%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP098^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:45 AM UTC 2026
% Result : Theorem 90.20s 68.69s
% Output : Refutation 90.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 161
% Syntax : Number of formulae : 324 ( 94 unt; 0 typ; 0 def)
% Number of atoms : 1288 ( 377 equ; 2 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 5240 ( 32 ~; 4 |; 42 &;4750 @)
% ( 0 <=>; 412 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 394 ( 394 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 3 con; 0-6 aty)
% Number of variables : 1602 ( 46 ^;1516 !; 40 ?;1602 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_type,type,
c: $tType ).
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(bounded_lattice_decl,type,
bounded_lattice:
!>[TA: $tType] : $o ).
thf(top_decl,type,
top:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_decl,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(bounded_lattice_top_decl,type,
bounded_lattice_top:
!>[TA: $tType] : $o ).
thf(finite_Fpow_decl,type,
finite_Fpow:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( set @ TA ) ) ) ).
thf(comp_decl,type,
comp:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB ) > ( TA > TC ) > TA > TB ) ).
thf(inj_on_decl,type,
inj_on:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > $o ) ).
thf(the_inv_into_decl,type,
the_inv_into:
!>[TA: $tType,TB: $tType] : ( ( set @ TB ) > ( TB > TA ) > TA > TB ) ).
thf(uminus_uminus_decl,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(sup_sup_decl,type,
sup_sup:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(top_top_decl,type,
top_top:
!>[TA: $tType] : TA ).
thf(image_decl,type,
image:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > ( set @ TA ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(f_decl,type,
f: a > b ).
thf(g_decl,type,
g: c > a ).
thf(h_decl,type,
h: c > a ).
thf(47,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice_2) ).
thf(333,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(20,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_subset__trans) ).
thf(234,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_comp2__conv) ).
thf(523,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(61,axiom,
! [TA: $tType] :
( ( bounded_lattice_top @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( top_top @ TA ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_sup__top__right) ).
thf(379,plain,
! [TA: $tType] :
( ( bounded_lattice_top @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ A @ ( top_top @ TA ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(148,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_Un__assoc) ).
thf(655,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(135,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) @ ( uminus_uminus @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_inj__image__Compl__subset) ).
thf(614,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) @ ( uminus_uminus @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(131,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_comp__def) ).
thf(597,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
( ( A = B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image @ TA @ TB @ C @ A ) )
= ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_Sup_OSUP__cong) ).
thf(217,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
( ( A = B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image @ TA @ TB @ C @ A ) )
= ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(30,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_subset__antisym) ).
thf(276,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(63,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_UNIV__I) ).
thf(384,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TA > TB,C: TB > TC,D: TB > TC] :
( ! [E: TB,F: TB] :
( ( member @ TB @ E @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( member @ TB @ F @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( C @ E )
= ( D @ F ) )
=> ( E = F ) ) ) )
=> ( ( ( comp @ TB @ TC @ TA @ C @ A )
= ( comp @ TB @ TC @ TA @ D @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_fun_Oinj__map__strong) ).
thf(472,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TA > TB,C: TB > TC,D: TB > TC] :
( ! [E: TB,F: TB] :
( ( member @ TB @ E @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( member @ TB @ F @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( ( C @ E )
= ( D @ F ) )
=> ( E = F ) ) ) )
=> ( ( ( comp @ TB @ TC @ TA @ C @ A )
= ( comp @ TB @ TC @ TA @ D @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(160,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_14_inj__image__eq__iff) ).
thf(698,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)],[160]) ).
thf(151,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_Un__subset__iff) ).
thf(670,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(5,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
=> ~ ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_ComplD) ).
thf(174,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
=> ~ ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ! [E: TA] :
( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_comp__eq__elim) ).
thf(404,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ! [E: TA] :
( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TA,B: TC > TA] :
( ( ? [C: TB > TC] :
( A
= ( comp @ TC @ TA @ TB @ B @ C ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) ) )
=> ? [D: TC] :
( C
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_ex__o__conv) ).
thf(504,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TA,B: TC > TA] :
( ( ? [C: TB > TC] :
( A
= ( comp @ TC @ TA @ TB @ B @ C ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) ) )
=> ? [D: TC] :
( C
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(162,axiom,
( ( comp @ a @ b @ c @ f @ g )
= ( comp @ a @ b @ c @ f @ h ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(702,plain,
( ( comp @ a @ b @ c @ f @ g )
= ( comp @ a @ b @ c @ f @ h ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(127,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC] :
( ( inj_on @ TB @ TC @ A @ ( top_top @ ( set @ TB ) ) )
=> ( inj_on @ ( TA > TB ) @ ( TA > TC ) @ ( comp @ TB @ TC @ TA @ A ) @ ( top_top @ ( set @ ( TA > TB ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_fun_Oinj__map) ).
thf(587,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC] :
( ( inj_on @ TB @ TC @ A @ ( top_top @ ( set @ TB ) ) )
=> ( inj_on @ ( TA > TB ) @ ( TA > TC ) @ ( comp @ TB @ TC @ TA @ A ) @ ( top_top @ ( set @ ( TA > TB ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(137,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_100_range__eqI) ).
thf(619,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)],[137]) ).
thf(118,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TC,B: TE > TD,C: TB > TC,D: TE > TB,E: TA > TE,F: TA > TB] :
( ( ( comp @ TD @ TC @ TE @ A @ B )
= ( comp @ TB @ TC @ TE @ C @ D ) )
=> ( ( ( comp @ TE @ TB @ TA @ D @ E )
= F )
=> ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TE @ TD @ TA @ B @ E ) )
= ( comp @ TB @ TC @ TA @ C @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_rewriteL__comp__comp2) ).
thf(559,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TC,B: TE > TD,C: TB > TC,D: TE > TB,E: TA > TE,F: TA > TB] :
( ( ( comp @ TD @ TC @ TE @ A @ B )
= ( comp @ TB @ TC @ TE @ C @ D ) )
=> ( ( ( comp @ TE @ TB @ TA @ D @ E )
= F )
=> ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TE @ TD @ TA @ B @ E ) )
= ( comp @ TB @ TC @ TA @ C @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(75,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_62_inj__eq) ).
thf(421,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)],[75]) ).
thf(134,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TA] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( ( B @ ( C @ D ) )
= ( B @ ( C @ E ) ) )
= ( ( B @ D )
= ( B @ E ) ) ) ) )
=> ( ( inj_on @ TA @ TA @ C @ A )
=> ( ( inj_on @ TA @ TB @ B @ ( image @ TA @ TA @ C @ A ) )
= ( inj_on @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_inj__on__image__iff) ).
thf(606,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TA] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( ( B @ ( C @ D ) )
= ( B @ ( C @ E ) ) )
= ( ( B @ D )
= ( B @ E ) ) ) ) )
=> ( ( inj_on @ TA @ TA @ C @ A )
=> ( ( inj_on @ TA @ TB @ B @ ( image @ TA @ TA @ C @ A ) )
= ( inj_on @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(44,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( uminus_uminus @ ( set @ TA ) @ A )
= ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_Compl__eq__Compl__iff) ).
thf(325,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( uminus_uminus @ ( set @ TA ) @ A )
= ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( C != D )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_inj__on__contraD) ).
thf(289,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( C != D )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(85,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_Un__absorb1) ).
thf(448,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TB] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ( A @ C )
= D )
=> ( ( member @ TA @ C @ B )
=> ( ( the_inv_into @ TA @ TB @ B @ A @ D )
= C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_the__inv__into__f__eq) ).
thf(179,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TB] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ( A @ C )
= D )
=> ( ( member @ TA @ C @ B )
=> ( ( the_inv_into @ TA @ TB @ B @ A @ D )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ TB ) > TB,B: TC > TB,C: TA > TC,D: set @ TA] :
( ( A @ ( image @ TC @ TB @ B @ ( image @ TA @ TC @ C @ D ) ) )
= ( A @ ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_Inf_OINF__image) ).
thf(376,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ TB ) > TB,B: TC > TB,C: TA > TC,D: set @ TA] :
( ( A @ ( image @ TC @ TB @ B @ ( image @ TA @ TC @ C @ D ) ) )
= ( A @ ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(138,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( inj_on @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_subset__inj__on) ).
thf(623,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( inj_on @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > TB,C: set @ TA] :
( ( ord_less_eq @ ( set @ TB ) @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ C )
& ( A
= ( image @ TA @ TB @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_subset__image__iff) ).
thf(485,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > TB,C: set @ TA] :
( ( ord_less_eq @ ( set @ TB ) @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ C )
& ( A
= ( image @ TA @ TB @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(51,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( set @ TA ) ) @ ( finite_Fpow @ TA @ A ) @ ( finite_Fpow @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_Fpow__mono) ).
thf(348,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( set @ TA ) ) @ ( finite_Fpow @ TA @ A ) @ ( finite_Fpow @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType] :
( ( inj_on @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ B )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_inj__on__def) ).
thf(211,plain,
! [TA: $tType,TB: $tType] :
( ( inj_on @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ B )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(145,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_top__apply) ).
thf(646,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(141,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ TB ) > TB,B: TC > TB,C: TA > TC,D: set @ TA] :
( ( A @ ( image @ TC @ TB @ B @ ( image @ TA @ TC @ C @ D ) ) )
= ( A @ ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Sup_OSUP__image) ).
thf(634,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( set @ TB ) > TB,B: TC > TB,C: TA > TC,D: set @ TA] :
( ( A @ ( image @ TC @ TB @ B @ ( image @ TA @ TC @ C @ D ) ) )
= ( A @ ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(87,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ~ ! [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ! [E: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ E @ C )
=> ( A
!= ( sup_sup @ ( set @ TA ) @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_subset__UnE) ).
thf(453,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ~ ! [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ! [E: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ E @ C )
=> ( A
!= ( sup_sup @ ( set @ TA ) @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(23,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ~ ( member @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_Compl__iff) ).
thf(243,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ~ ( member @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(101,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ ( sup_sup @ ( set @ TA ) @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_Un__mono) ).
thf(507,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ ( sup_sup @ ( set @ TA ) @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(67,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_64_injD) ).
thf(397,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)],[67]) ).
thf(156,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA,B: TB > TC,C: set @ TB,D: TA] :
( ( inj_on @ TC @ TA @ A @ ( image @ TB @ TC @ B @ C ) )
=> ( ( inj_on @ TB @ TC @ B @ C )
=> ( ( member @ TA @ D @ ( image @ TC @ TA @ A @ ( image @ TB @ TC @ B @ C ) ) )
=> ( ( the_inv_into @ TB @ TA @ C @ ( comp @ TC @ TA @ TB @ A @ B ) @ D )
= ( comp @ TC @ TB @ TA @ ( the_inv_into @ TB @ TC @ C @ B ) @ ( the_inv_into @ TC @ TA @ ( image @ TB @ TC @ B @ C ) @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_the__inv__into__comp) ).
thf(687,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA,B: TB > TC,C: set @ TB,D: TA] :
( ( inj_on @ TC @ TA @ A @ ( image @ TB @ TC @ B @ C ) )
=> ( ( inj_on @ TB @ TC @ B @ C )
=> ( ( member @ TA @ D @ ( image @ TC @ TA @ A @ ( image @ TB @ TC @ B @ C ) ) )
=> ( ( the_inv_into @ TB @ TA @ C @ ( comp @ TC @ TA @ TB @ A @ B ) @ D )
= ( comp @ TC @ TB @ TA @ ( the_inv_into @ TB @ TC @ C @ B ) @ ( the_inv_into @ TC @ TA @ ( image @ TB @ TC @ B @ C ) @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB] :
( ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) @ C )
= ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( member @ TB @ ( A @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_image__subset__iff) ).
thf(292,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TB] :
( ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) @ C )
= ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( member @ TB @ ( A @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
( ( A = B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image @ TA @ TB @ C @ A ) )
= ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_Inf_OINF__cong) ).
thf(201,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
( ( A = B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image @ TA @ TB @ C @ A ) )
= ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(56,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_Un__upper1) ).
thf(366,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(103,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_ball__Un) ).
thf(512,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(82,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_Un__absorb2) ).
thf(439,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(28,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_set__eq__subset) ).
thf(270,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ( ( image @ TA @ TB @ A @ B )
= ( image @ TA @ TB @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_inj__on__Un__image__eq__iff) ).
thf(529,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ( ( image @ TA @ TB @ A @ B )
= ( image @ TA @ TB @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(76,axiom,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice_1) ).
thf(424,plain,
! [TA: $tType] : ( bounded_lattice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(78,axiom,
! [TA: $tType] : ( top @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Otop_10) ).
thf(429,plain,
! [TA: $tType] : ( top @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(3,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_82_bex__imageD) ).
thf(165,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)],[3]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_inj__on__eq__iff) ).
thf(192,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(70,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Un__absorb) ).
thf(407,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(158,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( the_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A @ ( A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_the__inv__f__f) ).
thf(693,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( the_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A @ ( A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(91,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_iso__tuple__UNIV__I) ).
thf(467,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(139,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TB > TC,C: TB > TC] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( comp @ TB @ TC @ TA @ B @ A )
= ( comp @ TB @ TC @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_o__ext) ).
thf(625,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TB > TC,C: TB > TC] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( comp @ TB @ TC @ TA @ B @ A )
= ( comp @ TB @ TC @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(155,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > TB,C: set @ TA] :
( ( ord_less_eq @ ( set @ TB ) @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ C )
=> ( A
!= ( image @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_subset__imageE) ).
thf(682,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > TB,C: set @ TA] :
( ( ord_less_eq @ ( set @ TB ) @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ C )
=> ( A
!= ( image @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(115,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Un__UNIV__right) ).
thf(551,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(33,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_equalityD2) ).
thf(285,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TB > TA,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on @ TA @ TB @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_inj__on__inverseI) ).
thf(229,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TB > TA,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on @ TA @ TB @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: set @ TA,C: TC > TB] :
( ( inj_on @ TA @ TC @ A @ B )
=> ( ( inj_on @ TC @ TB @ C @ ( image @ TA @ TC @ A @ B ) )
=> ( inj_on @ TA @ TB @ ( comp @ TC @ TB @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_comp__inj__on) ).
thf(566,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: set @ TA,C: TC > TB] :
( ( inj_on @ TA @ TC @ A @ B )
=> ( ( inj_on @ TC @ TB @ C @ ( image @ TA @ TC @ A @ B ) )
=> ( inj_on @ TA @ TB @ ( comp @ TC @ TB @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(42,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_subset__refl) ).
thf(317,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(65,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_bex__Un) ).
thf(388,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( inj_on @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_inj__on__subset) ).
thf(499,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( inj_on @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: TA > TB,D: TA] :
( ( ( comp @ TC @ TB @ TA @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_comp__eq__dest__lhs) ).
thf(519,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: TA > TB,D: TA] :
( ( ( comp @ TC @ TB @ TA @ A @ B )
= C )
=> ( ( A @ ( B @ D ) )
= ( C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: ( set @ TB ) > $o] :
( ( ! [D: set @ TB] :
( ( ord_less_eq @ ( set @ TB ) @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: set @ TA] :
( ( ( ord_less_eq @ ( set @ TA ) @ D @ B )
& ( inj_on @ TA @ TB @ A @ D ) )
=> ( C @ ( image @ TA @ TB @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_all__subset__image__inj) ).
thf(578,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: ( set @ TB ) > $o] :
( ( ! [D: set @ TB] :
( ( ord_less_eq @ ( set @ TB ) @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: set @ TA] :
( ( ( ord_less_eq @ ( set @ TA ) @ D @ B )
& ( inj_on @ TA @ TB @ A @ D ) )
=> ( C @ ( image @ TA @ TB @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: TA] :
( ( inj_on @ TB @ TA @ A @ B )
=> ( ( member @ TA @ C @ ( image @ TB @ TA @ A @ B ) )
=> ( ( A @ ( the_inv_into @ TB @ TA @ B @ A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_f__the__inv__into__f) ).
thf(328,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: TA] :
( ( inj_on @ TB @ TA @ A @ B )
=> ( ( member @ TA @ C @ ( image @ TB @ TA @ A @ B ) )
=> ( ( A @ ( the_inv_into @ TB @ TA @ B @ A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(96,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_56_surjE) ).
thf(488,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)],[96]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Otop) ).
thf(225,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(116,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_99_rangeI) ).
thf(554,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)],[116]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( member @ TB @ ( A @ D ) @ ( image @ TA @ TB @ A @ C ) )
= ( member @ TA @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_SetInterval2_Oinj__on__image__mem__iff) ).
thf(537,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( member @ TB @ ( A @ D ) @ ( image @ TA @ TB @ A @ C ) )
= ( member @ TA @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(108,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_15_inj__image__mem__iff) ).
thf(526,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)],[108]) ).
thf(142,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_Un__least) ).
thf(637,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(161,axiom,
inj_on @ a @ b @ f @ ( sup_sup @ ( set @ a ) @ ( image @ c @ a @ g @ ( top_top @ ( set @ c ) ) ) @ ( image @ c @ a @ h @ ( top_top @ ( set @ c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(701,plain,
inj_on @ a @ b @ f @ ( sup_sup @ ( set @ a ) @ ( image @ c @ a @ g @ ( top_top @ ( set @ c ) ) ) @ ( image @ c @ a @ h @ ( top_top @ ( set @ c ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(104,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_UnI2) ).
thf(515,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: TA > TB] :
( ( comp @ TD @ TC @ TA @ A @ ( comp @ TB @ TD @ TA @ B @ C ) )
= ( comp @ TB @ TC @ TA @ ( comp @ TD @ TC @ TB @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_fun_Omap__comp) ).
thf(371,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: TA > TB] :
( ( comp @ TD @ TC @ TA @ A @ ( comp @ TB @ TD @ TA @ B @ C ) )
= ( comp @ TB @ TC @ TA @ ( comp @ TD @ TC @ TB @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(54,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_55_surjI) ).
thf(360,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)],[54]) ).
thf(40,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_equalityD1) ).
thf(311,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: set @ TA] :
( ( image @ TC @ TB @ A @ ( image @ TA @ TC @ B @ C ) )
= ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_image__comp) ).
thf(412,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC,C: set @ TA] :
( ( image @ TC @ TB @ A @ ( image @ TA @ TC @ B @ C ) )
= ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(31,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ B ) @ ( uminus_uminus @ ( set @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_Compl__anti__mono) ).
thf(279,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ B ) @ ( uminus_uminus @ ( set @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(126,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: ( set @ TB ) > $o] :
( ( ! [D: set @ TB] :
( ( ord_less_eq @ ( set @ TB ) @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ( C @ ( image @ TA @ TB @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_all__subset__image) ).
thf(584,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: ( set @ TB ) > $o] :
( ( ! [D: set @ TB] :
( ( ord_less_eq @ ( set @ TB ) @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ( C @ ( image @ TA @ TB @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_inj__onD) ).
thf(176,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(32,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_85_rev__image__eqI) ).
thf(281,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)],[32]) ).
thf(66,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_63_injI) ).
thf(391,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)],[66]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: TA > TB] :
( ( ( comp @ TB @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ A @ C ) )
=> ( ( inj_on @ TB @ TC @ A @ ( sup_sup @ ( set @ TB ) @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) @ ( image @ TA @ TB @ C @ ( top_top @ ( set @ TA ) ) ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_o__inj__on) ).
thf(445,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: TA > TB] :
( ( ( comp @ TB @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ A @ C ) )
=> ( ( inj_on @ TB @ TC @ A @ ( sup_sup @ ( set @ TB ) @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) @ ( image @ TA @ TB @ C @ ( top_top @ ( set @ TA ) ) ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(62,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_UnI1) ).
thf(382,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(48,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_subset__eq) ).
thf(335,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(21,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_81_image__iff) ).
thf(236,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)],[21]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB] :
( ! [C: TA,D: TA] :
( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on @ TA @ TB @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_inj__onI) ).
thf(350,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB] :
( ! [C: TA,D: TA] :
( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on @ TA @ TB @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TA > TB,C: TB > TC,D: TB > TC] :
( ( A = B )
=> ( ! [E: TB] :
( ( member @ TB @ E @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( comp @ TB @ TC @ TA @ C @ A )
= ( comp @ TB @ TC @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_o__cong) ).
thf(540,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TA > TB,C: TB > TC,D: TB > TC] :
( ( A = B )
=> ( ! [E: TB] :
( ( member @ TB @ E @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( comp @ TB @ TC @ TA @ C @ A )
= ( comp @ TB @ TC @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice_top @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Obounded__lattice__top) ).
thf(172,plain,
! [TA: $tType,TB: $tType] :
( ( bounded_lattice @ TA )
=> ( bounded_lattice_top @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(86,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_subset__UNIV) ).
thf(451,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(136,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_Compl__partition) ).
thf(616,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_comp__apply) ).
thf(509,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comp @ TA @ TB @ TC )
= ( ^ [A: TA > TB,B: TC > TA,C: TC] : ( A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(146,axiom,
! [TA: $tType] :
( ( bounded_lattice_top @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( top_top @ TA ) @ A )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_sup__top__left) ).
thf(649,plain,
! [TA: $tType] :
( ( bounded_lattice_top @ TA )
=> ! [A: TA] :
( ( sup_sup @ TA @ ( top_top @ TA ) @ A )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(80,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Un__iff) ).
thf(434,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(140,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_86_UNIV__eq__I) ).
thf(631,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)],[140]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( the_inv_into @ TA @ TB @ B @ A @ ( A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_the__inv__into__f__f) ).
thf(345,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( the_inv_into @ TA @ TB @ B @ A @ ( A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(111,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_Un__upper2) ).
thf(535,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(89,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_UnE) ).
thf(462,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(119,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > TB,C: set @ TA] :
( ( ord_less_eq @ ( set @ TB ) @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ C )
& ( inj_on @ TA @ TB @ B @ D )
& ( A
= ( image @ TA @ TB @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_subset__image__inj) ).
thf(563,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > TB,C: set @ TA] :
( ( ord_less_eq @ ( set @ TB ) @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ C )
& ( inj_on @ TA @ TB @ B @ D )
& ( A
= ( image @ TA @ TB @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(37,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_84_ball__imageD) ).
thf(299,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)],[37]) ).
thf(79,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_61_inj__def) ).
thf(431,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)],[79]) ).
thf(149,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA,B: set @ TC,C: TA > TB,D: TA > TB] :
( ( ( image @ TC @ TA @ A @ B )
= ( top_top @ ( set @ TA ) ) )
=> ( ! [E: TC] :
( ( member @ TC @ E @ B )
=> ( ( comp @ TA @ TB @ TC @ C @ A @ E )
= ( comp @ TA @ TB @ TC @ D @ A @ E ) ) )
=> ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_surj__fun__eq) ).
thf(658,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA,B: set @ TC,C: TA > TB,D: TA > TB] :
( ( ( image @ TC @ TA @ A @ B )
= ( top_top @ ( set @ TA ) ) )
=> ( ! [E: TC] :
( ( member @ TC @ E @ B )
=> ( ( comp @ TA @ TB @ TC @ C @ A @ E )
= ( comp @ TA @ TB @ TC @ D @ A @ E ) ) )
=> ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(77,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_13_range__ex1__eq) ).
thf(426,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)],[77]) ).
thf(128,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ( ( member @ TB @ ( A @ C ) @ ( image @ TA @ TB @ A @ D ) )
= ( member @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_Fun_Oinj__on__image__mem__iff) ).
thf(589,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ( ( member @ TB @ ( A @ C ) @ ( image @ TA @ TB @ A @ D ) )
= ( member @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(154,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_image__mono) ).
thf(680,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: TB > TA,C: TA > TC] :
( ( ( comp @ TA @ TC @ TB @ A @ B )
= ( comp @ TA @ TC @ TB @ C @ B ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ ( image @ TB @ TA @ B @ ( top_top @ ( set @ TB ) ) ) )
=> ( ( A @ D )
= ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_o__eq__conv) ).
thf(548,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: TB > TA,C: TA > TC] :
( ( ( comp @ TA @ TC @ TB @ A @ B )
= ( comp @ TA @ TC @ TB @ C @ B ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ ( image @ TB @ TA @ B @ ( top_top @ ( set @ TB ) ) ) )
=> ( ( A @ D )
= ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( inj_on @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) @ C )
=> ( inj_on @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_inj__on__imageI) ).
thf(374,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( inj_on @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) @ C )
=> ( inj_on @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(13,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_in__mono) ).
thf(209,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(157,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_57_surjD) ).
thf(690,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)],[157]) ).
thf(36,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_76_image__eqI) ).
thf(295,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)],[36]) ).
thf(152,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ A )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_Compl__partition2) ).
thf(673,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ A )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(46,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_ComplI) ).
thf(331,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(49,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o,C: set @ TA] :
( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( B @ D ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
=> ? [D: TA] :
( ( member @ TA @ D @ C )
& ( B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_bex__subset__imp__bex) ).
thf(338,plain,
! [TA: $tType,A: set @ TA,B: TA > $o,C: set @ TA] :
( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( B @ D ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
=> ? [D: TA] :
( ( member @ TA @ D @ C )
& ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(144,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) @ ( image @ TA @ TB @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_inj__image__subset__iff) ).
thf(643,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) @ ( image @ TA @ TB @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(132,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TD,B: TB > TC,C: TA > TB] :
( ( comp @ TB @ TD @ TA @ ( comp @ TC @ TD @ TB @ A @ B ) @ C )
= ( comp @ TC @ TD @ TA @ A @ ( comp @ TB @ TC @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_comp__assoc) ).
thf(600,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TD,B: TB > TC,C: TA > TB] :
( ( comp @ TB @ TD @ TA @ ( comp @ TC @ TD @ TB @ A @ B ) @ C )
= ( comp @ TC @ TD @ TA @ A @ ( comp @ TB @ TC @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC] :
( ( inj_on @ TC @ TB @ A @ ( top_top @ ( set @ TC ) ) )
=> ( ( inj_on @ TA @ TC @ B @ ( top_top @ ( set @ TA ) ) )
=> ( inj_on @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_inj__compose) ).
thf(386,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > TC] :
( ( inj_on @ TC @ TB @ A @ ( top_top @ ( set @ TC ) ) )
=> ( ( inj_on @ TA @ TC @ B @ ( top_top @ ( set @ TA ) ) )
=> ( inj_on @ TA @ TB @ ( comp @ TC @ TB @ TA @ A @ B ) @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(122,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB,B: TA > TD,C: TA > TB,D: TB > TC] :
( ( ( comp @ TD @ TB @ TA @ A @ B )
= C )
=> ( ( comp @ TD @ TC @ TA @ ( comp @ TB @ TC @ TD @ D @ A ) @ B )
= ( comp @ TB @ TC @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_rewriteR__comp__comp) ).
thf(571,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TB,B: TA > TD,C: TA > TB,D: TB > TC] :
( ( ( comp @ TD @ TB @ TA @ A @ B )
= C )
=> ( ( comp @ TD @ TC @ TA @ ( comp @ TB @ TC @ TD @ D @ A ) @ B )
= ( comp @ TB @ TC @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( inj_on @ TA @ TB @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_inj__imp__inj__on) ).
thf(595,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( inj_on @ TA @ TB @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TB > TA] :
( ( ( image @ TC @ TB @ A @ ( top_top @ ( set @ TC ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ( ( ( image @ TB @ TA @ B @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TC @ TA @ ( comp @ TB @ TA @ TC @ B @ A ) @ ( top_top @ ( set @ TC ) ) )
= ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_comp__surj) ).
thf(482,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TB > TA] :
( ( ( image @ TC @ TB @ A @ ( top_top @ ( set @ TC ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ( ( ( image @ TB @ TA @ B @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TC @ TA @ ( comp @ TB @ TA @ TC @ B @ A ) @ ( top_top @ ( set @ TC ) ) )
= ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(125,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: set @ TD,C: TA > TC,D: set @ TA,E: TC > TB] :
( ( ( image @ TD @ TC @ A @ B )
= ( image @ TA @ TC @ C @ D ) )
=> ( ( image @ TD @ TB @ ( comp @ TC @ TB @ TD @ E @ A ) @ B )
= ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ E @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_image__eq__imp__comp) ).
thf(581,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: set @ TD,C: TA > TC,D: set @ TA,E: TC > TB] :
( ( ( image @ TD @ TC @ A @ B )
= ( image @ TA @ TC @ C @ D ) )
=> ( ( image @ TD @ TB @ ( comp @ TC @ TB @ TD @ E @ A ) @ B )
= ( image @ TA @ TB @ ( comp @ TC @ TB @ TA @ E @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(57,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_54_surj__def) ).
thf(368,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)],[57]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TB,B: TD > TC,C: TA > TD] :
( ( comp @ TD @ TB @ TA @ ( comp @ TC @ TB @ TD @ A @ B ) @ C )
= ( ^ [D: TA] : ( A @ ( B @ ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_comp3__conv) ).
thf(363,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TC > TB,B: TD > TC,C: TA > TD] :
( ( comp @ TD @ TB @ TA @ ( comp @ TC @ TB @ TD @ A @ B ) @ C )
= ( ^ [D: TA] : ( A @ ( B @ ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(117,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TB,B: TE > TD,C: TE,D: TC > TB,E: TA > TC,F: TA] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ F ) ) )
=> ( ( comp @ TD @ TB @ TE @ A @ B @ C )
= ( comp @ TC @ TB @ TA @ D @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_comp__cong) ).
thf(556,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TD > TB,B: TE > TD,C: TE,D: TC > TB,E: TA > TC,F: TA] :
( ( ( A @ ( B @ C ) )
= ( D @ ( E @ F ) ) )
=> ( ( comp @ TD @ TB @ TE @ A @ B @ C )
= ( comp @ TC @ TB @ TA @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( inj_on @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) @ C )
=> ( inj_on @ TA @ TB @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_inj__on__imageI2) ).
thf(517,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( inj_on @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) @ C )
=> ( inj_on @ TA @ TB @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on @ TA @ TB @ B @ A )
= ( inj_on @ TA @ TB @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_inj__on__cong) ).
thf(319,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on @ TA @ TB @ B @ A )
= ( inj_on @ TA @ TB @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(147,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Un__left__commute) ).
thf(652,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: TB > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( ! [F: TA] :
( ( member @ TA @ F @ A )
=> ( E @ ( C @ F ) ) ) )
= ( ! [F: TA] :
( ( member @ TA @ F @ A )
=> ( E @ ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_ball__cong2) ).
thf(186,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: TB > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( ! [F: TA] :
( ( member @ TA @ F @ A )
=> ( E @ ( C @ F ) ) ) )
= ( ! [F: TA] :
( ( member @ TA @ F @ A )
=> ( E @ ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: set @ TA,C: TC > TB] :
( ( inj_on @ TA @ TC @ A @ B )
=> ( ( inj_on @ TC @ TB @ C @ ( image @ TA @ TC @ A @ B ) )
= ( inj_on @ TA @ TB @ ( comp @ TC @ TB @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_comp__inj__on__iff) ).
thf(418,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: set @ TA,C: TC > TB] :
( ( inj_on @ TA @ TC @ A @ B )
=> ( ( inj_on @ TC @ TB @ C @ ( image @ TA @ TC @ A @ B ) )
= ( inj_on @ TA @ TB @ ( comp @ TC @ TB @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(121,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_subset__Un__eq) ).
thf(568,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(24,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_83_image__cong) ).
thf(246,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)],[24]) ).
thf(15,axiom,
! [TA: $tType,A: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_double__complement) ).
thf(214,plain,
! [TA: $tType,A: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB,D: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TB @ C @ ( image @ TA @ TB @ A @ B ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ D )
=> ( member @ TA @ ( the_inv_into @ TA @ TB @ B @ A @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_the__inv__into__into) ).
thf(315,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB,D: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TB @ C @ ( image @ TA @ TB @ A @ B ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ D )
=> ( member @ TA @ ( the_inv_into @ TA @ TB @ B @ A @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(71,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_UNIV__witness) ).
thf(410,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: TB > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ A )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( ? [F: TA] :
( ( member @ TA @ F @ A )
& ( E @ ( C @ F ) ) ) )
= ( ? [F: TA] :
( ( member @ TA @ F @ A )
& ( E @ ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_bex__cong2) ).
thf(262,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: TB > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ A )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( ? [F: TA] :
( ( member @ TA @ F @ A )
& ( E @ ( C @ F ) ) ) )
= ( ? [F: TA] :
( ( member @ TA @ F @ A )
& ( E @ ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(8,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_Compl__subset__Compl__iff) ).
thf(183,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(29,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_subset__iff) ).
thf(273,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(133,axiom,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_Un__commute) ).
thf(603,plain,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TB > TA,C: set @ TA] :
( ! [D: TB] :
( ( member @ TB @ D @ A )
=> ( member @ TA @ ( B @ D ) @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( image @ TB @ TA @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_image__subsetI) ).
thf(305,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TB > TA,C: set @ TA] :
( ! [D: TB] :
( ( member @ TB @ D @ A )
=> ( member @ TA @ ( B @ D ) @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( image @ TB @ TA @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(22,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_subsetI) ).
thf(239,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(27,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_80_imageI) ).
thf(268,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)],[27]) ).
thf(53,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: set @ TA] : ( inj_on @ TA @ TA @ ( uminus_uminus @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_inj__uminus) ).
thf(358,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: set @ TA] : ( inj_on @ TA @ TA @ ( uminus_uminus @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(11,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o,C: set @ TA] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( B @ D ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ C )
=> ( B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_ball__subset__imp__ball) ).
thf(195,plain,
! [TA: $tType,A: set @ TA,B: TA > $o,C: set @ TA] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( B @ D ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ C )
=> ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( inj_on @ ( set @ TA ) @ ( set @ TB ) @ ( image @ TA @ TB @ A ) @ ( finite_Fpow @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_inj__on__image__Fpow) ).
thf(437,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( inj_on @ ( set @ TA ) @ ( set @ TB ) @ ( image @ TA @ TB @ A ) @ ( finite_Fpow @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(150,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TB > TC,C: TB > TC] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( comp @ TB @ TC @ TA @ B @ A )
= ( comp @ TB @ TC @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_fun_Omap__cong0) ).
thf(664,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TB > TC,C: TB > TC] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( comp @ TB @ TC @ TA @ B @ A )
= ( comp @ TB @ TC @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(68,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_UnCI) ).
thf(400,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(110,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_Un__left__absorb) ).
thf(532,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(159,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( inj_on @ TB @ TA @ ( the_inv_into @ TA @ TB @ B @ A ) @ ( image @ TA @ TB @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_inj__on__the__inv__into) ).
thf(696,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( inj_on @ TB @ TA @ ( the_inv_into @ TA @ TB @ B @ A ) @ ( image @ TA @ TB @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB,E: TA] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_comp__eq__dest) ).
thf(415,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TD,C: TB > TC,D: TA > TB,E: TA] :
( ( ( comp @ TD @ TC @ TA @ A @ B )
= ( comp @ TB @ TC @ TA @ C @ D ) )
=> ( ( A @ ( B @ E ) )
= ( C @ ( D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ( ( ( image @ TA @ TB @ A @ C )
= ( image @ TA @ TB @ A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_inj__on__image__eq__iff) ).
thf(464,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ( ( ( image @ TA @ TB @ A @ C )
= ( image @ TA @ TB @ A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(123,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
( ( image @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) @ ( top_top @ ( set @ TA ) ) )
= ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_fun_Oset__map) ).
thf(575,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
( ( image @ TA @ TC @ ( comp @ TB @ TC @ TA @ A @ B ) @ ( top_top @ ( set @ TA ) ) )
= ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( image @ TB @ TA @ ( the_inv_into @ TA @ TB @ B @ A ) @ ( image @ TA @ TB @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_the__inv__into__onto) ).
thf(459,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( image @ TB @ TA @ ( the_inv_into @ TA @ TB @ B @ A ) @ ( image @ TA @ TB @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(1,conjecture,
g = h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(2,negated_conjecture,
g != h,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(163,plain,
g != h,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: ( set @ TB ) > $o] :
( ( ? [D: set @ TB] :
( ( ord_less_eq @ ( set @ TB ) @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ B )
& ( inj_on @ TA @ TB @ A @ D )
& ( C @ ( image @ TA @ TB @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_ex__subset__image__inj) ).
thf(442,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: ( set @ TB ) > $o] :
( ( ? [D: set @ TB] :
( ( ord_less_eq @ ( set @ TB ) @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ B )
& ( inj_on @ TA @ TB @ A @ D )
& ( C @ ( image @ TA @ TB @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TB @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) @ ( image @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_image__Un) ).
thf(501,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TB @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) @ ( image @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ( ord_less_eq @ ( set @ TB ) @ ( uminus_uminus @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) ) @ ( image @ TA @ TB @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_surj__Compl__image__subset) ).
thf(469,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ( ord_less_eq @ ( set @ TB ) @ ( uminus_uminus @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) ) @ ( image @ TA @ TB @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(39,axiom,
! [TA: $tType] : ( bounded_lattice_top @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice__top_3) ).
thf(309,plain,
! [TA: $tType] : ( bounded_lattice_top @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(143,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TD,B: TA > TE,C: TB > TD,D: TA > TB,E: TD > TC,F: TB > TC] :
( ( ( comp @ TE @ TD @ TA @ A @ B )
= ( comp @ TB @ TD @ TA @ C @ D ) )
=> ( ( ( comp @ TD @ TC @ TB @ E @ C )
= F )
=> ( ( comp @ TE @ TC @ TA @ ( comp @ TD @ TC @ TE @ E @ A ) @ B )
= ( comp @ TB @ TC @ TA @ F @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_rewriteR__comp__comp2) ).
thf(639,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE > TD,B: TA > TE,C: TB > TD,D: TA > TB,E: TD > TC,F: TB > TC] :
( ( ( comp @ TE @ TD @ TA @ A @ B )
= ( comp @ TB @ TD @ TA @ C @ D ) )
=> ( ( ( comp @ TD @ TC @ TB @ E @ C )
= F )
=> ( ( comp @ TE @ TC @ TA @ ( comp @ TD @ TC @ TE @ E @ A ) @ B )
= ( comp @ TB @ TC @ TA @ F @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(153,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: TB > TC,D: TA > TB] :
( ( ( comp @ TD @ TC @ TB @ A @ B )
= C )
=> ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TB @ TD @ TA @ B @ D ) )
= ( comp @ TB @ TC @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_rewriteL__comp__comp) ).
thf(676,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TB > TD,C: TB > TC,D: TA > TB] :
( ( ( comp @ TD @ TC @ TB @ A @ B )
= C )
=> ( ( comp @ TD @ TC @ TA @ A @ ( comp @ TB @ TD @ TA @ B @ D ) )
= ( comp @ TB @ TC @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TA > TB,C: TB > TC,D: TB > TC] :
( ( A = B )
=> ( ! [E: TB] :
( ( member @ TB @ E @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( comp @ TB @ TC @ TA @ C @ A )
= ( comp @ TB @ TC @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_fun_Omap__cong) ).
thf(491,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TA > TB,C: TB > TC,D: TB > TC] :
( ( A = B )
=> ( ! [E: TB] :
( ( member @ TB @ E @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( comp @ TB @ TC @ TA @ C @ A )
= ( comp @ TB @ TC @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(129,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) @ A )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Un__UNIV__left) ).
thf(592,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) @ A )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(25,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_equalityE) ).
thf(254,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(18,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_subsetD) ).
thf(227,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(704,plain,
$false,
inference(e,[status(thm)],[333,234,523,379,655,614,597,217,276,384,472,698,670,174,404,504,702,587,619,559,421,606,325,289,448,179,376,623,485,348,211,646,634,453,243,507,397,687,292,201,366,512,439,270,529,424,429,165,192,407,693,467,625,682,551,285,229,566,317,388,499,519,578,328,488,225,554,537,526,637,701,515,371,360,311,412,279,584,176,281,391,445,382,335,236,350,540,172,451,616,509,649,434,631,345,535,462,563,299,431,658,426,589,680,548,374,209,690,295,673,331,338,643,600,386,571,595,482,581,368,363,556,517,319,652,186,418,568,246,214,315,410,262,183,273,603,305,239,268,358,195,437,664,400,532,696,415,464,575,459,163,442,501,469,309,639,676,491,592,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP098^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.22 % Computer : n006.cluster.edu
% 0.12/0.22 % Model : x86_64 x86_64
% 0.12/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.22 % Memory : 8046.5625MB
% 0.12/0.22 % OS : Linux 6.8.0-71-generic
% 0.12/0.22 % CPULimit : 300
% 0.12/0.22 % WCLimit : 300
% 0.12/0.22 % DateTime : Tue Sep 29 19:52:54 UTC 2026
% 0.12/0.22 % CPUTime :
% 0.12/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.63/0.54 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.56/0.88 % [INFO] Parsing done (340ms).
% 1.56/0.89 % [INFO] Running in sequential loop mode.
% 2.56/1.10 % [INFO] eprover registered as external prover.
% 2.56/1.10 % [INFO] Scanning for conjecture ...
% 2.92/1.18 % [INFO] Found a conjecture (or negated_conjecture) and 292 axioms. Running axiom selection ...
% 3.20/1.28 % [INFO] Axiom selection finished. Selected 160 axioms (removed 132 axioms).
% 4.05/1.49 % [INFO] Problem is higher-order (TPTP THF).
% 4.44/1.51 % [INFO] Type checking passed.
% 4.44/1.51 % [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 ...
% 90.20/68.69 % External prover 'e' found a proof!
% 90.20/68.69 % [INFO] Killing All external provers ...
% 90.20/68.69 % Time passed: 68372ms (effective reasoning time: 67794ms)
% 90.20/68.69 % 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)>
% 90.20/68.69 % Axioms used in derivation (160): fact_6_sup__top__right, fact_16_comp__surj, fact_71_Un__iff, fact_65_inj__on__imageI2, fact_87_UNIV__witness, fact_234_Compl__iff, fact_224_subset__image__inj, fact_130_bex__subset__imp__bex, fact_68_fun_Omap__cong, fact_220_inj__image__subset__iff, fact_216_subset__inj__on, fact_103_Sup_OSUP__image, fact_11_inj__on__imageI, fact_78_Un__UNIV__right, fact_60_inj__on__image__iff, fact_98_Un__left__commute, fact_221_rewriteL__comp__comp, fact_50_inj__on__cong, fact_113_the__inv__f__f, fact_235_Compl__eq__Compl__iff, fact_99_rangeI, fact_227_all__subset__image, fact_115_Inf_OINF__cong, fact_39_comp__eq__elim, fact_251_Compl__partition, fact_128_bex__cong2, fact_66_fun_Oinj__map__strong, fact_76_image__eqI, fact_124_subset__antisym, fact_59_image__comp, fact_211_Un__absorb1, fact_70_surj__fun__eq, fact_131_ball__subset__imp__ball, fact_171_equalityE, fact_239_Compl__anti__mono, fact_94_Un__assoc, fact_81_image__iff, fact_82_bex__imageD, fact_106_comp__cong, fact_214_subset__Un__eq, fact_127_Un__subset__iff, fact_43_inj__on__inverseI, fact_64_injD, fact_172_subset__eq, fact_49_inj__on__eq__iff, fact_111_inj__on__the__inv__into, fact_92_bex__Un, fact_89_UnE, fact_218_inj__on__image__eq__iff, fact_215_inj__on__subset, fact_225_ex__subset__image__inj, fact_14_inj__image__eq__iff, fact_110_the__inv__into__f__f, fact_51_inj__on__def, fact_210_Un__upper2, fact_85_rev__image__eqI, fact_62_inj__eq, fact_102_Inf_OINF__image, fact_178_subset__trans, fact_79_Un__UNIV__left, fact_238_Compl__subset__Compl__iff, fact_12_comp__inj__on__iff, fact_182_set__eq__subset, fact_91_UnI2, tcon_fun___Lattices_Obounded__lattice_2, fact_212_Un__absorb2, fact_209_Un__upper1, fact_2_o__inj__on, fact_112_f__the__inv__into__f, fact_170_subsetD, fact_7_inj__on__Un__image__eq__iff, fact_254_double__complement, fact_222_rewriteR__comp__comp, fact_57_surjD, fact_247_Fpow__mono, fact_69_fun_Oset__map, fact_86_UNIV__eq__I, fact_1_o__cong, tcon_Set_Oset___Lattices_Obounded__lattice__top_3, fact_67_fun_Omap__cong0, fact_40_comp__eq__dest, fact_41_comp__assoc, fact_213_subset__UnE, fact_137_subset__imageE, fact_169_in__mono, fact_120_the__inv__into__into, fact_61_inj__def, fact_139_image__mono, fact_96_Un__commute, fact_10_comp__inj__on, fact_104_the__inv__into__comp, fact_58_image__eq__imp__comp, fact_123_subsetI, fact_114_Sup_OSUP__cong, fact_90_UnI1, fact_55_surjI, fact_116_comp3__conv, tcon_fun___Lattices_Obounded__lattice__top, fact_253_ComplD, fact_80_imageI, tcon_fun___Orderings_Otop, tcon_Set_Oset___Lattices_Obounded__lattice_1, fact_75_top__apply, fact_52_inj__onI, fact_0_o__ext, fact_3_ex__o__conv, fact_84_ball__imageD, conj_1, fact_8_inj__compose, fact_207_Un__mono, fact_37_fun_Omap__comp, fact_56_surjE, fact_237_inj__uminus, fact_217_SetInterval2_Oinj__on__image__mem__iff, fact_44_inj__on__contraD, fact_15_inj__image__mem__iff, fact_23_comp__apply, tcon_Set_Oset___Orderings_Otop_10, fact_53_inj__onD, fact_95_Un__absorb, fact_72_UnCI, fact_4_o__eq__conv, fact_5_sup__top__left, fact_93_ball__Un, fact_9_fun_Oinj__map, fact_138_image__subsetI, fact_135_subset__image__iff, fact_83_image__cong, fact_229_inj__on__image__Fpow, fact_255_surj__Compl__image__subset, fact_13_range__ex1__eq, fact_74_UNIV__I, fact_173_equalityD1, fact_54_surj__def, fact_105_the__inv__into__onto, fact_63_injI, fact_73_iso__tuple__UNIV__I, fact_136_image__subset__iff, fact_174_equalityD2, fact_38_comp__eq__dest__lhs, fact_109_the__inv__into__f__eq, fact_219_Fun_Oinj__on__image__mem__iff, fact_129_ball__cong2, conj_0, fact_175_subset__iff, fact_101_image__Un, fact_42_comp__def, fact_228_inj__image__Compl__subset, fact_233_ComplI, fact_77_inj__imp__inj__on, fact_208_Un__least, fact_176_subset__refl, fact_226_all__subset__image__inj, fact_107_comp2__conv, fact_140_subset__UNIV, fact_223_rewriteL__comp__comp2, fact_121_rewriteR__comp__comp2, fact_97_Un__left__absorb, fact_100_range__eqI, fact_250_Compl__partition2
% 90.20/68.69 % No. of inferences in proof: 324
% 90.20/68.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 68372 ms resp. 67794 ms w/o parsing
% 90.99/68.80 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 90.99/68.81 % [INFO] Killing All external provers ...
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