%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP093^2 : 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 : n015.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 08:06:43 AM UTC 2026
% Result : Theorem 46.48s 26.78s
% Output : Refutation 48.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 289
% Syntax : Number of formulae : 580 ( 223 unt; 0 typ; 0 def)
% Number of atoms : 2035 ( 416 equ; 10 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 8107 ( 164 ~; 24 |; 128 &;7065 @)
% ( 0 <=>; 726 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 408 ( 408 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 44 usr; 8 con; 0-5 aty)
% Number of variables : 2368 ( 220 ^;2112 !; 36 ?;2368 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_unit_type,type,
product_unit: $tType ).
thf(nat_type,type,
nat: $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(finite_finite_decl,type,
finite_finite:
!>[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_Ca1785829860lChain_decl,type,
bNF_Ca1785829860lChain:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TB ) ) > ( TB > TA ) > $o ) ).
thf(finite_Fpow_decl,type,
finite_Fpow:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( set @ TA ) ) ) ).
thf(finite_card_decl,type,
finite_card:
!>[TA: $tType] : ( ( set @ TA ) > nat ) ).
thf(finite_finite2_decl,type,
finite_finite2:
!>[TA: $tType] : ( ( set @ 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(pair_p1033978749igraph_decl,type,
pair_p1033978749igraph:
!>[TA: $tType] : ( ( pair_p1731315293ph_ext @ TA @ product_unit ) > $o ) ).
thf(pair_pair_digraph_decl,type,
pair_pair_digraph:
!>[TA: $tType] : ( ( pair_p1731315293ph_ext @ TA @ product_unit ) > $o ) ).
thf(pair_p953238171igraph_decl,type,
pair_p953238171igraph:
!>[TA: $tType] : ( ( pair_p1731315293ph_ext @ TA @ product_unit ) > $o ) ).
thf(pair_p1373739070axioms_decl,type,
pair_p1373739070axioms:
!>[TA: $tType] : ( ( pair_p1731315293ph_ext @ TA @ product_unit ) > $o ) ).
thf(pair_pair_graph_decl,type,
pair_pair_graph:
!>[TA: $tType] : ( ( pair_p1731315293ph_ext @ TA @ product_unit ) > $o ) ).
thf(pair_p1282390076igraph_decl,type,
pair_p1282390076igraph:
!>[TA: $tType] : ( ( pair_p1731315293ph_ext @ TA @ product_unit ) > $o ) ).
thf(pair_p814123999axioms_decl,type,
pair_p814123999axioms:
!>[TA: $tType] : ( ( pair_p1731315293ph_ext @ TA @ product_unit ) > $o ) ).
thf(pair_pair_pre_more_decl,type,
pair_pair_pre_more:
!>[TA: $tType,TB: $tType] : ( ( pair_p1731315293ph_ext @ TB @ TA ) > TA ) ).
thf(pair_p1108258481update_decl,type,
pair_p1108258481update:
!>[TA: $tType,TB: $tType] : ( ( TB > TB ) > ( pair_p1731315293ph_ext @ TA @ TB ) > ( pair_p1731315293ph_ext @ TA @ TB ) ) ).
thf(pair_p1152105390ph_ext_decl,type,
pair_p1152105390ph_ext:
!>[TA: $tType,TB: $tType] : ( ( set @ TB ) > ( set @ ( product_prod @ TB @ TB ) ) > TA > ( pair_p1731315293ph_ext @ TB @ TA ) ) ).
thf(pair_pair_pre_parcs_decl,type,
pair_pair_pre_parcs:
!>[TA: $tType,TB: $tType] : ( ( pair_p1731315293ph_ext @ TB @ TA ) > ( set @ ( product_prod @ TB @ TB ) ) ) ).
thf(pair_pair_pre_pverts_decl,type,
pair_pair_pre_pverts:
!>[TA: $tType,TB: $tType] : ( ( pair_p1731315293ph_ext @ TB @ TA ) > ( set @ TB ) ) ).
thf(pair_p389585203_graph_decl,type,
pair_p389585203_graph:
!>[TA: $tType] : ( ( pair_p1731315293ph_ext @ TA @ product_unit ) > $o ) ).
thf(pair_p460180511igraph_decl,type,
pair_p460180511igraph:
!>[TA: $tType] : ( ( pair_p1731315293ph_ext @ TA @ product_unit ) > $o ) ).
thf(pair_p477239746axioms_decl,type,
pair_p477239746axioms:
!>[TA: $tType] : ( ( pair_p1731315293ph_ext @ TA @ product_unit ) > $o ) ).
thf(pair_pair_wf_digraph_decl,type,
pair_pair_wf_digraph:
!>[TA: $tType] : ( ( pair_p1731315293ph_ext @ TA @ product_unit ) > $o ) ).
thf(pair_subdivide_decl,type,
pair_subdivide:
!>[TA: $tType] : ( ( pair_p1731315293ph_ext @ TA @ product_unit ) > ( product_prod @ TA @ TA ) > TA > ( pair_p1731315293ph_ext @ TA @ product_unit ) ) ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(product_Sigma_decl,type,
product_Sigma:
!>[TA: $tType,TB: $tType] : ( ( set @ TB ) > ( TB > ( set @ TA ) ) > ( set @ ( product_prod @ TB @ TA ) ) ) ).
thf(produc2004651681e_prod_decl,type,
produc2004651681e_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ 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(product_case_prod_decl,type,
product_case_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_product_decl,type,
product_product:
!>[TA: $tType,TB: $tType] : ( ( set @ TB ) > ( set @ TA ) > ( set @ ( product_prod @ TB @ TA ) ) ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(is_empty_decl,type,
is_empty:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(g_decl,type,
g: pair_p1731315293ph_ext @ a @ product_unit ).
thf(n_decl,type,
n: nat ).
thf(129,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_33_less__eq__set__def) ).
thf(666,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)],[129]) ).
thf(66,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_62_order__subst1) ).
thf(481,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)],[66]) ).
thf(121,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_order__refl) ).
thf(645,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(203,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > ( set @ TB )] :
( ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( ( B @ C )
!= ( bot_bot @ ( set @ TB ) ) ) ) ) )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( finite_finite2 @ TB @ ( B @ C ) ) )
=> ( finite_finite2 @ ( product_prod @ TA @ TB ) @ ( product_Sigma @ TA @ TB @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_finite__SigmaI2) ).
thf(892,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > ( set @ TB )] :
( ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( ( B @ C )
!= ( bot_bot @ ( set @ TB ) ) ) ) ) )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( finite_finite2 @ TB @ ( B @ C ) ) )
=> ( finite_finite2 @ ( product_prod @ TA @ TB ) @ ( product_Sigma @ TA @ TB @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(65,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p953238171igraph @ TA @ A )
=> ( ( pair_p1282390076igraph @ TA @ A )
=> ( pair_pair_digraph @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_pair__digraph_Ointro) ).
thf(479,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p953238171igraph @ TA @ A )
=> ( ( pair_p1282390076igraph @ TA @ A )
=> ( pair_pair_digraph @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(270,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_152_prod__induct4) ).
thf(1105,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)],[270]) ).
thf(19,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_52_le__cases3) ).
thf(333,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)],[19]) ).
thf(249,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA] :
( ( ( product_Sigma @ TB @ TA @ A
@ ^ [C: TB] : B )
= ( bot_bot @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TB ) ) )
| ( B
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_Times__empty) ).
thf(1031,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA] :
( ( ( product_Sigma @ TB @ TA @ A
@ ^ [C: TB] : B )
= ( bot_bot @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TB ) ) )
| ( B
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(261,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_155_prod__cases6) ).
thf(1068,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)],[261]) ).
thf(237,axiom,
order_bot @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder__bot_20) ).
thf(994,plain,
order_bot @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(54,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_68_set__eq__subset) ).
thf(449,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)],[54]) ).
thf(105,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_27_subset__antisym) ).
thf(597,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)],[105]) ).
thf(193,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_153_prod__induct3) ).
thf(861,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)],[193]) ).
thf(99,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_51_antisym__conv) ).
thf(582,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)],[99]) ).
thf(158,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_176_predicate2I) ).
thf(762,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)],[158]) ).
thf(281,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ TA,D: TA > ( set @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( product_Sigma @ TA @ TB @ C @ D ) )
= ( ( member @ TA @ A @ C )
& ( member @ TB @ B @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_mem__Sigma__iff) ).
thf(1142,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ TA,D: TA > ( set @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( product_Sigma @ TA @ TB @ C @ D ) )
= ( ( member @ TA @ A @ C )
& ( member @ TB @ B @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(32,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_59_ord__le__eq__subst) ).
thf(379,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)],[32]) ).
thf(124,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_83_subset__Collect__iff) ).
thf(655,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)],[124]) ).
thf(76,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_72_subset__iff) ).
thf(511,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)],[76]) ).
thf(172,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_case_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_old_Oprod_Ocase) ).
thf(797,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_case_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(144,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_dual__order_Orefl) ).
thf(715,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(62,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_77_subsetD) ).
thf(472,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)],[62]) ).
thf(138,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_85_Collect__restrict) ).
thf(698,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)],[138]) ).
thf(223,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: set @ TA] : ( finite_finite2 @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_finite) ).
thf(945,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: set @ TA] : ( finite_finite2 @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(217,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TB] :
( ( pair_pair_pre_parcs @ TA @ TB @ ( pair_p1152105390ph_ext @ TA @ TB @ A @ B @ C ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_pair__pre__digraph_Oselect__convs_I2_J) ).
thf(930,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TB] :
( ( pair_pair_pre_parcs @ TA @ TB @ ( pair_p1152105390ph_ext @ TA @ TB @ A @ B @ C ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(205,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_151_prod__induct5) ).
thf(898,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)],[205]) ).
thf(239,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ B @ C )
& ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( C = D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_finite__has__maximal2) ).
thf(1001,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ B @ C )
& ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( C = D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(7,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(301,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(14,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_74_equalityD1) ).
thf(320,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)],[14]) ).
thf(267,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TB > $o] :
( ( collect @ ( product_prod @ TA @ TB )
@ ( product_case_prod @ TA @ TB @ $o
@ ^ [C: TA,D: TB] :
( ( A @ C )
& ( B @ D ) ) ) )
= ( product_Sigma @ TA @ TB @ ( collect @ TA @ A )
@ ^ [C: TA] : ( collect @ TB @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_Collect__case__prod) ).
thf(1095,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TB > $o] :
( ( collect @ ( product_prod @ TA @ TB )
@ ( product_case_prod @ TA @ TB @ $o
@ ^ [C: TA,D: TB] :
( ( A @ C )
& ( B @ D ) ) ) )
= ( product_Sigma @ TA @ TB @ ( collect @ TA @ A )
@ ^ [C: TA] : ( collect @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(40,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_106_subset__empty) ).
thf(404,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)],[40]) ).
thf(186,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_bot__set__def) ).
thf(841,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(45,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_70_Collect__mono) ).
thf(417,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)],[45]) ).
thf(148,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Finite__Set_Ofinite) ).
thf(724,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(146,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_emptyE) ).
thf(719,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(155,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_26_subsetI) ).
thf(751,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)],[155]) ).
thf(174,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_86_prop__restrict) ).
thf(802,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)],[174]) ).
thf(101,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p953238171igraph @ TA @ A )
=> ( ( pair_p460180511igraph @ TA @ A )
=> ( pair_p389585203_graph @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_pair__pseudo__graph_Ointro) ).
thf(587,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p953238171igraph @ TA @ A )
=> ( ( pair_p460180511igraph @ TA @ A )
=> ( pair_p389585203_graph @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(185,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(838,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(206,axiom,
! [TA: $tType,A: set @ TA,B: nat] :
( ~ ( finite_finite2 @ TA @ A )
=> ? [C: set @ TA] :
( ( finite_finite2 @ TA @ C )
& ( ( finite_card @ TA @ C )
= B )
& ( ord_less_eq @ ( set @ TA ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_infinite__arbitrarily__large) ).
thf(902,plain,
! [TA: $tType,A: set @ TA,B: nat] :
( ~ ( finite_finite2 @ TA @ A )
=> ? [C: set @ TA] :
( ( finite_finite2 @ TA @ C )
& ( ( finite_card @ TA @ C )
= B )
& ( ord_less_eq @ ( set @ TA ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(90,axiom,
! [TA: $tType] :
( ( pair_p389585203_graph @ TA )
= ( ^ [A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p953238171igraph @ TA @ A )
& ( pair_p460180511igraph @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_pair__pseudo__graph__def) ).
thf(559,plain,
! [TA: $tType] :
( ( pair_p389585203_graph @ TA )
= ( ^ [A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p953238171igraph @ TA @ A )
& ( pair_p460180511igraph @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(46,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
& ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_conj__subset__def) ).
thf(421,plain,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
& ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(228,axiom,
finite_finite @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Finite__Set_Ofinite_23) ).
thf(969,plain,
finite_finite @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(243,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: set @ TB,C: TB > ( set @ TA )] :
( ( member @ ( product_prod @ TB @ TA ) @ A @ ( product_Sigma @ TB @ TA @ B @ C ) )
=> ~ ! [D: TB] :
( ( member @ TB @ D @ B )
=> ! [E: TA] :
( ( member @ TA @ E @ ( C @ D ) )
=> ( A
!= ( product_Pair @ TB @ TA @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_SigmaE) ).
thf(1013,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: set @ TB,C: TB > ( set @ TA )] :
( ( member @ ( product_prod @ TB @ TA ) @ A @ ( product_Sigma @ TB @ TA @ B @ C ) )
=> ~ ! [D: TB] :
( ( member @ TB @ D @ B )
=> ! [E: TA] :
( ( member @ TA @ E @ ( C @ D ) )
=> ( A
!= ( product_Pair @ TB @ TA @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(273,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( finite_finite2 @ TA @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) )
=> ( ( finite_finite2 @ ( product_prod @ TA @ TA ) @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( pair_p1373739070axioms @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_pair__fin__digraph__axioms_Ointro) ).
thf(1115,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( finite_finite2 @ TA @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) )
=> ( ( finite_finite2 @ ( product_prod @ TA @ TA ) @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( pair_p1373739070axioms @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(117,axiom,
preorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_2) ).
thf(638,plain,
preorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(191,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB,C: TA > TB > $o] :
( ~ ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TB @ B )
=> ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ? [E: TB] :
( ( member @ TB @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: TB] :
( ( member @ TB @ D @ B )
& ~ ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_pigeonhole__infinite__rel) ).
thf(853,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB,C: TA > TB > $o] :
( ~ ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TB @ B )
=> ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ? [E: TB] :
( ( member @ TB @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: TB] :
( ( member @ TB @ D @ B )
& ~ ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(214,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ TB,C: set @ TA,D: set @ TA] :
( ( member @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) )
@ ( product_Sigma @ TA @ TB @ C
@ ^ [E: TA] : B )
@ ( product_Sigma @ TA @ TB @ D
@ ^ [E: TA] : B ) )
= ( ord_less_eq @ ( set @ TA ) @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_Times__subset__cancel2) ).
thf(924,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ TB,C: set @ TA,D: set @ TA] :
( ( member @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) )
@ ( product_Sigma @ TA @ TB @ C
@ ^ [E: TA] : B )
@ ( product_Sigma @ TA @ TB @ D
@ ^ [E: TA] : B ) )
= ( ord_less_eq @ ( set @ TA ) @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(70,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_wf_digraph @ TA @ A )
=> ( ( pair_p814123999axioms @ TA @ A )
=> ( pair_p1282390076igraph @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_pair__loopfree__digraph_Ointro) ).
thf(492,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_wf_digraph @ TA @ A )
=> ( ( pair_p814123999axioms @ TA @ A )
=> ( pair_p1282390076igraph @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(169,axiom,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_Set_Ois__empty__def) ).
thf(789,plain,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: TA > TB > TC,C: TA > TB > TC,D: product_prod @ TA @ TB] :
( ! [E: TA,F: TB] :
( ( ( product_Pair @ TA @ TB @ E @ F )
= A )
=> ( ( B @ E @ F )
= ( C @ E @ F ) ) )
=> ( ( D = A )
=> ( ( product_case_prod @ TA @ TB @ TC @ B @ D )
= ( product_case_prod @ TA @ TB @ TC @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_split__cong) ).
thf(623,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: TA > TB > TC,C: TA > TB > TC,D: product_prod @ TA @ TB] :
( ! [E: TA,F: TB] :
( ( ( product_Pair @ TA @ TB @ E @ F )
= A )
=> ( ( B @ E @ F )
= ( C @ E @ F ) ) )
=> ( ( D = A )
=> ( ( product_case_prod @ TA @ TB @ TC @ B @ D )
= ( product_case_prod @ TA @ TB @ TC @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > ( set @ TB ),D: TA > ( set @ TB )] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( product_Sigma @ TA @ TB @ A @ C )
= ( product_Sigma @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_Sigma__cong) ).
thf(514,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > ( set @ TB ),D: TA > ( set @ TB )] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( product_Sigma @ TA @ TB @ A @ C )
= ( product_Sigma @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(255,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit,B: product_prod @ TA @ TA,C: TA] :
( ( pair_pair_wf_digraph @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ B @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( ~ ( member @ TA @ C @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) )
=> ( pair_pair_wf_digraph @ TA @ ( pair_subdivide @ TA @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_pair__wf__digraph_Opair__wf__digraph__subdivide) ).
thf(1051,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit,B: product_prod @ TA @ TA,C: TA] :
( ( pair_pair_wf_digraph @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ B @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( ~ ( member @ TA @ C @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) )
=> ( pair_pair_wf_digraph @ TA @ ( pair_subdivide @ TA @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(252,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_171_pred__subset__eq2) ).
thf(1040,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)],[252]) ).
thf(271,axiom,
! [TA: $tType] :
( ( finite_Fpow @ TA )
= ( ^ [A: set @ TA] :
( collect @ ( set @ TA )
@ ^ [B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ B @ A )
& ( finite_finite2 @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_Fpow__def) ).
thf(1109,plain,
! [TA: $tType] :
( ( finite_Fpow @ TA )
= ( ^ [A: set @ TA] :
( collect @ ( set @ TA )
@ ^ [B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ B @ A )
& ( finite_finite2 @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(67,axiom,
linorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(485,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(279,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( ( ( finite_card @ TA @ B )
= ( finite_card @ TA @ A ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_card__subset__eq) ).
thf(1136,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( ( ( finite_card @ TA @ B )
= ( finite_card @ TA @ A ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(245,axiom,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB )] :
( ( product_Sigma @ TA @ TB @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_Sigma__empty1) ).
thf(1020,plain,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB )] :
( ( product_Sigma @ TA @ TB @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TB > TD,C: product_prod @ TA @ TB] :
( ( A @ ( product_case_prod @ TA @ TB @ TD @ B @ C ) )
= ( product_case_prod @ TA @ TB @ TC
@ ^ [D: TA,E: TB] : ( A @ ( B @ D @ E ) )
@ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_prod_Ocase__distrib) ).
thf(348,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TB > TD,C: product_prod @ TA @ TB] :
( ( A @ ( product_case_prod @ TA @ TB @ TD @ B @ C ) )
= ( product_case_prod @ TA @ TB @ TC
@ ^ [D: TA,E: TB] : ( A @ ( B @ D @ E ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(290,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( ord_less_eq @ nat @ ( finite_card @ TA @ B ) @ ( finite_card @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_card__mono) ).
thf(1169,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( ord_less_eq @ nat @ ( finite_card @ TA @ B ) @ ( finite_card @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(634,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(136,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_117_ex__in__conv) ).
thf(692,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)],[136]) ).
thf(4,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_119_bot_Oextremum__uniqueI) ).
thf(293,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)],[4]) ).
thf(37,axiom,
! [TA: $tType,A: set @ TA] : ( member @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ ( finite_Fpow @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_empty__in__Fpow) ).
thf(396,plain,
! [TA: $tType,A: set @ TA] : ( member @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ ( finite_Fpow @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(127,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_63_le__fun__def) ).
thf(660,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)],[127]) ).
thf(234,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB] :
( ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TB @ B )
=> ( finite_finite2 @ ( product_prod @ TA @ TB )
@ ( product_Sigma @ TA @ TB @ A
@ ^ [C: TA] : B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_finite__cartesian__product) ).
thf(988,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB] :
( ( finite_finite2 @ TA @ A )
=> ( ( finite_finite2 @ TB @ B )
=> ( finite_finite2 @ ( product_prod @ TA @ TB )
@ ( product_Sigma @ TA @ TB @ A
@ ^ [C: TA] : B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(188,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p389585203_graph @ TA @ A )
=> ( pair_p389585203_graph @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_pair__pseudo__graph_Opair__pseudo__graph) ).
thf(849,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(11,axiom,
bot @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_18) ).
thf(312,plain,
bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(107,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_digraph @ TA @ A )
=> ( ( pair_p389585203_graph @ TA @ A )
=> ( pair_pair_graph @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_pair__graph_Ointro) ).
thf(602,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_digraph @ TA @ A )
=> ( ( pair_p389585203_graph @ TA @ A )
=> ( pair_pair_graph @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(159,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_17) ).
thf(766,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(307,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_digraph @ TA @ A )
=> ( pair_pair_digraph @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_pair__digraph_Opair__digraph) ).
thf(292,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(55,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_120_bot_Oextremum__unique) ).
thf(452,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)],[55]) ).
thf(84,axiom,
! [TA: $tType,A: set @ TA] :
( ( finite_Fpow @ TA @ A )
!= ( bot_bot @ ( set @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_Fpow__not__empty) ).
thf(546,plain,
! [TA: $tType,A: set @ TA] :
( ( finite_Fpow @ TA @ A )
!= ( bot_bot @ ( set @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(285,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( ( ord_less_eq @ nat @ ( finite_card @ TA @ A ) @ ( finite_card @ TA @ B ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_card__seteq) ).
thf(1153,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( ( ord_less_eq @ nat @ ( finite_card @ TA @ A ) @ ( finite_card @ TA @ B ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(27,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_subset__refl) ).
thf(366,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(208,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( finite_finite2 @ TA @ A )
=> ~ ( finite_finite2 @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_infinite__super) ).
thf(910,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( finite_finite2 @ TA @ A )
=> ~ ( finite_finite2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(153,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p953238171igraph @ TA @ A )
=> ( pair_pair_wf_digraph @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_pair__fin__digraph_Oaxioms_I1_J) ).
thf(746,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p953238171igraph @ TA @ A )
=> ( pair_pair_wf_digraph @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(181,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA] :
( ( product_case_prod @ TB @ TA @ $o @ A @ ( product_Pair @ TB @ TA @ B @ C ) )
=> ( A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_case__prodD) ).
thf(825,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA] :
( ( product_case_prod @ TB @ TA @ $o @ A @ ( product_Pair @ TB @ TA @ B @ C ) )
=> ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(165,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_bot__apply) ).
thf(778,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(179,axiom,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_11) ).
thf(820,plain,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(35,axiom,
order_bot @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__bot_12) ).
thf(392,plain,
order_bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(47,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p460180511igraph @ TA @ A )
=> ( ( pair_p1282390076igraph @ TA @ A )
=> ( pair_p1033978749igraph @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_pair__bidirected__digraph_Ointro) ).
thf(424,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p460180511igraph @ TA @ A )
=> ( ( pair_p1282390076igraph @ TA @ A )
=> ( pair_p1033978749igraph @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(41,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_37_dual__order_Oantisym) ).
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)],[41]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TA > $o,B: TB,C: TC,D: TA] :
( ( product_case_prod @ TB @ TC @ ( TA > $o ) @ A @ ( product_Pair @ TB @ TC @ B @ C ) @ D )
=> ( A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_case__prodD_H) ).
thf(429,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TA > $o,B: TB,C: TC,D: TA] :
( ( product_case_prod @ TB @ TC @ ( TA > $o ) @ A @ ( product_Pair @ TB @ TC @ B @ C ) @ D )
=> ( A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(177,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_116_equals0I) ).
thf(815,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)],[177]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( produc2004651681e_prod @ TA @ TB @ TC )
= ( product_case_prod @ TA @ TB @ TC ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_internal__case__prod__def) ).
thf(467,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( produc2004651681e_prod @ TA @ TB @ TC )
= ( product_case_prod @ TA @ TB @ TC ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(25,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_graph @ TA @ A )
=> ( pair_p389585203_graph @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_pair__graph_Oaxioms_I2_J) ).
thf(361,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_graph @ TA @ A )
=> ( pair_p389585203_graph @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(198,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
| ( finite_finite2 @ TA @ ( collect @ TA @ B ) ) )
=> ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_finite__Collect__conjI) ).
thf(879,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
| ( finite_finite2 @ TA @ ( collect @ TA @ B ) ) )
=> ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(17,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_64_le__funI) ).
thf(329,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)],[17]) ).
thf(78,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_79_pred__subset__eq) ).
thf(522,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)],[78]) ).
thf(287,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit,B: product_prod @ TA @ TA,C: TA] :
( ( pair_p389585203_graph @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ B @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( ~ ( member @ TA @ C @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) )
=> ( pair_p389585203_graph @ TA @ ( pair_subdivide @ TA @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_pair__pseudo__graph_Opair__pseudo__graph__subdivide) ).
thf(1159,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit,B: product_prod @ TA @ TA,C: TA] :
( ( pair_p389585203_graph @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ B @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( ~ ( member @ TA @ C @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) )
=> ( pair_p389585203_graph @ TA @ ( pair_subdivide @ TA @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(263,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA,C: set @ TB,D: set @ TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TB @ TA ) )
@ ( product_Sigma @ TB @ TA @ A
@ ^ [E: TB] : B )
@ ( product_Sigma @ TB @ TA @ C
@ ^ [E: TB] : D ) )
= ( ( A
= ( bot_bot @ ( set @ TB ) ) )
| ( B
= ( bot_bot @ ( set @ TA ) ) )
| ( ( ord_less_eq @ ( set @ TB ) @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_times__subset__iff) ).
thf(1079,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA,C: set @ TB,D: set @ TA] :
( ( ord_less_eq @ ( set @ ( product_prod @ TB @ TA ) )
@ ( product_Sigma @ TB @ TA @ A
@ ^ [E: TB] : B )
@ ( product_Sigma @ TB @ TA @ C
@ ^ [E: TB] : D ) )
= ( ( A
= ( bot_bot @ ( set @ TB ) ) )
| ( B
= ( bot_bot @ ( set @ TA ) ) )
| ( ( ord_less_eq @ ( set @ TB ) @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(134,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_66_le__funD) ).
thf(682,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)],[134]) ).
thf(86,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p389585203_graph @ TA @ A )
=> ( pair_p460180511igraph @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_pair__pseudo__graph_Oaxioms_I2_J) ).
thf(551,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p389585203_graph @ TA @ A )
=> ( pair_p460180511igraph @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(15,axiom,
! [TA: $tType,A: TA > TA > $o] :
( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA )
@ ^ [B: TA,C: TA] :
( ( A @ B @ C )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_eq__subset) ).
thf(324,plain,
! [TA: $tType,A: TA > TA > $o] :
( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA )
@ ^ [B: TA,C: TA] :
( ( A @ B @ C )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(196,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o] :
( ( ord_less_eq @ ( TA > TB > $o ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ A ) ) @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_Collect__case__prod__mono) ).
thf(874,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o] :
( ( ord_less_eq @ ( TA > TB > $o ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ A ) ) @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(13,axiom,
! [TA: $tType] :
( ( pair_p1282390076igraph @ TA )
= ( ^ [A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_wf_digraph @ TA @ A )
& ( pair_p814123999axioms @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_pair__loopfree__digraph__def) ).
thf(317,plain,
! [TA: $tType] :
( ( pair_p1282390076igraph @ TA )
= ( ^ [A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_wf_digraph @ TA @ A )
& ( pair_p814123999axioms @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(110,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_40_linorder__wlog) ).
thf(615,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)],[110]) ).
thf(34,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_61_order__subst2) ).
thf(388,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)],[34]) ).
thf(23,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_38_dual__order_Oeq__iff) ).
thf(356,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)],[23]) ).
thf(103,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_78_in__mono) ).
thf(593,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)],[103]) ).
thf(73,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_56_linear) ).
thf(499,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)],[73]) ).
thf(151,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p1033978749igraph @ TA @ A )
=> ( pair_p1282390076igraph @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_pair__bidirected__digraph_Oaxioms_I2_J) ).
thf(742,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p1033978749igraph @ TA @ A )
=> ( pair_p1282390076igraph @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( product_case_prod @ TA @ TB @ $o
@ ^ [B: TA,C: TB] : $true
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_prod_Odisc__eq__case) ).
thf(578,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( product_case_prod @ TA @ TB @ $o
@ ^ [B: TA,C: TB] : $true
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(264,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit,B: product_prod @ TA @ TA,C: TA] :
( ( pair_p460180511igraph @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ B @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( ~ ( member @ TA @ C @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) )
=> ( pair_p460180511igraph @ TA @ ( pair_subdivide @ TA @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_pair__sym__digraph_Opair__sym__digraph__subdivide) ).
thf(1082,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit,B: product_prod @ TA @ TA,C: TA] :
( ( pair_p460180511igraph @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ B @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( ~ ( member @ TA @ C @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) )
=> ( pair_p460180511igraph @ TA @ ( pair_subdivide @ TA @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: $o,D: TB,E: TA] :
( ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ B )
& C )
=> ( C
& ( ( A @ D @ E )
=> ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_predicate2D__conj) ).
thf(488,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: $o,D: TB,E: TA] :
( ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ B )
& C )
=> ( C
& ( ( A @ D @ E )
=> ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(218,axiom,
! [TA: $tType,TB: $tType,A: set @ TA] :
( ( product_Sigma @ TA @ TB @ A
@ ^ [B: TA] : ( bot_bot @ ( set @ TB ) ) )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_Sigma__empty2) ).
thf(933,plain,
! [TA: $tType,TB: $tType,A: set @ TA] :
( ( product_Sigma @ TA @ TB @ A
@ ^ [B: TA] : ( bot_bot @ ( set @ TB ) ) )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(88,axiom,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_bot_Oextremum) ).
thf(554,plain,
! [TA: $tType] :
( ( order_bot @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( bot_bot @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(130,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_115_equals0D) ).
thf(669,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)],[130]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType,A: TA > TA,B: set @ TB,C: set @ ( product_prod @ TB @ TB ),D: TA] :
( ( pair_p1108258481update @ TA @ TB @ A @ ( pair_p1152105390ph_ext @ TB @ TA @ B @ C @ D ) )
= ( pair_p1152105390ph_ext @ TB @ TA @ B @ C @ ( A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_pair__pre__digraph_Oupdate__convs_I3_J) ).
thf(642,plain,
! [TA: $tType,TB: $tType,A: TA > TA,B: set @ TB,C: set @ ( product_prod @ TB @ TB ),D: TA] :
( ( pair_p1108258481update @ TA @ TB @ A @ ( pair_p1152105390ph_ext @ TB @ TA @ B @ C @ D ) )
= ( pair_p1152105390ph_ext @ TB @ TA @ B @ C @ ( A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(116,axiom,
order @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_3) ).
thf(637,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(133,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TB] :
( ( pair_pair_pre_pverts @ TA @ TB @ ( pair_p1152105390ph_ext @ TA @ TB @ A @ B @ C ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_pair__pre__digraph_Oselect__convs_I1_J) ).
thf(679,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA ),C: TB] :
( ( pair_pair_pre_pverts @ TA @ TB @ ( pair_p1152105390ph_ext @ TA @ TB @ A @ B @ C ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(229,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ TA,D: TA > ( set @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( product_Sigma @ TA @ TB @ C @ D ) )
=> ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_SigmaD1) ).
thf(970,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ TA,D: TA > ( set @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( product_Sigma @ TA @ TB @ C @ D ) )
=> ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(36,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_141_prod_Oinject) ).
thf(393,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)],[36]) ).
thf(122,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_159_Pair__inject) ).
thf(647,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)],[122]) ).
thf(284,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_case_prod @ TA @ TB @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_case__prod__Pair__iden) ).
thf(1150,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_case_prod @ TA @ TB @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(147,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ TB,C: set @ TA,D: set @ TA] :
( ( member @ TB @ A @ B )
=> ( ( ( product_Sigma @ TA @ TB @ C
@ ^ [E: TA] : B )
= ( product_Sigma @ TA @ TB @ D
@ ^ [E: TA] : B ) )
= ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Times__eq__cancel2) ).
thf(721,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ TB,C: set @ TA,D: set @ TA] :
( ( member @ TB @ A @ B )
=> ( ( ( product_Sigma @ TA @ TB @ C
@ ^ [E: TA] : B )
= ( product_Sigma @ TA @ TB @ D
@ ^ [E: TA] : B ) )
= ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(93,axiom,
! [TA: $tType,A: ( pair_p1731315293ph_ext @ TA @ product_unit ) > ( product_prod @ TA @ TA ) > TA > $o,B: pair_p1731315293ph_ext @ TA @ product_unit,C: product_prod @ TA @ TA,D: TA] :
( ! [E: pair_p1731315293ph_ext @ TA @ product_unit,F: TA,G: TA,H: TA] : ( A @ E @ ( product_Pair @ TA @ TA @ F @ G ) @ H )
=> ( A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_subdivide_Oinduct) ).
thf(569,plain,
! [TA: $tType,A: ( pair_p1731315293ph_ext @ TA @ product_unit ) > ( product_prod @ TA @ TA ) > TA > $o,B: pair_p1731315293ph_ext @ TA @ product_unit,C: product_prod @ TA @ TA,D: TA] :
( ! [E: pair_p1731315293ph_ext @ TA @ product_unit,F: TA,G: TA,H: TA] : ( A @ E @ ( product_Pair @ TA @ TA @ F @ G ) @ H )
=> ( A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TB > TA > ( set @ TC ),C: TB,D: TA] :
( ( member @ TC @ A @ ( B @ C @ D ) )
=> ( member @ TC @ A @ ( product_case_prod @ TB @ TA @ ( set @ TC ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_mem__case__prodI) ).
thf(371,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TB > TA > ( set @ TC ),C: TB,D: TA] :
( ( member @ TC @ A @ ( B @ C @ D ) )
=> ( member @ TC @ A @ ( product_case_prod @ TB @ TA @ ( set @ TC ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(258,axiom,
bot @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Obot_26) ).
thf(1060,plain,
bot @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: TB,D: TA] :
( ( ord_less_eq @ ( TB > TA > $o ) @ A @ B )
=> ( ( A @ C @ D )
=> ( B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_predicate2D) ).
thf(457,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: TB,D: TA] :
( ( ord_less_eq @ ( TB > TA > $o ) @ A @ B )
=> ( ( A @ C @ D )
=> ( B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(170,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_empty__def) ).
thf(792,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(220,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > ( set @ TB )] :
( ( member @ TA @ A @ B )
=> ( ( member @ TB @ C @ ( D @ A ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ C ) @ ( product_Sigma @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_SigmaI) ).
thf(938,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > ( set @ TB )] :
( ( member @ TA @ A @ B )
=> ( ( member @ TB @ C @ ( D @ A ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ C ) @ ( product_Sigma @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(38,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_73_equalityD2) ).
thf(398,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)],[38]) ).
thf(262,axiom,
! [TA: $tType,A: set @ TA,B: nat] :
( ! [C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ C @ A )
=> ( ( finite_finite2 @ TA @ C )
=> ( ord_less_eq @ nat @ ( finite_card @ TA @ C ) @ B ) ) )
=> ( ( finite_finite2 @ TA @ A )
& ( ord_less_eq @ nat @ ( finite_card @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_finite__if__finite__subsets__card__bdd) ).
thf(1071,plain,
! [TA: $tType,A: set @ TA,B: nat] :
( ! [C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ C @ A )
=> ( ( finite_finite2 @ TA @ C )
=> ( ord_less_eq @ nat @ ( finite_card @ TA @ C ) @ B ) ) )
=> ( ( finite_finite2 @ TA @ A )
& ( ord_less_eq @ nat @ ( finite_card @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(132,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: TC,C: TA > TB > ( set @ TC )] :
( ! [D: TA,E: TB] :
( ( A
= ( product_Pair @ TA @ TB @ D @ E ) )
=> ( member @ TC @ B @ ( C @ D @ E ) ) )
=> ( member @ TC @ B @ ( product_case_prod @ TA @ TB @ ( set @ TC ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_mem__case__prodI2) ).
thf(674,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: TC,C: TA > TB > ( set @ TC )] :
( ! [D: TA,E: TB] :
( ( A
= ( product_Pair @ TA @ TB @ D @ E ) )
=> ( member @ TC @ B @ ( C @ D @ E ) ) )
=> ( member @ TC @ B @ ( product_case_prod @ TA @ TB @ ( set @ TC ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(247,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( bNF_Ca1785829860lChain @ TA @ TB )
= ( ^ [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 )
=> ( ord_less_eq @ TB @ ( B @ C ) @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_relChain__def) ).
thf(1026,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( bNF_Ca1785829860lChain @ TA @ TB )
= ( ^ [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 )
=> ( ord_less_eq @ TB @ ( B @ C ) @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(80,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( set @ TA ) ) @ ( finite_Fpow @ TA @ A ) @ ( finite_Fpow @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_Fpow__mono) ).
thf(530,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( set @ TA ) ) @ ( finite_Fpow @ TA @ A ) @ ( finite_Fpow @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(163,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( finite_finite @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Finite__Set_Ofinite_8) ).
thf(773,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( finite_finite @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(201,axiom,
! [TA: $tType] : ( finite_finite2 @ TA @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_finite_OemptyI) ).
thf(888,plain,
! [TA: $tType] : ( finite_finite2 @ TA @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(6,axiom,
! [TA: $tType] :
( ( pair_pair_graph @ TA )
= ( ^ [A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_digraph @ TA @ A )
& ( pair_p389585203_graph @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_pair__graph__def) ).
thf(298,plain,
! [TA: $tType] :
( ( pair_pair_graph @ TA )
= ( ^ [A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_digraph @ TA @ A )
& ( pair_p389585203_graph @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
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(412,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(227,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_150_prod__induct6) ).
thf(965,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)],[227]) ).
thf(95,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_191_rev__predicate2D) ).
thf(573,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)],[95]) ).
thf(5,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_wf_digraph @ TA @ A )
=> ( ( pair_p477239746axioms @ TA @ A )
=> ( pair_p460180511igraph @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_pair__sym__digraph_Ointro) ).
thf(296,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_wf_digraph @ TA @ A )
=> ( ( pair_p477239746axioms @ TA @ A )
=> ( pair_p460180511igraph @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,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_160_prod__cases) ).
thf(375,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)],[31]) ).
thf(91,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_84_subset__CollectI) ).
thf(562,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)],[91]) ).
thf(240,axiom,
! [A: nat] :
( finite_finite2 @ nat
@ ( collect @ nat
@ ^ [B: nat] : ( ord_less_eq @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_finite__Collect__le__nat) ).
thf(1007,plain,
! [A: nat] :
( finite_finite2 @ nat
@ ( collect @ nat
@ ^ [B: nat] : ( ord_less_eq @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(39,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_empty__subsetI) ).
thf(402,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1,conjecture,
finite_finite2 @ ( product_prod @ a @ a ) @ ( pair_pair_pre_parcs @ a @ product_unit @ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( finite_finite2 @ ( product_prod @ a @ a ) @ ( pair_pair_pre_parcs @ a @ product_unit @ g ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(291,plain,
~ ( finite_finite2 @ ( product_prod @ a @ a ) @ ( pair_pair_pre_parcs @ a @ product_unit @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(225,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA] :
( ( finite_finite2 @ ( product_prod @ TB @ TA )
@ ( product_Sigma @ TB @ TA @ A
@ ^ [C: TB] : B ) )
= ( ( A
= ( bot_bot @ ( set @ TB ) ) )
| ( B
= ( bot_bot @ ( set @ TA ) ) )
| ( ( finite_finite2 @ TB @ A )
& ( finite_finite2 @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_finite__cartesian__product__iff) ).
thf(958,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA] :
( ( finite_finite2 @ ( product_prod @ TB @ TA )
@ ( product_Sigma @ TB @ TA @ A
@ ^ [C: TB] : B ) )
= ( ( A
= ( bot_bot @ ( set @ TB ) ) )
| ( B
= ( bot_bot @ ( set @ TA ) ) )
| ( ( finite_finite2 @ TB @ A )
& ( finite_finite2 @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(280,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB] :
( ( finite_finite2 @ ( product_prod @ TA @ TB )
@ ( product_Sigma @ TA @ TB @ A
@ ^ [C: TA] : B ) )
=> ( ( B
!= ( bot_bot @ ( set @ TB ) ) )
=> ( finite_finite2 @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_finite__cartesian__productD1) ).
thf(1139,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB] :
( ( finite_finite2 @ ( product_prod @ TA @ TB )
@ ( product_Sigma @ TA @ TB @ A
@ ^ [C: TA] : B ) )
=> ( ( B
!= ( bot_bot @ ( set @ TB ) ) )
=> ( finite_finite2 @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(219,axiom,
( ( finite_finite2 @ nat )
= ( ^ [A: set @ nat] :
? [B: nat] :
! [C: nat] :
( ( member @ nat @ C @ A )
=> ( ord_less_eq @ nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_finite__nat__set__iff__bounded__le) ).
thf(936,plain,
( ( finite_finite2 @ nat )
= ( ^ [A: set @ nat] :
? [B: nat] :
! [C: nat] :
( ( member @ nat @ C @ A )
=> ( ord_less_eq @ nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(12,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_147_old_Oprod_Oinducts) ).
thf(313,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)],[12]) ).
thf(168,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_65_le__funE) ).
thf(787,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)],[168]) ).
thf(224,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB,C: TB > TA > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [D: TB] :
( ( member @ TB @ D @ B )
=> ? [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: TB,E: TB,F: TA] :
( ( member @ TB @ D @ B )
=> ( ( member @ TB @ E @ B )
=> ( ( member @ TA @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq @ nat @ ( finite_card @ TB @ B ) @ ( finite_card @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_card__le__if__inj__on__rel) ).
thf(947,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB,C: TB > TA > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [D: TB] :
( ( member @ TB @ D @ B )
=> ? [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ D @ E ) ) )
=> ( ! [D: TB,E: TB,F: TA] :
( ( member @ TB @ D @ B )
=> ( ( member @ TB @ E @ B )
=> ( ( member @ TA @ F @ A )
=> ( ( C @ D @ F )
=> ( ( C @ E @ F )
=> ( D = E ) ) ) ) ) )
=> ( ord_less_eq @ nat @ ( finite_card @ TB @ B ) @ ( finite_card @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(212,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_156_prod__cases5) ).
thf(919,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)],[212]) ).
thf(175,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_102_all__not__in__conv) ).
thf(804,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)],[175]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > $o,B: TC > TA > TB,C: product_prod @ TC @ TA] :
( ( A @ ( product_case_prod @ TC @ TA @ TB @ B @ C ) )
=> ~ ! [D: TC,E: TA] :
( ( C
= ( product_Pair @ TC @ TA @ D @ E ) )
=> ~ ( A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_case__prodE2) ).
thf(604,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > $o,B: TC > TA > TB,C: product_prod @ TC @ TA] :
( ( A @ ( product_case_prod @ TC @ TA @ TB @ B @ C ) )
=> ~ ! [D: TC,E: TA] :
( ( C
= ( product_Pair @ TC @ TA @ D @ E ) )
=> ~ ( A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(242,axiom,
! [TA: $tType,A: TA > $o] :
( ~ ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
=> ? [B: TA] : ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_not__finite__existsD) ).
thf(1011,plain,
! [TA: $tType,A: TA > $o] :
( ~ ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
=> ? [B: TA] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(254,axiom,
! [TA: $tType,A: product_prod @ ( pair_p1731315293ph_ext @ TA @ product_unit ) @ ( product_prod @ ( product_prod @ TA @ TA ) @ TA )] :
~ ! [B: pair_p1731315293ph_ext @ TA @ product_unit,C: TA,D: TA,E: TA] :
( A
!= ( product_Pair @ ( pair_p1731315293ph_ext @ TA @ product_unit ) @ ( product_prod @ ( product_prod @ TA @ TA ) @ TA ) @ B @ ( product_Pair @ ( product_prod @ TA @ TA ) @ TA @ ( product_Pair @ TA @ TA @ C @ D ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_subdivide_Ocases) ).
thf(1048,plain,
! [TA: $tType,A: product_prod @ ( pair_p1731315293ph_ext @ TA @ product_unit ) @ ( product_prod @ ( product_prod @ TA @ TA ) @ TA )] :
~ ! [B: pair_p1731315293ph_ext @ TA @ product_unit,C: TA,D: TA,E: TA] :
( A
!= ( product_Pair @ ( pair_p1731315293ph_ext @ TA @ product_unit ) @ ( product_prod @ ( product_prod @ TA @ TA ) @ TA ) @ B @ ( product_Pair @ ( product_prod @ TA @ TA ) @ TA @ ( product_Pair @ TA @ TA @ C @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(235,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_prod__cases4) ).
thf(990,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(92,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_32_Collect__subset) ).
thf(567,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)],[92]) ).
thf(167,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_67_Collect__mono__iff) ).
thf(784,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)],[167]) ).
thf(274,axiom,
! [A: set @ nat] :
( ( ~ ( finite_finite2 @ nat @ A ) )
= ( ! [B: nat] :
? [C: nat] :
( ( ord_less_eq @ nat @ B @ C )
& ( member @ nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_infinite__nat__iff__unbounded__le) ).
thf(1117,plain,
! [A: set @ nat] :
( ( ~ ( finite_finite2 @ nat @ A ) )
= ( ! [B: nat] :
? [C: nat] :
( ( ord_less_eq @ nat @ B @ C )
& ( member @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(253,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ? [D: TB] : ( B @ C @ D ) )
=> ? [C: TA > TB] :
! [D: TA] :
( ( member @ TA @ D @ A )
=> ( B @ D @ ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_finite__set__choice) ).
thf(1043,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ? [D: TB] : ( B @ C @ D ) )
=> ? [C: TA > TB] :
! [D: TA] :
( ( member @ TA @ D @ A )
=> ( B @ D @ ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(51,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_44_ord__le__eq__trans) ).
thf(434,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)],[51]) ).
thf(202,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p953238171igraph @ TA @ A )
=> ( finite_finite2 @ TA @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_pair__fin__digraph_Opair__finite__verts) ).
thf(890,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p953238171igraph @ TA @ A )
=> ( finite_finite2 @ TA @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(64,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_42_order__trans) ).
thf(477,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)],[64]) ).
thf(33,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p953238171igraph @ TA @ A )
=> ( pair_p953238171igraph @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_pair__fin__digraph_Opair__fin__digraph) ).
thf(387,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(71,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p1033978749igraph @ TA @ A )
=> ( pair_p460180511igraph @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_pair__bidirected__digraph_Oaxioms_I1_J) ).
thf(494,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p1033978749igraph @ TA @ A )
=> ( pair_p460180511igraph @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA,C: set @ TB,D: set @ TA] :
( ( ( product_Sigma @ TB @ TA @ A
@ ^ [E: TB] : B )
= ( product_Sigma @ TB @ TA @ C
@ ^ [E: TB] : D ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( ( A
= ( bot_bot @ ( set @ TB ) ) )
| ( B
= ( bot_bot @ ( set @ TA ) ) ) )
& ( ( C
= ( bot_bot @ ( set @ TB ) ) )
| ( D
= ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_times__eq__iff) ).
thf(631,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA,C: set @ TB,D: set @ TA] :
( ( ( product_Sigma @ TB @ TA @ A
@ ^ [E: TB] : B )
= ( product_Sigma @ TB @ TA @ C
@ ^ [E: TB] : D ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( ( A
= ( bot_bot @ ( set @ TB ) ) )
| ( B
= ( bot_bot @ ( set @ TA ) ) ) )
& ( ( C
= ( bot_bot @ ( set @ TB ) ) )
| ( D
= ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(157,axiom,
! [TA: $tType,TB: $tType,A: ( pair_p1731315293ph_ext @ TA @ TB ) > $o,B: pair_p1731315293ph_ext @ TA @ TB] :
( ! [C: set @ TA,D: set @ ( product_prod @ TA @ TA ),E: TB] : ( A @ ( pair_p1152105390ph_ext @ TA @ TB @ C @ D @ E ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_pair__pre__digraph_Oinduct__scheme) ).
thf(758,plain,
! [TA: $tType,TB: $tType,A: ( pair_p1731315293ph_ext @ TA @ TB ) > $o,B: pair_p1731315293ph_ext @ TA @ TB] :
( ! [C: set @ TA,D: set @ ( product_prod @ TA @ TA ),E: TB] : ( A @ ( pair_p1152105390ph_ext @ TA @ TB @ C @ D @ E ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,A: pair_p1731315293ph_ext @ TA @ TB,B: pair_p1731315293ph_ext @ TA @ TB,C: TB,D: TB > TB,E: TB > TB] :
( ( A = B )
=> ( ( ( pair_pair_pre_more @ TA @ TB @ B )
= C )
=> ( ! [F: TB] :
( ( C = F )
=> ( ( D @ F )
= ( E @ F ) ) )
=> ( ( pair_p1108258481update @ TB @ TA @ D @ A )
= ( pair_p1108258481update @ TB @ TA @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_pair__pre__digraph_Ofold__congs_I3_J) ).
thf(535,plain,
! [TA: $tType,TB: $tType,A: pair_p1731315293ph_ext @ TA @ TB,B: pair_p1731315293ph_ext @ TA @ TB,C: TB,D: TB > TB,E: TB > TB] :
( ( A = B )
=> ( ( ( pair_pair_pre_more @ TA @ TB @ B )
= C )
=> ( ! [F: TB] :
( ( C = F )
=> ( ( D @ F )
= ( E @ F ) ) )
=> ( ( pair_p1108258481update @ TB @ TA @ D @ A )
= ( pair_p1108258481update @ TB @ TA @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(149,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p460180511igraph @ TA @ A )
=> ( pair_pair_wf_digraph @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_pair__sym__digraph_Oaxioms_I1_J) ).
thf(726,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p460180511igraph @ TA @ A )
=> ( pair_pair_wf_digraph @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(111,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p1282390076igraph @ TA @ A )
=> ( pair_pair_wf_digraph @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_pair__loopfree__digraph_Oaxioms_I1_J) ).
thf(621,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p1282390076igraph @ TA @ A )
=> ( pair_pair_wf_digraph @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(139,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ TB ) > TC] :
( ( product_case_prod @ TA @ TB @ TC
@ ^ [B: TA,C: TB] : ( A @ ( product_Pair @ TA @ TB @ B @ C ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_case__prod__eta) ).
thf(700,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ TB ) > TC] :
( ( product_case_prod @ TA @ TB @ TC
@ ^ [B: TA,C: TB] : ( A @ ( product_Pair @ TA @ TB @ B @ C ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(248,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit,B: TA,C: TA] :
( ( pair_p460180511igraph @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_pair__sym__digraph_Oarcs__symmetric) ).
thf(1029,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit,B: TA,C: TA] :
( ( pair_p460180511igraph @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ B ) @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(210,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_145_bot__empty__eq2) ).
thf(915,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)],[210]) ).
thf(222,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p953238171igraph @ TA @ A )
=> ( finite_finite2 @ ( product_prod @ TA @ TA ) @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_pair__fin__digraph_Opair__finite__arcs) ).
thf(943,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p953238171igraph @ TA @ A )
=> ( finite_finite2 @ ( product_prod @ TA @ TA ) @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(259,axiom,
ord @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oord_25) ).
thf(1061,plain,
ord @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(272,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > ( set @ TB )] :
( ( ( product_Sigma @ TA @ TB @ A @ B )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ( B @ C )
= ( bot_bot @ ( set @ TB ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_Sigma__empty__iff) ).
thf(1112,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > ( set @ TB )] :
( ( ( product_Sigma @ TA @ TB @ A @ B )
= ( bot_bot @ ( set @ ( product_prod @ TA @ TB ) ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ( B @ C )
= ( bot_bot @ ( set @ TB ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(209,axiom,
! [TA: $tType,TB: $tType,A: pair_p1731315293ph_ext @ TA @ TB] :
( A
= ( pair_p1152105390ph_ext @ TA @ TB @ ( pair_pair_pre_pverts @ TA @ TB @ A ) @ ( pair_pair_pre_parcs @ TA @ TB @ A ) @ ( pair_pair_pre_more @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_pair__pre__digraph_Osurjective) ).
thf(912,plain,
! [TA: $tType,TB: $tType,A: pair_p1731315293ph_ext @ TA @ TB] :
( A
= ( pair_p1152105390ph_ext @ TA @ TB @ ( pair_pair_pre_pverts @ TA @ TB @ A ) @ ( pair_pair_pre_parcs @ TA @ TB @ A ) @ ( pair_pair_pre_more @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(233,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit,B: product_prod @ TA @ TA,C: TA] :
( ( pair_pair_graph @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ B @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( ~ ( member @ TA @ C @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) )
=> ( pair_pair_graph @ TA @ ( pair_subdivide @ TA @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_pair__graph_Opair__graph__subdivide) ).
thf(986,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit,B: product_prod @ TA @ TA,C: TA] :
( ( pair_pair_graph @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ B @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( ~ ( member @ TA @ C @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) )
=> ( pair_pair_graph @ TA @ ( pair_subdivide @ TA @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(190,axiom,
! [TA: $tType,A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( finite_finite2 @ ( set @ TA )
@ ( collect @ ( set @ TA )
@ ^ [B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_finite__Collect__subsets) ).
thf(851,plain,
! [TA: $tType,A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( finite_finite2 @ ( set @ TA )
@ ( collect @ ( set @ TA )
@ ^ [B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(52,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_76_equalityE) ).
thf(438,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)],[52]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_case_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_case__prod__conv) ).
thf(431,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_case_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(123,axiom,
! [TA: $tType] : ( order_bot @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__bot_6) ).
thf(653,plain,
! [TA: $tType] : ( order_bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(213,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( product_prod @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Finite__Set_Ofinite_19) ).
thf(922,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( product_prod @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(125,axiom,
ord @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_4) ).
thf(658,plain,
ord @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(161,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_75_subset__eq) ).
thf(768,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)],[161]) ).
thf(182,axiom,
! [TA: $tType,A: nat,B: set @ TA] :
( ( ord_less_eq @ nat @ A @ ( finite_card @ TA @ B ) )
=> ? [C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ C @ B )
& ( ( finite_card @ TA @ C )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_card__Ex__subset) ).
thf(827,plain,
! [TA: $tType,A: nat,B: set @ TA] :
( ( ord_less_eq @ nat @ A @ ( finite_card @ TA @ B ) )
=> ? [C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ C @ B )
& ( ( finite_card @ TA @ C )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(115,axiom,
bot @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Obot_5) ).
thf(636,plain,
bot @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(137,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_173_old_Oprod_Orec) ).
thf(695,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)],[137]) ).
thf(56,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_54_le__cases) ).
thf(455,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)],[56]) ).
thf(199,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_174_less__by__empty) ).
thf(883,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)],[199]) ).
thf(250,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_158_prod__cases3) ).
thf(1034,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)],[250]) ).
thf(48,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_43_order__class_Oorder_Oantisym) ).
thf(426,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)],[48]) ).
thf(102,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_55_eq__refl) ).
thf(589,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)],[102]) ).
thf(171,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_predicate1D) ).
thf(795,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(128,axiom,
! [TA: $tType] :
( ( pair_p953238171igraph @ TA )
= ( ^ [A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_wf_digraph @ TA @ A )
& ( pair_p1373739070axioms @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_pair__fin__digraph__def) ).
thf(663,plain,
! [TA: $tType] :
( ( pair_p953238171igraph @ TA )
= ( ^ [A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_wf_digraph @ TA @ A )
& ( pair_p1373739070axioms @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(215,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit,B: TA,C: TA] :
( ( pair_pair_wf_digraph @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( member @ TA @ B @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_pair__wf__digraph_Oin__arcsD1) ).
thf(927,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit,B: TA,C: TA] :
( ( pair_pair_wf_digraph @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( member @ TA @ B @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(282,axiom,
! [A: nat > nat,B: nat] :
( ! [C: nat] : ( ord_less_eq @ nat @ C @ ( A @ C ) )
=> ( finite_finite2 @ nat
@ ( collect @ nat
@ ^ [C: nat] : ( ord_less_eq @ nat @ ( A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_finite__less__ub) ).
thf(1145,plain,
! [A: nat > nat,B: nat] :
( ! [C: nat] : ( ord_less_eq @ nat @ C @ ( A @ C ) )
=> ( finite_finite2 @ nat
@ ( collect @ nat
@ ^ [C: nat] : ( ord_less_eq @ nat @ ( A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(87,axiom,
finite_finite @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Finite__Set_Ofinite_15) ).
thf(553,plain,
finite_finite @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(184,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_39_dual__order_Otrans) ).
thf(836,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)],[184]) ).
thf(79,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: TA > TB > $o] :
( ! [C: TA,D: TB] :
( ( A
= ( product_Pair @ TA @ TB @ C @ D ) )
=> ( B @ C @ D ) )
=> ( product_case_prod @ TA @ TB @ $o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_case__prodI2) ).
thf(525,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: TA > TB > $o] :
( ! [C: TA,D: TB] :
( ( A
= ( product_Pair @ TA @ TB @ C @ D ) )
=> ( B @ C @ D ) )
=> ( product_case_prod @ TA @ TB @ $o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(143,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_103_Collect__empty__eq) ).
thf(712,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)],[143]) ).
thf(98,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_7) ).
thf(580,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(119,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_digraph @ TA @ A )
=> ( pair_pair_wf_digraph @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_pair__digraph_Opair__wf__digraph) ).
thf(640,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_digraph @ TA @ A )
=> ( pair_pair_wf_digraph @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(200,axiom,
( ord_less_eq @ ( set @ ( product_prod @ a @ a ) ) @ ( pair_pair_pre_parcs @ a @ product_unit @ g )
@ ( product_Sigma @ a @ a @ ( pair_pair_pre_pverts @ a @ product_unit @ g )
@ ^ [A: a] : ( pair_pair_pre_pverts @ a @ product_unit @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062parcs_AG_A_092_060subseteq_062_Apverts_AG_A_092_060times_062_Apverts_AG_092_060close_062) ).
thf(887,plain,
( ord_less_eq @ ( set @ ( product_prod @ a @ a ) ) @ ( pair_pair_pre_parcs @ a @ product_unit @ g )
@ ( product_Sigma @ a @ a @ ( pair_pair_pre_pverts @ a @ product_unit @ g )
@ ^ [A: a] : ( pair_pair_pre_pverts @ a @ product_unit @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(268,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB > $o] :
( ( collect @ ( product_prod @ TA @ TB )
@ ( product_case_prod @ TA @ TB @ $o
@ ^ [C: TA,D: TB] :
( ( A @ C )
& ( B @ C @ D ) ) ) )
= ( product_Sigma @ TA @ TB @ ( collect @ TA @ A )
@ ^ [C: TA] : ( collect @ TB @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_Collect__case__prod__Sigma) ).
thf(1098,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB > $o] :
( ( collect @ ( product_prod @ TA @ TB )
@ ( product_case_prod @ TA @ TB @ $o
@ ^ [C: TA,D: TB] :
( ( A @ C )
& ( B @ C @ D ) ) ) )
= ( product_Sigma @ TA @ TB @ ( collect @ TA @ A )
@ ^ [C: TA] : ( collect @ TB @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(236,axiom,
linorder @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Olinorder_22) ).
thf(993,plain,
linorder @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(141,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_bot__fun__def) ).
thf(705,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(286,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: set @ TA,C: set @ TB] :
( ( member @ ( product_prod @ TA @ TB ) @ A @ ( product_product @ TA @ TB @ B @ C ) )
= ( member @ ( product_prod @ TA @ TB ) @ A
@ ( product_Sigma @ TA @ TB @ B
@ ^ [D: TA] : C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_member__product) ).
thf(1156,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: set @ TA,C: set @ TB] :
( ( member @ ( product_prod @ TA @ TB ) @ A @ ( product_product @ TA @ TB @ B @ C ) )
= ( member @ ( product_prod @ TA @ TB ) @ A
@ ( product_Sigma @ TA @ TB @ B
@ ^ [D: TA] : C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(256,axiom,
! [TA: $tType,TB: $tType,A: pair_p1731315293ph_ext @ TA @ TB,B: pair_p1731315293ph_ext @ TA @ TB] :
( ( ( pair_pair_pre_pverts @ TA @ TB @ A )
= ( pair_pair_pre_pverts @ TA @ TB @ B ) )
=> ( ( ( pair_pair_pre_parcs @ TA @ TB @ A )
= ( pair_pair_pre_parcs @ TA @ TB @ B ) )
=> ( ( ( pair_pair_pre_more @ TA @ TB @ A )
= ( pair_pair_pre_more @ TA @ TB @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_pair__pre__digraph_Oequality) ).
thf(1053,plain,
! [TA: $tType,TB: $tType,A: pair_p1731315293ph_ext @ TA @ TB,B: pair_p1731315293ph_ext @ TA @ TB] :
( ( ( pair_pair_pre_pverts @ TA @ TB @ A )
= ( pair_pair_pre_pverts @ TA @ TB @ B ) )
=> ( ( ( pair_pair_pre_parcs @ TA @ TB @ A )
= ( pair_pair_pre_parcs @ TA @ TB @ B ) )
=> ( ( ( pair_pair_pre_more @ TA @ TB @ A )
= ( pair_pair_pre_more @ TA @ TB @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(131,axiom,
order @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_16) ).
thf(673,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(18,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p1282390076igraph @ TA @ A )
=> ( pair_p814123999axioms @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_pair__loopfree__digraph_Oaxioms_I2_J) ).
thf(331,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p1282390076igraph @ TA @ A )
=> ( pair_p814123999axioms @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(100,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p389585203_graph @ TA @ A )
=> ( pair_p953238171igraph @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_pair__pseudo__graph_Oaxioms_I1_J) ).
thf(585,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p389585203_graph @ TA @ A )
=> ( pair_p953238171igraph @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(145,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(717,plain,
! [TA: $tType,TB: $tType] :
( ( order_bot @ TA )
=> ( order_bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(61,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_digraph @ TA @ A )
=> ( pair_p1282390076igraph @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_pair__digraph_Oaxioms_I2_J) ).
thf(470,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_digraph @ TA @ A )
=> ( pair_p1282390076igraph @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
~ ( bot_bot @ ( TB > TA > $o ) @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_bot2E) ).
thf(359,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
~ ( bot_bot @ ( TB > TA > $o ) @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(277,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( ( finite_finite2 @ TA )
= ( ^ [A: set @ TA] : $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_finite__code) ).
thf(1130,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( ( finite_finite2 @ TA )
= ( ^ [A: set @ TA] : $true ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(152,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA] :
( ( A @ B @ C )
=> ( product_case_prod @ TB @ TA @ $o @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_case__prodI) ).
thf(744,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA] :
( ( A @ B @ C )
=> ( product_case_prod @ TB @ TA @ $o @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(140,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_69_subset__trans) ).
thf(703,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)],[140]) ).
thf(246,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
& ( finite_finite2 @ TA @ ( collect @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_finite__Collect__disjI) ).
thf(1023,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( finite_finite2 @ TA
@ ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite2 @ TA @ ( collect @ TA @ A ) )
& ( finite_finite2 @ TA @ ( collect @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(106,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_empty__iff) ).
thf(600,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(231,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_170_subrelI) ).
thf(978,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)],[231]) ).
thf(104,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_124_subset__emptyI) ).
thf(595,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)],[104]) ).
thf(109,axiom,
! [TA: $tType] :
( ( pair_p1033978749igraph @ TA )
= ( ^ [A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p460180511igraph @ TA @ A )
& ( pair_p1282390076igraph @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_pair__bidirected__digraph__def) ).
thf(612,plain,
! [TA: $tType] :
( ( pair_p1033978749igraph @ TA )
= ( ^ [A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p460180511igraph @ TA @ A )
& ( pair_p1282390076igraph @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(197,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_154_prod__cases7) ).
thf(876,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)],[197]) ).
thf(192,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ TA,D: TA > ( set @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( product_Sigma @ TA @ TB @ C @ D ) )
=> ( member @ TB @ B @ ( D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_SigmaD2) ).
thf(859,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ TA,D: TA > ( set @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( product_Sigma @ TA @ TB @ C @ D ) )
=> ( member @ TB @ B @ ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(53,axiom,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_bot__empty__eq) ).
thf(446,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(94,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p953238171igraph @ TA @ A )
=> ( pair_p1373739070axioms @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_pair__fin__digraph_Oaxioms_I2_J) ).
thf(571,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p953238171igraph @ TA @ A )
=> ( pair_p1373739070axioms @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(265,axiom,
! [TA: $tType,A: set @ TA,B: TA > TA > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
~ ( B @ C @ C )
=> ( ! [C: TA,D: TA,E: TA] :
( ( B @ C @ D )
=> ( ( B @ D @ E )
=> ( B @ C @ E ) ) )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ? [D: TA] :
( ( member @ TA @ D @ A )
& ( B @ C @ D ) ) )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_finite__transitivity__chain) ).
thf(1084,plain,
! [TA: $tType,A: set @ TA,B: TA > TA > $o] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
~ ( B @ C @ C )
=> ( ! [C: TA,D: TA,E: TA] :
( ( B @ C @ D )
=> ( ( B @ D @ E )
=> ( B @ C @ E ) ) )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ? [D: TA] :
( ( member @ TA @ D @ A )
& ( B @ C @ D ) ) )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(276,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit,B: TA,C: TA] :
( ( pair_p1282390076igraph @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( B != C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_pair__loopfree__digraph_Ono__loops_H) ).
thf(1126,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit,B: TA,C: TA] :
( ( pair_p1282390076igraph @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( B != C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(162,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_10) ).
thf(771,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(26,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_50_order__class_Oorder_Oeq__iff) ).
thf(363,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)],[26]) ).
thf(89,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_140_old_Oprod_Oinject) ).
thf(556,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)],[89]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > TC,B: ( product_prod @ TA @ TB ) > TC] :
( ! [C: TA,D: TB] :
( ( A @ C @ D )
= ( B @ ( product_Pair @ TA @ TB @ C @ D ) ) )
=> ( ( product_case_prod @ TA @ TB @ TC @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_cond__case__prod__eta) ).
thf(368,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB > TC,B: ( product_prod @ TA @ TB ) > TC] :
( ! [C: TA,D: TB] :
( ( A @ C @ D )
= ( B @ ( product_Pair @ TA @ TB @ C @ D ) ) )
=> ( ( product_case_prod @ TA @ TB @ TC @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(187,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TC > TA > ( set @ TB ),C: product_prod @ TC @ TA] :
( ( member @ TB @ A @ ( product_case_prod @ TC @ TA @ ( set @ TB ) @ B @ C ) )
=> ~ ! [D: TC,E: TA] :
( ( C
= ( product_Pair @ TC @ TA @ D @ E ) )
=> ~ ( member @ TB @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_mem__case__prodE) ).
thf(844,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TC > TA > ( set @ TB ),C: product_prod @ TC @ TA] :
( ( member @ TB @ A @ ( product_case_prod @ TC @ TA @ ( set @ TB ) @ B @ C ) )
=> ~ ! [D: TC,E: TA] :
( ( C
= ( product_Pair @ TC @ TA @ D @ E ) )
=> ~ ( member @ TB @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(226,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > ( set @ TB )] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( finite_finite2 @ TB @ ( B @ C ) ) )
=> ( finite_finite2 @ ( product_prod @ TA @ TB ) @ ( product_Sigma @ TA @ TB @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_finite__SigmaI) ).
thf(961,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > ( set @ TB )] :
( ( finite_finite2 @ TA @ A )
=> ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( finite_finite2 @ TB @ ( B @ C ) ) )
=> ( finite_finite2 @ ( product_prod @ TA @ TB ) @ ( product_Sigma @ TA @ TB @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,A: pair_p1731315293ph_ext @ TB @ TA] :
~ ! [B: set @ TB,C: set @ ( product_prod @ TB @ TB ),D: TA] :
( A
!= ( pair_p1152105390ph_ext @ TB @ TA @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_pair__pre__digraph_Ocases__scheme) ).
thf(304,plain,
! [TA: $tType,TB: $tType,A: pair_p1731315293ph_ext @ TB @ TA] :
~ ! [B: set @ TB,C: set @ ( product_prod @ TB @ TB ),D: TA] :
( A
!= ( pair_p1152105390ph_ext @ TB @ TA @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(260,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ C @ B )
& ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ TA @ D @ C )
=> ( C = D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_finite__has__minimal2) ).
thf(1062,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA,B: TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( member @ TA @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less_eq @ TA @ C @ B )
& ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( ord_less_eq @ TA @ D @ C )
=> ( C = D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(269,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_149_prod__induct7) ).
thf(1101,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)],[269]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_internal__case__prod__conv) ).
thf(351,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(166,axiom,
! [TA: $tType,TB: $tType,A: $o,B: TA > TB > $o] :
( ( product_case_prod @ TA @ TB @ $o
@ ^ [C: TA,D: TB] :
( A
& ( B @ C @ D ) ) )
= ( ^ [C: product_prod @ TA @ TB] :
( A
& ( product_case_prod @ TA @ TB @ $o @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_split__part) ).
thf(781,plain,
! [TA: $tType,TB: $tType,A: $o,B: TA > TB > $o] :
( ( product_case_prod @ TA @ TB @ $o
@ ^ [C: TA,D: TB] :
( A
& ( B @ C @ D ) ) )
= ( ^ [C: product_prod @ TA @ TB] :
( A
& ( product_case_prod @ TA @ TB @ $o @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(238,axiom,
! [TA: $tType,A: nat,B: set @ TA] :
( ( ord_less_eq @ nat @ A @ ( finite_card @ TA @ B ) )
=> ~ ! [C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ( ( finite_card @ TA @ C )
= A )
=> ~ ( finite_finite2 @ TA @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_obtain__subset__with__card__n) ).
thf(995,plain,
! [TA: $tType,A: nat,B: set @ TA] :
( ( ord_less_eq @ nat @ A @ ( finite_card @ TA @ B ) )
=> ~ ! [C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ( ( finite_card @ TA @ C )
= A )
=> ~ ( finite_finite2 @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(204,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit,B: product_prod @ TA @ TA,C: TA] :
( ( pair_p1033978749igraph @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ B @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( ~ ( member @ TA @ C @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) )
=> ( pair_p1033978749igraph @ TA @ ( pair_subdivide @ TA @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_pair__bidirected__digraph_Opair__bidirected__digraph__subdivide) ).
thf(896,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit,B: product_prod @ TA @ TA,C: TA] :
( ( pair_p1033978749igraph @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ B @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( ~ ( member @ TA @ C @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) )
=> ( pair_p1033978749igraph @ TA @ ( pair_subdivide @ TA @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(154,axiom,
! [TA: $tType] :
( ( pair_pair_digraph @ TA )
= ( ^ [A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p953238171igraph @ TA @ A )
& ( pair_p1282390076igraph @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_pair__digraph__def) ).
thf(748,plain,
! [TA: $tType] :
( ( pair_pair_digraph @ TA )
= ( ^ [A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_p953238171igraph @ TA @ A )
& ( pair_p1282390076igraph @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(216,axiom,
( finite_finite2 @ ( product_prod @ a @ a )
@ ( product_Sigma @ a @ a @ ( pair_pair_pre_pverts @ a @ product_unit @ g )
@ ^ [A: a] : ( pair_pair_pre_pverts @ a @ product_unit @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062finite_A_Ipverts_AG_A_092_060times_062_Apverts_AG_J_092_060close_062) ).
thf(929,plain,
( finite_finite2 @ ( product_prod @ a @ a )
@ ( product_Sigma @ a @ a @ ( pair_pair_pre_pverts @ a @ product_unit @ g )
@ ^ [A: a] : ( pair_pair_pre_pverts @ a @ product_unit @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(549,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(183,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_34_predicate1I) ).
thf(832,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)],[183]) ).
thf(135,axiom,
! [TA: $tType,TB: $tType,A: pair_p1731315293ph_ext @ TA @ TB,B: pair_p1731315293ph_ext @ TA @ TB,C: TB,D: TB > TB,E: TB > TB] :
( ( A = B )
=> ( ( ( pair_pair_pre_more @ TA @ TB @ B )
= C )
=> ( ! [F: TB] :
( ( F = C )
=> ( ( D @ F )
= ( E @ F ) ) )
=> ( ( pair_p1108258481update @ TB @ TA @ D @ A )
= ( pair_p1108258481update @ TB @ TA @ E @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_pair__pre__digraph_Ounfold__congs_I3_J) ).
thf(684,plain,
! [TA: $tType,TB: $tType,A: pair_p1731315293ph_ext @ TA @ TB,B: pair_p1731315293ph_ext @ TA @ TB,C: TB,D: TB > TB,E: TB > TB] :
( ( A = B )
=> ( ( ( pair_pair_pre_more @ TA @ TB @ B )
= C )
=> ( ! [F: TB] :
( ( F = C )
=> ( ( D @ F )
= ( E @ F ) ) )
=> ( ( pair_p1108258481update @ TB @ TA @ D @ A )
= ( pair_p1108258481update @ TB @ TA @ E @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(288,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ TA,D: TA > ( set @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( product_Sigma @ TA @ TB @ C @ D ) )
=> ~ ( ( member @ TA @ A @ C )
=> ~ ( member @ TB @ B @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_SigmaE2) ).
thf(1161,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ TA,D: TA > ( set @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( product_Sigma @ TA @ TB @ C @ D ) )
=> ~ ( ( member @ TA @ A @ C )
=> ~ ( member @ TB @ B @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(173,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_digraph @ TA @ A )
=> ( pair_p953238171igraph @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_pair__digraph_Oaxioms_I1_J) ).
thf(800,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_digraph @ TA @ A )
=> ( pair_p953238171igraph @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(278,axiom,
! [TA: $tType] :
( ( pair_p1373739070axioms @ TA )
= ( ^ [A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( finite_finite2 @ TA @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) )
& ( finite_finite2 @ ( product_prod @ TA @ TA ) @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_pair__fin__digraph__axioms__def) ).
thf(1133,plain,
! [TA: $tType] :
( ( pair_p1373739070axioms @ TA )
= ( ^ [A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( finite_finite2 @ TA @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) )
& ( finite_finite2 @ ( product_prod @ TA @ TA ) @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(42,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_53_order_Otrans) ).
thf(410,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)],[42]) ).
thf(178,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_wf_digraph @ TA @ A )
=> ( ( pair_p1373739070axioms @ TA @ A )
=> ( pair_p953238171igraph @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_pair__fin__digraph_Ointro) ).
thf(818,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_wf_digraph @ TA @ A )
=> ( ( pair_p1373739070axioms @ TA @ A )
=> ( pair_p953238171igraph @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(283,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( finite_finite2 @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_rev__finite__subset) ).
thf(1148,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( finite_finite2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(195,axiom,
( ( finite_finite2 @ a @ ( pair_pair_pre_pverts @ a @ product_unit @ g ) )
& ( ( finite_card @ a @ ( pair_pair_pre_pverts @ a @ product_unit @ g ) )
= n )
& ( ( pair_pair_pre_parcs @ a @ product_unit @ g )
= ( collect @ ( product_prod @ a @ a )
@ ( product_case_prod @ a @ a @ $o
@ ^ [A: a,B: a] :
( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B )
@ ( product_Sigma @ a @ a @ ( pair_pair_pre_pverts @ a @ product_unit @ g )
@ ^ [C: a] : ( pair_pair_pre_pverts @ a @ product_unit @ g ) ) )
& ( A != B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_calculation) ).
thf(867,plain,
( ( finite_finite2 @ a @ ( pair_pair_pre_pverts @ a @ product_unit @ g ) )
& ( ( finite_card @ a @ ( pair_pair_pre_pverts @ a @ product_unit @ g ) )
= n )
& ( ( pair_pair_pre_parcs @ a @ product_unit @ g )
= ( collect @ ( product_prod @ a @ a )
@ ( product_case_prod @ a @ a @ $o
@ ^ [A: a,B: a] :
( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ A @ B )
@ ( product_Sigma @ a @ a @ ( pair_pair_pre_pverts @ a @ product_unit @ g )
@ ^ [C: a] : ( pair_pair_pre_pverts @ a @ product_unit @ g ) ) )
& ( A != B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(194,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( finite_finite2 @ TA @ B )
=> ( finite_finite2 @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_finite__subset) ).
thf(865,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( finite_finite2 @ TA @ B )
=> ( finite_finite2 @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot) ).
thf(373,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(16,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_161_surj__pair) ).
thf(326,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)],[16]) ).
thf(211,axiom,
order @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Oorder_24) ).
thf(918,plain,
order @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TA > $o,B: product_prod @ TB @ TC,C: TA] :
( ( product_case_prod @ TB @ TC @ ( TA > $o ) @ A @ B @ C )
=> ~ ! [D: TB,E: TC] :
( ( B
= ( product_Pair @ TB @ TC @ D @ E ) )
=> ~ ( A @ D @ E @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_case__prodE_H) ).
thf(506,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TA > $o,B: product_prod @ TB @ TC,C: TA] :
( ( product_case_prod @ TB @ TC @ ( TA > $o ) @ A @ B @ C )
=> ~ ! [D: TB,E: TC] :
( ( B
= ( product_Pair @ TB @ TC @ D @ E ) )
=> ~ ( A @ D @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(176,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_60_ord__eq__le__subst) ).
thf(807,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)],[176]) ).
thf(257,axiom,
! [TA: $tType,A: set @ TA] :
( ~ ( finite_finite2 @ TA @ A )
=> ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_infinite__imp__nonempty) ).
thf(1056,plain,
! [TA: $tType,A: set @ TA] :
( ~ ( finite_finite2 @ TA @ A )
=> ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( product_case_prod @ TA @ TB @ ( TC > TD ) )
= ( ^ [A: TA > TB > TC > TD,B: product_prod @ TA @ TB,C: TC] :
( product_case_prod @ TA @ TB @ TD
@ ^ [D: TA,E: TB] : ( A @ D @ E @ C )
@ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_case__prod__app) ).
thf(532,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( product_case_prod @ TA @ TB @ ( TC > TD ) )
= ( ^ [A: TA > TB > TC > TD,B: product_prod @ TA @ TB,C: TC] :
( product_case_prod @ TA @ TB @ TD
@ ^ [D: TA,E: TB] : ( A @ D @ E @ C )
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(289,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > ( set @ TB ),D: TA > ( set @ TB )] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ord_less_eq @ ( set @ TB ) @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ ( product_Sigma @ TA @ TB @ A @ C ) @ ( product_Sigma @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_Sigma__mono) ).
thf(1165,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > ( set @ TB ),D: TA > ( set @ TB )] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ord_less_eq @ ( set @ TB ) @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ ( product_Sigma @ TA @ TB @ A @ C ) @ ( product_Sigma @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(44,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_9) ).
thf(415,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ ( product_prod @ TB @ TB ),C: TA,D: set @ TB,E: set @ ( product_prod @ TB @ TB ),F: TA] :
( ( ( pair_p1152105390ph_ext @ TB @ TA @ A @ B @ C )
= ( pair_p1152105390ph_ext @ TB @ TA @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_pair__pre__digraph_Oext__inject) ).
thf(474,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ ( product_prod @ TB @ TB ),C: TA,D: set @ TB,E: set @ ( product_prod @ TB @ TB ),F: TA] :
( ( ( pair_p1152105390ph_ext @ TB @ TA @ A @ B @ C )
= ( pair_p1152105390ph_ext @ TB @ TA @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(160,axiom,
linorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_14) ).
thf(767,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(266,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB] :
( ~ ( finite_finite2 @ TA @ A )
=> ( ~ ( finite_finite2 @ TB @ B )
=> ~ ( finite_finite2 @ ( product_prod @ TA @ TB )
@ ( product_Sigma @ TA @ TB @ A
@ ^ [C: TA] : B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_infinite__cartesian__product) ).
thf(1093,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TB] :
( ~ ( finite_finite2 @ TA @ A )
=> ( ~ ( finite_finite2 @ TB @ B )
=> ~ ( finite_finite2 @ ( product_prod @ TA @ TB )
@ ( product_Sigma @ TA @ TB @ A
@ ^ [C: TA] : B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(150,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ~ ! [D: nat] :
( ( A @ D )
=> ~ ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_bounded__Max__nat) ).
thf(728,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ~ ! [D: nat] :
( ( A @ D )
=> ~ ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(59,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_202_Collect__empty__eq__bot) ).
thf(464,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)],[59]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ ( product_prod @ TB @ TB ),C: TA] :
( ( pair_pair_pre_more @ TB @ TA @ ( pair_p1152105390ph_ext @ TB @ TA @ A @ B @ C ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_pair__pre__digraph_Oselect__convs_I3_J) ).
thf(575,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ ( product_prod @ TB @ TB ),C: TA] :
( ( pair_pair_pre_more @ TB @ TA @ ( pair_p1152105390ph_ext @ TB @ TA @ A @ B @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(244,axiom,
preorder @ product_unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Ounit___Orderings_Opreorder_21) ).
thf(1019,plain,
preorder @ product_unit,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: product_prod @ TB @ TA] :
( ( product_case_prod @ TB @ TA @ $o @ A @ B )
=> ~ ! [C: TB,D: TA] :
( ( B
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( A @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_case__prodE) ).
thf(459,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: product_prod @ TB @ TA] :
( ( product_case_prod @ TB @ TA @ $o @ A @ B )
=> ~ ! [C: TB,D: TA] :
( ( B
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(207,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit,B: TA,C: TA] :
( ( pair_pair_wf_digraph @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( member @ TA @ C @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_pair__wf__digraph_Oin__arcsD2) ).
thf(908,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit,B: TA,C: TA] :
( ( pair_pair_wf_digraph @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ B @ C ) @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( member @ TA @ C @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(180,axiom,
! [TA: $tType,TB: $tType] :
( ( product_product @ TA @ TB )
= ( ^ [A: set @ TA,B: set @ TB] :
( product_Sigma @ TA @ TB @ A
@ ^ [C: TA] : B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Product__Type_Oproduct__def) ).
thf(822,plain,
! [TA: $tType,TB: $tType] :
( ( product_product @ TA @ TB )
= ( ^ [A: set @ TA,B: set @ TB] :
( product_Sigma @ TA @ TB @ A
@ ^ [C: TA] : B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(189,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_graph @ TA @ A )
=> ( pair_pair_graph @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_pair__graph_Opair__graph) ).
thf(850,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(232,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_165_ssubst__Pair__rhs) ).
thf(982,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)],[232]) ).
thf(275,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ? [B: TA] :
( ( member @ TA @ B @ A )
& ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( B = C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_finite__has__maximal) ).
thf(1120,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ? [B: TA] :
( ( member @ TA @ B @ A )
& ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( B = C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TB,B: TC > TB > TA > $o,C: TA] :
( ! [D: TC,E: TB] :
( ( ( product_Pair @ TC @ TB @ D @ E )
= A )
=> ( B @ D @ E @ C ) )
=> ( product_case_prod @ TC @ TB @ ( TA > $o ) @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_case__prodI2_H) ).
thf(501,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ TB,B: TC > TB > TA > $o,C: TA] :
( ! [D: TC,E: TB] :
( ( ( product_Pair @ TC @ TB @ D @ E )
= A )
=> ( B @ D @ E @ C ) )
=> ( product_case_prod @ TC @ TB @ ( TA > $o ) @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(68,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_36_rev__predicate1D) ).
thf(486,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)],[68]) ).
thf(221,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_164_pred__equals__eq2) ).
thf(940,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)],[221]) ).
thf(22,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_graph @ TA @ A )
=> ( pair_pair_digraph @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_pair__graph_Oaxioms_I1_J) ).
thf(354,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_graph @ TA @ A )
=> ( pair_pair_digraph @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(241,axiom,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit,B: product_prod @ TA @ TA,C: TA] :
( ( pair_p1282390076igraph @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ B @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( ~ ( member @ TA @ C @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) )
=> ( pair_p1282390076igraph @ TA @ ( pair_subdivide @ TA @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_pair__loopfree__digraph_Opair__loopfree__digraph__subdivide) ).
thf(1009,plain,
! [TA: $tType,A: pair_p1731315293ph_ext @ TA @ product_unit,B: product_prod @ TA @ TA,C: TA] :
( ( pair_p1282390076igraph @ TA @ A )
=> ( ( member @ ( product_prod @ TA @ TA ) @ B @ ( pair_pair_pre_parcs @ TA @ product_unit @ A ) )
=> ( ~ ( member @ TA @ C @ ( pair_pair_pre_pverts @ TA @ product_unit @ A ) )
=> ( pair_p1282390076igraph @ TA @ ( pair_subdivide @ TA @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(83,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_104_empty__Collect__eq) ).
thf(543,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)],[83]) ).
thf(118,axiom,
order_bot @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder__bot_1) ).
thf(639,plain,
order_bot @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(156,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_58_eq__iff) ).
thf(755,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)],[156]) ).
thf(72,axiom,
! [TA: $tType] :
( ( pair_p460180511igraph @ TA )
= ( ^ [A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_wf_digraph @ TA @ A )
& ( pair_p477239746axioms @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_pair__sym__digraph__def) ).
thf(496,plain,
! [TA: $tType] :
( ( pair_p460180511igraph @ TA )
= ( ^ [A: pair_p1731315293ph_ext @ TA @ product_unit] :
( ( pair_pair_wf_digraph @ TA @ A )
& ( pair_p477239746axioms @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(142,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_49_ord__eq__le__trans) ).
thf(708,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)],[142]) ).
thf(230,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ? [B: TA] :
( ( member @ TA @ B @ A )
& ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( B = C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_finite__has__minimal) ).
thf(972,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: set @ TA] :
( ( finite_finite2 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ? [B: TA] :
( ( member @ TA @ B @ A )
& ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ( ord_less_eq @ TA @ C @ B )
=> ( B = C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(10,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_148_old_Oprod_Oexhaust) ).
thf(309,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)],[10]) ).
thf(126,axiom,
preorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_13) ).
thf(659,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(251,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA] :
( ( finite_finite2 @ ( product_prod @ TB @ TA )
@ ( product_Sigma @ TB @ TA @ A
@ ^ [C: TB] : B ) )
=> ( ( A
!= ( bot_bot @ ( set @ TB ) ) )
=> ( finite_finite2 @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_finite__cartesian__productD2) ).
thf(1037,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: set @ TA] :
( ( finite_finite2 @ ( product_prod @ TB @ TA )
@ ( product_Sigma @ TB @ TA @ A
@ ^ [C: TB] : B ) )
=> ( ( A
!= ( bot_bot @ ( set @ TB ) ) )
=> ( finite_finite2 @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(164,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_57_antisym) ).
thf(775,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)],[164]) ).
thf(1171,plain,
$false,
inference(e,[status(thm)],[666,481,645,892,479,1105,333,1031,1068,994,449,597,861,582,762,1142,379,655,511,797,715,472,698,945,930,898,1001,301,320,1095,404,841,417,724,719,751,802,587,838,902,559,421,969,1013,1115,638,853,924,492,789,623,514,1051,1040,1109,485,1136,1020,348,1169,634,692,293,396,660,988,849,312,602,766,307,292,452,546,1153,366,910,746,825,778,820,392,424,407,429,815,467,361,879,329,522,1159,1079,682,551,324,874,317,615,388,356,593,499,742,578,1082,488,933,554,669,642,637,679,970,393,647,1150,721,569,371,1060,457,792,938,398,1071,674,1026,530,773,888,298,412,965,573,296,375,562,1007,402,291,958,1139,936,313,787,947,919,804,604,1011,1048,990,567,784,1117,1043,434,890,477,387,494,631,758,535,726,621,700,1029,915,943,1061,1112,912,986,851,438,431,653,922,658,768,827,636,695,455,883,1034,426,589,795,663,927,1145,553,836,525,712,580,640,887,1098,993,705,1156,1053,673,331,585,717,470,359,1130,744,703,1023,600,978,595,612,876,859,446,571,1084,1126,771,363,556,368,844,961,304,1062,1101,351,781,995,896,748,929,549,832,684,1161,800,1133,410,818,1148,867,865,373,326,918,506,807,1056,532,1165,415,474,767,1093,728,464,575,1019,459,908,822,850,982,1120,501,486,940,354,1009,543,639,755,496,708,972,309,659,1037,775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP093^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % 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
% 0.09/0.19 % Computer : n015.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 19:56:03 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 0.87/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.42/1.21 % [INFO] Parsing done (429ms).
% 2.42/1.22 % [INFO] Running in sequential loop mode.
% 3.54/1.62 % [INFO] eprover registered as external prover.
% 3.54/1.63 % [INFO] Scanning for conjecture ...
% 3.70/1.79 % [INFO] Found a conjecture (or negated_conjecture) and 289 axioms. Running axiom selection ...
% 4.16/1.94 % [INFO] Axiom selection finished. Selected 288 axioms (removed 1 axioms).
% 5.06/2.29 % [INFO] Problem is higher-order (TPTP THF).
% 5.36/2.33 % [INFO] Type checking passed.
% 5.36/2.33 % [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 ...
% 46.48/26.77 % External prover 'e' found a proof!
% 46.48/26.77 % [INFO] Killing All external provers ...
% 46.48/26.77 % Time passed: 26438ms (effective reasoning time: 25539ms)
% 46.48/26.77 % 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)>
% 46.48/26.77 % Axioms used in derivation (288): fact_235_pair__digraph_Ointro, tcon_fun___Orderings_Obot, fact_136_pair__wf__digraph_Opair__wf__digraph__subdivide, fact_137_Set_Ois__empty__def, fact_145_bot__empty__eq2, fact_111_Sigma__empty__iff, fact_132_finite__SigmaI2, tcon_Set_Oset___Orderings_Oord_10, fact_10_rev__finite__subset, fact_126_Fpow__mono, fact_66_le__funD, tcon_Product__Type_Ounit___Orderings_Olinorder_22, fact_18_pigeonhole__infinite__rel, fact_171_pred__subset__eq2, fact_91_pair__pre__digraph_Oselect__convs_I2_J, fact_163_subdivide_Ocases, fact_5_pair__fin__digraph__axioms__def, fact_157_prod__cases4, fact_83_subset__Collect__iff, fact_112_empty__in__Fpow, fact_19_pair__fin__digraph_Opair__fin__digraph, tcon_HOL_Obool___Orderings_Olinorder_14, fact_160_prod__cases, fact_222_case__prod__app, fact_210_mem__case__prodE, tcon_Product__Type_Ounit___Orderings_Opreorder_21, fact_249_pair__bidirected__digraph_Ointro, fact_114_emptyE, fact_44_ord__le__eq__trans, fact_175_calculation, tcon_Nat_Onat___Orderings_Olinorder, fact_240_pair__loopfree__digraph_Ointro, fact_58_eq__iff, fact_201_obtain__subset__with__card__n, tcon_fun___Finite__Set_Ofinite, fact_158_prod__cases3, fact_4_finite, fact_106_subset__empty, fact_231_pair__digraph_Opair__wf__digraph, fact_189_old_Oprod_Ocase, fact_123_infinite__imp__nonempty, fact_98_pair__pre__digraph_Ofold__congs_I3_J, fact_159_Pair__inject, fact_146_bot__set__def, fact_68_set__eq__subset, fact_167_SigmaD1, fact_255_pair__sym__digraph__def, fact_162_subdivide_Oinduct, fact_89_pair__pre__digraph_Oinduct__scheme, fact_9_infinite__super, fact_35_predicate1D, fact_39_dual__order_Otrans, fact_49_ord__eq__le__trans, fact_12_finite__Collect__conjI, fact_164_pred__equals__eq2, fact_85_Collect__restrict, fact_13_finite__Collect__disjI, fact_95_pair__fin__digraph__def, fact_168_SigmaD2, fact_102_all__not__in__conv, tcon_fun___Orderings_Oord, tcon_Set_Oset___Finite__Set_Ofinite_8, fact_250_pair__bidirected__digraph__def, fact_237_pair__graph_Oaxioms_I1_J, fact_144_bot__empty__eq, fact_187_case__prod__eta, fact_93_pair__pre__digraph_Oselect__convs_I3_J, fact_140_old_Oprod_Oinject, fact_73_equalityD2, fact_69_subset__trans, fact_169_SigmaE2, fact_134_finite__cartesian__productD2, fact_118_bot__fun__def, fact_133_finite__cartesian__productD1, fact_227_pair__loopfree__digraph_Opair__loopfree__digraph__subdivide, fact_211_finite__nat__set__iff__bounded__le, fact_204_mem__case__prodI2, fact_172_relChain__def, tcon_HOL_Obool___Finite__Set_Ofinite_15, fact_135_finite__transitivity__chain, fact_129_finite__has__minimal, fact_199_card__seteq, fact_236_pair__digraph_Oaxioms_I1_J, tcon_HOL_Obool___Orderings_Oord_17, fact_57_antisym, tcon_HOL_Obool___Orderings_Obot_18, fact_206_case__prodI2_H, fact_173_old_Oprod_Orec, fact_81_member__product, tcon_Product__Type_Ounit___Orderings_Oord_25, fact_193_Collect__case__prod__Sigma, fact_200_card__mono, fact_108_Times__empty, fact_178_case__prod__conv, fact_52_le__cases3, fact_215_card__le__if__inj__on__rel, fact_46_Collect__mem__eq, fact_232_pair__digraph_Oaxioms_I2_J, fact_127_pair__fin__digraph_Oaxioms_I1_J, fact_176_predicate2I, fact_79_pred__subset__eq, fact_67_Collect__mono__iff, tcon_Product__Type_Ounit___Orderings_Oorder_24, fact_197_infinite__arbitrarily__large, fact_103_Collect__empty__eq, fact_182_bot2E, fact_94_Fpow__def, fact_247_pair__sym__digraph_Oaxioms_I1_J, fact_205_mem__case__prodI, fact_101_empty__iff, fact_37_dual__order_Oantisym, fact_214_finite__less__ub, fact_154_prod__cases7, fact_254_pair__sym__digraph_Ointro, fact_78_in__mono, fact_143_mem__Sigma__iff, fact_153_prod__induct3, fact_116_equals0I, fact_212_infinite__nat__iff__unbounded__le, fact_139_pair__wf__digraph_Oin__arcsD1, tcon_Set_Oset___Orderings_Obot_11, fact_77_subsetD, fact_223_pair__bidirected__digraph_Opair__bidirected__digraph__subdivide, fact_29_pair__pre__digraph_Oequality, fact_14_finite__Collect__subsets, fact_115_equals0D, fact_72_subset__iff, fact_181_Collect__case__prod, fact_60_ord__eq__le__subst, fact_105_empty__subsetI, fact_165_ssubst__Pair__rhs, fact_107_Sigma__empty1, fact_36_rev__predicate1D, fact_124_subset__emptyI, fact_202_Collect__empty__eq__bot, fact_31_Times__eq__cancel2, fact_55_eq__refl, fact_209_case__prodE_H, fact_174_less__by__empty, fact_245_pair__sym__digraph_Oarcs__symmetric, tcon_Product__Type_Ounit___Orderings_Oorder__bot_20, fact_148_old_Oprod_Oexhaust, fact_184_case__prodD, fact_251_pair__pseudo__graph__def, fact_142_SigmaI, fact_6_pair__fin__digraph__axioms_Ointro, fact_45_mem__Collect__eq, fact_156_prod__cases5, fact_26_subsetI, fact_53_order_Otrans, fact_130_pair__pre__digraph_Oupdate__convs_I3_J, fact_234_pair__digraph__def, fact_100_bot__apply, tcon_HOL_Obool___Orderings_Oorder_16, fact_138_pair__wf__digraph_Oin__arcsD2, fact_110_empty__def, fact_113_Fpow__not__empty, fact_225_case__prod__Pair__iden, fact_74_equalityD1, fact_32_Collect__subset, fact_179_case__prodI2, fact_233_pair__digraph_Opair__digraph, fact_33_less__eq__set__def, fact_15_finite__SigmaI, fact_177_split__part, fact_61_order__subst2, fact_241_pair__loopfree__digraph__def, fact_90_pair__pre__digraph_Ocases__scheme, fact_195_prod_Ocase__distrib, fact_96_pair__fin__digraph_Ointro, tcon_Nat_Onat___Orderings_Opreorder_2, fact_21_pair__fin__digraph_Opair__finite__verts, fact_22_finite__has__minimal2, fact_87_conj__subset__def, fact_40_linorder__wlog, tcon_Nat_Onat___Orderings_Oorder__bot_1, fact_220_pair__pseudo__graph_Opair__pseudo__graph, fact_2__092_060open_062parcs_AG_A_092_060subseteq_062_Apverts_AG_A_092_060times_062_Apverts_AG_092_060close_062, fact_47_Collect__cong, fact_161_surj__pair, fact_25_Sigma__mono, fact_24_Times__subset__cancel2, fact_92_pair__pre__digraph_Oselect__convs_I1_J, tcon_fun___Orderings_Oorder__bot, fact_70_Collect__mono, fact_207_finite__Collect__le__nat, fact_128_finite__has__maximal, fact_186_case__prodE2, fact_104_empty__Collect__eq, fact_54_le__cases, fact_150_prod__induct6, fact_30_Sigma__cong, fact_65_le__funE, fact_1__092_060open_062finite_A_Ipverts_AG_A_092_060times_062_Apverts_AG_J_092_060close_062, fact_117_ex__in__conv, tcon_Set_Oset___Orderings_Oorder_9, fact_122_finite_OemptyI, tcon_Nat_Onat___Orderings_Oorder_3, fact_64_le__funI, fact_191_rev__predicate2D, fact_84_subset__CollectI, fact_218_pair__graph_Oaxioms_I2_J, fact_38_dual__order_Oeq__iff, fact_62_order__subst1, fact_198_finite__if__finite__subsets__card__bdd, fact_20_finite__cartesian__product, fact_155_prod__cases6, fact_76_equalityE, fact_8_finite__subset, fact_0_finite__code, fact_166_SigmaE, tcon_fun___Orderings_Opreorder, fact_63_le__fun__def, fact_27_subset__antisym, fact_244_internal__case__prod__def, fact_97_pair__pre__digraph_Ounfold__congs_I3_J, tcon_Product__Type_Ounit___Orderings_Obot_26, fact_16_pair__fin__digraph_Oaxioms_I2_J, fact_75_subset__eq, fact_151_prod__induct5, tcon_Product__Type_Oprod___Finite__Set_Ofinite_19, fact_248_pair__pseudo__graph_Oaxioms_I2_J, fact_43_order__class_Oorder_Oantisym, fact_23_infinite__cartesian__product, fact_99_finite__cartesian__product__iff, fact_51_antisym__conv, fact_34_predicate1I, fact_180_case__prodI, fact_188_cond__case__prod__eta, fact_121_bot_Oextremum, fact_213_bounded__Max__nat, fact_88_pair__pre__digraph_Oext__inject, tcon_fun___Orderings_Oorder, fact_86_prop__restrict, fact_141_prod_Oinject, fact_185_case__prodE, fact_147_old_Oprod_Oinducts, fact_224_predicate2D__conj, fact_252_pair__pseudo__graph_Ointro, fact_170_subrelI, fact_11_finite__has__maximal2, fact_229_pair__bidirected__digraph_Oaxioms_I2_J, fact_228_pair__graph_Ointro, fact_190_split__cong, fact_226_eq__subset, fact_109_Sigma__empty2, fact_3_finite__set__choice, tcon_Nat_Onat___Orderings_Oord_4, fact_149_prod__induct7, fact_41_dual__order_Orefl, fact_196_card__subset__eq, fact_203_card__Ex__subset, tcon_Set_Oset___Orderings_Opreorder_7, fact_239_pair__graph__def, fact_230_pair__loopfree__digraph_Oaxioms_I1_J, tcon_Set_Oset___Orderings_Oorder__bot_6, fact_253_internal__case__prod__conv, fact_192_predicate2D, tcon_HOL_Obool___Orderings_Opreorder_13, fact_216_pair__pseudo__graph_Opair__pseudo__graph__subdivide, fact_246_pair__bidirected__digraph_Oaxioms_I1_J, fact_217_pair__graph_Opair__graph__subdivide, fact_219_pair__graph_Opair__graph, fact_152_prod__induct4, fact_183_Collect__case__prod__mono, fact_56_linear, fact_243_pair__sym__digraph_Opair__sym__digraph__subdivide, fact_7_pair__fin__digraph_Opair__finite__arcs, fact_59_ord__le__eq__subst, fact_194_prod_Odisc__eq__case, fact_42_order__trans, fact_125_times__eq__iff, tcon_Nat_Onat___Orderings_Obot_5, fact_119_bot_Oextremum__uniqueI, fact_17_not__finite__existsD, tcon_HOL_Obool___Orderings_Oorder__bot_12, fact_208_case__prodD_H, fact_50_order__class_Oorder_Oeq__iff, fact_238_pair__loopfree__digraph_Ono__loops_H, fact_82_Product__Type_Oproduct__def, fact_28_order__refl, fact_80_pair__pre__digraph_Osurjective, fact_221_pair__pseudo__graph_Oaxioms_I1_J, fact_242_pair__loopfree__digraph_Oaxioms_I2_J, fact_120_bot_Oextremum__unique, fact_71_subset__refl, tcon_Product__Type_Ounit___Finite__Set_Ofinite_23, fact_131_times__subset__iff
% 46.48/26.77 % No. of inferences in proof: 580
% 46.48/26.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 26438 ms resp. 25539 ms w/o parsing
% 48.16/27.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 48.16/27.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------