%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP028^2 : 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 : n007.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 08:06:28 AM UTC 2026
% Result : Theorem 171.95s 144.73s
% Output : Refutation 172.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 204
% Syntax : Number of formulae : 410 ( 162 unt; 0 typ; 0 def)
% Number of atoms : 1570 ( 346 equ; 8 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 6948 ( 100 ~; 12 |; 52 &;6384 @)
% ( 0 <=>; 400 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 9 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 380 ( 380 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 33 usr; 9 con; 0-9 aty)
% Number of variables : 1910 ( 56 ^;1804 !; 50 ?;1910 :)
% Comments :
%------------------------------------------------------------------------------
thf(e_type,type,
e: $tType ).
thf(a_type,type,
a: $tType ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(top_decl,type,
top:
!>[TA: $tType] : $o ).
thf(bNF_Ca1785829860lChain_decl,type,
bNF_Ca1785829860lChain:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TB ) ) > ( TB > TA ) > $o ) ).
thf(bNF_csquare_decl,type,
bNF_csquare:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( set @ TD ) > ( TC > TB ) > ( TA > TB ) > ( TD > TC ) > ( TD > TA ) > $o ) ).
thf(bNF_Greatest_image2_decl,type,
bNF_Greatest_image2:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( set @ TC ) > ( TC > TB ) > ( TC > TA ) > ( set @ ( product_prod @ TB @ TA ) ) ) ).
thf(finite_Fpow_decl,type,
finite_Fpow:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( set @ TA ) ) ) ).
thf(fun_in_rel_decl,type,
fun_in_rel:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > TB > TA > $o ) ).
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(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(product_map_prod_decl,type,
product_map_prod:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > TC ) > ( TB > TA ) > ( product_prod @ TD @ TB ) > ( product_prod @ TC @ TA ) ) ).
thf(product_case_prod_decl,type,
product_case_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_fst_decl,type,
product_fst:
!>[TA: $tType,TB: $tType] : ( ( product_prod @ TB @ TA ) > TB ) ).
thf(product_snd_decl,type,
product_snd:
!>[TA: $tType,TB: $tType] : ( ( product_prod @ TB @ TA ) > TA ) ).
thf(product_swap_decl,type,
product_swap:
!>[TA: $tType,TB: $tType] : ( ( product_prod @ TB @ TA ) > ( product_prod @ TA @ TB ) ) ).
thf(domain_decl,type,
domain:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > ( set @ TB ) ) ).
thf(range_decl,type,
range:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > ( set @ TA ) ) ).
thf(converse_decl,type,
converse:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TA ) ) > ( set @ ( product_prod @ TA @ TB ) ) ) ).
thf(inv_image_decl,type,
inv_image:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TB ) ) > ( TA > TB ) > ( set @ ( product_prod @ TA @ TA ) ) ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(pow_decl,type,
pow:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( set @ 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(c_decl,type,
c: set @ ( product_prod @ ( set @ a ) @ ( a > e ) ) ).
thf(a1_decl,type,
a1: set @ a ).
thf(a2_decl,type,
a2: set @ a ).
thf(a3_decl,type,
a3: set @ a ).
thf(b1_decl,type,
b1: a > e ).
thf(b2_decl,type,
b2: a > e ).
thf(b3_decl,type,
b3: a > e ).
thf(thesis_decl,type,
thesis: $o ).
thf(139,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( image @ ( product_prod @ TA @ TB ) @ ( product_prod @ TB @ TA ) @ ( product_swap @ TA @ TB ) @ C ) )
= ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_pair__in__swap__image) ).
thf(656,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( image @ ( product_prod @ TA @ TB ) @ ( product_prod @ TB @ TA ) @ ( product_swap @ TA @ TB ) @ C ) )
= ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(170,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_16_image__subsetI) ).
thf(760,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)],[170]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: TA > TB > $o] :
( ( member @ ( product_prod @ TA @ TB ) @ A @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ B ) ) )
=> ( B @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_Product__Type_OCollect__case__prodD) ).
thf(479,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: TA > TB > $o] :
( ( member @ ( product_prod @ TA @ TB ) @ A @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ B ) ) )
=> ( B @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TA] :
( ( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= C )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_snd__eqD) ).
thf(518,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TA] :
( ( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= C )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_ord__eq__le__subst) ).
thf(481,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_le__funD) ).
thf(333,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TC,B: TB > TD,C: product_prod @ TA @ TB] :
( ( product_fst @ TC @ TD @ ( product_map_prod @ TA @ TC @ TB @ TD @ A @ B @ C ) )
= ( A @ ( product_fst @ TA @ TB @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_fst__map__prod) ).
thf(628,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TC,B: TB > TD,C: product_prod @ TA @ TB] :
( ( product_fst @ TC @ TD @ ( product_map_prod @ TA @ TC @ TB @ TD @ A @ B @ C ) )
= ( A @ ( product_fst @ TA @ TB @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(175,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( pow @ TA @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_Pow__iff) ).
thf(777,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( pow @ TA @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( product_case_prod @ TA @ TB @ TC )
= ( ^ [A: TA > TB > TC,B: product_prod @ TA @ TB] : ( A @ ( product_fst @ TA @ TB @ B ) @ ( product_snd @ TA @ TB @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_prod_Ocase__eq__if) ).
thf(555,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( product_case_prod @ TA @ TB @ TC )
= ( ^ [A: TA > TB > TC,B: product_prod @ TA @ TB] : ( A @ ( product_fst @ TA @ TB @ B ) @ ( product_snd @ TA @ TB @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType] :
( ( image @ ( product_prod @ TA @ TB ) @ TA @ ( product_fst @ TA @ TB ) @ ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_range__fst) ).
thf(582,plain,
! [TA: $tType,TB: $tType] :
( ( image @ ( product_prod @ TA @ TB ) @ TA @ ( product_fst @ TA @ TB ) @ ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(160,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( image @ TB @ TA @ A @ B ) @ C )
=> ( ord_less_eq @ ( set @ ( set @ TA ) ) @ ( image @ ( set @ TB ) @ ( set @ TA ) @ ( image @ TB @ TA @ A ) @ ( pow @ TB @ B ) ) @ ( pow @ TA @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_image__Pow__mono) ).
thf(730,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( image @ TB @ TA @ A @ B ) @ C )
=> ( ord_less_eq @ ( set @ ( set @ TA ) ) @ ( image @ ( set @ TB ) @ ( set @ TA ) @ ( image @ TB @ TA @ A ) @ ( pow @ TB @ B ) ) @ ( pow @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_top__apply) ).
thf(308,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TB @ A @ ( range @ TA @ TB @ B ) )
=> ~ ! [C: TA] :
~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_RangeE) ).
thf(269,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TB @ A @ ( range @ TA @ TB @ B ) )
=> ~ ! [C: TA] :
~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: TA > TB > TC,C: TA > TB > TC,D: product_prod @ TA @ TB] :
( ! [E: TA,F: TB] :
( ( ( product_Pair @ TA @ TB @ E @ F )
= A )
=> ( ( B @ E @ F )
= ( C @ E @ F ) ) )
=> ( ( D = A )
=> ( ( product_case_prod @ TA @ TB @ TC @ B @ D )
= ( product_case_prod @ TA @ TB @ TC @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_split__cong) ).
thf(384,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ TB,B: TA > TB > TC,C: TA > TB > TC,D: product_prod @ TA @ TB] :
( ! [E: TA,F: TB] :
( ( ( product_Pair @ TA @ TB @ E @ F )
= A )
=> ( ( B @ E @ F )
= ( C @ E @ F ) ) )
=> ( ( D = A )
=> ( ( product_case_prod @ TA @ TB @ TC @ B @ D )
= ( product_case_prod @ TA @ TB @ TC @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_fst @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= ( product_snd @ TA @ TB @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_fst__swap) ).
thf(500,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_fst @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= ( product_snd @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(183,axiom,
member @ ( product_prod @ ( set @ a ) @ ( a > e ) ) @ ( product_Pair @ ( set @ a ) @ ( a > e ) @ a3 @ b3 ) @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__092_060open_062_Ia3_M_Ab3_J_A_092_060in_062_AC_092_060close_062) ).
thf(797,plain,
member @ ( product_prod @ ( set @ a ) @ ( a > e ) ) @ ( product_Pair @ ( set @ a ) @ ( a > e ) @ a3 @ b3 ) @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(156,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_UNIV__witness) ).
thf(715,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_prod__cases5) ).
thf(472,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(151,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_179_surj__def) ).
thf(698,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)],[151]) ).
thf(155,axiom,
? [A: set @ a] :
( ( member @ ( set @ a ) @ A @ ( image @ ( product_prod @ ( set @ a ) @ ( a > e ) ) @ ( set @ a ) @ ( product_fst @ ( set @ a ) @ ( a > e ) ) @ c ) )
& ( ord_less_eq @ ( set @ a ) @ a1 @ A )
& ( ord_less_eq @ ( set @ a ) @ a2 @ A )
& ( ord_less_eq @ ( set @ a ) @ a3 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062_092_060exists_062a_092_060in_062fst_A_096_AC_O_Aa1_A_092_060subseteq_062_Aa_A_092_060and_062_Aa2_A_092_060subseteq_062_Aa_A_092_060and_062_Aa3_A_092_060subseteq_062_Aa_092_060close_062) ).
thf(709,plain,
? [A: set @ a] :
( ( member @ ( set @ a ) @ A @ ( image @ ( product_prod @ ( set @ a ) @ ( a > e ) ) @ ( set @ a ) @ ( product_fst @ ( set @ a ) @ ( a > e ) ) @ c ) )
& ( ord_less_eq @ ( set @ a ) @ a1 @ A )
& ( ord_less_eq @ ( set @ a ) @ a2 @ A )
& ( ord_less_eq @ ( set @ a ) @ a3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(137,axiom,
! [TA: $tType,TB: $tType] :
( ( image @ ( product_prod @ TB @ TA ) @ TA @ ( product_snd @ TB @ TA ) @ ( top_top @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_range__snd) ).
thf(651,plain,
! [TA: $tType,TB: $tType] :
( ( image @ ( product_prod @ TB @ TA ) @ TA @ ( product_snd @ TB @ TA ) @ ( top_top @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(159,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A != B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ~ ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_sets__not__eq) ).
thf(724,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A != B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ~ ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o] :
( ( ord_less_eq @ ( TA > TB > $o ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ A ) ) @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_Collect__case__prod__mono) ).
thf(542,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o] :
( ( ord_less_eq @ ( TA > TB > $o ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ A ) ) @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_prod__cases6) ).
thf(289,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,A: TB,B: product_prod @ TB @ TA] :
( ( A
= ( product_fst @ TB @ TA @ B ) )
= ( ? [C: TA] :
( B
= ( product_Pair @ TB @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_eq__fst__iff) ).
thf(316,plain,
! [TA: $tType,TB: $tType,A: TB,B: product_prod @ TB @ TA] :
( ( A
= ( product_fst @ TB @ TA @ B ) )
= ( ? [C: TA] :
( B
= ( product_Pair @ TB @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,A: TB,B: product_prod @ TA @ TB] :
( ( A
= ( product_snd @ TA @ TB @ B ) )
= ( ? [C: TA] :
( B
= ( product_Pair @ TA @ TB @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_eq__snd__iff) ).
thf(216,plain,
! [TA: $tType,TB: $tType,A: TB,B: product_prod @ TA @ TB] :
( ( A
= ( product_snd @ TA @ TB @ B ) )
= ( ? [C: TA] :
( B
= ( product_Pair @ TA @ TB @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(85,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(475,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(168,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_73_all__subset__image) ).
thf(756,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)],[168]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_Pair__inject) ).
thf(253,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(188,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_subrelI) ).
thf(806,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(53,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_5) ).
thf(353,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(191,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_52_ball__imageD) ).
thf(821,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)],[191]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ B @ A ) @ ( converse @ TA @ TB @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_converse_Ointros) ).
thf(348,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ B @ A ) @ ( converse @ TA @ TB @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(117,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_178_range__eqI) ).
thf(574,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)],[117]) ).
thf(126,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_17_subset__imageE) ).
thf(602,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)],[126]) ).
thf(132,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_53_image__cong) ).
thf(634,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)],[132]) ).
thf(174,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_180_surjI) ).
thf(774,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)],[174]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ A @ ( converse @ TA @ TB @ B ) )
=> ~ ! [C: TA,D: TB] :
( ( A
= ( product_Pair @ TB @ TA @ D @ C ) )
=> ~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_converseE) ).
thf(396,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ A @ ( converse @ TA @ TB @ B ) )
=> ~ ! [C: TA,D: TB] :
( ( A
= ( product_Pair @ TB @ TA @ D @ C ) )
=> ~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_le__funE) ).
thf(243,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TA @ A @ ( domain @ TA @ TB @ B ) )
=> ~ ! [C: TB] :
~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_Domain_Ocases) ).
thf(428,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TA @ A @ ( domain @ TA @ TB @ B ) )
=> ~ ! [C: TB] :
~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(197,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_97_Fpow__mono) ).
thf(849,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)],[197]) ).
thf(1,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ thesis,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(206,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( domain @ TB @ TA @ ( converse @ TA @ TB @ A ) )
= ( range @ TA @ TB @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_Domain__converse) ).
thf(292,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( domain @ TB @ TA @ ( converse @ TA @ TB @ A ) )
= ( range @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: TB,D: TA] :
( ( ord_less_eq @ ( TB > TA > $o ) @ A @ B )
=> ( ( A @ C @ D )
=> ( B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_predicate2D) ).
thf(248,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: TB,D: TA] :
( ( ord_less_eq @ ( TB > TA > $o ) @ A @ B )
=> ( ( A @ C @ D )
=> ( B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_prod__cases4) ).
thf(512,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(145,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( member @ ( set @ TA ) @ A @ ( pow @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_PowI) ).
thf(678,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( member @ ( set @ TA ) @ A @ ( pow @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(181,axiom,
! [TA: $tType,A: set @ TA] : ( member @ ( set @ TA ) @ A @ ( pow @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_Pow__top) ).
thf(793,plain,
! [TA: $tType,A: set @ TA] : ( member @ ( set @ TA ) @ A @ ( pow @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(189,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_109_Sup_OSUP__cong) ).
thf(810,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)],[189]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( converse @ TB @ TA @ ( converse @ TA @ TB @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_converse__converse) ).
thf(534,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( converse @ TB @ TA @ ( converse @ TA @ TB @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(184,axiom,
member @ ( product_prod @ ( set @ a ) @ ( a > e ) ) @ ( product_Pair @ ( set @ a ) @ ( a > e ) @ a1 @ b1 ) @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__092_060open_062_Ia1_M_Ab1_J_A_092_060in_062_AC_092_060close_062) ).
thf(798,plain,
member @ ( product_prod @ ( set @ a ) @ ( a > e ) ) @ ( product_Pair @ ( set @ a ) @ ( a > e ) @ a1 @ b1 ) @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_old_Oprod_Oinject) ).
thf(302,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(202,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB,C: set @ ( product_prod @ TA @ TA ),D: TB > TA] :
( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ A @ B ) @ ( inv_image @ TA @ TB @ C @ D ) )
= ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_in__inv__image) ).
thf(862,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB,C: set @ ( product_prod @ TA @ TA ),D: TB > TA] :
( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ A @ B ) @ ( inv_image @ TA @ TB @ C @ D ) )
= ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TB @ A @ ( range @ TA @ TB @ B ) )
= ( ? [C: TA] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_Range__iff) ).
thf(561,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TB @ A @ ( range @ TA @ TB @ B ) )
= ( ? [C: TA] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(62,axiom,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_top1I) ).
thf(392,plain,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(66,axiom,
! [TA: $tType,A: TA > TA > $o] :
( ! [B: TA] : ( A @ B @ B )
=> ( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_refl__ge__eq) ).
thf(407,plain,
! [TA: $tType,A: TA > TA > $o] :
( ! [B: TA] : ( A @ B @ B )
=> ( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(179,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TA > TC,E: TB > TD] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( member @ ( product_prod @ TC @ TD ) @ ( product_Pair @ TC @ TD @ ( D @ A ) @ ( E @ B ) ) @ ( image @ ( product_prod @ TA @ TB ) @ ( product_prod @ TC @ TD ) @ ( product_map_prod @ TA @ TC @ TB @ TD @ D @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_map__prod__imageI) ).
thf(788,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TA > TC,E: TB > TD] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( member @ ( product_prod @ TC @ TD ) @ ( product_Pair @ TC @ TD @ ( D @ A ) @ ( E @ B ) ) @ ( image @ ( product_prod @ TA @ TB ) @ ( product_prod @ TC @ TD ) @ ( product_map_prod @ TA @ TC @ TB @ TD @ D @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(114,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_subset__UNIV) ).
thf(566,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(129,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_61_subset__iff) ).
thf(625,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)],[129]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_surjective__pairing) ).
thf(522,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_prod__cases7) ).
thf(493,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType] :
( ( (=) @ ( product_prod @ TA @ TB ) )
= ( ^ [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
& ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_prod__eq__iff) ).
thf(324,plain,
! [TA: $tType,TB: $tType] :
( ( (=) @ ( product_prod @ TA @ TB ) )
= ( ^ [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
& ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o] :
( ! [C: TA,D: TB] :
( ( A @ C @ D )
=> ( B @ C @ D ) )
=> ( ord_less_eq @ ( TA > TB > $o ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_predicate2I) ).
thf(285,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA > TB > $o] :
( ! [C: TA,D: TB] :
( ( A @ C @ D )
=> ( B @ C @ D ) )
=> ( ord_less_eq @ ( TA > TB > $o ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TB @ TA )] :
( ( member @ TB @ A @ ( domain @ TB @ TA @ B ) )
= ( ? [C: TA] : ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_Domain__iff) ).
thf(224,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TB @ TA )] :
( ( member @ TB @ A @ ( domain @ TB @ TA @ B ) )
= ( ? [C: TA] : ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(118,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_59_subset__trans) ).
thf(578,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)],[118]) ).
thf(205,axiom,
! [A: set @ a] :
( ( member @ ( set @ a ) @ A @ ( image @ ( product_prod @ ( set @ a ) @ ( a > e ) ) @ ( set @ a ) @ ( product_fst @ ( set @ a ) @ ( a > e ) ) @ c ) )
=> ( ( ord_less_eq @ ( set @ a ) @ a1 @ A )
=> ( ( ord_less_eq @ ( set @ a ) @ a2 @ A )
=> ( ( ord_less_eq @ ( set @ a ) @ a3 @ A )
=> thesis ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(869,plain,
! [A: set @ a] :
( ( member @ ( set @ a ) @ A @ ( image @ ( product_prod @ ( set @ a ) @ ( a > e ) ) @ ( set @ a ) @ ( product_fst @ ( set @ a ) @ ( a > e ) ) @ c ) )
=> ( ( ord_less_eq @ ( set @ a ) @ a1 @ A )
=> ( ( ord_less_eq @ ( set @ a ) @ a2 @ A )
=> ( ( ord_less_eq @ ( set @ a ) @ a3 @ A )
=> thesis ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(177,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_19_subset__image__iff) ).
thf(783,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)],[177]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_prod_Oinject) ).
thf(537,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(148,axiom,
! [TA: $tType,TB: $tType] :
( ( image @ ( product_prod @ TB @ TA ) @ ( product_prod @ TA @ TB ) @ ( product_swap @ TB @ TA ) @ ( top_top @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_surj__swap) ).
thf(686,plain,
! [TA: $tType,TB: $tType] :
( ( image @ ( product_prod @ TB @ TA ) @ ( product_prod @ TA @ TB ) @ ( product_swap @ TB @ TA ) @ ( top_top @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(133,axiom,
( ( ord_less_eq @ ( set @ a ) @ a1 @ a2 )
| ( ord_less_eq @ ( set @ a ) @ a2 @ a1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062a1_A_092_060subseteq_062_Aa2_A_092_060or_062_Aa2_A_092_060subseteq_062_Aa1_092_060close_062) ).
thf(642,plain,
( ( ord_less_eq @ ( set @ a ) @ a1 @ a2 )
| ( ord_less_eq @ ( set @ a ) @ a2 @ a1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(89,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_le__convert) ).
thf(489,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ A @ C )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TB @ TA ),C: TA > $o] :
( ( member @ TA @ A @ ( range @ TB @ TA @ B ) )
=> ( ! [D: TB,E: TA] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ D @ E ) @ B )
=> ( C @ E ) )
=> ( C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_Range_Oinducts) ).
thf(547,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TB @ TA ),C: TA > $o] :
( ( member @ TA @ A @ ( range @ TB @ TA @ B ) )
=> ( ! [D: TB,E: TA] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ D @ E ) @ B )
=> ( C @ E ) )
=> ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(154,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_12_subset__antisym) ).
thf(706,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)],[154]) ).
thf(135,axiom,
! [TA: $tType] : ( top @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Otop_4) ).
thf(647,plain,
! [TA: $tType] : ( top @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(152,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_195_UNIV__eq__I) ).
thf(701,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)],[152]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_swap @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= ( product_Pair @ TB @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_swap__simp) ).
thf(515,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_swap @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= ( product_Pair @ TB @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(138,axiom,
( ( ord_less_eq @ ( set @ a ) @ a1 @ a3 )
| ( ord_less_eq @ ( set @ a ) @ a3 @ a1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__092_060open_062a1_A_092_060subseteq_062_Aa3_A_092_060or_062_Aa3_A_092_060subseteq_062_Aa1_092_060close_062) ).
thf(654,plain,
( ( ord_less_eq @ ( set @ a ) @ a1 @ a3 )
| ( ord_less_eq @ ( set @ a ) @ a3 @ a1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_snd__conv) ).
thf(503,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB] :
( ( A @ B @ C )
=> ( A @ ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ C @ B ) ) @ ( product_fst @ TB @ TA @ ( product_Pair @ TB @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_exI__realizer) ).
thf(343,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB] :
( ( A @ B @ C )
=> ( A @ ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ C @ B ) ) @ ( product_fst @ TB @ TA @ ( product_Pair @ TB @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(187,axiom,
member @ ( set @ a ) @ a2 @ ( image @ ( product_prod @ ( set @ a ) @ ( a > e ) ) @ ( set @ a ) @ ( product_fst @ ( set @ a ) @ ( a > e ) ) @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_A_I2_J) ).
thf(805,plain,
member @ ( set @ a ) @ a2 @ ( image @ ( product_prod @ ( set @ a ) @ ( a > e ) ) @ ( set @ a ) @ ( product_fst @ ( set @ a ) @ ( a > e ) ) @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Otop) ).
thf(311,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_fst__conv) ).
thf(558,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(102,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_ord__eq__le__trans) ).
thf(530,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(141,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_subset__self) ).
thf(662,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: TA,C: TB] :
( ( A
= ( product_Pair @ TA @ TB @ B @ C ) )
=> ( ( product_fst @ TA @ TB @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_fstI) ).
thf(298,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: TA,C: TB] :
( ( A
= ( product_Pair @ TA @ TB @ B @ C ) )
=> ( ( product_fst @ TA @ TB @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > $o,B: TA > TB > TC,C: product_prod @ TA @ TB] :
( ( A @ ( product_case_prod @ TA @ TB @ TC @ B @ C ) )
= ( ( C
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ C ) @ ( product_snd @ TA @ TB @ C ) ) )
=> ( A @ ( B @ ( product_fst @ TA @ TB @ C ) @ ( product_snd @ TA @ TB @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_prod_Osplit__sel) ).
thf(412,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > $o,B: TA > TB > TC,C: product_prod @ TA @ TB] :
( ( A @ ( product_case_prod @ TA @ TB @ TC @ B @ C ) )
= ( ( C
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ C ) @ ( product_snd @ TA @ TB @ C ) ) )
=> ( A @ ( B @ ( product_fst @ TA @ TB @ C ) @ ( product_snd @ TA @ TB @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_case_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_old_Oprod_Ocase) ).
thf(425,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_case_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TB @ A @ ( range @ TA @ TB @ B ) )
= ( ? [C: TA,D: TB] :
( ( A = D )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_Range_Osimps) ).
thf(430,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TB @ A @ ( range @ TA @ TB @ B ) )
= ( ? [C: TA,D: TB] :
( ( A = D )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > $o,B: TA > TB > TC,C: product_prod @ TA @ TB] :
( ( A @ ( product_case_prod @ TA @ TB @ TC @ B @ C ) )
= ( ~ ( ( C
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ C ) @ ( product_snd @ TA @ TB @ C ) ) )
& ~ ( A @ ( B @ ( product_fst @ TA @ TB @ C ) @ ( product_snd @ TA @ TB @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_prod_Osplit__sel__asm) ).
thf(264,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > $o,B: TA > TB > TC,C: product_prod @ TA @ TB] :
( ( A @ ( product_case_prod @ TA @ TB @ TC @ B @ C ) )
= ( ~ ( ( C
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ C ) @ ( product_snd @ TA @ TB @ C ) ) )
& ~ ( A @ ( B @ ( product_fst @ TA @ TB @ C ) @ ( product_snd @ TA @ TB @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(149,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_101_mem__in__image2) ).
thf(689,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)],[149]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( converse @ TA @ TB @ C ) )
= ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_converse__iff) ).
thf(444,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( converse @ TA @ TB @ C ) )
= ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(162,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_18_image__subset__iff) ).
thf(733,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)],[162]) ).
thf(161,axiom,
member @ ( set @ a ) @ a1 @ ( image @ ( product_prod @ ( set @ a ) @ ( a > e ) ) @ ( set @ a ) @ ( product_fst @ ( set @ a ) @ ( a > e ) ) @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_A_I1_J) ).
thf(732,plain,
member @ ( set @ a ) @ a1 @ ( image @ ( product_prod @ ( set @ a ) @ ( a > e ) ) @ ( set @ a ) @ ( product_fst @ ( set @ a ) @ ( a > e ) ) @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(195,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_15_image__mono) ).
thf(843,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)],[195]) ).
thf(173,axiom,
( ( ord_less_eq @ ( set @ a ) @ a2 @ a3 )
| ( ord_less_eq @ ( set @ a ) @ a3 @ a2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062a2_A_092_060subseteq_062_Aa3_A_092_060or_062_Aa3_A_092_060subseteq_062_Aa2_092_060close_062) ).
thf(772,plain,
( ( ord_less_eq @ ( set @ a ) @ a2 @ a3 )
| ( ord_less_eq @ ( set @ a ) @ a3 @ a2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(165,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_100_mem__in__image3) ).
thf(743,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)],[165]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: $o,D: TB,E: TA] :
( ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ B )
& C )
=> ( C
& ( ( A @ D @ E )
=> ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_predicate2D__conj) ).
thf(281,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB > TA > $o,C: $o,D: TB,E: TA] :
( ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ B )
& C )
=> ( C
& ( ( A @ D @ E )
=> ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_le__fun__def) ).
thf(259,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(60,axiom,
! [TA: $tType,A: TA > TA > $o,B: TA] :
( ( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA ) @ A )
=> ( A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_ge__eq__refl) ).
thf(382,plain,
! [TA: $tType,A: TA > TA > $o,B: TA] :
( ( ord_less_eq @ ( TA > TA > $o ) @ ( (=) @ TA ) @ A )
=> ( A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ TB ) @ ( range @ TA @ TB @ A ) @ ( range @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_Range__mono) ).
thf(572,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ TB ) @ ( range @ TA @ TB @ A ) @ ( range @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TB ),B: TA > TB] :
( ( converse @ TA @ TA @ ( inv_image @ TB @ TA @ A @ B ) )
= ( inv_image @ TB @ TA @ ( converse @ TB @ TB @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_converse__inv__image) ).
thf(313,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TB ),B: TA > TB] :
( ( converse @ TA @ TA @ ( inv_image @ TB @ TA @ A @ B ) )
= ( inv_image @ TB @ TA @ ( converse @ TB @ TB @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(82,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(466,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType] :
( ( product_swap @ TA @ TB )
= ( ^ [A: product_prod @ TA @ TB] : ( product_Pair @ TB @ TA @ ( product_snd @ TA @ TB @ A ) @ ( product_fst @ TA @ TB @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_prod_Oswap__def) ).
thf(335,plain,
! [TA: $tType,TB: $tType] :
( ( product_swap @ TA @ TB )
= ( ^ [A: product_prod @ TA @ TB] : ( product_Pair @ TB @ TA @ ( product_snd @ TA @ TB @ A ) @ ( product_fst @ TA @ TB @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(153,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( domain @ TA @ TB @ A ) @ ( domain @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_Domain__mono) ).
thf(704,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( domain @ TA @ TB @ A ) @ ( domain @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( range @ TB @ TA @ ( converse @ TA @ TB @ A ) )
= ( domain @ TA @ TB @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_Range__converse) ).
thf(350,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( range @ TB @ TA @ ( converse @ TA @ TB @ A ) )
= ( domain @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ ( fun_in_rel @ TA @ TB @ B ) ) ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_Collect__case__prod__in__rel__leE) ).
thf(540,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ ( fun_in_rel @ TA @ TB @ B ) ) ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(143,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 )
=> ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_proper__subset) ).
thf(672,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 )
=> ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(171,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( D = B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_ssubst__Pair__rhs) ).
thf(764,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( ( D = B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TD,B: TB > TC,C: product_prod @ TA @ TB] :
( ( product_snd @ TD @ TC @ ( product_map_prod @ TA @ TD @ TB @ TC @ A @ B @ C ) )
= ( B @ ( product_snd @ TA @ TB @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_snd__map__prod) ).
thf(219,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TD,B: TB > TC,C: product_prod @ TA @ TB] :
( ( product_snd @ TD @ TC @ ( product_map_prod @ TA @ TD @ TB @ TC @ A @ B @ C ) )
= ( B @ ( product_snd @ TA @ TB @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_prod__induct4) ).
thf(274,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(163,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_55_image__iff) ).
thf(736,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)],[163]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TB @ A @ ( range @ TA @ TB @ B ) )
=> ~ ! [C: TA] :
~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_Range_Ocases) ).
thf(362,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TB @ A @ ( range @ TA @ TB @ B ) )
=> ~ ! [C: TA] :
~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( converse @ TA @ TB @ C ) )
= ( ? [D: TA,E: TB] :
( ( A = E )
& ( B = D )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ E ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_converse_Osimps) ).
thf(245,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( converse @ TA @ TB @ C ) )
= ( ? [D: TA,E: TB] :
( ( A = E )
& ( B = D )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ E ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(136,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_UNIV__I) ).
thf(649,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_swap @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_swap__swap) ).
thf(271,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_swap @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(125,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TB @ TA ) ) @ A @ ( converse @ TA @ TB @ B ) )
= ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ ( converse @ TB @ TA @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_converse__subset__swap) ).
thf(599,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TB @ TA ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TB @ TA ) ) @ A @ ( converse @ TA @ TB @ B ) )
= ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ ( converse @ TB @ TA @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(131,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( image @ ( product_prod @ TA @ TB ) @ TA @ ( product_fst @ TA @ TB ) @ A )
= ( domain @ TA @ TB @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_fst__eq__Domain) ).
thf(631,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( image @ ( product_prod @ TA @ TB ) @ TA @ ( product_fst @ TA @ TB ) @ A )
= ( domain @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(128,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_95_eqsets__sub) ).
thf(621,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)],[128]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType] :
( ( converse @ TB @ TA @ ( top_top @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_converse__UNIV) ).
thf(330,plain,
! [TA: $tType,TB: $tType] :
( ( converse @ TB @ TA @ ( top_top @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB,D: product_prod @ TA @ TB] :
( ( A @ B @ C )
=> ( ( D
= ( product_Pair @ TA @ TB @ B @ C ) )
=> ( A @ ( product_fst @ TA @ TB @ D ) @ ( product_snd @ TA @ TB @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_BNF__Greatest__Fixpoint_Osubst__Pair) ).
thf(462,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB,D: product_prod @ TA @ TB] :
( ( A @ B @ C )
=> ( ( D
= ( product_Pair @ TA @ TB @ B @ C ) )
=> ( A @ ( product_fst @ TA @ TB @ D ) @ ( product_snd @ TA @ TB @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(50,axiom,
! [TA: $tType] :
( ( pow @ TA @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_Pow__UNIV) ).
thf(345,plain,
! [TA: $tType] :
( ( pow @ TA @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(200,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( set @ TA ) ) @ ( pow @ TA @ A ) @ ( pow @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_Pow__mono) ).
thf(858,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( set @ TA ) ) @ ( pow @ TA @ A ) @ ( pow @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(185,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
| ( ord_less_eq @ ( set @ TA ) @ B @ A ) )
=> ( ~ ( member @ TA @ C @ A )
=> ( ( member @ TA @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_sub__which2) ).
thf(799,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
| ( ord_less_eq @ ( set @ TA ) @ B @ A ) )
=> ( ~ ( member @ TA @ C @ A )
=> ( ( member @ TA @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_PairE__lemma) ).
thf(213,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(176,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_58_set__eq__subset) ).
thf(780,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)],[176]) ).
thf(79,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA] :
( ( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= C )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_fst__eqD) ).
thf(455,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA] :
( ( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= C )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( member @ TA @ A @ ( domain @ TA @ TB @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_Domain_ODomainI) ).
thf(394,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( member @ TA @ A @ ( domain @ TA @ TB @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_prod__induct5) ).
thf(438,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(172,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_51_rev__image__eqI) ).
thf(768,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)],[172]) ).
thf(192,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TC @ TD,B: TA > TC,C: TB > TD,D: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TC @ TD ) @ A @ ( image @ ( product_prod @ TA @ TB ) @ ( product_prod @ TC @ TD ) @ ( product_map_prod @ TA @ TC @ TB @ TD @ B @ C ) @ D ) )
=> ~ ! [E: TA,F: TB] :
( ( A
= ( product_Pair @ TC @ TD @ ( B @ E ) @ ( C @ F ) ) )
=> ~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ F ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_prod__fun__imageE) ).
thf(827,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TC @ TD,B: TA > TC,C: TB > TD,D: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TC @ TD ) @ A @ ( image @ ( product_prod @ TA @ TB ) @ ( product_prod @ TC @ TD ) @ ( product_map_prod @ TA @ TC @ TB @ TD @ B @ C ) @ D ) )
=> ~ ! [E: TA,F: TB] :
( ( A
= ( product_Pair @ TC @ TD @ ( B @ E ) @ ( C @ F ) ) )
=> ~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ F ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( product_case_prod @ TA @ TB @ TC )
= ( ^ [A: TA > TB > TC,B: product_prod @ TA @ TB] : ( A @ ( product_fst @ TA @ TB @ B ) @ ( product_snd @ TA @ TB @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_case__prod__beta) ).
thf(278,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( product_case_prod @ TA @ TB @ TC )
= ( ^ [A: TA > TB > TC,B: product_prod @ TA @ TB] : ( A @ ( product_fst @ TA @ TB @ B ) @ ( product_snd @ TA @ TB @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(204,axiom,
member @ ( set @ a ) @ a3 @ ( image @ ( product_prod @ ( set @ a ) @ ( a > e ) ) @ ( set @ a ) @ ( product_fst @ ( set @ a ) @ ( a > e ) ) @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_A_I3_J) ).
thf(868,plain,
member @ ( set @ a ) @ a3 @ ( image @ ( product_prod @ ( set @ a ) @ ( a > e ) ) @ ( set @ a ) @ ( product_fst @ ( set @ a ) @ ( a > e ) ) @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(267,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(198,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_11_subsetI) ).
thf(851,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)],[198]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_prod__induct3) ).
thf(374,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TB,C: TD,D: TA] :
( ( product_map_prod @ TD @ TC @ TA @ TB @ A @ B @ ( product_Pair @ TD @ TA @ C @ D ) )
= ( product_Pair @ TC @ TB @ ( A @ C ) @ ( B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_map__prod__simp) ).
thf(355,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TB,C: TD,D: TA] :
( ( product_map_prod @ TD @ TC @ TA @ TB @ A @ B @ ( product_Pair @ TD @ TA @ C @ D ) )
= ( product_Pair @ TC @ TB @ ( A @ C ) @ ( B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( converse @ TA @ TB @ C ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_converse_Ocases) ).
thf(553,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( converse @ TA @ TB @ C ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(182,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_66_in__mono) ).
thf(795,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)],[182]) ).
thf(146,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
| ( ord_less_eq @ ( set @ TA ) @ B @ A ) )
=> ( ( member @ TA @ C @ A )
=> ( ~ ( member @ TA @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_sub__which1) ).
thf(680,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
| ( ord_less_eq @ ( set @ TA ) @ B @ A ) )
=> ( ( member @ TA @ C @ A )
=> ( ~ ( member @ TA @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(100,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_top__set__def) ).
thf(525,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(32,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(295,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(43,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_prod_Oexhaust__sel) ).
thf(327,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(164,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA > TC,C: TA,D: TB,E: TA > TB,F: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member @ TA @ C @ F )
=> ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ A @ D ) @ ( bNF_Greatest_image2 @ TA @ TC @ TB @ F @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_image2__eqI) ).
thf(739,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA > TC,C: TA,D: TB,E: TA > TB,F: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member @ TA @ C @ F )
=> ( member @ ( product_prod @ TC @ TB ) @ ( product_Pair @ TC @ TB @ A @ D ) @ ( bNF_Greatest_image2 @ TA @ TC @ TB @ F @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(119,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( image @ TB @ TA @ A @ B ) @ C )
=> ( ord_less_eq @ ( set @ ( set @ TA ) ) @ ( image @ ( set @ TB ) @ ( set @ TA ) @ ( image @ TB @ TA @ A ) @ ( finite_Fpow @ TB @ B ) ) @ ( finite_Fpow @ TA @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_image__Fpow__mono) ).
thf(580,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( image @ TB @ TA @ A @ B ) @ C )
=> ( ord_less_eq @ ( set @ ( set @ TA ) ) @ ( image @ ( set @ TB ) @ ( set @ TA ) @ ( image @ TB @ TA @ A ) @ ( finite_Fpow @ TB @ B ) ) @ ( finite_Fpow @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(199,axiom,
! [TA: $tType,TB: $tType] :
( ( domain @ TA @ TB )
= ( image @ ( product_prod @ TA @ TB ) @ TA @ ( product_fst @ TA @ TB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_Domain__fst) ).
thf(855,plain,
! [TA: $tType,TB: $tType] :
( ( domain @ TA @ TB )
= ( image @ ( product_prod @ TA @ TB ) @ TA @ ( product_fst @ TA @ TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(121,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_182_surjD) ).
thf(585,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)],[121]) ).
thf(157,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( bNF_Ca1785829860lChain @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TA ),B: TA > TB] :
! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( ord_less_eq @ TB @ ( B @ C ) @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_relChain__def) ).
thf(717,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( bNF_Ca1785829860lChain @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TA ),B: TA > TB] :
! [C: TA,D: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ A )
=> ( ord_less_eq @ TB @ ( B @ C ) @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(194,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TB @ TA ) ) @ ( converse @ TA @ TB @ A ) @ ( converse @ TA @ TB @ B ) )
= ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_converse__mono) ).
thf(840,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TB @ TA ) ) @ ( converse @ TA @ TB @ A ) @ ( converse @ TA @ TB @ B ) )
= ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
& ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_prod_Oexpand) ).
thf(338,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
& ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_old_Oprod_Oexhaust) ).
thf(544,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(196,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ~ ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ~ ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_not__sub) ).
thf(845,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ~ ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ~ ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(169,axiom,
member @ ( product_prod @ ( set @ a ) @ ( a > e ) ) @ ( product_Pair @ ( set @ a ) @ ( a > e ) @ a2 @ b2 ) @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9__092_060open_062_Ia2_M_Ab2_J_A_092_060in_062_AC_092_060close_062) ).
thf(759,plain,
member @ ( product_prod @ ( set @ a ) @ ( a > e ) ) @ ( product_Pair @ ( set @ a ) @ ( a > e ) @ a2 @ b2 ) @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_prod__cases3) ).
thf(250,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(11,axiom,
top @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Otop_9) ).
thf(231,plain,
top @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(122,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA] :
( ( ( image @ TB @ TA @ A @ B )
= C )
=> ( ( image @ ( set @ TB ) @ ( set @ TA ) @ ( image @ TB @ TA @ A ) @ ( pow @ TB @ B ) )
= ( pow @ TA @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_image__Pow__surj) ).
thf(588,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: set @ TA] :
( ( ( image @ TB @ TA @ A @ B )
= C )
=> ( ( image @ ( set @ TB ) @ ( set @ TA ) @ ( image @ TB @ TA @ A ) @ ( pow @ TB @ B ) )
= ( pow @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_snd @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= ( product_fst @ TA @ TB @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_snd__swap) ).
thf(319,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_snd @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= ( product_fst @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(166,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Collect__mono) ).
thf(748,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TA @ TB ),C: TA > $o] :
( ( member @ TA @ A @ ( domain @ TA @ TB @ B ) )
=> ( ! [D: TA,E: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ E ) @ B )
=> ( C @ D ) )
=> ( C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_Domain_Oinducts) ).
thf(401,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TA @ TB ),C: TA > $o] :
( ( member @ TA @ A @ ( domain @ TA @ TB @ B ) )
=> ( ! [D: TA,E: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ D @ E ) @ B )
=> ( C @ D ) )
=> ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(69,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_ge__convert) ).
thf(418,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(178,axiom,
! [A: product_prod @ ( set @ a ) @ ( a > e )] :
( ( member @ ( product_prod @ ( set @ a ) @ ( a > e ) ) @ A @ c )
=> ! [B: product_prod @ ( set @ a ) @ ( a > e )] :
( ( member @ ( product_prod @ ( set @ a ) @ ( a > e ) ) @ B @ c )
=> ( ( ord_less_eq @ ( set @ a ) @ ( product_fst @ ( set @ a ) @ ( a > e ) @ A ) @ ( product_fst @ ( set @ a ) @ ( a > e ) @ B ) )
| ( ord_less_eq @ ( set @ a ) @ ( product_fst @ ( set @ a ) @ ( a > e ) @ B ) @ ( product_fst @ ( set @ a ) @ ( a > e ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062_092_060forall_062a_092_060in_062C_O_A_092_060forall_062b_092_060in_062C_O_Afst_Aa_A_092_060subseteq_062_Afst_Ab_A_092_060or_062_Afst_Ab_A_092_060subseteq_062_Afst_Aa_092_060close_062) ).
thf(786,plain,
! [A: product_prod @ ( set @ a ) @ ( a > e )] :
( ( member @ ( product_prod @ ( set @ a ) @ ( a > e ) ) @ A @ c )
=> ! [B: product_prod @ ( set @ a ) @ ( a > e )] :
( ( member @ ( product_prod @ ( set @ a ) @ ( a > e ) ) @ B @ c )
=> ( ( ord_less_eq @ ( set @ a ) @ ( product_fst @ ( set @ a ) @ ( a > e ) @ A ) @ ( product_fst @ ( set @ a ) @ ( a > e ) @ B ) )
| ( ord_less_eq @ ( set @ a ) @ ( product_fst @ ( set @ a ) @ ( a > e ) @ B ) @ ( product_fst @ ( set @ a ) @ ( a > e ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(115,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ~ ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ~ ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_not__subseteq) ).
thf(568,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ~ ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ~ ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_old_Oprod_Oinducts) ).
thf(378,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_prod__induct6) ).
thf(235,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType] :
( ( fun_in_rel @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TB ),B: TA,C: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_in__rel__def) ).
thf(207,plain,
! [TA: $tType,TB: $tType] :
( ( fun_in_rel @ TA @ TB )
= ( ^ [A: set @ ( product_prod @ TA @ TB ),B: TA,C: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(86,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_10) ).
thf(478,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TC > TA > ( set @ TB ),C: product_prod @ TC @ TA] :
( ( member @ TB @ A @ ( product_case_prod @ TC @ TA @ ( set @ TB ) @ B @ C ) )
=> ~ ! [D: TC,E: TA] :
( ( C
= ( product_Pair @ TC @ TA @ D @ E ) )
=> ~ ( member @ TB @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_mem__case__prodE) ).
thf(433,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: TC > TA > ( set @ TB ),C: product_prod @ TC @ TA] :
( ( member @ TB @ A @ ( product_case_prod @ TC @ TA @ ( set @ TB ) @ B @ C ) )
=> ~ ! [D: TC,E: TA] :
( ( C
= ( product_Pair @ TC @ TA @ D @ E ) )
=> ~ ( member @ TB @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( converse @ TA @ TB @ C ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_converseD) ).
thf(510,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( converse @ TA @ TB @ C ) )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(193,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_110_Inf_OINF__cong) ).
thf(832,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)],[193]) ).
thf(147,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_56_imageI) ).
thf(684,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)],[147]) ).
thf(167,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: set @ TB,D: TA] :
( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( member @ TB @ ( B @ E ) @ C ) )
=> ( ( member @ TA @ D @ A )
=> ( member @ TB @ ( B @ D ) @ ( image @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_mem__in__image1) ).
thf(752,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: set @ TB,D: TA] :
( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( member @ TB @ ( B @ E ) @ C ) )
=> ( ( member @ TA @ D @ A )
=> ( member @ TB @ ( B @ D ) @ ( image @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_ord__le__eq__subst) ).
thf(447,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( member @ TB @ B @ ( range @ TA @ TB @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_Range_Ointros) ).
thf(262,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( member @ TB @ B @ ( range @ TA @ TB @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(190,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA,B: TC > TB] :
( ( ( image @ TD @ TA @ A @ ( top_top @ ( set @ TD ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( ( image @ TC @ TB @ B @ ( top_top @ ( set @ TC ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ( ( image @ ( product_prod @ TD @ TC ) @ ( product_prod @ TA @ TB ) @ ( product_map_prod @ TD @ TA @ TC @ TB @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ TD @ TC ) ) ) )
= ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_map__prod__surj) ).
thf(818,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA,B: TC > TB] :
( ( ( image @ TD @ TA @ A @ ( top_top @ ( set @ TD ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( ( image @ TC @ TB @ B @ ( top_top @ ( set @ TC ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ( ( image @ ( product_prod @ TD @ TC ) @ ( product_prod @ TA @ TB ) @ ( product_map_prod @ TD @ TA @ TC @ TB @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ TD @ TC ) ) ) )
= ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(203,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_63_subset__eq) ).
thf(865,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)],[203]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TA @ A @ ( domain @ TA @ TB @ B ) )
= ( ? [C: TA,D: TB] :
( ( A = C )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_Domain_Osimps) ).
thf(422,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TA @ A @ ( domain @ TA @ TB @ B ) )
= ( ? [C: TA,D: TB] :
( ( A = C )
& ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(180,axiom,
! [TA: $tType,A: set @ TA] :
~ ? [B: TA > ( set @ TA )] :
( ( image @ TA @ ( set @ TA ) @ B @ A )
= ( pow @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_Cantors__paradox) ).
thf(790,plain,
! [TA: $tType,A: set @ TA] :
~ ? [B: TA > ( set @ TA )] :
( ( image @ TA @ ( set @ TA ) @ B @ A )
= ( pow @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(113,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_65_subsetD) ).
thf(564,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)],[113]) ).
thf(35,axiom,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_top__empty__eq) ).
thf(305,plain,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_prod_Ocollapse) ).
thf(210,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_prod__induct7) ).
thf(239,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: product_prod @ TA @ TB] :
( ( A @ ( product_snd @ TA @ TB @ B ) @ ( product_fst @ TA @ TB @ B ) )
=> ~ ! [C: TA,D: TB] :
~ ( A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_exE__realizer_H) ).
thf(341,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: product_prod @ TA @ TB] :
( ( A @ ( product_snd @ TA @ TB @ B ) @ ( product_fst @ TA @ TB @ B ) )
=> ~ ! [C: TA,D: TB] :
~ ( A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(94,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_ord__le__eq__trans) ).
thf(506,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_prod__cases) ).
thf(358,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(142,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_64_equalityE) ).
thf(664,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)],[142]) ).
thf(158,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_62_equalityD2) ).
thf(720,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)],[158]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType] :
( ( range @ TA @ TB )
= ( image @ ( product_prod @ TA @ TB ) @ TB @ ( product_snd @ TA @ TB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_Range__snd) ).
thf(415,plain,
! [TA: $tType,TB: $tType] :
( ( range @ TA @ TB )
= ( image @ ( product_prod @ TA @ TB ) @ TB @ ( product_snd @ TA @ TB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(201,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_177_rangeI) ).
thf(860,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)],[201]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( bNF_csquare @ TA @ TD @ TC @ TB )
= ( ^ [A: set @ TA,B: TD > TC,C: TB > TC,D: TA > TD,E: TA > TB] :
! [F: TA] :
( ( member @ TA @ F @ A )
=> ( ( B @ ( D @ F ) )
= ( C @ ( E @ F ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_csquare__def) ).
thf(596,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( bNF_csquare @ TA @ TD @ TC @ TB )
= ( ^ [A: set @ TA,B: TD > TC,C: TB > TC,D: TA > TD,E: TA > TB] :
! [F: TA] :
( ( member @ TA @ F @ A )
=> ( ( B @ ( D @ F ) )
= ( C @ ( E @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_le__funI) ).
thf(528,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(134,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Collect__mono__iff) ).
thf(644,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
=> ( ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_prod__eqI) ).
thf(459,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
=> ( ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(150,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_54_bex__imageD) ).
thf(691,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)],[150]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TA @ A @ ( domain @ TA @ TB @ B ) )
=> ~ ! [C: TB] :
~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_DomainE) ).
thf(442,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ ( product_prod @ TA @ TB )] :
( ( member @ TA @ A @ ( domain @ TA @ TB @ B ) )
=> ~ ! [C: TB] :
~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(127,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TB ),C: set @ TB,D: TA > TB > $o,E: TA > TB > $o] :
( ( A
= ( image @ ( product_prod @ TA @ TB ) @ TA @ ( product_fst @ TA @ TB ) @ B ) )
=> ( ( C
= ( image @ ( product_prod @ TA @ TB ) @ TB @ ( product_snd @ TA @ TB ) @ B ) )
=> ( ! [F: TA] :
( ( member @ TA @ F @ A )
=> ! [G: TB] :
( ( member @ TB @ G @ C )
=> ( ( D @ F @ G )
=> ( E @ F @ G ) ) ) )
=> ( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ B @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ D ) ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ B @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_Collect__split__mono__strong) ).
thf(607,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TB ),C: set @ TB,D: TA > TB > $o,E: TA > TB > $o] :
( ( A
= ( image @ ( product_prod @ TA @ TB ) @ TA @ ( product_fst @ TA @ TB ) @ B ) )
=> ( ( C
= ( image @ ( product_prod @ TA @ TB ) @ TB @ ( product_snd @ TA @ TB ) @ B ) )
=> ( ! [F: TA] :
( ( member @ TA @ F @ A )
=> ! [G: TB] :
( ( member @ TB @ G @ C )
=> ( ( D @ F @ G )
=> ( E @ F @ G ) ) ) )
=> ( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ B @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ D ) ) )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ B @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: TB,C: TA] :
( ( A
= ( product_Pair @ TB @ TA @ B @ C ) )
=> ( ( product_snd @ TB @ TA @ A )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_sndI) ).
thf(227,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA,B: TB,C: TA] :
( ( A
= ( product_Pair @ TB @ TA @ B @ C ) )
=> ( ( product_snd @ TB @ TA @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ ( fun_in_rel @ TA @ TB @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_Collect__case__prod__in__rel__leI) ).
thf(322,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ ( collect @ ( product_prod @ TA @ TB ) @ ( product_case_prod @ TA @ TB @ $o @ ( fun_in_rel @ TA @ TB @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(186,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ ( set @ TA ) ) @ ( finite_Fpow @ TA @ A ) @ ( pow @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Fpow__subset__Pow) ).
thf(803,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ ( set @ TA ) ) @ ( finite_Fpow @ TA @ A ) @ ( pow @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ( converse @ TA @ TB @ A )
= ( converse @ TA @ TB @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_converse__inject) ).
thf(469,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ( converse @ TA @ TB @ A )
= ( converse @ TA @ TB @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(140,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_181_surjE) ).
thf(659,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)],[140]) ).
thf(144,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( pow @ TA @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_PowD) ).
thf(676,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( pow @ TA @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: TB > TA > $o] :
( ( A @ B @ C )
=> ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ D )
=> ( D @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_rev__predicate2D) ).
thf(222,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: TB > TA > $o] :
( ( A @ B @ C )
=> ( ( ord_less_eq @ ( TB > TA > $o ) @ A @ D )
=> ( D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(123,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_13_image__eqI) ).
thf(592,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)],[123]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB ),D: TB > TA > $o] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( converse @ TA @ TB @ C ) )
=> ( ! [E: TA,F: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ F ) @ C )
=> ( D @ F @ E ) )
=> ( D @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_converse_Oinducts) ).
thf(496,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB ),D: TB > TA > $o] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( converse @ TA @ TB @ C ) )
=> ( ! [E: TA,F: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ F ) @ C )
=> ( D @ F @ E ) )
=> ( D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > $o,D: TA] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( product_fst @ TB @ TA @ ( product_Pair @ TB @ TA @ B @ D ) ) )
& ( C @ ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_conjI__realizer) ).
thf(364,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > $o,D: TA] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( product_fst @ TB @ TA @ ( product_Pair @ TB @ TA @ B @ D ) ) )
& ( C @ ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( image @ ( product_prod @ TA @ TB ) @ TB @ ( product_snd @ TA @ TB ) @ A )
= ( range @ TA @ TB @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_snd__eq__Range) ).
thf(232,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] :
( ( image @ ( product_prod @ TA @ TB ) @ TB @ ( product_snd @ TA @ TB ) @ A )
= ( range @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(871,plain,
$false,
inference(e,[status(thm)],[656,760,479,518,481,333,628,777,555,582,730,308,269,384,500,797,715,472,698,709,651,724,542,289,316,216,475,756,253,806,353,821,348,574,602,634,774,396,243,428,849,206,292,248,512,678,793,810,534,798,302,862,561,392,407,788,566,625,522,493,324,285,224,578,869,783,537,686,642,489,547,706,647,701,515,654,503,343,805,311,558,530,662,298,412,425,430,264,689,444,733,732,843,772,743,281,259,382,572,313,466,335,704,350,540,672,764,219,274,736,362,245,649,271,599,631,621,330,462,345,858,799,213,780,455,394,438,768,827,278,868,267,851,374,355,553,795,680,525,295,327,739,580,855,585,717,840,338,544,845,759,250,231,588,319,748,401,418,786,568,378,235,207,478,433,510,832,684,752,447,262,818,865,422,790,564,305,210,239,341,506,358,664,720,415,860,596,528,644,459,691,442,607,227,322,803,469,659,676,222,592,496,364,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP028^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.21 % Computer : n007.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 19:36:26 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 0.89/0.63 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.97/0.92 % [INFO] Parsing done (286ms).
% 1.97/0.93 % [INFO] Running in sequential loop mode.
% 2.77/1.17 % [INFO] eprover registered as external prover.
% 2.77/1.17 % [INFO] Scanning for conjecture ...
% 3.03/1.26 % [INFO] Found a conjecture (or negated_conjecture) and 271 axioms. Running axiom selection ...
% 3.41/1.36 % [INFO] Axiom selection finished. Selected 203 axioms (removed 68 axioms).
% 4.53/1.65 % [INFO] Problem is higher-order (TPTP THF).
% 4.53/1.68 % [INFO] Type checking passed.
% 4.53/1.69 % [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 ...
% 171.95/144.72 % External prover 'e' found a proof!
% 171.95/144.72 % [INFO] Killing All external provers ...
% 171.95/144.72 % Time passed: 144360ms (effective reasoning time: 143790ms)
% 171.95/144.72 % 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)>
% 171.95/144.73 % Axioms used in derivation (203): tcon_Set_Oset___Orderings_Otop_4, fact_97_Fpow__mono, fact_70_fst__conv, fact_140_Domain_Ocases, fact_199_snd__eq__Range, fact_128_in__inv__image, fact_194_prod__eqI, fact_49_le__funE, fact_157_converse_Osimps, fact_146_Domain__converse, fact_138_DomainE, fact_162_surj__swap, fact_98_le__convert, fact_72_fstI, fact_168_Pow__UNIV, fact_195_UNIV__eq__I, fact_118_image__Pow__surj, fact_74_relChain__def, fact_63_subset__eq, fact_137_Range_Oinducts, fact_180_surjI, fact_61_subset__iff, fact_149_converse__converse, fact_101_mem__in__image2, fact_170_snd__map__prod, fact_86_prod__cases5, fact_58_set__eq__subset, fact_131_Range__mono, fact_1__092_060open_062_092_060exists_062a_092_060in_062fst_A_096_AC_O_Aa1_A_092_060subseteq_062_Aa_A_092_060and_062_Aa2_A_092_060subseteq_062_Aa_A_092_060and_062_Aa3_A_092_060subseteq_062_Aa_092_060close_062, fact_224_mem__case__prodE, fact_9__092_060open_062_Ia2_M_Ab2_J_A_092_060in_062_AC_092_060close_062, fact_229_Collect__case__prod__in__rel__leE, fact_96_sub__which1, fact_228_ge__eq__refl, fact_230_Collect__case__prod__in__rel__leI, fact_69_eq__fst__iff, fact_107_sub__which2, fact_3__092_060open_062a1_A_092_060subseteq_062_Aa3_A_092_060or_062_Aa3_A_092_060subseteq_062_Aa1_092_060close_062, tcon_fun___Orderings_Oord, fact_188_sndI, fact_85_prod__cases6, fact_189_snd__eqD, fact_114_Pow__iff, fact_13_image__eqI, fact_84_prod__cases7, fact_231_in__rel__def, fact_178_range__eqI, fact_159_converseE, fact_4__092_060open_062a2_A_092_060subseteq_062_Aa3_A_092_060or_062_Aa3_A_092_060subseteq_062_Aa2_092_060close_062, fact_103_proper__subset, fact_220_prod_Osplit__sel__asm, tcon_Set_Oset___Orderings_Oord_5, fact_142_Domain_ODomainI, fact_190_snd__conv, fact_99_ge__convert, fact_219_prod_Osplit__sel, fact_129_fst__eq__Domain, fact_181_surjE, fact_60_Collect__mono, fact_29_ord__eq__le__trans, fact_217_Collect__case__prod__mono, fact_81_prod__induct5, fact_214_prod_Ocase__eq__if, fact_226_predicate2D, fact_113_PowI, fact_53_image__cong, fact_102_mem__in__image1, fact_59_subset__trans, fact_78_old_Oprod_Oexhaust, fact_46_Collect__mem__eq, fact_2__092_060open_062a1_A_092_060subseteq_062_Aa2_A_092_060or_062_Aa2_A_092_060subseteq_062_Aa1_092_060close_062, fact_223_predicate2I, fact_133_Range__iff, fact_164_map__prod__imageI, fact_71_fst__eqD, fact_112_ssubst__Pair__rhs, fact_94_not__sub, fact_117_Pow__mono, fact_39_ord__le__eq__subst, fact_87_prod__cases4, fact_95_eqsets__sub, fact_169_fst__map__prod, fact_5_A_I3_J, fact_115_Pow__top, fact_153_converse__mono, fact_208_Collect__split__mono__strong, fact_12_subset__antisym, fact_20_PairE__lemma, fact_213_Product__Type_OCollect__case__prodD, fact_191_eq__snd__iff, fact_193_prod_Oexpand, fact_73_all__subset__image, fact_141_Domain_Osimps, fact_44_le__funI, fact_155_converse_Oinducts, fact_28_ord__le__eq__trans, fact_105_subset__self, fact_151_swap__swap, fact_166_UNIV__I, fact_67_prod_Oinject, fact_152_converse__iff, fact_201_prod__fun__imageE, fact_197_surjective__pairing, fact_89_Pair__inject, fact_196_UNIV__witness, fact_17_subset__imageE, fact_11_subsetI, fact_111_subrelI, tcon_HOL_Obool___Orderings_Otop_9, tcon_HOL_Obool___Orderings_Oord_10, fact_45_mem__Collect__eq, fact_90_prod__cases, fact_174_snd__swap, fact_79_prod__induct7, fact_172_prod_Ocollapse, fact_6_A_I2_J, fact_88_prod__cases3, fact_145_Range__converse, fact_43_le__fun__def, fact_222_split__cong, fact_160_converseD, fact_104_not__subseteq, fact_171_converse__UNIV, fact_66_in__mono, fact_16_image__subsetI, fact_143_Domain_Oinducts, fact_247_csquare__def, fact_192_prod__eq__iff, fact_161_converse__subset__swap, fact_135_Range_Osimps, fact_136_Range_Ointros, fact_163_prod_Oswap__def, fact_250_image2__eqI, fact_68_old_Oprod_Oinject, fact_198_prod_Oexhaust__sel, fact_183_map__prod__surj, fact_47_Collect__cong, fact_200_Range__snd, fact_167_map__prod__simp, fact_83_prod__induct3, fact_10__092_060open_062_Ia3_M_Ab3_J_A_092_060in_062_AC_092_060close_062, fact_40_ord__eq__le__subst, fact_165_top__apply, tcon_fun___Orderings_Otop, fact_77_old_Oprod_Oinducts, fact_7_A_I1_J, fact_233_predicate2D__conj, fact_106_sets__not__eq, fact_207_exE__realizer_H, fact_134_Range_Ocases, fact_203_conjI__realizer, fact_139_Domain__iff, fact_177_rangeI, fact_187_subset__UNIV, fact_64_equalityE, fact_50_le__funD, fact_18_image__subset__iff, fact_215_case__prod__beta, fact_150_converse__inject, fact_176_range__snd, fact_119_Fpow__subset__Pow, fact_202_exI__realizer, fact_132_RangeE, fact_210_top1I, fact_100_mem__in__image3, fact_108_image__Pow__mono, fact_144_Domain__mono, fact_54_bex__imageD, fact_57_Collect__mono__iff, fact_227_refl__ge__eq, fact_52_ball__imageD, fact_120_Cantors__paradox, fact_110_Inf_OINF__cong, fact_179_surj__def, fact_225_rev__predicate2D, fact_175_range__fst, fact_55_image__iff, fact_205_top__set__def, fact_8__092_060open_062_Ia1_M_Ab1_J_A_092_060in_062_AC_092_060close_062, fact_109_Sup_OSUP__cong, fact_82_prod__induct4, fact_148_swap__simp, fact_156_converse_Ointros, fact_182_surjD, fact_130_Domain__fst, fact_56_imageI, conj_0, fact_51_rev__image__eqI, fact_218_old_Oprod_Ocase, fact_116_PowD, fact_15_image__mono, fact_0__092_060open_062_092_060forall_062a_092_060in_062C_O_A_092_060forall_062b_092_060in_062C_O_Afst_Aa_A_092_060subseteq_062_Afst_Ab_A_092_060or_062_Afst_Ab_A_092_060subseteq_062_Afst_Aa_092_060close_062, fact_65_subsetD, fact_158_converse_Ocases, fact_19_subset__image__iff, fact_154_converse__inv__image, fact_62_equalityD2, fact_173_fst__swap, fact_206_top__empty__eq, fact_80_prod__induct6, fact_93_image__Fpow__mono, fact_204_BNF__Greatest__Fixpoint_Osubst__Pair, fact_147_pair__in__swap__image
% 171.95/144.73 % No. of inferences in proof: 410
% 171.95/144.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 144360 ms resp. 143790 ms w/o parsing
% 172.71/144.95 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 172.71/144.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------