%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP176^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:07:04 AM UTC 2026
% Result : Theorem 163.87s 136.78s
% Output : Refutation 165.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 275
% Syntax : Number of formulae : 552 ( 231 unt; 0 typ; 0 def)
% Number of atoms : 2211 ( 531 equ; 12 cnn)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 9379 ( 134 ~; 19 |; 92 &;8532 @)
% ( 0 <=>; 602 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 254 ( 254 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 45 usr; 10 con; 0-6 aty)
% Number of variables : 2265 ( 162 ^;2075 !; 28 ?;2265 :)
% Comments :
%------------------------------------------------------------------------------
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(bot_decl,type,
bot:
!>[TA: $tType] : $o ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(order_bot_decl,type,
order_bot:
!>[TA: $tType] : $o ).
thf(bNF_Greatest_univ_decl,type,
bNF_Greatest_univ:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > TA ) ).
thf(equiv_congruent_decl,type,
equiv_congruent:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TB ) ) > ( TB > TA ) > $o ) ).
thf(equiv_congruent2_decl,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_decl,type,
equiv_equiv:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(equiv_proj_decl,type,
equiv_proj:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > TB > ( set @ TA ) ) ).
thf(hilbert_Eps_decl,type,
hilbert_Eps:
!>[TA: $tType] : ( ( TA > $o ) > TA ) ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(standard_S_Idt_decl,type,
standard_S_Idt:
!>[TA: $tType] : ( standard_Constant @ TA ) ).
thf(getRel_decl,type,
getRel:
!>[TA: $tType,TB: $tType] : ( TB > ( labeled_graph @ TB @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) ) ).
thf(graph_homomorphism_decl,type,
graph_homomorphism:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( labeled_graph @ TC @ TB ) > ( labeled_graph @ TC @ TA ) > ( set @ ( product_prod @ TB @ TA ) ) > $o ) ).
thf(graph_union_decl,type,
graph_union:
!>[TA: $tType,TB: $tType] : ( ( labeled_graph @ TB @ TA ) > ( labeled_graph @ TB @ TA ) > ( labeled_graph @ TB @ TA ) ) ).
thf(labeled_LG_decl,type,
labeled_LG:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ) ) > ( set @ TA ) > ( labeled_graph @ TB @ TA ) ) ).
thf(labele1974067554_graph_decl,type,
labele1974067554_graph:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( ( set @ ( product_prod @ TC @ ( product_prod @ TB @ TB ) ) ) > ( set @ TB ) > TA ) > ( labeled_graph @ TC @ TB ) > TA ) ).
thf(labeled_edges_decl,type,
labeled_edges:
!>[TA: $tType,TB: $tType] : ( ( labeled_graph @ TB @ TA ) > ( set @ ( product_prod @ TB @ ( product_prod @ TA @ TA ) ) ) ) ).
thf(labeled_vertices_decl,type,
labeled_vertices:
!>[TA: $tType,TB: $tType] : ( ( labeled_graph @ TB @ TA ) > ( set @ TA ) ) ).
thf(restrict_decl,type,
restrict:
!>[TA: $tType,TB: $tType] : ( ( labeled_graph @ TB @ TA ) > ( labeled_graph @ TB @ TA ) ) ).
thf(order_1409979114der_on_decl,type,
order_1409979114der_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(product_rec_prod_decl,type,
product_rec_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(image_decl,type,
image:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > ( set @ TB ) > ( set @ TA ) ) ).
thf(converse_decl,type,
converse:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > ( set @ ( product_prod @ TA @ TB ) ) ) ).
thf(refl_on_decl,type,
refl_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(total_on_decl,type,
total_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(is_singleton_decl,type,
is_singleton:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(the_elem_decl,type,
the_elem:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(g_decl,type,
g: labeled_graph @ ( standard_Constant @ a ) @ b ).
thf(p_decl,type,
p: b > b > $o ).
thf(f_decl,type,
f: b > b ).
thf(x_decl,type,
x: b ).
thf(y_decl,type,
y: b ).
thf(237,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_221_subset__insertI) ).
thf(1036,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)],[237]) ).
thf(233,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_20_insertCI) ).
thf(1024,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)],[233]) ).
thf(27,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_predicate1I) ).
thf(365,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(158,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_236_univ__commute) ).
thf(760,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)],[158]) ).
thf(64,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_78_old_Oprod_Oinject) ).
thf(479,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)],[64]) ).
thf(180,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) @ ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_equiv__class__subset) ).
thf(846,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) @ ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(79,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_188_eq__refl) ).
thf(518,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)],[79]) ).
thf(211,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_62_doubleton__eq__iff) ).
thf(941,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)],[211]) ).
thf(199,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_bot_Oextremum) ).
thf(909,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(17,axiom,
bot @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_10) ).
thf(333,plain,
bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(253,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( converse @ TA @ TB @ C ) )
= ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_converse__iff) ).
thf(1083,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( converse @ TA @ TB @ C ) )
= ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(59,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_146_labeled__graph_Osel_I2_J) ).
thf(468,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)],[59]) ).
thf(164,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ? [C: TA] :
( ( A @ C )
& ! [D: TA] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ( A @ B )
=> ( ( hilbert_Eps @ TA @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_some1__equality) ).
thf(777,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ? [C: TA] :
( ( A @ C )
& ! [D: TA] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ( A @ B )
=> ( ( hilbert_Eps @ TA @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType] :
( ( labeled_vertices @ TA @ TB )
= ( labele1974067554_graph @ TA @ TB @ ( set @ TB )
@ ^ [A: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ),B: set @ TB] : B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_vertices__def) ).
thf(555,plain,
! [TA: $tType,TB: $tType] :
( ( labeled_vertices @ TA @ TB )
= ( labele1974067554_graph @ TA @ TB @ ( set @ TB )
@ ^ [A: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ),B: set @ TB] : B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(231,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_231_congruent2I) ).
thf(1005,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)],[231]) ).
thf(134,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_227_congruent2D) ).
thf(683,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)],[134]) ).
thf(151,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( B @ D ) )
=> ( ! [D: TA] :
( ( ( member @ TA @ D @ A )
& ( B @ D ) )
=> ( C @ D ) )
=> ( C
@ ( hilbert_Eps @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ A )
& ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_someI2__bex) ).
thf(730,plain,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( B @ D ) )
=> ( ! [D: TA] :
( ( ( member @ TA @ D @ A )
& ( B @ D ) )
=> ( C @ D ) )
=> ( C
@ ( hilbert_Eps @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ A )
& ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(227,axiom,
! [TA: $tType,A: TA] :
( ( collect @ TA @ ( (=) @ TA @ A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_singleton__conv2) ).
thf(994,plain,
! [TA: $tType,A: TA] :
( ( collect @ TA @ ( (=) @ TA @ A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(270,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_205_Collect__mono) ).
thf(1142,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)],[270]) ).
thf(106,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_142_graph__empty__e) ).
thf(597,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)],[106]) ).
thf(239,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_133_congruentD) ).
thf(1041,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)],[239]) ).
thf(32,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(385,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(268,axiom,
! [TA: $tType,TB: $tType,A: set @ TB] :
( ( image @ TB @ TA @ ( bot_bot @ ( set @ ( product_prod @ TB @ TA ) ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Image__empty1) ).
thf(1137,plain,
! [TA: $tType,TB: $tType,A: set @ TB] :
( ( image @ TB @ TA @ ( bot_bot @ ( set @ ( product_prod @ TB @ TA ) ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(83,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_rev__predicate1D) ).
thf(533,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(72,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_106_prod__cases3) ).
thf(500,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)],[72]) ).
thf(155,axiom,
equiv_equiv @ b @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_equiv) ).
thf(747,plain,
equiv_equiv @ b @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(85,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_153_labeled__graph_Osplit__sel__asm) ).
thf(538,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)],[85]) ).
thf(207,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ( equiv_equiv @ TA @ C @ A )
=> ( ( equiv_equiv @ TA @ C @ B )
=> ( ( image @ TA @ TA @ A @ ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_refines__equiv__class__eq) ).
thf(930,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ( equiv_equiv @ TA @ C @ A )
=> ( ( equiv_equiv @ TA @ C @ B )
=> ( ( image @ TA @ TA @ A @ ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(276,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_121_refl__onD1) ).
thf(1164,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)],[276]) ).
thf(169,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_225_restrict__subsD) ).
thf(797,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)],[169]) ).
thf(247,axiom,
! [A: b] :
( ( member @ b @ A @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) )
=> ( member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ A @ A ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_A_092_060Longrightarrow_062_A_Ix_M_Ax_J_A_092_060in_062_AgetRel_AS__Idt_AG_092_060close_062) ).
thf(1063,plain,
! [A: b] :
( ( member @ b @ A @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) )
=> ( member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ A @ A ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(20,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_193_ord__eq__le__subst) ).
thf(340,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)],[20]) ).
thf(196,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_30_ex__in__conv) ).
thf(898,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)],[196]) ).
thf(43,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(417,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)],[43]) ).
thf(13,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_196_le__fun__def) ).
thf(320,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)],[13]) ).
thf(50,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_104_prod__cases5) ).
thf(436,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)],[50]) ).
thf(220,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_equiv__class__self) ).
thf(973,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(241,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_Collect__restrict) ).
thf(1046,plain,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(146,axiom,
member @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ b @ b ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ b @ b ) @ ( standard_S_Idt @ a ) @ ( product_Pair @ b @ b @ x @ y ) ) @ ( labeled_edges @ ( standard_Constant @ a ) @ b @ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70__092_060open_062_IS__Idt_M_Ax_M_Ay_J_A_092_060in_062_Aedges_AG_092_060close_062) ).
thf(719,plain,
member @ ( product_prod @ ( standard_Constant @ a ) @ ( product_prod @ b @ b ) ) @ ( product_Pair @ ( standard_Constant @ a ) @ ( product_prod @ b @ b ) @ ( standard_S_Idt @ a ) @ ( product_Pair @ b @ b @ x @ y ) ) @ ( labeled_edges @ ( standard_Constant @ a ) @ b @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(29,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_192_ord__le__eq__subst) ).
thf(372,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)],[29]) ).
thf(114,axiom,
! [A: b] :
( ( ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ A @ ( bot_bot @ ( set @ b ) ) ) )
= ( bot_bot @ ( set @ b ) ) )
= ( ~ ( member @ b @ A @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_r2) ).
thf(619,plain,
! [A: b] :
( ( ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ A @ ( bot_bot @ ( set @ b ) ) ) )
= ( bot_bot @ ( set @ b ) ) )
= ( ~ ( member @ b @ A @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(141,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_singletonI) ).
thf(702,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(157,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ? [C: TA] : ( A @ C )
=> ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( B @ ( hilbert_Eps @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_someI2__ex) ).
thf(751,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ? [C: TA] : ( A @ C )
=> ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( B @ ( hilbert_Eps @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(183,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_38_insert__ident) ).
thf(853,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)],[183]) ).
thf(191,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_126_is__singleton__def) ).
thf(881,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)],[191]) ).
thf(11,axiom,
order_bot @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__bot_6) ).
thf(316,plain,
order_bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(104,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_subset__singletonD) ).
thf(591,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(260,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_19_insert__iff) ).
thf(1109,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)],[260]) ).
thf(123,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_124_is__singletonI_H) ).
thf(646,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)],[123]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: TB > TA > $o] :
( ( A @ B @ C )
=> ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ D )
=> ( D @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_rev__predicate2D) ).
thf(348,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: TB > TA > $o] :
( ( A @ B @ C )
=> ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ D )
=> ( D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(243,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_210_subset__eq) ).
thf(1051,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)],[243]) ).
thf(176,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_215_subrelI) ).
thf(821,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)],[176]) ).
thf(160,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_151_linear__order__on__singleton) ).
thf(766,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)],[160]) ).
thf(36,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_199_le__funD) ).
thf(397,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)],[36]) ).
thf(187,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_220_subset__insert) ).
thf(866,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)],[187]) ).
thf(47,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_161_labeled__graph_Ocase__eq__if) ).
thf(428,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)],[47]) ).
thf(264,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB ),C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: TA] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ A ) @ B )
=> ~ ( member @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_ImageE) ).
thf(1119,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB ),C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: TA] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ A ) @ B )
=> ~ ( member @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(163,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_equiv__class__eq) ).
thf(774,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
=> ( ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(8,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_103_prod__cases6) ).
thf(307,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)],[8]) ).
thf(54,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ 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_191_eq__iff) ).
thf(452,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ 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)],[54]) ).
thf(30,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ 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_183_order__class_Oorder_Oeq__iff) ).
thf(380,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ 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)],[30]) ).
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 @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_refl__onD2) ).
thf(678,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)],[132]) ).
thf(82,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_181_ord__le__eq__trans) ).
thf(529,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)],[82]) ).
thf(127,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TB @ TA ) ) @ A @ ( converse @ TA @ TB @ B ) )
= ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ ( converse @ TB @ TA @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_converse__subset__swap) ).
thf(661,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TB @ TA ) ) @ A @ ( converse @ TA @ TB @ B ) )
= ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ ( converse @ TB @ TA @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(205,axiom,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_the__elem__eq) ).
thf(925,plain,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(273,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( B = C )
& ( A @ C ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( ~ ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( B = C )
& ( A @ C ) ) )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Collect__conv__if2) ).
thf(1153,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( B = C )
& ( A @ C ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( ~ ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( B = C )
& ( A @ C ) ) )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(173,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_37_insert__absorb) ).
thf(810,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)],[173]) ).
thf(249,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_144_total__onI) ).
thf(1067,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)],[249]) ).
thf(245,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_114_getRel__dom_I2_J) ).
thf(1057,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)],[245]) ).
thf(77,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_102_prod__cases7) ).
thf(512,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)],[77]) ).
thf(51,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_order__class_Oorder_Oantisym) ).
thf(439,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(18,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_250_graph__union__idemp_I1_J) ).
thf(334,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)],[18]) ).
thf(214,axiom,
! [TA: $tType,TB: $tType] :
( ( bNF_Greatest_univ @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA] :
( A
@ ( hilbert_Eps @ TA
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_univ__def) ).
thf(957,plain,
! [TA: $tType,TB: $tType] :
( ( bNF_Greatest_univ @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA] :
( A
@ ( hilbert_Eps @ TA
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(177,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_235_subset__emptyI) ).
thf(825,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)],[177]) ).
thf(232,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_216_bot_Oextremum__uniqueI) ).
thf(1021,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)],[232]) ).
thf(6,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_187_le__cases) ).
thf(302,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)],[6]) ).
thf(265,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_211_equalityE) ).
thf(1123,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)],[265]) ).
thf(40,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_antisym__conv) ).
thf(407,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(138,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_bot__apply) ).
thf(693,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(202,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_31_equals0I) ).
thf(916,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)],[202]) ).
thf(235,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_125_refl__on__singleton) ).
thf(1032,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)],[235]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(361,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(116,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ C ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( ~ ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ C ) ) )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_Collect__conv__if) ).
thf(625,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ C ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( ~ ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ C ) ) )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(49,axiom,
preorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_7) ).
thf(435,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(69,axiom,
order @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_8) ).
thf(493,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(95,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_173_singleton__insert__inj__eq) ).
thf(566,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)],[95]) ).
thf(66,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_101_prod__induct3) ).
thf(484,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)],[66]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_bot__fun__def) ).
thf(583,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(80,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_99_prod__induct5) ).
thf(522,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)],[80]) ).
thf(179,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_232_congruent2__commuteI) ).
thf(830,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)],[179]) ).
thf(274,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA )] :
( ( image @ TB @ TA @ A @ ( bot_bot @ ( set @ TB ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_Image__empty2) ).
thf(1159,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA )] :
( ( image @ TB @ TA @ A @ ( bot_bot @ ( set @ TB ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(57,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(461,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(255,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
= ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_pred__equals__eq2) ).
thf(1089,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
= ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(190,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA] :
( ( ( hilbert_Eps @ TA @ A )
= B )
=> ( ( A @ C )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_some__eq__imp) ).
thf(874,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA] :
( ( ( hilbert_Eps @ TA @ A )
= B )
=> ( ( A @ C )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(12,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_109_surj__pair) ).
thf(317,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)],[12]) ).
thf(213,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ! [D: TA] :
( ( A @ D )
=> ( C @ D ) )
=> ( C @ ( hilbert_Eps @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_someI2) ).
thf(948,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ! [D: TA] :
( ( A @ D )
=> ( C @ D ) )
=> ( C @ ( hilbert_Eps @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(149,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_35_insert__commute) ).
thf(725,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)],[149]) ).
thf(33,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( order_1409979114der_on @ TA @ A @ ( converse @ TA @ TA @ B ) )
= ( order_1409979114der_on @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_linear__order__on__converse) ).
thf(388,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( order_1409979114der_on @ TA @ A @ ( converse @ TA @ TA @ B ) )
= ( order_1409979114der_on @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(188,axiom,
! [TA: $tType,A: TA > $o] :
( ( A @ ( hilbert_Eps @ TA @ A ) )
= ( ? [B: TA] : ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_some__eq__ex) ).
thf(869,plain,
! [TA: $tType,A: TA > $o] :
( ( A @ ( hilbert_Eps @ TA @ A ) )
= ( ? [B: TA] : ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(44,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_253_graph__union__preserves__restrict) ).
thf(420,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)],[44]) ).
thf(225,axiom,
( ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ x @ ( bot_bot @ ( set @ b ) ) ) )
= ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ y @ ( bot_bot @ ( set @ b ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062getRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_AgetRel_AS__Idt_AG_A_096_096_A_123y_125_092_060close_062) ).
thf(989,plain,
( ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ x @ ( bot_bot @ ( set @ b ) ) ) )
= ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ y @ ( bot_bot @ ( set @ b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(222,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( converse @ TA @ TB @ C ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_converse_Ocases) ).
thf(980,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( converse @ TA @ TB @ C ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(39,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_182_ord__eq__le__trans) ).
thf(403,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)],[39]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(471,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(192,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_138_total__on__singleton) ).
thf(884,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)],[192]) ).
thf(67,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_141_labeled__graph_Ocollapse) ).
thf(488,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)],[67]) ).
thf(208,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_18_insert__absorb2) ).
thf(933,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)],[208]) ).
thf(81,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_147_labeled__graph_Oexhaust) ).
thf(526,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)],[81]) ).
thf(219,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB ),C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_Image__iff) ).
thf(970,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB ),C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(197,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E ) ) )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_subset__CollectI) ).
thf(901,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E ) ) )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(135,axiom,
( f
= ( ^ [A: b] :
( if @ b
@ ( ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ A @ ( bot_bot @ ( set @ b ) ) ) )
= ( bot_bot @ ( set @ b ) ) )
@ A
@ ( hilbert_Eps @ b @ ( p @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_f) ).
thf(686,plain,
( f
= ( ^ [A: b] :
( if @ b
@ ( ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ A @ ( bot_bot @ ( set @ b ) ) ) )
= ( bot_bot @ ( set @ b ) ) )
@ A
@ ( hilbert_Eps @ b @ ( p @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(250,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_empty__iff) ).
thf(1075,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(62,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_197_le__funI) ).
thf(476,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)],[62]) ).
thf(115,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ( equiv_equiv @ TA @ C @ A )
=> ( ( equiv_equiv @ TA @ C @ B )
=> ( ( image @ TA @ TA @ B @ ( image @ TA @ TA @ A @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_refines__equiv__class__eq2) ).
thf(622,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: set @ ( product_prod @ TA @ TA ),C: set @ TA,D: TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TA ) ) @ A @ B )
=> ( ( equiv_equiv @ TA @ C @ A )
=> ( ( equiv_equiv @ TA @ C @ B )
=> ( ( image @ TA @ TA @ B @ ( image @ TA @ TA @ A @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(262,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: set @ TA] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( member @ TA @ A @ D )
=> ( member @ TB @ B @ ( image @ TA @ TB @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_ImageI) ).
thf(1114,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: set @ TA] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( member @ TA @ A @ D )
=> ( member @ TB @ B @ ( image @ TA @ TB @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(228,axiom,
! [A: b] :
( ( member @ b @ A @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) )
= ( p @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_r1) ).
thf(997,plain,
! [A: b] :
( ( member @ b @ A @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) )
= ( p @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(246,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_pred__subset__eq) ).
thf(1060,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(200,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_172_singleton__insert__inj__eq_H) ).
thf(911,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)],[200]) ).
thf(96,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_empty__subsetI) ).
thf(569,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) > ( set @ TB ) > TD,C: labeled_graph @ TA @ TB] :
( ( A @ ( labele1974067554_graph @ TA @ TB @ TD @ B @ C ) )
= ( labele1974067554_graph @ TA @ TB @ TC
@ ^ [D: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ),E: set @ TB] : ( A @ ( B @ D @ E ) )
@ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_labeled__graph_Ocase__distrib) ).
thf(515,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) ) > ( set @ TB ) > TD,C: labeled_graph @ TA @ TB] :
( ( A @ ( labele1974067554_graph @ TA @ TB @ TD @ B @ C ) )
= ( labele1974067554_graph @ TA @ TB @ TC
@ ^ [D: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ),E: set @ TB] : ( A @ ( B @ D @ E ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(272,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_empty__def) ).
thf(1150,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(266,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( collect @ TA
@ ^ [C: TA] :
( ( C = A )
| ( C = B ) ) )
= ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_tuple__disj) ).
thf(1131,plain,
! [TA: $tType,A: TA,B: TA] :
( ( collect @ TA
@ ^ [C: TA] :
( ( C = A )
| ( C = B ) ) )
= ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(124,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_Collect__subset) ).
thf(654,plain,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(73,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_dual__order_Otrans) ).
thf(503,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType] :
( ( equiv_proj @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TB ),B: TA] : ( image @ TA @ TB @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_proj__def) ).
thf(605,plain,
! [TA: $tType,TB: $tType] :
( ( equiv_proj @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TB ),B: TA] : ( image @ TA @ TB @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(167,axiom,
( f
= ( ^ [A: b] :
( if @ b
@ ( ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ A @ ( bot_bot @ ( set @ b ) ) ) )
= ( bot_bot @ ( set @ b ) ) )
@ A
@ ( hilbert_Eps @ b @ ( p @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__092_060open_062f_A_092_060equiv_062_A_092_060lambda_062x_O_Aif_AgetRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_A_123_125_Athen_Ax_Aelse_AEps_A_IP_Ax_J_092_060close_062) ).
thf(792,plain,
( f
= ( ^ [A: b] :
( if @ b
@ ( ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ A @ ( bot_bot @ ( set @ b ) ) ) )
= ( bot_bot @ ( set @ b ) ) )
@ A
@ ( hilbert_Eps @ b @ ( p @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(118,axiom,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( C = A )
| ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_insert__compr) ).
thf(633,plain,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( C = A )
| ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(172,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_34_mk__disjoint__insert) ).
thf(805,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)],[172]) ).
thf(75,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_9) ).
thf(508,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(86,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_95_old_Oprod_Oinducts) ).
thf(541,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)],[86]) ).
thf(244,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_113_getRel__dom_I1_J) ).
thf(1054,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)],[244]) ).
thf(92,axiom,
! [A: b,B: b,C: standard_Constant @ a] :
( ( member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ A @ B ) @ ( getRel @ ( standard_Constant @ a ) @ b @ C @ g ) )
=> ( equiv_congruent @ b @ ( set @ b ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g )
@ ^ [D: b] : ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ C @ g ) @ ( insert @ b @ D @ ( bot_bot @ ( set @ b ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_congr_I1_J) ).
thf(558,plain,
! [A: b,B: b,C: standard_Constant @ a] :
( ( member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ A @ B ) @ ( getRel @ ( standard_Constant @ a ) @ b @ C @ g ) )
=> ( equiv_congruent @ b @ ( set @ b ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g )
@ ^ [D: b] : ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ C @ g ) @ ( insert @ b @ D @ ( bot_bot @ ( set @ b ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(254,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_207_subset__iff) ).
thf(1086,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)],[254]) ).
thf(210,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_135_Collect__empty__eq__bot) ).
thf(938,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)],[210]) ).
thf(168,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_15_Collect__empty__eq) ).
thf(794,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)],[168]) ).
thf(102,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_145_total__on__empty) ).
thf(586,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)],[102]) ).
thf(198,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_203_set__eq__subset) ).
thf(906,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)],[198]) ).
thf(217,axiom,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_insertI1) ).
thf(965,plain,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(271,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_209_equalityD1) ).
thf(1146,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)],[271]) ).
thf(184,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_247_less__by__empty) ).
thf(856,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)],[184]) ).
thf(154,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA,D: TA > $o] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_prop__restrict) ).
thf(745,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA,D: TA > $o] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(3,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_185_le__cases3) ).
thf(279,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)],[3]) ).
thf(221,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_39_Set_Oset__insert) ).
thf(975,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)],[221]) ).
thf(45,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_96_old_Oprod_Oexhaust) ).
thf(423,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)],[45]) ).
thf(153,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_219_insert__mono) ).
thf(743,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)],[153]) ).
thf(87,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_157_labeled__graph_Ocase) ).
thf(545,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)],[87]) ).
thf(42,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_100_prod__induct4) ).
thf(413,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)],[42]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType] :
( ( converse @ TB @ TA @ ( bot_bot @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_converse__empty) ).
thf(577,plain,
! [TA: $tType,TB: $tType] :
( ( converse @ TB @ TA @ ( bot_bot @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(144,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( A @ ( hilbert_Eps @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_someI) ).
thf(711,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( A @ ( hilbert_Eps @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(121,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_222_subset__insertI2) ).
thf(641,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)],[121]) ).
thf(34,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_149_labeled__graph_Osel_I1_J) ).
thf(391,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)],[34]) ).
thf(209,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_123_refl__on__empty) ).
thf(936,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)],[209]) ).
thf(10,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_139_labeled__graph_Oinject) ).
thf(313,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)],[10]) ).
thf(111,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_40_insertI2) ).
thf(611,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)],[111]) ).
thf(259,axiom,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_5) ).
thf(1107,plain,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(256,axiom,
! [A: b,B: b,C: standard_Constant @ a] :
( ( member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ A @ B ) @ ( getRel @ ( standard_Constant @ a ) @ b @ C @ g ) )
=> ( equiv_congruent @ b @ ( set @ b ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g )
@ ^ [D: b] : ( image @ b @ b @ ( converse @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ C @ g ) ) @ ( insert @ b @ D @ ( bot_bot @ ( set @ b ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_congr_I2_J) ).
thf(1092,plain,
! [A: b,B: b,C: standard_Constant @ a] :
( ( member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ A @ B ) @ ( getRel @ ( standard_Constant @ a ) @ b @ C @ g ) )
=> ( equiv_congruent @ b @ ( set @ b ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g )
@ ^ [D: b] : ( image @ b @ b @ ( converse @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ C @ g ) ) @ ( insert @ b @ D @ ( bot_bot @ ( set @ b ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(142,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_42_insertE) ).
thf(704,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)],[142]) ).
thf(22,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_98_prod__induct6) ).
thf(350,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)],[22]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( TA > TB > $o )
@ ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
@ ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
= ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_pred__subset__eq2) ).
thf(672,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( TA > TB > $o )
@ ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
@ ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
= ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(203,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_228_proj__iff) ).
thf(919,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)],[203]) ).
thf(171,axiom,
member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ x @ y ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062_Ix_M_Ay_J_A_092_060in_062_AgetRel_AS__Idt_AG_092_060close_062) ).
thf(804,plain,
member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ x @ y ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(242,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
= ( ( ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( member @ TA @ C @ A )
& ( member @ TA @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_equiv__class__eq__iff) ).
thf(1048,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
= ( ( ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( member @ TA @ C @ A )
& ( member @ TA @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(76,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_71_restrict__idemp) ).
thf(509,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)],[76]) ).
thf(113,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_64_singletonD) ).
thf(616,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)],[113]) ).
thf(186,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( converse @ TA @ TB @ C ) )
= ( ? [D: TA,E: TB] :
( ( A = E )
& ( B = D )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ E ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_converse_Osimps) ).
thf(863,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( converse @ TA @ TB @ C ) )
= ( ? [D: TA,E: TB] :
( ( A = E )
& ( B = D )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ E ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(194,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_226_congruent2I_H) ).
thf(890,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)],[194]) ).
thf(117,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: set @ ( product_prod @ TA @ TB )] :
( ( member @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ C ) @ D )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_rev__ImageI) ).
thf(631,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: set @ ( product_prod @ TA @ TB )] :
( ( member @ TA @ A @ B )
=> ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ C ) @ D )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(89,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(552,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(84,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( refl_on @ TA @ A @ ( converse @ TA @ TA @ B ) )
= ( refl_on @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_refl__on__converse) ).
thf(535,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( refl_on @ TA @ A @ ( converse @ TA @ TA @ B ) )
= ( refl_on @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(14,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_dual__order_Oeq__iff) ).
thf(323,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(105,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_127_is__singletonE) ).
thf(594,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)],[105]) ).
thf(275,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_3) ).
thf(1162,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(181,axiom,
! [A: b] :
( ( member @ b @ A @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) )
=> ( member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ A @ ( hilbert_Eps @ b @ ( p @ A ) ) ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_vert__P) ).
thf(848,plain,
! [A: b] :
( ( member @ b @ A @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) )
=> ( member @ ( product_prod @ b @ b ) @ ( product_Pair @ b @ b @ A @ ( hilbert_Eps @ b @ ( p @ A ) ) ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(16,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_dual__order_Oantisym) ).
thf(330,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(261,axiom,
! [TA: $tType] : ( order_bot @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__bot_1) ).
thf(1112,plain,
! [TA: $tType] : ( order_bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(70,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_105_prod__cases4) ).
thf(494,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)],[70]) ).
thf(252,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_less__eq__set__def) ).
thf(1080,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(37,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_179_order__trans) ).
thf(399,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)],[37]) ).
thf(55,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_251_graph__union__idemp_I2_J) ).
thf(455,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)],[55]) ).
thf(110,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_14_empty__Collect__eq) ).
thf(608,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)],[110]) ).
thf(35,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_77_prod_Oinject) ).
thf(394,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)],[35]) ).
thf(94,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_60_singleton__inject) ).
thf(563,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)],[94]) ).
thf(229,axiom,
! [TA: $tType,A: TA] :
( ( hilbert_Eps @ TA @ ( (=) @ TA @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_some__sym__eq__trivial) ).
thf(1000,plain,
! [TA: $tType,A: TA] :
( ( hilbert_Eps @ TA @ ( (=) @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(74,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_82_vertices__restrict) ).
thf(505,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)],[74]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( 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_194_order__subst2) ).
thf(431,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( 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)],[48]) ).
thf(204,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_154_graph__homomorphism__empty) ).
thf(922,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)],[204]) ).
thf(161,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_202_Collect__mono__iff) ).
thf(768,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)],[161]) ).
thf(178,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(827,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(119,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( insert @ TA @ A @ ( collect @ TA @ B ) )
= ( collect @ TA
@ ^ [C: TA] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_insert__Collect) ).
thf(636,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( insert @ TA @ A @ ( collect @ TA @ B ) )
= ( collect @ TA
@ ^ [C: TA] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(240,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_120_refl__onD) ).
thf(1044,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)],[240]) ).
thf(61,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_252_graph__union__idemp_I3_J) ).
thf(473,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)],[61]) ).
thf(236,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) @ ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
=> ( ( member @ TA @ C @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_subset__equiv__class) ).
thf(1034,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) @ ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
=> ( ( member @ TA @ C @ A )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(131,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_170_subset__empty) ).
thf(675,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)],[131]) ).
thf(46,axiom,
! [TA: $tType] :
( ( order @ 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_186_order_Otrans) ).
thf(426,plain,
! [TA: $tType] :
( ( order @ 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)],[46]) ).
thf(212,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_32_equals0D) ).
thf(944,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)],[212]) ).
thf(133,axiom,
! [TA: $tType,TB: $tType] :
( ( labeled_edges @ TA @ TB )
= ( labele1974067554_graph @ TA @ TB @ ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) )
@ ^ [A: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ),B: set @ TB] : A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_edges__def) ).
thf(680,plain,
! [TA: $tType,TB: $tType] :
( ( labeled_edges @ TA @ TB )
= ( labele1974067554_graph @ TA @ TB @ ( set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ) )
@ ^ [A: set @ ( product_prod @ TA @ ( product_prod @ TB @ TB ) ),B: set @ TB] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(88,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_148_labeled__graph_Oinduct) ).
thf(548,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)],[88]) ).
thf(267,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_bot__set__def) ).
thf(1134,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(90,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(553,plain,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA )
=> ( order_bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(56,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_115_old_Oprod_Orec) ).
thf(458,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)],[56]) ).
thf(230,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_emptyE) ).
thf(1003,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB ),C: TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_Image__singleton__iff) ).
thf(580,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB ),C: TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(137,axiom,
! [TA: $tType,A: TA] :
( ( collect @ TA
@ ^ [B: TA] : ( B = A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_singleton__conv) ).
thf(690,plain,
! [TA: $tType,A: TA] :
( ( collect @ TA
@ ^ [B: TA] : ( B = A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(189,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
~ ( bot_bot @ ( TB > TA > $o ) @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_bot2E) ).
thf(872,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
~ ( bot_bot @ ( TB > TA > $o ) @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(143,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB ),D: TB > TA > $o] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( converse @ TA @ TB @ C ) )
=> ( ! [E: TA,F: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ F ) @ C )
=> ( D @ F @ E ) )
=> ( D @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_converse_Oinducts) ).
thf(707,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB ),D: TB > TA > $o] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( converse @ TA @ TB @ C ) )
=> ( ! [E: TA,F: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ F ) @ C )
=> ( D @ F @ E ) )
=> ( D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(258,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( ! [C: TA] :
( ( A @ C )
=> ( C = B ) )
=> ( ( hilbert_Eps @ TA @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_some__equality) ).
thf(1098,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( ! [C: TA] :
( ( A @ C )
=> ( C = B ) )
=> ( ( hilbert_Eps @ TA @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(9,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_85_labeled__graph_Oexpand) ).
thf(310,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)],[9]) ).
thf(166,axiom,
refl_on @ b @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_local_Orefl) ).
thf(791,plain,
refl_on @ b @ ( labeled_vertices @ ( standard_Constant @ a ) @ b @ g ) @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(238,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_217_bot_Oextremum__unique) ).
thf(1038,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)],[238]) ).
thf(122,axiom,
! [A: b] :
( ( ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ A @ ( bot_bot @ ( set @ b ) ) ) )
!= ( bot_bot @ ( set @ b ) ) )
=> ( ( hilbert_Eps @ b @ ( p @ ( hilbert_Eps @ b @ ( p @ A ) ) ) )
= ( hilbert_Eps @ b @ ( p @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_P__eq) ).
thf(643,plain,
! [A: b] :
( ( ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ A @ ( bot_bot @ ( set @ b ) ) ) )
!= ( bot_bot @ ( set @ b ) ) )
=> ( ( hilbert_Eps @ b @ ( p @ ( hilbert_Eps @ b @ ( p @ A ) ) ) )
= ( hilbert_Eps @ b @ ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(125,axiom,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA,D: set @ TA] :
( ( ( image @ TA @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( image @ TA @ TA @ A @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) )
=> ( ( equiv_equiv @ TA @ D @ A )
=> ( ( member @ TA @ C @ D )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_eq__equiv__class) ).
thf(656,plain,
! [TA: $tType,A: set @ ( product_prod @ TA @ TA ),B: TA,C: TA,D: set @ TA] :
( ( ( image @ TA @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( image @ TA @ TA @ A @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) )
=> ( ( equiv_equiv @ TA @ D @ A )
=> ( ( member @ TA @ C @ D )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(112,axiom,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_bot__empty__eq) ).
thf(613,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(107,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_136_graph__single) ).
thf(600,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)],[107]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( A
= ( labeled_LG @ TA @ TB @ ( labeled_edges @ TA @ TB @ A ) @ ( labeled_vertices @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_labeled__graph_Oexhaust__sel) ).
thf(497,plain,
! [TA: $tType,TB: $tType,A: labeled_graph @ TA @ TB] :
( A
= ( labeled_LG @ TA @ TB @ ( labeled_edges @ TA @ TB @ A ) @ ( labeled_vertices @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(226,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_246_graph__unionI) ).
thf(991,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)],[226]) ).
thf(257,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_208_equalityD2) ).
thf(1094,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)],[257]) ).
thf(269,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_2) ).
thf(1140,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(53,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_107_Pair__inject) ).
thf(446,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)],[53]) ).
thf(97,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_241_ssubst__Pair__rhs) ).
thf(571,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)],[97]) ).
thf(26,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_198_le__funE) ).
thf(363,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)],[26]) ).
thf(65,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_order__refl) ).
thf(482,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(136,axiom,
( g
= ( restrict @ ( standard_Constant @ a ) @ b @ g ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I1_J) ).
thf(688,plain,
( g
= ( restrict @ ( standard_Constant @ a ) @ b @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(162,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_116_is__singleton__the__elem) ).
thf(771,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)],[162]) ).
thf(174,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ A @ ( converse @ TA @ TB @ B ) )
=> ~ ! [C: TA,D: TB] :
( ( A
= ( product_Pair @ TB @ TA @ D @ C ) )
=> ~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_converseE) ).
thf(813,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ A @ ( converse @ TA @ TB @ B ) )
=> ~ ! [C: TA,D: TB] :
( ( A
= ( product_Pair @ TB @ TA @ D @ C ) )
=> ~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(216,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ B @ A ) @ ( converse @ TA @ TB @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_converse_Ointros) ).
thf(963,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ B @ A ) @ ( converse @ TA @ TB @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( converse @ TB @ TA @ ( converse @ TA @ TB @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_converse__converse) ).
thf(304,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( converse @ TB @ TA @ ( converse @ TA @ TB @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(38,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_dual__order_Orefl) ).
thf(401,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(165,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_132_congruentI) ).
thf(786,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)],[165]) ).
thf(103,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_insert__not__empty) ).
thf(588,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(140,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_subset__Collect__iff) ).
thf(699,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(195,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB ),C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ A @ C ) @ ( image @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_Image__mono) ).
thf(896,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB ),C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ A @ C ) @ ( image @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(156,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_171_insert__subset) ).
thf(748,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)],[156]) ).
thf(234,axiom,
( p
= ( ^ [A: b,B: b] : ( member @ b @ B @ ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ A @ ( bot_bot @ ( set @ b ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_P) ).
thf(1030,plain,
( p
= ( ^ [A: b,B: b] : ( member @ b @ B @ ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ A @ ( bot_bot @ ( set @ b ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(201,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_160_lnear__order__on__empty) ).
thf(914,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)],[201]) ).
thf(129,axiom,
! [TA: $tType,A: TA > $o] :
( ? [B: TA] : ( A @ B )
=> ( A @ ( hilbert_Eps @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_someI__ex) ).
thf(667,plain,
! [TA: $tType,A: TA > $o] :
( ? [B: TA] : ( A @ B )
=> ( A @ ( hilbert_Eps @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(159,axiom,
! [TA: $tType,A: set @ TA] :
( ( member @ TA
@ ( hilbert_Eps @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
@ A )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_some__in__eq) ).
thf(763,plain,
! [TA: $tType,A: set @ TA] :
( ( member @ TA
@ ( hilbert_Eps @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
@ A )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot) ).
thf(383,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(251,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_eq__equiv__class__iff) ).
thf(1077,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TA,D: TA] :
( ( equiv_equiv @ TA @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( ( image @ TA @ TA @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( image @ TA @ TA @ B @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(63,axiom,
linorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder) ).
thf(478,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(145,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_36_insert__eq__iff) ).
thf(716,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)],[145]) ).
thf(170,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_167_subsetI) ).
thf(800,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)],[170]) ).
thf(263,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: TB] :
( ( image @ TB @ TA @ A @ ( insert @ TB @ B @ ( bot_bot @ ( set @ TB ) ) ) )
= ( collect @ TA
@ ^ [C: TA] : ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_Image__singleton) ).
thf(1116,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: TB] :
( ( image @ TB @ TA @ A @ ( insert @ TB @ B @ ( bot_bot @ ( set @ TB ) ) ) )
= ( collect @ TA
@ ^ [C: TA] : ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(5,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_189_linear) ).
thf(300,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)],[5]) ).
thf(175,axiom,
! [TA: $tType,A: TA] :
( ( hilbert_Eps @ TA
@ ^ [B: TA] : ( B = A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_some__eq__trivial) ).
thf(818,plain,
! [TA: $tType,A: TA] :
( ( hilbert_Eps @ TA
@ ^ [B: TA] : ( B = A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( converse @ TA @ TB @ C ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_converseD) ).
thf(603,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( converse @ TA @ TB @ C ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ( converse @ TA @ TB @ A )
= ( converse @ TA @ TB @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_converse__inject) ).
thf(410,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ( converse @ TA @ TB @ A )
= ( converse @ TA @ TB @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(218,axiom,
! [TA: $tType,TB: $tType] :
( ( bot_bot @ ( TA > TB > $o ) )
= ( ^ [A: TA,B: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_bot__empty__eq2) ).
thf(967,plain,
! [TA: $tType,TB: $tType] :
( ( bot_bot @ ( TA > TB > $o ) )
= ( ^ [A: TA,B: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ 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_195_order__subst1) ).
thf(326,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ 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)],[15]) ).
thf(4,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_177_linorder__wlog) ).
thf(294,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)],[4]) ).
thf(24,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( total_on @ TA @ A @ ( converse @ TA @ TA @ B ) )
= ( total_on @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_total__on__converse) ).
thf(358,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ( total_on @ TA @ A @ ( converse @ TA @ TA @ B ) )
= ( total_on @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(128,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_63_singleton__iff) ).
thf(664,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)],[128]) ).
thf(215,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( hilbert_Eps @ TA @ A )
= ( hilbert_Eps @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_Eps__cong) ).
thf(960,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( hilbert_Eps @ TA @ A )
= ( hilbert_Eps @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(248,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_4) ).
thf(1065,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(139,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_143_total__on__def) ).
thf(696,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)],[139]) ).
thf(147,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TB @ TA ) ) @ ( converse @ TA @ TB @ A ) @ ( converse @ TA @ TB @ B ) )
= ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_converse__mono) ).
thf(720,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TB @ TA ) ) @ ( converse @ TA @ TB @ A ) @ ( converse @ TA @ TB @ B ) )
= ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(193,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_137_refl__on__domain) ).
thf(886,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)],[193]) ).
thf(206,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_213_in__mono) ).
thf(928,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)],[206]) ).
thf(224,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_204_subset__trans) ).
thf(987,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)],[224]) ).
thf(58,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_97_prod__induct7) ).
thf(464,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)],[58]) ).
thf(98,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_234_insert__subsetI) ).
thf(575,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)],[98]) ).
thf(185,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_16_all__not__in__conv) ).
thf(860,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)],[185]) ).
thf(148,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_subset__refl) ).
thf(723,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(182,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_166_subset__antisym) ).
thf(850,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)],[182]) ).
thf(223,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( A @ ( hilbert_Eps @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_tfl__some) ).
thf(982,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( A @ ( hilbert_Eps @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(1,conjecture,
( ( hilbert_Eps @ b
@ ^ [A: b] : ( member @ b @ A @ ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ x @ ( bot_bot @ ( set @ b ) ) ) ) ) )
= ( hilbert_Eps @ b
@ ^ [A: b] : ( member @ b @ A @ ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ y @ ( bot_bot @ ( set @ b ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( hilbert_Eps @ b
@ ^ [A: b] : ( member @ b @ A @ ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ x @ ( bot_bot @ ( set @ b ) ) ) ) ) )
!= ( hilbert_Eps @ b
@ ^ [A: b] : ( member @ b @ A @ ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ y @ ( bot_bot @ ( set @ b ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(277,plain,
( ( hilbert_Eps @ b
@ ^ [A: b] : ( member @ b @ A @ ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ x @ ( bot_bot @ ( set @ b ) ) ) ) ) )
!= ( hilbert_Eps @ b
@ ^ [A: b] : ( member @ b @ A @ ( image @ b @ b @ ( getRel @ ( standard_Constant @ a ) @ b @ ( standard_S_Idt @ a ) @ g ) @ ( insert @ b @ y @ ( bot_bot @ ( set @ b ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(52,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_108_prod__cases) ).
thf(442,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)],[52]) ).
thf(28,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_antisym) ).
thf(369,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(150,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_212_subsetD) ).
thf(728,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)],[150]) ).
thf(152,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_223_subset__singleton__iff) ).
thf(740,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)],[152]) ).
thf(19,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_152_labeled__graph_Osplit__sel) ).
thf(337,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)],[19]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o] :
( ! [C: TA,D: TB] :
( ( A @ C @ D )
=> ( B @ C @ D ) )
=> ( ord_less_eq @ ( TA > TB > $o ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_predicate2I) ).
thf(354,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o] :
( ! [C: TA,D: TB] :
( ( A @ C @ D )
=> ( B @ C @ D ) )
=> ( ord_less_eq @ ( TA > TB > $o ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(126,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_162_congruent2__implies__congruent) ).
thf(659,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)],[126]) ).
thf(93,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(560,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(120,axiom,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_is__singletonI) ).
thf(639,plain,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(491,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(1167,plain,
$false,
inference(e,[status(thm)],[1036,1024,365,760,479,846,518,941,909,333,1083,468,777,555,1005,683,730,994,1142,597,1041,385,1137,533,500,747,538,930,1164,797,1063,340,898,417,320,436,973,1046,719,372,619,702,751,853,881,316,591,1109,646,348,1051,821,766,397,866,428,1119,774,307,452,380,678,529,661,925,1153,810,1067,1057,512,439,334,957,825,1021,302,1123,407,693,916,1032,361,625,435,493,566,484,583,522,830,1159,461,1089,874,317,948,725,388,869,420,989,980,403,471,884,488,933,526,970,901,686,1075,476,622,1114,997,1060,911,569,515,1150,1131,654,503,605,792,633,805,508,541,1054,558,1086,938,794,586,906,965,1146,856,745,279,975,423,743,545,413,577,711,641,391,936,313,611,1107,1092,704,350,672,919,804,1048,509,616,863,890,631,552,535,323,594,1162,848,330,1112,494,1080,399,455,608,394,563,1000,505,431,922,768,827,636,1044,473,1034,675,426,944,680,548,1134,553,458,1003,580,690,872,707,1098,310,791,1038,643,656,613,600,497,991,1094,1140,446,571,363,482,688,771,813,963,304,401,786,588,699,896,748,1030,914,667,763,383,1077,478,716,800,1116,300,818,603,410,967,326,294,358,664,960,1065,696,720,886,928,987,464,575,860,723,850,982,277,442,369,728,740,337,354,659,560,639,491]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP176^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 20:12:36 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.91/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.08/1.16 % [INFO] Parsing done (370ms).
% 2.08/1.17 % [INFO] Running in sequential loop mode.
% 3.23/1.55 % [INFO] eprover registered as external prover.
% 3.23/1.56 % [INFO] Scanning for conjecture ...
% 3.67/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 275 axioms. Running axiom selection ...
% 4.32/1.92 % [INFO] Axiom selection finished. Selected 274 axioms (removed 1 axioms).
% 5.38/2.27 % [INFO] Problem is higher-order (TPTP THF).
% 5.81/2.30 % [INFO] Type checking passed.
% 5.81/2.31 % [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 ...
% 163.87/136.78 % External prover 'e' found a proof!
% 163.87/136.78 % [INFO] Killing All external provers ...
% 163.87/136.78 % Time passed: 136455ms (effective reasoning time: 135603ms)
% 163.87/136.78 % 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)>
% 163.87/136.78 % Axioms used in derivation (274): fact_76_bot__apply, tcon_fun___Orderings_Obot, fact_160_lnear__order__on__empty, fact_208_equalityD2, fact_223_subset__singleton__iff, fact_53_insert__compr, fact_201_Collect__subset, fact_55_some__eq__ex, fact_131_eq__equiv__class, fact_5__092_060open_062f_A_092_060equiv_062_A_092_060lambda_062x_O_Aif_AgetRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_A_123_125_Athen_Ax_Aelse_AEps_A_IP_Ax_J_092_060close_062, fact_203_set__eq__subset, fact_58_someI__ex, fact_36_insert__eq__iff, tcon_HOL_Obool___Orderings_Opreorder_7, fact_184_antisym__conv, fact_167_subsetI, fact_216_bot_Oextremum__uniqueI, fact_251_graph__union__idemp_I2_J, fact_138_total__on__singleton, tcon_HOL_Obool___Orderings_Oord_9, tcon_Set_Oset___Orderings_Oorder__bot_1, fact_175_dual__order_Oeq__iff, fact_50_someI, fact_211_equalityE, fact_100_prod__induct4, fact_176_dual__order_Otrans, fact_134_equiv__class__self, fact_241_ssubst__Pair__rhs, fact_174_dual__order_Oantisym, fact_9_Image__empty1, fact_240_univ__def, fact_210_subset__eq, fact_213_in__mono, fact_163_proj__def, fact_93_bot__empty__eq, fact_188_eq__refl, fact_133_congruentD, fact_231_congruent2I, fact_56_someI2__bex, fact_63_singleton__iff, fact_75_the__elem__eq, fact_80_converse__converse, fact_57_someI2__ex, fact_222_subset__insertI2, fact_253_graph__union__preserves__restrict, fact_86_converse_Oinducts, tcon_fun___Orderings_Oord, fact_139_labeled__graph_Oinject, fact_52_insert__Collect, tcon_Set_Oset___Orderings_Oorder_3, fact_127_is__singletonE, fact_71_restrict__idemp, fact_204_subset__trans, fact_235_subset__emptyI, fact_218_bot_Oextremum, fact_132_congruentI, tcon_HOL_Obool___Orderings_Olinorder, fact_110_bot__fun__def, fact_129_eq__equiv__class__iff, fact_158_edges__def, fact_232_congruent2__commuteI, fact_206_subset__refl, fact_1_assms_I1_J, fact_106_prod__cases3, fact_148_labeled__graph_Oinduct, fact_143_total__on__def, fact_192_ord__le__eq__subst, fact_255_rev__predicate1D, fact_61_insert__not__empty, fact_13_some__eq__trivial, fact_181_ord__le__eq__trans, fact_177_linorder__wlog, tcon_HOL_Obool___Orderings_Oorder__bot_6, fact_3_P, fact_29_Image__singleton, fact_77_prod_Oinject, fact_84__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_A_092_060Longrightarrow_062_A_Ix_M_Ax_J_A_092_060in_062_AgetRel_AS__Idt_AG_092_060close_062, fact_150_labeled__graph_Oexhaust__sel, fact_182_ord__eq__le__trans, fact_20_insertCI, fact_46_Collect__mem__eq, fact_237_pred__subset__eq, fact_180_order__class_Oorder_Oantisym, fact_74_congr_I2_J, fact_172_singleton__insert__inj__eq_H, fact_35_insert__commute, fact_104_prod__cases5, fact_91_converseD, fact_198_le__funE, fact_169_empty__subsetI, fact_185_le__cases3, fact_254_rev__predicate2D, fact_83_converse__empty, fact_96_old_Oprod_Oexhaust, fact_67_some__in__eq, fact_2_P__eq, fact_88_converse_Osimps, fact_65_Collect__conv__if2, fact_40_insertI2, fact_252_graph__union__idemp_I3_J, fact_116_is__singleton__the__elem, fact_43_some__eq__imp, fact_16_all__not__in__conv, help_If_1_1_T, fact_7_singleton__conv2, fact_4__092_060open_062_Ix_M_Ay_J_A_092_060in_062_AgetRel_AS__Idt_AG_092_060close_062, fact_21_some__sym__eq__trivial, fact_113_getRel__dom_I1_J, fact_194_order__subst2, fact_98_prod__induct6, fact_105_prod__cases4, fact_233_subset__equiv__class, fact_42_insertE, fact_164_equiv__class__subset, fact_248_predicate2I, fact_115_old_Oprod_Orec, fact_202_Collect__mono__iff, fact_111_local_Orefl, fact_144_total__onI, fact_122_refl__onD2, fact_6_singleton__conv, fact_17_empty__iff, fact_33_emptyE, fact_28_ImageE, fact_234_insert__subsetI, fact_87_converse_Ointros, fact_220_subset__insert, fact_205_Collect__mono, fact_200_Image__mono, fact_49_Eps__cong, fact_25_pred__equals__eq2, fact_45_mem__Collect__eq, fact_18_insert__absorb2, fact_108_prod__cases, fact_199_le__funD, fact_124_is__singletonI_H, fact_227_congruent2D, fact_79_converse__inject, fact_69_vert__P, fact_125_refl__on__singleton, fact_59_someI2, fact_64_singletonD, fact_157_labeled__graph_Ocase, fact_191_eq__iff, fact_243_subset__CollectI, fact_130_equiv__class__eq, fact_66_Collect__conv__if, fact_103_prod__cases6, fact_242_subset__Collect__iff, tcon_HOL_Obool___Orderings_Oorder_8, fact_85_labeled__graph_Oexpand, fact_140_total__on__converse, fact_228_proj__iff, fact_152_labeled__graph_Osplit__sel, fact_197_le__funI, fact_225_restrict__subsD, fact_107_Pair__inject, fact_114_getRel__dom_I2_J, fact_120_refl__onD, fact_187_le__cases, fact_47_Collect__cong, fact_70__092_060open_062_IS__Idt_M_Ax_M_Ay_J_A_092_060in_062_Aedges_AG_092_060close_062, fact_245_prop__restrict, fact_159_vertices__def, fact_60_singleton__inject, tcon_fun___Orderings_Oorder__bot, fact_34_mk__disjoint__insert, help_If_2_1_T, fact_94_bot__empty__eq2, fact_236_univ__commute, fact_19_insert__iff, fact_156_labeled__graph_Ocase__distrib, fact_146_labeled__graph_Osel_I2_J, help_If_3_1_T, fact_37_insert__absorb, fact_95_old_Oprod_Oinducts, fact_78_old_Oprod_Oinject, fact_15_Collect__empty__eq, fact_68_congr_I1_J, fact_224_subset__singletonD, fact_183_order__class_Oorder_Oeq__iff, fact_149_labeled__graph_Osel_I1_J, fact_26_rev__ImageI, fact_22_ImageI, fact_190_antisym, fact_41_insertI1, fact_14_empty__Collect__eq, fact_250_graph__union__idemp_I1_J, fact_126_is__singleton__def, fact_207_subset__iff, fact_171_insert__subset, fact_193_ord__eq__le__subst, fact_54_some1__equality, fact_217_bot_Oextremum__unique, fact_230_refines__equiv__class__eq, fact_170_subset__empty, tcon_fun___Orderings_Opreorder, fact_38_insert__ident, fact_166_subset__antisym, fact_195_order__subst1, fact_151_linear__order__on__singleton, fact_136_graph__single, fact_118_is__singletonI, fact_215_subrelI, fact_238_less__eq__set__def, fact_226_congruent2I_H, fact_0__092_060open_062getRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_AgetRel_AS__Idt_AG_A_096_096_A_123y_125_092_060close_062, fact_161_labeled__graph_Ocase__eq__if, fact_27_Image__iff, fact_162_congruent2__implies__congruent, fact_246_graph__unionI, fact_11_singletonI, fact_142_graph__empty__e, fact_153_labeled__graph_Osplit__sel__asm, fact_137_refl__on__domain, tcon_Set_Oset___Orderings_Obot_5, fact_219_insert__mono, fact_168_converse__mono, fact_196_le__fun__def, fact_101_prod__induct3, fact_32_equals0D, fact_82_vertices__restrict, fact_186_order_Otrans, fact_73_r1, fact_12_some__equality, tcon_fun___Orderings_Oorder, fact_173_singleton__insert__inj__eq, fact_117_refl__on__converse, fact_92_bot__set__def, fact_145_total__on__empty, fact_135_Collect__empty__eq__bot, tcon_HOL_Obool___Orderings_Obot_10, fact_249_predicate1I, tcon_Set_Oset___Orderings_Opreorder_2, fact_119_bot2E, fact_123_refl__on__empty, fact_30_ex__in__conv, fact_189_linear, fact_221_subset__insertI, fact_212_subsetD, fact_97_prod__induct7, fact_109_surj__pair, fact_179_order__trans, fact_165_order__refl, fact_23_f, fact_209_equalityD1, fact_99_prod__induct5, fact_239_pred__subset__eq2, fact_39_Set_Oset__insert, fact_244_Collect__restrict, fact_72_r2, fact_147_labeled__graph_Oexhaust, fact_154_graph__homomorphism__empty, fact_89_converse_Ocases, fact_155_linear__order__on__converse, fact_178_dual__order_Orefl, fact_247_less__by__empty, fact_229_refines__equiv__class__eq2, fact_81_converse__iff, fact_51_empty__def, fact_121_refl__onD1, tcon_Set_Oset___Orderings_Oord_4, fact_90_converseE, fact_44_tfl__some, fact_112_equiv, fact_214_converse__subset__swap, fact_128_equiv__class__eq__iff, fact_141_labeled__graph_Ocollapse, fact_10_Image__empty2, fact_31_equals0I, fact_8_tuple__disj, fact_24_Image__singleton__iff, fact_102_prod__cases7, fact_62_doubleton__eq__iff
% 163.87/136.78 % No. of inferences in proof: 552
% 163.87/136.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 136455 ms resp. 135603 ms w/o parsing
% 165.32/137.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 165.32/137.07 % [INFO] Killing All external provers ...
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