,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(34,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( sup_sup @ TA @ B @ C ) )
=> ( ( sup_sup @ TA @ D @ A )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_boolean__algebra__cancel_Osup2) ).
thf(361,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( sup_sup @ TA @ B @ C ) )
=> ( ( sup_sup @ TA @ D @ A )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(213,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_prod__cases6) ).
thf(879,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(83,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A = C )
& ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_singleton__insert__inj__eq_H) ).
thf(493,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A = C )
& ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > $o,B: ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) > ( set @ TB ) > TC,C: labeled_graph @ TA @ TB] :
( ( A @ ( labele1974067554_graph @ TA @ TB @ TC @ B @ C ) )
= ( ~ ( ( C
= ( labeled_LG @ TA @ TB @ ( labeled_edges @ TA @ TB @ C ) @ ( labeled_vertices @ TA @ TB @ C ) ) )
& ~ ( A @ ( B @ ( labeled_edges @ TA @ TB @ C ) @ ( labeled_vertices @ TA @ TB @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_labeled__graph_Osplit__sel__asm) ).
thf(551,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > $o,B: ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) > ( set @ TB ) > TC,C: labeled_graph @ TA @ TB] :
( ( A @ ( labele1974067554_graph @ TA @ TB @ TC @ B @ C ) )
= ( ~ ( ( C
= ( labeled_LG @ TA @ TB @ ( labeled_edges @ TA @ TB @ C ) @ ( labeled_vertices @ TA @ TB @ C ) ) )
& ~ ( A @ ( B @ ( labeled_edges @ TA @ TB @ C ) @ ( labeled_vertices @ TA @ TB @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(203,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB,C: TB,D: TB,E: allegorical_term @ TA] :
( ( graph_homomorphism @ TA @ TB @ TB @ A @ B @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ C @ D ) @ ( semantics @ TA @ TB @ A @ E ) )
=> ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ C @ D ) @ ( semantics @ TA @ TB @ B @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_subgraph__semantics) ).
thf(842,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB,C: TB,D: TB,E: allegorical_term @ TA] :
( ( graph_homomorphism @ TA @ TB @ TB @ A @ B @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ C @ D ) @ ( semantics @ TA @ TB @ A @ E ) )
=> ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ C @ D ) @ ( semantics @ TA @ TB @ B @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(261,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( id_on @ TA @ C ) )
= ( ( A = B )
& ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Id__on__iff) ).
thf(1012,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( id_on @ TA @ C ) )
= ( ( A = B )
& ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(205,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_prod__induct3) ).
thf(852,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > $o,B: ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) > ( set @ TB ) > TC,C: labeled_graph @ TA @ TB] :
( ( A @ ( labele1974067554_graph @ TA @ TB @ TC @ B @ C ) )
= ( ( C
= ( labeled_LG @ TA @ TB @ ( labeled_edges @ TA @ TB @ C ) @ ( labeled_vertices @ TA @ TB @ C ) ) )
=> ( A @ ( B @ ( labeled_edges @ TA @ TB @ C ) @ ( labeled_vertices @ TA @ TB @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_labeled__graph_Osplit__sel) ).
thf(435,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > $o,B: ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) > ( set @ TB ) > TC,C: labeled_graph @ TA @ TB] :
( ( A @ ( labele1974067554_graph @ TA @ TB @ TC @ B @ C ) )
= ( ( C
= ( labeled_LG @ TA @ TB @ ( labeled_edges @ TA @ TB @ C ) @ ( labeled_vertices @ TA @ TB @ C ) ) )
=> ( A @ ( B @ ( labeled_edges @ TA @ TB @ C ) @ ( labeled_vertices @ TA @ TB @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(19,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_inf__sup__aci_I7_J) ).
thf(324,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(247,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TC @ TA,B: labeled_graph @ TC @ TB,C: set @ ( product_prod @ TA @ TB )] :
( ( graph_homomorphism @ TC @ TA @ TB @ A @ B @ C )
=> ( extensible @ TC @ TA @ TB @ ( product_Pair @ ( labeled_graph @ TC @ TA ) @ ( labeled_graph @ TC @ TA ) @ A @ A ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_extensible__refl) ).
thf(974,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TC @ TA,B: labeled_graph @ TC @ TB,C: set @ ( product_prod @ TA @ TB )] :
( ( graph_homomorphism @ TC @ TA @ TB @ A @ B @ C )
=> ( extensible @ TC @ TA @ TB @ ( product_Pair @ ( labeled_graph @ TC @ TA ) @ ( labeled_graph @ TC @ TA ) @ A @ A ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(141,axiom,
bot @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_16) ).
thf(650,plain,
bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(263,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB,C: set @ ( product_prod @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC ) ),D: itself @ TD] :
( ( graph_homomorphism @ TA @ TB @ TB @ A @ B @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) )
=> ( ! [E: labeled_graph @ TA @ TD] :
( ( consequence_graph @ TA @ TC @ TD @ C @ E )
=> ( maintained @ TA @ TB @ TD @ ( product_Pair @ ( labeled_graph @ TA @ TB ) @ ( labeled_graph @ TA @ TB ) @ A @ B ) @ E ) )
=> ( least @ TD @ TA @ TC @ TB @ D @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_leastI) ).
thf(1017,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB,C: set @ ( product_prod @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC ) ),D: itself @ TD] :
( ( graph_homomorphism @ TA @ TB @ TB @ A @ B @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) )
=> ( ! [E: labeled_graph @ TA @ TD] :
( ( consequence_graph @ TA @ TC @ TD @ C @ E )
=> ( maintained @ TA @ TB @ TD @ ( product_Pair @ ( labeled_graph @ TA @ TB ) @ ( labeled_graph @ TA @ TB ) @ A @ B ) @ E ) )
=> ( least @ TD @ TA @ TC @ TB @ D @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(49,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( sup_sup @ TA @ A @ B )
= ( bot_bot @ TA ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_sup__bot_Oeq__neutr__iff) ).
thf(403,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( sup_sup @ TA @ A @ B )
= ( bot_bot @ TA ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(32,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_9) ).
thf(356,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(185,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( field @ TA @ ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ ( field @ TA @ A ) @ ( field @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_Field__Un) ).
thf(783,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( field @ TA @ ( sup_sup @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ ( field @ TA @ A ) @ ( field @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: labeled_graph @ TA @ TB,B: TC > TD,C: TB > TC] :
( ( map_graph @ TB @ TD @ TA @ ( bNF_Gr @ TB @ TD @ ( labeled_vertices @ TA @ TB @ A ) @ ( comp @ TC @ TD @ TB @ B @ C ) ) @ A )
= ( map_graph @ TC @ TD @ TA @ ( bNF_Gr @ TC @ TD @ ( labeled_vertices @ TA @ TC @ ( map_graph @ TB @ TC @ TA @ ( bNF_Gr @ TB @ TC @ ( labeled_vertices @ TA @ TB @ A ) @ C ) @ A ) ) @ B ) @ ( map_graph @ TB @ TC @ TA @ ( bNF_Gr @ TB @ TC @ ( labeled_vertices @ TA @ TB @ A ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_map__graph__fn__comp) ).
thf(499,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: labeled_graph @ TA @ TB,B: TC > TD,C: TB > TC] :
( ( map_graph @ TB @ TD @ TA @ ( bNF_Gr @ TB @ TD @ ( labeled_vertices @ TA @ TB @ A ) @ ( comp @ TC @ TD @ TB @ B @ C ) ) @ A )
= ( map_graph @ TC @ TD @ TA @ ( bNF_Gr @ TC @ TD @ ( labeled_vertices @ TA @ TC @ ( map_graph @ TB @ TC @ TA @ ( bNF_Gr @ TB @ TC @ ( labeled_vertices @ TA @ TB @ A ) @ C ) @ A ) ) @ B ) @ ( map_graph @ TB @ TC @ TA @ ( bNF_Gr @ TB @ TC @ ( labeled_vertices @ TA @ TB @ A ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(253,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TB,C: TA,D: labeled_graph @ TA @ TB,E: TC,F: set @ ( product_prod @ TB @ TC ),G: TC] :
( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ A @ B ) @ ( getRel @ TA @ TB @ C @ D ) )
=> ( ( member @ ( product_prod @ TB @ TC ) @ ( product_Pair @ TB @ TC @ A @ E ) @ F )
=> ( ( member @ ( product_prod @ TB @ TC ) @ ( product_Pair @ TB @ TC @ B @ G ) @ F )
=> ( member @ ( product_prod @ TC @ TC ) @ ( product_Pair @ TC @ TC @ E @ G ) @ ( getRel @ TA @ TC @ C @ ( map_graph @ TB @ TC @ TA @ F @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_getRel__homR) ).
thf(989,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TB,C: TA,D: labeled_graph @ TA @ TB,E: TC,F: set @ ( product_prod @ TB @ TC ),G: TC] :
( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ A @ B ) @ ( getRel @ TA @ TB @ C @ D ) )
=> ( ( member @ ( product_prod @ TB @ TC ) @ ( product_Pair @ TB @ TC @ A @ E ) @ F )
=> ( ( member @ ( product_prod @ TB @ TC ) @ ( product_Pair @ TB @ TC @ B @ G ) @ F )
=> ( member @ ( product_prod @ TC @ TC ) @ ( product_Pair @ TC @ TC @ E @ G ) @ ( getRel @ TA @ TC @ C @ ( map_graph @ TB @ TC @ TA @ F @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(173,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TC,B: labeled_graph @ TA @ TB,C: labeled_graph @ TA @ TC] :
( ! [D: set @ ( product_prod @ TC @ TB )] :
( ( graph_homomorphism @ TA @ TC @ TB @ A @ B @ D )
=> ( extensible @ TA @ TC @ TB @ ( product_Pair @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC ) @ A @ C ) @ B @ D ) )
=> ( maintained @ TA @ TC @ TB @ ( product_Pair @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC ) @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_maintainedI) ).
thf(742,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TC,B: labeled_graph @ TA @ TB,C: labeled_graph @ TA @ TC] :
( ! [D: set @ ( product_prod @ TC @ TB )] :
( ( graph_homomorphism @ TA @ TC @ TB @ A @ B @ D )
=> ( extensible @ TA @ TC @ TB @ ( product_Pair @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC ) @ A @ C ) @ B @ D ) )
=> ( maintained @ TA @ TC @ TB @ ( product_Pair @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC ) @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( ( graph_homomorphism @ TA @ TB @ TB @ A @ A @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) )
= ( A
= ( restrict @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_subgraph__refl) ).
thf(578,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( ( graph_homomorphism @ TA @ TB @ TB @ A @ A @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) )
= ( A
= ( restrict @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(266,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] :
( ( labeled_edges @ TA @ TB @ ( graph_union @ TA @ TB @ A @ B ) )
= ( sup_sup @ ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) @ ( labeled_edges @ TA @ TB @ A ) @ ( labeled_edges @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_graph__union__edges) ).
thf(1028,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] :
( ( labeled_edges @ TA @ TB @ ( graph_union @ TA @ TB @ A @ B ) )
= ( sup_sup @ ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) @ ( labeled_edges @ TA @ TB @ A ) @ ( labeled_edges @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(105,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_empty__subsetI) ).
thf(554,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(99,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_le__supI) ).
thf(537,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(154,axiom,
graph_homomorphism @ ( standard_Constant @ v2 ) @ v @ v @ ( map_graph @ v @ v @ ( standard_Constant @ v2 ) @ ( bNF_Gr @ v @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) @ h ) @ g ) @ g @ ( id_on @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ ( map_graph @ v @ v @ ( standard_Constant @ v2 ) @ ( bNF_Gr @ v @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) @ h ) @ g ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_h_I3_J) ).
thf(686,plain,
graph_homomorphism @ ( standard_Constant @ v2 ) @ v @ v @ ( map_graph @ v @ v @ ( standard_Constant @ v2 ) @ ( bNF_Gr @ v @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) @ h ) @ g ) @ g @ ( id_on @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ ( map_graph @ v @ v @ ( standard_Constant @ v2 ) @ ( bNF_Gr @ v @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) @ h ) @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(138,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TD,B: TB > TC,C: TA > TB] :
( ( comp @ TB @ TD @ TA @ ( comp @ TC @ TD @ TB @ A @ B ) @ C )
= ( comp @ TC @ TD @ TA @ A @ ( comp @ TB @ TC @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_comp__assoc) ).
thf(642,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TD,B: TB > TC,C: TA > TB] :
( ( comp @ TB @ TD @ TA @ ( comp @ TC @ TD @ TB @ A @ B ) @ C )
= ( comp @ TC @ TD @ TA @ A @ ( comp @ TB @ TC @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(95,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_empty__Collect__eq) ).
thf(526,plain,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(161,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( id_on @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_Id__onI) ).
thf(706,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( id_on @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(140,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) )
| ( ( A
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) )
| ( ( A
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
& ( B
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Un__singleton__iff) ).
thf(647,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) )
| ( ( A
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) )
| ( ( A
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
& ( B
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(251,axiom,
( ( m @ xa )
= ( m @ y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__C1_C_I3_J) ).
thf(985,plain,
( ( m @ xa )
= ( m @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(159,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_prod__induct7) ).
thf(701,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(143,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_Un__empty__right) ).
thf(654,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(166,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_singleton__iff) ).
thf(721,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(130,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_sup__ge1) ).
thf(622,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(201,axiom,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_ex__in__conv) ).
thf(837,plain,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(275,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA )] :
( ( field @ TA @ ( insert @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ C ) )
= ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ ( field @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_Field__insert) ).
thf(1050,plain,
! [TA: $tType,A: TA,B: TA,C: set @ ( product_prod @ TA @ TA )] :
( ( field @ TA @ ( insert @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ C ) )
= ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ ( field @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(70,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_sup__bot__right) ).
thf(457,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(134,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TC @ TA,B: set @ ( product_prod @ TA @ TB ),C: set @ ( product_prod @ TA @ TB ),D: labeled_graph @ TC @ TA,E: set @ ( product_prod @ TA @ TB )] :
( ( agree_on @ TC @ TA @ TB @ A @ B @ C )
=> ( ( agree_on @ TC @ TA @ TB @ D @ E @ B )
=> ( ( graph_homomorphism @ TC @ TA @ TA @ D @ A @ ( id_on @ TA @ ( labeled_vertices @ TC @ TA @ D ) ) )
=> ( agree_on @ TC @ TA @ TB @ D @ E @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_agree__on__subg__compose) ).
thf(633,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TC @ TA,B: set @ ( product_prod @ TA @ TB ),C: set @ ( product_prod @ TA @ TB ),D: labeled_graph @ TC @ TA,E: set @ ( product_prod @ TA @ TB )] :
( ( agree_on @ TC @ TA @ TB @ A @ B @ C )
=> ( ( agree_on @ TC @ TA @ TB @ D @ E @ B )
=> ( ( graph_homomorphism @ TC @ TA @ TA @ D @ A @ ( id_on @ TA @ ( labeled_vertices @ TC @ TA @ D ) ) )
=> ( agree_on @ TC @ TA @ TB @ D @ E @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(89,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( insert @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_Un__insert__left) ).
thf(508,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( insert @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(144,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] :
( ( graph_homomorphism @ TA @ TB @ TB @ A @ B @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) )
= ( ( A
= ( restrict @ TA @ TB @ A ) )
& ( B
= ( restrict @ TA @ TB @ B ) )
& ( ( graph_union @ TA @ TB @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_subgraph__def) ).
thf(657,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] :
( ( graph_homomorphism @ TA @ TB @ TB @ A @ B @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) )
= ( ( A
= ( restrict @ TA @ TB @ A ) )
& ( B
= ( restrict @ TA @ TB @ B ) )
& ( ( graph_union @ TA @ TB @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(265,axiom,
? [A: v2 > v] :
! [B: v2] :
( ( member @ v2 @ B @ c )
=> ( member @ ( product_prod @ v @ v ) @ ( product_Pair @ v @ v @ ( A @ B ) @ ( A @ B ) ) @ ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Const @ v2 @ B ) @ ( map_graph @ v @ v @ ( standard_Constant @ v2 ) @ ( bNF_Gr @ v @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) @ h ) @ g ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17__092_060open_062_092_060exists_062f_O_A_092_060forall_062x_O_Ax_A_092_060in_062_AC_A_092_060longrightarrow_062_A_If_Ax_M_Af_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062) ).
thf(1026,plain,
? [A: v2 > v] :
! [B: v2] :
( ( member @ v2 @ B @ c )
=> ( member @ ( product_prod @ v @ v ) @ ( product_Pair @ v @ v @ ( A @ B ) @ ( A @ B ) ) @ ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Const @ v2 @ B ) @ ( map_graph @ v @ v @ ( standard_Constant @ v2 ) @ ( bNF_Gr @ v @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) @ h ) @ g ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(239,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_UnI1) ).
thf(953,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(165,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ TB,D: TB > TA] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( bNF_Gr @ TB @ TA @ C @ D ) )
=> ( ( D @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_GrD2) ).
thf(718,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ TB,D: TB > TA] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( bNF_Gr @ TB @ TA @ C @ D ) )
=> ( ( D @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(216,axiom,
! [TA: $tType,A: product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ TA ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ TA )] :
( ( maintained @ ( standard_Constant @ v2 ) @ TA @ v @ A @ g )
=> ( maintained @ ( standard_Constant @ v2 ) @ TA @ v @ A @ ( map_graph @ v @ v @ ( standard_Constant @ v2 ) @ ( bNF_Gr @ v @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) @ h ) @ g ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_mg) ).
thf(888,plain,
! [TA: $tType,A: product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ TA ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ TA )] :
( ( maintained @ ( standard_Constant @ v2 ) @ TA @ v @ A @ g )
=> ( maintained @ ( standard_Constant @ v2 ) @ TA @ v @ A @ ( map_graph @ v @ v @ ( standard_Constant @ v2 ) @ ( bNF_Gr @ v @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) @ h ) @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(10,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( sup_sup @ TA @ B @ C ) )
=> ( ( sup_sup @ TA @ A @ D )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_boolean__algebra__cancel_Osup1) ).
thf(298,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( sup_sup @ TA @ B @ C ) )
=> ( ( sup_sup @ TA @ A @ D )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB,C: labeled_graph @ TA @ TB] :
( ( graph_homomorphism @ TA @ TB @ TB @ A @ B @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) )
=> ( ( graph_homomorphism @ TA @ TB @ TB @ B @ C @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ B ) ) )
=> ( graph_homomorphism @ TA @ TB @ TB @ A @ C @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_subgraph__trans) ).
thf(425,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB,C: labeled_graph @ TA @ TB] :
( ( graph_homomorphism @ TA @ TB @ TB @ A @ B @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) )
=> ( ( graph_homomorphism @ TA @ TB @ TB @ B @ C @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ B ) ) )
=> ( graph_homomorphism @ TA @ TB @ TB @ A @ C @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(59,axiom,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_is__singletonI) ).
thf(430,plain,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(206,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_insertE) ).
thf(856,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounde1808546759up_bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__semilattice__sup__bot) ).
thf(296,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounde1808546759up_bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TB,B: TB > TC] :
( ( map_graph @ TB @ TC @ TA @ ( bNF_Gr @ TB @ TC @ ( labeled_vertices @ TA @ TB @ A ) @ B ) @ A )
= ( restrict @ TA @ TC @ ( map_graph @ TB @ TC @ TA @ ( bNF_Gr @ TB @ TC @ ( labeled_vertices @ TA @ TB @ A ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_map__graph__fn__graphI) ).
thf(444,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TB,B: TB > TC] :
( ( map_graph @ TB @ TC @ TA @ ( bNF_Gr @ TB @ TC @ ( labeled_vertices @ TA @ TB @ A ) @ B ) @ A )
= ( restrict @ TA @ TC @ ( map_graph @ TB @ TC @ TA @ ( bNF_Gr @ TB @ TC @ ( labeled_vertices @ TA @ TB @ A ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(170,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_prod__cases7) ).
thf(733,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(121,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TC @ TA,B: set @ ( product_prod @ TA @ TB ),C: set @ ( product_prod @ TA @ TB ),D: set @ ( product_prod @ TA @ TB )] :
( ( agree_on @ TC @ TA @ TB @ A @ B @ C )
=> ( ( agree_on @ TC @ TA @ TB @ A @ C @ D )
=> ( agree_on @ TC @ TA @ TB @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_agree__on__trans) ).
thf(601,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TC @ TA,B: set @ ( product_prod @ TA @ TB ),C: set @ ( product_prod @ TA @ TB ),D: set @ ( product_prod @ TA @ TB )] :
( ( agree_on @ TC @ TA @ TB @ A @ B @ C )
=> ( ( agree_on @ TC @ TA @ TB @ A @ C @ D )
=> ( agree_on @ TC @ TA @ TB @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(115,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] :
( ( labeled_vertices @ TA @ TB @ ( graph_union @ TA @ TB @ A @ B ) )
= ( sup_sup @ ( set @ TB ) @ ( labeled_vertices @ TA @ TB @ A ) @ ( labeled_vertices @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_graph__union__vertices) ).
thf(584,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] :
( ( labeled_vertices @ TA @ TB @ ( graph_union @ TA @ TB @ A @ B ) )
= ( sup_sup @ ( set @ TB ) @ ( labeled_vertices @ TA @ TB @ A ) @ ( labeled_vertices @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(195,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_subsetI) ).
thf(819,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(108,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_Un__left__absorb) ).
thf(562,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(197,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB,C: TA,D: labeled_graph @ TA @ TB,E: labeled_graph @ TA @ TB] :
( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ A @ B ) @ ( getRel @ TA @ TB @ C @ D ) )
=> ( ( graph_homomorphism @ TA @ TB @ TB @ D @ E @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ D ) ) )
=> ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ A @ B ) @ ( getRel @ TA @ TB @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_getRel__subgraph) ).
thf(826,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB,C: TA,D: labeled_graph @ TA @ TB,E: labeled_graph @ TA @ TB] :
( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ A @ B ) @ ( getRel @ TA @ TB @ C @ D ) )
=> ( ( graph_homomorphism @ TA @ TB @ TB @ D @ E @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ D ) ) )
=> ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ A @ B ) @ ( getRel @ TA @ TB @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(291,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(241,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_insert__absorb) ).
thf(958,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(3,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_inf__sup__aci_I8_J) ).
thf(281,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(102,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_Collect__empty__eq) ).
thf(545,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(41,axiom,
lattice @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Olattice_15) ).
thf(382,plain,
lattice @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(15,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_sup_Ocommute) ).
thf(313,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(279,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( A = B )
=> ( ( member @ TA @ A @ C )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( id_on @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Id__on__eqI) ).
thf(1058,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( A = B )
=> ( ( member @ TA @ A @ C )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ B ) @ ( id_on @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( least_559130134_graph @ TA @ TD @ TC @ TB )
= ( ^ [A: itself @ TA,B: set @ ( product_prod @ ( labeled_graph @ TD @ TC ) @ ( labeled_graph @ TD @ TC ) ),C: labeled_graph @ TD @ TB,D: labeled_graph @ TD @ TB] :
( ( consequence_graph @ TD @ TC @ TB @ B @ D )
& ( least @ TA @ TD @ TC @ TB @ A @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_least__consequence__graph__def) ).
thf(466,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( least_559130134_graph @ TA @ TD @ TC @ TB )
= ( ^ [A: itself @ TA,B: set @ ( product_prod @ ( labeled_graph @ TD @ TC ) @ ( labeled_graph @ TD @ TC ) ),C: labeled_graph @ TD @ TB,D: labeled_graph @ TD @ TB] :
( ( consequence_graph @ TD @ TC @ TB @ B @ D )
& ( least @ TA @ TD @ TC @ TB @ A @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(23,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_sup__commute) ).
thf(335,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ( ( sup_sup @ TA )
= ( ^ [A: TA,B: TA] : ( sup_sup @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(150,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) @ ( labeled_edges @ TA @ TB @ A ) @ ( labeled_edges @ TA @ TB @ B ) )
=> ( ( ord_less_eq @ ( set @ TB ) @ ( labeled_vertices @ TA @ TB @ A ) @ ( labeled_vertices @ TA @ TB @ B ) )
=> ( ( graph_union @ TA @ TB @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_graph__unionI) ).
thf(672,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) @ ( labeled_edges @ TA @ TB @ A ) @ ( labeled_edges @ TA @ TB @ B ) )
=> ( ( ord_less_eq @ ( set @ TB ) @ ( labeled_vertices @ TA @ TB @ A ) @ ( labeled_vertices @ TA @ TB @ B ) )
=> ( ( graph_union @ TA @ TB @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TB @ TC ),B: labeled_graph @ TA @ TB] : ( edge_preserving @ TB @ TC @ TA @ A @ ( labeled_edges @ TA @ TB @ B ) @ ( labeled_edges @ TA @ TC @ ( map_graph @ TB @ TC @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_map__graph__edge__preserving) ).
thf(406,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TB @ TC ),B: labeled_graph @ TA @ TB] : ( edge_preserving @ TB @ TC @ TA @ A @ ( labeled_edges @ TA @ TB @ B ) @ ( labeled_edges @ TA @ TC @ ( map_graph @ TB @ TC @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(199,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_bex__Un) ).
thf(831,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(152,axiom,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_bot__empty__eq) ).
thf(681,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(55,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_insert__not__empty) ).
thf(419,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(171,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_ball__Un) ).
thf(736,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(272,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TC,B: labeled_graph @ TA @ TB,C: set @ ( product_prod @ TC @ TB ),D: TC,E: TC,F: allegorical_term @ TA,G: TB,H: TB] :
( ( graph_homomorphism @ TA @ TC @ TB @ A @ B @ C )
=> ( ( member @ ( product_prod @ TC @ TC ) @ ( product_Pair @ TC @ TC @ D @ E ) @ ( semantics @ TA @ TC @ A @ F ) )
=> ( ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ D @ G ) @ C )
=> ( ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ E @ H ) @ C )
=> ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ G @ H ) @ ( semantics @ TA @ TB @ B @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_graph__homomorphism__semantics) ).
thf(1043,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TC,B: labeled_graph @ TA @ TB,C: set @ ( product_prod @ TC @ TB ),D: TC,E: TC,F: allegorical_term @ TA,G: TB,H: TB] :
( ( graph_homomorphism @ TA @ TC @ TB @ A @ B @ C )
=> ( ( member @ ( product_prod @ TC @ TC ) @ ( product_Pair @ TC @ TC @ D @ E ) @ ( semantics @ TA @ TC @ A @ F ) )
=> ( ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ D @ G ) @ C )
=> ( ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ E @ H ) @ C )
=> ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ G @ H ) @ ( semantics @ TA @ TB @ B @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(128,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( ( graph_union @ TA @ TB @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_graph__union__idemp_I1_J) ).
thf(616,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( ( graph_union @ TA @ TB @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(178,axiom,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_insertI1) ).
thf(764,plain,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(249,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_equals0I) ).
thf(979,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(123,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_le__supI2) ).
thf(604,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(217,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_prod__cases) ).
thf(890,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(77,axiom,
! [TA: $tType,A: set @ TA] :
( ( is_singleton @ TA @ A )
=> ~ ! [B: TA] :
( A
!= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_is__singletonE) ).
thf(477,plain,
! [TA: $tType,A: set @ TA] :
( ( is_singleton @ TA @ A )
=> ~ ! [B: TA] :
( A
!= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TB )
=> ( ( sup_sup @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( sup_sup @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_sup__apply) ).
thf(367,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TB )
=> ( ( sup_sup @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( sup_sup @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(98,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_inf__sup__ord_I4_J) ).
thf(535,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ A @ ( sup_sup @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(125,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( ( B
= ( bot_bot @ ( set @ TA ) ) )
& ( C
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
| ( ( B
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
& ( C
= ( bot_bot @ ( set @ TA ) ) ) )
| ( ( B
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
& ( C
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_singleton__Un__iff) ).
thf(609,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( ( B
= ( bot_bot @ ( set @ TA ) ) )
& ( C
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
| ( ( B
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
& ( C
= ( bot_bot @ ( set @ TA ) ) ) )
| ( ( B
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
& ( C
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(189,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_UnCI) ).
thf(799,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(79,axiom,
bot @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Obot_6) ).
thf(483,plain,
bot @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( ( map_graph @ TB @ TB @ TA @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) @ A )
= ( restrict @ TA @ TB @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_map__graph__fn__id_I2_J) ).
thf(520,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( ( map_graph @ TB @ TB @ TA @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) @ A )
= ( restrict @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(243,axiom,
! [A: product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat )] :
( ( member @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) ) @ A @ ( standa438229444_rules @ v2 @ c @ l ) )
=> ( maintained @ ( standard_Constant @ v2 ) @ nat @ v @ A @ g ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_assms_I1_J) ).
thf(964,plain,
! [A: product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat )] :
( ( member @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) ) @ A @ ( standa438229444_rules @ v2 @ c @ l ) )
=> ( maintained @ ( standard_Constant @ v2 ) @ nat @ v @ A @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(226,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_prod_Oinject) ).
thf(915,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(236,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TC @ ( product_prod @ TA @ TA ) ),B: set @ TA,C: labeled_graph @ TC @ TB,D: set @ ( product_prod @ TA @ TB ),E: set @ ( product_prod @ TC @ ( product_prod @ TA @ TA ) )] :
( ( graph_homomorphism @ TC @ TA @ TB @ ( labeled_LG @ TC @ TA @ A @ B ) @ C @ D )
=> ( ( extensible @ TC @ TA @ TB @ ( product_Pair @ ( labeled_graph @ TC @ TA ) @ ( labeled_graph @ TC @ TA ) @ ( labeled_LG @ TC @ TA @ A @ B ) @ ( labeled_LG @ TC @ TA @ E @ B ) ) @ C @ D )
= ( graph_homomorphism @ TC @ TA @ TB @ ( labeled_LG @ TC @ TA @ E @ B ) @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_extensible__refl__concr) ).
thf(943,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TC @ ( product_prod @ TA @ TA ) ),B: set @ TA,C: labeled_graph @ TC @ TB,D: set @ ( product_prod @ TA @ TB ),E: set @ ( product_prod @ TC @ ( product_prod @ TA @ TA ) )] :
( ( graph_homomorphism @ TC @ TA @ TB @ ( labeled_LG @ TC @ TA @ A @ B ) @ C @ D )
=> ( ( extensible @ TC @ TA @ TB @ ( product_Pair @ ( labeled_graph @ TC @ TA ) @ ( labeled_graph @ TC @ TA ) @ ( labeled_LG @ TC @ TA @ A @ B ) @ ( labeled_LG @ TC @ TA @ E @ B ) ) @ C @ D )
= ( graph_homomorphism @ TC @ TA @ TB @ ( labeled_LG @ TC @ TA @ E @ B ) @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TA )
=> ( semilattice_sup @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Lattices_Osemilattice__sup) ).
thf(330,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TA )
=> ( semilattice_sup @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(232,axiom,
! [TA: $tType,A: TA] :
( ( standard_S_Bot @ TA )
!= ( standard_S_Const @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_Standard__Constant_Odistinct_I9_J) ).
thf(932,plain,
! [TA: $tType,A: TA] :
( ( standard_S_Bot @ TA )
!= ( standard_S_Const @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(225,axiom,
! [TA: $tType] :
( ( id_on @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Id__on__empty) ).
thf(912,plain,
! [TA: $tType] :
( ( id_on @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(184,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(780,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(262,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_insertI2) ).
thf(1015,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(46,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_bot__set__def) ).
thf(394,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(258,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_old_Oprod_Oinject) ).
thf(1000,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(228,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_Un__iff) ).
thf(922,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(87,axiom,
bounded_lattice @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice) ).
thf(505,plain,
bounded_lattice @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(62,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] : ( total_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_total__on__empty) ).
thf(438,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] : ( total_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(117,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TB,B: set @ ( product_prod @ TB @ TC )] :
( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ( map_graph @ TB @ TC @ TA @ B @ A )
= ( restrict @ TA @ TC @ ( map_graph @ TB @ TC @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_map__graph__preserves__restricted) ).
thf(589,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TB,B: set @ ( product_prod @ TB @ TC )] :
( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ( map_graph @ TB @ TC @ TA @ B @ A )
= ( restrict @ TA @ TC @ ( map_graph @ TB @ TC @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(188,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_prod__induct6) ).
thf(795,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] :
( ( graph_union @ TA @ TB @ A @ ( graph_union @ TA @ TB @ B @ A ) )
= ( graph_union @ TA @ TB @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_graph__union__idemp_I3_J) ).
thf(487,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] :
( ( graph_union @ TA @ TB @ A @ ( graph_union @ TA @ TB @ B @ A ) )
= ( graph_union @ TA @ TB @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(193,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: labeled_graph @ TA @ TB,B: TD > TB,C: TB > TD,D: product_prod @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC )] :
( ! [E: TB] :
( ( member @ TB @ E @ ( labeled_vertices @ TA @ TB @ A ) )
=> ( ( comp @ TD @ TB @ TB @ B @ C @ E )
= E ) )
=> ( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ( maintained @ TA @ TC @ TD @ D @ ( map_graph @ TB @ TD @ TA @ ( bNF_Gr @ TB @ TD @ ( labeled_vertices @ TA @ TB @ A ) @ C ) @ A ) )
=> ( maintained @ TA @ TC @ TB @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_maintained__preserved__by__isomorphism) ).
thf(812,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: labeled_graph @ TA @ TB,B: TD > TB,C: TB > TD,D: product_prod @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC )] :
( ! [E: TB] :
( ( member @ TB @ E @ ( labeled_vertices @ TA @ TB @ A ) )
=> ( ( comp @ TD @ TB @ TB @ B @ C @ E )
= E ) )
=> ( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ( maintained @ TA @ TC @ TD @ D @ ( map_graph @ TB @ TD @ TA @ ( bNF_Gr @ TB @ TD @ ( labeled_vertices @ TA @ TB @ A ) @ C ) @ A ) )
=> ( maintained @ TA @ TC @ TB @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(175,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_Pair__inject) ).
thf(749,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(26,axiom,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_11) ).
thf(342,plain,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(274,axiom,
member @ ( product_prod @ v @ v ) @ ( product_Pair @ v @ v @ x @ x ) @ ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Top @ v2 ) @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_top__nonempty) ).
thf(1049,plain,
member @ ( product_prod @ v @ v ) @ ( product_Pair @ v @ v @ x @ x ) @ ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Top @ v2 ) @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(82,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_Un__left__commute) ).
thf(490,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(151,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_insertCI) ).
thf(675,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(146,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_Un__assoc) ).
thf(663,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_comp__def) ).
thf(548,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(245,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_equals0D) ).
thf(968,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(196,axiom,
! [TA: $tType] :
( ( field @ TA @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_Field__empty) ).
thf(823,plain,
! [TA: $tType] :
( ( field @ TA @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(156,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] :
( ( graph_homomorphism @ TA @ TB @ TB @ A @ B @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) @ ( labeled_edges @ TA @ TB @ ( restrict @ TA @ TB @ A ) ) @ ( labeled_edges @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_subgraph__subset_I2_J) ).
thf(690,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] :
( ( graph_homomorphism @ TA @ TB @ TB @ A @ B @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) @ ( labeled_edges @ TA @ TB @ ( restrict @ TA @ TB @ A ) ) @ ( labeled_edges @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(160,axiom,
member @ ( product_prod @ v @ v ) @ ( product_Pair @ v @ v @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Const @ v2 @ xa ) @ ( map_graph @ v @ v @ ( standard_Constant @ v2 ) @ ( bNF_Gr @ v @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) @ h ) @ g ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062) ).
thf(705,plain,
member @ ( product_prod @ v @ v ) @ ( product_Pair @ v @ v @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Const @ v2 @ xa ) @ ( map_graph @ v @ v @ ( standard_Constant @ v2 ) @ ( bNF_Gr @ v @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) @ h ) @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB,C: set @ ( product_prod @ TB @ TC )] :
( ( graph_homomorphism @ TA @ TB @ TB @ A @ B @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) )
=> ( graph_homomorphism @ TA @ TC @ TC @ ( map_graph @ TB @ TC @ TA @ C @ A ) @ ( map_graph @ TB @ TC @ TA @ C @ B ) @ ( id_on @ TC @ ( labeled_vertices @ TA @ TC @ ( map_graph @ TB @ TC @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_map__graph__preserves__subgraph) ).
thf(414,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB,C: set @ ( product_prod @ TB @ TC )] :
( ( graph_homomorphism @ TA @ TB @ TB @ A @ B @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) )
=> ( graph_homomorphism @ TA @ TC @ TC @ ( map_graph @ TB @ TC @ TA @ C @ A ) @ ( map_graph @ TB @ TC @ TA @ C @ B ) @ ( id_on @ TC @ ( labeled_vertices @ TA @ TC @ ( map_graph @ TB @ TC @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(20,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_sup_Oleft__commute) ).
thf(327,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) )
= ( sup_sup @ TA @ B @ ( sup_sup @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(172,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ TB,D: TB > TA] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( bNF_Gr @ TB @ TA @ C @ D ) )
= ( ( member @ TB @ A @ C )
& ( ( D @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_in__Gr) ).
thf(739,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ TB,D: TB > TA] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( bNF_Gr @ TB @ TA @ C @ D ) )
= ( ( member @ TB @ A @ C )
& ( ( D @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(14,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_sup__idem) ).
thf(310,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(163,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: TB,C: TB,D: allegorical_term @ TA] :
( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ B @ C ) @ ( semantics @ TA @ TB @ A @ D ) )
=> ( member @ TB @ B @ ( labeled_vertices @ TA @ TB @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_semantics__in__vertices_I1_J) ).
thf(712,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: TB,C: TB,D: allegorical_term @ TA] :
( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ B @ C ) @ ( semantics @ TA @ TB @ A @ D ) )
=> ( member @ TB @ B @ ( labeled_vertices @ TA @ TB @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(259,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TB,B: TB > TC,C: TB > TC] :
( ! [D: TB] :
( ( member @ TB @ D @ ( labeled_vertices @ TA @ TB @ A ) )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( map_graph @ TB @ TC @ TA @ ( bNF_Gr @ TB @ TC @ ( labeled_vertices @ TA @ TB @ A ) @ B ) @ A )
= ( map_graph @ TB @ TC @ TA @ ( bNF_Gr @ TB @ TC @ ( labeled_vertices @ TA @ TB @ A ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_map__graph__fn__eqI) ).
thf(1003,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TB,B: TB > TC,C: TB > TC] :
( ! [D: TB] :
( ( member @ TB @ D @ ( labeled_vertices @ TA @ TB @ A ) )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( map_graph @ TB @ TC @ TA @ ( bNF_Gr @ TB @ TC @ ( labeled_vertices @ TA @ TB @ A ) @ B ) @ A )
= ( map_graph @ TB @ TC @ TA @ ( bNF_Gr @ TB @ TC @ ( labeled_vertices @ TA @ TB @ A ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(276,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_emptyE) ).
thf(1053,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(86,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_insert__commute) ).
thf(502,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(202,axiom,
! [A: v2] :
( ( member @ v2 @ A @ c )
=> ( member @ ( product_prod @ v @ v ) @ ( product_Pair @ v @ v @ ( m @ A ) @ ( m @ A ) ) @ ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Const @ v2 @ A ) @ ( map_graph @ v @ v @ ( standard_Constant @ v2 ) @ ( bNF_Gr @ v @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) @ h ) @ g ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_m) ).
thf(840,plain,
! [A: v2] :
( ( member @ v2 @ A @ c )
=> ( member @ ( product_prod @ v @ v ) @ ( product_Pair @ v @ v @ ( m @ A ) @ ( m @ A ) ) @ ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Const @ v2 @ A ) @ ( map_graph @ v @ v @ ( standard_Constant @ v2 ) @ ( bNF_Gr @ v @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) @ h ) @ g ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(72,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_sup__bot__left) ).
thf(463,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_bot__fun__def) ).
thf(338,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(238,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_UnE) ).
thf(951,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(223,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( bNF_Gr @ TA @ TB @ ( insert @ TA @ A @ B ) @ C )
= ( insert @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ ( C @ A ) ) @ ( bNF_Gr @ TA @ TB @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_Gr__insert) ).
thf(907,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( bNF_Gr @ TA @ TB @ ( insert @ TA @ A @ B ) @ C )
= ( insert @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ ( C @ A ) ) @ ( bNF_Gr @ TA @ TB @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(270,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_surj__pair) ).
thf(1038,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(37,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( ( ord_less_eq @ TA @ A @ C )
& ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_sup_Obounded__iff) ).
thf(370,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( ( ord_less_eq @ TA @ A @ C )
& ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(127,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ),B: set @ TB] :
( ( labeled_edges @ TA @ TB @ ( labeled_LG @ TA @ TB @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_labeled__graph_Osel_I1_J) ).
thf(613,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ),B: set @ TB] :
( ( labeled_edges @ TA @ TB @ ( labeled_LG @ TA @ TB @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(168,axiom,
( ( maintained @ ( standard_Constant @ v2 ) @ nat @ v @ ( standa244753842y_rule @ ( standard_Constant @ v2 ) ) @ g )
= ( ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g )
!= ( bot_bot @ ( set @ v ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67__092_060open_062maintained_Anonempty__rule_AG_H_A_061_A_Ivertices_AG_H_A_092_060noteq_062_A_123_125_J_092_060close_062) ).
thf(727,plain,
( ( maintained @ ( standard_Constant @ v2 ) @ nat @ v @ ( standa244753842y_rule @ ( standard_Constant @ v2 ) ) @ g )
= ( ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g )
!= ( bot_bot @ ( set @ v ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( ( labeled_LG @ TA @ TB @ ( labeled_edges @ TA @ TB @ A ) @ ( labeled_vertices @ TA @ TB @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_labeled__graph_Ocollapse) ).
thf(386,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( ( labeled_LG @ TA @ TB @ ( labeled_edges @ TA @ TB @ A ) @ ( labeled_vertices @ TA @ TB @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(119,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] :
( ( graph_union @ TA @ TB @ A @ ( graph_union @ TA @ TB @ A @ B ) )
= ( graph_union @ TA @ TB @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_graph__union__idemp_I2_J) ).
thf(595,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] :
( ( graph_union @ TA @ TB @ A @ ( graph_union @ TA @ TB @ A @ B ) )
= ( graph_union @ TA @ TB @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(126,axiom,
preorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_4) ).
thf(612,plain,
preorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(211,axiom,
member @ ( product_prod @ v @ v ) @ ( product_Pair @ v @ v @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Const @ v2 @ y ) @ ( map_graph @ v @ v @ ( standard_Constant @ v2 ) @ ( bNF_Gr @ v @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) @ h ) @ g ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ay_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062) ).
thf(876,plain,
member @ ( product_prod @ v @ v ) @ ( product_Pair @ v @ v @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Const @ v2 @ y ) @ ( map_graph @ v @ v @ ( standard_Constant @ v2 ) @ ( bNF_Gr @ v @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) @ h ) @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(207,axiom,
! [TA: $tType] :
( ( standa438229444_rules @ TA )
= ( ^ [A: set @ TA,B: set @ ( standard_Constant @ TA )] : ( sup_sup @ ( set @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) ) ) @ ( sup_sup @ ( set @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) ) ) @ ( standa1138209853_rules @ TA @ A ) @ ( standa2002409347_rules @ TA @ B ) ) @ ( insert @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) ) @ ( standa400804411p_rule @ ( standard_Constant @ TA ) @ ( standard_S_Top @ TA ) ) @ ( insert @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) ) @ ( standa244753842y_rule @ ( standard_Constant @ TA ) ) @ ( bot_bot @ ( set @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_standard__rules__def) ).
thf(859,plain,
! [TA: $tType] :
( ( standa438229444_rules @ TA )
= ( ^ [A: set @ TA,B: set @ ( standard_Constant @ TA )] : ( sup_sup @ ( set @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) ) ) @ ( sup_sup @ ( set @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) ) ) @ ( standa1138209853_rules @ TA @ A ) @ ( standa2002409347_rules @ TA @ B ) ) @ ( insert @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) ) @ ( standa400804411p_rule @ ( standard_Constant @ TA ) @ ( standard_S_Top @ TA ) ) @ ( insert @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) ) @ ( standa244753842y_rule @ ( standard_Constant @ TA ) ) @ ( bot_bot @ ( set @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ TA ) @ nat ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(254,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(991,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(132,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( sup_sup @ TA @ A @ B )
= ( bot_bot @ TA ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_sup__eq__bot__iff) ).
thf(627,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( sup_sup @ TA @ A @ B )
= ( bot_bot @ TA ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ),B: set @ TA] :
( ( labeled_vertices @ TB @ TA @ ( labeled_LG @ TB @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_labeled__graph_Osel_I2_J) ).
thf(450,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ),B: set @ TA] :
( ( labeled_vertices @ TB @ TA @ ( labeled_LG @ TB @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(106,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_doubleton__eq__iff) ).
thf(556,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(100,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_insert__absorb2) ).
thf(539,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(248,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_insert__eq__iff) ).
thf(976,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_comp__apply) ).
thf(581,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(204,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ! [C: TA,D: TA] :
( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) )
=> ( total_on @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_total__onI) ).
thf(844,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ! [C: TA,D: TA] :
( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) )
=> ( total_on @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(242,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TA] :
( ( labeled_LG @ TB @ TA @ ( insert @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TB @ ( product_prod @ TA @ TA ) @ A @ ( product_Pair @ TA @ TA @ B @ C ) ) @ ( bot_bot @ ( set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ) ) ) ) @ ( insert @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( restrict @ TB @ TA @ ( labeled_LG @ TB @ TA @ ( insert @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TB @ ( product_prod @ TA @ TA ) @ A @ ( product_Pair @ TA @ TA @ B @ C ) ) @ ( bot_bot @ ( set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ) ) ) ) @ ( insert @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_graph__single) ).
thf(961,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TA] :
( ( labeled_LG @ TB @ TA @ ( insert @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TB @ ( product_prod @ TA @ TA ) @ A @ ( product_Pair @ TA @ TA @ B @ C ) ) @ ( bot_bot @ ( set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ) ) ) ) @ ( insert @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( restrict @ TB @ TA @ ( labeled_LG @ TB @ TA @ ( insert @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ) @ ( product_Pair @ TB @ ( product_prod @ TA @ TA ) @ A @ ( product_Pair @ TA @ TA @ B @ C ) ) @ ( bot_bot @ ( set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ) ) ) ) @ ( insert @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( ( restrict @ TA @ TB @ ( restrict @ TA @ TB @ A ) )
= ( restrict @ TA @ TB @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_restrict__idemp) ).
thf(517,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( ( restrict @ TA @ TB @ ( restrict @ TA @ TB @ A ) )
= ( restrict @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(17,axiom,
! [TA: $tType] : ( bounde1808546759up_bot @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7) ).
thf(319,plain,
! [TA: $tType] : ( bounde1808546759up_bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(237,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_Set_Oset__insert) ).
thf(946,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(30,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_sup_Oidem) ).
thf(351,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(186,axiom,
~ ! [A: v2 > v] :
~ ! [B: v2] :
( ( member @ v2 @ B @ c )
=> ( member @ ( product_prod @ v @ v ) @ ( product_Pair @ v @ v @ ( A @ B ) @ ( A @ B ) ) @ ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Const @ v2 @ B ) @ ( map_graph @ v @ v @ ( standard_Constant @ v2 ) @ ( bNF_Gr @ v @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) @ h ) @ g ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_A_I_092_060And_062x_O_Ax_A_092_060in_062_AC_A_092_060Longrightarrow_062_A_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(786,plain,
~ ! [A: v2 > v] :
~ ! [B: v2] :
( ( member @ v2 @ B @ c )
=> ( member @ ( product_prod @ v @ v ) @ ( product_Pair @ v @ v @ ( A @ B ) @ ( A @ B ) ) @ ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Const @ v2 @ B ) @ ( map_graph @ v @ v @ ( standard_Constant @ v2 ) @ ( bNF_Gr @ v @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) @ h ) @ g ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(256,axiom,
! [TA: $tType] :
( ( total_on @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_total__on__def) ).
thf(995,plain,
! [TA: $tType] :
( ( total_on @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TC @ TA,B: set @ ( product_prod @ TA @ TB )] : ( agree_on @ TC @ TA @ TB @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_agree__on__refl) ).
thf(568,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TC @ TA,B: set @ ( product_prod @ TA @ TB )] : ( agree_on @ TC @ TA @ TB @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(6,axiom,
semilattice_sup @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Lattices_Osemilattice__sup_3) ).
thf(290,plain,
semilattice_sup @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(148,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: TB,C: TB,D: allegorical_term @ TA] :
( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ B @ C ) @ ( semantics @ TA @ TB @ A @ D ) )
=> ( member @ TB @ C @ ( labeled_vertices @ TA @ TB @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_semantics__in__vertices_I2_J) ).
thf(667,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: TB,C: TB,D: allegorical_term @ TA] :
( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ B @ C ) @ ( semantics @ TA @ TB @ A @ D ) )
=> ( member @ TB @ C @ ( labeled_vertices @ TA @ TB @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( agree_on @ TA @ TB @ TC )
= ( ^ [A: labeled_graph @ TA @ TB,B: set @ ( product_prod @ TB @ TC ),C: set @ ( product_prod @ TB @ TC )] : ( agree_on @ TA @ TB @ TC @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_agree__on__comm) ).
thf(383,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( agree_on @ TA @ TB @ TC )
= ( ^ [A: labeled_graph @ TA @ TB,B: set @ ( product_prod @ TB @ TC ),C: set @ ( product_prod @ TB @ TC )] : ( agree_on @ TA @ TB @ TC @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(220,axiom,
! [TA: $tType,A: TA] :
( ( standard_S_Top @ TA )
!= ( standard_S_Const @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Standard__Constant_Odistinct_I5_J) ).
thf(899,plain,
! [TA: $tType,A: TA] :
( ( standard_S_Top @ TA )
!= ( standard_S_Const @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(153,axiom,
! [A: product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat )] :
( ( member @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) ) @ A @ ( sup_sup @ ( set @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) ) ) @ ( sup_sup @ ( set @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) ) ) @ ( standa1138209853_rules @ v2 @ c ) @ ( standa2002409347_rules @ v2 @ l ) ) @ ( insert @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) ) @ ( standa400804411p_rule @ ( standard_Constant @ v2 ) @ ( standard_S_Top @ v2 ) ) @ ( insert @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) ) @ ( standa244753842y_rule @ ( standard_Constant @ v2 ) ) @ ( bot_bot @ ( set @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) ) ) ) ) ) ) )
=> ( maintained @ ( standard_Constant @ v2 ) @ nat @ v @ A @ g ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_mnt) ).
thf(684,plain,
! [A: product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat )] :
( ( member @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) ) @ A @ ( sup_sup @ ( set @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) ) ) @ ( sup_sup @ ( set @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) ) ) @ ( standa1138209853_rules @ v2 @ c ) @ ( standa2002409347_rules @ v2 @ l ) ) @ ( insert @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) ) @ ( standa400804411p_rule @ ( standard_Constant @ v2 ) @ ( standard_S_Top @ v2 ) ) @ ( insert @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) ) @ ( standa244753842y_rule @ ( standard_Constant @ v2 ) ) @ ( bot_bot @ ( set @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ v2 ) @ nat ) ) ) ) ) ) ) )
=> ( maintained @ ( standard_Constant @ v2 ) @ nat @ v @ A @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot) ).
thf(346,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(273,axiom,
~ ! [A: v] :
~ ( member @ v @ A @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(1045,plain,
~ ! [A: v] :
~ ( member @ v @ A @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(5,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_sup__left__idem) ).
thf(287,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ A @ ( sup_sup @ TA @ A @ B ) )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(66,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_Un__insert__right) ).
thf(447,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(60,axiom,
! [TA: $tType] :
( ( standard_S_Top @ TA )
!= ( standard_S_Bot @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Standard__Constant_Odistinct_I1_J) ).
thf(432,plain,
! [TA: $tType] :
( ( standard_S_Top @ TA )
!= ( standard_S_Bot @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(194,axiom,
member @ v @ x @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_x) ).
thf(818,plain,
member @ v @ x @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(56,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_Un__subset__iff) ).
thf(422,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(187,axiom,
! [TA: $tType,A: product_prod @ TA @ TA,B: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ A @ ( id_on @ TA @ B ) )
=> ~ ! [C: TA] :
( ( member @ TA @ C @ B )
=> ( A
!= ( product_Pair @ TA @ TA @ C @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_Id__onE) ).
thf(790,plain,
! [TA: $tType,A: product_prod @ TA @ TA,B: set @ TA] :
( ( member @ ( product_prod @ TA @ TA ) @ A @ ( id_on @ TA @ B ) )
=> ~ ! [C: TA] :
( ( member @ TA @ C @ B )
=> ( A
!= ( product_Pair @ TA @ TA @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(38,axiom,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA] : ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_insert__is__Un) ).
thf(373,plain,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA] : ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(122,axiom,
bounde1808546759up_bot @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_12) ).
thf(603,plain,
bounde1808546759up_bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(12,axiom,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ B )
= ( sup_sup @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_sup_Oright__idem) ).
thf(305,plain,
! [TA: $tType] :
( ( semilattice_sup @ TA )
=> ! [A: TA,B: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ B )
= ( sup_sup @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(227,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_prod__induct5) ).
thf(918,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(25,axiom,
semilattice_sup @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Osemilattice__sup_13) ).
thf(341,plain,
semilattice_sup @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TC @ TB,B: labeled_graph @ TC @ TB,C: labeled_graph @ TC @ TA,D: set @ ( product_prod @ TA @ TB )] :
( ( graph_homomorphism @ TC @ TB @ TB @ A @ B @ ( id_on @ TB @ ( labeled_vertices @ TC @ TB @ A ) ) )
=> ( ( graph_homomorphism @ TC @ TA @ TB @ C @ A @ D )
=> ( graph_homomorphism @ TC @ TA @ TB @ C @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_subgraph__preserves__hom) ).
thf(506,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TC @ TB,B: labeled_graph @ TC @ TB,C: labeled_graph @ TC @ TA,D: set @ ( product_prod @ TA @ TB )] :
( ( graph_homomorphism @ TC @ TB @ TB @ A @ B @ ( id_on @ TB @ ( labeled_vertices @ TC @ TB @ A ) ) )
=> ( ( graph_homomorphism @ TC @ TA @ TB @ C @ A @ D )
=> ( graph_homomorphism @ TC @ TA @ TB @ C @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(33,axiom,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_inf__sup__aci_I6_J) ).
thf(358,plain,
! [TA: $tType] :
( ( lattice @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( sup_sup @ TA @ ( sup_sup @ TA @ A @ B ) @ C )
= ( sup_sup @ TA @ A @ ( sup_sup @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(198,axiom,
! [A: v2] :
? [B: v] :
( ( member @ v2 @ A @ c )
=> ( member @ ( product_prod @ v @ v ) @ ( product_Pair @ v @ v @ B @ B ) @ ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Const @ v2 @ A ) @ ( map_graph @ v @ v @ ( standard_Constant @ v2 ) @ ( bNF_Gr @ v @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) @ h ) @ g ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16__092_060open_062_092_060forall_062c_O_A_092_060exists_062v_O_Ac_A_092_060in_062_AC_A_092_060longrightarrow_062_A_Iv_M_Av_J_A_092_060in_062_AgetRel_A_IS__Const_Ac_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062) ).
thf(828,plain,
! [A: v2] :
? [B: v] :
( ( member @ v2 @ A @ c )
=> ( member @ ( product_prod @ v @ v ) @ ( product_Pair @ v @ v @ B @ B ) @ ( getRel @ ( standard_Constant @ v2 ) @ v @ ( standard_S_Const @ v2 @ A ) @ ( map_graph @ v @ v @ ( standard_Constant @ v2 ) @ ( bNF_Gr @ v @ v @ ( labeled_vertices @ ( standard_Constant @ v2 ) @ v @ g ) @ h ) @ g ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(135,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( labele1974067554_graph @ TA @ TB @ TC )
= ( ^ [A: ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) > ( set @ TB ) > TC,B: labeled_graph @ TA @ TB] : ( A @ ( labeled_edges @ TA @ TB @ B ) @ ( labeled_vertices @ TA @ TB @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_labeled__graph_Ocase__eq__if) ).
thf(635,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( labele1974067554_graph @ TA @ TB @ TC )
= ( ^ [A: ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) > ( set @ TB ) > TC,B: labeled_graph @ TA @ TB] : ( A @ ( labeled_edges @ TA @ TB @ B ) @ ( labeled_vertices @ TA @ TB @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(97,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Un__empty) ).
thf(532,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(240,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TB @ TC,B: labeled_graph @ TB @ TA,C: set @ ( product_prod @ TC @ TA ),D: allegorical_term @ TB] :
( ( graph_homomorphism @ TB @ TC @ TA @ A @ B @ C )
=> ( ( ( semantics @ TB @ TC @ A @ D )
!= ( bot_bot @ ( set @ ( product_prod @ TC @ TC ) ) ) )
=> ( ( semantics @ TB @ TA @ B @ D )
!= ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_graph__homomorphism__nonempty) ).
thf(955,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TB @ TC,B: labeled_graph @ TB @ TA,C: set @ ( product_prod @ TC @ TA ),D: allegorical_term @ TB] :
( ( graph_homomorphism @ TB @ TC @ TA @ A @ B @ C )
=> ( ( ( semantics @ TB @ TC @ A @ D )
!= ( bot_bot @ ( set @ ( product_prod @ TC @ TC ) ) ) )
=> ( ( semantics @ TB @ TA @ B @ D )
!= ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(230,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TC @ TB ),B: set @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ),C: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ),D: set @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) )] :
( ( edge_preserving @ TC @ TB @ TA @ A @ B @ C )
=> ( ( edge_preserving @ TC @ TB @ TA @ A @ D @ C )
=> ( edge_preserving @ TC @ TB @ TA @ A @ ( sup_sup @ ( set @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ) ) @ B @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_edge__preserving__unionI) ).
thf(928,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TC @ TB ),B: set @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ),C: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ),D: set @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) )] :
( ( edge_preserving @ TC @ TB @ TA @ A @ B @ C )
=> ( ( edge_preserving @ TC @ TB @ TA @ A @ D @ C )
=> ( edge_preserving @ TC @ TB @ TA @ A @ ( sup_sup @ ( set @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ) ) @ B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(219,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ TA,D: TA > TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( bNF_Gr @ TA @ TB @ C @ D ) )
=> ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_GrD1) ).
thf(897,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ TA,D: TA > TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( bNF_Gr @ TA @ TB @ C @ D ) )
=> ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(180,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( bNF_Gr @ TA @ TB @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_Gr__empty) ).
thf(767,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( bNF_Gr @ TA @ TB @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(268,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_singletonD) ).
thf(1033,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(48,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_sup__bot_Oleft__neutral) ).
thf(400,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( bot_bot @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(131,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB,E: TA] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_comp__eq__dest) ).
thf(624,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB,E: TA] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(252,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] : ( agree_on @ TC @ TA @ TB @ ( labeled_LG @ TC @ TA @ ( bot_bot @ ( set @ ( product_prod @ TC @ ( product_prod @ TA @ TA ) ) ) ) @ ( bot_bot @ ( set @ TA ) ) ) @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_agree__on__empty) ).
thf(987,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] : ( agree_on @ TC @ TA @ TB @ ( labeled_LG @ TC @ TA @ ( bot_bot @ ( set @ ( product_prod @ TC @ ( product_prod @ TA @ TA ) ) ) ) @ ( bot_bot @ ( set @ TA ) ) ) @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TB )
=> ( ( sup_sup @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( sup_sup @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_sup__fun__def) ).
thf(332,plain,
! [TA: $tType,TB: $tType] :
( ( semilattice_sup @ TB )
=> ( ( sup_sup @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB,C: TA] : ( sup_sup @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(58,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_sup__bot_Oright__neutral) ).
thf(427,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( bot_bot @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(250,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( least @ TA @ TD @ TC @ TB )
= ( ^ [A: itself @ TA,B: set @ ( product_prod @ ( labeled_graph @ TD @ TC ) @ ( labeled_graph @ TD @ TC ) ),C: labeled_graph @ TD @ TB,D: labeled_graph @ TD @ TB] :
( ( graph_homomorphism @ TD @ TB @ TB @ C @ D @ ( id_on @ TB @ ( labeled_vertices @ TD @ TB @ C ) ) )
& ! [E: labeled_graph @ TD @ TA] :
( ( consequence_graph @ TD @ TC @ TA @ B @ E )
=> ( maintained @ TD @ TB @ TA @ ( product_Pair @ ( labeled_graph @ TD @ TB ) @ ( labeled_graph @ TD @ TB ) @ C @ D ) @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_least__def) ).
thf(982,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( least @ TA @ TD @ TC @ TB )
= ( ^ [A: itself @ TA,B: set @ ( product_prod @ ( labeled_graph @ TD @ TC ) @ ( labeled_graph @ TD @ TC ) ),C: labeled_graph @ TD @ TB,D: labeled_graph @ TD @ TB] :
( ( graph_homomorphism @ TD @ TB @ TB @ C @ D @ ( id_on @ TB @ ( labeled_vertices @ TD @ TB @ C ) ) )
& ! [E: labeled_graph @ TD @ TA] :
( ( consequence_graph @ TD @ TC @ TA @ B @ E )
=> ( maintained @ TD @ TB @ TA @ ( product_Pair @ ( labeled_graph @ TD @ TB ) @ ( labeled_graph @ TD @ TB ) @ C @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(64,axiom,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice_1) ).
thf(442,plain,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(190,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( standard_S_Const @ TA @ A )
= ( standard_S_Const @ TA @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Standard__Constant_Oinject) ).
thf(803,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( standard_S_Const @ TA @ A )
= ( standard_S_Const @ TA @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(31,axiom,
! [TA: $tType] : ( lattice @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Olattice_10) ).
thf(354,plain,
! [TA: $tType] : ( lattice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(182,axiom,
! [A: standard_Constant @ v2,B: v,C: v] :
( ( member @ ( product_prod @ ( standard_Constant @ v2 ) @ ( product_prod @ v @ v ) ) @ ( product_Pair @ ( standard_Constant @ v2 ) @ ( product_prod @ v @ v ) @ A @ ( product_Pair @ v @ v @ B @ C ) ) @ ( labeled_edges @ ( standard_Constant @ v2 ) @ v @ g ) )
= ( member @ ( product_prod @ ( standard_Constant @ v2 ) @ ( product_prod @ v @ v ) ) @ ( product_Pair @ ( standard_Constant @ v2 ) @ ( product_prod @ v @ v ) @ A @ ( product_Pair @ v @ v @ ( h @ B ) @ ( h @ C ) ) ) @ ( labeled_edges @ ( standard_Constant @ v2 ) @ v @ g ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_h_I4_J) ).
thf(775,plain,
! [A: standard_Constant @ v2,B: v,C: v] :
( ( member @ ( product_prod @ ( standard_Constant @ v2 ) @ ( product_prod @ v @ v ) ) @ ( product_Pair @ ( standard_Constant @ v2 ) @ ( product_prod @ v @ v ) @ A @ ( product_Pair @ v @ v @ B @ C ) ) @ ( labeled_edges @ ( standard_Constant @ v2 ) @ v @ g ) )
= ( member @ ( product_prod @ ( standard_Constant @ v2 ) @ ( product_prod @ v @ v ) ) @ ( product_Pair @ ( standard_Constant @ v2 ) @ ( product_prod @ v @ v ) @ A @ ( product_Pair @ v @ v @ ( h @ B ) @ ( h @ C ) ) ) @ ( labeled_edges @ ( standard_Constant @ v2 ) @ v @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(137,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( ( graph_homomorphism @ TA @ TB @ TB @ A @ ( restrict @ TA @ TB @ A ) @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) )
= ( A
= ( restrict @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_subgraph__restrict) ).
thf(639,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( ( graph_homomorphism @ TA @ TB @ TB @ A @ ( restrict @ TA @ TB @ A ) @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) )
= ( A
= ( restrict @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(176,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TB,B: TB > TB,C: product_prod @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC )] :
( ( graph_homomorphism @ TA @ TB @ TB @ ( map_graph @ TB @ TB @ TA @ ( bNF_Gr @ TB @ TB @ ( labeled_vertices @ TA @ TB @ A ) @ B ) @ A ) @ A @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ ( map_graph @ TB @ TB @ TA @ ( bNF_Gr @ TB @ TB @ ( labeled_vertices @ TA @ TB @ A ) @ B ) @ A ) ) ) )
=> ( ! [D: TB] :
( ( member @ TB @ D @ ( labeled_vertices @ TA @ TB @ A ) )
=> ( ( comp @ TB @ TB @ TB @ B @ B @ D )
= ( B @ D ) ) )
=> ( ( maintained @ TA @ TC @ TB @ C @ A )
=> ( maintained @ TA @ TC @ TB @ C @ ( map_graph @ TB @ TB @ TA @ ( bNF_Gr @ TB @ TB @ ( labeled_vertices @ TA @ TB @ A ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_idemp__embedding__maintained__preserved) ).
thf(755,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TA @ TB,B: TB > TB,C: product_prod @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC )] :
( ( graph_homomorphism @ TA @ TB @ TB @ ( map_graph @ TB @ TB @ TA @ ( bNF_Gr @ TB @ TB @ ( labeled_vertices @ TA @ TB @ A ) @ B ) @ A ) @ A @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ ( map_graph @ TB @ TB @ TA @ ( bNF_Gr @ TB @ TB @ ( labeled_vertices @ TA @ TB @ A ) @ B ) @ A ) ) ) )
=> ( ! [D: TB] :
( ( member @ TB @ D @ ( labeled_vertices @ TA @ TB @ A ) )
=> ( ( comp @ TB @ TB @ TB @ B @ B @ D )
= ( B @ D ) ) )
=> ( ( maintained @ TA @ TC @ TB @ C @ A )
=> ( maintained @ TA @ TC @ TB @ C @ ( map_graph @ TB @ TB @ TA @ ( bNF_Gr @ TB @ TB @ ( labeled_vertices @ TA @ TB @ A ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(118,axiom,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( bot_bot @ TA )
= ( sup_sup @ TA @ A @ B ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_bot__eq__sup__iff) ).
thf(592,plain,
! [TA: $tType] :
( ( bounde1808546759up_bot @ TA )
=> ! [A: TA,B: TA] :
( ( ( bot_bot @ TA )
= ( sup_sup @ TA @ A @ B ) )
= ( ( A
= ( bot_bot @ TA ) )
& ( B
= ( bot_bot @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(162,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_old_Oprod_Oinducts) ).
thf(708,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(214,axiom,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_all__not__in__conv) ).
thf(882,plain,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(246,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_UnI2) ).
thf(972,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TC @ TA,B: TA > TB] :
( ( A
= ( restrict @ TC @ TA @ A ) )
=> ( graph_homomorphism @ TC @ TA @ TB @ A @ ( map_graph @ TA @ TB @ TC @ ( bNF_Gr @ TA @ TB @ ( labeled_vertices @ TC @ TA @ A ) @ B ) @ A ) @ ( bNF_Gr @ TA @ TB @ ( labeled_vertices @ TC @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_graph__homo) ).
thf(469,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TC @ TA,B: TA > TB] :
( ( A
= ( restrict @ TC @ TA @ A ) )
=> ( graph_homomorphism @ TC @ TA @ TB @ A @ ( map_graph @ TA @ TB @ TC @ ( bNF_Gr @ TA @ TB @ ( labeled_vertices @ TC @ TA @ A ) @ B ) @ A ) @ ( bNF_Gr @ TA @ TB @ ( labeled_vertices @ TC @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(235,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_prod__cases4) ).
thf(940,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(233,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TB,C: TA,D: labeled_graph @ TA @ TB,E: TB > TC] :
( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ A @ B ) @ ( getRel @ TA @ TB @ C @ D ) )
=> ( ( member @ TB @ A @ ( labeled_vertices @ TA @ TB @ D ) )
=> ( ( member @ TB @ B @ ( labeled_vertices @ TA @ TB @ D ) )
=> ( member @ ( product_prod @ TC @ TC ) @ ( product_Pair @ TC @ TC @ ( E @ A ) @ ( E @ B ) ) @ ( getRel @ TA @ TC @ C @ ( map_graph @ TB @ TC @ TA @ ( bNF_Gr @ TB @ TC @ ( labeled_vertices @ TA @ TB @ D ) @ E ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_getRel__hom) ).
thf(935,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TB,C: TA,D: labeled_graph @ TA @ TB,E: TB > TC] :
( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ A @ B ) @ ( getRel @ TA @ TB @ C @ D ) )
=> ( ( member @ TB @ A @ ( labeled_vertices @ TA @ TB @ D ) )
=> ( ( member @ TB @ B @ ( labeled_vertices @ TA @ TB @ D ) )
=> ( member @ ( product_prod @ TC @ TC ) @ ( product_Pair @ TC @ TC @ ( E @ A ) @ ( E @ B ) ) @ ( getRel @ TA @ TC @ C @ ( map_graph @ TB @ TC @ TA @ ( bNF_Gr @ TB @ TC @ ( labeled_vertices @ TA @ TB @ D ) @ E ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(260,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_insert__ident) ).
thf(1009,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] :
( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ( B
= ( restrict @ TA @ TB @ B ) )
=> ( ( graph_union @ TA @ TB @ A @ B )
= ( restrict @ TA @ TB @ ( graph_union @ TA @ TB @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_graph__union__preserves__restrict) ).
thf(496,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] :
( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ( B
= ( restrict @ TA @ TB @ B ) )
=> ( ( graph_union @ TA @ TB @ A @ B )
= ( restrict @ TA @ TB @ ( graph_union @ TA @ TB @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(69,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(454,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(2563,plain,
$false,
inference(e,[status(thm)],[645,1036,365,760,1031,666,408,523,994,308,873,1041,440,511,715,472,698,930,670,885,565,651,389,570,344,1055,724,587,619,542,460,902,559,638,870,606,416,316,284,770,475,321,376,834,514,937,806,966,348,574,905,480,766,280,293,453,660,998,411,397,687,877,692,380,529,925,810,1057,910,894,746,302,862,598,392,630,729,1021,778,484,361,879,493,551,842,1012,852,435,324,974,650,1017,403,356,783,499,989,742,578,1028,554,537,686,642,526,706,647,985,701,654,721,622,837,1050,457,633,508,657,1026,953,718,888,298,425,430,856,296,444,733,601,584,819,562,826,291,958,281,545,382,313,1058,466,335,672,406,831,681,419,736,1043,616,764,979,604,890,477,367,535,609,799,483,520,964,915,943,330,932,912,780,1015,394,1000,922,505,438,589,795,487,812,749,342,1049,490,675,663,548,968,823,690,705,414,327,739,310,712,1003,1053,502,840,463,338,951,907,1038,370,613,727,386,595,612,876,859,991,627,450,556,539,976,581,844,961,517,319,946,351,786,995,568,290,667,383,899,684,346,1045,287,447,432,818,422,790,373,603,305,918,341,506,358,828,635,532,955,928,897,767,1033,400,624,987,332,427,982,442,803,354,775,639,755,592,708,882,972,469,940,935,1009,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP180^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.07/0.12 % Computer : n012.cluster.edu
% 0.07/0.12 % Model : x86_64 x86_64
% 0.07/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.12 % Memory : 8046.5625MB
% 0.07/0.12 % OS : Linux 6.8.0-71-generic
% 0.07/0.12 % CPULimit : 300
% 0.07/0.12 % WCLimit : 300
% 0.07/0.12 % DateTime : Tue Sep 29 20:07:19 UTC 2026
% 0.07/0.12 % CPUTime :
% 0.07/0.12 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.40/0.40 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.62 % [INFO] Parsing done (215ms).
% 1.24/0.62 % [INFO] Running in sequential loop mode.
% 1.74/0.81 % [INFO] eprover registered as external prover.
% 1.74/0.82 % [INFO] Scanning for conjecture ...
% 1.96/0.91 % [INFO] Found a conjecture (or negated_conjecture) and 278 axioms. Running axiom selection ...
% 1.96/1.00 % [INFO] Axiom selection finished. Selected 277 axioms (removed 1 axioms).
% 3.08/1.21 % [INFO] Problem is higher-order (TPTP THF).
% 3.08/1.24 % [INFO] Type checking passed.
% 3.08/1.24 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 37.67/11.17 % External prover 'e' found a proof!
% 37.67/11.17 % [INFO] Killing All external provers ...
% 37.67/11.17 % Time passed: 10984ms (effective reasoning time: 10546ms)
% 37.67/11.17 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 37.67/11.18 % Axioms used in derivation (277): fact_150_singleton__inject, fact_182_sup__bot_Oright__neutral, fact_26_Standard__Constant_Odistinct_I9_J, fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, tcon_fun___Orderings_Obot, fact_38_prod__cases6, fact_114_map__graph__in, fact_197_graph__union__edges, fact_187_sup__left__idem, fact_77_h_I4_J, fact_184_sup__bot_Oleft__neutral, fact_68_maintained__preserved__by__isomorphism, tcon_HOL_Obool___Lattices_Osemilattice__sup_13, fact_196_edge__preserving__unionI, fact_52_map__graph__preserves__subgraph, fact_199_sup_Oleft__commute, fact_6__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ay_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062, fact_58_restrict__idemp, fact_207_inf__sup__aci_I5_J, fact_154_Un__left__commute, fact_147_singleton__iff, fact_169_UnI2, fact_105_least__consequence__graph__def, fact_141_Un__singleton__iff, fact_156_Un__left__absorb, tcon_Nat_Onat___Orderings_Obot_6, fact_16__092_060open_062_092_060forall_062c_O_A_092_060exists_062v_O_Ac_A_092_060in_062_AC_A_092_060longrightarrow_062_A_Iv_M_Av_J_A_092_060in_062_AgetRel_A_IS__Const_Ac_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062, fact_222_extensibleI, fact_22_getRel__map__fn, fact_137_Gr__insert, fact_102_leastI, fact_232_Field__insert, fact_69_idemp__embedding__maintained__preserved, tcon_HOL_Obool___Orderings_Obot_16, fact_85_nonempty__rule, fact_119_insert__iff, fact_243_singleton__insert__inj__eq, fact_124_graph__union__idemp_I1_J, fact_131_graph__union__preserves__restrict, fact_39_prod__cases5, fact_203_sup_Oassoc, fact_120_insertCI, fact_149_insert__not__empty, fact_148_doubleton__eq__iff, fact_41_prod__cases3, fact_50_map__graph__fn__id_I2_J, fact_229_total__on__empty, fact_99_least__consequence__graphI, fact_35_prod__induct4, fact_202_sup__assoc, fact_56_Id__on__empty, fact_210_inf__sup__aci_I8_J, fact_189_sup__idem, fact_76_tr, fact_96_comp__eq__dest__lhs, fact_226_agree__on__empty, fact_251_le__supI, tcon_Set_Oset___Lattices_Osemilattice__sup_8, fact_4__C1_C_I2_J, fact_2__C1_C_I3_J, fact_163_insertI2, fact_126_graph__union__idemp_I3_J, fact_159_insert__ident, fact_3__C1_C_I1_J, fact_79_maintained__refl, fact_213_is__singletonI, fact_151_labeled__graph_Oexhaust, fact_158_insert__absorb, fact_143_graph__union__def, fact_89_equals0D, fact_104_map__graph__edge__preserving, fact_84_all__not__in__conv, fact_117_subgraph__def, tcon_fun___Lattices_Obounded__semilattice__sup__bot, fact_217_is__singleton__def, fact_246_Field__Un, fact_218_labeled__graph_Osplit__sel, fact_237_le__sup__iff, fact_146_singletonD, fact_185_sup__bot_Oeq__neutr__iff, fact_155_insert__commute, fact_53_subgraph__refl, tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7, fact_219_labeled__graph_Osplit__sel__asm, fact_8_h_I3_J, fact_107_bot__set__def, fact_216_is__singletonE, fact_110_edge__preserving__atomic, fact_93_comp__assoc, fact_46_Collect__mem__eq, fact_29_getRel__subgraph, fact_21_h_I1_J, tcon_HOL_Obool___Lattices_Olattice_15, fact_116_graph__homomorphism__empty, fact_175_graph__homomorphism__nonempty, fact_127_singletonI, tcon_Set_Oset___Orderings_Opreorder_9, fact_215_is__singletonI_H, fact_78_old_Oprod_Orec, fact_27_getRel__dom_I1_J, fact_64_map__graph__fn__comp, tcon_fun___Lattices_Obounded__lattice_2, fact_178_semantics__in__vertices_I2_J, fact_25_Standard__Constant_Odistinct_I5_J, fact_54_subgraph__restrict, fact_109_consequence__graphD_I1_J, fact_240_subset__empty, fact_71_Id__on__eqI, fact_248_inf__sup__ord_I4_J, fact_18__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_A_I_092_060And_062x_O_Ax_A_092_060in_062_AC_A_092_060Longrightarrow_062_A_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, tcon_fun___Lattices_Osemilattice__sup, fact_250_le__supE, fact_142_singleton__Un__iff, fact_214_is__singleton__the__elem, fact_97_edge__preserving__on__graphI, fact_200_sup__commute, fact_239_empty__subsetI, fact_81_empty__Collect__eq, fact_23_getRel__hom, fact_160_Set_Oset__insert, fact_255_le__supI2, fact_75_map__graph__fn__eqI, tcon_Set_Oset___Lattices_Olattice_10, fact_153_mk__disjoint__insert, fact_32_prod__induct7, fact_204_boolean__algebra__cancel_Osup2, tcon_Set_Oset___Orderings_Obot_11, fact_17__092_060open_062_092_060exists_062f_O_A_092_060forall_062x_O_Ax_A_092_060in_062_AC_A_092_060longrightarrow_062_A_If_Ax_M_Af_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062, fact_183_sup__bot_Oneutr__eq__iff, fact_128_Un__empty, fact_233_subgraph__subset_I2_J, fact_254_le__supI1, fact_20_surj__pair, fact_205_boolean__algebra__cancel_Osup1, fact_140_insert__is__Un, fact_230_agree__on__trans, fact_231_agree__on__subg__compose, fact_31_old_Oprod_Oexhaust, fact_190_sup_Oidem, fact_133_labeled__graph_Ocollapse, fact_238_sup_Obounded__iff, fact_134_extensible__refl, fact_157_insert__eq__iff, fact_179_semantics__in__vertices_I1_J, fact_193_sup__bot__right, fact_171_UnE, fact_177_standard__rules__def, fact_45_mem__Collect__eq, fact_130_Un__insert__left, fact_12_m, fact_73_subgraph__preserves__hom, fact_59_in__Gr, fact_14_cf, fact_62_vertices__restrict, fact_11_old_Oprod_Oinject, fact_0_x, fact_223_total__on__singleton, fact_152_labeled__graph_Oinduct, fact_82_Collect__empty__eq, fact_121_Un__iff, fact_221_labeled__graph_Ocase__eq__if, fact_145_Un__empty__right, fact_44_mg, fact_13_top__nonempty, fact_74_subgraph__trans, fact_227_total__onI, fact_247_graph__unionI, fact_19_getRel__homR, fact_80_comp__apply, fact_90_equals0I, fact_220_labeled__graph_Ocase, fact_72_Id__on__iff, fact_57_Gr__empty, fact_37_prod__cases7, fact_47_Collect__cong, fact_198_sup__left__commute, fact_180_subgraph__semantics, fact_201_sup_Ocommute, fact_42_Pair__inject, fact_55_graph__homomorphism__Id, fact_144_Un__empty__left, tcon_Set_Oset___Lattices_Obounded__lattice_1, fact_63_map__graph__preserves__restricted, fact_65_assms_I1_J, fact_28_getRel__dom_I2_J, fact_194_bot__eq__sup__iff, fact_49_graph__homo, fact_252_sup__ge1, fact_70_Id__onE, fact_168_bex__Un, fact_88_emptyE, fact_123_labeled__graph_Oinject, fact_15__092_060open_062_092_060And_062c_O_Ac_A_092_060in_062_AC_A_092_060Longrightarrow_062_A_092_060exists_062v_O_A_Iv_M_Av_J_A_092_060in_062_AgetRel_A_IS__Const_Ac_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062, fact_206_sup__fun__def, fact_172_labeled__graph_Osel_I2_J, fact_94_comp__eq__dest, fact_9_Standard__Constant_Oinject, fact_191_sup__apply, tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_12, fact_242_Un__subset__iff, fact_108_consequence__graphD_I3_J, fact_188_sup_Oleft__idem, tcon_fun___Orderings_Opreorder, fact_34_prod__induct5, fact_132_graph__union__vertices, fact_122_UnCI, fact_224_agree__on__refl, fact_7_gr_I1_J, fact_100_GrD2, fact_170_UnI1, fact_60_Gr__not__in, fact_125_graph__union__idemp_I2_J, fact_173_labeled__graph_Osel_I1_J, fact_225_agree__on__comm, fact_112_least__def, fact_24_Standard__Constant_Odistinct_I1_J, fact_113_mnt, fact_245_Field__empty, fact_209_inf__sup__aci_I7_J, fact_176_labeled__graph_Oexhaust__sel, fact_91_ex__in__conv, fact_166_insertE, fact_136_constant__rules__empty, fact_167_ball__Un, fact_67__092_060open_062maintained_Anonempty__rule_AG_H_A_061_A_Ivertices_AG_H_A_092_060noteq_062_A_123_125_J_092_060close_062, fact_98_bot__apply, fact_186_sup_Oright__idem, fact_174_graph__homomorphism__semantics, fact_30_old_Oprod_Oinducts, fact_165_Un__assoc, fact_103_edge__preserving__Id, fact_212_Collect__empty__eq__bot, fact_115_maintainedI, fact_211_the__elem__eq, tcon_HOL_Obool___Orderings_Opreorder_14, fact_129_Un__insert__right, fact_5__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062, fact_118_insert__absorb2, fact_43_prod__cases, fact_162_Un__absorb, fact_101_GrD1, fact_234_order__refl, fact_139_graph__single, fact_244_singleton__insert__inj__eq_H, fact_111_bot__fun__def, fact_61_Id__onI, fact_195_sup__eq__bot__iff, fact_228_total__on__def, fact_241_insert__subset, fact_33_prod__induct6, fact_164_insertI1, tcon_Nat_Onat___Lattices_Olattice_5, tcon_HOL_Obool___Lattices_Obounded__lattice, fact_10_prod_Oinject, fact_192_sup__bot__left, fact_83_empty__iff, fact_249_inf__sup__ord_I3_J, fact_40_prod__cases4, tcon_Nat_Onat___Orderings_Opreorder_4, fact_236_subset__antisym, fact_87_labeled__graph_Oexpand, tcon_Nat_Onat___Lattices_Osemilattice__sup_3, fact_95_comp__eq__elim, fact_138_extensible__refl__concr, fact_51_map__graph__fn__graphI, fact_106_bot__empty__eq, fact_253_sup__ge2, fact_181_maintainedD, fact_161_Un__commute, fact_135_graph__empty__e, fact_92_comp__def, tcon_fun___Lattices_Olattice, fact_208_inf__sup__aci_I6_J, fact_66_ne, fact_235_subsetI, fact_36_prod__induct3, fact_86__092_060open_062maintainedA_A_Iidentity__rules_AL_J_AG_H_092_060close_062
% 37.67/11.18 % No. of inferences in proof: 558
% 37.67/11.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10984 ms resp. 10546 ms w/o parsing
% 38.30/11.31 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 38.30/11.32 % [INFO] Killing All external provers ...
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