TSTP Solution File: ITP144^2 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP144^2 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:48:12 EDT 2024
% Result : Theorem 41.10s 30.67s
% Output : Refutation 41.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 290
% Syntax : Number of formulae : 545 ( 182 unt; 37 typ; 0 def)
% Number of atoms : 1691 ( 662 equ; 4 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 6334 ( 123 ~; 10 |; 100 &;5619 @)
% ( 0 <=>; 482 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 599 ( 599 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 38 usr; 6 con; 0-7 aty)
% Number of variables : 2121 ( 188 ^1828 !; 54 ?;2121 :)
% ( 51 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(bot_type,type,
bot:
!>[TA: $tType] : $o ).
thf(ord_type,type,
ord:
!>[TA: $tType] : $o ).
thf(top_type,type,
top:
!>[TA: $tType] : $o ).
thf(ab_group_add_type,type,
ab_group_add:
!>[TA: $tType] : $o ).
thf(bNF_pick_middlep_type,type,
bNF_pick_middlep:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > $o ) > ( TB > TA > $o ) > TC > TA > TB ) ).
thf(bNF_Gr932048252omCard_type,type,
bNF_Gr932048252omCard:
!>[TA: $tType,TB: $tType] : ( ( set @ TB ) > ( set @ ( product_prod @ TA @ TA ) ) > TA > TB ) ).
thf(bNF_Greatest_toCard_type,type,
bNF_Greatest_toCard:
!>[TA: $tType,TB: $tType] : ( ( set @ TB ) > ( set @ ( product_prod @ TA @ TA ) ) > TB > TA ) ).
thf(bNF_Gr1978856366d_pred_type,type,
bNF_Gr1978856366d_pred:
!>[TA: $tType,TB: $tType] : ( ( set @ TB ) > ( set @ ( product_prod @ TA @ TA ) ) > ( TB > TA ) > $o ) ).
thf(bNF_Greatest_univ_type,type,
bNF_Greatest_univ:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > TA ) ).
thf(bij_betw_type,type,
bij_betw:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > ( set @ TA ) > $o ) ).
thf(fun_upd_type,type,
fun_upd:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > TB > TA > TB > TA ) ).
thf(inj_on_type,type,
inj_on:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > $o ) ).
thf(minus_minus_type,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(hilbert_Eps_type,type,
hilbert_Eps:
!>[TA: $tType] : ( ( TA > $o ) > TA ) ).
thf(hilbert_bijection_type,type,
hilbert_bijection:
!>[TA: $tType] : ( ( TA > TA ) > $o ) ).
thf(hilbert_inv_into_type,type,
hilbert_inv_into:
!>[TA: $tType,TB: $tType] : ( ( set @ TB ) > ( TB > TA ) > TA > TB ) ).
thf(lattices_ord_arg_max_type,type,
lattices_ord_arg_max:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( TB > $o ) > TB ) ).
thf(lattic1534546155max_on_type,type,
lattic1534546155max_on:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > TB ) ).
thf(lattic2130478198rg_max_type,type,
lattic2130478198rg_max:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( TB > $o ) > TB > $o ) ).
thf(bot_bot_type,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(top_top_type,type,
top_top:
!>[TA: $tType] : TA ).
thf(quotient3_type,type,
quotient3:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > ( TB > TA ) > ( TA > TB ) > $o ) ).
thf(quot_type_type,type,
quot_type:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > ( ( set @ TB ) > TA ) > ( TA > ( set @ TB ) ) > $o ) ).
thf(quot_abs_type,type,
quot_abs:
!>[TA: $tType,TB: $tType] : ( ( TB > TB > $o ) > ( ( set @ TB ) > TA ) > TB > TA ) ).
thf(quot_rep_type,type,
quot_rep:
!>[TA: $tType,TB: $tType] : ( ( TB > ( set @ TA ) ) > TB > TA ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(image_type,type,
image:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > ( set @ TA ) ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(is_empty_type,type,
is_empty:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(is_singleton_type,type,
is_singleton:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(remove_type,type,
remove:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(the_elem_type,type,
the_elem:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(p_type,type,
p: a > $o ).
thf(q_type,type,
q: a > b > $o ).
thf(179,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_UNIV__eq__I) ).
thf(787,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(34,axiom,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_is__singletonI) ).
thf(347,plain,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(139,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( ( image @ TA @ TB @ A @ B )
= ( bot_bot @ ( set @ TB ) ) )
= ( B
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_image__is__empty) ).
thf(666,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( ( image @ TA @ TB @ A @ B )
= ( bot_bot @ ( set @ TB ) ) )
= ( B
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA,E: TA] :
( ( quotient3 @ TA @ TB @ A @ B @ C )
=> ( ( A @ D @ E )
=> ( A @ E @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_Quotient3__refl2) ).
thf(352,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA,E: TA] :
( ( quotient3 @ TA @ TB @ A @ B @ C )
=> ( ( A @ D @ E )
=> ( A @ E @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(219,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA] :
( ( A @ ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A @ B ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_surj__iff__all) ).
thf(909,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA] :
( ( A @ ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(125,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_singleton__inject) ).
thf(628,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(238,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( hilbert_Eps @ TA @ A )
= ( hilbert_Eps @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Eps__cong) ).
thf(977,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( hilbert_Eps @ TA @ A )
= ( hilbert_Eps @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A @ ( A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_inv__f__f) ).
thf(523,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A @ ( A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(166,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( bij_betw @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TB ) ) )
=> ~ ! [C: TA] :
( ( B
= ( A @ C ) )
=> ~ ! [D: TA] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_bij__pointE) ).
thf(741,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( bij_betw @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TB ) ) )
=> ~ ! [C: TA] :
( ( B
= ( A @ C ) )
=> ~ ! [D: TA] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(135,axiom,
! [TA: $tType,A: TA > TA] :
( ( hilbert_bijection @ TA @ A )
=> ( inj_on @ TA @ TA @ ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A ) @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_bijection_Oinj__inv) ).
thf(655,plain,
! [TA: $tType,A: TA > TA] :
( ( hilbert_bijection @ TA @ A )
=> ( inj_on @ TA @ TA @ ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A ) @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(114,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_empty__Diff) ).
thf(597,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(204,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: ( set @ TB ) > TA,C: TA > ( set @ TB )] :
( ( quot_type @ TB @ TA @ A @ B @ C )
=> ( quotient3 @ TB @ TA @ A @ ( quot_abs @ TB @ TA @ A @ B ) @ ( quot_rep @ TA @ TB @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_quot__type_OQuotient) ).
thf(861,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: ( set @ TB ) > TA,C: TA > ( set @ TB )] :
( ( quot_type @ TB @ TA @ A @ B @ C )
=> ( quotient3 @ TB @ TA @ A @ ( quot_abs @ TB @ TA @ A @ B ) @ ( quot_rep @ TA @ TB @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_imageI) ).
thf(384,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(183,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_DiffD2) ).
thf(797,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(189,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB] :
( ! [C: TA] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_surjI) ).
thf(814,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB] :
( ! [C: TA] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(167,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ! [C: TB] :
( ( B @ ( A @ C ) )
= C )
=> ( ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_surj__imp__inv__eq) ).
thf(747,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ! [C: TB] :
( ( B @ ( A @ C ) )
= C )
=> ( ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( bij_betw @ TA @ TB @ A @ B @ ( bot_bot @ ( set @ TB ) ) )
=> ( B
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_bij__betw__empty2) ).
thf(538,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( bij_betw @ TA @ TB @ A @ B @ ( bot_bot @ ( set @ TB ) ) )
=> ( B
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(141,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_UNIV__def) ).
thf(670,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(194,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( collect @ TB
@ ^ [B: TB] :
? [C: TA] :
( B
= ( A @ C ) ) )
= ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_full__SetCompr__eq) ).
thf(829,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( collect @ TB
@ ^ [B: TB] :
? [C: TA] :
( B
= ( A @ C ) ) )
= ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( bij_betw @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TB ) ) )
=> ( ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_inv__inv__eq) ).
thf(565,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( bij_betw @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TB ) ) )
=> ( ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(198,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_UNIV__witness) ).
thf(841,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(59,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_Set_Oset__insert) ).
thf(417,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(49,axiom,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_is__singleton__the__elem) ).
thf(389,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(106,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_Diff__iff) ).
thf(570,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
= ( ( inj_on @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
& ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_bij__def) ).
thf(372,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
= ( ( inj_on @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
& ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(111,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ C ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( ~ ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ C ) ) )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_Collect__conv__if) ).
thf(587,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ C ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( ~ ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( C = B )
& ( A @ C ) ) )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(197,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_54_equals0I) ).
thf(838,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)],[197]) ).
thf(222,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( A
= ( hilbert_Eps @ TA
@ ^ [C: TA] :
~ ( B @ C ) ) )
=> ( ( ! [C: TA] : ( B @ C ) )
= ( B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_verit__sko__forall__indirect) ).
thf(917,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( A
= ( hilbert_Eps @ TA
@ ^ [C: TA] :
~ ( B @ C ) ) )
=> ( ( ! [C: TA] : ( B @ C ) )
= ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(153,axiom,
! [TA: $tType] :
( ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) )
@ ^ [A: TA] : A )
= ( ^ [A: TA] : A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_inv__identity) ).
thf(702,plain,
! [TA: $tType] :
( ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) )
@ ^ [A: TA] : A )
= ( ^ [A: TA] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(185,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_Diff__insert__absorb) ).
thf(802,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ? [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_bex__imageD) ).
thf(344,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ? [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(190,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ A @ ( image @ TA @ TB @ ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A ) @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_image__f__inv__f) ).
thf(817,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ A @ ( image @ TA @ TB @ ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A ) @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( member @ TB @ B @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
= ( ? [C: TA] :
( ( B
= ( A @ C ) )
& ! [D: TA] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_range__ex1__eq) ).
thf(559,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( member @ TB @ B @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
= ( ? [C: TA] :
( ( B
= ( A @ C ) )
& ! [D: TA] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(60,axiom,
! [TA: $tType] :
( ( remove @ TA )
= ( ^ [A: TA,B: set @ TA] : ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_remove__def) ).
thf(421,plain,
! [TA: $tType] :
( ( remove @ TA )
= ( ^ [A: TA,B: set @ TA] : ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(117,axiom,
! [TA: $tType,A: TA > TA,B: TA] :
( ( hilbert_bijection @ TA @ A )
=> ( ( A @ ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_bijection_Oinv__right) ).
thf(606,plain,
! [TA: $tType,A: TA > TA,B: TA] :
( ( hilbert_bijection @ TA @ A )
=> ( ( A @ ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(211,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_65_Collect__empty__eq__bot) ).
thf(881,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)],[211]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA,C: TA > TB,D: TA] :
( ( quotient3 @ TB @ TA @ A @ B @ C )
=> ( ( B @ ( C @ D ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_Quotient3__abs__rep) ).
thf(261,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA,C: TA > TB,D: TA] :
( ( quotient3 @ TB @ TA @ A @ B @ C )
=> ( ( B @ ( C @ D ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(170,axiom,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_bot__empty__eq) ).
thf(756,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_ball__imageD) ).
thf(321,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(131,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] : ( inj_on @ TA @ TB @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_inj__on__empty) ).
thf(646,plain,
! [TA: $tType,TB: $tType,A: TA > TB] : ( inj_on @ TA @ TB @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(79,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_insert__Diff__single) ).
thf(480,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(147,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB,D: TA] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ( ( member @ TA @ D @ B )
=> ( ( hilbert_inv_into @ TA @ TB @ B @ A @ ( A @ D ) )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_bij__betw__inv__into__left) ).
thf(687,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB,D: TA] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ( ( member @ TA @ D @ B )
=> ( ( hilbert_inv_into @ TA @ TB @ B @ A @ ( A @ D ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(11,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_Diff__idemp) ).
thf(280,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(127,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB,D: TA] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ( ( member @ TA @ D @ B )
=> ( ( hilbert_inv_into @ TB @ TA @ C @ ( hilbert_inv_into @ TA @ TB @ B @ A ) @ D )
= ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_inv__into__inv__into__eq) ).
thf(634,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB,D: TA] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ( ( member @ TA @ D @ B )
=> ( ( hilbert_inv_into @ TB @ TA @ C @ ( hilbert_inv_into @ TA @ TB @ B @ A ) @ D )
= ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(206,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TA] :
( ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
=> ( ( B
= ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A @ C ) )
= ( ( A @ B )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_bij__inv__eq__iff) ).
thf(866,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TA] :
( ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
=> ( ( B
= ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A @ C ) )
= ( ( A @ B )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(137,axiom,
! [TA: $tType,A: TA > TA,B: TA,C: TA] :
( ( hilbert_bijection @ TA @ A )
=> ( ( B
= ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A @ C ) )
= ( ( A @ B )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_bijection_Oinv__right__eq__iff) ).
thf(660,plain,
! [TA: $tType,A: TA > TA,B: TA,C: TA] :
( ( hilbert_bijection @ TA @ A )
=> ( ( B
= ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A @ C ) )
= ( ( A @ B )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA,C: TA > TB,D: TA] :
( ( quotient3 @ TB @ TA @ A @ B @ C )
=> ( A @ ( C @ D ) @ ( C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Quotient3__rep__reflp) ).
thf(307,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA,C: TA > TB,D: TA] :
( ( quotient3 @ TB @ TA @ A @ B @ C )
=> ( A @ ( C @ D ) @ ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(13,axiom,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_top__conj_I2_J) ).
thf(292,plain,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(45,axiom,
bot @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_6) ).
thf(380,plain,
bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(228,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: ( set @ TA ) > TB,C: TB > ( set @ TA ),D: TA] :
( ( quot_type @ TA @ TB @ A @ B @ C )
=> ( ( A @ D @ D )
=> ( ( A
@ ( hilbert_Eps @ TA
@ ^ [E: TA] : ( member @ TA @ E @ ( collect @ TA @ ( A @ D ) ) ) ) )
= ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_quot__type_Osome__collect) ).
thf(942,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: ( set @ TA ) > TB,C: TB > ( set @ TA ),D: TA] :
( ( quot_type @ TA @ TB @ A @ B @ C )
=> ( ( A @ D @ D )
=> ( ( A
@ ( hilbert_Eps @ TA
@ ^ [E: TA] : ( member @ TA @ E @ ( collect @ TA @ ( A @ D ) ) ) ) )
= ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(224,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( A
= ( hilbert_Eps @ TA @ B ) )
=> ( ( ? [C: TA] : ( B @ C ) )
= ( B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_verit__sko__ex__indirect) ).
thf(925,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( A
= ( hilbert_Eps @ TA @ B ) )
=> ( ( ? [C: TA] : ( B @ C ) )
= ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(172,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(761,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA > $o] :
( ( collect @ TB
@ ^ [C: TB] :
? [D: TA] :
( ( C
= ( A @ D ) )
& ( B @ D ) ) )
= ( image @ TA @ TB @ A @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_setcompr__eq__image) ).
thf(381,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA > $o] :
( ( collect @ TB
@ ^ [C: TB] :
? [D: TA] :
( ( C
= ( A @ D ) )
& ( B @ D ) ) )
= ( image @ TA @ TB @ A @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(157,axiom,
! [TA: $tType,A: TA] :
( ( collect @ TA @ ( (=) @ TA @ A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_singleton__conv2) ).
thf(714,plain,
! [TA: $tType,A: TA] :
( ( collect @ TA @ ( (=) @ TA @ A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(7,axiom,
! [TA: $tType,A: set @ TA] :
( ( is_singleton @ TA @ A )
=> ~ ! [B: TA] :
( A
!= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_is__singletonE) ).
thf(270,plain,
! [TA: $tType,A: set @ TA] :
( ( is_singleton @ TA @ A )
=> ~ ! [B: TA] :
( A
!= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(93,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(529,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( bij_betw @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TB ) ) )
=> ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_bij__is__inj) ).
thf(334,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( bij_betw @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TB ) ) )
=> ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(35,axiom,
! [TA: $tType,A: TA > TA,B: TA,C: TA] :
( ( hilbert_bijection @ TA @ A )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_bijection_Oeq__iff) ).
thf(349,plain,
! [TA: $tType,A: TA > TA,B: TA,C: TA] :
( ( hilbert_bijection @ TA @ A )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(191,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ C ) )
= ( member @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_inj__image__mem__iff) ).
thf(820,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ C ) )
= ( member @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA] :
( ( ( A
= ( bot_bot @ ( set @ TB ) ) )
=> ( ( image @ TB @ TA
@ ^ [C: TB] : B
@ A )
= ( bot_bot @ ( set @ TA ) ) ) )
& ( ( A
!= ( bot_bot @ ( set @ TB ) ) )
=> ( ( image @ TB @ TA
@ ^ [C: TB] : B
@ A )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_image__constant__conv) ).
thf(392,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA] :
( ( ( A
= ( bot_bot @ ( set @ TB ) ) )
=> ( ( image @ TB @ TA
@ ^ [C: TB] : B
@ A )
= ( bot_bot @ ( set @ TA ) ) ) )
& ( ( A
!= ( bot_bot @ ( set @ TB ) ) )
=> ( ( image @ TB @ TA
@ ^ [C: TB] : B
@ A )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(61,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_insert__ident) ).
thf(424,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA,E: TA] :
( ( quotient3 @ TA @ TB @ A @ B @ C )
=> ( ( A @ D @ E )
=> ( ( B @ D )
= ( B @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Quotient3__rel__abs) ).
thf(275,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA,E: TA] :
( ( quotient3 @ TA @ TB @ A @ B @ C )
=> ( ( A @ D @ E )
=> ( ( B @ D )
= ( B @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(162,axiom,
! [TA: $tType,A: TA > TA] :
( ( hilbert_bijection @ TA @ A )
=> ( ( image @ TA @ TA @ ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A ) @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_bijection_Osurj__inv) ).
thf(729,plain,
! [TA: $tType,A: TA > TA] :
( ( hilbert_bijection @ TA @ A )
=> ( ( image @ TA @ TA @ ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A ) @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(55,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_insert__absorb2) ).
thf(407,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(149,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB] :
( ( inj_on @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
=> ( ! [C: TA] :
( ( A @ ( B @ C ) )
= C )
=> ( ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_inj__imp__inv__eq) ).
thf(693,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB] :
( ( inj_on @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
=> ( ! [C: TA] :
( ( A @ ( B @ C ) )
= C )
=> ( ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(75,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_mk__disjoint__insert) ).
thf(467,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(40,axiom,
! [TA: $tType,A: TA > TA] :
( ( hilbert_bijection @ TA @ A )
=> ( ( image @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_bijection_Osurj) ).
thf(361,plain,
! [TA: $tType,A: TA > TA] :
( ( hilbert_bijection @ TA @ A )
=> ( ( image @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ~ ! [C: TA] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_surjE) ).
thf(625,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ~ ! [C: TA] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(210,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(879,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA,E: TA] :
( ( quotient3 @ TA @ TB @ A @ B @ C )
=> ( ( A @ D @ E )
=> ( A @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_Quotient3__refl1) ).
thf(329,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA,E: TA] :
( ( quotient3 @ TA @ TB @ A @ B @ C )
=> ( ( A @ D @ E )
=> ( A @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(83,axiom,
! [TA: $tType,A: set @ TA] :
( ( image @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_image__ident) ).
thf(493,plain,
! [TA: $tType,A: set @ TA] :
( ( image @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(145,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( inj_on @ TA @ TB @ ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A ) @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_surj__imp__inj__inv) ).
thf(682,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( inj_on @ TA @ TB @ ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A ) @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA,C: TA] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_inj__def) ).
thf(551,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA,C: TA] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(201,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA,D: TA] :
( ( bij_betw @ TB @ TA @ A @ B @ C )
=> ( ( member @ TA @ D @ C )
=> ( ( A @ ( hilbert_inv_into @ TB @ TA @ B @ A @ D ) )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_bij__betw__inv__into__right) ).
thf(852,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA,D: TA] :
( ( bij_betw @ TB @ TA @ A @ B @ C )
=> ( ( member @ TA @ D @ C )
=> ( ( A @ ( hilbert_inv_into @ TB @ TA @ B @ A @ D ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA,E: TA,F: TA,G: TA] :
( ( quotient3 @ TA @ TB @ A @ B @ C )
=> ( ( A @ D @ E )
=> ( ( A @ F @ G )
=> ( ( A @ D @ F )
= ( A @ E @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_equals__rsp) ).
thf(435,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA,E: TA,F: TA,G: TA] :
( ( quotient3 @ TA @ TB @ A @ B @ C )
=> ( ( A @ D @ E )
=> ( ( A @ F @ G )
=> ( ( A @ D @ F )
= ( A @ E @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ( bij_betw @ TB @ TA @ ( hilbert_inv_into @ TA @ TB @ B @ A ) @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_bij__betw__inv__into) ).
thf(324,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB] :
( ( bij_betw @ TA @ TB @ A @ B @ C )
=> ( bij_betw @ TB @ TA @ ( hilbert_inv_into @ TA @ TB @ B @ A ) @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(237,axiom,
! [TA: $tType] :
( ( '!' @ TA )
= ( ^ [A: TA > $o] :
( A
@ ( hilbert_Eps @ TA
@ ^ [B: TA] :
~ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_verit__sko__forall) ).
thf(974,plain,
! [TA: $tType] :
( ( '!' @ TA )
= ( ^ [A: TA > $o] :
( A
@ ( hilbert_Eps @ TA
@ ^ [B: TA] :
~ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(151,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC] :
( ( inj_on @ TA @ TC @ A @ ( top_top @ ( set @ TA ) ) )
=> ( inj_on @ TA @ ( TB > TC )
@ ^ [B: TA,C: TB] : ( A @ B )
@ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_inj__fun) ).
thf(697,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC] :
( ( inj_on @ TA @ TC @ A @ ( top_top @ ( set @ TA ) ) )
=> ( inj_on @ TA @ ( TB > TC )
@ ^ [B: TA,C: TB] : ( A @ B )
@ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_rev__image__eqI) ).
thf(317,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(250,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( ! [C: TA] :
( ( A @ C )
=> ( C = B ) )
=> ( ( hilbert_Eps @ TA @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_some__equality) ).
thf(1017,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( ! [C: TA] :
( ( A @ C )
=> ( C = B ) )
=> ( ( hilbert_Eps @ TA @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(120,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(615,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)],[120]) ).
thf(38,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA] :
( inj_on @ TA @ TA
@ ^ [B: TA] : ( minus_minus @ TA @ B @ A )
@ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_inj__diff__right) ).
thf(356,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA] :
( inj_on @ TA @ TA
@ ^ [B: TA] : ( minus_minus @ TA @ B @ A )
@ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(207,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( ( bot_bot @ ( set @ TB ) )
= ( image @ TA @ TB @ A @ B ) )
= ( B
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_empty__is__image) ).
thf(869,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( ( bot_bot @ ( set @ TB ) )
= ( image @ TA @ TB @ A @ B ) )
= ( B
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_image__iff) ).
thf(499,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(133,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] : ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_rangeI) ).
thf(650,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] : ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(229,axiom,
! [TA: $tType,A: TA > $o] :
( ( A @ ( hilbert_Eps @ TA @ A ) )
= ( ? [B: TA] : ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_some__eq__ex) ).
thf(948,plain,
! [TA: $tType,A: TA > $o] :
( ( A @ ( hilbert_Eps @ TA @ A ) )
= ( ? [B: TA] : ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(239,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ? [C: TA] : ( A @ C )
=> ( ( B
= ( hilbert_Eps @ TA @ A ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_exE__some) ).
thf(980,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ? [C: TA] : ( A @ C )
=> ( ( B
= ( hilbert_Eps @ TA @ A ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_image__eqI) ).
thf(403,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(76,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_insert__absorb) ).
thf(471,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(212,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_empty__def) ).
thf(884,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(140,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_5) ).
thf(669,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA > $o,C: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
=> ( B @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A @ D ) ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_inj__transfer) ).
thf(526,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA > $o,C: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
=> ( B @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A @ D ) ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(128,axiom,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( C = A )
| ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_insert__compr) ).
thf(637,plain,
! [TA: $tType] :
( ( insert @ TA )
= ( ^ [A: TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( C = A )
| ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(144,axiom,
! [TA: $tType,A: TA > TA,B: TA,C: TA] :
( ( hilbert_bijection @ TA @ A )
=> ( ( ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A @ B )
= C )
= ( ( A @ C )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_bijection_Oinv__left__eq__iff) ).
thf(679,plain,
! [TA: $tType,A: TA > TA,B: TA,C: TA] :
( ( hilbert_bijection @ TA @ A )
=> ( ( ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A @ B )
= C )
= ( ( A @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ TB,C: TA] :
( ( member @ TB @ A @ B )
=> ( ( image @ TB @ TA
@ ^ [D: TB] : C
@ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_image__constant) ).
thf(554,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ TB,C: TA] :
( ( member @ TB @ A @ B )
=> ( ( image @ TB @ TA
@ ^ [D: TB] : C
@ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(169,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_singleton__iff) ).
thf(753,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(123,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_doubleton__eq__iff) ).
thf(622,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(244,axiom,
! [TA: $tType,TB: $tType] :
( ( hilbert_inv_into @ TA @ TB )
= ( ^ [A: set @ TA,B: TA > TB,C: TB] :
( hilbert_Eps @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ A )
& ( ( B @ D )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_inv__into__def2) ).
thf(997,plain,
! [TA: $tType,TB: $tType] :
( ( hilbert_inv_into @ TA @ TB )
= ( ^ [A: set @ TA,B: TA > TB,C: TB] :
( hilbert_Eps @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ A )
& ( ( B @ D )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(165,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_Diff__UNIV) ).
thf(738,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB,C: TB > TB > $o] :
( ! [D: TA] :
( ( A @ ( B @ D ) )
= D )
=> ( ! [D: TA] : ( C @ ( B @ D ) @ ( B @ D ) )
=> ( ! [D: TB,E: TB] :
( ( C @ D @ E )
= ( ( C @ D @ D )
& ( C @ E @ E )
& ( ( A @ D )
= ( A @ E ) ) ) )
=> ( quotient3 @ TB @ TA @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_Quotient3I) ).
thf(457,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB,C: TB > TB > $o] :
( ! [D: TA] :
( ( A @ ( B @ D ) )
= D )
=> ( ! [D: TA] : ( C @ ( B @ D ) @ ( B @ D ) )
=> ( ! [D: TB,E: TB] :
( ( C @ D @ E )
= ( ( C @ D @ D )
& ( C @ E @ E )
& ( ( A @ D )
= ( A @ E ) ) ) )
=> ( quotient3 @ TB @ TA @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(177,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ D )
= ( B @ C ) ) )
=> ( ( the_elem @ TB @ ( image @ TA @ TB @ B @ A ) )
= ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_the__elem__image__unique) ).
thf(779,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ D )
= ( B @ C ) ) )
=> ( ( the_elem @ TB @ ( image @ TA @ TB @ B @ A ) )
= ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(181,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_insert__not__empty) ).
thf(792,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(186,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_Diff__cancel) ).
thf(805,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(20,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_insert__eq__iff) ).
thf(311,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(223,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( B @ D ) )
=> ( ! [D: TA] :
( ( ( member @ TA @ D @ A )
& ( B @ D ) )
=> ( C @ D ) )
=> ( C
@ ( hilbert_Eps @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ A )
& ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_someI2__bex) ).
thf(921,plain,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( B @ D ) )
=> ( ! [D: TA] :
( ( ( member @ TA @ D @ A )
& ( B @ D ) )
=> ( C @ D ) )
=> ( C
@ ( hilbert_Eps @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ A )
& ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(97,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_55_ex__in__conv) ).
thf(541,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)],[97]) ).
thf(136,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ! [B: TB,C: TB] :
( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) )
=> ( ! [B: TA] :
? [C: TB] :
( B
= ( A @ C ) )
=> ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_bijI_H) ).
thf(657,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ! [B: TB,C: TB] :
( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) )
=> ( ! [B: TA] :
? [C: TB] :
( B
= ( A @ C ) )
=> ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType] :
( ( quot_abs @ TA @ TB )
= ( quot_abs @ TA @ TB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_quot__type_Oabs_Ocong) ).
thf(398,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(252,axiom,
! [TA: $tType,TB: $tType] :
( ( bNF_Greatest_univ @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA] :
( A
@ ( hilbert_Eps @ TA
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_univ__def) ).
thf(1026,plain,
! [TA: $tType,TB: $tType] :
( ( bNF_Greatest_univ @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA] :
( A
@ ( hilbert_Eps @ TA
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(175,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA] :
( ( bij_betw @ TB @ TA @ A @ ( bot_bot @ ( set @ TB ) ) @ B )
=> ( B
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_bij__betw__empty1) ).
thf(773,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA] :
( ( bij_betw @ TB @ TA @ A @ ( bot_bot @ ( set @ TB ) ) @ B )
=> ( B
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(15,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( minus_minus @ ( set @ TA ) @ C @ B ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_insert__Diff__if) ).
thf(298,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( minus_minus @ ( set @ TA ) @ C @ B ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(57,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA] :
( ( image @ TA @ TA
@ ^ [B: TA] : ( minus_minus @ TA @ B @ A )
@ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_surj__diff__right) ).
thf(412,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA] :
( ( image @ TA @ TA
@ ^ [B: TA] : ( minus_minus @ TA @ B @ A )
@ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(168,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( hilbert_inv_into @ TA @ TB @ B @ A @ ( A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_inv__into__f__f) ).
thf(750,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( hilbert_inv_into @ TA @ TB @ B @ A @ ( A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(121,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_empty__iff) ).
thf(618,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(5,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_insert__commute) ).
thf(264,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: ( set @ TB ) > TA,C: TA > ( set @ TB ),D: TA] :
( ( quot_type @ TB @ TA @ A @ B @ C )
=> ( ( B @ ( C @ D ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_quot__type_Orep__inverse) ).
thf(573,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: ( set @ TB ) > TA,C: TA > ( set @ TB ),D: TA] :
( ( quot_type @ TB @ TA @ A @ B @ C )
=> ( ( B @ ( C @ D ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType] :
( ( quotient3 @ TA @ TB )
= ( ^ [A: TA > TA > $o,B: TA > TB,C: TB > TA] :
( ! [D: TB] :
( ( B @ ( C @ D ) )
= D )
& ! [D: TB] : ( A @ ( C @ D ) @ ( C @ D ) )
& ! [D: TA,E: TA] :
( ( A @ D @ E )
= ( ( A @ D @ D )
& ( A @ E @ E )
& ( ( B @ D )
= ( B @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_Quotient3__def) ).
thf(444,plain,
! [TA: $tType,TB: $tType] :
( ( quotient3 @ TA @ TB )
= ( ^ [A: TA > TA > $o,B: TA > TB,C: TB > TA] :
( ! [D: TB] :
( ( B @ ( C @ D ) )
= D )
& ! [D: TB] : ( A @ ( C @ D ) @ ( C @ D ) )
& ! [D: TA,E: TA] :
( ( A @ D @ E )
= ( ( A @ D @ D )
& ( A @ E @ E )
& ( ( B @ D )
= ( B @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(44,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_insertCI) ).
thf(375,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA,C: TB] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_range__eq__singletonD) ).
thf(584,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA,C: TB] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(247,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ! [D: TA] :
( ( A @ D )
=> ( C @ D ) )
=> ( C @ ( hilbert_Eps @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_someI2) ).
thf(1007,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ! [D: TA] :
( ( A @ D )
=> ( C @ D ) )
=> ( C @ ( hilbert_Eps @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(163,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB > TA,C: set @ TB] :
( ( member @ TA @ A @ ( image @ TB @ TA @ B @ C ) )
=> ( ( B @ ( hilbert_inv_into @ TB @ TA @ C @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_f__inv__into__f) ).
thf(732,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB > TA,C: set @ TB] :
( ( member @ TA @ A @ ( image @ TB @ TA @ B @ C ) )
=> ( ( B @ ( hilbert_inv_into @ TB @ TA @ C @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(199,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( B = C )
& ( A @ C ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( ~ ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( B = C )
& ( A @ C ) ) )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_Collect__conv__if2) ).
thf(843,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( B = C )
& ( A @ C ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
& ( ~ ( A @ B )
=> ( ( collect @ TA
@ ^ [C: TA] :
( ( B = C )
& ( A @ C ) ) )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(232,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( bNF_pick_middlep @ TA @ TB @ TC )
= ( ^ [A: TA > TB > $o,B: TB > TC > $o,C: TA,D: TC] :
( hilbert_Eps @ TB
@ ^ [E: TB] :
( ( A @ C @ E )
& ( B @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_pick__middlep__def) ).
thf(958,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( bNF_pick_middlep @ TA @ TB @ TC )
= ( ^ [A: TA > TB > $o,B: TB > TC > $o,C: TA,D: TC] :
( hilbert_Eps @ TB
@ ^ [E: TB] :
( ( A @ C @ E )
& ( B @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(103,axiom,
! [TA: $tType,A: TA > TA,B: TA,C: TA] :
( ( hilbert_bijection @ TA @ A )
=> ( ( ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A @ B )
= ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_bijection_Oeq__inv__iff) ).
thf(562,plain,
! [TA: $tType,A: TA > TA,B: TA,C: TA] :
( ( hilbert_bijection @ TA @ A )
=> ( ( ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A @ B )
= ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(217,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: ( set @ TB ) > TA,C: TA > ( set @ TB ),D: TA,E: TA] :
( ( quot_type @ TB @ TA @ A @ B @ C )
=> ( ( ( C @ D )
= ( C @ E ) )
= ( D = E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_quot__type_Orep__inject) ).
thf(904,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: ( set @ TB ) > TA,C: TA > ( set @ TB ),D: TA,E: TA] :
( ( quot_type @ TB @ TA @ A @ B @ C )
=> ( ( ( C @ D )
= ( C @ E ) )
= ( D = E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(209,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TB] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( ( A @ C )
= D )
=> ( ( hilbert_inv_into @ TA @ TB @ B @ A @ D )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_inv__into__f__eq) ).
thf(875,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TB] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( ( A @ C )
= D )
=> ( ( hilbert_inv_into @ TA @ TB @ B @ A @ D )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(193,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA] :
? [C: TB] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_surj__def) ).
thf(826,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA] :
? [C: TB] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(156,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_singletonD) ).
thf(711,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(173,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_53_equals0D) ).
thf(764,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)],[173]) ).
thf(216,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA] :
( ( A
= ( B @ C ) )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_range__eqI) ).
thf(900,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA] :
( ( A
= ( B @ C ) )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(178,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_DiffE) ).
thf(784,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(241,axiom,
! [TA: $tType,TB: $tType] :
( ( bNF_Gr932048252omCard @ TA @ TB )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TB @ TB ),C: TB] :
( hilbert_Eps @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ A )
& ( ( bNF_Greatest_toCard @ TA @ TB @ A @ B @ D )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_fromCard__def) ).
thf(990,plain,
! [TA: $tType,TB: $tType] :
( ( bNF_Gr932048252omCard @ TA @ TB )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TB @ TB ),C: TB] :
( hilbert_Eps @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ A )
& ( ( bNF_Greatest_toCard @ TA @ TB @ A @ B @ D )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) )
= ( image @ TA @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_insert__image) ).
thf(451,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) )
= ( image @ TA @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(16,axiom,
! [TA: $tType,A: set @ TA] :
( inj_on @ TA @ ( set @ TA )
@ ^ [B: TA] : ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_inj__singleton) ).
thf(303,plain,
! [TA: $tType,A: set @ TA] :
( inj_on @ TA @ ( set @ TA )
@ ^ [B: TA] : ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(205,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_insert__UNIV) ).
thf(863,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(214,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: ( set @ TA ) > TB,C: TB > ( set @ TA ),D: set @ TA] :
( ( quot_type @ TA @ TB @ A @ B @ C )
=> ( ? [E: TA] :
( ( A @ E @ E )
& ( D
= ( collect @ TA @ ( A @ E ) ) ) )
=> ( ( C @ ( B @ D ) )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_quot__type_Oabs__inverse) ).
thf(890,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: ( set @ TA ) > TB,C: TB > ( set @ TA ),D: set @ TA] :
( ( quot_type @ TA @ TB @ A @ B @ C )
=> ( ? [E: TA] :
( ( A @ E @ E )
& ( D
= ( collect @ TA @ ( A @ E ) ) ) )
=> ( ( C @ ( B @ D ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) )
= ( image @ TA @ TC
@ ^ [D: TA] : ( A @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_image__image) ).
thf(477,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) )
= ( image @ TA @ TC
@ ^ [D: TA] : ( A @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(126,axiom,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_top__empty__eq) ).
thf(631,plain,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ? [C: TA] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_surjD) ).
thf(535,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ? [C: TA] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(118,axiom,
! [TA: $tType,A: TA] :
( ( collect @ TA
@ ^ [B: TA] : ( B = A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_singleton__conv) ).
thf(609,plain,
! [TA: $tType,A: TA] :
( ( collect @ TA
@ ^ [B: TA] : ( B = A ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_injD) ).
thf(594,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(80,axiom,
! [TA: $tType] :
( ( hilbert_bijection @ TA )
= ( ^ [A: TA > TA] : ( bij_betw @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_bijection__def) ).
thf(483,plain,
! [TA: $tType] :
( ( hilbert_bijection @ TA )
= ( ^ [A: TA > TA] : ( bij_betw @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(253,axiom,
! [TA: $tType,A: TA > $o,B: $o] :
( ( ( A @ ( hilbert_Eps @ TA @ A ) )
= B )
=> ( ( ? [C: TA] : ( A @ C ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_verit__sko__ex_H) ).
thf(1029,plain,
! [TA: $tType,A: TA > $o,B: $o] :
( ( ( A @ ( hilbert_Eps @ TA @ A ) )
= B )
=> ( ( ? [C: TA] : ( A @ C ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(234,axiom,
! [TA: $tType,A: TA] :
( ( hilbert_Eps @ TA @ ( (=) @ TA @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_some__sym__eq__trivial) ).
thf(964,plain,
! [TA: $tType,A: TA] :
( ( hilbert_Eps @ TA @ ( (=) @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(221,axiom,
! [TA: $tType,A: TA > $o] :
( ? [B: TA] : ( A @ B )
=> ( A @ ( hilbert_Eps @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_someI__ex) ).
thf(915,plain,
! [TA: $tType,A: TA > $o] :
( ? [B: TA] : ( A @ B )
=> ( A @ ( hilbert_Eps @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(251,axiom,
! [TA: $tType,A: TA > $o,B: $o] :
( ( ( A
@ ( hilbert_Eps @ TA
@ ^ [C: TA] :
~ ( A @ C ) ) )
= B )
=> ( ( ! [C: TA] : ( A @ C ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_verit__sko__forall_H) ).
thf(1022,plain,
! [TA: $tType,A: TA > $o,B: $o] :
( ( ( A
@ ( hilbert_Eps @ TA
@ ^ [C: TA] :
~ ( A @ C ) ) )
= B )
=> ( ( ! [C: TA] : ( A @ C ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(226,axiom,
! [TA: $tType,A: set @ TA] :
( ( member @ TA
@ ( hilbert_Eps @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
@ A )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_some__in__eq) ).
thf(932,plain,
! [TA: $tType,A: set @ TA] :
( ( member @ TA
@ ( hilbert_Eps @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
@ A )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(203,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_bot__set__def) ).
thf(858,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(42,axiom,
! [TA: $tType,A: set @ ( set @ TA ),B: TA,C: set @ TA] :
( ! [D: set @ TA] :
( ( member @ ( set @ TA ) @ D @ A )
=> ~ ( member @ TA @ B @ D ) )
=> ( ( member @ ( set @ TA ) @ C @ ( image @ ( set @ TA ) @ ( set @ TA ) @ ( insert @ TA @ B ) @ A ) )
= ( ( member @ TA @ B @ C )
& ( member @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ C @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_in__image__insert__iff) ).
thf(367,plain,
! [TA: $tType,A: set @ ( set @ TA ),B: TA,C: set @ TA] :
( ! [D: set @ TA] :
( ( member @ ( set @ TA ) @ D @ A )
=> ~ ( member @ TA @ B @ D ) )
=> ( ( member @ ( set @ TA ) @ C @ ( image @ ( set @ TA ) @ ( set @ TA ) @ ( insert @ TA @ B ) @ A ) )
= ( ( member @ TA @ B @ C )
& ( member @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ C @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(184,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( collect @ TB
@ ^ [C: TB] :
? [D: TA] :
( ( C
= ( A @ D ) )
& ( member @ TA @ D @ B ) ) )
= ( image @ TA @ TB @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_Setcompr__eq__image) ).
thf(799,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( collect @ TB
@ ^ [C: TB] :
? [D: TA] :
( ( C
= ( A @ D ) )
& ( member @ TA @ D @ B ) ) )
= ( image @ TA @ TB @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(161,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_bot__fun__def) ).
thf(726,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(200,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: ( set @ TA ) > TB,C: TB > ( set @ TA ),D: TB] :
( ( quot_type @ TA @ TB @ A @ B @ C )
=> ? [E: TA] :
( ( A @ E @ E )
& ( ( C @ D )
= ( collect @ TA @ ( A @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_quot__type_Orep__prop) ).
thf(848,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: ( set @ TA ) > TB,C: TB > ( set @ TA ),D: TB] :
( ( quot_type @ TA @ TB @ A @ B @ C )
=> ? [E: TA] :
( ( A @ E @ E )
& ( ( C @ D )
= ( collect @ TA @ ( A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(90,axiom,
! [TA: $tType,A: TA > TA,B: TA,C: TA] :
( ( hilbert_bijection @ TA @ A )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_bijection_OeqI) ).
thf(520,plain,
! [TA: $tType,A: TA > TA,B: TA,C: TA] :
( ( hilbert_bijection @ TA @ A )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(52,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_insertI2) ).
thf(399,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(174,axiom,
! [TA: $tType,A: $o] :
( ( A
=> ( ( collect @ TA
@ ^ [B: TA] : A )
= ( top_top @ ( set @ TA ) ) ) )
& ( ~ A
=> ( ( collect @ TA
@ ^ [B: TA] : A )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_Collect__const) ).
thf(768,plain,
! [TA: $tType,A: $o] :
( ( A
=> ( ( collect @ TA
@ ^ [B: TA] : A )
= ( top_top @ ( set @ TA ) ) ) )
& ( ~ A
=> ( ( collect @ TA
@ ^ [B: TA] : A )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Otop) ).
thf(278,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(245,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: ( set @ TA ) > TB,C: TB > ( set @ TA ),D: TB] :
( ( quot_type @ TA @ TB @ A @ B @ C )
=> ( ( quot_rep @ TB @ TA @ C @ D )
= ( hilbert_Eps @ TA
@ ^ [E: TA] : ( member @ TA @ E @ ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_quot__type_Orep__def) ).
thf(1000,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: ( set @ TA ) > TB,C: TB > ( set @ TA ),D: TB] :
( ( quot_type @ TA @ TB @ A @ B @ C )
=> ( ( quot_rep @ TB @ TA @ C @ D )
= ( hilbert_Eps @ TA
@ ^ [E: TA] : ( member @ TA @ E @ ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(6,axiom,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_the__elem__eq) ).
thf(267,plain,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(220,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ? [C: TA] : ( A @ C )
=> ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( B @ ( hilbert_Eps @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_someI2__ex) ).
thf(912,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ? [C: TA] : ( A @ C )
=> ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( B @ ( hilbert_Eps @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(146,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_emptyE) ).
thf(685,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB,D: TB] :
( ( ( member @ TA @ A @ B )
=> ( ( image @ TA @ TB @ ( fun_upd @ TA @ TB @ C @ A @ D ) @ B )
= ( insert @ TB @ D @ ( image @ TA @ TB @ C @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( image @ TA @ TB @ ( fun_upd @ TA @ TB @ C @ A @ D ) @ B )
= ( image @ TA @ TB @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_fun__upd__image) ).
thf(505,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB,D: TB] :
( ( ( member @ TA @ A @ B )
=> ( ( image @ TA @ TB @ ( fun_upd @ TA @ TB @ C @ A @ D ) @ B )
= ( insert @ TB @ D @ ( image @ TA @ TB @ C @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( image @ TA @ TB @ ( fun_upd @ TA @ TB @ C @ A @ D ) @ B )
= ( image @ TA @ TB @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( insert @ TA @ B @ C ) )
= ( ( inj_on @ TA @ TB @ A @ C )
& ~ ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ ( minus_minus @ ( set @ TA ) @ C @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_inj__on__insert) ).
thf(438,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( insert @ TA @ B @ C ) )
= ( ( inj_on @ TA @ TB @ A @ C )
& ~ ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ ( minus_minus @ ( set @ TA ) @ C @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(82,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_Diff__insert2) ).
thf(490,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(182,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_DiffI) ).
thf(795,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(138,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
!= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_empty__not__UNIV) ).
thf(663,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
!= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(1,conjecture,
! [A: a] :
( ~ ( p @ A )
| ( q @ A @ ( hilbert_Eps @ b @ ( q @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ! [A: a] :
( ~ ( p @ A )
| ( q @ A @ ( hilbert_Eps @ b @ ( q @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(255,plain,
~ ! [A: a] :
( ~ ( p @ A )
| ( q @ A @ ( hilbert_Eps @ b @ ( q @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(132,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_DiffD1) ).
thf(648,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(188,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
=> ( member @ TA @ ( hilbert_inv_into @ TA @ TB @ C @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_inv__into__into) ).
thf(812,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
=> ( member @ TA @ ( hilbert_inv_into @ TA @ TB @ C @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(192,axiom,
! [TA: $tType] :
( ( minus_minus @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ~ ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_set__diff__eq) ).
thf(823,plain,
! [TA: $tType] :
( ( minus_minus @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ~ ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(176,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( A @ ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_surj__f__inv__f) ).
thf(776,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( A @ ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(202,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_Diff__empty) ).
thf(855,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(148,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_inj__eq) ).
thf(690,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(129,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A ) @ ( image @ TA @ TB @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_image__inv__f__f) ).
thf(640,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A ) @ ( image @ TA @ TB @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_bij__is__surj) ).
thf(295,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(208,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_37_empty__Collect__eq) ).
thf(872,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)],[208]) ).
thf(154,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( lattic1534546155max_on @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA] :
( lattices_ord_arg_max @ TA @ TB @ A
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_arg__max__on__def) ).
thf(705,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( lattic1534546155max_on @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA] :
( lattices_ord_arg_max @ TA @ TB @ A
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(213,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TB > TA,C: TA,D: TA] :
( ( ( hilbert_inv_into @ TB @ TA @ A @ B @ C )
= ( hilbert_inv_into @ TB @ TA @ A @ B @ D ) )
=> ( ( member @ TA @ C @ ( image @ TB @ TA @ B @ A ) )
=> ( ( member @ TA @ D @ ( image @ TB @ TA @ B @ A ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_inv__into__injective) ).
thf(887,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TB > TA,C: TA,D: TA] :
( ( ( hilbert_inv_into @ TB @ TA @ A @ B @ C )
= ( hilbert_inv_into @ TB @ TA @ A @ B @ D ) )
=> ( ( member @ TA @ C @ ( image @ TB @ TA @ B @ A ) )
=> ( ( member @ TA @ D @ ( image @ TB @ TA @ B @ A ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(242,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( A @ ( hilbert_Eps @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_tfl__some) ).
thf(993,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( A @ ( hilbert_Eps @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( bij_betw @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TB ) ) )
=> ( bij_betw @ TB @ TA @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A ) @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_bij__imp__bij__inv) ).
thf(557,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( bij_betw @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TB ) ) )
=> ( bij_betw @ TB @ TA @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A ) @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(246,axiom,
! [TA: $tType,A: TA,B: TA > $o,C: TA > $o] :
( ( A
= ( hilbert_Eps @ TA @ B ) )
=> ( ! [D: TA] :
( ( B @ D )
= ( C @ D ) )
=> ( ( ? [D: TA] : ( C @ D ) )
= ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_verit__sko__ex__indirect2) ).
thf(1003,plain,
! [TA: $tType,A: TA,B: TA > $o,C: TA > $o] :
( ( A
= ( hilbert_Eps @ TA @ B ) )
=> ( ! [D: TA] :
( ( B @ D )
= ( C @ D ) )
=> ( ( ? [D: TA] : ( C @ D ) )
= ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(142,axiom,
! [TA: $tType,A: TA > TA,B: TA] :
( ( hilbert_bijection @ TA @ A )
=> ( ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A @ ( A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_bijection_Oinv__left) ).
thf(673,plain,
! [TA: $tType,A: TA > TA,B: TA] :
( ( hilbert_bijection @ TA @ A )
=> ( ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A @ ( A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(27,axiom,
top @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Otop_4) ).
thf(331,plain,
top @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(66,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( minus_minus @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_insert__Diff1) ).
thf(441,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( minus_minus @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(158,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > TA] :
( ! [C: TB] :
( ( A @ ( B @ C ) )
= C )
=> ( ! [C: TA] :
( ( B @ ( A @ C ) )
= C )
=> ( ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_inv__equality) ).
thf(717,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > TA] :
( ! [C: TB] :
( ( A @ ( B @ C ) )
= C )
=> ( ! [C: TA] :
( ( B @ ( A @ C ) )
= C )
=> ( ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( inj_on @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
=> ( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_bijI) ).
thf(502,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( inj_on @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
=> ( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot) ).
thf(463,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( image @ TA @ TB @ A @ B )
= ( image @ TA @ TB @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_inj__image__eq__iff) ).
thf(338,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( image @ TA @ TB @ A @ B )
= ( image @ TA @ TB @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ! [B: TA,C: TA] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_injI) ).
thf(576,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ! [B: TA,C: TA] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( image @ TB @ TA @ A @ ( bot_bot @ ( set @ TB ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_image__empty) ).
thf(643,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( image @ TB @ TA @ A @ ( bot_bot @ ( set @ TB ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(230,axiom,
! [TA: $tType,A: TA,B: TA,C: TA > $o] :
( ( A = B )
=> ( ( ( hilbert_Eps @ TA @ C )
= B )
= ( ( hilbert_Eps @ TA @ C )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_verit__sko__forall_H_H) ).
thf(951,plain,
! [TA: $tType,A: TA,B: TA,C: TA > $o] :
( ( A = B )
=> ( ( ( hilbert_Eps @ TA @ C )
= B )
= ( ( hilbert_Eps @ TA @ C )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(187,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: TB] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( A @ B )
= C )
=> ( ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A @ C )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_inv__f__eq) ).
thf(808,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: TB] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( A @ B )
= C )
=> ( ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(98,axiom,
! [TA: $tType,A: set @ TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [B: TA,C: TA] :
( ( member @ TA @ B @ A )
=> ( ( member @ TA @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_is__singletonI_H) ).
thf(544,plain,
! [TA: $tType,A: set @ TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [B: TA,C: TA] :
( ( member @ TA @ B @ A )
=> ( ( member @ TA @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(218,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_singletonI) ).
thf(907,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA,E: TA] :
( ( quotient3 @ TA @ TB @ A @ B @ C )
=> ( ( A @ D @ E )
=> ( A @ D @ ( C @ ( B @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_rep__abs__rsp) ).
thf(336,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA,E: TA] :
( ( quotient3 @ TA @ TB @ A @ B @ C )
=> ( ( A @ D @ E )
=> ( A @ D @ ( C @ ( B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(115,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ( collect @ TB
@ ^ [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) ) )
= ( image @ TA @ TB @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_Compr__image__eq) ).
thf(600,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ( collect @ TB
@ ^ [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) ) )
= ( image @ TA @ TB @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(48,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_Diff__insert0) ).
thf(386,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA,C: TA > TB,D: TA,E: TA] :
( ( quotient3 @ TB @ TA @ A @ B @ C )
=> ( ( A @ ( C @ D ) @ ( C @ E ) )
= ( D = E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_Quotient3__rel__rep) ).
thf(314,plain,
! [TA: $tType,TB: $tType,A: TB > TB > $o,B: TB > TA,C: TA > TB,D: TA,E: TA] :
( ( quotient3 @ TB @ TA @ A @ B @ C )
=> ( ( A @ ( C @ D ) @ ( C @ E ) )
= ( D = E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(119,axiom,
! [TA: $tType,A: TA > TA,B: TA,C: TA] :
( ( hilbert_bijection @ TA @ A )
=> ( ( ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A @ B )
= ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_bijection_Oeq__invI) ).
thf(612,plain,
! [TA: $tType,A: TA > TA,B: TA,C: TA] :
( ( hilbert_bijection @ TA @ A )
=> ( ( ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A @ B )
= ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( bij_betw @ TB @ TA @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A ) @ ( image @ TA @ TB @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_inj__imp__bij__betw__inv) ).
thf(465,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( bij_betw @ TB @ TA @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A ) @ ( image @ TA @ TB @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(69,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(450,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o] :
( ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ A @ ( collect @ TB @ B ) )
= ( collect @ TA
@ ^ [C: TA] : ( B @ ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_bij__image__Collect__eq) ).
thf(581,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB > $o] :
( ( bij_betw @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) @ ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ A @ ( collect @ TB @ B ) )
= ( collect @ TA
@ ^ [C: TA] : ( B @ ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(171,axiom,
! [TA: $tType,A: TA > TA] :
( ( hilbert_bijection @ TA @ A )
=> ( bij_betw @ TA @ TA @ ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A ) @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_bijection_Obij__inv) ).
thf(759,plain,
! [TA: $tType,A: TA > TA] :
( ( hilbert_bijection @ TA @ A )
=> ( bij_betw @ TA @ TA @ ( hilbert_inv_into @ TA @ TA @ ( top_top @ ( set @ TA ) ) @ A ) @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(248,axiom,
! [TA: $tType,A: TA,B: TA > $o,C: TA > $o] :
( ( A
= ( hilbert_Eps @ TA
@ ^ [D: TA] :
~ ( B @ D ) ) )
=> ( ! [D: TA] :
( ( B @ D )
= ( C @ D ) )
=> ( ( ! [D: TA] : ( C @ D ) )
= ( B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_verit__sko__forall__indirect2) ).
thf(1010,plain,
! [TA: $tType,A: TA,B: TA > $o,C: TA > $o] :
( ( A
= ( hilbert_Eps @ TA
@ ^ [D: TA] :
~ ( B @ D ) ) )
=> ( ! [D: TA] :
( ( B @ D )
= ( C @ D ) )
=> ( ( ! [D: TA] : ( C @ D ) )
= ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(152,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
( ( image @ TA @ TC
@ ^ [C: TA] : ( A @ ( B @ C ) )
@ ( top_top @ ( set @ TA ) ) )
= ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_range__composition) ).
thf(699,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
( ( image @ TA @ TC
@ ^ [C: TA] : ( A @ ( B @ C ) )
@ ( top_top @ ( set @ TA ) ) )
= ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(233,axiom,
! [TA: $tType,TB: $tType] :
( ( hilbert_inv_into @ TA @ TB )
= ( ^ [A: set @ TA,B: TA > TB,C: TB] :
( hilbert_Eps @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ A )
& ( ( B @ D )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_inv__into__def) ).
thf(961,plain,
! [TA: $tType,TB: $tType] :
( ( hilbert_inv_into @ TA @ TB )
= ( ^ [A: set @ TA,B: TA > TB,C: TB] :
( hilbert_Eps @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ A )
& ( ( B @ D )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(89,axiom,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_is__singleton__def) ).
thf(517,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(3,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ B )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_translation__subtract__diff) ).
thf(258,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ B )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(134,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_38_Collect__empty__eq) ).
thf(652,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)],[134]) ).
thf(53,axiom,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_top1I) ).
thf(401,plain,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(243,axiom,
! [A: a] :
( ( p @ A )
=> ? [B: b] : ( q @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(995,plain,
! [A: a] :
( ( p @ A )
=> ? [B: b] : ( q @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(105,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_iso__tuple__UNIV__I) ).
thf(568,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image @ TA @ TB @ C @ A )
= ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_image__cong) ).
thf(510,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image @ TA @ TB @ C @ A )
= ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(225,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A )
= ( ^ [B: TA] :
( hilbert_Eps @ TB
@ ^ [C: TB] :
( ( A @ C )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_inv__def) ).
thf(929,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( hilbert_inv_into @ TB @ TA @ ( top_top @ ( set @ TB ) ) @ A )
= ( ^ [B: TA] :
( hilbert_Eps @ TB
@ ^ [C: TB] :
( ( A @ C )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(195,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
=> ~ ! [C: TA] :
( A
!= ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_rangeE) ).
thf(832,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
=> ~ ! [C: TA] :
( A
!= ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(122,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_2) ).
thf(620,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(68,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_insert__iff) ).
thf(447,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TA @ TB @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) @ ( image @ TA @ TB @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_image__set__diff) ).
thf(432,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TA @ TB @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) @ ( image @ TA @ TB @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(196,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_insert__Diff) ).
thf(835,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(180,axiom,
! [TA: $tType] : ( top @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Otop_1) ).
thf(790,plain,
! [TA: $tType] : ( top @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(8,axiom,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_3) ).
thf(273,plain,
! [TA: $tType] : ( bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_bot__apply) ).
thf(603,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TB )
=> ( ( bot_bot @ ( TA > TB ) )
= ( ^ [A: TA] : ( bot_bot @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(164,axiom,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Set_Ois__empty__def) ).
thf(735,plain,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(56,axiom,
! [TA: $tType,A: set @ TA] :
( inj_on @ TA @ TA
@ ^ [B: TA] : B
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_inj__on__id2) ).
thf(410,plain,
! [TA: $tType,A: set @ TA] :
( inj_on @ TA @ TA
@ ^ [B: TA] : B
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(235,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ? [C: TA] :
( ( A @ C )
& ! [D: TA] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ( A @ B )
=> ( ( hilbert_Eps @ TA @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_some1__equality) ).
thf(967,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ? [C: TA] :
( ( A @ C )
& ! [D: TA] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ( A @ B )
=> ( ( hilbert_Eps @ TA @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(17,axiom,
! [TA: $tType,A: TA > TA] :
( ( bij_betw @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TA ) ) )
=> ( hilbert_bijection @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_bijection_Ointro) ).
thf(305,plain,
! [TA: $tType,A: TA > TA] :
( ( bij_betw @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TA ) ) )
=> ( hilbert_bijection @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB] :
( ( bij_betw @ TB @ TA @ A @ B @ ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_bij__betw__imp__surj) ).
thf(326,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB] :
( ( bij_betw @ TB @ TA @ A @ B @ ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(32,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_Diff__insert) ).
thf(341,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(39,axiom,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_top__conj_I1_J) ).
thf(358,plain,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(254,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA] :
( ( A @ B )
=> ( ~ ( A @ C )
=> ( ( ( hilbert_Eps @ TA @ A )
= C )
=> ( ( hilbert_Eps @ TA @ A )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Nitpick_OEps__psimp) ).
thf(1033,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA] :
( ( A @ B )
=> ( ~ ( A @ C )
=> ( ( ( hilbert_Eps @ TA @ A )
= C )
=> ( ( hilbert_Eps @ TA @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A ) @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_inj__imp__surj__inv) ).
thf(532,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ ( hilbert_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A ) @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(150,axiom,
! [TA: $tType,TB: $tType] :
( ( quot_rep @ TA @ TB )
= ( quot_rep @ TA @ TB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_quot__type_Orep_Ocong) ).
thf(696,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(159,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_top__apply) ).
thf(720,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(231,axiom,
! [TA: $tType,A: TA] :
( ( hilbert_Eps @ TA
@ ^ [B: TA] : ( B = A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_some__eq__trivial) ).
thf(955,plain,
! [TA: $tType,A: TA] :
( ( hilbert_Eps @ TA
@ ^ [B: TA] : ( B = A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB,D: set @ TB] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ~ ( member @ TB @ C @ D )
=> ( ( ( insert @ TB @ C @ D )
= ( image @ TA @ TB @ A @ B ) )
=> ~ ! [E: TA,F: set @ TA] :
( ~ ( member @ TA @ E @ F )
=> ( ( B
= ( insert @ TA @ E @ F ) )
=> ( ( C
= ( A @ E ) )
=> ( D
!= ( image @ TA @ TB @ A @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_inj__img__insertE) ).
thf(283,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB,D: set @ TB] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ~ ( member @ TB @ C @ D )
=> ( ( ( insert @ TB @ C @ D )
= ( image @ TA @ TB @ A @ B ) )
=> ~ ! [E: TA,F: set @ TA] :
( ~ ( member @ TA @ E @ F )
=> ( ( B
= ( insert @ TA @ E @ F ) )
=> ( ( C
= ( A @ E ) )
=> ( D
!= ( image @ TA @ TB @ A @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(58,axiom,
! [TA: $tType,A: TA > TA] :
( ( hilbert_bijection @ TA @ A )
=> ( inj_on @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_bijection_Oinj) ).
thf(415,plain,
! [TA: $tType,A: TA > TA] :
( ( hilbert_bijection @ TA @ A )
=> ( inj_on @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(215,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_top__set__def) ).
thf(897,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(77,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( insert @ TA @ A @ ( collect @ TA @ B ) )
= ( collect @ TA
@ ^ [C: TA] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_insert__Collect) ).
thf(474,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( insert @ TA @ A @ ( collect @ TA @ B ) )
= ( collect @ TA
@ ^ [C: TA] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(240,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( lattices_ord_arg_max @ TA @ TB )
= ( ^ [A: TA > TB,B: TA > $o] : ( hilbert_Eps @ TA @ ( lattic2130478198rg_max @ TA @ TB @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_arg__max__def) ).
thf(987,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( lattices_ord_arg_max @ TA @ TB )
= ( ^ [A: TA > TB,B: TA > $o] : ( hilbert_Eps @ TA @ ( lattic2130478198rg_max @ TA @ TB @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(28,axiom,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_insertI1) ).
thf(332,plain,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA] :
( ( quotient3 @ TA @ TB @ A @ B @ C )
=> ( ( A @ D @ D )
=> ( A @ ( C @ ( B @ D ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_Quotient3__rep__abs) ).
thf(427,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA] :
( ( quotient3 @ TA @ TB @ A @ B @ C )
=> ( ( A @ D @ D )
=> ( A @ ( C @ ( B @ D ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(160,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_39_all__not__in__conv) ).
thf(723,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)],[160]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: TA] :
( ( A
= ( B @ D ) )
=> ~ ( member @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_imageE) ).
thf(486,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: TA] :
( ( A
= ( B @ D ) )
=> ~ ( member @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA,E: TA] :
( ( quotient3 @ TA @ TB @ A @ B @ C )
=> ( ( A @ D @ E )
=> ( A @ ( C @ ( B @ D ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_rep__abs__rsp__left) ).
thf(354,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA,E: TA] :
( ( quotient3 @ TA @ TB @ A @ B @ C )
=> ( ( A @ D @ E )
=> ( A @ ( C @ ( B @ D ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(227,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA] :
( ( ( hilbert_Eps @ TA @ A )
= B )
=> ( ( A @ C )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_some__eq__imp) ).
thf(935,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA] :
( ( ( hilbert_Eps @ TA @ A )
= B )
=> ( ( A @ C )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(19,axiom,
! [TA: $tType,A: TA > TA] :
( ( hilbert_bijection @ TA @ A )
=> ( bij_betw @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_bijection_Obij) ).
thf(309,plain,
! [TA: $tType,A: TA > TA] :
( ( hilbert_bijection @ TA @ A )
=> ( bij_betw @ TA @ TA @ A @ ( top_top @ ( set @ TA ) ) @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(143,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: ( set @ TA ) > TB,C: TB > ( set @ TA ),D: TA] :
( ( quot_type @ TA @ TB @ A @ B @ C )
=> ( ( quot_abs @ TA @ TB @ A @ B @ D )
= ( B @ ( collect @ TA @ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_quot__type_Oabs__def) ).
thf(676,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: ( set @ TA ) > TB,C: TB > ( set @ TA ),D: TA] :
( ( quot_type @ TA @ TB @ A @ B @ C )
=> ( ( quot_abs @ TA @ TB @ A @ B @ D )
= ( B @ ( collect @ TA @ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(112,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_UNIV__I) ).
thf(592,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: set @ TA] :
( ( image @ TA @ TB @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_image__insert) ).
thf(364,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: set @ TA] :
( ( image @ TA @ TB @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(155,axiom,
! [TA: $tType,TB: $tType,A: TA] :
( ( image @ TB @ TA
@ ^ [B: TB] : A
@ ( top_top @ ( set @ TB ) ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_range__constant) ).
thf(708,plain,
! [TA: $tType,TB: $tType,A: TA] :
( ( image @ TB @ TA
@ ^ [B: TB] : A
@ ( top_top @ ( set @ TB ) ) )
= ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(84,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_insertE) ).
thf(496,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA,E: TA] :
( ( quotient3 @ TA @ TB @ A @ B @ C )
=> ( ( ( A @ D @ D )
& ( A @ E @ E )
& ( ( B @ D )
= ( B @ E ) ) )
= ( A @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Quotient3__rel) ).
thf(454,plain,
! [TA: $tType,TB: $tType,A: TA > TA > $o,B: TA > TB,C: TB > TA,D: TA,E: TA] :
( ( quotient3 @ TA @ TB @ A @ B @ C )
=> ( ( ( A @ D @ D )
& ( A @ E @ E )
& ( ( B @ D )
= ( B @ E ) ) )
= ( A @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(249,axiom,
! [TA: $tType,TB: $tType] :
( ( bNF_Greatest_toCard @ TA @ TB )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TB @ TB )] : ( hilbert_Eps @ ( TA > TB ) @ ( bNF_Gr1978856366d_pred @ TA @ TB @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_toCard__def) ).
thf(1014,plain,
! [TA: $tType,TB: $tType] :
( ( bNF_Greatest_toCard @ TA @ TB )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TB @ TB )] : ( hilbert_Eps @ ( TA > TB ) @ ( bNF_Gr1978856366d_pred @ TA @ TB @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(236,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( A @ ( hilbert_Eps @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_someI) ).
thf(972,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( A @ B )
=> ( A @ ( hilbert_Eps @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(1040,plain,
$false,
inference(e,[status(thm)],[787,347,666,352,909,628,977,523,741,655,597,861,384,797,814,747,538,670,829,565,841,417,389,570,372,587,838,917,702,802,344,817,559,421,606,881,261,756,321,646,480,687,280,634,866,660,307,292,380,942,925,761,381,714,270,529,334,349,820,392,424,275,729,407,693,467,361,625,879,329,493,682,551,852,435,324,974,697,317,1017,615,356,869,499,650,948,980,403,471,884,669,526,637,679,554,753,622,997,738,457,779,792,805,311,921,541,657,398,1026,773,298,412,750,618,264,573,444,375,584,1007,732,843,958,562,904,875,826,711,764,900,784,990,451,303,863,890,477,631,535,609,594,483,1029,964,915,1022,932,858,367,799,726,848,520,399,768,278,1000,267,912,685,505,438,490,795,663,255,648,812,823,776,855,690,640,295,872,705,887,993,557,1003,673,331,441,717,502,463,338,576,643,951,808,544,907,336,600,386,314,612,465,450,581,759,1010,699,961,517,258,652,401,995,568,510,929,832,620,447,432,835,790,273,603,735,410,967,305,326,341,358,1033,532,696,720,955,283,415,897,474,987,332,427,723,486,354,935,309,676,592,364,708,496,454,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP144^2 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n011.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 6 14:24:54 EDT 2024
% 0.15/0.36 % CPUTime :
% 1.02/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.66/1.15 % [INFO] Parsing done (264ms).
% 2.04/1.16 % [INFO] Running in sequential loop mode.
% 2.63/1.37 % [INFO] eprover registered as external prover.
% 2.63/1.38 % [INFO] cvc4 registered as external prover.
% 2.63/1.38 % [INFO] Scanning for conjecture ...
% 2.94/1.47 % [INFO] Found a conjecture and 269 axioms. Running axiom selection ...
% 3.17/1.57 % [INFO] Axiom selection finished. Selected 252 axioms (removed 17 axioms).
% 3.81/1.75 % [INFO] Problem is higher-order (TPTP THF).
% 3.81/1.77 % [INFO] Type checking passed.
% 3.81/1.77 % [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 ...
% 41.10/30.66 % External prover 'e' found a proof!
% 41.10/30.67 % [INFO] Killing All external provers ...
% 41.10/30.67 % Time passed: 30146ms (effective reasoning time: 29500ms)
% 41.10/30.67 % 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)>
% 41.10/30.67 % Axioms used in derivation (252): fact_178_inv__into__into, fact_213_injI, fact_11_some__eq__ex, tcon_fun___Orderings_Obot, fact_244_insert__Diff, fact_43_toCard__def, fact_76_UNIV__witness, fact_7_verit__sko__forall_H_H, fact_19_verit__sko__ex__indirect2, fact_129_insert__UNIV, fact_82_iso__tuple__UNIV__I, fact_3_verit__sko__ex_H, fact_117_insert__compr, fact_222_range__ex1__eq, fact_201_full__SetCompr__eq, fact_52_emptyE, fact_145_image__ident, fact_227_inj__on__insert, fact_182_rangeE, fact_208_surjD, fact_224_inj__image__mem__iff, fact_253_top__conj_I1_J, fact_98_Quotient3__rel__abs, fact_4_verit__sko__forall, fact_240_inj__diff__right, fact_163_image__cong, fact_86_bijection_Oinv__right__eq__iff, fact_230_Diff__iff, fact_53_equals0D, fact_245_Diff__insert, fact_216_bij__betw__empty2, fact_101_Quotient3__refl2, fact_136_bijection_Oinv__left, fact_153_inj__imp__bij__betw__inv, fact_228_top__conj_I2_J, fact_31_exE__some, fact_248_DiffD1, fact_66_bot__empty__eq, fact_206_bij__is__inj, fact_15_someI, tcon_fun___Orderings_Oord, fact_181_Setcompr__eq__image, tcon_HOL_Obool___Orderings_Oord_5, fact_127_singleton__iff, fact_157_surj__imp__inj__inv, fact_191_bijection__def, fact_24_some__in__eq, fact_116_insert__ident, fact_186_inv__inv__eq, fact_146_top1I, fact_149_image__empty, fact_137_bijection_Oinv__right, fact_166_rev__image__eqI, fact_215_inj__def, fact_158_bijI_H, fact_193_surj__imp__inv__eq, fact_154_inj__transfer, fact_160_imageI, fact_139_the__elem__eq, fact_119_insertI2, fact_233_empty__Diff, fact_115_insert__absorb, fact_135_bijection_Oeq__invI, fact_92_singletonI, fact_74_UNIV__def, fact_254_remove__def, fact_184_bij__imp__bij__inv, fact_94_singleton__conv2, fact_198_bijection_Osurj, fact_99_Quotient3__abs__rep, fact_220_inj__fun, fact_65_Collect__empty__eq__bot, fact_83_quot__type_OQuotient, fact_229_DiffI, fact_210_surjI, fact_235_insert__Diff1, fact_46_Collect__mem__eq, fact_112_insert__commute, fact_8_someI__ex, tcon_Set_Oset___Orderings_Oord_2, fact_217_bij__betw__empty1, fact_106_equals__rsp, fact_41_bot__apply, fact_111_mk__disjoint__insert, fact_42_quot__type_Orep__def, fact_0_some__equality, fact_171_bij__image__Collect__eq, fact_90_insert__iff, tcon_HOL_Obool___Orderings_Obot_6, fact_238_Diff__UNIV, fact_38_Collect__empty__eq, fact_133_is__singleton__def, fact_138_is__singleton__the__elem, fact_79_quot__type_Oabs_Ocong, fact_130_Collect__conv__if, fact_169_rangeI, fact_110_bijection_OeqI, fact_21_Nitpick_OEps__psimp, fact_32_quot__type_Orep__inverse, fact_113_insert__Collect, tcon_HOL_Obool___Orderings_Otop_4, fact_247_DiffE, fact_174_bij__betw__inv__into__left, fact_85_is__singletonI, fact_33_quot__type_Oabs__inverse, fact_62_Set_Ois__empty__def, fact_199_image__constant, fact_200_image__constant__conv, fact_140_range__constant, fact_234_Diff__cancel, fact_89_insert__absorb2, fact_239_surj__diff__right, fact_192_bijection_Obij, fact_231_Diff__idemp, fact_205_bijI, fact_45_mem__Collect__eq, fact_189_inv__f__f, fact_70_top__apply, fact_13_tfl__some, fact_126_doubleton__eq__iff, fact_179_inv__into__injective, fact_203_inj__on__empty, fact_237_insert__Diff__single, fact_195_surj__iff__all, fact_2_some__sym__eq__trivial, fact_18_some1__equality, fact_6_verit__sko__forall_H, fact_9_someI2__ex, fact_197_bijection_Oinj, fact_26_inv__into__def, fact_177_f__inv__into__f, fact_255_fun__upd__image, fact_100_rep__abs__rsp__left, fact_29_arg__max__def, fact_131_Collect__conv__if2, tcon_Set_Oset___Orderings_Otop_1, fact_164_ball__imageD, fact_176_inv__into__f__eq, fact_223_inj__image__eq__iff, fact_104_Quotient3__def, fact_35_quot__type_Orep__prop, fact_134_is__singletonE, fact_17_verit__sko__forall__indirect, fact_185_bij__inv__eq__iff, fact_159_imageE, fact_236_Diff__insert0, fact_63_quot__type_Oabs__def, fact_47_Collect__cong, fact_155_image__inv__f__f, fact_20_verit__sko__ex__indirect, fact_93_singleton__conv, fact_102_Quotient3__refl1, fact_95_Quotient3__rep__reflp, fact_148_empty__is__image, fact_168_the__elem__image__unique, help_If_3_1_T, fact_39_all__not__in__conv, fact_14_Eps__cong, fact_232_Diff__empty, fact_226_bij__betw__imp__surj, tcon_fun___Orderings_Otop, fact_165_image__image, fact_156_inj__imp__surj__inv, fact_190_bijection_Ointro, fact_23_pick__middlep__def, fact_221_inj__img__insertE, fact_144_image__eqI, fact_122_top__empty__eq, fact_75_UNIV__eq__I, fact_91_insertCI, fact_71_UNIV__I, fact_81_inv__equality, fact_10_someI2__bex, fact_211_surj__def, fact_51_bot__fun__def, fact_242_Diff__insert__absorb, fact_16_verit__sko__forall__indirect2, fact_50_quot__type_Orep_Ocong, fact_175_bij__betw__inv__into__right, fact_170_range__eqI, fact_54_equals0I, fact_202_range__eq__singletonD, fact_22_univ__def, fact_196_surj__f__inv__f, fact_87_bijection_Oinv__left__eq__iff, fact_246_in__image__insert__iff, fact_212_injD, fact_56_empty__def, fact_69_is__singletonI_H, fact_218_bij__pointE, fact_107_Quotient3I, fact_1_some__eq__trivial, fact_225_bij__is__surj, fact_204_bij__def, fact_252_image__set__diff, fact_27_quot__type_Osome__collect, fact_5_someI2, fact_173_inv__into__inv__into__eq, fact_67_inv__def, fact_105_rep__abs__rsp, fact_209_surjE, fact_128_singletonD, fact_143_bijection_Obij__inv, fact_214_inj__eq, fact_187_inj__imp__inv__eq, fact_109_bijection_Oeq__iff, fact_25_inv__into__def2, fact_152_inv__into__f__f, fact_183_range__composition, fact_34_quot__type_Orep__inject, fact_80_empty__not__UNIV, fact_124_singleton__inject, fact_249_DiffD2, fact_141_bijection_Osurj__inv, fact_241_translation__subtract__diff, fact_97_Quotient3__rel__rep, fact_161_image__iff, fact_114_insert__eq__iff, fact_167_Compr__image__eq, fact_251_insert__Diff__if, fact_188_inv__f__eq, fact_121_insertE, fact_250_set__diff__eq, fact_147_image__is__empty, fact_243_Diff__insert2, fact_123_top__set__def, fact_28_fromCard__def, fact_36_arg__max__on__def, fact_180_setcompr__eq__image, fact_125_insert__not__empty, tcon_Set_Oset___Orderings_Obot_3, fact_219_inj__singleton, conj_0, fact_103_Quotient3__rel, fact_120_insertI1, fact_207_inj__on__id2, fact_118_Set_Oset__insert, fact_194_image__f__inv__f, fact_72_Collect__const, fact_142_bijection_Oinj__inv, fact_73_inv__identity, fact_162_bex__imageD, fact_96_Quotient3__rep__abs, fact_12_some__eq__imp, fact_88_bijection_Oeq__inv__iff, fact_40_empty__iff, fact_37_empty__Collect__eq, fact_172_bij__betw__inv__into, fact_49_bot__set__def, fact_55_ex__in__conv, fact_150_image__insert, fact_151_insert__image
% 41.10/30.67 % No. of inferences in proof: 508
% 41.10/30.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 30146 ms resp. 29500 ms w/o parsing
% 41.88/30.86 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 41.88/30.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------