%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP138^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n019.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 08:06:55 AM UTC 2026
% Result : Theorem 34.84s 13.19s
% Output : Refutation 36.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 288
% Syntax : Number of formulae : 578 ( 246 unt; 0 typ; 0 def)
% Number of atoms : 2266 ( 543 equ; 8 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 8278 ( 162 ~; 2 |; 138 &;7193 @)
% ( 0 <=>; 783 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 578 ( 578 >; 0 *; 0 +; 0 <<)
% Number of symbols : 47 ( 43 usr; 8 con; 0-6 aty)
% Number of variables : 2401 ( 203 ^;2138 !; 60 ?;2401 :)
% Comments :
%------------------------------------------------------------------------------
thf(paraco415392788lle_tv_type,type,
paraco415392788lle_tv: $tType ).
thf(paraco414474393lle_fm_type,type,
paraco414474393lle_fm: $tType ).
thf(char_type,type,
char: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(top_decl,type,
top:
!>[TA: $tType] : $o ).
thf(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(no_bot_decl,type,
no_bot:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(finite_lattice_decl,type,
finite_lattice:
!>[TA: $tType] : $o ).
thf(order_top_decl,type,
order_top:
!>[TA: $tType] : $o ).
thf(complete_Sup_decl,type,
complete_Sup:
!>[TA: $tType] : $o ).
thf(comple187826305attice_decl,type,
comple187826305attice:
!>[TA: $tType] : $o ).
thf(comple1035589618norder_decl,type,
comple1035589618norder:
!>[TA: $tType] : $o ).
thf(condit378418413attice_decl,type,
condit378418413attice:
!>[TA: $tType] : $o ).
thf(condit1037483654norder_decl,type,
condit1037483654norder:
!>[TA: $tType] : $o ).
thf(complete_Sup_Sup_decl,type,
complete_Sup_Sup:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(finite_Fpow_decl,type,
finite_Fpow:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( set @ TA ) ) ) ).
thf(swap_decl,type,
swap:
!>[TA: $tType,TB: $tType] : ( TB > TB > ( TB > TA ) > TB > TA ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(order_Greatest_decl,type,
order_Greatest:
!>[TA: $tType] : ( ( TA > $o ) > TA ) ).
thf(order_strict_mono_decl,type,
order_strict_mono:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > $o ) ).
thf(top_top_decl,type,
top_top:
!>[TA: $tType] : TA ).
thf(paraco506338565domain_decl,type,
paraco506338565domain: ( set @ nat ) > ( set @ paraco415392788lle_tv ) ).
thf(paraco876059933e_eval_decl,type,
paraco876059933e_eval: ( ( list @ char ) > paraco415392788lle_tv ) > paraco414474393lle_fm > paraco415392788lle_tv ).
thf(paraco2100061555le_Con_decl,type,
paraco2100061555le_Con: paraco414474393lle_fm > paraco414474393lle_fm > paraco414474393lle_fm ).
thf(paraco2084319816le_Eql_decl,type,
paraco2084319816le_Eql: paraco414474393lle_fm > paraco414474393lle_fm > paraco414474393lle_fm ).
thf(paraco1628874225le_Eql_decl,type,
paraco1628874225le_Eql: paraco414474393lle_fm > paraco414474393lle_fm > paraco414474393lle_fm ).
thf(paraco329115265le_Neg_decl,type,
paraco329115265le_Neg: paraco414474393lle_fm > paraco414474393lle_fm ).
thf(paraco27778325le_Pro_decl,type,
paraco27778325le_Pro: ( list @ char ) > paraco414474393lle_fm ).
thf(paraco251304083_Truth_decl,type,
paraco251304083_Truth: paraco414474393lle_fm ).
thf(paraco2040174112le_Det_decl,type,
paraco2040174112le_Det: $o > paraco415392788lle_tv ).
thf(paraco152590079rec_tv_decl,type,
paraco152590079rec_tv:
!>[TA: $tType] : ( ( $o > TA ) > ( nat > TA ) > paraco415392788lle_tv > TA ) ).
thf(paraco769098683_valid_decl,type,
paraco769098683_valid: paraco414474393lle_fm > $o ).
thf(paraco2086025920lid_in_decl,type,
paraco2086025920lid_in: ( set @ nat ) > paraco414474393lle_fm > $o ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(powp_decl,type,
powp:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) > $o ) ).
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(p_decl,type,
p: paraco414474393lle_fm ).
thf(89,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/sandbox2/benchmark/theBenchmark.p',fact_57_subset__iff) ).
thf(645,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)],[89]) ).
thf(51,axiom,
complete_Sup @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Complete__Lattices_OSup_16) ).
thf(479,plain,
complete_Sup @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(173,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_predicate1I) ).
thf(909,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( TA > $o ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(280,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_subset__refl) ).
thf(1295,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(228,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: set @ TB,C: TA] :
( ( complete_Sup_Sup @ ( TA > $o ) @ ( image @ TB @ ( TA > $o ) @ A @ B ) @ C )
=> ~ ! [D: TB] :
( ( member @ TB @ D @ B )
=> ~ ( A @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_SUP1__E) ).
thf(1110,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: set @ TB,C: TA] :
( ( complete_Sup_Sup @ ( TA > $o ) @ ( image @ TB @ ( TA > $o ) @ A @ B ) @ C )
=> ~ ! [D: TB] :
( ( member @ TB @ D @ B )
=> ~ ( A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(225,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA > $o,B: TA] :
( ( A @ B )
=> ( ! [C: TA] :
( ( A @ C )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ( order_Greatest @ TA @ A )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_Greatest__equality) ).
thf(1083,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA > $o,B: TA] :
( ( A @ B )
=> ( ! [C: TA] :
( ( A @ C )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ( order_Greatest @ TA @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(189,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/sandbox2/benchmark/theBenchmark.p',fact_41_le__funD) ).
thf(962,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)],[189]) ).
thf(252,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/sandbox2/benchmark/theBenchmark.p',fact_235_subrelI) ).
thf(1200,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)],[252]) ).
thf(102,axiom,
! [TA: $tType,A: set @ ( set @ TA )] : ( ord_less_eq @ ( set @ ( set @ TA ) ) @ A @ ( pow @ TA @ ( complete_Sup_Sup @ ( set @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_subset__Pow__Union) ).
thf(683,plain,
! [TA: $tType,A: set @ ( set @ TA )] : ( ord_less_eq @ ( set @ ( set @ TA ) ) @ A @ ( pow @ TA @ ( complete_Sup_Sup @ ( set @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(118,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_eq__iff) ).
thf(730,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(199,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/sandbox2/benchmark/theBenchmark.p',fact_51_imageI) ).
thf(994,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)],[199]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType] :
( ( swap @ TA @ TB )
= ( ^ [A: TA,B: TA] : ( swap @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_swap__commute) ).
thf(308,plain,
! [TA: $tType,TB: $tType] :
( ( swap @ TA @ TB )
= ( ^ [A: TA,B: TA] : ( swap @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(38,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/sandbox2/benchmark/theBenchmark.p',fact_238_ssubst__Pair__rhs) ).
thf(440,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)],[38]) ).
thf(159,axiom,
! [TA: $tType,A: set @ ( set @ TA ),B: set @ ( set @ TA )] :
( ! [C: set @ TA] :
( ( member @ ( set @ TA ) @ C @ A )
=> ? [D: set @ TA] :
( ( member @ ( set @ TA ) @ D @ B )
& ( ord_less_eq @ ( set @ TA ) @ C @ D ) ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( complete_Sup_Sup @ ( set @ TA ) @ A ) @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_Union__subsetI) ).
thf(861,plain,
! [TA: $tType,A: set @ ( set @ TA ),B: set @ ( set @ TA )] :
( ! [C: set @ TA] :
( ( member @ ( set @ TA ) @ C @ A )
=> ? [D: set @ TA] :
( ( member @ ( set @ TA ) @ D @ B )
& ( ord_less_eq @ ( set @ TA ) @ C @ D ) ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( complete_Sup_Sup @ ( set @ TA ) @ A ) @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(29,axiom,
! [TA: $tType,A: set @ ( TA > $o ),B: TA] :
( ( complete_Sup_Sup @ ( TA > $o ) @ A @ B )
=> ~ ! [C: TA > $o] :
( ( member @ ( TA > $o ) @ C @ A )
=> ~ ( C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_Sup1__E) ).
thf(408,plain,
! [TA: $tType,A: set @ ( TA > $o ),B: TA] :
( ( complete_Sup_Sup @ ( TA > $o ) @ A @ B )
=> ~ ! [C: TA > $o] :
( ( member @ ( TA > $o ) @ C @ A )
=> ~ ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(193,axiom,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco876059933e_eval @ A @ ( paraco2084319816le_Eql @ B @ C ) )
= ( paraco2040174112le_Det
@ ( ( paraco876059933e_eval @ A @ B )
= ( paraco876059933e_eval @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_eval__equality__simplify) ).
thf(977,plain,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco876059933e_eval @ A @ ( paraco2084319816le_Eql @ B @ C ) )
= ( paraco2040174112le_Det
@ ( ( paraco876059933e_eval @ A @ B )
= ( paraco876059933e_eval @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(63,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_subset__UNIV) ).
thf(523,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(77,axiom,
! [TA: $tType] : ( comple187826305attice @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_7) ).
thf(582,plain,
! [TA: $tType] : ( comple187826305attice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(163,axiom,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TB )
=> ! [A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ord_less_eq @ TB @ ( C @ A ) @ ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_SUP__upper) ).
thf(873,plain,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TB )
=> ! [A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ord_less_eq @ TB @ ( C @ A ) @ ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(41,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco2100061555le_Con @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_fm_Odistinct_I13_J) ).
thf(449,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco2100061555le_Con @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(285,axiom,
! [TA: $tType,A: set @ ( set @ TA ),B: set @ ( set @ TA )] :
( ( ord_less_eq @ ( set @ ( set @ TA ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( complete_Sup_Sup @ ( set @ TA ) @ A ) @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_Union__mono) ).
thf(1310,plain,
! [TA: $tType,A: set @ ( set @ TA ),B: set @ ( set @ TA )] :
( ( ord_less_eq @ ( set @ ( set @ TA ) ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( complete_Sup_Sup @ ( set @ TA ) @ A ) @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',fact_61_equalityE) ).
thf(550,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)],[67]) ).
thf(113,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_dual__order_Orefl) ).
thf(715,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(273,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/sandbox2/benchmark/theBenchmark.p',fact_39_le__funI) ).
thf(1275,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)],[273]) ).
thf(145,axiom,
! [TA: $tType] : ( condit378418413attice @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Conditionally__Complete__Lattices_Oconditionally__complete__lattice_6) ).
thf(814,plain,
! [TA: $tType] : ( condit378418413attice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(270,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_equalityD2) ).
thf(1260,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)],[270]) ).
thf(221,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/sandbox2/benchmark/theBenchmark.p',fact_100_Sup_OSUP__cong) ).
thf(1063,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)],[221]) ).
thf(125,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > ( set @ TB ),D: TA > ( set @ TB )] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ord_less_eq @ ( set @ TB ) @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ TB ) @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ C @ A ) ) @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_UN__mono) ).
thf(747,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > ( set @ TB ),D: TA > ( set @ TB )] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ord_less_eq @ ( set @ TB ) @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ TB ) @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ C @ A ) ) @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(174,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_UNIV__I) ).
thf(913,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(27,axiom,
preorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_18) ).
thf(404,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(202,axiom,
! [TA: $tType] :
( ( complete_Sup_Sup @ ( set @ TA ) )
= ( ^ [A: set @ ( set @ TA )] :
( collect @ TA
@ ^ [B: TA] : ( complete_Sup_Sup @ $o @ ( image @ ( set @ TA ) @ $o @ ( member @ TA @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_Sup__set__def) ).
thf(1001,plain,
! [TA: $tType] :
( ( complete_Sup_Sup @ ( set @ TA ) )
= ( ^ [A: set @ ( set @ TA )] :
( collect @ TA
@ ^ [B: TA] : ( complete_Sup_Sup @ $o @ ( image @ ( set @ TA ) @ $o @ ( member @ TA @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(234,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
& ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_conj__subset__def) ).
thf(1127,plain,
! [TA: $tType,A: set @ TA,B: TA > $o,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ B ) )
& ( ord_less_eq @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(134,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_le__cases) ).
thf(782,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(111,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(709,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(167,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > ( set @ TC ),B: TA > TB,C: set @ TA] :
( ( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TA @ ( set @ TC )
@ ^ [D: TA] : ( A @ ( B @ D ) )
@ C ) )
= ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ A @ ( image @ TA @ TB @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_UN__extend__simps_I10_J) ).
thf(885,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > ( set @ TC ),B: TA > TB,C: set @ TA] :
( ( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TA @ ( set @ TC )
@ ^ [D: TA] : ( A @ ( B @ D ) )
@ C ) )
= ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ A @ ( image @ TA @ TB @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(267,axiom,
! [TA: $tType] : ( order_top @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__top_9) ).
thf(1254,plain,
! [TA: $tType] : ( order_top @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: TB > $o] :
( ( ! [D: TB] :
( ( member @ TB @ D @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ! [E: TB] :
( ( member @ TB @ E @ ( A @ D ) )
=> ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_ball__UN) ).
thf(651,plain,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: TB > $o] :
( ( ! [D: TB] :
( ( member @ TB @ D @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ! [E: TB] :
( ( member @ TB @ E @ ( A @ D ) )
=> ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(219,axiom,
! [TA: $tType,A: set @ TA] :
( ( powp @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= ( ^ [B: set @ TA] : ( member @ ( set @ TA ) @ B @ ( pow @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_Powp__Pow__eq) ).
thf(1055,plain,
! [TA: $tType,A: set @ TA] :
( ( powp @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= ( ^ [B: set @ TA] : ( member @ ( set @ TA ) @ B @ ( pow @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(271,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/sandbox2/benchmark/theBenchmark.p',fact_87_surjD) ).
thf(1264,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)],[271]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(460,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(79,axiom,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_top__empty__eq) ).
thf(587,plain,
! [TA: $tType] :
( ( top_top @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(154,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_order__trans) ).
thf(838,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(176,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ TA @ ( complete_Sup_Sup @ TA @ A ) @ ( complete_Sup_Sup @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_Sup__subset__mono) ).
thf(917,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ TA @ ( complete_Sup_Sup @ TA @ A ) @ ( complete_Sup_Sup @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(126,axiom,
! [TA: $tType,A: set @ ( set @ TA ),B: set @ TA] :
( ! [C: set @ TA] :
( ( member @ ( set @ TA ) @ C @ A )
=> ( ord_less_eq @ ( set @ TA ) @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( complete_Sup_Sup @ ( set @ TA ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_Union__least) ).
thf(751,plain,
! [TA: $tType,A: set @ ( set @ TA ),B: set @ TA] :
( ! [C: set @ TA] :
( ( member @ ( set @ TA ) @ C @ A )
=> ( ord_less_eq @ ( set @ TA ) @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( complete_Sup_Sup @ ( set @ TA ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(140,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ ( complete_Sup_Sup @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_Sup__upper2) ).
thf(802,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ ( complete_Sup_Sup @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(24,axiom,
! [A: list @ char,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco27778325le_Pro @ A )
!= ( paraco2100061555le_Con @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_fm_Odistinct_I5_J) ).
thf(344,plain,
! [A: list @ char,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco27778325le_Pro @ A )
!= ( paraco2100061555le_Con @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(170,axiom,
condit378418413attice @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__lattice_1) ).
thf(902,plain,
condit378418413attice @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(237,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ! [D: TA] :
( ( A @ D )
=> ( ord_less_eq @ TA @ D @ B ) )
=> ( ! [D: TA] :
( ( A @ D )
=> ( ! [E: TA] :
( ( A @ E )
=> ( ord_less_eq @ TA @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_Greatest @ TA @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_GreatestI2__order) ).
thf(1147,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ! [D: TA] :
( ( A @ D )
=> ( ord_less_eq @ TA @ D @ B ) )
=> ( ! [D: TA] :
( ( A @ D )
=> ( ! [E: TA] :
( ( A @ E )
=> ( ord_less_eq @ TA @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_Greatest @ TA @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(162,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TB] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ ( swap @ TB @ TA @ B @ C @ A ) @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_surj__imp__surj__swap) ).
thf(870,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TB] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ ( swap @ TB @ TA @ B @ C @ A ) @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(192,axiom,
! [TA: $tType,TB: $tType] :
( ( complete_Sup @ TB )
=> ! [A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ C @ A ) )
= ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_SUP__cong) ).
thf(969,plain,
! [TA: $tType,TB: $tType] :
( ( complete_Sup @ TB )
=> ! [A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ C @ A ) )
= ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(207,axiom,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA )
& ( order @ TB ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_strict_mono @ TA @ TB @ A )
=> ( ( ord_less_eq @ TB @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_strict__mono__less__eq) ).
thf(1013,plain,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA )
& ( order @ TB ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_strict_mono @ TA @ TB @ A )
=> ( ( ord_less_eq @ TB @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,A: set @ ( TB > TA > $o ),B: TB,C: TA] :
( ( complete_Sup_Sup @ ( TB > TA > $o ) @ A @ B @ C )
=> ~ ! [D: TB > TA > $o] :
( ( member @ ( TB > TA > $o ) @ D @ A )
=> ~ ( D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_Sup2__E) ).
thf(416,plain,
! [TA: $tType,TB: $tType,A: set @ ( TB > TA > $o ),B: TB,C: TA] :
( ( complete_Sup_Sup @ ( TB > TA > $o ) @ A @ B @ C )
=> ~ ! [D: TB > TA > $o] :
( ( member @ ( TB > TA > $o ) @ D @ A )
=> ~ ( D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(18,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( ( paraco769098683_valid @ ( paraco2100061555le_Con @ A @ B ) )
= ( ( paraco769098683_valid @ A )
& ( paraco769098683_valid @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_conjunction) ).
thf(325,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( ( paraco769098683_valid @ ( paraco2100061555le_Con @ A @ B ) )
= ( ( paraco769098683_valid @ A )
& ( paraco769098683_valid @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(14,axiom,
order_top @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__top_17) ).
thf(316,plain,
order_top @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(142,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_dual__order_Otrans) ).
thf(806,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(191,axiom,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ ( set @ TA )] :
( ( complete_Sup_Sup @ ( set @ TB )
@ ( image @ ( set @ TA ) @ ( set @ TB )
@ ^ [C: set @ TA] : ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ C ) )
@ B ) )
= ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_UN__extend__simps_I8_J) ).
thf(966,plain,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ ( set @ TA )] :
( ( complete_Sup_Sup @ ( set @ TB )
@ ( image @ ( set @ TA ) @ ( set @ TB )
@ ^ [C: set @ TA] : ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ C ) )
@ B ) )
= ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(148,axiom,
! [TA: $tType] :
( ( comple1035589618norder @ TA )
=> ! [A: set @ TA] :
( ( ( complete_Sup_Sup @ TA @ A )
= ( top_top @ TA ) )
= ( ! [B: TA] :
( ( ord_less @ TA @ B @ ( top_top @ TA ) )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less @ TA @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_Sup__eq__top__iff) ).
thf(821,plain,
! [TA: $tType] :
( ( comple1035589618norder @ TA )
=> ! [A: set @ TA] :
( ( ( complete_Sup_Sup @ TA @ A )
= ( top_top @ TA ) )
= ( ! [B: TA] :
( ( ord_less @ TA @ B @ ( top_top @ TA ) )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(480,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(74,axiom,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA] :
( ord_less_eq @ ( set @ ( set @ TB ) )
@ ( complete_Sup_Sup @ ( set @ ( set @ TB ) )
@ ( image @ TA @ ( set @ ( set @ TB ) )
@ ^ [C: TA] : ( pow @ TB @ ( A @ C ) )
@ B ) )
@ ( pow @ TB @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_UN__Pow__subset) ).
thf(574,plain,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA] :
( ord_less_eq @ ( set @ ( set @ TB ) )
@ ( complete_Sup_Sup @ ( set @ ( set @ TB ) )
@ ( image @ TA @ ( set @ ( set @ TB ) )
@ ^ [C: TA] : ( pow @ TB @ ( A @ C ) )
@ B ) )
@ ( pow @ TB @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(209,axiom,
! [TA: $tType,A: set @ TA] :
~ ? [B: TA > ( set @ TA )] :
( ( image @ TA @ ( set @ TA ) @ B @ A )
= ( pow @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_Cantors__paradox) ).
thf(1020,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)],[209]) ).
thf(25,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( ( ( paraco329115265le_Neg @ A )
= ( paraco329115265le_Neg @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_fm_Oinject_I2_J) ).
thf(348,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( ( ( paraco329115265le_Neg @ A )
= ( paraco329115265le_Neg @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(246,axiom,
! [TA: $tType,A: set @ ( set @ TA )] :
( ( complete_Sup_Sup @ ( TA > $o )
@ ( image @ ( set @ TA ) @ ( TA > $o )
@ ^ [B: set @ TA,C: TA] : ( member @ TA @ C @ B )
@ A ) )
= ( ^ [B: TA] : ( member @ TA @ B @ ( complete_Sup_Sup @ ( set @ TA ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_SUP__Sup__eq) ).
thf(1183,plain,
! [TA: $tType,A: set @ ( set @ TA )] :
( ( complete_Sup_Sup @ ( TA > $o )
@ ( image @ ( set @ TA ) @ ( TA > $o )
@ ^ [B: set @ TA,C: TA] : ( member @ TA @ C @ B )
@ A ) )
= ( ^ [B: TA] : ( member @ TA @ B @ ( complete_Sup_Sup @ ( set @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(276,axiom,
! [TA: $tType,A: $o > TA,B: nat > TA,C: $o] :
( ( paraco152590079rec_tv @ TA @ A @ B @ ( paraco2040174112le_Det @ C ) )
= ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_tv_Osimps_I7_J) ).
thf(1283,plain,
! [TA: $tType,A: $o > TA,B: nat > TA,C: $o] :
( ( paraco152590079rec_tv @ TA @ A @ B @ ( paraco2040174112le_Det @ C ) )
= ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TB )
=> ! [A: TA > TB,B: TA > TB,C: set @ TA] :
( ! [D: TA] : ( ord_less_eq @ TB @ ( A @ D ) @ ( B @ D ) )
=> ( ord_less_eq @ TB @ ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ A @ C ) ) @ ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_SUP__mono_H) ).
thf(602,plain,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TB )
=> ! [A: TA > TB,B: TA > TB,C: set @ TA] :
( ! [D: TA] : ( ord_less_eq @ TB @ ( A @ D ) @ ( B @ D ) )
=> ( ord_less_eq @ TB @ ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ A @ C ) ) @ ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(241,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/sandbox2/benchmark/theBenchmark.p',fact_76_subset__image__iff) ).
thf(1169,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)],[241]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType] :
( ( order_top @ TA )
=> ( order_top @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__top) ).
thf(293,plain,
! [TA: $tType,TB: $tType] :
( ( order_top @ TA )
=> ( order_top @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA > TB] :
( ( swap @ TA @ TB @ A @ B @ C @ A )
= ( C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_swap__apply_I1_J) ).
thf(453,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA > TB] :
( ( swap @ TA @ TB @ A @ B @ C @ A )
= ( C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(231,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/sandbox2/benchmark/theBenchmark.p',fact_77_image__subset__iff) ).
thf(1119,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)],[231]) ).
thf(94,axiom,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
=> ( A
= ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_top_Oextremum__uniqueI) ).
thf(660,plain,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
=> ( A
= ( top_top @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(265,axiom,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: set @ TB,B: TB > TA,C: TA] :
( ! [D: TB] :
( ( member @ TB @ D @ A )
=> ( ord_less_eq @ TA @ ( B @ D ) @ C ) )
=> ( ! [D: TA] :
( ! [E: TB] :
( ( member @ TB @ E @ A )
=> ( ord_less_eq @ TA @ ( B @ E ) @ D ) )
=> ( ord_less_eq @ TA @ C @ D ) )
=> ( ( complete_Sup_Sup @ TA @ ( image @ TB @ TA @ B @ A ) )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_SUP__eqI) ).
thf(1242,plain,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: set @ TB,B: TB > TA,C: TA] :
( ! [D: TB] :
( ( member @ TB @ D @ A )
=> ( ord_less_eq @ TA @ ( B @ D ) @ C ) )
=> ( ! [D: TA] :
( ! [E: TB] :
( ( member @ TB @ E @ A )
=> ( ord_less_eq @ TA @ ( B @ E ) @ D ) )
=> ( ord_less_eq @ TA @ C @ D ) )
=> ( ( complete_Sup_Sup @ TA @ ( image @ TB @ TA @ B @ A ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(65,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/sandbox2/benchmark/theBenchmark.p',fact_52_Collect__mono__iff) ).
thf(527,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)],[65]) ).
thf(12,axiom,
condit378418413attice @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Conditionally__Complete__Lattices_Oconditionally__complete__lattice_14) ).
thf(312,plain,
condit378418413attice @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(223,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ TB,C: TB > ( set @ TA ),D: set @ TA] :
( ( member @ TB @ A @ B )
=> ( ! [E: TB] :
( ( member @ TB @ E @ B )
=> ( ( C @ E )
= D ) )
=> ( ( complete_Sup_Sup @ ( set @ TA ) @ ( image @ TB @ ( set @ TA ) @ C @ B ) )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_UN__constant__eq) ).
thf(1074,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ TB,C: TB > ( set @ TA ),D: set @ TA] :
( ( member @ TB @ A @ B )
=> ( ! [E: TB] :
( ( member @ TB @ E @ B )
=> ( ( C @ E )
= D ) )
=> ( ( complete_Sup_Sup @ ( set @ TA ) @ ( image @ TB @ ( set @ TA ) @ C @ B ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(100,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA,D: TA > $o] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_prop__restrict) ).
thf(678,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA,D: TA > $o] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(138,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/sandbox2/benchmark/theBenchmark.p',fact_43_ball__imageD) ).
thf(793,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)],[138]) ).
thf(129,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_linorder__wlog) ).
thf(761,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(62,axiom,
! [A: $o,B: $o] :
( ( ( paraco2040174112le_Det @ A )
= ( paraco2040174112le_Det @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_tv_Oinject_I1_J) ).
thf(512,plain,
! [A: $o,B: $o] :
( ( ( paraco2040174112le_Det @ A )
= ( paraco2040174112le_Det @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(185,axiom,
complete_Sup @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Complete__Lattices_OSup_2) ).
thf(942,plain,
complete_Sup @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(216,axiom,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_top1I) ).
thf(1042,plain,
! [TA: $tType,A: TA] : ( top_top @ ( TA > $o ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(7,axiom,
ord @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_22) ).
thf(302,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TB )
=> ! [A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ord_less_eq @ TB @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_less_eq @ TB @ ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ C @ A ) ) @ ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_SUP__subset__mono) ).
thf(598,plain,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TB )
=> ! [A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ord_less_eq @ TB @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_less_eq @ TB @ ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ C @ A ) ) @ ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(69,axiom,
( paraco769098683_valid
= ( ^ [A: paraco414474393lle_fm] :
! [B: ( list @ char ) > paraco415392788lle_tv] :
( ( paraco876059933e_eval @ B @ A )
= ( paraco2040174112le_Det @ $true ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_valid__def) ).
thf(561,plain,
( paraco769098683_valid
= ( ^ [A: paraco414474393lle_fm] :
! [B: ( list @ char ) > paraco415392788lle_tv] :
( ( paraco876059933e_eval @ B @ A )
= ( paraco2040174112le_Det @ $true ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
= ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_pred__equals__eq2) ).
thf(297,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
= ( ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(136,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/sandbox2/benchmark/theBenchmark.p',fact_118_PowI) ).
thf(788,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)],[136]) ).
thf(47,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( ( paraco2084319816le_Eql @ A @ B )
= ( paraco2084319816le_Eql @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_fm_Oinject_I4_J) ).
thf(467,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( ( paraco2084319816le_Eql @ A @ B )
= ( paraco2084319816le_Eql @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: set @ TB,C: TB > TC > TA > $o,D: TC,E: TA] :
( ( member @ TB @ A @ B )
=> ( ( C @ A @ D @ E )
=> ( complete_Sup_Sup @ ( TC > TA > $o ) @ ( image @ TB @ ( TC > TA > $o ) @ C @ B ) @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_SUP2__I) ).
thf(566,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB,B: set @ TB,C: TB > TC > TA > $o,D: TC,E: TA] :
( ( member @ TB @ A @ B )
=> ( ( C @ A @ D @ E )
=> ( complete_Sup_Sup @ ( TC > TA > $o ) @ ( image @ TB @ ( TC > TA > $o ) @ C @ B ) @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(165,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/sandbox2/benchmark/theBenchmark.p',fact_86_surjE) ).
thf(879,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)],[165]) ).
thf(244,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/sandbox2/benchmark/theBenchmark.p',fact_79_image__subsetI) ).
thf(1178,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)],[244]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comple187826305attice @ TB )
=> ! [A: set @ TC,B: set @ TA,C: TC > TB,D: TA > TB] :
( ! [E: TC] :
( ( member @ TC @ E @ A )
=> ? [F: TA] :
( ( member @ TA @ F @ B )
& ( ord_less_eq @ TB @ ( C @ E ) @ ( D @ F ) ) ) )
=> ( ord_less_eq @ TB @ ( complete_Sup_Sup @ TB @ ( image @ TC @ TB @ C @ A ) ) @ ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_SUP__mono) ).
thf(665,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comple187826305attice @ TB )
=> ! [A: set @ TC,B: set @ TA,C: TC > TB,D: TA > TB] :
( ! [E: TC] :
( ( member @ TC @ E @ A )
=> ? [F: TA] :
( ( member @ TA @ F @ B )
& ( ord_less_eq @ TB @ ( C @ E ) @ ( D @ F ) ) ) )
=> ( ord_less_eq @ TB @ ( complete_Sup_Sup @ TB @ ( image @ TC @ TB @ C @ A ) ) @ ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(211,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_UNIV__def) ).
thf(1027,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(43,axiom,
! [A: list @ char] :
( ( paraco27778325le_Pro @ A )
!= paraco251304083_Truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_fm_Odistinct_I1_J) ).
thf(456,plain,
! [A: list @ char] :
( ( paraco27778325le_Pro @ A )
!= paraco251304083_Truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(157,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: TA] :
( ( A
= ( B @ D ) )
=> ~ ( member @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_imageE) ).
thf(852,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: TA] :
( ( A
= ( B @ D ) )
=> ~ ( member @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(36,axiom,
! [A: list @ char,B: list @ char] :
( ( ( paraco27778325le_Pro @ A )
= ( paraco27778325le_Pro @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_fm_Oinject_I1_J) ).
thf(435,plain,
! [A: list @ char,B: list @ char] :
( ( ( paraco27778325le_Pro @ A )
= ( paraco27778325le_Pro @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA > TB] :
( ( swap @ TA @ TB @ A @ B @ C @ B )
= ( C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_swap__apply_I2_J) ).
thf(493,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA > TB] :
( ( swap @ TA @ TB @ A @ B @ C @ B )
= ( C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(254,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > ( set @ TB )] :
( ( member @ TA @ A @ B )
=> ( ( member @ TB @ C @ ( D @ A ) )
=> ( member @ TB @ C @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_UN__I) ).
thf(1210,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > ( set @ TB )] :
( ( member @ TA @ A @ B )
=> ( ( member @ TB @ C @ ( D @ A ) )
=> ( member @ TB @ C @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(76,axiom,
! [TA: $tType,A: TA,B: set @ ( set @ TA )] :
( ( member @ TA @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) )
=> ~ ! [C: set @ TA] :
( ( member @ TA @ A @ C )
=> ~ ( member @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_UnionE) ).
thf(578,plain,
! [TA: $tType,A: TA,B: set @ ( set @ TA )] :
( ( member @ TA @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) )
=> ~ ! [C: set @ TA] :
( ( member @ TA @ A @ C )
=> ~ ( member @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(264,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/sandbox2/benchmark/theBenchmark.p',fact_34_ord__le__eq__subst) ).
thf(1234,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)],[264]) ).
thf(262,axiom,
! [TA: $tType] :
( ( pow @ TA )
= ( ^ [A: set @ TA] :
( collect @ ( set @ TA )
@ ^ [B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_Pow__def) ).
thf(1227,plain,
! [TA: $tType] :
( ( pow @ TA )
= ( ^ [A: set @ TA] :
( collect @ ( set @ TA )
@ ^ [B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(194,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/sandbox2/benchmark/theBenchmark.p',fact_9_image__eqI) ).
thf(980,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)],[194]) ).
thf(204,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( set @ TA ),C: TA] :
( ( member @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_UnionI) ).
thf(1006,plain,
! [TA: $tType,A: set @ TA,B: set @ ( set @ TA ),C: TA] :
( ( member @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(32,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( ( paraco2100061555le_Con @ A @ B )
= ( paraco2100061555le_Con @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_fm_Oinject_I3_J) ).
thf(420,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( ( paraco2100061555le_Con @ A @ B )
= ( paraco2100061555le_Con @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(58,axiom,
! [TA: $tType,A: ( set @ TA ) > TA,B: set @ TA] :
( ( A
@ ( image @ TA @ TA
@ ^ [C: TA] : C
@ B ) )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Sup_OSUP__identity__eq) ).
thf(499,plain,
! [TA: $tType,A: ( set @ TA ) > TA,B: set @ TA] :
( ( A
@ ( image @ TA @ TA
@ ^ [C: TA] : C
@ B ) )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(197,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( complete_Sup @ TC )
=> ! [A: TA > TB > TC,B: set @ TA,C: TB] :
( ( complete_Sup_Sup @ ( TB > TC ) @ ( image @ TA @ ( TB > TC ) @ A @ B ) @ C )
= ( complete_Sup_Sup @ TC
@ ( image @ TA @ TC
@ ^ [D: TA] : ( A @ D @ C )
@ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_SUP__apply) ).
thf(989,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( complete_Sup @ TC )
=> ! [A: TA > TB > TC,B: set @ TA,C: TB] :
( ( complete_Sup_Sup @ ( TB > TC ) @ ( image @ TA @ ( TB > TC ) @ A @ B ) @ C )
= ( complete_Sup_Sup @ TC
@ ( image @ TA @ TC
@ ^ [D: TA] : ( A @ D @ C )
@ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(158,axiom,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: set @ TB,B: TB > TA,C: TA] :
( ! [D: TB] :
( ( member @ TB @ D @ A )
=> ( ord_less_eq @ TA @ ( B @ D ) @ C ) )
=> ( ord_less_eq @ TA @ ( complete_Sup_Sup @ TA @ ( image @ TB @ TA @ B @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_SUP__least) ).
thf(857,plain,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: set @ TB,B: TB > TA,C: TA] :
( ! [D: TB] :
( ( member @ TB @ D @ A )
=> ( ord_less_eq @ TA @ ( B @ D ) @ C ) )
=> ( ord_less_eq @ TA @ ( complete_Sup_Sup @ TA @ ( image @ TB @ TA @ B @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(269,axiom,
condit1037483654norder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder) ).
thf(1259,plain,
condit1037483654norder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ( condit378418413attice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Conditionally__Complete__Lattices_Oconditionally__complete__lattice) ).
thf(317,plain,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ( condit378418413attice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(19,axiom,
! [A: list @ char,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco27778325le_Pro @ A )
!= ( paraco2084319816le_Eql @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_fm_Odistinct_I7_J) ).
thf(328,plain,
! [A: list @ char,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco27778325le_Pro @ A )
!= ( paraco2084319816le_Eql @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(22,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco329115265le_Neg @ A )
!= ( paraco1628874225le_Eql @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_fm_Odistinct_I23_J) ).
thf(339,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco329115265le_Neg @ A )
!= ( paraco1628874225le_Eql @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(245,axiom,
preorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_3) ).
thf(1182,plain,
preorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(97,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: set @ TA,B: TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ ( complete_Sup_Sup @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_Sup__least) ).
thf(669,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: set @ TA,B: TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ ( complete_Sup_Sup @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(256,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_13) ).
thf(1214,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(215,axiom,
! [TA: $tType,A: set @ ( set @ TA ),B: TA > $o] :
( ( ? [C: TA] :
( ( member @ TA @ C @ ( complete_Sup_Sup @ ( set @ TA ) @ A ) )
& ( B @ C ) ) )
= ( ? [C: set @ TA] :
( ( member @ ( set @ TA ) @ C @ A )
& ? [D: TA] :
( ( member @ TA @ D @ C )
& ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_UN__ball__bex__simps_I3_J) ).
thf(1039,plain,
! [TA: $tType,A: set @ ( set @ TA ),B: TA > $o] :
( ( ? [C: TA] :
( ( member @ TA @ C @ ( complete_Sup_Sup @ ( set @ TA ) @ A ) )
& ( B @ C ) ) )
= ( ? [C: set @ TA] :
( ( member @ ( set @ TA ) @ C @ A )
& ? [D: TA] :
( ( member @ TA @ D @ C )
& ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(110,axiom,
! [TA: $tType] :
( ( complete_Sup_Sup @ ( set @ TA ) @ ( top_top @ ( set @ ( set @ TA ) ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_Union__UNIV) ).
thf(706,plain,
! [TA: $tType] :
( ( complete_Sup_Sup @ ( set @ TA ) @ ( top_top @ ( set @ ( set @ TA ) ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(279,axiom,
! [TA: $tType,TB: $tType] :
( ( complete_Sup @ TB )
=> ( ( complete_Sup_Sup @ ( TA > TB ) )
= ( ^ [A: set @ ( TA > TB ),B: TA] :
( complete_Sup_Sup @ TB
@ ( image @ ( TA > TB ) @ TB
@ ^ [C: TA > TB] : ( C @ B )
@ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_Sup__fun__def) ).
thf(1292,plain,
! [TA: $tType,TB: $tType] :
( ( complete_Sup @ TB )
=> ( ( complete_Sup_Sup @ ( TA > TB ) )
= ( ^ [A: set @ ( TA > TB ),B: TA] :
( complete_Sup_Sup @ TB
@ ( image @ ( TA > TB ) @ TB
@ ^ [C: TA > TB] : ( C @ B )
@ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(182,axiom,
( paraco2086025920lid_in
= ( ^ [A: set @ nat,B: paraco414474393lle_fm] :
! [C: ( list @ char ) > paraco415392788lle_tv] :
( ( ord_less_eq @ ( set @ paraco415392788lle_tv ) @ ( image @ ( list @ char ) @ paraco415392788lle_tv @ C @ ( top_top @ ( set @ ( list @ char ) ) ) ) @ ( paraco506338565domain @ A ) )
=> ( ( paraco876059933e_eval @ C @ B )
= ( paraco2040174112le_Det @ $true ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_valid__in__def) ).
thf(933,plain,
( paraco2086025920lid_in
= ( ^ [A: set @ nat,B: paraco414474393lle_fm] :
! [C: ( list @ char ) > paraco415392788lle_tv] :
( ( ord_less_eq @ ( set @ paraco415392788lle_tv ) @ ( image @ ( list @ char ) @ paraco415392788lle_tv @ C @ ( top_top @ ( set @ ( list @ char ) ) ) ) @ ( paraco506338565domain @ A ) )
=> ( ( paraco876059933e_eval @ C @ B )
= ( paraco2040174112le_Det @ $true ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(208,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/sandbox2/benchmark/theBenchmark.p',fact_129_image__Pow__surj) ).
thf(1016,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)],[208]) ).
thf(80,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/sandbox2/benchmark/theBenchmark.p',fact_112_image__Pow__mono) ).
thf(590,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)],[80]) ).
thf(229,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/sandbox2/benchmark/theBenchmark.p',fact_40_le__funE) ).
thf(1114,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)],[229]) ).
thf(281,axiom,
! [TA: $tType,A: set @ TA] :
( ( complete_Sup_Sup @ ( set @ TA ) @ ( pow @ TA @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_Union__Pow__eq) ).
thf(1297,plain,
! [TA: $tType,A: set @ TA] :
( ( complete_Sup_Sup @ ( set @ TA ) @ ( pow @ TA @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(92,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( ord_less_eq @ TA @ C @ D ) ) )
=> ( ord_less_eq @ TA @ ( complete_Sup_Sup @ TA @ A ) @ ( complete_Sup_Sup @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_Sup__mono) ).
thf(654,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( ord_less_eq @ TA @ C @ D ) ) )
=> ( ord_less_eq @ TA @ ( complete_Sup_Sup @ TA @ A ) @ ( complete_Sup_Sup @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(249,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ ( set @ TA ) ) @ ( finite_Fpow @ TA @ A ) @ ( pow @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_Fpow__subset__Pow) ).
thf(1192,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)],[249]) ).
thf(195,axiom,
( ( paraco506338565domain
@ ( collect @ nat
@ ^ [A: nat] : $true ) )
= ( collect @ paraco415392788lle_tv
@ ^ [A: paraco415392788lle_tv] : $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_universal__domain) ).
thf(984,plain,
( ( paraco506338565domain
@ ( collect @ nat
@ ^ [A: nat] : $true ) )
= ( collect @ paraco415392788lle_tv
@ ^ [A: paraco415392788lle_tv] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(133,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_dual__order_Oantisym) ).
thf(779,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(61,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/sandbox2/benchmark/theBenchmark.p',fact_7_subsetI) ).
thf(508,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)],[61]) ).
thf(11,axiom,
comple187826305attice @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_15) ).
thf(311,plain,
comple187826305attice @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(178,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > ( set @ TB )] :
( ( member @ TA @ A @ B )
=> ( ord_less_eq @ ( set @ TB ) @ ( C @ A ) @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_UN__upper) ).
thf(921,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > ( set @ TB )] :
( ( member @ TA @ A @ B )
=> ( ord_less_eq @ ( set @ TB ) @ ( C @ A ) @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(277,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/sandbox2/benchmark/theBenchmark.p',fact_50_image__iff) ).
thf(1286,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)],[277]) ).
thf(240,axiom,
! [TA: $tType] : ( top @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Otop_12) ).
thf(1167,plain,
! [TA: $tType] : ( top @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(66,axiom,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco876059933e_eval @ A @ C ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco2040174112le_Det @ $true ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco876059933e_eval @ A @ C ) )
=> ( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco876059933e_eval @ A @ C ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( ( ( paraco876059933e_eval @ A @ C )
= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco876059933e_eval @ A @ B ) ) )
& ( ( ( paraco876059933e_eval @ A @ C )
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco2040174112le_Det @ $false ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ C ) ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco2040174112le_Det @ $false ) )
=> ( ( ( ( paraco876059933e_eval @ A @ C )
= ( paraco2040174112le_Det @ $false ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ B ) ) ) )
& ( ( ( paraco876059933e_eval @ A @ C )
!= ( paraco2040174112le_Det @ $false ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco2040174112le_Det @ $false ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_eval__equality) ).
thf(530,plain,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco876059933e_eval @ A @ C ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco2040174112le_Det @ $true ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco876059933e_eval @ A @ C ) )
=> ( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco876059933e_eval @ A @ C ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( ( ( paraco876059933e_eval @ A @ C )
= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco876059933e_eval @ A @ B ) ) )
& ( ( ( paraco876059933e_eval @ A @ C )
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco2040174112le_Det @ $false ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ C ) ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco2040174112le_Det @ $false ) )
=> ( ( ( ( paraco876059933e_eval @ A @ C )
= ( paraco2040174112le_Det @ $false ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ B ) ) ) )
& ( ( ( paraco876059933e_eval @ A @ C )
!= ( paraco2040174112le_Det @ $false ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco1628874225le_Eql @ B @ C ) )
= ( paraco2040174112le_Det @ $false ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(168,axiom,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_top__conj_I2_J) ).
thf(888,plain,
! [TA: $tType,A: $o,B: TA] :
( ( A
& ( top_top @ ( TA > $o ) @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(23,axiom,
order @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_20) ).
thf(343,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(288,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ( collect @ TB
@ ^ [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) ) )
= ( image @ TA @ TB @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_Compr__image__eq) ).
thf(1318,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ( collect @ TB
@ ^ [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) ) )
= ( image @ TA @ TB @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(68,axiom,
! [TA: $tType,A: ( set @ TA ) > TA,B: set @ TA] :
( ( A
@ ( image @ TA @ TA
@ ^ [C: TA] : C
@ B ) )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_Inf_OINF__identity__eq) ).
thf(558,plain,
! [TA: $tType,A: ( set @ TA ) > TA,B: set @ TA] :
( ( A
@ ( image @ TA @ TA
@ ^ [C: TA] : C
@ B ) )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(222,axiom,
! [TA: $tType,TB: $tType] :
( ( complete_Sup @ TB )
=> ( ( complete_Sup_Sup @ ( TA > TB ) )
= ( ^ [A: set @ ( TA > TB ),B: TA] :
( complete_Sup_Sup @ TB
@ ( image @ ( TA > TB ) @ TB
@ ^ [C: TA > TB] : ( C @ B )
@ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_Sup__apply) ).
thf(1071,plain,
! [TA: $tType,TB: $tType] :
( ( complete_Sup @ TB )
=> ( ( complete_Sup_Sup @ ( TA > TB ) )
= ( ^ [A: set @ ( TA > TB ),B: TA] :
( complete_Sup_Sup @ TB
@ ( image @ ( TA > TB ) @ TB
@ ^ [C: TA > TB] : ( C @ B )
@ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(30,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco1628874225le_Eql @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_fm_Odistinct_I17_J) ).
thf(412,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco1628874225le_Eql @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(149,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/sandbox2/benchmark/theBenchmark.p',fact_38_le__fun__def) ).
thf(824,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)],[149]) ).
thf(124,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/sandbox2/benchmark/theBenchmark.p',fact_54_subset__trans) ).
thf(745,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)],[124]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA > TB] :
( ( swap @ TA @ TB @ A @ B @ ( swap @ TA @ TB @ A @ B @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_swap__nilpotent) ).
thf(444,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA > TB] :
( ( swap @ TA @ TB @ A @ B @ ( swap @ TA @ TB @ A @ B @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(119,axiom,
! [TA: $tType] :
( ( comple1035589618norder @ TA )
=> ! [A: TA,B: set @ TA] :
( ( ord_less_eq @ TA @ A @ ( complete_Sup_Sup @ TA @ B ) )
= ( ! [C: TA] :
( ( ord_less @ TA @ C @ A )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( ord_less @ TA @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_le__Sup__iff) ).
thf(733,plain,
! [TA: $tType] :
( ( comple1035589618norder @ TA )
=> ! [A: TA,B: set @ TA] :
( ( ord_less_eq @ TA @ A @ ( complete_Sup_Sup @ TA @ B ) )
= ( ! [C: TA] :
( ( ord_less @ TA @ C @ A )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( ord_less @ TA @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: TB > $o] :
( ( ? [D: TB] :
( ( member @ TB @ D @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ B )
& ? [E: TB] :
( ( member @ TB @ E @ ( A @ D ) )
& ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_bex__UN) ).
thf(584,plain,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: TB > $o] :
( ( ? [D: TB] :
( ( member @ TB @ D @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ B )
& ? [E: TB] :
( ( member @ TB @ E @ ( A @ D ) )
& ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(147,axiom,
! [TA: $tType] : ( complete_Sup @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Complete__Lattices_OSup_8) ).
thf(819,plain,
! [TA: $tType] : ( complete_Sup @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(33,axiom,
! [A: list @ char,B: paraco414474393lle_fm] :
( ( paraco27778325le_Pro @ A )
!= ( paraco329115265le_Neg @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_fm_Odistinct_I3_J) ).
thf(423,plain,
! [A: list @ char,B: paraco414474393lle_fm] :
( ( paraco27778325le_Pro @ A )
!= ( paraco329115265le_Neg @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(106,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/sandbox2/benchmark/theBenchmark.p',fact_106_image__Fpow__mono) ).
thf(694,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)],[106]) ).
thf(123,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_iso__tuple__UNIV__I) ).
thf(743,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(164,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_order__subst1) ).
thf(875,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(268,axiom,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: TB > $o] :
( ( ? [D: TB] :
( ( member @ TB @ D @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ B )
& ? [E: TB] :
( ( member @ TB @ E @ ( A @ D ) )
& ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_UN__ball__bex__simps_I4_J) ).
thf(1256,plain,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: TB > $o] :
( ( ? [D: TB] :
( ( member @ TB @ D @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ B )
& ? [E: TB] :
( ( member @ TB @ E @ ( A @ D ) )
& ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(156,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comple187826305attice @ TB )
=> ! [A: set @ TC,B: set @ TA,C: TC > TB,D: TA > TB] :
( ! [E: TC] :
( ( member @ TC @ E @ A )
=> ? [F: TA] :
( ( member @ TA @ F @ B )
& ( ord_less_eq @ TB @ ( C @ E ) @ ( D @ F ) ) ) )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ? [F: TC] :
( ( member @ TC @ F @ A )
& ( ord_less_eq @ TB @ ( D @ E ) @ ( C @ F ) ) ) )
=> ( ( complete_Sup_Sup @ TB @ ( image @ TC @ TB @ C @ A ) )
= ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_SUP__eq) ).
thf(843,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comple187826305attice @ TB )
=> ! [A: set @ TC,B: set @ TA,C: TC > TB,D: TA > TB] :
( ! [E: TC] :
( ( member @ TC @ E @ A )
=> ? [F: TA] :
( ( member @ TA @ F @ B )
& ( ord_less_eq @ TB @ ( C @ E ) @ ( D @ F ) ) ) )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ? [F: TC] :
( ( member @ TC @ F @ A )
& ( ord_less_eq @ TB @ ( D @ E ) @ ( C @ F ) ) ) )
=> ( ( complete_Sup_Sup @ TB @ ( image @ TC @ TB @ C @ A ) )
= ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(233,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_order__refl) ).
thf(1125,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(13,axiom,
! [TA: $tType] :
( ( comple1035589618norder @ TA )
=> ! [A: TA,B: set @ TA] :
( ( ord_less @ TA @ A @ ( complete_Sup_Sup @ TA @ B ) )
= ( ? [C: TA] :
( ( member @ TA @ C @ B )
& ( ord_less @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_less__Sup__iff) ).
thf(313,plain,
! [TA: $tType] :
( ( comple1035589618norder @ TA )
=> ! [A: TA,B: set @ TA] :
( ( ord_less @ TA @ A @ ( complete_Sup_Sup @ TA @ B ) )
= ( ? [C: TA] :
( ( member @ TA @ C @ B )
& ( ord_less @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(286,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/sandbox2/benchmark/theBenchmark.p',fact_24_ord__eq__le__trans) ).
thf(1312,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)],[286]) ).
thf(261,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_order__class_Oorder_Oeq__iff) ).
thf(1224,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(220,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E ) ) )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_subset__CollectI) ).
thf(1058,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ A )
& ( C @ E ) ) )
@ ( collect @ TA
@ ^ [E: TA] :
( ( member @ TA @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(227,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/sandbox2/benchmark/theBenchmark.p',fact_119_Pow__iff) ).
thf(1107,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)],[227]) ).
thf(46,axiom,
linorder @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_19) ).
thf(466,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(226,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_le__cases3) ).
thf(1092,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(177,axiom,
( ( complete_Sup_Sup @ $o )
= ( member @ $o @ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_Sup__bool__def) ).
thf(919,plain,
( ( complete_Sup_Sup @ $o )
= ( member @ $o @ $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(141,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/sandbox2/benchmark/theBenchmark.p',fact_62_subsetD) ).
thf(804,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)],[141]) ).
thf(85,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/sandbox2/benchmark/theBenchmark.p',fact_53_set__eq__subset) ).
thf(604,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)],[85]) ).
thf(250,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > ( set @ TB ),C: set @ TA] :
( ( image @ TB @ TC @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) )
= ( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TA @ ( set @ TC )
@ ^ [D: TA] : ( image @ TB @ TC @ A @ ( B @ D ) )
@ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_image__UN) ).
thf(1194,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > ( set @ TB ),C: set @ TA] :
( ( image @ TB @ TC @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) )
= ( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TA @ ( set @ TC )
@ ^ [D: TA] : ( image @ TB @ TC @ A @ ( B @ D ) )
@ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(151,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/sandbox2/benchmark/theBenchmark.p',fact_128_Pow__mono) ).
thf(831,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)],[151]) ).
thf(135,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TA > $o,B: set @ TB,C: TC,D: TA] :
( ( complete_Sup_Sup @ ( TC > TA > $o ) @ ( image @ TB @ ( TC > TA > $o ) @ A @ B ) @ C @ D )
=> ~ ! [E: TB] :
( ( member @ TB @ E @ B )
=> ~ ( A @ E @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_SUP2__E) ).
thf(784,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC > TA > $o,B: set @ TB,C: TC,D: TA] :
( ( complete_Sup_Sup @ ( TC > TA > $o ) @ ( image @ TB @ ( TC > TA > $o ) @ A @ B ) @ C @ D )
=> ~ ! [E: TB] :
( ( member @ TB @ E @ B )
=> ~ ( A @ E @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(120,axiom,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_top__conj_I1_J) ).
thf(736,plain,
! [TA: $tType,A: TA,B: $o] :
( ( ( top_top @ ( TA > $o ) @ A )
& B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(200,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( image @ TA @ TB @ ( swap @ TA @ TB @ A @ C @ D ) @ B )
= ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_swap__image__eq) ).
thf(996,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( image @ TA @ TB @ ( swap @ TA @ TB @ A @ C @ D ) @ B )
= ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(243,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > ( set @ TB ),B: TC > ( set @ TA ),C: TC,D: set @ TB] :
( ( ord_less_eq @ ( set @ TB ) @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ ( B @ C ) ) ) @ D )
= ( ord_less_eq @ ( set @ TA ) @ ( B @ C )
@ ( collect @ TA
@ ^ [E: TA] : ( ord_less_eq @ ( set @ TB ) @ ( A @ E ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_UN__image__subset) ).
thf(1175,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > ( set @ TB ),B: TC > ( set @ TA ),C: TC,D: set @ TB] :
( ( ord_less_eq @ ( set @ TB ) @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ ( B @ C ) ) ) @ D )
= ( ord_less_eq @ ( set @ TA ) @ ( B @ C )
@ ( collect @ TA
@ ^ [E: TA] : ( ord_less_eq @ ( set @ TB ) @ ( A @ E ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(8,axiom,
top @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Otop_21) ).
thf(303,plain,
top @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(232,axiom,
! [TA: $tType,TB: $tType,A: TB > ( set @ TA ),B: set @ TB] :
( ( complete_Sup_Sup @ ( TA > $o )
@ ( image @ TB @ ( TA > $o )
@ ^ [C: TB,D: TA] : ( member @ TA @ D @ ( A @ C ) )
@ B ) )
= ( ^ [C: TA] : ( member @ TA @ C @ ( complete_Sup_Sup @ ( set @ TA ) @ ( image @ TB @ ( set @ TA ) @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_SUP__UN__eq) ).
thf(1122,plain,
! [TA: $tType,TB: $tType,A: TB > ( set @ TA ),B: set @ TB] :
( ( complete_Sup_Sup @ ( TA > $o )
@ ( image @ TB @ ( TA > $o )
@ ^ [C: TB,D: TA] : ( member @ TA @ D @ ( A @ C ) )
@ B ) )
= ( ^ [C: TA] : ( member @ TA @ C @ ( complete_Sup_Sup @ ( set @ TA ) @ ( image @ TB @ ( set @ TA ) @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: set @ ( TB > TA > $o ),C: TB,D: TA] :
( ( member @ ( TB > TA > $o ) @ A @ B )
=> ( ( A @ C @ D )
=> ( complete_Sup_Sup @ ( TB > TA > $o ) @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_Sup2__I) ).
thf(477,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: set @ ( TB > TA > $o ),C: TB,D: TA] :
( ( member @ ( TB > TA > $o ) @ A @ B )
=> ( ( A @ C @ D )
=> ( complete_Sup_Sup @ ( TB > TA > $o ) @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(144,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) )
= ( image @ TA @ TC
@ ^ [D: TA] : ( A @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_image__image) ).
thf(811,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) )
= ( image @ TA @ TC
@ ^ [D: TA] : ( A @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(224,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB,C: TB > TA] :
( ( ( image @ TB @ TA @ ( swap @ TB @ TA @ A @ B @ C ) @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
= ( ( image @ TB @ TA @ C @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_surj__swap__iff) ).
thf(1080,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB,C: TB > TA] :
( ( ( image @ TB @ TA @ ( swap @ TB @ TA @ A @ B @ C ) @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
= ( ( image @ TB @ TA @ C @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(128,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(758,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(146,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/sandbox2/benchmark/theBenchmark.p',fact_84_surj__def) ).
thf(816,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)],[146]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ( comple187826305attice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Complete__Lattices_Ocomplete__lattice) ).
thf(323,plain,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ( comple187826305attice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(190,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/sandbox2/benchmark/theBenchmark.p',fact_63_in__mono) ).
thf(964,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)],[190]) ).
thf(175,axiom,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( top_top @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_top__greatest) ).
thf(915,plain,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(186,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/sandbox2/benchmark/theBenchmark.p',fact_44_image__cong) ).
thf(943,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)],[186]) ).
thf(45,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( paraco2084319816le_Eql @ A @ B )
!= ( paraco1628874225le_Eql @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_fm_Odistinct_I29_J) ).
thf(462,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( paraco2084319816le_Eql @ A @ B )
!= ( paraco1628874225le_Eql @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(139,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_top__apply) ).
thf(799,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(238,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/sandbox2/benchmark/theBenchmark.p',fact_85_surjI) ).
thf(1162,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)],[238]) ).
thf(103,axiom,
! [TA: $tType,A: TA,B: set @ ( set @ TA )] :
( ( member @ TA @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) )
= ( ? [C: set @ TA] :
( ( member @ ( set @ TA ) @ C @ B )
& ( member @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_Union__iff) ).
thf(685,plain,
! [TA: $tType,A: TA,B: set @ ( set @ TA )] :
( ( member @ TA @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) )
= ( ? [C: set @ TA] :
( ( member @ ( set @ TA ) @ C @ B )
& ( member @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(161,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_UNIV__witness) ).
thf(868,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(196,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/sandbox2/benchmark/theBenchmark.p',fact_60_subset__eq) ).
thf(986,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)],[196]) ).
thf(70,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_top__set__def) ).
thf(563,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(266,axiom,
! [A: product_prod @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm] :
( ! [B: ( list @ char ) > paraco415392788lle_tv,C: list @ char] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ ( paraco27778325le_Pro @ C ) ) )
=> ( ! [B: ( list @ char ) > paraco415392788lle_tv] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ paraco251304083_Truth ) )
=> ( ! [B: ( list @ char ) > paraco415392788lle_tv,C: paraco414474393lle_fm] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ ( paraco329115265le_Neg @ C ) ) )
=> ( ! [B: ( list @ char ) > paraco415392788lle_tv,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ ( paraco2100061555le_Con @ C @ D ) ) )
=> ( ! [B: ( list @ char ) > paraco415392788lle_tv,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ ( paraco2084319816le_Eql @ C @ D ) ) )
=> ~ ! [B: ( list @ char ) > paraco415392788lle_tv,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ ( paraco1628874225le_Eql @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_eval_Ocases) ).
thf(1250,plain,
! [A: product_prod @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm] :
( ! [B: ( list @ char ) > paraco415392788lle_tv,C: list @ char] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ ( paraco27778325le_Pro @ C ) ) )
=> ( ! [B: ( list @ char ) > paraco415392788lle_tv] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ paraco251304083_Truth ) )
=> ( ! [B: ( list @ char ) > paraco415392788lle_tv,C: paraco414474393lle_fm] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ ( paraco329115265le_Neg @ C ) ) )
=> ( ! [B: ( list @ char ) > paraco415392788lle_tv,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ ( paraco2100061555le_Con @ C @ D ) ) )
=> ( ! [B: ( list @ char ) > paraco415392788lle_tv,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ ( paraco2084319816le_Eql @ C @ D ) ) )
=> ~ ! [B: ( list @ char ) > paraco415392788lle_tv,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( A
!= ( product_Pair @ ( ( list @ char ) > paraco415392788lle_tv ) @ paraco414474393lle_fm @ B @ ( paraco1628874225le_Eql @ C @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(35,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco2084319816le_Eql @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_fm_Odistinct_I15_J) ).
thf(431,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco2084319816le_Eql @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(93,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_linear) ).
thf(658,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(131,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ ( set @ TA )] :
( ( image @ TA @ TB @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) )
= ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ ( set @ TA ) @ ( set @ TB ) @ ( image @ TA @ TB @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_image__Union) ).
thf(768,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ ( set @ TA )] :
( ( image @ TA @ TB @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) )
= ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ ( set @ TA ) @ ( set @ TB ) @ ( image @ TA @ TB @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(150,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/sandbox2/benchmark/theBenchmark.p',fact_42_rev__image__eqI) ).
thf(827,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)],[150]) ).
thf(87,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/sandbox2/benchmark/theBenchmark.p',fact_49_bex__imageD) ).
thf(636,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)],[87]) ).
thf(217,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/sandbox2/benchmark/theBenchmark.p',fact_35_ord__eq__le__subst) ).
thf(1044,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)],[217]) ).
thf(60,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/sandbox2/benchmark/theBenchmark.p',fact_8_subset__antisym) ).
thf(505,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)],[60]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Otop) ).
thf(438,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(213,axiom,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA )
& ( linorder @ TB ) )
=> ! [A: TB > TA,B: TA > TB] :
( ( order_strict_mono @ TB @ TA @ A )
=> ( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ! [C: TB] :
( ( B @ ( A @ C ) )
= C )
=> ( order_strict_mono @ TA @ TB @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_strict__mono__inv) ).
thf(1034,plain,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA )
& ( linorder @ TB ) )
=> ! [A: TB > TA,B: TA > TB] :
( ( order_strict_mono @ TB @ TA @ A )
=> ( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ! [C: TB] :
( ( B @ ( A @ C ) )
= C )
=> ( order_strict_mono @ TA @ TB @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA,D: TA > TB] :
( ( A != B )
=> ( ( C != B )
=> ( ( swap @ TA @ TB @ A @ C @ ( swap @ TA @ TB @ C @ B @ ( swap @ TA @ TB @ A @ C @ D ) ) )
= ( swap @ TA @ TB @ A @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_swap__triple) ).
thf(490,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA,D: TA > TB] :
( ( A != B )
=> ( ( C != B )
=> ( ( swap @ TA @ TB @ A @ C @ ( swap @ TA @ TB @ C @ B @ ( swap @ TA @ TB @ A @ C @ D ) ) )
= ( swap @ TA @ TB @ A @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(283,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_eq__refl) ).
thf(1304,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(101,axiom,
! [TA: $tType] :
( ( pow @ TA @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_Pow__UNIV) ).
thf(680,plain,
! [TA: $tType] :
( ( pow @ TA @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(95,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_order_Otrans) ).
thf(663,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(274,axiom,
! [TA: $tType] :
( ( complete_Sup @ TA )
=> ! [A: set @ TA] :
( ( complete_Sup_Sup @ TA
@ ( image @ TA @ TA
@ ^ [B: TA] : B
@ A ) )
= ( complete_Sup_Sup @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_SUP__identity__eq) ).
thf(1277,plain,
! [TA: $tType] :
( ( complete_Sup @ TA )
=> ! [A: set @ TA] :
( ( complete_Sup_Sup @ TA
@ ( image @ TA @ TA
@ ^ [B: TA] : B
@ A ) )
= ( complete_Sup_Sup @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > ( set @ TC ),B: TA > ( set @ TB ),C: set @ TA] :
( ( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TA @ ( set @ TC )
@ ^ [D: TA] : ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ A @ ( B @ D ) ) )
@ C ) )
= ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_UN__extend__simps_I9_J) ).
thf(648,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > ( set @ TC ),B: TA > ( set @ TB ),C: set @ TA] :
( ( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TA @ ( set @ TC )
@ ^ [D: TA] : ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ A @ ( B @ D ) ) )
@ C ) )
= ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(184,axiom,
! [A: ( list @ char ) > paraco415392788lle_tv,B: list @ char] :
( ( paraco876059933e_eval @ A @ ( paraco27778325le_Pro @ B ) )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_eval_Osimps_I1_J) ).
thf(939,plain,
! [A: ( list @ char ) > paraco415392788lle_tv,B: list @ char] :
( ( paraco876059933e_eval @ A @ ( paraco27778325le_Pro @ B ) )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(64,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_Collect__restrict) ).
thf(525,plain,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(112,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_less__eq__set__def) ).
thf(712,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: set @ ( TA > $o ),C: TA] :
( ( member @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( complete_Sup_Sup @ ( TA > $o ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_Sup1__I) ).
thf(295,plain,
! [TA: $tType,A: TA > $o,B: set @ ( TA > $o ),C: TA] :
( ( member @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( complete_Sup_Sup @ ( TA > $o ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(188,axiom,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco876059933e_eval @ A @ C ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2084319816le_Eql @ B @ C ) )
= ( paraco2040174112le_Det @ $true ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco876059933e_eval @ A @ C ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2084319816le_Eql @ B @ C ) )
= ( paraco2040174112le_Det @ $false ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_eval_Osimps_I5_J) ).
thf(954,plain,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco876059933e_eval @ A @ C ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2084319816le_Eql @ B @ C ) )
= ( paraco2040174112le_Det @ $true ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco876059933e_eval @ A @ C ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2084319816le_Eql @ B @ C ) )
= ( paraco2040174112le_Det @ $false ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(121,axiom,
order @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_4) ).
thf(739,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(272,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/sandbox2/benchmark/theBenchmark.p',fact_99_Inf_OINF__cong) ).
thf(1267,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)],[272]) ).
thf(263,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB > TA,C: set @ TA] :
( ! [D: TB] :
( ( A @ D )
=> ( member @ TA @ ( B @ D ) @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( image @ TB @ TA @ B @ ( collect @ TB @ A ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_image__Collect__subsetI) ).
thf(1230,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB > TA,C: set @ TA] :
( ! [D: TB] :
( ( A @ D )
=> ( member @ TA @ ( B @ D ) @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( image @ TB @ TA @ B @ ( collect @ TB @ A ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(98,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_pred__subset__eq) ).
thf(673,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(282,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: set @ TA,B: TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ! [C: TA] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ord_less_eq @ TA @ D @ C ) )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ( complete_Sup_Sup @ TA @ A )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_Sup__eqI) ).
thf(1300,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: set @ TA,B: TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ! [C: TA] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ord_less_eq @ TA @ D @ C ) )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ( complete_Sup_Sup @ TA @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(247,axiom,
! [TA: $tType,A: set @ ( set @ TA ),B: TA > $o] :
( ( ! [C: TA] :
( ( member @ TA @ C @ ( complete_Sup_Sup @ ( set @ TA ) @ A ) )
=> ( B @ C ) ) )
= ( ! [C: set @ TA] :
( ( member @ ( set @ TA ) @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ C )
=> ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_UN__ball__bex__simps_I1_J) ).
thf(1186,plain,
! [TA: $tType,A: set @ ( set @ TA ),B: TA > $o] :
( ( ! [C: TA] :
( ( member @ TA @ C @ ( complete_Sup_Sup @ ( set @ TA ) @ A ) )
=> ( B @ C ) ) )
= ( ! [C: set @ TA] :
( ( member @ ( set @ TA ) @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ C )
=> ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(114,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_order__class_Oorder_Oantisym) ).
thf(717,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(59,axiom,
! [A: ( list @ char ) > paraco415392788lle_tv] :
( ( paraco876059933e_eval @ A @ paraco251304083_Truth )
= ( paraco2040174112le_Det @ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_eval_Osimps_I2_J) ).
thf(502,plain,
! [A: ( list @ char ) > paraco415392788lle_tv] :
( ( paraco876059933e_eval @ A @ paraco251304083_Truth )
= ( paraco2040174112le_Det @ $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(155,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( TA > TB > $o )
@ ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
@ ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
= ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_pred__subset__eq2) ).
thf(840,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB ),B: set @ ( product_prod @ TA @ TB )] :
( ( ord_less_eq @ ( TA > TB > $o )
@ ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
@ ^ [C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) )
= ( ord_less_eq @ ( set @ ( product_prod @ TA @ TB ) ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(235,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_antisym) ).
thf(1130,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(258,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] : ( top_top @ ( TB > TA > $o ) @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_top2I) ).
thf(1218,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] : ( top_top @ ( TB > TA > $o ) @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(88,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/sandbox2/benchmark/theBenchmark.p',fact_110_Fpow__mono) ).
thf(643,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)],[88]) ).
thf(259,axiom,
ord @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_5) ).
thf(1220,plain,
ord @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(172,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_10) ).
thf(907,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(48,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( paraco2100061555le_Con @ A @ B )
!= ( paraco1628874225le_Eql @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_fm_Odistinct_I27_J) ).
thf(470,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( paraco2100061555le_Con @ A @ B )
!= ( paraco1628874225le_Eql @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(75,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/sandbox2/benchmark/theBenchmark.p',fact_80_image__mono) ).
thf(576,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)],[75]) ).
thf(187,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > ( set @ TC ),B: TA > ( set @ TB ),C: set @ TA] :
( ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) ) )
= ( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TA @ ( set @ TC )
@ ^ [D: TA] : ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ A @ ( B @ D ) ) )
@ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_UN__UN__flatten) ).
thf(951,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > ( set @ TC ),B: TA > ( set @ TB ),C: set @ TA] :
( ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) ) )
= ( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TA @ ( set @ TC )
@ ^ [D: TA] : ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ A @ ( B @ D ) ) )
@ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(143,axiom,
! [TA: $tType,TB: $tType] :
( ( top_top @ ( TA > TB > $o ) )
= ( ^ [A: TA,B: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_top__empty__eq2) ).
thf(808,plain,
! [TA: $tType,TB: $tType] :
( ( top_top @ ( TA > TB > $o ) )
= ( ^ [A: TA,B: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA,D: TA > TB] :
( ( A != B )
=> ( ( A != C )
=> ( ( swap @ TA @ TB @ B @ C @ D @ A )
= ( D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_swap__apply_I3_J) ).
thf(336,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TA,D: TA > TB] :
( ( A != B )
=> ( ( A != C )
=> ( ( swap @ TA @ TB @ B @ C @ D @ A )
= ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(109,axiom,
! [TA: $tType] :
( ( complete_Sup_Sup @ ( TA > $o ) )
= ( ^ [A: set @ ( TA > $o ),B: TA] : ( member @ TA @ B @ ( complete_Sup_Sup @ ( set @ TA ) @ ( image @ ( TA > $o ) @ ( set @ TA ) @ ( collect @ TA ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_Sup__SUP__eq) ).
thf(703,plain,
! [TA: $tType] :
( ( complete_Sup_Sup @ ( TA > $o ) )
= ( ^ [A: set @ ( TA > $o ),B: TA] : ( member @ TA @ B @ ( complete_Sup_Sup @ ( set @ TA ) @ ( image @ ( TA > $o ) @ ( set @ TA ) @ ( collect @ TA ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(210,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( set @ TB ),C: set @ TA] :
( ( member @ TB @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) )
=> ~ ! [D: TA] :
( ( member @ TA @ D @ C )
=> ~ ( member @ TB @ A @ ( B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_UN__E) ).
thf(1023,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( set @ TB ),C: set @ TA] :
( ( member @ TB @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) )
=> ~ ! [D: TA] :
( ( member @ TA @ D @ C )
=> ~ ( member @ TB @ A @ ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(260,axiom,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: TB > $o] :
( ( ! [D: TB] :
( ( member @ TB @ D @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ! [E: TB] :
( ( member @ TB @ E @ ( A @ D ) )
=> ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_UN__ball__bex__simps_I2_J) ).
thf(1221,plain,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: TB > $o] :
( ( ! [D: TB] :
( ( member @ TB @ D @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ! [E: TB] :
( ( member @ TB @ E @ ( A @ D ) )
=> ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(218,axiom,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TB )
=> ! [A: TA > TB,B: set @ TA,C: TB] :
( ( ord_less_eq @ TB @ ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ A @ B ) ) @ C )
= ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ord_less_eq @ TB @ ( A @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_SUP__le__iff) ).
thf(1052,plain,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TB )
=> ! [A: TA > TB,B: set @ TA,C: TB] :
( ( ord_less_eq @ TB @ ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ A @ B ) ) @ C )
= ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ord_less_eq @ TB @ ( A @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(117,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ( ( complete_Sup_Sup @ TA @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_Sup__UNIV) ).
thf(727,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ( ( complete_Sup_Sup @ TA @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(205,axiom,
! [TA: $tType,A: set @ TA] : ( member @ ( set @ TA ) @ A @ ( pow @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_Pow__top) ).
thf(1008,plain,
! [TA: $tType,A: set @ TA] : ( member @ ( set @ TA ) @ A @ ( pow @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > ( set @ ( product_prod @ TA @ TC ) ),B: set @ TB] :
( ( complete_Sup_Sup @ ( TA > TC > $o )
@ ( image @ TB @ ( TA > TC > $o )
@ ^ [C: TB,D: TA,E: TC] : ( member @ ( product_prod @ TA @ TC ) @ ( product_Pair @ TA @ TC @ D @ E ) @ ( A @ C ) )
@ B ) )
= ( ^ [C: TA,D: TC] : ( member @ ( product_prod @ TA @ TC ) @ ( product_Pair @ TA @ TC @ C @ D ) @ ( complete_Sup_Sup @ ( set @ ( product_prod @ TA @ TC ) ) @ ( image @ TB @ ( set @ ( product_prod @ TA @ TC ) ) @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_SUP__UN__eq2) ).
thf(571,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > ( set @ ( product_prod @ TA @ TC ) ),B: set @ TB] :
( ( complete_Sup_Sup @ ( TA > TC > $o )
@ ( image @ TB @ ( TA > TC > $o )
@ ^ [C: TB,D: TA,E: TC] : ( member @ ( product_prod @ TA @ TC ) @ ( product_Pair @ TA @ TC @ D @ E ) @ ( A @ C ) )
@ B ) )
= ( ^ [C: TA,D: TC] : ( member @ ( product_prod @ TA @ TC ) @ ( product_Pair @ TA @ TC @ C @ D ) @ ( complete_Sup_Sup @ ( set @ ( product_prod @ TA @ TC ) ) @ ( image @ TB @ ( set @ ( product_prod @ TA @ TC ) ) @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(287,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_predicate1D) ).
thf(1316,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ( A @ C )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(181,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/sandbox2/benchmark/theBenchmark.p',fact_123_PowD) ).
thf(931,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)],[181]) ).
thf(53,axiom,
! [A: list @ char,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco27778325le_Pro @ A )
!= ( paraco1628874225le_Eql @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_fm_Odistinct_I9_J) ).
thf(482,plain,
! [A: list @ char,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco27778325le_Pro @ A )
!= ( paraco1628874225le_Eql @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(289,axiom,
! [TA: $tType,A: set @ TA] :
( ( image @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_image__ident) ).
thf(1321,plain,
! [TA: $tType,A: set @ TA] :
( ( image @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(248,axiom,
! [TA: $tType] :
( ( finite_lattice @ TA )
=> ( ( top_top @ TA )
= ( complete_Sup_Sup @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_top__finite__def) ).
thf(1189,plain,
! [TA: $tType] :
( ( finite_lattice @ TA )
=> ( ( top_top @ TA )
= ( complete_Sup_Sup @ TA @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(206,axiom,
! [TA: $tType,TB: $tType,A: set @ ( set @ ( product_prod @ TA @ TB ) )] :
( ( complete_Sup_Sup @ ( TA > TB > $o )
@ ( image @ ( set @ ( product_prod @ TA @ TB ) ) @ ( TA > TB > $o )
@ ^ [B: set @ ( product_prod @ TA @ TB ),C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B )
@ A ) )
= ( ^ [B: TA,C: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ C ) @ ( complete_Sup_Sup @ ( set @ ( product_prod @ TA @ TB ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_SUP__Sup__eq2) ).
thf(1010,plain,
! [TA: $tType,TB: $tType,A: set @ ( set @ ( product_prod @ TA @ TB ) )] :
( ( complete_Sup_Sup @ ( TA > TB > $o )
@ ( image @ ( set @ ( product_prod @ TA @ TB ) ) @ ( TA > TB > $o )
@ ^ [B: set @ ( product_prod @ TA @ TB ),C: TA,D: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B )
@ A ) )
= ( ^ [B: TA,C: TB] : ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ C ) @ ( complete_Sup_Sup @ ( set @ ( product_prod @ TA @ TB ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(278,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( A != B )
=> ( ord_less @ ( set @ TA ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_psubsetI) ).
thf(1289,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( A != B )
=> ( ord_less @ ( set @ TA ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(132,axiom,
! [TA: $tType] :
( ( ( condit378418413attice @ TA )
& ( no_bot @ TA ) )
=> ! [A: set @ TA,B: TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ! [C: TA] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ord_less_eq @ TA @ D @ C ) )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ( complete_Sup_Sup @ TA @ A )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_cSup__eq) ).
thf(771,plain,
! [TA: $tType] :
( ( ( condit378418413attice @ TA )
& ( no_bot @ TA ) )
=> ! [A: set @ TA,B: TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ! [C: TA] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ord_less_eq @ TA @ D @ C ) )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ( complete_Sup_Sup @ TA @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( set @ TB ),C: set @ TA] :
( ( member @ TB @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( member @ TB @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_UN__iff) ).
thf(688,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( set @ TB ),C: set @ TA] :
( ( member @ TB @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( member @ TB @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(171,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/sandbox2/benchmark/theBenchmark.p',fact_55_Collect__mono) ).
thf(903,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)],[171]) ).
thf(257,axiom,
( paraco876059933e_eval
= ( ^ [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm] : ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ ( paraco329115265le_Neg @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_double__negation) ).
thf(1216,plain,
( paraco876059933e_eval
= ( ^ [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm] : ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ ( paraco329115265le_Neg @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(169,axiom,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm] :
( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco2040174112le_Det @ $false ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ B ) )
= ( paraco2040174112le_Det @ $true ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco2040174112le_Det @ $false ) )
=> ( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ B ) )
= ( paraco2040174112le_Det @ $false ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ B ) )
= ( paraco876059933e_eval @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_eval__negation) ).
thf(891,plain,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm] :
( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco2040174112le_Det @ $false ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ B ) )
= ( paraco2040174112le_Det @ $true ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco2040174112le_Det @ $false ) )
=> ( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ B ) )
= ( paraco2040174112le_Det @ $false ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ B ) )
= ( paraco876059933e_eval @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(108,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_equalityD1) ).
thf(699,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)],[108]) ).
thf(16,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco329115265le_Neg @ A )
!= ( paraco2100061555le_Con @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_fm_Odistinct_I19_J) ).
thf(319,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco329115265le_Neg @ A )
!= ( paraco2100061555le_Con @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(9,axiom,
! [A: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco329115265le_Neg @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_fm_Odistinct_I11_J) ).
thf(304,plain,
! [A: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco329115265le_Neg @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(26,axiom,
! [A: paraco414474393lle_fm > $o,B: paraco414474393lle_fm] :
( ! [C: list @ char] : ( A @ ( paraco27778325le_Pro @ C ) )
=> ( ( A @ paraco251304083_Truth )
=> ( ! [C: paraco414474393lle_fm] :
( ( A @ C )
=> ( A @ ( paraco329115265le_Neg @ C ) ) )
=> ( ! [C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco2100061555le_Con @ C @ D ) ) ) )
=> ( ! [C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco2084319816le_Eql @ C @ D ) ) ) )
=> ( ! [C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco1628874225le_Eql @ C @ D ) ) ) )
=> ( A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_fm_Oinduct) ).
thf(351,plain,
! [A: paraco414474393lle_fm > $o,B: paraco414474393lle_fm] :
( ! [C: list @ char] : ( A @ ( paraco27778325le_Pro @ C ) )
=> ( ( A @ paraco251304083_Truth )
=> ( ! [C: paraco414474393lle_fm] :
( ( A @ C )
=> ( A @ ( paraco329115265le_Neg @ C ) ) )
=> ( ! [C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco2100061555le_Con @ C @ D ) ) ) )
=> ( ! [C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco2084319816le_Eql @ C @ D ) ) ) )
=> ( ! [C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( A @ C )
=> ( ( A @ D )
=> ( A @ ( paraco1628874225le_Eql @ C @ D ) ) ) )
=> ( A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(212,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TB > ( set @ TA ),C: set @ TA] :
( ! [D: TB] :
( ( member @ TB @ D @ A )
=> ( ord_less_eq @ ( set @ TA ) @ ( B @ D ) @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( complete_Sup_Sup @ ( set @ TA ) @ ( image @ TB @ ( set @ TA ) @ B @ A ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_UN__least) ).
thf(1030,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TB > ( set @ TA ),C: set @ TA] :
( ! [D: TB] :
( ( member @ TB @ D @ A )
=> ( ord_less_eq @ ( set @ TA ) @ ( B @ D ) @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( complete_Sup_Sup @ ( set @ TA ) @ ( image @ TB @ ( set @ TA ) @ B @ A ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(72,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_antisym__conv) ).
thf(568,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(1,conjecture,
( ( ! [A: ( list @ char ) > paraco415392788lle_tv] :
( ( paraco876059933e_eval @ A @ p )
= ( paraco2040174112le_Det @ $true ) ) )
!= ( ~ ! [A: ( list @ char ) > paraco415392788lle_tv] :
( ( ord_less_eq @ ( set @ paraco415392788lle_tv ) @ ( image @ ( list @ char ) @ paraco415392788lle_tv @ A @ ( top_top @ ( set @ ( list @ char ) ) ) )
@ ( paraco506338565domain
@ ( collect @ nat
@ ^ [B: nat] : $true ) ) )
=> ( ( paraco876059933e_eval @ A @ p )
= ( paraco2040174112le_Det @ $true ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( ( ! [A: ( list @ char ) > paraco415392788lle_tv] :
( ( paraco876059933e_eval @ A @ p )
= ( paraco2040174112le_Det @ $true ) ) )
!= ( ~ ! [A: ( list @ char ) > paraco415392788lle_tv] :
( ( ord_less_eq @ ( set @ paraco415392788lle_tv ) @ ( image @ ( list @ char ) @ paraco415392788lle_tv @ A @ ( top_top @ ( set @ ( list @ char ) ) ) )
@ ( paraco506338565domain
@ ( collect @ nat
@ ^ [B: nat] : $true ) ) )
=> ( ( paraco876059933e_eval @ A @ p )
= ( paraco2040174112le_Det @ $true ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(290,plain,
~ ( ( ( ! [A: ( list @ char ) > paraco415392788lle_tv] :
( ( paraco876059933e_eval @ A @ p )
= ( paraco2040174112le_Det @ $true ) ) )
!= ( ~ ! [A: ( list @ char ) > paraco415392788lle_tv] :
( ( ord_less_eq @ ( set @ paraco415392788lle_tv ) @ ( image @ ( list @ char ) @ paraco415392788lle_tv @ A @ ( top_top @ ( set @ ( list @ char ) ) ) )
@ ( paraco506338565domain
@ ( collect @ nat
@ ^ [B: nat] : $true ) ) )
=> ( ( paraco876059933e_eval @ A @ p )
= ( paraco2040174112le_Det @ $true ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(284,axiom,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: TB > TA,B: set @ TB,C: TA,D: TB] :
( ( ord_less @ TA @ ( complete_Sup_Sup @ TA @ ( image @ TB @ TA @ A @ B ) ) @ C )
=> ( ( member @ TB @ D @ B )
=> ( ord_less @ TA @ ( A @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_SUP__lessD) ).
thf(1308,plain,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: TB > TA,B: set @ TB,C: TA,D: TB] :
( ( ord_less @ TA @ ( complete_Sup_Sup @ TA @ ( image @ TB @ TA @ A @ B ) ) @ C )
=> ( ( member @ TB @ D @ B )
=> ( ord_less @ TA @ ( A @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(255,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( complete_Sup_Sup @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_Sup__upper) ).
thf(1212,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ ( complete_Sup_Sup @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(230,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_dual__order_Oeq__iff) ).
thf(1116,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(236,axiom,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco876059933e_eval @ A @ C ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2100061555le_Con @ B @ C ) )
= ( paraco876059933e_eval @ A @ B ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco876059933e_eval @ A @ C ) )
=> ( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2100061555le_Con @ B @ C ) )
= ( paraco876059933e_eval @ A @ C ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( ( ( paraco876059933e_eval @ A @ C )
= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2100061555le_Con @ B @ C ) )
= ( paraco876059933e_eval @ A @ B ) ) )
& ( ( ( paraco876059933e_eval @ A @ C )
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2100061555le_Con @ B @ C ) )
= ( paraco2040174112le_Det @ $false ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_eval_Osimps_I4_J) ).
thf(1133,plain,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco876059933e_eval @ A @ C ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2100061555le_Con @ B @ C ) )
= ( paraco876059933e_eval @ A @ B ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco876059933e_eval @ A @ C ) )
=> ( ( ( ( paraco876059933e_eval @ A @ B )
= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2100061555le_Con @ B @ C ) )
= ( paraco876059933e_eval @ A @ C ) ) )
& ( ( ( paraco876059933e_eval @ A @ B )
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( ( ( paraco876059933e_eval @ A @ C )
= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2100061555le_Con @ B @ C ) )
= ( paraco876059933e_eval @ A @ B ) ) )
& ( ( ( paraco876059933e_eval @ A @ C )
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( paraco876059933e_eval @ A @ ( paraco2100061555le_Con @ B @ C ) )
= ( paraco2040174112le_Det @ $false ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType] :
( ( complete_Sup @ TA )
=> ( complete_Sup @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Complete__Lattices_OSup) ).
thf(300,plain,
! [TA: $tType,TB: $tType] :
( ( complete_Sup @ TA )
=> ( complete_Sup @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(201,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ord_less_eq @ ( ( set @ TA ) > $o ) @ ( powp @ TA @ A ) @ ( powp @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_Powp__mono) ).
thf(999,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( TA > $o ) @ A @ B )
=> ( ord_less_eq @ ( ( set @ TA ) > $o ) @ ( powp @ TA @ A ) @ ( powp @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(447,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(275,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/sandbox2/benchmark/theBenchmark.p',fact_88_all__subset__image) ).
thf(1280,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)],[275]) ).
thf(152,axiom,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Collect__subset) ).
thf(833,plain,
! [TA: $tType,A: set @ TA,B: TA > $o] :
( ord_less_eq @ ( set @ TA )
@ ( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(153,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_UNIV__eq__I) ).
thf(835,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)],[153]) ).
thf(28,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( ( paraco1628874225le_Eql @ A @ B )
= ( paraco1628874225le_Eql @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_fm_Oinject_I5_J) ).
thf(405,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( ( paraco1628874225le_Eql @ A @ B )
= ( paraco1628874225le_Eql @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(137,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_subset__Collect__iff) ).
thf(790,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(160,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comple187826305attice @ TC )
=> ! [A: TB > TA > TC,B: set @ TA,C: set @ TB] :
( ( complete_Sup_Sup @ TC
@ ( image @ TB @ TC
@ ^ [D: TB] : ( complete_Sup_Sup @ TC @ ( image @ TA @ TC @ ( A @ D ) @ B ) )
@ C ) )
= ( complete_Sup_Sup @ TC
@ ( image @ TA @ TC
@ ^ [D: TA] :
( complete_Sup_Sup @ TC
@ ( image @ TB @ TC
@ ^ [E: TB] : ( A @ E @ D )
@ C ) )
@ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_SUP__commute) ).
thf(865,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comple187826305attice @ TC )
=> ! [A: TB > TA > TC,B: set @ TA,C: set @ TB] :
( ( complete_Sup_Sup @ TC
@ ( image @ TB @ TC
@ ^ [D: TB] : ( complete_Sup_Sup @ TC @ ( image @ TA @ TC @ ( A @ D ) @ B ) )
@ C ) )
= ( complete_Sup_Sup @ TC
@ ( image @ TA @ TC
@ ^ [D: TA] :
( complete_Sup_Sup @ TC
@ ( image @ TB @ TC
@ ^ [E: TB] : ( A @ E @ D )
@ C ) )
@ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(251,axiom,
! [TA: $tType,TB: $tType] :
( ( comple1035589618norder @ TB )
=> ! [A: TB,B: TA > TB,C: set @ TA] :
( ( ord_less @ TB @ A @ ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ B @ C ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_less__SUP__iff) ).
thf(1197,plain,
! [TA: $tType,TB: $tType] :
( ( comple1035589618norder @ TB )
=> ! [A: TB,B: TA > TB,C: set @ TA] :
( ( ord_less @ TB @ A @ ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ B @ C ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(107,axiom,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
= ( A
= ( top_top @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_top_Oextremum__unique) ).
thf(696,plain,
! [TA: $tType] :
( ( order_top @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( top_top @ TA ) @ A )
= ( A
= ( top_top @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(180,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
( ( image @ TA @ TC
@ ^ [C: TA] : ( A @ ( B @ C ) )
@ ( top_top @ ( set @ TA ) ) )
= ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_range__composition) ).
thf(928,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
( ( image @ TA @ TC
@ ^ [C: TA] : ( A @ ( B @ C ) )
@ ( top_top @ ( set @ TA ) ) )
= ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(242,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: set @ TA,B: TA] :
( ( ord_less_eq @ TA @ ( complete_Sup_Sup @ TA @ A ) @ B )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_Sup__le__iff) ).
thf(1172,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: set @ TA,B: TA] :
( ( ord_less_eq @ TA @ ( complete_Sup_Sup @ TA @ A ) @ B )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA )
& ( order @ TB ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_strict_mono @ TA @ TB @ A )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_strict__mono__eq) ).
thf(474,plain,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA )
& ( order @ TB ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_strict_mono @ TA @ TB @ A )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(130,axiom,
linorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(767,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(115,axiom,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: set @ TB] :
( ( ord_less_eq @ ( set @ TB ) @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) @ C )
= ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ord_less_eq @ ( set @ TB ) @ ( A @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_UN__subset__iff) ).
thf(720,plain,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: set @ TB] :
( ( ord_less_eq @ ( set @ TB ) @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) @ C )
= ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ord_less_eq @ ( set @ TB ) @ ( A @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(239,axiom,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TB )
=> ! [A: TA,B: set @ TA,C: TB,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ TB @ C @ ( D @ A ) )
=> ( ord_less_eq @ TB @ C @ ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_SUP__upper2) ).
thf(1165,plain,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TB )
=> ! [A: TA,B: set @ TA,C: TB,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ TB @ C @ ( D @ A ) )
=> ( ord_less_eq @ TB @ C @ ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(122,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(740,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)],[122]) ).
thf(20,axiom,
! [A: paraco414474393lle_fm] :
( ! [B: list @ char] :
( A
!= ( paraco27778325le_Pro @ B ) )
=> ( ( A != paraco251304083_Truth )
=> ( ! [B: paraco414474393lle_fm] :
( A
!= ( paraco329115265le_Neg @ B ) )
=> ( ! [B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( A
!= ( paraco2100061555le_Con @ B @ C ) )
=> ( ! [B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( A
!= ( paraco2084319816le_Eql @ B @ C ) )
=> ~ ! [B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( A
!= ( paraco1628874225le_Eql @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_fm_Oexhaust) ).
thf(332,plain,
! [A: paraco414474393lle_fm] :
( ! [B: list @ char] :
( A
!= ( paraco27778325le_Pro @ B ) )
=> ( ( A != paraco251304083_Truth )
=> ( ! [B: paraco414474393lle_fm] :
( A
!= ( paraco329115265le_Neg @ B ) )
=> ( ! [B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( A
!= ( paraco2100061555le_Con @ B @ C ) )
=> ( ! [B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( A
!= ( paraco2084319816le_Eql @ B @ C ) )
=> ~ ! [B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( A
!= ( paraco1628874225le_Eql @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(34,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( paraco2100061555le_Con @ A @ B )
!= ( paraco2084319816le_Eql @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_fm_Odistinct_I25_J) ).
thf(427,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm,D: paraco414474393lle_fm] :
( ( paraco2100061555le_Con @ A @ B )
!= ( paraco2084319816le_Eql @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(82,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
=> ( C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_rev__predicate1D) ).
thf(596,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ( ord_less_eq @ ( TA > $o ) @ A @ C )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(198,axiom,
! [TA: $tType,TB: $tType,A: TB,B: set @ TB,C: TB > TA > $o,D: TA] :
( ( member @ TB @ A @ B )
=> ( ( C @ A @ D )
=> ( complete_Sup_Sup @ ( TA > $o ) @ ( image @ TB @ ( TA > $o ) @ C @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_SUP1__I) ).
thf(992,plain,
! [TA: $tType,TB: $tType,A: TB,B: set @ TB,C: TB > TA > $o,D: TA] :
( ( member @ TB @ A @ B )
=> ( ( C @ A @ D )
=> ( complete_Sup_Sup @ ( TA > $o ) @ ( image @ TB @ ( TA > $o ) @ C @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_order__subst2) ).
thf(723,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(203,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_11) ).
thf(1004,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType] :
( ( comple1035589618norder @ TA )
=> ! [A: TB > TA,B: set @ TB] :
( ( ( complete_Sup_Sup @ TA @ ( image @ TB @ TA @ A @ B ) )
= ( top_top @ TA ) )
= ( ! [C: TA] :
( ( ord_less @ TA @ C @ ( top_top @ TA ) )
=> ? [D: TB] :
( ( member @ TB @ D @ B )
& ( ord_less @ TA @ C @ ( A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_SUP__eq__top__iff) ).
thf(691,plain,
! [TA: $tType,TB: $tType] :
( ( comple1035589618norder @ TA )
=> ! [A: TB > TA,B: set @ TB] :
( ( ( complete_Sup_Sup @ TA @ ( image @ TB @ TA @ A @ B ) )
= ( top_top @ TA ) )
= ( ! [C: TA] :
( ( ord_less @ TA @ C @ ( top_top @ TA ) )
=> ? [D: TB] :
( ( member @ TB @ D @ B )
& ( ord_less @ TA @ C @ ( A @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(86,axiom,
! [TA: $tType] :
( ( condit1037483654norder @ TA )
=> ! [A: TA,B: TA,C: TA > $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( C @ A )
=> ( ~ ( C @ B )
=> ? [D: TA] :
( ( ord_less_eq @ TA @ A @ D )
& ( ord_less_eq @ TA @ D @ B )
& ! [E: TA] :
( ( ( ord_less_eq @ TA @ A @ E )
& ( ord_less @ TA @ E @ D ) )
=> ( C @ E ) )
& ! [E: TA] :
( ! [F: TA] :
( ( ( ord_less_eq @ TA @ A @ F )
& ( ord_less @ TA @ F @ E ) )
=> ( C @ F ) )
=> ( ord_less_eq @ TA @ E @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_complete__interval) ).
thf(607,plain,
! [TA: $tType] :
( ( condit1037483654norder @ TA )
=> ! [A: TA,B: TA,C: TA > $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( C @ A )
=> ( ~ ( C @ B )
=> ? [D: TA] :
( ( ord_less_eq @ TA @ A @ D )
& ( ord_less_eq @ TA @ D @ B )
& ! [E: TA] :
( ( ( ord_less_eq @ TA @ A @ E )
& ( ord_less @ TA @ E @ D ) )
=> ( C @ E ) )
& ! [E: TA] :
( ! [F: TA] :
( ( ( ord_less_eq @ TA @ A @ F )
& ( ord_less @ TA @ F @ E ) )
=> ( C @ F ) )
=> ( ord_less_eq @ TA @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(54,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco329115265le_Neg @ A )
!= ( paraco2084319816le_Eql @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_fm_Odistinct_I21_J) ).
thf(486,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco329115265le_Neg @ A )
!= ( paraco2084319816le_Eql @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(183,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/sandbox2/benchmark/theBenchmark.p',fact_23_ord__le__eq__trans) ).
thf(935,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)],[183]) ).
thf(179,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/sandbox2/benchmark/theBenchmark.p',fact_78_subset__imageE) ).
thf(923,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)],[179]) ).
thf(214,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/sandbox2/benchmark/theBenchmark.p',fact_82_rangeI) ).
thf(1037,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)],[214]) ).
thf(253,axiom,
! [TA: $tType] :
( ( condit378418413attice @ TA )
=> ! [A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ! [C: TA] :
( ( member @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) )
=> ( ( complete_Sup_Sup @ TA @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_cSup__eq__maximum) ).
thf(1204,plain,
! [TA: $tType] :
( ( condit378418413attice @ TA )
=> ! [A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ! [C: TA] :
( ( member @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) )
=> ( ( complete_Sup_Sup @ TA @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(81,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/sandbox2/benchmark/theBenchmark.p',fact_81_range__eqI) ).
thf(592,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)],[81]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA > TB] :
( ( swap @ TA @ TB @ A @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_swap__self) ).
thf(496,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA > TB] :
( ( swap @ TA @ TB @ A @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(166,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comple187826305attice @ TC )
=> ! [A: TB > TC,B: TA > ( set @ TB ),C: set @ TA] :
( ( complete_Sup_Sup @ TC @ ( image @ TB @ TC @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) ) )
= ( complete_Sup_Sup @ TC
@ ( image @ TA @ TC
@ ^ [D: TA] : ( complete_Sup_Sup @ TC @ ( image @ TB @ TC @ A @ ( B @ D ) ) )
@ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_SUP__UNION) ).
thf(882,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comple187826305attice @ TC )
=> ! [A: TB > TC,B: TA > ( set @ TB ),C: set @ TA] :
( ( complete_Sup_Sup @ TC @ ( image @ TB @ TC @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) ) )
= ( complete_Sup_Sup @ TC
@ ( image @ TA @ TC
@ ^ [D: TA] : ( complete_Sup_Sup @ TC @ ( image @ TB @ TC @ A @ ( B @ D ) ) )
@ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(127,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
=> ~ ! [C: TA] :
( A
!= ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_rangeE) ).
thf(755,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
=> ~ ! [C: TA] :
( A
!= ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(99,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( set @ TA )] :
( ( member @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_Union__upper) ).
thf(676,plain,
! [TA: $tType,A: set @ TA,B: set @ ( set @ TA )] :
( ( member @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(1532,plain,
$false,
inference(e,[status(thm)],[645,479,909,1295,1110,1083,962,1200,683,730,994,308,440,861,408,977,523,582,873,449,1310,550,715,1275,814,1260,1063,747,913,404,1001,1127,782,709,885,1254,651,1055,1264,460,587,838,917,751,802,344,902,1147,870,969,1013,416,325,316,806,966,821,480,574,1020,348,1183,1283,602,1169,293,453,1119,660,1242,527,312,1074,678,793,761,512,942,1042,302,598,561,297,788,467,566,879,1178,665,1027,456,852,435,493,1210,578,1234,1227,980,1006,420,499,989,857,1259,317,328,339,1182,669,1214,1039,706,1292,933,1016,590,1114,1297,654,1192,984,779,508,311,921,1286,1167,530,888,343,1318,558,1071,412,824,745,444,733,584,819,423,694,743,875,1256,843,1125,313,1312,1224,1058,1107,466,1092,919,804,604,1194,831,784,736,996,1175,303,1122,477,811,1080,758,816,323,964,915,943,462,799,1162,685,868,986,563,1250,431,658,768,827,636,1044,505,438,1034,490,1304,680,663,1277,648,939,525,712,295,954,739,1267,1230,673,1300,1186,717,502,840,1130,1218,643,1220,907,470,576,951,808,336,703,1023,1221,1052,727,1008,571,1316,931,482,1321,1189,1010,1289,771,688,903,1216,891,699,319,304,351,1030,568,290,1308,1212,1116,1133,300,999,447,1280,833,835,405,790,865,1197,696,928,1172,474,767,720,1165,740,332,427,596,992,723,1004,691,607,486,935,923,1037,1204,592,496,882,755,676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP138^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n019.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 19:59:18 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.70/0.59 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.07/0.90 % [INFO] Parsing done (312ms).
% 2.07/0.91 % [INFO] Running in sequential loop mode.
% 3.05/1.21 % [INFO] eprover registered as external prover.
% 3.05/1.21 % [INFO] Scanning for conjecture ...
% 3.25/1.37 % [INFO] Found a conjecture (or negated_conjecture) and 288 axioms. Running axiom selection ...
% 3.84/1.51 % [INFO] Axiom selection finished. Selected 287 axioms (removed 1 axioms).
% 4.69/1.71 % [INFO] Problem is higher-order (TPTP THF).
% 4.69/1.73 % [INFO] Type checking passed.
% 4.69/1.73 % [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 ...
% 34.84/13.18 % External prover 'e' found a proof!
% 34.84/13.18 % [INFO] Killing All external provers ...
% 34.84/13.18 % Time passed: 12879ms (effective reasoning time: 12266ms)
% 34.84/13.18 % 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)>
% 34.84/13.19 % Axioms used in derivation (287): fact_115_Greatest__equality, fact_12_range__composition, fact_202_SUP__mono_H, fact_39_le__funI, fact_206_fm_Odistinct_I1_J, fact_187_UN__Pow__subset, fact_240_cSup__eq, fact_246_Sup__eq__top__iff, fact_160_Union__Pow__eq, fact_182_Sup__mono, fact_74_top_Oextremum__unique, fact_4_UNIV__I, fact_79_image__subsetI, fact_183_Sup__eqI, fact_152_eval__equality, fact_195_Union__mono, tcon_Nat_Onat___Orderings_Olinorder, fact_65_UNIV__eq__I, fact_189_Sup__subset__mono, fact_230_Sup__SUP__eq, fact_232_SUP__Sup__eq, tcon_Nat_Onat___Orderings_Oord_5, fact_28_order_Otrans, fact_227_Sup__set__def, tcon_Nat_Onat___Complete__Lattices_OSup_2, fact_231_SUP__UN__eq2, fact_107_eval_Osimps_I5_J, fact_162_fm_Oinject_I1_J, tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder, fact_0_universal__domain, fact_219_eval_Ocases, fact_69_Collect__restrict, fact_220_cSup__eq__maximum, fact_175_Union__least, fact_124_Cantors__paradox, fact_188_SUP__eq, fact_176_Union__upper, fact_173_SUP__commute, fact_167_SUP__identity__eq, fact_134_eval__negation, fact_1_tv_Oinject_I1_J, fact_2_valid__in__def, fact_82_rangeI, fact_13_image__Collect__subsetI, fact_125_Pow__def, fact_233_Sup1__E, fact_226_SUP1__I, tcon_fun___Orderings_Oord, fact_156_UN__ball__bex__simps_I4_J, fact_244_Sup2__I, fact_16_dual__order_Oantisym, fact_171_Sup__fun__def, fact_221_UN__ball__bex__simps_I3_J, fact_161_fm_Oinject_I5_J, fact_50_image__iff, fact_62_subsetD, fact_33_eq__iff, fact_158_bex__UN, tcon_HOL_Obool___Complete__Lattices_OSup_16, fact_209_image__UN, fact_210_UN__mono, fact_59_equalityD1, fact_149_fm_Odistinct_I19_J, fact_137_swap__self, fact_83_subset__UNIV, fact_44_image__cong, fact_114_Powp__mono, fact_108_fm_Oinject_I4_J, fact_216_image__Union, fact_95_predicate1I, fact_128_Pow__mono, fact_85_surjI, fact_117_fm_Oinject_I3_J, fact_110_Fpow__mono, fact_14_top__set__def, tcon_HOL_Obool___Conditionally__Complete__Lattices_Oconditionally__complete__lattice_14, tcon_HOL_Obool___Orderings_Oord_22, fact_144_swap__triple, fact_34_ord__le__eq__subst, fact_184_UN__UN__flatten, tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_15, fact_97_predicate1D, fact_21_order__trans, fact_84_surj__def, fact_29_le__cases, fact_234_UnionE, fact_46_Collect__mem__eq, fact_166_SUP__apply, fact_25_order__class_Oorder_Oeq__iff, fact_142_swap__image__eq, fact_120_Pow__UNIV, fact_253_le__Sup__iff, fact_170_SUP__UNION, fact_19_linorder__wlog, fact_214_UN__subset__iff, fact_91_subset__Collect__iff, fact_100_Sup_OSUP__cong, fact_190_eval_Osimps_I1_J, fact_87_surjD, fact_245_top2I, fact_153_fm_Oexhaust, fact_18_dual__order_Otrans, fact_111_eval__equality__simplify, fact_86_surjE, fact_88_all__subset__image, fact_165_UN__I, fact_163_Sup__apply, fact_102_Inf_OINF__identity__eq, fact_26_antisym__conv, fact_238_ssubst__Pair__rhs, fact_76_subset__image__iff, tcon_HOL_Obool___Orderings_Oorder__top_17, tcon_Set_Oset___Conditionally__Complete__Lattices_Oconditionally__complete__lattice_6, fact_150_fm_Odistinct_I11_J, fact_35_ord__eq__le__subst, tcon_Nat_Onat___Orderings_Opreorder_3, fact_27_le__cases3, fact_194_fm_Odistinct_I29_J, tcon_Set_Oset___Orderings_Oorder_11, tcon_HOL_Obool___Orderings_Olinorder_19, fact_15_less__eq__set__def, fact_32_antisym, fact_186_UN__extend__simps_I9_J, fact_8_subset__antisym, tcon_fun___Conditionally__Complete__Lattices_Oconditionally__complete__lattice, tcon_Set_Oset___Orderings_Otop_12, fact_80_image__mono, tcon_Nat_Onat___Orderings_Oorder_4, fact_58_equalityD2, fact_92_subset__CollectI, fact_239_top__empty__eq2, fact_208_UN__extend__simps_I10_J, fact_224_Union__iff, fact_193_fm_Odistinct_I27_J, fact_17_dual__order_Oeq__iff, fact_126_fm_Odistinct_I25_J, fact_252_complete__interval, fact_196_fm_Odistinct_I5_J, fact_106_image__Fpow__mono, fact_169_SUP__cong, fact_40_le__funE, fact_105_eval_Osimps_I2_J, fact_75_top__greatest, fact_45_mem__Collect__eq, fact_109_fm_Odistinct_I15_J, fact_24_ord__eq__le__trans, fact_254_less__SUP__iff, fact_247_SUP2__I, fact_135_surj__swap__iff, fact_72_UNIV__def, tcon_Set_Oset___Orderings_Opreorder_10, tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_7, fact_139_swap__apply_I2_J, fact_201_SUP__least, fact_30_eq__refl, fact_179_Sup__le__iff, fact_212_UN__upper, fact_141_fm_Oinject_I2_J, fact_6_top__apply, fact_255_SUP__lessD, fact_154_fm_Oinduct, fact_41_le__funD, fact_70_prop__restrict, fact_205_SUP__upper2, fact_250_Sup__bool__def, fact_57_subset__iff, fact_123_PowD, fact_172_SUP__UN__eq, tcon_fun___Complete__Lattices_OSup, fact_145_strict__mono__eq, fact_68_imageE, fact_235_subrelI, fact_11_rangeE, fact_47_Collect__cong, tcon_Set_Oset___Orderings_Oord_13, fact_31_linear, fact_9_image__eqI, fact_3_image__ident, fact_129_image__Pow__surj, fact_178_Sup__upper2, fact_242_SUP__eq__top__iff, fact_223_UnionI, fact_99_Inf_OINF__cong, tcon_fun___Orderings_Otop, fact_10_order__refl, fact_249_Sup2__E, tcon_Set_Oset___Complete__Lattices_OSup_8, fact_94_Sup_OSUP__identity__eq, fact_243_psubsetI, fact_54_subset__trans, fact_159_ball__UN, fact_197_fm_Odistinct_I7_J, fact_211_UN__least, fact_49_bex__imageD, fact_248_SUP2__E, fact_112_image__Pow__mono, fact_131_Fpow__subset__Pow, fact_192_fm_Odistinct_I3_J, fact_143_swap__commute, fact_181_Sup__least, fact_93_conj__subset__def, fact_168_Sup__UNIV, fact_241_UN__constant__eq, tcon_fun___Orderings_Opreorder, fact_71_Collect__subset, fact_121_Pow__top, fact_177_Union__subsetI, fact_61_equalityE, tcon_fun___Orderings_Oorder__top, fact_199_SUP__eqI, fact_67_image__image, fact_118_PowI, fact_215_Union__UNIV, fact_140_swap__apply_I3_J, fact_22_order__class_Oorder_Oantisym, tcon_fun___Complete__Lattices_Ocomplete__lattice, fact_78_subset__imageE, fact_147_strict__mono__less__eq, fact_138_swap__apply_I1_J, fact_42_rev__image__eqI, fact_204_SUP__le__iff, fact_198_fm_Odistinct_I17_J, fact_52_Collect__mono__iff, fact_174_fm_Odistinct_I9_J, fact_217_UN__extend__simps_I8_J, fact_146_double__negation, fact_228_SUP1__E, fact_200_SUP__mono, fact_237_pred__equals__eq2, fact_203_SUP__upper, fact_116_GreatestI2__order, tcon_fun___Orderings_Oorder, fact_130_conjunction, fact_43_ball__imageD, tcon_Set_Oset___Orderings_Oorder__top_9, fact_56_subset__refl, fact_20_dual__order_Orefl, fact_251_less__Sup__iff, fact_213_UN__image__subset, fact_122_Powp__Pow__eq, fact_101_top__empty__eq, fact_23_ord__le__eq__trans, fact_51_imageI, fact_180_Sup__upper, fact_81_range__eqI, fact_119_Pow__iff, fact_164_UN__iff, fact_55_Collect__mono, fact_191_fm_Odistinct_I23_J, fact_96_top1I, fact_38_le__fun__def, fact_89_valid__def, fact_207_subset__Pow__Union, tcon_HOL_Obool___Orderings_Oorder_20, fact_98_rev__predicate1D, fact_113_eval_Osimps_I4_J, fact_225_Sup1__I, tcon_HOL_Obool___Orderings_Opreorder_18, fact_63_in__mono, fact_151_surj__imp__surj__swap, fact_60_subset__eq, tcon_HOL_Obool___Orderings_Otop_21, fact_7_subsetI, fact_66_Compr__image__eq, fact_127_fm_Odistinct_I13_J, fact_132_tv_Osimps_I7_J, fact_37_order__subst1, fact_157_UN__ball__bex__simps_I2_J, fact_64_UNIV__witness, fact_103_top__conj_I2_J, fact_5_iso__tuple__UNIV__I, tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__lattice_1, fact_36_order__subst2, fact_218_top__finite__def, fact_136_swap__nilpotent, fact_185_UN__E, fact_77_image__subset__iff, fact_229_SUP__Sup__eq2, fact_53_set__eq__subset, fact_155_SUP__subset__mono, fact_236_pred__subset__eq2, fact_73_top_Oextremum__uniqueI, fact_104_top__conj_I1_J, fact_90_pred__subset__eq, fact_133_strict__mono__inv, fact_148_fm_Odistinct_I21_J, fact_222_UN__ball__bex__simps_I1_J
% 34.84/13.19 % No. of inferences in proof: 578
% 34.84/13.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 12879 ms resp. 12266 ms w/o parsing
% 36.54/13.51 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 36.54/13.51 % [INFO] Killing All external provers ...
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