TSTP Solution File: ITP175^2 by Leo-III---1.7.10
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP175^2 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:48:31 EDT 2024
% Result : Theorem 173.51s 152.88s
% Output : Refutation 174.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 324
% Syntax : Number of formulae : 588 ( 191 unt; 62 typ; 0 def)
% Number of atoms : 2313 ( 444 equ; 2 cnn)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 10999 ( 132 ~; 14 |; 68 &;10155 @)
% ( 0 <=>; 630 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 10 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 247 ( 247 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 64 usr; 12 con; 0-8 aty)
% Number of variables : 2381 ( 72 ^2202 !; 12 ?;2381 :)
% ( 95 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(bot_type,type,
bot:
!>[TA: $tType] : $o ).
thf(ord_type,type,
ord:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_type,type,
preorder:
!>[TA: $tType] : $o ).
thf(order_bot_type,type,
order_bot:
!>[TA: $tType] : $o ).
thf(bNF_Gr1317331620lImage_type,type,
bNF_Gr1317331620lImage:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TB ) ) > ( TB > TA ) > ( set @ ( product_prod @ TA @ TA ) ) ) ).
thf(bNF_Greatest_univ_type,type,
bNF_Greatest_univ:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > TA ) ).
thf(equiv_congruent_type,type,
equiv_congruent:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TB ) ) > ( TB > TA ) > $o ) ).
thf(equiv_congruent2_type,type,
equiv_congruent2:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( set @ ( product_prod @ TC @ TC ) ) > ( set @ ( product_prod @ TB @ TB ) ) > ( TC > 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(equiv_quotient_type,type,
equiv_quotient:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > ( set @ ( set @ 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(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(on_triple_type,type,
on_triple:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( set @ ( product_prod @ TC @ TB ) ) > ( set @ ( product_prod @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) ) ) ).
thf(restrict_type,type,
restrict:
!>[TA: $tType,TB: $tType] : ( ( labeled_graph @ TB @ TA ) > ( labeled_graph @ TB @ TA ) ) ).
thf(idempotent_type,type,
idempotent:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(order_1409979114der_on_type,type,
order_1409979114der_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(order_preorder_on_type,type,
order_preorder_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
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(produc2004651681e_prod_type,type,
produc2004651681e_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ 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(refl_on_type,type,
refl_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(sym_type,type,
sym:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(total_on_type,type,
total_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(trans_type,type,
trans:
!>[TA: $tType] : ( ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
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(fin_maintained_type,type,
fin_maintained:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( product_prod @ ( labeled_graph @ TC @ TB ) @ ( labeled_graph @ TC @ TB ) ) > ( labeled_graph @ TC @ 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(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(is_empty_type,type,
is_empty:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(is_singleton_type,type,
is_singleton:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(the_elem_type,type,
the_elem:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(standa1068660421e_rule_type,type,
standa1068660421e_rule:
!>[TA: $tType] : ( TA > TA > ( product_prod @ ( labeled_graph @ TA @ nat ) @ ( labeled_graph @ 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(same_fst_type,type,
same_fst:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TB > ( set @ ( product_prod @ TA @ TA ) ) ) > ( set @ ( product_prod @ ( product_prod @ TB @ TA ) @ ( product_prod @ TB @ TA ) ) ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(g_type,type,
g: labeled_graph @ a @ b ).
thf(i_type,type,
i: a ).
thf(l_type,type,
l: a ).
thf(y_type,type,
y: b ).
thf(z_type,type,
z: b ).
thf(141,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_75_insert__eq__iff) ).
thf(645,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)],[141]) ).
thf(74,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( idempotent @ TA @ A )
=> ( trans @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_idempotent__impl__trans) ).
thf(479,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( idempotent @ TA @ A )
=> ( trans @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(93,axiom,
! [TA: $tType] :
( ( equiv_equiv @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( refl_on @ TA @ A @ B )
& ( sym @ TA @ B )
& ( trans @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_equiv__def) ).
thf(518,plain,
! [TA: $tType] :
( ( equiv_equiv @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( refl_on @ TA @ A @ B )
& ( sym @ TA @ B )
& ( trans @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(70,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_226_least__consequence__graph__def) ).
thf(468,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)],[70]) ).
thf(149,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_15_old_Oprod_Oinducts) ).
thf(666,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)],[149]) ).
thf(75,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_216_subgraph__preserves__hom) ).
thf(481,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)],[75]) ).
thf(250,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_69_ex__in__conv) ).
thf(977,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)],[250]) ).
thf(156,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(683,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(8,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_linear) ).
thf(276,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(176,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_152_insert__subset) ).
thf(741,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)],[176]) ).
thf(39,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_insert__not__empty) ).
thf(379,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(91,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( equiv_equiv @ TA @ A @ B )
=> ~ ( ( refl_on @ TA @ A @ B )
=> ( ( sym @ TA @ B )
=> ~ ( trans @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_equivE) ).
thf(511,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( equiv_equiv @ TA @ A @ B )
=> ~ ( ( refl_on @ TA @ A @ B )
=> ( ( sym @ TA @ B )
=> ~ ( trans @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(131,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_95_graph__empty__e) ).
thf(614,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)],[131]) ).
thf(5,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_9) ).
thf(269,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(41,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_148_subset__antisym) ).
thf(385,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)],[41]) ).
thf(98,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_175_set__eq__subset) ).
thf(533,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)],[98]) ).
thf(105,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_84_doubleton__eq__iff) ).
thf(550,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)],[105]) ).
thf(84,axiom,
preorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_2) ).
thf(500,plain,
preorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(190,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_63_insert__iff) ).
thf(797,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)],[190]) ).
thf(239,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ! [B: TA,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) )
=> ( trans @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_transI) ).
thf(945,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ! [B: TA,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) )
=> ( trans @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(178,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TB @ TB ),C: TA > TB > TC] :
( ! [D: TA,E: TA,F: TB,G: TB] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ A )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ F @ G ) @ B )
=> ( ( C @ D @ F )
= ( C @ E @ G ) ) ) )
=> ( equiv_congruent2 @ TA @ TB @ TC @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_congruent2I_H) ).
thf(747,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TB @ TB ),C: TA > TB > TC] :
( ! [D: TA,E: TA,F: TB,G: TB] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ A )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ F @ G ) @ B )
=> ( ( C @ D @ F )
= ( C @ E @ G ) ) ) )
=> ( equiv_congruent2 @ TA @ TB @ TC @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(227,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_225_leastI) ).
thf(913,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)],[227]) ).
thf(165,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_149_subsetI) ).
thf(709,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)],[165]) ).
thf(203,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_89_graph__single) ).
thf(841,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)],[203]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_ord__eq__le__subst) ).
thf(288,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(110,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] : ( total_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_total__on__empty) ).
thf(565,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] : ( total_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(113,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_120_agree__on__refl) ).
thf(570,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)],[113]) ).
thf(87,axiom,
! [TA: $tType,A: set @ TA] : ( sym @ TA @ ( id_on @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_sym__Id__on) ).
thf(504,plain,
! [TA: $tType,A: set @ TA] : ( sym @ TA @ ( id_on @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(201,axiom,
equiv_equiv @ b @ ( labeled_vertices @ a @ b @ g ) @ ( getRel @ a @ b @ i @ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_eq) ).
thf(838,plain,
equiv_equiv @ b @ ( labeled_vertices @ a @ b @ g ) @ ( getRel @ a @ b @ i @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(162,axiom,
! [TA: $tType,A: TA] : ( trans @ 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_54_trans__singleton) ).
thf(702,plain,
! [TA: $tType,A: TA] : ( trans @ 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)],[162]) ).
thf(240,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_28_reflexivity__rule) ).
thf(949,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)],[240]) ).
thf(192,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( set @ TA ) @ ( equiv_proj @ TA @ TA @ B @ C ) @ ( equiv_quotient @ TA @ A @ B ) )
= ( member @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_proj__in__iff) ).
thf(802,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( set @ TA ) @ ( equiv_proj @ TA @ TA @ B @ C ) @ ( equiv_quotient @ TA @ A @ B ) )
= ( member @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(27,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_eq__refl) ).
thf(344,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(101,axiom,
linorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_13) ).
thf(542,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(67,axiom,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_is__singleton__def) ).
thf(460,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(108,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_96_labeled__graph_Oexhaust) ).
thf(559,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)],[108]) ).
thf(247,axiom,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_bot__empty__eq) ).
thf(969,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(128,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 )
=> ( ( ( equiv_quotient @ TA @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) @ B )
= ( equiv_quotient @ TA @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) @ B ) )
= ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_eq__equiv__class__iff2) ).
thf(606,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 )
=> ( ( ( equiv_quotient @ TA @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) @ B )
= ( equiv_quotient @ TA @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) @ B ) )
= ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot) ).
thf(284,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(181,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_118_graph__homomorphism__empty) ).
thf(770,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)],[181]) ).
thf(217,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_16_old_Oprod_Oexhaust) ).
thf(881,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)],[217]) ).
thf(53,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_82_singleton__inject) ).
thf(416,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)],[53]) ).
thf(231,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_169_subset__insert) ).
thf(924,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)],[231]) ).
thf(121,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_146_getRel__subgraph) ).
thf(591,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)],[121]) ).
thf(22,axiom,
! [TA: $tType] : ( order_bot @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__bot_6) ).
thf(321,plain,
! [TA: $tType] : ( order_bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(38,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_bot_Oextremum__uniqueI) ).
thf(376,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
=> ( A
= ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(77,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_empty__subsetI) ).
thf(485,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_le__funD) ).
thf(348,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(30,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_239_graph__union__idemp_I1_J) ).
thf(353,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)],[30]) ).
thf(246,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_internal__case__prod__conv) ).
thf(966,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(126,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_37_refl__onD1) ).
thf(602,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)],[126]) ).
thf(10,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_ord__le__eq__trans) ).
thf(280,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(159,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_73_mk__disjoint__insert) ).
thf(692,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)],[159]) ).
thf(173,axiom,
! [TA: $tType] :
( ( total_on @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_total__on__def) ).
thf(734,plain,
! [TA: $tType] :
( ( total_on @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(46,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( refl_on @ TA @ A @ B )
=> ( ( sym @ TA @ B )
=> ( ( trans @ TA @ B )
=> ( equiv_equiv @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_equivI) ).
thf(396,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( refl_on @ TA @ A @ B )
=> ( ( sym @ TA @ B )
=> ( ( trans @ TA @ B )
=> ( equiv_equiv @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(255,axiom,
( ( refl_on @ b @ ( labeled_vertices @ a @ b @ g ) @ ( getRel @ a @ b @ i @ g ) )
& ! [A: b,B: b] :
( ( member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ A @ B ) @ ( getRel @ a @ b @ i @ g ) )
=> ( member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ B @ A ) @ ( getRel @ a @ b @ i @ g ) ) )
& ( trans @ b @ ( getRel @ a @ b @ i @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062refl__on_A_Ivertices_AG_J_A_IgetRel_AI_AG_J_A_092_060and_062_A_I_092_060forall_062x_Ay_O_A_Ix_M_Ay_J_A_092_060in_062_AgetRel_AI_AG_A_092_060longrightarrow_062_A_Iy_M_Ax_J_A_092_060in_062_AgetRel_AI_AG_J_A_092_060and_062_Atrans_A_IgetRel_AI_AG_J_092_060close_062) ).
thf(988,plain,
( ( refl_on @ b @ ( labeled_vertices @ a @ b @ g ) @ ( getRel @ a @ b @ i @ g ) )
& ! [A: b,B: b] :
( ( member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ A @ B ) @ ( getRel @ a @ b @ i @ g ) )
=> ( member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ B @ A ) @ ( getRel @ a @ b @ i @ g ) ) )
& ( trans @ b @ ( getRel @ a @ b @ i @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(3,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_le__cases) ).
thf(265,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(89,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_107_labeled__graph_Osel_I2_J) ).
thf(507,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)],[89]) ).
thf(96,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_22_vertices__restrict) ).
thf(527,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)],[96]) ).
thf(19,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_order__trans) ).
thf(307,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(154,axiom,
maintained @ a @ nat @ b @ ( standa1068660421e_rule @ a @ i @ l ) @ g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_m) ).
thf(678,plain,
maintained @ a @ nat @ b @ ( standa1068660421e_rule @ a @ i @ l ) @ g,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(147,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_81_insertE) ).
thf(661,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)],[147]) ).
thf(103,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_215_subgraph__trans) ).
thf(546,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)],[103]) ).
thf(188,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_subset__emptyI) ).
thf(793,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(226,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_243_subgraph__def2) ).
thf(910,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)],[226]) ).
thf(184,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TC,D: TA,E: TB,F: TB,G: set @ ( product_prod @ TC @ TB )] :
( ( member @ ( product_prod @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) @ ( product_Pair @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TA @ ( product_prod @ TC @ TC ) @ A @ ( product_Pair @ TC @ TC @ B @ C ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ TB ) @ D @ ( product_Pair @ TB @ TB @ E @ F ) ) ) @ ( on_triple @ TC @ TB @ TA @ G ) )
= ( ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ B @ E ) @ G )
& ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ C @ F ) @ G )
& ( A = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_on__triple) ).
thf(778,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TC,D: TA,E: TB,F: TB,G: set @ ( product_prod @ TC @ TB )] :
( ( member @ ( product_prod @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) @ ( product_Pair @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TA @ ( product_prod @ TC @ TC ) @ A @ ( product_Pair @ TC @ TC @ B @ C ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ TB ) @ D @ ( product_Pair @ TB @ TB @ E @ F ) ) ) @ ( on_triple @ TC @ TB @ TA @ G ) )
= ( ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ B @ E ) @ G )
& ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ C @ F ) @ G )
& ( A = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(241,axiom,
! [TA: $tType] :
( ( sym @ TA )
= ( ^ [A: set @ ( product_prod @ TA @ TA )] :
! [B: TA,C: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_sym__def) ).
thf(952,plain,
! [TA: $tType] :
( ( sym @ TA )
= ( ^ [A: set @ ( product_prod @ TA @ TA )] :
! [B: TA,C: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_le__funI) ).
thf(302,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(209,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_125_extensibleI) ).
thf(862,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)],[209]) ).
thf(124,axiom,
! [TA: $tType] : ( order_1409979114der_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_lnear__order__on__empty) ).
thf(598,plain,
! [TA: $tType] : ( order_1409979114der_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(135,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TA,D: TC,E: TB,F: TB,G: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( product_prod @ TC @ ( product_prod @ TA @ TA ) ) @ ( product_prod @ TC @ ( product_prod @ TB @ TB ) ) ) @ ( product_Pair @ ( product_prod @ TC @ ( product_prod @ TA @ TA ) ) @ ( product_prod @ TC @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TC @ ( product_prod @ TA @ TA ) @ A @ ( product_Pair @ TA @ TA @ B @ C ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TB ) @ D @ ( product_Pair @ TB @ TB @ E @ F ) ) ) @ ( on_triple @ TA @ TB @ TC @ G ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ F ) @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_on__tripleD_I3_J) ).
thf(630,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TA,D: TC,E: TB,F: TB,G: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( product_prod @ TC @ ( product_prod @ TA @ TA ) ) @ ( product_prod @ TC @ ( product_prod @ TB @ TB ) ) ) @ ( product_Pair @ ( product_prod @ TC @ ( product_prod @ TA @ TA ) ) @ ( product_prod @ TC @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TC @ ( product_prod @ TA @ TA ) @ A @ ( product_Pair @ TA @ TA @ B @ C ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TB ) @ D @ ( product_Pair @ TB @ TB @ E @ F ) ) ) @ ( on_triple @ TA @ TB @ TC @ G ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ F ) @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(58,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( equiv_quotient @ TA @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_quotient__empty) ).
thf(429,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ( equiv_quotient @ TA @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(243,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_162_Id__on__eqI) ).
thf(957,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)],[243]) ).
thf(221,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ! [B: TA,C: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ A ) )
=> ( sym @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_symI) ).
thf(894,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA )] :
( ! [B: TA,C: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ A ) )
=> ( sym @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(228,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: set @ TA,E: TA,F: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( set @ TA ) @ C @ ( equiv_quotient @ TA @ A @ B ) )
=> ( ( member @ ( set @ TA ) @ D @ ( equiv_quotient @ TA @ A @ B ) )
=> ( ( member @ TA @ E @ C )
=> ( ( member @ TA @ F @ D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ B )
=> ( C = D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_quotient__eqI) ).
thf(916,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: set @ TA,E: TA,F: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( set @ TA ) @ C @ ( equiv_quotient @ TA @ A @ B ) )
=> ( ( member @ ( set @ TA ) @ D @ ( equiv_quotient @ TA @ A @ B ) )
=> ( ( member @ TA @ E @ C )
=> ( ( member @ TA @ F @ D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ B )
=> ( C = D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(33,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_64_insert__absorb2) ).
thf(361,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)],[33]) ).
thf(216,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TB,D: TB,E: TA > ( set @ ( product_prod @ TB @ TB ) )] :
( ( A @ B )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ C @ D ) @ ( E @ B ) )
=> ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ C ) @ ( product_Pair @ TA @ TB @ B @ D ) ) @ ( same_fst @ TA @ TB @ A @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_same__fstI) ).
thf(879,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TB,D: TB,E: TA > ( set @ ( product_prod @ TB @ TB ) )] :
( ( A @ B )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ C @ D ) @ ( E @ B ) )
=> ( member @ ( product_prod @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) ) @ ( product_Pair @ ( product_prod @ TA @ TB ) @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ C ) @ ( product_Pair @ TA @ TB @ B @ D ) ) @ ( same_fst @ TA @ TB @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(60,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_177_Collect__mono) ).
thf(435,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)],[60]) ).
thf(198,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_122_graph__homomorphism__semantics) ).
thf(830,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)],[198]) ).
thf(81,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( ( equiv_quotient @ TA @ A @ B )
= ( bot_bot @ ( set @ ( set @ TA ) ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_quotient__is__empty) ).
thf(493,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( ( equiv_quotient @ TA @ A @ B )
= ( bot_bot @ ( set @ ( set @ TA ) ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(116,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
= ( A
= ( bot_bot @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_bot_Oextremum__unique) ).
thf(578,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( bot_bot @ TA ) )
= ( A
= ( bot_bot @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(214,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( set @ TA ) @ C @ ( equiv_quotient @ TA @ A @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_in__quotient__imp__subset) ).
thf(874,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( set @ TA ) @ C @ ( equiv_quotient @ TA @ A @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(143,axiom,
! [TA: $tType] : ( trans @ TA @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_trans__empty) ).
thf(650,plain,
! [TA: $tType] : ( trans @ TA @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(261,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_insert__subsetI) ).
thf(1006,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(42,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( refl_on @ TA @ A @ B )
=> ( ( trans @ TA @ B )
=> ( idempotent @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_refl__trans__impl__idempotent) ).
thf(388,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( refl_on @ TA @ A @ B )
=> ( ( trans @ TA @ B )
=> ( idempotent @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(31,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_236_subgraph__def) ).
thf(356,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)],[31]) ).
thf(122,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ ( product_prod @ TC @ TC ),D: TA > TC > TB,E: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( equiv_congruent2 @ TA @ TC @ TB @ B @ C @ D )
=> ( ( member @ TA @ E @ A )
=> ( equiv_congruent @ TC @ TB @ C @ ( D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_congruent2__implies__congruent) ).
thf(593,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ ( product_prod @ TC @ TC ),D: TA > TC > TB,E: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( equiv_congruent2 @ TA @ TC @ TB @ B @ C @ D )
=> ( ( member @ TA @ E @ A )
=> ( equiv_congruent @ TC @ TB @ C @ ( D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(212,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_223_proj__iff) ).
thf(869,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)],[212]) ).
thf(55,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_74_insert__commute) ).
thf(420,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)],[55]) ).
thf(251,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_51_refl__on__singleton) ).
thf(980,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)],[251]) ).
thf(49,axiom,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_the__elem__eq) ).
thf(403,plain,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(71,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_subset__refl) ).
thf(471,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(218,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( D = B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_ssubst__Pair__rhs) ).
thf(884,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( D = B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_le__fun__def) ).
thf(339,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(157,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_14_prod__cases7) ).
thf(686,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)],[157]) ).
thf(138,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TC,D: TA,E: TB,F: TB,G: set @ ( product_prod @ TC @ TB )] :
( ( member @ ( product_prod @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) @ ( product_Pair @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TA @ ( product_prod @ TC @ TC ) @ A @ ( product_Pair @ TC @ TC @ B @ C ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ TB ) @ D @ ( product_Pair @ TB @ TB @ E @ F ) ) ) @ ( on_triple @ TC @ TB @ TA @ G ) )
=> ( D = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_on__tripleD_I1_J) ).
thf(637,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TC,D: TA,E: TB,F: TB,G: set @ ( product_prod @ TC @ TB )] :
( ( member @ ( product_prod @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) @ ( product_Pair @ ( product_prod @ TA @ ( product_prod @ TC @ TC ) ) @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TA @ ( product_prod @ TC @ TC ) @ A @ ( product_Pair @ TC @ TC @ B @ C ) ) @ ( product_Pair @ TA @ ( product_prod @ TB @ TB ) @ D @ ( product_Pair @ TB @ TB @ E @ F ) ) ) @ ( on_triple @ TC @ TB @ TA @ G ) )
=> ( D = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(155,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_71_equals0D) ).
thf(679,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)],[155]) ).
thf(258,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_126_maintainedI) ).
thf(997,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)],[258]) ).
thf(92,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_238_graph__union__idemp_I2_J) ).
thf(515,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)],[92]) ).
thf(175,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_156_Id__on__empty) ).
thf(738,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)],[175]) ).
thf(66,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_247_labeled__graph_Oexhaust__sel) ).
thf(457,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)],[66]) ).
thf(253,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_117_agree__on__empty) ).
thf(984,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)],[253]) ).
thf(112,axiom,
bot @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_16) ).
thf(569,plain,
bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(86,axiom,
order_bot @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__bot_11) ).
thf(503,plain,
order_bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(236,axiom,
! [A: product_prod @ ( labeled_graph @ a @ nat ) @ ( labeled_graph @ a @ nat )] :
( ( member @ ( product_prod @ ( labeled_graph @ a @ nat ) @ ( labeled_graph @ a @ nat ) ) @ A @ ( insert @ ( product_prod @ ( labeled_graph @ a @ nat ) @ ( labeled_graph @ a @ nat ) ) @ ( standa245363227y_rule @ a @ i ) @ ( insert @ ( product_prod @ ( labeled_graph @ a @ nat ) @ ( labeled_graph @ a @ nat ) ) @ ( standa2114124375e_rule @ a @ i ) @ ( insert @ ( product_prod @ ( labeled_graph @ a @ nat ) @ ( labeled_graph @ a @ nat ) ) @ ( standa1805702094y_rule @ a @ i ) @ ( bot_bot @ ( set @ ( product_prod @ ( labeled_graph @ a @ nat ) @ ( labeled_graph @ a @ nat ) ) ) ) ) ) ) )
=> ( maintained @ a @ nat @ b @ A @ g ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_mA) ).
thf(938,plain,
! [A: product_prod @ ( labeled_graph @ a @ nat ) @ ( labeled_graph @ a @ nat )] :
( ( member @ ( product_prod @ ( labeled_graph @ a @ nat ) @ ( labeled_graph @ a @ nat ) ) @ A @ ( insert @ ( product_prod @ ( labeled_graph @ a @ nat ) @ ( labeled_graph @ a @ nat ) ) @ ( standa245363227y_rule @ a @ i ) @ ( insert @ ( product_prod @ ( labeled_graph @ a @ nat ) @ ( labeled_graph @ a @ nat ) ) @ ( standa2114124375e_rule @ a @ i ) @ ( insert @ ( product_prod @ ( labeled_graph @ a @ nat ) @ ( labeled_graph @ a @ nat ) ) @ ( standa1805702094y_rule @ a @ i ) @ ( bot_bot @ ( set @ ( product_prod @ ( labeled_graph @ a @ nat ) @ ( labeled_graph @ a @ nat ) ) ) ) ) ) ) )
=> ( maintained @ a @ nat @ b @ A @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(193,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_13_prod__cases6) ).
thf(805,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)],[193]) ).
thf(47,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_248_labeled__graph_Oexpand) ).
thf(398,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)],[47]) ).
thf(97,axiom,
! [TA: $tType] :
( ( order_preorder_on @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( refl_on @ TA @ A @ B )
& ( trans @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_preorder__on__def) ).
thf(530,plain,
! [TA: $tType] :
( ( order_preorder_on @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( refl_on @ TA @ A @ B )
& ( trans @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(219,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_86_singletonD) ).
thf(888,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)],[219]) ).
thf(182,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: set @ TA,E: TA,F: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( set @ TA ) @ C @ ( equiv_quotient @ TA @ A @ B ) )
=> ( ( member @ ( set @ TA ) @ D @ ( equiv_quotient @ TA @ A @ B ) )
=> ( ( member @ TA @ E @ C )
=> ( ( member @ TA @ F @ D )
=> ( ( C = D )
= ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_quotient__eq__iff) ).
thf(773,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: set @ TA,E: TA,F: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( set @ TA ) @ C @ ( equiv_quotient @ TA @ A @ B ) )
=> ( ( member @ ( set @ TA ) @ D @ ( equiv_quotient @ TA @ A @ B ) )
=> ( ( member @ TA @ E @ C )
=> ( ( member @ TA @ F @ D )
=> ( ( C = D )
= ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ F ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(119,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_bot_Oextremum) ).
thf(586,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(225,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_78_Set_Oset__insert) ).
thf(906,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)],[225]) ).
thf(1,conjecture,
member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ z @ y ) @ ( getRel @ a @ b @ i @ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ z @ y ) @ ( getRel @ a @ b @ i @ g ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(264,plain,
~ ( member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ z @ y ) @ ( getRel @ a @ b @ i @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(158,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_221_maintainedD2) ).
thf(689,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)],[158]) ).
thf(63,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_213_subset__singletonD) ).
thf(444,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)],[63]) ).
thf(118,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC ),B: labeled_graph @ TA @ TB] :
( ( maintained @ TA @ TC @ TB @ A @ B )
=> ( fin_maintained @ TA @ TC @ TB @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_maintained__then__fin__maintained) ).
thf(584,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ ( labeled_graph @ TA @ TC ) @ ( labeled_graph @ TA @ TC ),B: labeled_graph @ TA @ TB] :
( ( maintained @ TA @ TC @ TB @ A @ B )
=> ( fin_maintained @ TA @ TC @ TB @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(56,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_157_subgraph__refl) ).
thf(423,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)],[56]) ).
thf(172,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA,D: TA] :
( ( trans @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_transE) ).
thf(732,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA,D: TA] :
( ( trans @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(12,axiom,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_10) ).
thf(286,plain,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(52,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_240_graph__union__preserves__restrict) ).
thf(413,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)],[52]) ).
thf(109,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_155_singleton__insert__inj__eq_H) ).
thf(562,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)],[109]) ).
thf(249,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_153_Id__onI) ).
thf(975,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)],[249]) ).
thf(44,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_252_labeled__graph_Osplit__sel__asm) ).
thf(391,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)],[44]) ).
thf(235,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_singletonI) ).
thf(936,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(40,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_bot__set__def) ).
thf(382,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(114,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_154_singleton__insert__inj__eq) ).
thf(572,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)],[114]) ).
thf(83,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_170_subset__insertI) ).
thf(498,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)],[83]) ).
thf(69,axiom,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_is__singletonI) ).
thf(466,plain,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(229,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_6_old_Oprod_Oinject) ).
thf(919,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)],[229]) ).
thf(163,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_250_graph__union__iff) ).
thf(704,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)],[163]) ).
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_67_Collect__empty__eq) ).
thf(350,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(127,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ord_less_eq @ ( set @ ( product_prod @ ( set @ TA ) @ ( set @ TA ) ) ) @ ( bNF_Gr1317331620lImage @ TA @ ( set @ TA ) @ B @ ( equiv_proj @ TA @ TA @ B ) ) @ ( id_on @ ( set @ TA ) @ ( equiv_quotient @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_relImage__proj) ).
thf(604,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ord_less_eq @ ( set @ ( product_prod @ ( set @ TA ) @ ( set @ TA ) ) ) @ ( bNF_Gr1317331620lImage @ TA @ ( set @ TA ) @ B @ ( equiv_proj @ TA @ TA @ B ) ) @ ( id_on @ ( set @ TA ) @ ( equiv_quotient @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(54,axiom,
linorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(419,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(111,axiom,
! [TA: $tType,A: set @ TA] : ( refl_on @ TA @ A @ ( id_on @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_refl__on__Id__on) ).
thf(567,plain,
! [TA: $tType,A: set @ TA] : ( refl_on @ TA @ A @ ( id_on @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(174,axiom,
member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ y @ z ) @ ( getRel @ a @ b @ i @ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_aI) ).
thf(737,plain,
member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ y @ z ) @ ( getRel @ a @ b @ i @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(271,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(223,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_66_all__not__in__conv) ).
thf(900,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)],[223]) ).
thf(50,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(406,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)],[50]) ).
thf(73,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_121_agree__on__trans) ).
thf(477,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)],[73]) ).
thf(195,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_20_prod__induct4) ).
thf(811,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)],[195]) ).
thf(129,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_245_graph__unionI) ).
thf(609,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)],[129]) ).
thf(23,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_le__cases3) ).
thf(323,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(170,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_251_subgraph__subset_I2_J) ).
thf(726,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)],[170]) ).
thf(76,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_160_subgraph__subset_I1_J) ).
thf(483,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)],[76]) ).
thf(205,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ! [C: TA,D: TA] :
( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) )
=> ( total_on @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_total__onI) ).
thf(848,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ! [C: TA,D: TA] :
( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) )
=> ( total_on @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(245,axiom,
! [TA: $tType,A: TA] : ( total_on @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) @ ( insert @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_total__on__singleton) ).
thf(964,plain,
! [TA: $tType,A: TA] : ( total_on @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) @ ( insert @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ A @ A ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(238,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA] :
( ( sym @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_symD) ).
thf(943,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA] :
( ( sym @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(150,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(668,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(207,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_emptyE) ).
thf(858,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(35,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_94_labeled__graph_Oinject) ).
thf(367,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)],[35]) ).
thf(94,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_237_graph__union__idemp_I3_J) ).
thf(521,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)],[94]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(278,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(259,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_123_graph__homomorphism__nonempty) ).
thf(1000,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)],[259]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_bot__fun__def) ).
thf(299,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_order__refl) ).
thf(267,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(61,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_244_labeled__graph_Ocollapse) ).
thf(438,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)],[61]) ).
thf(230,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_184_subsetD) ).
thf(922,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)],[230]) ).
thf(45,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_176_subset__trans) ).
thf(394,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)],[45]) ).
thf(254,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_79_insertI2) ).
thf(986,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)],[254]) ).
thf(72,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_181_equalityD1) ).
thf(473,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)],[72]) ).
thf(79,axiom,
preorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_12) ).
thf(490,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(57,axiom,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_Set_Ois__empty__def) ).
thf(426,plain,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(189,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA] :
( ( sym @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_symE) ).
thf(795,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA] :
( ( sym @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(104,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_220_agree__on__subg__compose) ).
thf(548,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)],[104]) ).
thf(232,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TA,D: TC,E: TB,F: TB,G: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( product_prod @ TC @ ( product_prod @ TA @ TA ) ) @ ( product_prod @ TC @ ( product_prod @ TB @ TB ) ) ) @ ( product_Pair @ ( product_prod @ TC @ ( product_prod @ TA @ TA ) ) @ ( product_prod @ TC @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TC @ ( product_prod @ TA @ TA ) @ A @ ( product_Pair @ TA @ TA @ B @ C ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TB ) @ D @ ( product_Pair @ TB @ TB @ E @ F ) ) ) @ ( on_triple @ TA @ TB @ TC @ G ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ E ) @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_on__tripleD_I2_J) ).
thf(927,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TA,D: TC,E: TB,F: TB,G: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ ( product_prod @ TC @ ( product_prod @ TA @ TA ) ) @ ( product_prod @ TC @ ( product_prod @ TB @ TB ) ) ) @ ( product_Pair @ ( product_prod @ TC @ ( product_prod @ TA @ TA ) ) @ ( product_prod @ TC @ ( product_prod @ TB @ TB ) ) @ ( product_Pair @ TC @ ( product_prod @ TA @ TA ) @ A @ ( product_Pair @ TA @ TA @ B @ C ) ) @ ( product_Pair @ TC @ ( product_prod @ TB @ TB ) @ D @ ( product_Pair @ TB @ TB @ E @ F ) ) ) @ ( on_triple @ TA @ TB @ TC @ G ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ E ) @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(132,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_30_refl__on__domain) ).
thf(617,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)],[132]) ).
thf(26,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_7) ).
thf(342,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(106,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_249_labeled__graph_Osel_I1_J) ).
thf(553,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)],[106]) ).
thf(142,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_185_in__mono) ).
thf(648,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)],[142]) ).
thf(78,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_Collect__empty__eq__bot) ).
thf(487,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(183,axiom,
( g
= ( restrict @ a @ b @ g ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_g) ).
thf(776,plain,
( g
= ( restrict @ a @ b @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(206,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: TA] :
( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ( maintained @ TA @ nat @ TB @ ( standa1805702094y_rule @ TA @ B ) @ A )
=> ( sym @ TB @ ( getRel @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_symmetry__rule) ).
thf(855,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: TA] :
( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ( maintained @ TA @ nat @ TB @ ( standa1805702094y_rule @ TA @ B ) @ A )
=> ( sym @ TB @ ( getRel @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(139,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_12_prod__cases5) ).
thf(640,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)],[139]) ).
thf(14,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_ord__eq__le__trans) ).
thf(295,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(213,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_36_refl__onD) ).
thf(872,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)],[213]) ).
thf(164,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_21_prod__induct3) ).
thf(707,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)],[164]) ).
thf(51,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_180_equalityD2) ).
thf(409,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)],[51]) ).
thf(166,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_9_Pair__inject) ).
thf(712,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)],[166]) ).
thf(260,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_26_old_Oprod_Orec) ).
thf(1003,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)],[260]) ).
thf(152,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_50_semantics__in__vertices_I2_J) ).
thf(673,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)],[152]) ).
thf(62,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_253_labeled__graph_Osplit__sel) ).
thf(441,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)],[62]) ).
thf(36,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_255_labeled__graph_Ocase__eq__if) ).
thf(370,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)],[36]) ).
thf(167,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_76_insert__absorb) ).
thf(717,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)],[167]) ).
thf(68,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_61_nonempty__rule) ).
thf(463,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)],[68]) ).
thf(194,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_7_surj__pair) ).
thf(808,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)],[194]) ).
thf(32,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_159_graph__homomorphism__Id) ).
thf(359,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)],[32]) ).
thf(140,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_31_refl__onD2) ).
thf(643,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)],[140]) ).
thf(177,axiom,
! [TA: $tType] :
( ( trans @ TA )
= ( ^ [A: set @ ( product_prod @ TA @ TA )] :
! [B: TA,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_Relation_Otrans__def) ).
thf(744,plain,
! [TA: $tType] :
( ( trans @ TA )
= ( ^ [A: set @ ( product_prod @ TA @ TA )] :
! [B: TA,C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(145,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_11_prod__cases4) ).
thf(656,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)],[145]) ).
thf(125,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_empty__iff) ).
thf(600,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(210,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_182_subset__eq) ).
thf(864,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)],[210]) ).
thf(262,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_17_prod__induct7) ).
thf(1008,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)],[262]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_ord__le__eq__subst) ).
thf(314,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
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_167_subrelI) ).
thf(595,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(130,axiom,
! [TA: $tType] : ( order_preorder_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_preorder__on__empty) ).
thf(612,plain,
! [TA: $tType] : ( order_preorder_on @ TA @ ( bot_bot @ ( set @ TA ) ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(215,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_163_Id__on__iff) ).
thf(876,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)],[215]) ).
thf(134,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_10_prod__cases3) ).
thf(627,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)],[134]) ).
thf(65,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_183_equalityE) ).
thf(450,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)],[65]) ).
thf(107,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_158_subgraph__restrict) ).
thf(556,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)],[107]) ).
thf(151,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: TA,E: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( set @ TA ) @ C @ ( equiv_quotient @ TA @ A @ B ) )
=> ( ( member @ TA @ D @ C )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B )
=> ( member @ TA @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_in__quotient__imp__closed) ).
thf(671,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: TA,E: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( set @ TA ) @ C @ ( equiv_quotient @ TA @ A @ B ) )
=> ( ( member @ TA @ D @ C )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B )
=> ( member @ TA @ E @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(224,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_77_insert__ident) ).
thf(903,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)],[224]) ).
thf(220,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA > TB,C: TA,D: TA] :
( ( equiv_congruent @ TA @ TB @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( ( B @ C )
= ( B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_congruentD) ).
thf(891,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA > TB,C: TA,D: TA] :
( ( equiv_congruent @ TA @ TB @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( ( B @ C )
= ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(263,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_70_equals0I) ).
thf(1010,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)],[263]) ).
thf(204,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA > TB] :
( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( ( B @ C )
= ( B @ D ) ) )
=> ( equiv_congruent @ TA @ TB @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_congruentI) ).
thf(844,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA > TB] :
( ! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( ( B @ C )
= ( B @ D ) ) )
=> ( equiv_congruent @ TA @ TB @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(234,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_62_insertCI) ).
thf(931,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)],[234]) ).
thf(100,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( ( bot_bot @ ( set @ ( set @ TA ) ) )
= ( equiv_quotient @ TA @ A @ B ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_quotient__is__empty2) ).
thf(539,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( ( bot_bot @ ( set @ ( set @ TA ) ) )
= ( equiv_quotient @ TA @ A @ B ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(95,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_151_subset__empty) ).
thf(524,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)],[95]) ).
thf(117,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_227_consequence__graphD_I3_J) ).
thf(581,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)],[117]) ).
thf(17,axiom,
ord @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_4) ).
thf(304,plain,
ord @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(144,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_161_Id__onE) ).
thf(652,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)],[144]) ).
thf(43,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_15) ).
thf(390,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(136,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_246_restrict__subsD) ).
thf(632,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)],[136]) ).
thf(48,axiom,
! [TA: $tType,A: set @ TA] : ( trans @ TA @ ( id_on @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_trans__Id__on) ).
thf(401,plain,
! [TA: $tType,A: set @ TA] : ( trans @ TA @ ( id_on @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(186,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( set @ TA ) @ C @ ( equiv_quotient @ TA @ A @ B ) )
=> ( C
!= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_in__quotient__imp__non__empty) ).
thf(786,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( set @ TA ) @ C @ ( equiv_quotient @ TA @ A @ B ) )
=> ( C
!= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(185,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_44_equivalence) ).
thf(781,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)],[185]) ).
thf(257,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: TA,E: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( set @ TA ) @ C @ ( equiv_quotient @ TA @ A @ B ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ D @ ( insert @ TA @ E @ ( bot_bot @ ( set @ TA ) ) ) ) @ C )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_in__quotient__imp__in__rel) ).
thf(995,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: TA,E: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( set @ TA ) @ C @ ( equiv_quotient @ TA @ A @ B ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ D @ ( insert @ TA @ E @ ( bot_bot @ ( set @ TA ) ) ) ) @ C )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(120,axiom,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_is__singleton__the__elem) ).
thf(588,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(161,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_5_prod_Oinject) ).
thf(699,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)],[161]) ).
thf(244,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA > TB,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( equiv_congruent @ TA @ TB @ B @ C )
=> ( ( member @ TA @ D @ A )
=> ( ( bNF_Greatest_univ @ TA @ TB @ C @ ( equiv_proj @ TA @ TA @ B @ D ) )
= ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_univ__commute) ).
thf(961,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA > TB,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( equiv_congruent @ TA @ TB @ B @ C )
=> ( ( member @ TA @ D @ A )
=> ( ( bNF_Greatest_univ @ TA @ TB @ C @ ( equiv_proj @ TA @ TA @ B @ D ) )
= ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(196,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA > TA > TB] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ! [D: TA,E: TA] :
( ( member @ TA @ D @ A )
=> ( ( member @ TA @ E @ A )
=> ( ( C @ D @ E )
= ( C @ E @ D ) ) ) )
=> ( ! [D: TA,E: TA,F: TA] :
( ( member @ TA @ F @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B )
=> ( ( C @ F @ D )
= ( C @ F @ E ) ) ) )
=> ( equiv_congruent2 @ TA @ TA @ TB @ B @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_congruent2__commuteI) ).
thf(813,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA > TA > TB] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ! [D: TA,E: TA] :
( ( member @ TA @ D @ A )
=> ( ( member @ TA @ E @ A )
=> ( ( C @ D @ E )
= ( C @ E @ D ) ) ) )
=> ( ! [D: TA,E: TA,F: TA] :
( ( member @ TA @ F @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ B )
=> ( ( C @ F @ D )
= ( C @ F @ E ) ) ) )
=> ( equiv_congruent2 @ TA @ TA @ TB @ B @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(90,axiom,
order_bot @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder__bot_1) ).
thf(510,plain,
order_bot @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(233,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_18_prod__induct6) ).
thf(929,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)],[233]) ).
thf(199,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_224_least__consequence__graphI) ).
thf(832,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)],[199]) ).
thf(99,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_254_labeled__graph_Ocase) ).
thf(536,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)],[99]) ).
thf(191,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_27_maintained__refl) ).
thf(800,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)],[191]) ).
thf(133,axiom,
! [TA: $tType,A: set @ TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [B: TA,C: TA] :
( ( member @ TA @ B @ A )
=> ( ( member @ TA @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_is__singletonI_H) ).
thf(620,plain,
! [TA: $tType,A: set @ TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [B: TA,C: TA] :
( ( member @ TA @ B @ A )
=> ( ( member @ TA @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(179,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TB,D: set @ ( product_prod @ TB @ TB ),E: TA > TB > TC] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( equiv_equiv @ TB @ C @ D )
=> ( ! [F: TA,G: TA,H: TB] :
( ( member @ TB @ H @ C )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ F @ G ) @ B )
=> ( ( E @ F @ H )
= ( E @ G @ H ) ) ) )
=> ( ! [F: TB,G: TB,H: TA] :
( ( member @ TA @ H @ A )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ F @ G ) @ D )
=> ( ( E @ H @ F )
= ( E @ H @ G ) ) ) )
=> ( equiv_congruent2 @ TA @ TB @ TC @ B @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_congruent2I) ).
thf(752,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: set @ TB,D: set @ ( product_prod @ TB @ TB ),E: TA > TB > TC] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( equiv_equiv @ TB @ C @ D )
=> ( ! [F: TA,G: TA,H: TB] :
( ( member @ TB @ H @ C )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ F @ G ) @ B )
=> ( ( E @ F @ H )
= ( E @ G @ H ) ) ) )
=> ( ! [F: TB,G: TB,H: TA] :
( ( member @ TA @ H @ A )
=> ( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ F @ G ) @ D )
=> ( ( E @ H @ F )
= ( E @ H @ G ) ) ) )
=> ( equiv_congruent2 @ TA @ TB @ TC @ B @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(64,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_68_empty__Collect__eq) ).
thf(447,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)],[64]) ).
thf(59,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_29_restrict__idemp) ).
thf(432,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)],[59]) ).
thf(200,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_85_singleton__iff) ).
thf(835,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)],[200]) ).
thf(187,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_49_semantics__in__vertices_I1_J) ).
thf(790,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)],[187]) ).
thf(37,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_119_agree__on__comm) ).
thf(373,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)],[37]) ).
thf(211,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_128_extensible__refl) ).
thf(867,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)],[211]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_bot__apply) ).
thf(273,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_le__funE) ).
thf(305,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(88,axiom,
bot @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Obot_5) ).
thf(506,plain,
bot @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(148,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_129_maintainedD) ).
thf(664,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)],[148]) ).
thf(197,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_222_subgraph__semantics) ).
thf(828,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)],[197]) ).
thf(137,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA,D: TA] :
( ( trans @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_transD) ).
thf(635,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA,D: TA] :
( ( trans @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(160,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ ( product_prod @ TB @ TB ),C: TB > TA,D: set @ TA] :
( ( equiv_equiv @ TB @ A @ B )
=> ( ( equiv_congruent @ TB @ TA @ B @ C )
=> ( ! [E: TB] :
( ( member @ TB @ E @ A )
=> ( member @ TA @ ( C @ E ) @ D ) )
=> ! [E: set @ TB] :
( ( member @ ( set @ TB ) @ E @ ( equiv_quotient @ TB @ A @ B ) )
=> ( member @ TA @ ( bNF_Greatest_univ @ TB @ TA @ C @ E ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_univ__preserves) ).
thf(696,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ ( product_prod @ TB @ TB ),C: TB > TA,D: set @ TA] :
( ( equiv_equiv @ TB @ A @ B )
=> ( ( equiv_congruent @ TB @ TA @ B @ C )
=> ( ! [E: TB] :
( ( member @ TB @ E @ A )
=> ( member @ TA @ ( C @ E ) @ D ) )
=> ! [E: set @ TB] :
( ( member @ ( set @ TB ) @ E @ ( equiv_quotient @ TB @ A @ B ) )
=> ( member @ TA @ ( bNF_Greatest_univ @ TB @ TA @ C @ E ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(168,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_24_getRel__dom_I2_J) ).
thf(720,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)],[168]) ).
thf(242,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_53_refl__on__empty) ).
thf(955,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)],[242]) ).
thf(222,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_230_least__def) ).
thf(897,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)],[222]) ).
thf(180,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_179_subset__iff) ).
thf(767,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)],[180]) ).
thf(202,axiom,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_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)],[202]) ).
thf(171,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( A
= ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_less__by__empty) ).
thf(728,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA )] :
( ( A
= ( bot_bot @ ( set @ ( product_prod @ TA @ TA ) ) ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(115,axiom,
! [TA: $tType,A: set @ TA] :
( ( is_singleton @ TA @ A )
=> ~ ! [B: TA] :
( A
!= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_is__singletonE) ).
thf(575,plain,
! [TA: $tType,A: set @ TA] :
( ( is_singleton @ TA @ A )
=> ~ ! [B: TA] :
( A
!= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(208,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_8_prod__cases) ).
thf(860,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)],[208]) ).
thf(256,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: TA] :
( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ( maintained @ TA @ nat @ TB @ ( standa2114124375e_rule @ TA @ B ) @ A )
=> ( trans @ TB @ ( getRel @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_transitive__rule) ).
thf(992,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB,B: TA] :
( ( A
= ( restrict @ TA @ TB @ A ) )
=> ( ( maintained @ TA @ nat @ TB @ ( standa2114124375e_rule @ TA @ B ) @ A )
=> ( trans @ TB @ ( getRel @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(169,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TC @ TC ),B: set @ ( product_prod @ TA @ TA ),C: TC > TA > TB,D: TC,E: TC,F: TA,G: TA] :
( ( equiv_congruent2 @ TC @ TA @ TB @ A @ B @ C )
=> ( ( member @ ( product_prod @ TC @ TC ) @ ( product_Pair @ TC @ TC @ D @ E ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ F @ G ) @ B )
=> ( ( C @ D @ F )
= ( C @ E @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_congruent2D) ).
thf(723,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: set @ ( product_prod @ TC @ TC ),B: set @ ( product_prod @ TA @ TA ),C: TC > TA > TB,D: TC,E: TC,F: TA,G: TA] :
( ( equiv_congruent2 @ TC @ TA @ TB @ A @ B @ C )
=> ( ( member @ ( product_prod @ TC @ TC ) @ ( product_Pair @ TC @ TC @ D @ E ) @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ F @ G ) @ B )
=> ( ( C @ D @ F )
= ( C @ E @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(252,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_228_consequence__graphD_I1_J) ).
thf(982,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)],[252]) ).
thf(85,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_171_subset__insertI2) ).
thf(501,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)],[85]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA )
=> ( order_bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__bot) ).
thf(337,plain,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA )
=> ( order_bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(237,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_127_extensible__refl__concr) ).
thf(940,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)],[237]) ).
thf(102,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_174_Collect__mono__iff) ).
thf(543,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)],[102]) ).
thf(153,axiom,
! [TA: $tType,A: TA] : ( order_1409979114der_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_91_linear__order__on__singleton) ).
thf(676,plain,
! [TA: $tType,A: TA] : ( order_1409979114der_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)],[153]) ).
thf(80,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_168_insert__mono) ).
thf(491,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)],[80]) ).
thf(82,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_97_labeled__graph_Oinduct) ).
thf(496,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)],[82]) ).
thf(34,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_214_subset__singleton__iff) ).
thf(364,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)],[34]) ).
thf(248,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_23_getRel__dom_I1_J) ).
thf(972,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)],[248]) ).
thf(20,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_linorder__wlog) ).
thf(309,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(146,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_19_prod__induct5) ).
thf(659,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)],[146]) ).
thf(1013,plain,
$false,
inference(e,[status(thm)],[645,479,518,468,666,481,977,683,276,741,379,511,614,269,385,533,550,500,797,945,747,913,709,841,288,565,570,504,838,702,949,802,344,542,460,559,969,606,284,770,881,416,924,591,321,376,485,348,353,966,602,280,692,734,396,988,265,507,527,307,678,661,546,793,910,778,952,302,862,598,630,429,957,894,916,361,879,435,830,493,578,874,650,1006,388,356,593,869,420,980,403,471,884,339,686,637,679,997,515,738,457,984,569,503,938,805,398,530,888,773,586,906,264,689,444,584,423,732,286,413,562,975,391,936,382,572,498,466,919,704,350,604,419,567,737,271,900,406,477,811,609,323,726,483,848,964,943,668,858,367,521,278,1000,299,267,438,922,394,986,473,490,426,795,548,927,617,342,553,648,487,776,855,640,295,872,707,409,712,1003,673,441,370,717,463,808,359,643,744,656,600,864,1008,314,595,612,876,627,450,556,671,903,891,1010,844,931,539,524,581,304,652,390,632,401,786,781,995,588,699,961,813,510,929,832,536,800,620,752,447,432,835,790,373,867,273,305,506,664,828,635,696,720,955,897,767,839,728,575,860,992,723,982,501,337,940,543,676,491,496,364,972,309,659]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP175^2 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 6 14:44:09 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.94/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.91/1.17 % [INFO] Parsing done (271ms).
% 1.91/1.18 % [INFO] Running in sequential loop mode.
% 2.75/1.39 % [INFO] eprover registered as external prover.
% 2.75/1.39 % [INFO] cvc4 registered as external prover.
% 2.75/1.39 % [INFO] Scanning for conjecture ...
% 2.91/1.50 % [INFO] Found a conjecture and 278 axioms. Running axiom selection ...
% 3.35/1.59 % [INFO] Axiom selection finished. Selected 261 axioms (removed 17 axioms).
% 4.24/1.81 % [INFO] Problem is higher-order (TPTP THF).
% 4.24/1.83 % [INFO] Type checking passed.
% 4.24/1.83 % [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 ...
% 173.51/152.88 % External prover 'e' found a proof!
% 173.51/152.88 % [INFO] Killing All external provers ...
% 173.51/152.88 % Time passed: 152351ms (effective reasoning time: 151702ms)
% 173.51/152.88 % 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)>
% 173.51/152.88 % Axioms used in derivation (261): fact_78_Set_Oset__insert, tcon_fun___Orderings_Obot, fact_253_labeled__graph_Osplit__sel, fact_40_preorder__on__def, fact_67_Collect__empty__eq, fact_134_quotient__is__empty2, fact_9_Pair__inject, fact_185_in__mono, fact_209_le__funI, fact_0__092_060open_062refl__on_A_Ivertices_AG_J_A_IgetRel_AI_AG_J_A_092_060and_062_A_I_092_060forall_062x_Ay_O_A_Ix_M_Ay_J_A_092_060in_062_AgetRel_AI_AG_A_092_060longrightarrow_062_A_Iy_M_Ax_J_A_092_060in_062_AgetRel_AI_AG_J_A_092_060and_062_Atrans_A_IgetRel_AI_AG_J_092_060close_062, fact_136_quotient__empty, fact_247_labeled__graph_Oexhaust__sel, fact_118_graph__homomorphism__empty, fact_231_less__by__empty, fact_154_singleton__insert__inj__eq, fact_146_getRel__subgraph, fact_51_refl__on__singleton, fact_27_maintained__refl, fact_37_refl__onD1, tcon_Nat_Onat___Orderings_Olinorder, fact_11_prod__cases4, fact_18_prod__induct6, fact_108_is__singleton__the__elem, fact_112_is__singletonE, tcon_HOL_Obool___Orderings_Opreorder_12, fact_75_insert__eq__iff, fact_254_labeled__graph_Ocase, fact_249_labeled__graph_Osel_I1_J, fact_69_ex__in__conv, fact_240_graph__union__preserves__restrict, fact_153_Id__onI, tcon_HOL_Obool___Orderings_Obot_16, fact_172_trans__Id__on, fact_94_labeled__graph_Oinject, fact_171_subset__insertI2, fact_142_congruent2D, fact_250_graph__union__iff, fact_36_refl__onD, fact_226_least__consequence__graph__def, fact_98_bot__empty__eq, fact_222_subgraph__semantics, fact_189_linorder__wlog, fact_109_is__singletonI_H, fact_22_vertices__restrict, fact_227_consequence__graphD_I3_J, fact_224_least__consequence__graphI, fact_215_subgraph__trans, fact_106_total__on__empty, fact_62_insertCI, fact_179_subset__iff, tcon_fun___Orderings_Oord, fact_248_labeled__graph_Oexpand, fact_84_doubleton__eq__iff, fact_193_ord__le__eq__trans, fact_229_proj__in__iff, fact_57_on__tripleD_I1_J, fact_208_le__fun__def, fact_147_order__refl, fact_15_old_Oprod_Oinducts, fact_38_mA, fact_228_consequence__graphD_I1_J, fact_212_sym__Id__on, fact_243_subgraph__def2, fact_161_Id__onE, tcon_HOL_Obool___Orderings_Oord_15, fact_144_in__quotient__imp__in__rel, fact_43_refl__trans__impl__idempotent, fact_120_agree__on__refl, fact_255_labeled__graph_Ocase__eq__if, fact_155_singleton__insert__inj__eq_H, fact_168_insert__mono, fact_219_in__quotient__imp__subset, fact_199_le__cases, fact_223_proj__iff, fact_6_old_Oprod_Oinject, fact_216_subgraph__preserves__hom, fact_88_bot__apply, fact_162_Id__on__eqI, fact_81_insertE, fact_181_equalityD1, fact_232_insert__subsetI, fact_194_ord__eq__le__trans, fact_115_equivI, fact_5_prod_Oinject, tcon_HOL_Obool___Orderings_Oorder__bot_11, fact_21_prod__induct3, fact_131_congruent2I, fact_19_prod__induct5, fact_205_ord__eq__le__subst, fact_204_ord__le__eq__subst, fact_46_Collect__mem__eq, fact_44_equivalence, tcon_Set_Oset___Orderings_Obot_10, fact_244_labeled__graph_Ocollapse, fact_151_subset__empty, fact_138_quotient__eq__iff, fact_178_subset__refl, fact_90_is__singletonI, fact_26_old_Oprod_Orec, fact_14_prod__cases7, fact_233_ssubst__Pair__rhs, fact_34_transI, fact_99_bot__set__def, fact_130_Set_Ois__empty__def, fact_210_le__funE, fact_213_subset__singletonD, fact_63_insert__iff, fact_58_on__tripleD_I2_J, fact_191_order__trans, fact_64_insert__absorb2, fact_150_empty__subsetI, fact_103_symD, fact_183_equalityE, fact_176_subset__trans, fact_230_least__def, fact_52_preorder__on__empty, fact_24_getRel__dom_I2_J, tcon_Set_Oset___Orderings_Oord_9, fact_220_agree__on__subg__compose, fact_77_insert__ident, fact_29_restrict__idemp, fact_50_semantics__in__vertices_I2_J, fact_235_univ__commute, fact_149_subsetI, fact_201_linear, fact_164_bot_Oextremum__uniqueI, fact_71_equals0D, fact_234_subset__emptyI, fact_95_graph__empty__e, fact_152_insert__subset, fact_87_the__elem__eq, fact_211_le__funD, fact_41_on__triple, fact_13_prod__cases6, fact_10_prod__cases3, fact_49_semantics__in__vertices_I1_J, fact_85_singleton__iff, fact_7_surj__pair, fact_177_Collect__mono, fact_197_le__cases3, fact_121_agree__on__trans, fact_116_equiv__def, fact_45_mem__Collect__eq, fact_1_aI, fact_221_maintainedD2, fact_127_extensible__refl__concr, fact_200_eq__refl, fact_128_extensible__refl, fact_72_emptyE, fact_80_insertI1, fact_214_subset__singleton__iff, fact_101_symI, fact_239_graph__union__idemp_I1_J, fact_79_insertI2, fact_28_reflexivity__rule, fact_123_graph__homomorphism__nonempty, fact_59_on__tripleD_I3_J, fact_102_symE, fact_86_singletonD, fact_217_congruentD, tcon_Nat_Onat___Orderings_Opreorder_2, fact_165_bot_Oextremum__unique, fact_133_eq__equiv__class__iff2, fact_141_congruent2I_H, fact_237_graph__union__idemp_I3_J, fact_167_subrelI, tcon_Nat_Onat___Orderings_Oorder__bot_1, fact_251_subgraph__subset_I2_J, fact_110_lnear__order__on__empty, fact_65_empty__iff, fact_12_prod__cases5, fact_47_Collect__cong, fact_93_symmetry__rule, tcon_fun___Orderings_Oorder__bot, tcon_HOL_Obool___Orderings_Olinorder_13, fact_156_Id__on__empty, fact_70_equals0I, fact_126_maintainedI, fact_61_nonempty__rule, fact_124_Collect__empty__eq__bot, fact_140_in__quotient__imp__non__empty, fact_25_transitive__rule, fact_225_leastI, fact_60_singletonI, fact_132_congruent2__commuteI, fact_180_equalityD2, fact_218_congruentI, fact_105_total__onI, fact_55_idempotent__impl__trans, tcon_fun___Orderings_Opreorder, fact_173_refl__on__Id__on, fact_23_getRel__dom_I1_J, fact_159_graph__homomorphism__Id, fact_42_maintained__then__fin__maintained, fact_160_subgraph__subset_I1_J, fact_8_prod__cases, fact_96_labeled__graph_Oexhaust, fact_236_subgraph__def, fact_39_internal__case__prod__conv, fact_89_graph__single, fact_182_subset__eq, fact_76_insert__absorb, fact_97_labeled__graph_Oinduct, fact_184_subsetD, fact_175_set__eq__subset, fact_82_singleton__inject, fact_157_subgraph__refl, fact_122_graph__homomorphism__semantics, fact_163_Id__on__iff, fact_31_refl__onD2, fact_238_graph__union__idemp_I2_J, fact_111_bot__fun__def, tcon_Nat_Onat___Orderings_Oord_4, fact_242_relImage__proj, fact_252_labeled__graph_Osplit__sel__asm, fact_246_restrict__subsD, fact_125_extensibleI, fact_114_equivE, fact_17_prod__induct7, fact_139_quotient__eqI, tcon_Set_Oset___Orderings_Oorder__bot_6, fact_16_old_Oprod_Oexhaust, fact_129_maintainedD, fact_4_eq, tcon_Set_Oset___Orderings_Opreorder_7, fact_3_m, fact_56_trans__empty, fact_100_sym__def, fact_54_trans__singleton, fact_74_insert__commute, fact_113_is__singleton__def, fact_241_univ__preserves, fact_66_all__not__in__conv, fact_169_subset__insert, fact_158_subgraph__restrict, fact_91_linear__order__on__singleton, fact_104_total__on__def, tcon_Nat_Onat___Orderings_Obot_5, fact_2_g, fact_92_total__on__singleton, fact_20_prod__induct4, fact_148_subset__antisym, fact_83_insert__not__empty, fact_53_refl__on__empty, fact_174_Collect__mono__iff, fact_117_agree__on__empty, fact_166_bot_Oextremum, fact_143_congruent2__implies__congruent, fact_32_transD, fact_119_agree__on__comm, fact_245_graph__unionI, fact_137_in__quotient__imp__closed, fact_135_quotient__is__empty, fact_68_empty__Collect__eq, fact_73_mk__disjoint__insert, fact_35_Relation_Otrans__def, fact_170_subset__insertI, fact_30_refl__on__domain, fact_107_labeled__graph_Osel_I2_J, fact_33_transE, fact_145_same__fstI
% 173.51/152.88 % No. of inferences in proof: 526
% 173.51/152.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 152351 ms resp. 151702 ms w/o parsing
% 174.21/153.04 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 174.21/153.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------