TSTP Solution File: ITP177^2 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP177^2 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:48:33 EDT 2024
% Result : Theorem 36.71s 22.16s
% Output : Refutation 37.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 312
% Syntax : Number of formulae : 574 ( 218 unt; 52 typ; 0 def)
% Number of atoms : 2390 ( 508 equ; 4 cnn)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 13018 ( 130 ~; 15 |; 84 &;12281 @)
% ( 0 <=>; 508 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 10 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 212 ( 212 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 55 usr; 14 con; 0-8 aty)
% Number of variables : 2584 ( 114 ^2371 !; 18 ?;2584 :)
% ( 81 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(bNF_Gr_type,type,
bNF_Gr:
!>[TA: $tType,TB: $tType] : ( ( set @ TB ) > ( TB > TA ) > ( set @ ( product_prod @ TB @ TA ) ) ) ).
thf(equiv_congruent_type,type,
equiv_congruent:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TB ) ) > ( TB > TA ) > $o ) ).
thf(equiv_equiv_type,type,
equiv_equiv:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(equiv_proj_type,type,
equiv_proj:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > TB > ( set @ TA ) ) ).
thf(hilbert_Eps_type,type,
hilbert_Eps:
!>[TA: $tType] : ( ( TA > $o ) > TA ) ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(standard_S_Idt_type,type,
standard_S_Idt:
!>[TA: $tType] : ( standard_Constant @ TA ) ).
thf(getRel_type,type,
getRel:
!>[TA: $tType,TB: $tType] : ( TB > ( labeled_graph @ TB @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) ) ).
thf(semantics_type,type,
semantics:
!>[TA: $tType,TB: $tType] : ( ( labeled_graph @ TB @ TA ) > ( allegorical_term @ TB ) > ( set @ ( product_prod @ TA @ TA ) ) ) ).
thf(edge_preserving_type,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_type,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_type,type,
graph_union:
!>[TA: $tType,TB: $tType] : ( ( labeled_graph @ TB @ TA ) > ( labeled_graph @ TB @ TA ) > ( labeled_graph @ TB @ TA ) ) ).
thf(labeled_LG_type,type,
labeled_LG:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ) ) > ( set @ TA ) > ( labeled_graph @ TB @ TA ) ) ).
thf(labele1974067554_graph_type,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_type,type,
labeled_edges:
!>[TA: $tType,TB: $tType] : ( ( labeled_graph @ TB @ TA ) > ( set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ) ) ) ).
thf(labeled_vertices_type,type,
labeled_vertices:
!>[TA: $tType,TB: $tType] : ( ( labeled_graph @ TB @ TA ) > ( set @ TA ) ) ).
thf(map_graph_type,type,
map_graph:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( set @ ( product_prod @ TC @ TB ) ) > ( labeled_graph @ TA @ TC ) > ( labeled_graph @ TA @ TB ) ) ).
thf(restrict_type,type,
restrict:
!>[TA: $tType,TB: $tType] : ( ( labeled_graph @ TB @ TA ) > ( labeled_graph @ TB @ TA ) ) ).
thf(bot_bot_type,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(product_rec_prod_type,type,
product_rec_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(id_on_type,type,
id_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) ) ).
thf(image_type,type,
image:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > ( set @ TB ) > ( set @ TA ) ) ).
thf(refl_on_type,type,
refl_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(relcomp_type,type,
relcomp:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( set @ ( product_prod @ TC @ TB ) ) > ( set @ ( product_prod @ TB @ TA ) ) > ( set @ ( product_prod @ TC @ TA ) ) ) ).
thf(agree_on_type,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_type,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_type,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_type,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_type,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_type,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_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(image2_type,type,
image2:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > ( set @ TA ) ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(the_elem_type,type,
the_elem:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(standa2002409347_rules_type,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_type,type,
standa244753842y_rule:
!>[TA: $tType] : ( product_prod @ ( labeled_graph @ TA @ nat ) @ ( labeled_graph @ TA @ nat ) ) ).
thf(standa245363227y_rule_type,type,
standa245363227y_rule:
!>[TA: $tType] : ( TA > ( product_prod @ ( labeled_graph @ TA @ nat ) @ ( labeled_graph @ TA @ nat ) ) ) ).
thf(standa1805702094y_rule_type,type,
standa1805702094y_rule:
!>[TA: $tType] : ( TA > ( product_prod @ ( labeled_graph @ TA @ nat ) @ ( labeled_graph @ TA @ nat ) ) ) ).
thf(standa2114124375e_rule_type,type,
standa2114124375e_rule:
!>[TA: $tType] : ( TA > ( product_prod @ ( labeled_graph @ TA @ nat ) @ ( labeled_graph @ TA @ nat ) ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(g_type,type,
g: labeled_graph @ ( standard_Constant @ a ) @ b ).
thf(l_type,type,
l: set @ ( standard_Constant @ a ) ).
thf(p_type,type,
p: b > b > $o ).
thf(f_type,type,
f: b > b ).
thf(l2_type,type,
l2: standard_Constant @ a ).
thf(x_type,type,
x: b ).
thf(y_type,type,
y: b ).
thf(140,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TC @ TA,B: labeled_graph @ TC @ TB,C: set @ ( product_prod @ TA @ TB ),D: TA,E: TB] :
( ( graph_homomorphism @ TC @ TA @ TB @ A @ B @ C )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ E ) @ C )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ E ) @ ( relcomp @ TA @ TA @ TB @ ( id_on @ TA @ ( labeled_vertices @ TC @ TA @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_Id__on__vertices__identity_I1_J) ).
thf(645,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: labeled_graph @ TC @ TA,B: labeled_graph @ TC @ TB,C: set @ ( product_prod @ TA @ TB ),D: TA,E: TB] :
( ( graph_homomorphism @ TC @ TA @ TB @ A @ B @ C )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ E ) @ C )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ E ) @ ( relcomp @ TA @ TA @ TB @ ( id_on @ TA @ ( labeled_vertices @ TC @ TA @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(199,axiom,
( ( graph_union @ ( standard_Constant @ a ) @ b @ ( map_graph @ b @ b @ ( standard_Constant @ a ) @ ( bNF_Gr @ b @ b @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) @ f ) @ g ) @ g )
= g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__092_060open_062graph__union_A_Imap__graph__fn_AG_Af_J_AG_A_061_AG_092_060close_062) ).
thf(809,plain,
( ( graph_union @ ( standard_Constant @ a ) @ b @ ( map_graph @ b @ b @ ( standard_Constant @ a ) @ ( bNF_Gr @ b @ b @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) @ f ) @ g ) @ g )
= g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(181,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_empty__iff) ).
thf(760,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(31,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_Collect__mono) ).
thf(347,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(26,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/sandbox/benchmark/theBenchmark.p',fact_74_prod__cases) ).
thf(333,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)],[26]) ).
thf(233,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/sandbox/benchmark/theBenchmark.p',fact_24_labeled__graph_Ocollapse) ).
thf(893,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)],[233]) ).
thf(250,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_subset__Collect__iff) ).
thf(941,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(187,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/sandbox/benchmark/theBenchmark.p',fact_199_mk__disjoint__insert) ).
thf(777,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)],[187]) ).
thf(148,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/sandbox/benchmark/theBenchmark.p',fact_35_map__graph__fn__eqI) ).
thf(666,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)],[148]) ).
thf(81,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/sandbox/benchmark/theBenchmark.p',fact_71_map__graph__edge__preserving) ).
thf(481,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)],[81]) ).
thf(258,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_equiv__class__eq) ).
thf(962,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(76,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/sandbox/benchmark/theBenchmark.p',fact_79_prod__cases4) ).
thf(468,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)],[76]) ).
thf(53,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_Collect__mono__iff) ).
thf(408,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(153,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/sandbox/benchmark/theBenchmark.p',fact_29_map__graph__fn__id_I2_J) ).
thf(683,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)],[153]) ).
thf(170,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/sandbox/benchmark/theBenchmark.p',fact_68_GrD2) ).
thf(730,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)],[170]) ).
thf(19,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( B = C )
& ( A @ C ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( ~ ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( B = C )
& ( A @ C ) ) )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_Collect__conv__if2) ).
thf(308,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( B = C )
& ( A @ C ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( ~ ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( B = C )
& ( A @ C ) ) )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',fact_81_prod__cases6) ).
thf(379,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)],[43]) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',fact_66_prod_Oinject) ).
thf(511,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)],[92]) ).
thf(122,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_emptyE) ).
thf(597,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(220,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/sandbox/benchmark/theBenchmark.p',fact_52_getRel__dom_I2_J) ).
thf(861,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)],[220]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TC @ TB )] :
( ( relcomp @ TA @ TC @ TB @ ( bot_bot @ ( set @ ( product_prod @ TA @ TC ) ) ) @ A )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_relcomp__empty1) ).
thf(523,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TC @ TB )] :
( ( relcomp @ TA @ TC @ TB @ ( bot_bot @ ( set @ ( product_prod @ TA @ TC ) ) ) @ A )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(182,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: set @ TA] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( member @ TA @ A @ D )
=> ( member @ TB @ B @ ( image @ TA @ TB @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_ImageI) ).
thf(762,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: set @ TA] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( member @ TA @ A @ D )
=> ( member @ TB @ B @ ( image @ TA @ TB @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(5,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/sandbox/benchmark/theBenchmark.p',fact_210_doubleton__eq__iff) ).
thf(269,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)],[5]) ).
thf(151,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 )] :
( ( graph_homomorphism @ TC @ TA @ TB @ ( graph_union @ TC @ TA @ A @ B ) @ C @ D )
=> ( ( B
= ( restrict @ TC @ TA @ B ) )
=> ( graph_homomorphism @ TC @ TA @ TB @ B @ C @ ( relcomp @ TA @ TA @ TB @ ( id_on @ TA @ ( labeled_vertices @ TC @ TA @ B ) ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_graph__homo__union__id_I2_J) ).
thf(677,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 )] :
( ( graph_homomorphism @ TC @ TA @ TB @ ( graph_union @ TC @ TA @ A @ B ) @ C @ D )
=> ( ( B
= ( restrict @ TC @ TA @ B ) )
=> ( graph_homomorphism @ TC @ TA @ TB @ B @ C @ ( relcomp @ TA @ TA @ TB @ ( id_on @ TA @ ( labeled_vertices @ TC @ TA @ B ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: labeled_graph @ TD @ TC,B: labeled_graph @ TD @ TA,C: set @ ( product_prod @ TC @ TA ),D: labeled_graph @ TD @ TB,E: set @ ( product_prod @ TA @ TB )] :
( ( graph_homomorphism @ TD @ TC @ TA @ A @ B @ C )
=> ( ( graph_homomorphism @ TD @ TA @ TB @ B @ D @ E )
=> ( graph_homomorphism @ TD @ TC @ TB @ A @ D @ ( relcomp @ TC @ TA @ TB @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_graph__homomorphism__composes) ).
thf(385,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: labeled_graph @ TD @ TC,B: labeled_graph @ TD @ TA,C: set @ ( product_prod @ TC @ TA ),D: labeled_graph @ TD @ TB,E: set @ ( product_prod @ TA @ TB )] :
( ( graph_homomorphism @ TD @ TC @ TA @ A @ B @ C )
=> ( ( graph_homomorphism @ TD @ TA @ TB @ B @ D @ E )
=> ( graph_homomorphism @ TD @ TC @ TB @ A @ D @ ( relcomp @ TC @ TA @ TB @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(105,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/sandbox/benchmark/theBenchmark.p',fact_97_consequence__graphD_I3_J) ).
thf(550,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)],[105]) ).
thf(194,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA,D: set @ TA] :
( ( ( image @ TA @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( image @ TA @ TA @ A @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) )
=> ( ( equiv_equiv @ TA @ D @ A )
=> ( ( member @ TA @ C @ D )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_eq__equiv__class) ).
thf(797,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA,D: set @ TA] :
( ( ( image @ TA @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( image @ TA @ TA @ A @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) )
=> ( ( equiv_equiv @ TA @ D @ A )
=> ( ( member @ TA @ C @ D )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(245,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/sandbox/benchmark/theBenchmark.p',fact_98_graph__homomorphism__semantics) ).
thf(930,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)],[245]) ).
thf(208,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TB @ TC ),B: labeled_graph @ TA @ TB] :
( ( labeled_vertices @ TA @ TC @ ( map_graph @ TB @ TC @ TA @ A @ B ) )
= ( image @ TB @ TC @ A @ ( labeled_vertices @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_map__graph__selectors_I1_J) ).
thf(829,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TB @ TC ),B: labeled_graph @ TA @ TB] :
( ( labeled_vertices @ TA @ TC @ ( map_graph @ TB @ TC @ TA @ A @ B ) )
= ( image @ TB @ TC @ A @ ( labeled_vertices @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(213,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/sandbox/benchmark/theBenchmark.p',fact_49_in__Gr) ).
thf(841,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)],[213]) ).
thf(230,axiom,
! [A: standard_Constant @ a,B: b,C: b] :
( ( member @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ b @ b ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ b @ b ) @ A @ ( product_Pair @ b @ b @ B @ C ) ) @ ( labeled_edges @ ( standard_Constant @ a ) @ b @ g ) )
=> ( ( member @ b @ B @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) )
=> ( ( member @ b @ C @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) )
=> ( member @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ b @ b ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ b @ b ) @ A @ ( product_Pair @ b @ b @ ( f @ B ) @ ( f @ C ) ) ) @ ( labeled_edges @ ( standard_Constant @ a ) @ b @ g ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_gu1) ).
thf(885,plain,
! [A: standard_Constant @ a,B: b,C: b] :
( ( member @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ b @ b ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ b @ b ) @ A @ ( product_Pair @ b @ b @ B @ C ) ) @ ( labeled_edges @ ( standard_Constant @ a ) @ b @ g ) )
=> ( ( member @ b @ B @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) )
=> ( ( member @ b @ C @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) )
=> ( member @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ b @ b ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ b @ b ) @ A @ ( product_Pair @ b @ b @ ( f @ B ) @ ( f @ C ) ) ) @ ( labeled_edges @ ( standard_Constant @ a ) @ b @ g ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(21,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_subset__insertI2) ).
thf(320,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(47,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_equalityD2) ).
thf(389,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(112,axiom,
! [TA: $tType,A: TA] :
( ( collect @ TA
@ ^ [B: TA] : ( B = A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_singleton__conv) ).
thf(570,plain,
! [TA: $tType,A: TA] :
( ( collect @ TA
@ ^ [B: TA] : ( B = A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(166,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/sandbox/benchmark/theBenchmark.p',fact_33_subgraph__def) ).
thf(719,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)],[166]) ).
thf(40,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ( equiv_equiv @ TA @ C @ A )
=> ( ( equiv_equiv @ TA @ C @ B )
=> ( ( image @ TA @ TA @ A @ ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_refines__equiv__class__eq) ).
thf(372,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ( equiv_equiv @ TA @ C @ A )
=> ( ( equiv_equiv @ TA @ C @ B )
=> ( ( image @ TA @ TA @ A @ ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(130,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_refl__onD) ).
thf(619,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(240,axiom,
! [A: b] :
( ( member @ b @ ( f @ A ) @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) )
=> ( member @ b @ A @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062_092_060And_062xa_O_A_092_060lbrakk_062f_Axa_A_092_060in_062_Avertices_AG_059_Axa_A_092_060notin_062_Avertices_AG_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062) ).
thf(917,plain,
! [A: b] :
( ( member @ b @ ( f @ A ) @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) )
=> ( member @ b @ A @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(30,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/sandbox/benchmark/theBenchmark.p',fact_122_Gr__insert) ).
thf(344,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)],[30]) ).
thf(73,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/sandbox/benchmark/theBenchmark.p',fact_36_labeled__graph_Oinduct) ).
thf(460,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)],[73]) ).
thf(137,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/sandbox/benchmark/theBenchmark.p',fact_25_subgraph__refl) ).
thf(638,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)],[137]) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',fact_65_old_Oprod_Oinject) ).
thf(289,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)],[12]) ).
thf(68,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/sandbox/benchmark/theBenchmark.p',fact_124_agree__on__empty) ).
thf(448,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)],[68]) ).
thf(202,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) @ ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_equiv__class__subset) ).
thf(817,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) @ ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(236,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/sandbox/benchmark/theBenchmark.p',fact_40_labeled__graph_Oexpand) ).
thf(902,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)],[236]) ).
thf(227,axiom,
member @ b @ ( f @ y ) @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_fv_I2_J) ).
thf(881,plain,
member @ b @ ( f @ y ) @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(56,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_subset__trans) ).
thf(416,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(79,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_set__eq__subset) ).
thf(475,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( ( graph_union @ TA @ TB @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_graph__union__idemp_I1_J) ).
thf(492,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)],[85]) ).
thf(93,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/sandbox/benchmark/theBenchmark.p',fact_32_labeled__graph_Osel_I1_J) ).
thf(514,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)],[93]) ).
thf(248,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/sandbox/benchmark/theBenchmark.p',fact_72_edge__preserving__atomic) ).
thf(937,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)],[248]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA )] :
( ( image @ TB @ TA @ A @ ( bot_bot @ ( set @ TB ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_Image__empty2) ).
thf(353,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA )] :
( ( image @ TB @ TA @ A @ ( bot_bot @ ( set @ TB ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(237,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ( member @ TA @ C @ A )
& ( member @ TA @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_refl__on__domain) ).
thf(905,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ( member @ TA @ C @ A )
& ( member @ TA @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(124,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 )] :
( ( graph_homomorphism @ TC @ TA @ TB @ ( graph_union @ TC @ TA @ A @ B ) @ C @ D )
=> ( ( A
= ( restrict @ TC @ TA @ A ) )
=> ( graph_homomorphism @ TC @ TA @ TB @ A @ C @ ( relcomp @ TA @ TA @ TB @ ( id_on @ TA @ ( labeled_vertices @ TC @ TA @ A ) ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_graph__homo__union__id_I1_J) ).
thf(602,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 )] :
( ( graph_homomorphism @ TC @ TA @ TB @ ( graph_union @ TC @ TA @ A @ B ) @ C @ D )
=> ( ( A
= ( restrict @ TC @ TA @ A ) )
=> ( graph_homomorphism @ TC @ TA @ TB @ A @ C @ ( relcomp @ TA @ TA @ TB @ ( id_on @ TA @ ( labeled_vertices @ TC @ TA @ A ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(157,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: TA] :
( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ! [C: product_prod @ ( labeled_graph @ TA @ nat ) @ ( labeled_graph @ TA @ nat )] :
( ( member @ ( product_prod @ ( labeled_graph @ TA @ nat ) @ ( labeled_graph @ TA @ nat ) ) @ C @ ( insert @ ( product_prod @ ( labeled_graph @ TA @ nat ) @ ( labeled_graph @ TA @ nat ) ) @ ( standa245363227y_rule @ TA @ B ) @ ( insert @ ( product_prod @ ( labeled_graph @ TA @ nat ) @ ( labeled_graph @ TA @ nat ) ) @ ( standa2114124375e_rule @ TA @ B ) @ ( insert @ ( product_prod @ ( labeled_graph @ TA @ nat ) @ ( labeled_graph @ TA @ nat ) ) @ ( standa1805702094y_rule @ TA @ B ) @ ( bot_bot @ ( set @ ( product_prod @ ( labeled_graph @ TA @ nat ) @ ( labeled_graph @ TA @ nat ) ) ) ) ) ) ) )
=> ( maintained @ TA @ nat @ TB @ C @ A ) )
=> ( equiv_equiv @ TB @ ( labeled_vertices @ TA @ TB @ A ) @ ( getRel @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_equivalence) ).
thf(692,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: TA] :
( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ! [C: product_prod @ ( labeled_graph @ TA @ nat ) @ ( labeled_graph @ TA @ nat )] :
( ( member @ ( product_prod @ ( labeled_graph @ TA @ nat ) @ ( labeled_graph @ TA @ nat ) ) @ C @ ( insert @ ( product_prod @ ( labeled_graph @ TA @ nat ) @ ( labeled_graph @ TA @ nat ) ) @ ( standa245363227y_rule @ TA @ B ) @ ( insert @ ( product_prod @ ( labeled_graph @ TA @ nat ) @ ( labeled_graph @ TA @ nat ) ) @ ( standa2114124375e_rule @ TA @ B ) @ ( insert @ ( product_prod @ ( labeled_graph @ TA @ nat ) @ ( labeled_graph @ TA @ nat ) ) @ ( standa1805702094y_rule @ TA @ B ) @ ( bot_bot @ ( set @ ( product_prod @ ( labeled_graph @ TA @ nat ) @ ( labeled_graph @ TA @ nat ) ) ) ) ) ) ) )
=> ( maintained @ TA @ nat @ TB @ C @ A ) )
=> ( equiv_equiv @ TB @ ( labeled_vertices @ TA @ TB @ A ) @ ( getRel @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TB @ TC ),C: set @ TA] :
( ( image @ TA @ TC @ ( relcomp @ TA @ TB @ TC @ A @ B ) @ C )
= ( image @ TB @ TC @ B @ ( image @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_relcomp__Image) ).
thf(453,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TB @ TC ),C: set @ TA] :
( ( image @ TA @ TC @ ( relcomp @ TA @ TB @ TC @ A @ B ) @ C )
= ( image @ TB @ TC @ B @ ( image @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(49,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/sandbox/benchmark/theBenchmark.p',fact_88_old_Oprod_Orec) ).
thf(396,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)],[49]) ).
thf(54,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/sandbox/benchmark/theBenchmark.p',fact_92_maintainedI) ).
thf(411,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)],[54]) ).
thf(13,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_insert__absorb2) ).
thf(292,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)],[13]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( image2 @ TB @ TA @ A @ ( bot_bot @ ( set @ TB ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_image__empty) ).
thf(439,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( image2 @ TB @ TA @ A @ ( bot_bot @ ( set @ TB ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(243,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/sandbox/benchmark/theBenchmark.p',fact_225_nonempty__rule) ).
thf(925,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)],[243]) ).
thf(38,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_empty__def) ).
thf(366,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(100,axiom,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_subset__insertI) ).
thf(534,plain,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(164,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_refl__onD1) ).
thf(714,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(256,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_subset__eq) ).
thf(957,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(254,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_insert__absorb) ).
thf(952,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)],[254]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',fact_20_graph__union__idemp_I2_J) ).
thf(561,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)],[109]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: set @ ( product_prod @ TD @ TC ),B: set @ ( product_prod @ TC @ TA ),C: set @ ( product_prod @ TA @ TB )] :
( ( relcomp @ TD @ TA @ TB @ ( relcomp @ TD @ TC @ TA @ A @ B ) @ C )
= ( relcomp @ TD @ TC @ TB @ A @ ( relcomp @ TC @ TA @ TB @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_O__assoc) ).
thf(297,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: set @ ( product_prod @ TD @ TC ),B: set @ ( product_prod @ TC @ TA ),C: set @ ( product_prod @ TA @ TB )] :
( ( relcomp @ TD @ TA @ TB @ ( relcomp @ TD @ TC @ TA @ A @ B ) @ C )
= ( relcomp @ TD @ TC @ TB @ A @ ( relcomp @ TC @ TA @ TB @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(134,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/sandbox/benchmark/theBenchmark.p',fact_30_map__graph__fn__graphI) ).
thf(630,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)],[134]) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',fact_93_extensible__refl__concr) ).
thf(429,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)],[61]) ).
thf(7,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/sandbox/benchmark/theBenchmark.p',fact_23_graph__union__preserves__restrict) ).
thf(275,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)],[7]) ).
thf(191,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_subset__insert) ).
thf(788,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(215,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/sandbox/benchmark/theBenchmark.p',fact_16_vertices__restrict) ).
thf(847,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)],[215]) ).
thf(217,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/sandbox/benchmark/theBenchmark.p',fact_171_subsetI) ).
thf(852,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)],[217]) ).
thf(117,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/sandbox/benchmark/theBenchmark.p',fact_160_agree__on__subg__compose) ).
thf(583,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)],[117]) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',fact_108_extensibleI) ).
thf(456,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)],[71]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TA @ TC )] :
( ( relcomp @ TA @ TC @ TB @ A @ ( bot_bot @ ( set @ ( product_prod @ TC @ TB ) ) ) )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_relcomp__empty2) ).
thf(324,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TA @ TC )] :
( ( relcomp @ TA @ TC @ TB @ A @ ( bot_bot @ ( set @ ( product_prod @ TC @ TB ) ) ) )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(158,axiom,
! [TA: $tType,TB: $tType] :
( ( labeled_vertices @ TA @ TB )
= ( labele1974067554_graph @ TA @ TB @ ( set @ TB )
@ ^ [A: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ),B: set @ TB] : B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_vertices__def) ).
thf(697,plain,
! [TA: $tType,TB: $tType] :
( ( labeled_vertices @ TA @ TB )
= ( labele1974067554_graph @ TA @ TB @ ( set @ TB )
@ ^ [A: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ),B: set @ TB] : B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(224,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_insertI2) ).
thf(874,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)],[224]) ).
thf(142,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/sandbox/benchmark/theBenchmark.p',fact_103_labeled__graph_Ocase__eq__if) ).
thf(650,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)],[142]) ).
thf(168,axiom,
! [A: b] :
( ( member @ b @ A @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) )
=> ( member @ b @ ( f @ A ) @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_gu2) ).
thf(725,plain,
! [A: b] :
( ( member @ b @ A @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) )
=> ( member @ b @ ( f @ A ) @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(34,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_empty__subsetI) ).
thf(356,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(223,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/sandbox/benchmark/theBenchmark.p',fact_174_insertCI) ).
thf(869,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)],[223]) ).
thf(127,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/sandbox/benchmark/theBenchmark.p',fact_91_map__graph__in) ).
thf(610,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)],[127]) ).
thf(58,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/sandbox/benchmark/theBenchmark.p',fact_100_labeled__graph_Ocase) ).
thf(420,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)],[58]) ).
thf(88,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/sandbox/benchmark/theBenchmark.p',fact_18_labeled__graph_Oinject) ).
thf(499,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)],[88]) ).
thf(95,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_equalityD1) ).
thf(519,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(174,axiom,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_all__not__in__conv) ).
thf(742,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)],[174]) ).
thf(77,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/sandbox/benchmark/theBenchmark.p',fact_95_extensible__refl) ).
thf(471,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)],[77]) ).
thf(229,axiom,
member @ b @ ( f @ x ) @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_fv_I1_J) ).
thf(884,plain,
member @ b @ ( f @ x ) @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(178,axiom,
member @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ b @ b ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ b @ b ) @ l2 @ ( product_Pair @ b @ b @ ( f @ x ) @ ( f @ y ) ) ) @ ( labeled_edges @ ( standard_Constant @ a ) @ b @ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_a) ).
thf(753,plain,
member @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ b @ b ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ b @ b ) @ l2 @ ( product_Pair @ b @ b @ ( f @ x ) @ ( f @ y ) ) ) @ ( labeled_edges @ ( standard_Constant @ a ) @ b @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(154,axiom,
! [A: product_prod @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ a ) @ nat )] :
( ( member @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) ) @ A @ ( standa2002409347_rules @ a @ l ) )
=> ( maintained @ ( standard_Constant @ a ) @ nat @ b @ A @ g ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_assms_I2_J) ).
thf(686,plain,
! [A: product_prod @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ a ) @ nat )] :
( ( member @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) ) @ A @ ( standa2002409347_rules @ a @ l ) )
=> ( maintained @ ( standard_Constant @ a ) @ nat @ b @ A @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(97,axiom,
! [TA: $tType,A: set @ TA] : ( refl_on @ TA @ A @ ( id_on @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_refl__on__Id__on) ).
thf(526,plain,
! [TA: $tType,A: set @ TA] : ( refl_on @ TA @ A @ ( id_on @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(84,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/sandbox/benchmark/theBenchmark.p',fact_200_insert__commute) ).
thf(489,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)],[84]) ).
thf(261,axiom,
! [A: b] :
( ( member @ b @ A @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) )
=> ( member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ A @ ( hilbert_Eps @ b @ ( p @ A ) ) ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_vert__P) ).
thf(970,plain,
! [A: b] :
( ( member @ b @ A @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) )
=> ( member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ A @ ( hilbert_Eps @ b @ ( p @ A ) ) ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(104,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_subset__singletonD) ).
thf(547,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(211,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_in__mono) ).
thf(837,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(48,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_empty__Collect__eq) ).
thf(393,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)],[48]) ).
thf(141,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_equals0I) ).
thf(647,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)],[141]) ).
thf(125,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/sandbox/benchmark/theBenchmark.p',fact_90_leastI) ).
thf(605,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)],[125]) ).
thf(197,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD,B: labeled_graph @ TC @ TD,C: TD > TA,D: TB,E: set @ ( product_prod @ TA @ TB )] :
( ( member @ TD @ A @ ( labeled_vertices @ TC @ TD @ B ) )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ ( C @ A ) @ D ) @ E )
=> ( member @ ( product_prod @ TD @ TB ) @ ( product_Pair @ TD @ TB @ A @ D ) @ ( relcomp @ TD @ TA @ TB @ ( bNF_Gr @ TD @ TA @ ( labeled_vertices @ TC @ TD @ B ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_in__on__graph) ).
thf(805,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD,B: labeled_graph @ TC @ TD,C: TD > TA,D: TB,E: set @ ( product_prod @ TA @ TB )] :
( ( member @ TD @ A @ ( labeled_vertices @ TC @ TD @ B ) )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ ( C @ A ) @ D ) @ E )
=> ( member @ ( product_prod @ TD @ TB ) @ ( product_Pair @ TD @ TB @ A @ D ) @ ( relcomp @ TD @ TA @ TB @ ( bNF_Gr @ TD @ TA @ ( labeled_vertices @ TC @ TD @ B ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(91,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/sandbox/benchmark/theBenchmark.p',fact_127_graph__homomorphism__empty) ).
thf(508,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)],[91]) ).
thf(102,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/sandbox/benchmark/theBenchmark.p',fact_82_prod__cases7) ).
thf(541,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)],[102]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,A: set @ TB] :
( ( image @ TB @ TA @ ( bot_bot @ ( set @ ( product_prod @ TB @ TA ) ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_Image__empty1) ).
thf(558,plain,
! [TA: $tType,TB: $tType,A: set @ TB] :
( ( image @ TB @ TA @ ( bot_bot @ ( set @ ( product_prod @ TB @ TA ) ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(193,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/sandbox/benchmark/theBenchmark.p',fact_201_insert__eq__iff) ).
thf(794,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)],[193]) ).
thf(146,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_Collect__subset) ).
thf(662,plain,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(135,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/sandbox/benchmark/theBenchmark.p',fact_107_labeled__graph_Osplit__sel__asm) ).
thf(633,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)],[135]) ).
thf(36,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/sandbox/benchmark/theBenchmark.p',fact_96_least__consequence__graph__def) ).
thf(360,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)],[36]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ C ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( ~ ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ C ) ) )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_Collect__conv__if) ).
thf(264,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ C ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( ~ ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ C ) ) )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(175,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) @ A )
=> ( ( ( equiv_proj @ TA @ TA @ B @ C )
= ( equiv_proj @ TA @ TA @ B @ D ) )
= ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_proj__iff) ).
thf(745,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) @ A )
=> ( ( ( equiv_proj @ TA @ TA @ B @ C )
= ( equiv_proj @ TA @ TA @ B @ D ) )
= ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(113,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_subset__refl) ).
thf(573,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(259,axiom,
! [A: b] :
( ( member @ b @ A @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) )
=> ( member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ A @ A ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_A_092_060Longrightarrow_062_A_Ix_M_Ax_J_A_092_060in_062_AgetRel_AS__Idt_AG_092_060close_062) ).
thf(965,plain,
! [A: b] :
( ( member @ b @ A @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) )
=> ( member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ A @ A ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(177,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/sandbox/benchmark/theBenchmark.p',fact_39_labeled__graph_Oexhaust__sel) ).
thf(750,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)],[177]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: labeled_graph @ TD @ TC,B: set @ ( product_prod @ TC @ TA ),C: set @ ( product_prod @ TC @ TA ),D: set @ ( product_prod @ TA @ TB )] :
( ( agree_on @ TD @ TC @ TA @ A @ B @ C )
=> ( agree_on @ TD @ TC @ TB @ A @ ( relcomp @ TC @ TA @ TB @ B @ D ) @ ( relcomp @ TC @ TA @ TB @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_agree__on__ext) ).
thf(375,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: labeled_graph @ TD @ TC,B: set @ ( product_prod @ TC @ TA ),C: set @ ( product_prod @ TC @ TA ),D: set @ ( product_prod @ TA @ TB )] :
( ( agree_on @ TD @ TC @ TA @ A @ B @ C )
=> ( agree_on @ TD @ TC @ TB @ A @ ( relcomp @ TC @ TA @ TB @ B @ D ) @ ( relcomp @ TC @ TA @ TB @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(171,axiom,
! [A: b,B: b] :
( ( member @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ b @ b ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ b @ b ) @ ( standard_S_Idt @ a ) @ ( product_Pair @ b @ b @ A @ B ) ) @ ( labeled_edges @ ( standard_Constant @ a ) @ b @ g ) )
=> ( ( hilbert_Eps @ b @ ( p @ A ) )
= ( hilbert_Eps @ b @ ( p @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_idt__eq) ).
thf(733,plain,
! [A: b,B: b] :
( ( member @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ b @ b ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ b @ b ) @ ( standard_S_Idt @ a ) @ ( product_Pair @ b @ b @ A @ B ) ) @ ( labeled_edges @ ( standard_Constant @ a ) @ b @ g ) )
=> ( ( hilbert_Eps @ b @ ( p @ A ) )
= ( hilbert_Eps @ b @ ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(203,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TB,C: set @ ( product_prod @ TC @ TA ),D: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ A @ B ) @ ( relcomp @ TC @ TA @ TB @ C @ D ) )
=> ~ ! [E: TA] :
( ( member @ ( product_prod @ TC @ TA ) @ ( product_Pair @ TC @ TA @ A @ E ) @ C )
=> ~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_relcompEpair) ).
thf(819,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TB,C: set @ ( product_prod @ TC @ TA ),D: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ A @ B ) @ ( relcomp @ TC @ TA @ TB @ C @ D ) )
=> ~ ! [E: TA] :
( ( member @ ( product_prod @ TC @ TA ) @ ( product_Pair @ TC @ TA @ A @ E ) @ C )
=> ~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(59,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/sandbox/benchmark/theBenchmark.p',fact_114_agree__on__comm) ).
thf(423,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)],[59]) ).
thf(51,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(402,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(185,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TB,C: set @ ( product_prod @ TC @ TA ),D: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ A @ B ) @ ( relcomp @ TC @ TA @ TB @ C @ D ) )
=> ~ ! [E: TA] :
( ( member @ ( product_prod @ TC @ TA ) @ ( product_Pair @ TC @ TA @ A @ E ) @ C )
=> ~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_relcomp_Ocases) ).
thf(772,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TB,C: set @ ( product_prod @ TC @ TA ),D: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ A @ B ) @ ( relcomp @ TC @ TA @ TB @ C @ D ) )
=> ~ ! [E: TA] :
( ( member @ ( product_prod @ TC @ TA ) @ ( product_Pair @ TC @ TA @ A @ E ) @ C )
=> ~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType] :
( ( labeled_edges @ TA @ TB )
= ( labele1974067554_graph @ TA @ TB @ ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) )
@ ^ [A: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ),B: set @ TB] : A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_edges__def) ).
thf(286,plain,
! [TA: $tType,TB: $tType] :
( ( labeled_edges @ TA @ TB )
= ( labele1974067554_graph @ TA @ TB @ ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) )
@ ^ [A: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ),B: set @ TB] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: set @ ( product_prod @ TD @ TC ),B: set @ ( product_prod @ TA @ ( product_prod @ TD @ TD ) ),C: set @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ),D: set @ ( product_prod @ TC @ TB ),E: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) )] :
( ( edge_preserving @ TD @ TC @ TA @ A @ B @ C )
=> ( ( edge_preserving @ TC @ TB @ TA @ D @ C @ E )
=> ( edge_preserving @ TD @ TB @ TA @ ( relcomp @ TD @ TC @ TB @ A @ D ) @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_compose__preserves__edge__preserving) ).
thf(281,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: set @ ( product_prod @ TD @ TC ),B: set @ ( product_prod @ TA @ ( product_prod @ TD @ TD ) ),C: set @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ),D: set @ ( product_prod @ TC @ TB ),E: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) )] :
( ( edge_preserving @ TD @ TC @ TA @ A @ B @ C )
=> ( ( edge_preserving @ TC @ TB @ TA @ D @ C @ E )
=> ( edge_preserving @ TD @ TB @ TA @ ( relcomp @ TD @ TC @ TB @ A @ D ) @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(206,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/sandbox/benchmark/theBenchmark.p',fact_99_consequence__graphD_I1_J) ).
thf(826,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)],[206]) ).
thf(115,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/sandbox/benchmark/theBenchmark.p',fact_161_singleton__insert__inj__eq) ).
thf(577,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)],[115]) ).
thf(163,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/sandbox/benchmark/theBenchmark.p',fact_89_least__consequence__graphI) ).
thf(711,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)],[163]) ).
thf(138,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_subsetD) ).
thf(641,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( ( bot_bot @ ( set @ TB ) )
= ( image2 @ TA @ TB @ A @ B ) )
= ( B
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_empty__is__image) ).
thf(445,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( ( bot_bot @ ( set @ TB ) )
= ( image2 @ TA @ TB @ A @ B ) )
= ( B
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(44,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/sandbox/benchmark/theBenchmark.p',fact_129_graph__single) ).
thf(382,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)],[44]) ).
thf(20,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_equalityE) ).
thf(313,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(27,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ( equiv_equiv @ TA @ C @ A )
=> ( ( equiv_equiv @ TA @ C @ B )
=> ( ( image @ TA @ TA @ B @ ( image @ TA @ TA @ A @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_refines__equiv__class__eq2) ).
thf(335,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ( equiv_equiv @ TA @ C @ A )
=> ( ( equiv_equiv @ TA @ C @ B )
=> ( ( image @ TA @ TA @ B @ ( image @ TA @ TA @ A @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(241,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/sandbox/benchmark/theBenchmark.p',fact_207_insertE) ).
thf(919,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)],[241]) ).
thf(252,axiom,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( C = A )
| ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_insert__compr) ).
thf(947,plain,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( C = A )
| ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',fact_170_subset__antisym) ).
thf(350,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)],[32]) ).
thf(183,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_singletonD) ).
thf(764,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)],[183]) ).
thf(189,axiom,
! [A: b,B: b,C: standard_Constant @ a] :
( ( member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ A @ B ) @ ( getRel @ ( standard_Constant @ a ) @ b @ C @ g ) )
=> ( equiv_congruent @ b @ ( set @ b ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g )
@ ^ [D: b] : ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ C @ g ) @ ( insert @ b @ D @ ( bot_bot @ ( set @ b ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_congr_I1_J) ).
thf(784,plain,
! [A: b,B: b,C: standard_Constant @ a] :
( ( member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ A @ B ) @ ( getRel @ ( standard_Constant @ a ) @ b @ C @ g ) )
=> ( equiv_congruent @ b @ ( set @ b ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g )
@ ^ [D: b] : ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ C @ g ) @ ( insert @ b @ D @ ( bot_bot @ ( set @ b ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(172,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/sandbox/benchmark/theBenchmark.p',fact_55_Id__on__eqI) ).
thf(736,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)],[172]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TC @ TB ),B: set @ ( product_prod @ TC @ TB ),C: set @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ),D: set @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ),E: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TC @ TB ) ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ) ) @ C @ D )
=> ( ( edge_preserving @ TC @ TB @ TA @ B @ D @ E )
=> ( edge_preserving @ TC @ TB @ TA @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_edge__preserving__subset) ).
thf(377,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TC @ TB ),B: set @ ( product_prod @ TC @ TB ),C: set @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ),D: set @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ),E: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TC @ TB ) ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ) ) @ C @ D )
=> ( ( edge_preserving @ TC @ TB @ TA @ B @ D @ E )
=> ( edge_preserving @ TC @ TB @ TA @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(111,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(567,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(123,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_subrelI) ).
thf(599,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(226,axiom,
graph_homomorphism @ ( standard_Constant @ a ) @ b @ b @ ( map_graph @ b @ b @ ( standard_Constant @ a ) @ ( bNF_Gr @ b @ b @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) @ f ) @ g ) @ g @ ( id_on @ b @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ ( map_graph @ b @ b @ ( standard_Constant @ a ) @ ( bNF_Gr @ b @ b @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) @ f ) @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_subg) ).
thf(880,plain,
graph_homomorphism @ ( standard_Constant @ a ) @ b @ b @ ( map_graph @ b @ b @ ( standard_Constant @ a ) @ ( bNF_Gr @ b @ b @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) @ f ) @ g ) @ g @ ( id_on @ b @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ ( map_graph @ b @ b @ ( standard_Constant @ a ) @ ( bNF_Gr @ b @ b @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) @ f ) @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( ( image2 @ TA @ TB @ A @ B )
= ( bot_bot @ ( set @ TB ) ) )
= ( B
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_image__is__empty) ).
thf(434,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( ( image2 @ TA @ TB @ A @ B )
= ( bot_bot @ ( set @ TB ) ) )
= ( B
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(129,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/sandbox/benchmark/theBenchmark.p',fact_101_semantics__in__vertices_I1_J) ).
thf(616,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)],[129]) ).
thf(17,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/sandbox/benchmark/theBenchmark.p',fact_182_graph__homomorphism__nonempty) ).
thf(303,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)],[17]) ).
thf(232,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB ),C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: TA] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ A ) @ B )
=> ~ ( member @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_ImageE) ).
thf(890,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB ),C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: TA] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ A ) @ B )
=> ~ ( member @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(180,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/sandbox/benchmark/theBenchmark.p',fact_109_subgraph__subset_I2_J) ).
thf(758,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)],[180]) ).
thf(219,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TC ),D: set @ ( product_prod @ TC @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( relcomp @ TA @ TC @ TB @ C @ D ) )
= ( ? [E: TA,F: TC,G: TB] :
( ( A = E )
& ( B = G )
& ( member @ ( product_prod @ TA @ TC ) @ ( product_Pair @ TA @ TC @ E @ F ) @ C )
& ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ F @ G ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_relcomp_Osimps) ).
thf(858,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TC ),D: set @ ( product_prod @ TC @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( relcomp @ TA @ TC @ TB @ C @ D ) )
= ( ? [E: TA,F: TC,G: TB] :
( ( A = E )
& ( B = G )
& ( member @ ( product_prod @ TA @ TC ) @ ( product_Pair @ TA @ TC @ E @ F ) @ C )
& ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ F @ G ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(131,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/sandbox/benchmark/theBenchmark.p',fact_31_graph__homo) ).
thf(621,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)],[131]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',fact_37_labeled__graph_Oexhaust) ).
thf(483,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)],[82]) ).
thf(159,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
= ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_pred__equals__eq2) ).
thf(700,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
= ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(25,axiom,
! [TA: $tType,A: TA] :
( ( collect @ TA @ ( (=) @ TA @ A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_singleton__conv2) ).
thf(330,plain,
! [TA: $tType,A: TA] :
( ( collect @ TA @ ( (=) @ TA @ A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(200,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/sandbox/benchmark/theBenchmark.p',fact_61_getRel__homR) ).
thf(811,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)],[200]) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',fact_85_prod__induct5) ).
thf(387,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)],[46]) ).
thf(74,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_subset__singleton__iff) ).
thf(462,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(246,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/sandbox/benchmark/theBenchmark.p',fact_14_labeled__graph_Osel_I2_J) ).
thf(932,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)],[246]) ).
thf(239,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/sandbox/benchmark/theBenchmark.p',fact_63_edge__preserving__on__graphI) ).
thf(912,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)],[239]) ).
thf(50,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( collect @ TA
@ ^ [C: TA] :
( ( C = A )
| ( C = B ) ) )
= ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_tuple__disj) ).
thf(399,plain,
! [TA: $tType,A: TA,B: TA] :
( ( collect @ TA
@ ^ [C: TA] :
( ( C = A )
| ( C = B ) ) )
= ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(136,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/sandbox/benchmark/theBenchmark.p',fact_38_subgraph__preserves__hom) ).
thf(636,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)],[136]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_old_Oprod_Oexhaust) ).
thf(278,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)],[8]) ).
thf(126,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/sandbox/benchmark/theBenchmark.p',fact_41_getRel__hom) ).
thf(608,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)],[126]) ).
thf(18,axiom,
! [TA: $tType,A: TA] : ( refl_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/sandbox/benchmark/theBenchmark.p',fact_131_refl__on__singleton) ).
thf(306,plain,
! [TA: $tType,A: TA] : ( refl_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)],[18]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType] :
( ( equiv_proj @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TB ),B: TA] : ( image @ TA @ TB @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_proj__def) ).
thf(505,plain,
! [TA: $tType,TB: $tType] :
( ( equiv_proj @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TB ),B: TA] : ( image @ TA @ TB @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(143,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB ),C: TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_Image__singleton__iff) ).
thf(653,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB ),C: TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(242,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(922,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB ),C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ A @ C ) @ ( image @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_Image__mono) ).
thf(473,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB ),C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ A @ C ) @ ( image @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(167,axiom,
! [A: b] :
( ( ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ A @ ( bot_bot @ ( set @ b ) ) ) )
= ( bot_bot @ ( set @ b ) ) )
= ( ~ ( member @ b @ A @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_r2) ).
thf(722,plain,
! [A: b] :
( ( ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ A @ ( bot_bot @ ( set @ b ) ) ) )
= ( bot_bot @ ( set @ b ) ) )
= ( ~ ( member @ b @ A @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(150,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/sandbox/benchmark/theBenchmark.p',fact_104_subgraph__semantics) ).
thf(675,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)],[150]) ).
thf(60,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( insert @ TA @ A @ ( collect @ TA @ B ) )
= ( collect @ TA
@ ^ [C: TA] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_insert__Collect) ).
thf(426,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( insert @ TA @ A @ ( collect @ TA @ B ) )
= ( collect @ TA
@ ^ [C: TA] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(119,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/sandbox/benchmark/theBenchmark.p',fact_128_graph__unionI) ).
thf(589,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)],[119]) ).
thf(152,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_homomorphism @ TA @ TB @ TB @ A @ B @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) )
= ( ( ord_less_eq @ ( set @ TB ) @ ( labeled_vertices @ TA @ TB @ A ) @ ( labeled_vertices @ TA @ TB @ B ) )
& ( ord_less_eq @ ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) @ ( labeled_edges @ TA @ TB @ A ) @ ( labeled_edges @ TA @ TB @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_subgraph__def2) ).
thf(680,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_homomorphism @ TA @ TB @ TB @ A @ B @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) ) )
= ( ( ord_less_eq @ ( set @ TB ) @ ( labeled_vertices @ TA @ TB @ A ) @ ( labeled_vertices @ TA @ TB @ B ) )
& ( ord_less_eq @ ( 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)],[152]) ).
thf(249,axiom,
( p
= ( ^ [A: b,B: b] : ( member @ b @ B @ ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ A @ ( bot_bot @ ( set @ b ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_P) ).
thf(939,plain,
( p
= ( ^ [A: b,B: b] : ( member @ b @ B @ ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ A @ ( bot_bot @ ( set @ b ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(179,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E ) ) )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_subset__CollectI) ).
thf(754,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E ) ) )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) > ( set @ TB ) > TD,C: labeled_graph @ TA @ TB] :
( ( A @ ( labele1974067554_graph @ TA @ TB @ TD @ B @ C ) )
= ( labele1974067554_graph @ TA @ TB @ TC
@ ^ [D: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ),E: set @ TB] : ( A @ ( B @ D @ E ) )
@ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_labeled__graph_Ocase__distrib) ).
thf(553,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) > ( set @ TB ) > TD,C: labeled_graph @ TA @ TB] :
( ( A @ ( labele1974067554_graph @ TA @ TB @ TD @ B @ C ) )
= ( labele1974067554_graph @ TA @ TB @ TC
@ ^ [D: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ),E: set @ TB] : ( A @ ( B @ D @ E ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(99,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/sandbox/benchmark/theBenchmark.p',fact_80_prod__cases5) ).
thf(531,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)],[99]) ).
thf(251,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/sandbox/benchmark/theBenchmark.p',fact_106_least__def) ).
thf(944,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)],[251]) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',fact_84_prod__induct4) ).
thf(458,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)],[72]) ).
thf(205,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/sandbox/benchmark/theBenchmark.p',fact_203_insert__ident) ).
thf(823,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)],[205]) ).
thf(156,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: TB] :
( ( graph_homomorphism @ TA @ TC @ TB @ A @ B @ C )
=> ( ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ D @ E ) @ C )
=> ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ D @ E ) @ ( relcomp @ TC @ TB @ TB @ C @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_Id__on__vertices__identity_I2_J) ).
thf(690,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: TB] :
( ( graph_homomorphism @ TA @ TC @ TB @ A @ B @ C )
=> ( ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ D @ E ) @ C )
=> ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ D @ E ) @ ( relcomp @ TC @ TB @ TB @ C @ ( id_on @ TB @ ( labeled_vertices @ TA @ TB @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',fact_70_edge__preserving__Id) ).
thf(295,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)],[14]) ).
thf(161,axiom,
equiv_equiv @ b @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_equiv) ).
thf(707,plain,
equiv_equiv @ b @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(231,axiom,
! [A: b] :
( ( member @ b @ A @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) )
= ( p @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_r1) ).
thf(887,plain,
! [A: b] :
( ( member @ b @ A @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) )
= ( p @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(55,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/sandbox/benchmark/theBenchmark.p',fact_83_prod__induct3) ).
thf(414,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)],[55]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_surj__pair) ).
thf(327,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)],[24]) ).
thf(3,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(263,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(116,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/sandbox/benchmark/theBenchmark.p',fact_94_labeled__graph_Osplit__sel) ).
thf(580,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)],[116]) ).
thf(218,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/sandbox/benchmark/theBenchmark.p',fact_54_Id__on__iff) ).
thf(855,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)],[218]) ).
thf(192,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/sandbox/benchmark/theBenchmark.p',fact_102_semantics__in__vertices_I2_J) ).
thf(791,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)],[192]) ).
thf(118,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TA,C: set @ ( product_prod @ TB @ TC ),D: set @ ( product_prod @ TC @ TA ),E: TB > TA > $o] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( relcomp @ TB @ TC @ TA @ C @ D ) )
=> ( ! [F: TB,G: TC,H: TA] :
( ( member @ ( product_prod @ TB @ TC ) @ ( product_Pair @ TB @ TC @ F @ G ) @ C )
=> ( ( member @ ( product_prod @ TC @ TA ) @ ( product_Pair @ TC @ TA @ G @ H ) @ D )
=> ( E @ F @ H ) ) )
=> ( E @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_relcomp_Oinducts) ).
thf(585,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TA,C: set @ ( product_prod @ TB @ TC ),D: set @ ( product_prod @ TC @ TA ),E: TB > TA > $o] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( relcomp @ TB @ TC @ TA @ C @ D ) )
=> ( ! [F: TB,G: TC,H: TA] :
( ( member @ ( product_prod @ TB @ TC ) @ ( product_Pair @ TB @ TC @ F @ G ) @ C )
=> ( ( member @ ( product_prod @ TC @ TA ) @ ( product_Pair @ TC @ TA @ G @ H ) @ D )
=> ( E @ F @ H ) ) )
=> ( E @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(89,axiom,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_subset__empty) ).
thf(502,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)],[89]) ).
thf(28,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 )
=> ~ ! [E: set @ ( product_prod @ TA @ TB )] :
( ( graph_homomorphism @ TC @ TA @ TB @ B @ C @ E )
=> ~ ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_maintainedD2) ).
thf(338,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 )
=> ~ ! [E: set @ ( product_prod @ TA @ TB )] :
( ( graph_homomorphism @ TC @ TA @ TB @ B @ C @ E )
=> ~ ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(139,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_singletonI) ).
thf(643,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(103,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/sandbox/benchmark/theBenchmark.p',fact_19_graph__union__idemp_I3_J) ).
thf(544,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)],[103]) ).
thf(160,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_equals0D) ).
thf(703,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)],[160]) ).
thf(144,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_singleton__iff) ).
thf(656,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)],[144]) ).
thf(128,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB ),C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_Image__iff) ).
thf(613,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB ),C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(221,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: TA] :
( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ( maintained @ TA @ nat @ TB @ ( standa245363227y_rule @ TA @ B ) @ A )
=> ( refl_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) @ ( getRel @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_reflexivity__rule) ).
thf(864,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: TA] :
( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ( maintained @ TA @ nat @ TB @ ( standa245363227y_rule @ TA @ B ) @ A )
=> ( refl_on @ TB @ ( labeled_vertices @ TA @ TB @ A ) @ ( getRel @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(169,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] :
( ( ( graph_union @ TA @ TB @ A @ B )
= B )
= ( ( 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 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_graph__union__iff) ).
thf(727,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: labeled_graph @ TA @ TB] :
( ( ( graph_union @ TA @ TB @ A @ B )
= B )
= ( ( 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 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(121,axiom,
( ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ ( map_graph @ b @ b @ ( standard_Constant @ a ) @ ( bNF_Gr @ b @ b @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) @ f ) @ g ) )
= ( image2 @ b @ ( product_prod @ b @ b )
@ ^ [A: b] : ( product_Pair @ b @ b @ A @ A )
@ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ ( map_graph @ b @ b @ ( standard_Constant @ a ) @ ( bNF_Gr @ b @ b @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) @ f ) @ g ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_ident) ).
thf(595,plain,
( ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ ( map_graph @ b @ b @ ( standard_Constant @ a ) @ ( bNF_Gr @ b @ b @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) @ f ) @ g ) )
= ( image2 @ b @ ( product_prod @ b @ b )
@ ^ [A: b] : ( product_Pair @ b @ b @ A @ A )
@ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ ( map_graph @ b @ b @ ( standard_Constant @ a ) @ ( bNF_Gr @ b @ b @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) @ f ) @ g ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(87,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/sandbox/benchmark/theBenchmark.p',fact_113_agree__on__refl) ).
thf(497,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)],[87]) ).
thf(225,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/sandbox/benchmark/theBenchmark.p',fact_56_Id__onE) ).
thf(876,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)],[225]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) @ ( labeled_edges @ TA @ TB @ A ) @ ( labeled_edges @ TA @ TB @ ( restrict @ TA @ TB @ A ) ) )
=> ( A
= ( restrict @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_restrict__subsD) ).
thf(465,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) @ ( labeled_edges @ TA @ TB @ A ) @ ( labeled_edges @ TA @ TB @ ( restrict @ TA @ TB @ A ) ) )
=> ( A
= ( restrict @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(133,axiom,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_ex__in__conv) ).
thf(627,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)],[133]) ).
thf(69,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/sandbox/benchmark/theBenchmark.p',fact_78_prod__cases3) ).
thf(450,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)],[69]) ).
thf(149,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/sandbox/benchmark/theBenchmark.p',fact_204_Set_Oset__insert) ).
thf(671,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)],[149]) ).
thf(155,axiom,
( g
= ( restrict @ ( standard_Constant @ a ) @ b @ g ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_assms_I1_J) ).
thf(688,plain,
( g
= ( restrict @ ( standard_Constant @ a ) @ b @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(86,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/sandbox/benchmark/theBenchmark.p',fact_86_prod__induct6) ).
thf(495,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)],[86]) ).
thf(214,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/sandbox/benchmark/theBenchmark.p',fact_178_insert__subset) ).
thf(844,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)],[214]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( ( restrict @ TA @ TB @ ( restrict @ TA @ TB @ A ) )
= ( restrict @ TA @ TB @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_restrict__idemp) ).
thf(363,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)],[37]) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',fact_87_prod__induct7) ).
thf(556,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)],[107]) ).
thf(201,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/sandbox/benchmark/theBenchmark.p',fact_42_getRel__map__fn) ).
thf(813,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)],[201]) ).
thf(94,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/sandbox/benchmark/theBenchmark.p',fact_62_maintained__refl) ).
thf(517,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)],[94]) ).
thf(188,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 )] :
! [D: TB] :
( ( member @ TB @ D @ ( labeled_vertices @ TA @ TB @ A ) )
=> ( ( image @ TB @ TC @ B @ ( insert @ TB @ D @ ( bot_bot @ ( set @ TB ) ) ) )
= ( image @ TB @ TC @ C @ ( insert @ TB @ D @ ( bot_bot @ ( set @ TB ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_agree__on__def) ).
thf(781,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 )] :
! [D: TB] :
( ( member @ TB @ D @ ( labeled_vertices @ TA @ TB @ A ) )
=> ( ( image @ TB @ TC @ B @ ( insert @ TB @ D @ ( bot_bot @ ( set @ TB ) ) ) )
= ( image @ TB @ TC @ C @ ( insert @ TB @ D @ ( bot_bot @ ( set @ TB ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(234,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/sandbox/benchmark/theBenchmark.p',fact_53_getRel__dom_I1_J) ).
thf(896,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)],[234]) ).
thf(176,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/sandbox/benchmark/theBenchmark.p',fact_27_graph__homomorphism__Id) ).
thf(748,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)],[176]) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',fact_147_agree__on__trans) ).
thf(418,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)],[57]) ).
thf(190,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 @ TB ) @ ( labeled_vertices @ TA @ TB @ A ) @ ( labeled_vertices @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_subgraph__subset_I1_J) ).
thf(786,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 @ TB ) @ ( labeled_vertices @ TA @ TB @ A ) @ ( labeled_vertices @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(80,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/sandbox/benchmark/theBenchmark.p',fact_162_singleton__insert__inj__eq_H) ).
thf(478,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)],[80]) ).
thf(6,axiom,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_the__elem__eq) ).
thf(272,plain,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(235,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TB @ ( C @ A ) @ ( image2 @ TA @ TB @ C @ B ) )
= ( image2 @ TA @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_insert__image) ).
thf(899,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TB @ ( C @ A ) @ ( image2 @ TA @ TB @ C @ B ) )
= ( image2 @ TA @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(209,axiom,
! [A: b] :
( ( ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ A @ ( bot_bot @ ( set @ b ) ) ) )
!= ( bot_bot @ ( set @ b ) ) )
=> ( ( hilbert_Eps @ b @ ( p @ ( hilbert_Eps @ b @ ( p @ A ) ) ) )
= ( hilbert_Eps @ b @ ( p @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_P__eq) ).
thf(832,plain,
! [A: b] :
( ( ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ A @ ( bot_bot @ ( set @ b ) ) ) )
!= ( bot_bot @ ( set @ b ) ) )
=> ( ( hilbert_Eps @ b @ ( p @ ( hilbert_Eps @ b @ ( p @ A ) ) ) )
= ( hilbert_Eps @ b @ ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(101,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/sandbox/benchmark/theBenchmark.p',fact_75_Pair__inject) ).
thf(536,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)],[101]) ).
thf(165,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_eq__equiv__class__iff) ).
thf(716,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(195,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/sandbox/benchmark/theBenchmark.p',fact_26_subgraph__restrict) ).
thf(800,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)],[195]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',fact_119_Gr__empty) ).
thf(300,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)],[16]) ).
thf(62,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_insert__mono) ).
thf(432,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(260,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_subset__iff) ).
thf(967,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(52,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(405,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)],[52]) ).
thf(222,axiom,
! [A: product_prod @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ a ) @ nat )] :
( ( member @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) ) @ A @ ( insert @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) ) @ ( standa245363227y_rule @ ( standard_Constant @ a ) @ ( standard_S_Idt @ a ) ) @ ( insert @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) ) @ ( standa2114124375e_rule @ ( standard_Constant @ a ) @ ( standard_S_Idt @ a ) ) @ ( insert @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) ) @ ( standa1805702094y_rule @ ( standard_Constant @ a ) @ ( standard_S_Idt @ a ) ) @ ( bot_bot @ ( set @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) ) ) ) ) ) ) )
=> ( maintained @ ( standard_Constant @ a ) @ nat @ b @ A @ g ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_ma) ).
thf(867,plain,
! [A: product_prod @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ a ) @ nat )] :
( ( member @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) ) @ A @ ( insert @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) ) @ ( standa245363227y_rule @ ( standard_Constant @ a ) @ ( standard_S_Idt @ a ) ) @ ( insert @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) ) @ ( standa2114124375e_rule @ ( standard_Constant @ a ) @ ( standard_S_Idt @ a ) ) @ ( insert @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) ) @ ( standa1805702094y_rule @ ( standard_Constant @ a ) @ ( standard_S_Idt @ a ) ) @ ( bot_bot @ ( set @ ( product_prod @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) @ ( labeled_graph @ ( standard_Constant @ a ) @ nat ) ) ) ) ) ) ) )
=> ( maintained @ ( standard_Constant @ a ) @ nat @ b @ A @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(253,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/sandbox/benchmark/theBenchmark.p',fact_51_Id__onI) ).
thf(950,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)],[253]) ).
thf(210,axiom,
( f
= ( ^ [A: b] :
( if @ b
@ ( ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ A @ ( bot_bot @ ( set @ b ) ) ) )
= ( bot_bot @ ( set @ b ) ) )
@ A
@ ( hilbert_Eps @ b @ ( p @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_f) ).
thf(835,plain,
( f
= ( ^ [A: b] :
( if @ b
@ ( ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ A @ ( bot_bot @ ( set @ b ) ) ) )
= ( bot_bot @ ( set @ b ) ) )
@ A
@ ( hilbert_Eps @ b @ ( p @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(1,conjecture,
member @ b @ x @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( member @ b @ x @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(262,plain,
~ ( member @ b @ x @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(110,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/sandbox/benchmark/theBenchmark.p',fact_208_singleton__inject) ).
thf(564,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)],[110]) ).
thf(29,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_Collect__empty__eq) ).
thf(341,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)],[29]) ).
thf(64,axiom,
! [TA: $tType] : ( refl_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_refl__on__empty) ).
thf(437,plain,
! [TA: $tType] : ( refl_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(184,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TB,B: set @ ( product_prod @ TC @ TA ),C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TC @ TB ) @ A @ ( relcomp @ TC @ TA @ TB @ B @ C ) )
=> ~ ! [D: TC,E: TA,F: TB] :
( ( A
= ( product_Pair @ TC @ TB @ D @ F ) )
=> ( ( member @ ( product_prod @ TC @ TA ) @ ( product_Pair @ TC @ TA @ D @ E ) @ B )
=> ~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ F ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_relcompE) ).
thf(767,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TB,B: set @ ( product_prod @ TC @ TA ),C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TC @ TB ) @ A @ ( relcomp @ TC @ TA @ TB @ B @ C ) )
=> ~ ! [D: TC,E: TA,F: TB] :
( ( A
= ( product_Pair @ TC @ TB @ D @ F ) )
=> ( ( member @ ( product_prod @ TC @ TA ) @ ( product_Pair @ TC @ TA @ D @ E ) @ B )
=> ~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ F ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',fact_48_getRel__subgraph) ).
thf(664,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)],[147]) ).
thf(207,axiom,
refl_on @ b @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_local_Orefl) ).
thf(828,plain,
refl_on @ b @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(257,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/sandbox/benchmark/theBenchmark.p',fact_28_map__graph__preserves__subgraph) ).
thf(960,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)],[257]) ).
thf(255,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/sandbox/benchmark/theBenchmark.p',fact_34_subgraph__trans) ).
thf(955,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)],[255]) ).
thf(10,axiom,
! [TA: $tType] :
( ( id_on @ TA @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_Id__on__empty) ).
thf(283,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)],[10]) ).
thf(244,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_equiv__class__self) ).
thf(928,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(35,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/sandbox/benchmark/theBenchmark.p',fact_105_maintainedD) ).
thf(358,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)],[35]) ).
thf(198,axiom,
( f
= ( ^ [A: b] :
( if @ b
@ ( ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ A @ ( bot_bot @ ( set @ b ) ) ) )
= ( bot_bot @ ( set @ b ) ) )
@ A
@ ( hilbert_Eps @ b @ ( p @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112__092_060open_062f_A_092_060equiv_062_A_092_060lambda_062x_O_Aif_AgetRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_A_123_125_Athen_Ax_Aelse_AEps_A_IP_Ax_J_092_060close_062) ).
thf(807,plain,
( f
= ( ^ [A: b] :
( if @ b
@ ( ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ A @ ( bot_bot @ ( set @ b ) ) ) )
= ( bot_bot @ ( set @ b ) ) )
@ A
@ ( hilbert_Eps @ b @ ( p @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(173,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_refl__onD2) ).
thf(740,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( refl_on @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( member @ TA @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',fact_77_old_Oprod_Oinducts) ).
thf(575,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)],[114]) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',fact_22_map__graph__preserves__restricted) ).
thf(528,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)],[98]) ).
thf(238,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/sandbox/benchmark/theBenchmark.p',fact_50_Gr__not__in) ).
thf(908,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)],[238]) ).
thf(204,axiom,
member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ ( f @ x ) @ ( f @ y ) ) @ ( getRel @ ( standard_Constant @ a ) @ b @ l2 @ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_gr) ).
thf(822,plain,
member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ ( f @ x ) @ ( f @ y ) ) @ ( getRel @ ( standard_Constant @ a ) @ b @ l2 @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(216,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) @ ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
=> ( ( member @ TA @ C @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_subset__equiv__class) ).
thf(850,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) @ ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
=> ( ( member @ TA @ C @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(66,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_insert__not__empty) ).
thf(442,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',fact_181_graph__empty__e) ).
thf(369,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)],[39]) ).
thf(132,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(624,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(212,axiom,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_insertI1) ).
thf(839,plain,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TC @ TA ),B: set @ ( product_prod @ TC @ TA ),C: set @ ( product_prod @ TA @ TB ),D: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TC @ TA ) ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ C @ D )
=> ( ord_less_eq @ ( set @ ( product_prod @ TC @ TB ) ) @ ( relcomp @ TC @ TA @ TB @ A @ C ) @ ( relcomp @ TC @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_relcomp__mono) ).
thf(322,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TC @ TA ),B: set @ ( product_prod @ TC @ TA ),C: set @ ( product_prod @ TA @ TB ),D: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TC @ TA ) ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ C @ D )
=> ( ord_less_eq @ ( set @ ( product_prod @ TC @ TB ) ) @ ( relcomp @ TC @ TA @ TB @ A @ C ) @ ( relcomp @ TC @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: set @ TA] :
( ( image2 @ TA @ TB @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TB @ ( A @ B ) @ ( image2 @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_image__insert) ).
thf(486,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: set @ TA] :
( ( image2 @ TA @ TB @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TB @ ( A @ B ) @ ( image2 @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(196,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: labeled_graph @ TC @ TD,B: labeled_graph @ TC @ TA,C: set @ ( product_prod @ TD @ TA ),D: TA > TB] :
( ( graph_homomorphism @ TC @ TD @ TA @ A @ B @ C )
=> ( graph_homomorphism @ TC @ TD @ TB @ A @ ( map_graph @ TA @ TB @ TC @ ( bNF_Gr @ TA @ TB @ ( labeled_vertices @ TC @ TA @ B ) @ D ) @ B ) @ ( relcomp @ TD @ TA @ TB @ C @ ( bNF_Gr @ TA @ TB @ ( labeled_vertices @ TC @ TA @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_graph__homomorphism__on__graph) ).
thf(803,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: labeled_graph @ TC @ TD,B: labeled_graph @ TC @ TA,C: set @ ( product_prod @ TD @ TA ),D: TA > TB] :
( ( graph_homomorphism @ TC @ TD @ TA @ A @ B @ C )
=> ( graph_homomorphism @ TC @ TD @ TB @ A @ ( map_graph @ TA @ TB @ TC @ ( bNF_Gr @ TA @ TB @ ( labeled_vertices @ TC @ TA @ B ) @ D ) @ B ) @ ( relcomp @ TD @ TA @ TB @ C @ ( bNF_Gr @ TA @ TB @ ( labeled_vertices @ TC @ TA @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(247,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: set @ ( product_prod @ TC @ TA ),D: TB,E: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TC @ TA ) @ ( product_Pair @ TC @ TA @ A @ B ) @ C )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ D ) @ E )
=> ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ A @ D ) @ ( relcomp @ TC @ TA @ TB @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_relcomp_OrelcompI) ).
thf(935,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: set @ ( product_prod @ TC @ TA ),D: TB,E: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TC @ TA ) @ ( product_Pair @ TC @ TA @ A @ B ) @ C )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ D ) @ E )
=> ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ A @ D ) @ ( relcomp @ TC @ TA @ TB @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(145,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
= ( ( ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( member @ TA @ C @ A )
& ( member @ TA @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_equiv__class__eq__iff) ).
thf(659,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
= ( ( ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( member @ TA @ C @ A )
& ( member @ TA @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(186,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: set @ ( product_prod @ TA @ TB )] :
( ( member @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ C ) @ D )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_rev__ImageI) ).
thf(775,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: set @ ( product_prod @ TA @ TB )] :
( ( member @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ C ) @ D )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: TB] :
( ( image @ TB @ TA @ A @ ( insert @ TB @ B @ ( bot_bot @ ( set @ TB ) ) ) )
= ( collect @ TA
@ ^ [C: TA] : ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_Image__singleton) ).
thf(592,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: TB] :
( ( image @ TB @ TA @ A @ ( insert @ TB @ B @ ( bot_bot @ ( set @ TB ) ) ) )
= ( collect @ TA
@ ^ [C: TA] : ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',fact_173_insert__iff) ).
thf(708,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)],[162]) ).
thf(228,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/sandbox/benchmark/theBenchmark.p',fact_69_GrD1) ).
thf(882,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)],[228]) ).
thf(974,plain,
$false,
inference(e,[status(thm)],[645,809,760,347,333,893,941,777,666,481,962,468,408,683,730,308,379,511,597,861,523,762,269,677,385,550,797,930,829,841,885,320,389,570,719,372,619,917,344,460,638,289,448,817,902,881,416,475,492,514,937,353,905,602,692,453,396,411,292,439,925,366,534,714,957,952,561,297,630,429,275,788,847,852,583,456,324,697,874,650,725,356,869,610,420,499,519,742,471,884,753,686,526,489,970,547,837,393,647,605,805,508,541,558,794,662,633,360,264,745,573,965,750,375,733,819,423,402,772,286,281,826,577,711,641,445,382,313,335,919,947,350,764,784,736,377,567,599,880,434,616,303,890,758,858,621,483,700,330,811,387,462,932,912,399,636,278,608,306,505,653,922,473,722,675,426,589,680,939,754,553,531,944,458,823,690,295,707,887,414,327,263,580,855,791,585,502,338,643,544,703,656,613,864,727,595,497,876,465,627,450,671,688,495,844,363,556,813,517,781,896,748,418,786,478,272,899,832,536,716,800,300,432,967,405,867,950,835,262,564,341,437,767,664,828,960,955,283,928,358,807,740,575,528,908,822,850,442,369,624,839,322,486,803,935,659,775,592,708,882]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP177^2 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n028.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 14:20:08 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.01/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.00/1.18 % [INFO] Parsing done (276ms).
% 2.00/1.19 % [INFO] Running in sequential loop mode.
% 2.72/1.42 % [INFO] eprover registered as external prover.
% 2.72/1.42 % [INFO] cvc4 registered as external prover.
% 2.72/1.42 % [INFO] Scanning for conjecture ...
% 3.08/1.54 % [INFO] Found a conjecture and 259 axioms. Running axiom selection ...
% 3.45/1.64 % [INFO] Axiom selection finished. Selected 259 axioms (removed 0 axioms).
% 4.48/1.92 % [INFO] Problem is higher-order (TPTP THF).
% 4.48/1.94 % [INFO] Type checking passed.
% 4.48/1.94 % [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 ...
% 36.71/22.15 % External prover 'e' found a proof!
% 36.71/22.15 % [INFO] Killing All external provers ...
% 36.71/22.15 % Time passed: 21622ms (effective reasoning time: 20955ms)
% 36.71/22.15 % 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)>
% 36.71/22.15 % Axioms used in derivation (259): fact_81_prod__cases6, fact_101_semantics__in__vertices_I1_J, fact_220_equiv__class__eq__iff, fact_142_relcomp__mono, fact_4_assms_I1_J, fact_209_insert__not__empty, fact_218_subset__singletonD, fact_65_old_Oprod_Oinject, fact_232_tuple__disj, fact_227_proj__iff, fact_162_singleton__insert__inj__eq_H, fact_21_graph__union__idemp_I1_J, fact_110_graph__homo__union__id_I1_J, fact_160_agree__on__subg__compose, fact_254_image__insert, fact_207_insertE, fact_197_subsetD, fact_139_relcompEpair, fact_31_graph__homo, fact_28_map__graph__preserves__subgraph, fact_148_agree__on__ext, fact_26_subgraph__restrict, fact_236_empty__def, fact_230_f, fact_59_refl__onD, fact_98_graph__homomorphism__semantics, fact_75_Pair__inject, fact_248_Collect__subset, fact_43_idt__eq, fact_11__092_060open_062graph__union_A_Imap__graph__fn_AG_Af_J_AG_A_061_AG_092_060close_062, fact_156_maintainedD2, fact_111_graph__homo__union__id_I2_J, fact_70_edge__preserving__Id, fact_229_equivalence, fact_214_subset__insertI, fact_138_relcomp_Ocases, fact_52_getRel__dom_I2_J, fact_105_maintainedD, fact_57_refl__onD2, fact_41_getRel__hom, fact_224_refines__equiv__class__eq, fact_102_semantics__in__vertices_I2_J, fact_171_subsetI, fact_10_equiv, fact_187_Collect__mono__iff, fact_7_gr, fact_179_relcomp__empty1, fact_134_ImageE, fact_159_graph__homomorphism__on__graph, fact_124_agree__on__empty, fact_135_relcomp_OrelcompI, fact_177_singletonI, fact_205_insertI2, fact_146_edge__preserving__subset, fact_42_getRel__map__fn, fact_35_map__graph__fn__eqI, fact_212_singletonD, fact_221_eq__equiv__class__iff, fact_161_singleton__insert__inj__eq, fact_123_map__graph__selectors_I1_J, fact_32_labeled__graph_Osel_I1_J, fact_40_labeled__graph_Oexpand, fact_56_Id__onE, fact_122_Gr__insert, fact_112__092_060open_062f_A_092_060equiv_062_A_092_060lambda_062x_O_Aif_AgetRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_A_123_125_Athen_Ax_Aelse_AEps_A_IP_Ax_J_092_060close_062, fact_2_fv_I1_J, fact_253_image__is__empty, fact_114_agree__on__comm, fact_251_image__empty, fact_243_vertices__def, fact_166_empty__Collect__eq, fact_208_singleton__inject, fact_1_fv_I2_J, fact_72_edge__preserving__atomic, fact_145_agree__on__def, fact_173_insert__iff, fact_223_eq__equiv__class, fact_92_maintainedI, fact_143_Image__mono, fact_66_prod_Oinject, fact_201_insert__eq__iff, fact_100_labeled__graph_Ocase, fact_46_Collect__mem__eq, fact_240_Collect__conv__if2, fact_215_subset__insert, fact_115_ImageI, fact_151_compose__preserves__edge__preserving, fact_106_least__def, fact_60_refl__on__Id__on, fact_199_mk__disjoint__insert, fact_234_singleton__conv2, fact_241_Image__singleton, fact_222_equiv__class__eq, fact_137_relcomp_Osimps, fact_33_subgraph__def, fact_97_consequence__graphD_I3_J, fact_39_labeled__graph_Oexhaust__sel, fact_119_Gr__empty, fact_167_Collect__empty__eq, fact_108_extensibleI, fact_129_graph__single, fact_29_map__graph__fn__id_I2_J, fact_54_Id__on__iff, fact_48_getRel__subgraph, fact_178_insert__subset, fact_136_relcomp_Oinducts, fact_121_P__eq, fact_130_r2, fact_252_empty__is__image, help_If_1_1_T, fact_141_relcomp__Image, fact_69_GrD1, fact_210_doubleton__eq__iff, fact_206_insertI1, fact_50_Gr__not__in, fact_169_empty__iff, fact_192_subset__iff, fact_149_refl__on__empty, fact_235_P, fact_165_refines__equiv__class__eq2, fact_67_refl__on__domain, fact_49_in__Gr, fact_194_equalityD1, fact_85_prod__induct5, fact_153_restrict__subsD, fact_239_Collect__conv__if, fact_15_subg, fact_237_insert__compr, fact_126_in__on__graph, fact_19_graph__union__idemp_I3_J, fact_186_emptyE, fact_38_subgraph__preserves__hom, fact_189_subset__trans, fact_184_equals0I, fact_14_labeled__graph_Osel_I2_J, fact_74_prod__cases, fact_147_agree__on__trans, fact_140_relcompE, fact_176_subset__empty, fact_249_congr_I1_J, fact_37_labeled__graph_Oexhaust, fact_133_Image__iff, fact_45_mem__Collect__eq, fact_5_r1, fact_62_maintained__refl, fact_61_getRel__homR, fact_152_graph__union__iff, fact_127_graph__homomorphism__empty, fact_238_insert__Collect, fact_16_vertices__restrict, fact_204_Set_Oset__insert, fact_247_subset__Collect__iff, fact_116_Image__empty2, fact_80_prod__cases5, fact_24_labeled__graph_Ocollapse, fact_117_Image__empty1, fact_190_Collect__mono, fact_23_graph__union__preserves__restrict, fact_125_Image__singleton__iff, fact_188_set__eq__subset, fact_96_least__consequence__graph__def, fact_182_graph__homomorphism__nonempty, fact_246_subset__CollectI, fact_79_prod__cases4, fact_90_leastI, fact_180_relcomp__empty2, fact_53_getRel__dom_I1_J, fact_78_prod__cases3, fact_8_a, fact_47_Collect__cong, help_If_3_1_T, fact_77_old_Oprod_Oinducts, fact_83_prod__induct3, help_If_2_1_T, fact_68_GrD2, fact_245_pred__equals__eq2, fact_44_vert__P, fact_168_all__not__in__conv, fact_118_Id__on__empty, fact_203_insert__ident, fact_154_subgraph__def2, fact_91_map__graph__in, fact_144_O__assoc, fact_225_nonempty__rule, fact_55_Id__on__eqI, fact_150_subrelI, fact_183_ex__in__conv, fact_113_agree__on__refl, fact_94_labeled__graph_Osplit__sel, fact_95_extensible__refl, fact_170_subset__antisym, fact_157_Id__on__vertices__identity_I2_J, fact_6_assms_I2_J, fact_58_refl__onD1, fact_104_subgraph__semantics, fact_99_consequence__graphD_I1_J, fact_175_empty__subsetI, fact_158_Id__on__vertices__identity_I1_J, fact_87_prod__induct7, fact_86_prod__induct6, fact_191_subset__refl, fact_128_graph__unionI, fact_84_prod__induct4, fact_82_prod__cases7, fact_27_graph__homomorphism__Id, fact_93_extensible__refl__concr, fact_12_gu1, fact_30_map__graph__fn__graphI, fact_20_graph__union__idemp_I2_J, fact_131_refl__on__singleton, fact_242_edges__def, fact_231_the__elem__eq, fact_107_labeled__graph_Osplit__sel__asm, fact_172_insert__absorb2, fact_18_labeled__graph_Oinject, fact_73_surj__pair, fact_219_equiv__class__self, fact_198_in__mono, fact_132_rev__ImageI, fact_228_proj__def, fact_196_equalityE, fact_88_old_Oprod_Orec, fact_185_equals0D, fact_163_equiv__class__subset, fact_213_subset__insertI2, fact_0__092_060open_062_092_060And_062xa_O_A_092_060lbrakk_062f_Axa_A_092_060in_062_Avertices_AG_059_Axa_A_092_060notin_062_Avertices_AG_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062, fact_255_insert__image, fact_63_edge__preserving__on__graphI, fact_36_labeled__graph_Oinduct, fact_9_local_Orefl, fact_174_insertCI, fact_164_subset__equiv__class, fact_244_labeled__graph_Ocase__distrib, fact_200_insert__commute, fact_51_Id__onI, fact_71_map__graph__edge__preserving, fact_233_singleton__conv, fact_89_least__consequence__graphI, fact_76_old_Oprod_Oexhaust, fact_155_subgraph__subset_I1_J, fact_193_equalityD2, fact_13__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_A_092_060Longrightarrow_062_A_Ix_M_Ax_J_A_092_060in_062_AgetRel_AS__Idt_AG_092_060close_062, fact_217_subset__singleton__iff, fact_120_graph__homomorphism__composes, fact_211_singleton__iff, fact_216_insert__mono, fact_109_subgraph__subset_I2_J, fact_250_ident, fact_34_subgraph__trans, fact_103_labeled__graph_Ocase__eq__if, fact_17_restrict__idemp, fact_64_reflexivity__rule, fact_25_subgraph__refl, fact_181_graph__empty__e, fact_22_map__graph__preserves__restricted, fact_3_gu2, fact_195_subset__eq, fact_202_insert__absorb, fact_226_ma
% 36.71/22.15 % No. of inferences in proof: 522
% 36.71/22.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 21622 ms resp. 20955 ms w/o parsing
% 37.68/22.38 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 37.68/22.38 % [INFO] Killing All external provers ...
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