%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP135^2 : 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 : n018.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 08:06:54 AM UTC 2026
% Result : Theorem 120.45s 94.62s
% Output : Refutation 121.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 254
% Syntax : Number of formulae : 510 ( 245 unt; 0 typ; 0 def)
% Number of atoms : 1786 ( 659 equ; 10 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 7440 ( 216 ~; 9 |; 78 &;6511 @)
% ( 0 <=>; 626 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 476 ( 476 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 50 usr; 9 con; 0-8 aty)
% Number of variables : 2287 ( 68 ^;2197 !; 22 ?;2287 :)
% 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(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(inj_on_decl,type,
inj_on:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > $o ) ).
thf(the_inv_into_decl,type,
the_inv_into:
!>[TA: $tType,TB: $tType] : ( ( set @ TB ) > ( TB > TA ) > TA > TB ) ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(top_top_decl,type,
top_top:
!>[TA: $tType] : TA ).
thf(paraco753463838ge_int_decl,type,
paraco753463838ge_int: ( nat > nat ) > ( ( list @ char ) > paraco415392788lle_tv ) > ( list @ char ) > paraco415392788lle_tv ).
thf(paraco1920534163nge_tv_decl,type,
paraco1920534163nge_tv: ( nat > nat ) > paraco415392788lle_tv > paraco415392788lle_tv ).
thf(paraco2077297190tv_rel_decl,type,
paraco2077297190tv_rel: ( product_prod @ ( nat > nat ) @ paraco415392788lle_tv ) > ( product_prod @ ( nat > nat ) @ paraco415392788lle_tv ) > $o ).
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(paraco1246693743ase_fm_decl,type,
paraco1246693743ase_fm:
!>[TA: $tType] : ( ( ( list @ char ) > TA ) > TA > ( paraco414474393lle_fm > TA ) > ( paraco414474393lle_fm > paraco414474393lle_fm > TA ) > ( paraco414474393lle_fm > paraco414474393lle_fm > TA ) > ( paraco414474393lle_fm > paraco414474393lle_fm > TA ) > paraco414474393lle_fm > TA ) ).
thf(paraco2040174112le_Det_decl,type,
paraco2040174112le_Det: $o > paraco415392788lle_tv ).
thf(paraco676387099_Indet_decl,type,
paraco676387099_Indet: nat > paraco415392788lle_tv ).
thf(paraco490622181ase_tv_decl,type,
paraco490622181ase_tv:
!>[TA: $tType] : ( ( $o > TA ) > ( nat > TA ) > paraco415392788lle_tv > TA ) ).
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(product_apfst_decl,type,
product_apfst:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB ) > ( product_prod @ TC @ TA ) > ( product_prod @ TB @ TA ) ) ).
thf(product_apsnd_decl,type,
product_apsnd:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB ) > ( product_prod @ TA @ TC ) > ( product_prod @ TA @ TB ) ) ).
thf(product_case_bool_decl,type,
product_case_bool:
!>[TA: $tType] : ( TA > TA > $o > TA ) ).
thf(product_curry_decl,type,
product_curry:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( ( product_prod @ TC @ TB ) > TA ) > TC > TB > TA ) ).
thf(produc2004651681e_prod_decl,type,
produc2004651681e_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_map_prod_decl,type,
product_map_prod:
!>[TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( ( TD > TC ) > ( TB > TA ) > ( product_prod @ TD @ TB ) > ( product_prod @ TC @ TA ) ) ).
thf(product_rec_prod_decl,type,
product_rec_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_fst_decl,type,
product_fst:
!>[TA: $tType,TB: $tType] : ( ( product_prod @ TB @ TA ) > TB ) ).
thf(product_snd_decl,type,
product_snd:
!>[TA: $tType,TB: $tType] : ( ( product_prod @ TB @ TA ) > TA ) ).
thf(product_swap_decl,type,
product_swap:
!>[TA: $tType,TB: $tType] : ( ( product_prod @ TB @ TA ) > ( product_prod @ TA @ TB ) ) ).
thf(inv_image_decl,type,
inv_image:
!>[TA: $tType,TB: $tType] : ( ( set @ ( product_prod @ TB @ TB ) ) > ( TA > TB ) > ( set @ ( product_prod @ TA @ TA ) ) ) ).
thf(total_on_decl,type,
total_on:
!>[TA: $tType] : ( ( set @ TA ) > ( set @ ( product_prod @ TA @ TA ) ) > $o ) ).
thf(image_decl,type,
image:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > ( set @ TA ) ) ).
thf(accp_decl,type,
accp:
!>[TA: $tType] : ( ( TA > TA > $o ) > TA > $o ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(f_decl,type,
f: nat > nat ).
thf(i_decl,type,
i: ( list @ char ) > paraco415392788lle_tv ).
thf(p1_decl,type,
p1: paraco414474393lle_fm ).
thf(p2_decl,type,
p2: paraco414474393lle_fm ).
thf(109,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_fst @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= ( product_snd @ TA @ TB @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_fst__swap) ).
thf(629,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_fst @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= ( product_snd @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(215,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_old_Oprod_Oinject) ).
thf(1024,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(217,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_69_eval_Ocases) ).
thf(1031,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)],[217]) ).
thf(196,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_old_Oprod_Oexhaust) ).
thf(962,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(189,axiom,
! [A: nat > nat] :
( ( inj_on @ nat @ nat @ A @ ( top_top @ ( set @ nat ) ) )
=> ( inj_on @ paraco415392788lle_tv @ paraco415392788lle_tv @ ( paraco1920534163nge_tv @ A ) @ ( top_top @ ( set @ paraco415392788lle_tv ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_change__tv__injection) ).
thf(941,plain,
! [A: nat > nat] :
( ( inj_on @ nat @ nat @ A @ ( top_top @ ( set @ nat ) ) )
=> ( inj_on @ paraco415392788lle_tv @ paraco415392788lle_tv @ ( paraco1920534163nge_tv @ A ) @ ( top_top @ ( set @ paraco415392788lle_tv ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(251,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_17_eval__negation) ).
thf(1158,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)],[251]) ).
thf(233,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(1073,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(122,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_24_fm_Odistinct_I27_J) ).
thf(677,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)],[122]) ).
thf(221,axiom,
! [A: product_prod @ ( nat > nat ) @ paraco415392788lle_tv] :
( ! [B: nat > nat,C: $o] :
( A
!= ( product_Pair @ ( nat > nat ) @ paraco415392788lle_tv @ B @ ( paraco2040174112le_Det @ C ) ) )
=> ~ ! [B: nat > nat,C: nat] :
( A
!= ( product_Pair @ ( nat > nat ) @ paraco415392788lle_tv @ B @ ( paraco676387099_Indet @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_change__tv_Ocases) ).
thf(1041,plain,
! [A: product_prod @ ( nat > nat ) @ paraco415392788lle_tv] :
( ! [B: nat > nat,C: $o] :
( A
!= ( product_Pair @ ( nat > nat ) @ paraco415392788lle_tv @ B @ ( paraco2040174112le_Det @ C ) ) )
=> ~ ! [B: nat > nat,C: nat] :
( A
!= ( product_Pair @ ( nat > nat ) @ paraco415392788lle_tv @ B @ ( paraco676387099_Indet @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(169,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA,D: $o] :
( ( A @ ( product_case_bool @ TA @ B @ C @ D ) )
= ( ( D
=> ( A @ B ) )
& ( ~ D
=> ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_bool_Osplit__sel) ).
thf(878,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA,D: $o] :
( ( A @ ( product_case_bool @ TA @ B @ C @ D ) )
= ( ( D
=> ( A @ B ) )
& ( ~ D
=> ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(58,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_228_eq__iff) ).
thf(440,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)],[58]) ).
thf(77,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_219_le__funE) ).
thf(511,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)],[77]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TC,C: TA] :
( ( product_apsnd @ TA @ TB @ TC @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( product_Pair @ TC @ TB @ B @ ( A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_apsnd__conv) ).
thf(550,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB,B: TC,C: TA] :
( ( product_apsnd @ TA @ TB @ TC @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( product_Pair @ TC @ TB @ B @ ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(128,axiom,
! [TA: $tType] : ( top @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Otop_7) ).
thf(698,plain,
! [TA: $tType] : ( top @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(143,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_155_surjE) ).
thf(747,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)],[143]) ).
thf(27,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_189_subset__imageE) ).
thf(340,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)],[27]) ).
thf(185,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_old_Oprod_Oinducts) ).
thf(930,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB] :
( ( inj_on @ ( product_prod @ TC @ TA ) @ ( product_prod @ TC @ TB ) @ ( product_apsnd @ TA @ TB @ TC @ A ) @ ( top_top @ ( set @ ( product_prod @ TC @ TA ) ) ) )
= ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_inj__apsnd) ).
thf(670,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB] :
( ( inj_on @ ( product_prod @ TC @ TA ) @ ( product_prod @ TC @ TB ) @ ( product_apsnd @ TA @ TB @ TC @ A ) @ ( top_top @ ( set @ ( product_prod @ TC @ TA ) ) ) )
= ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_prod_Ocollapse) ).
thf(417,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TC,C: TA] :
( ( product_apfst @ TC @ TB @ TA @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( product_Pair @ TB @ TA @ ( A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_apfst__conv) ).
thf(651,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TC,C: TA] :
( ( product_apfst @ TC @ TB @ TA @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( product_Pair @ TB @ TA @ ( A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Otop) ).
thf(389,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TA )
=> ( top @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(74,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_232_le__cases) ).
thf(504,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)],[74]) ).
thf(192,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_prod__induct3) ).
thf(949,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_swap @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= ( product_Pair @ TB @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_swap__simp) ).
thf(460,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_swap @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= ( product_Pair @ TB @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(186,axiom,
preorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_1) ).
thf(934,plain,
preorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(31,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_243_dual__order_Otrans) ).
thf(357,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)],[31]) ).
thf(248,axiom,
! [A: paraco415392788lle_tv > $o,B: paraco415392788lle_tv] :
( ( A @ ( paraco2040174112le_Det @ $true ) )
=> ( ( A @ ( paraco2040174112le_Det @ $false ) )
=> ( ! [C: nat] : ( A @ ( paraco676387099_Indet @ C ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_string__tv_Oinduct) ).
thf(1147,plain,
! [A: paraco415392788lle_tv > $o,B: paraco415392788lle_tv] :
( ( A @ ( paraco2040174112le_Det @ $true ) )
=> ( ( A @ ( paraco2040174112le_Det @ $false ) )
=> ( ! [C: nat] : ( A @ ( paraco676387099_Indet @ C ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( image @ ( product_prod @ TA @ TB ) @ ( product_prod @ TB @ TA ) @ ( product_swap @ TA @ TB ) @ C ) )
= ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_pair__in__swap__image) ).
thf(606,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TB @ TA ) @ ( product_Pair @ TB @ TA @ A @ B ) @ ( image @ ( product_prod @ TA @ TB ) @ ( product_prod @ TB @ TA ) @ ( product_swap @ TA @ TB ) @ C ) )
= ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
=> ( ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_prod__eqI) ).
thf(284,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
=> ( ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(170,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TB,D: $o] :
( ( A @ ( product_case_bool @ TB @ B @ C @ D ) )
= ( product_case_bool @ TA @ ( A @ B ) @ ( A @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_bool_Ocase__distrib) ).
thf(881,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TB,D: $o] :
( ( A @ ( product_case_bool @ TB @ B @ C @ D ) )
= ( product_case_bool @ TA @ ( A @ B ) @ ( A @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( the_inv_into @ TA @ TB @ B @ A @ ( A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_the__inv__into__f__f) ).
thf(289,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( the_inv_into @ TA @ TB @ B @ A @ ( A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(255,axiom,
( ( paraco1920534163nge_tv @ f @ ( paraco876059933e_eval @ i @ p2 ) )
= ( paraco2040174112le_Det @ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062change__tv_Af_A_Ieval_Ai_Ap2_J_A_061_ADet_ATrue_092_060close_062) ).
thf(1232,plain,
( ( paraco1920534163nge_tv @ f @ ( paraco876059933e_eval @ i @ p2 ) )
= ( paraco2040174112le_Det @ $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(183,axiom,
! [A: list @ char,B: list @ char] :
( ( ( paraco27778325le_Pro @ A )
= ( paraco27778325le_Pro @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_fm_Oinject_I1_J) ).
thf(924,plain,
! [A: list @ char,B: list @ char] :
( ( ( paraco27778325le_Pro @ A )
= ( paraco27778325le_Pro @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(156,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_prod__cases5) ).
thf(789,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
& ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_prod_Oexpand) ).
thf(591,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
& ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(59,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_234_le__cases3) ).
thf(443,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)],[59]) ).
thf(107,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_236_order__class_Oorder_Oeq__iff) ).
thf(623,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)],[107]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB,D: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TB @ C @ ( image @ TA @ TB @ A @ B ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ D )
=> ( member @ TA @ ( the_inv_into @ TA @ TB @ B @ A @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_the__inv__into__into) ).
thf(485,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB,D: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TB @ C @ ( image @ TA @ TB @ A @ B ) )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ D )
=> ( member @ TA @ ( the_inv_into @ TA @ TB @ B @ A @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(93,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_173_subset__antisym) ).
thf(574,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)],[93]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA] :
( ( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= C )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_fst__eqD) ).
thf(353,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA] :
( ( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= C )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(225,axiom,
! [A: ( nat > nat ) > paraco415392788lle_tv > $o,B: nat > nat,C: paraco415392788lle_tv] :
( ! [D: nat > nat,E: $o] : ( A @ D @ ( paraco2040174112le_Det @ E ) )
=> ( ! [D: nat > nat,E: nat] : ( A @ D @ ( paraco676387099_Indet @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_change__tv_Oinduct) ).
thf(1051,plain,
! [A: ( nat > nat ) > paraco415392788lle_tv > $o,B: nat > nat,C: paraco415392788lle_tv] :
( ! [D: nat > nat,E: $o] : ( A @ D @ ( paraco2040174112le_Det @ E ) )
=> ( ! [D: nat > nat,E: nat] : ( A @ D @ ( paraco676387099_Indet @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(242,axiom,
! [A: nat > nat,B: paraco415392788lle_tv,C: paraco415392788lle_tv] :
( ( ( paraco1920534163nge_tv @ A @ B )
= C )
=> ( ! [D: $o] :
( ( B
= ( paraco2040174112le_Det @ D ) )
=> ( C
!= ( paraco2040174112le_Det @ D ) ) )
=> ~ ! [D: nat] :
( ( B
= ( paraco676387099_Indet @ D ) )
=> ( C
!= ( paraco676387099_Indet @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_change__tv_Oelims) ).
thf(1109,plain,
! [A: nat > nat,B: paraco415392788lle_tv,C: paraco415392788lle_tv] :
( ( ( paraco1920534163nge_tv @ A @ B )
= C )
=> ( ! [D: $o] :
( ( B
= ( paraco2040174112le_Det @ D ) )
=> ( C
!= ( paraco2040174112le_Det @ D ) ) )
=> ~ ! [D: nat] :
( ( B
= ( paraco676387099_Indet @ D ) )
=> ( C
!= ( paraco676387099_Indet @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > TB,C: set @ TA] :
( ( ord_less_eq @ ( set @ TB ) @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ C )
& ( inj_on @ TA @ TB @ B @ D )
& ( A
= ( image @ TA @ TB @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_subset__image__inj) ).
thf(321,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > TB,C: set @ TA] :
( ( ord_less_eq @ ( set @ TB ) @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ D @ C )
& ( inj_on @ TA @ TB @ B @ D )
& ( A
= ( image @ TA @ TB @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(203,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_27_fm_Odistinct_I21_J) ).
thf(981,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)],[203]) ).
thf(252,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_34_eval__equality) ).
thf(1169,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)],[252]) ).
thf(126,axiom,
! [TA: $tType,A: $o > TA,B: nat > TA,C: nat] :
( ( paraco490622181ase_tv @ TA @ A @ B @ ( paraco676387099_Indet @ C ) )
= ( B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_tv_Osimps_I6_J) ).
thf(692,plain,
! [TA: $tType,A: $o > TA,B: nat > TA,C: nat] :
( ( paraco490622181ase_tv @ TA @ A @ B @ ( paraco676387099_Indet @ C ) )
= ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(194,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB,C: set @ ( product_prod @ TA @ TA ),D: TB > TA] :
( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ A @ B ) @ ( inv_image @ TA @ TB @ C @ D ) )
= ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_in__inv__image) ).
thf(956,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB,C: set @ ( product_prod @ TA @ TA ),D: TB > TA] :
( ( member @ ( product_prod @ TB @ TB ) @ ( product_Pair @ TB @ TB @ A @ B ) @ ( inv_image @ TA @ TB @ C @ D ) )
= ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(45,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_217_subset__trans) ).
thf(396,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)],[45]) ).
thf(54,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_190_image__subsetI) ).
thf(428,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)],[54]) ).
thf(240,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_35_double__negation) ).
thf(1104,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)],[240]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(312,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(234,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_52_eval_Osimps_I1_J) ).
thf(1074,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)],[234]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_prod_Oexhaust__sel) ).
thf(292,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(40,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_211_subset__eq) ).
thf(380,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)],[40]) ).
thf(117,axiom,
! [A: nat,B: nat] :
( ( ( paraco676387099_Indet @ A )
= ( paraco676387099_Indet @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_tv_Oinject_I2_J) ).
thf(661,plain,
! [A: nat,B: nat] :
( ( ( paraco676387099_Indet @ A )
= ( paraco676387099_Indet @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(158,axiom,
! [TA: $tType,A: $o > TA,B: nat > TA,C: nat] :
( ( paraco152590079rec_tv @ TA @ A @ B @ ( paraco676387099_Indet @ C ) )
= ( B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_tv_Osimps_I8_J) ).
thf(793,plain,
! [TA: $tType,A: $o > TA,B: nat > TA,C: nat] :
( ( paraco152590079rec_tv @ TA @ A @ B @ ( paraco676387099_Indet @ C ) )
= ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(163,axiom,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA,G: paraco414474393lle_fm,H: paraco414474393lle_fm] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco2084319816le_Eql @ G @ H ) )
= ( E @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_fm_Osimps_I40_J) ).
thf(810,plain,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA,G: paraco414474393lle_fm,H: paraco414474393lle_fm] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco2084319816le_Eql @ G @ H ) )
= ( E @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(35,axiom,
! [TA: $tType] : ( order @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_6) ).
thf(366,plain,
! [TA: $tType] : ( order @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ( ( member @ TB @ ( A @ C ) @ ( image @ TA @ TB @ A @ D ) )
= ( member @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_inj__on__image__mem__iff) ).
thf(534,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ( ( member @ TB @ ( A @ C ) @ ( image @ TA @ TB @ A @ D ) )
= ( member @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(231,axiom,
! [A: paraco415392788lle_tv] :
( ( A
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( A
!= ( paraco2040174112le_Det @ $false ) )
=> ~ ! [B: nat] :
( A
!= ( paraco676387099_Indet @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_string__tv_Ocases) ).
thf(1067,plain,
! [A: paraco415392788lle_tv] :
( ( A
!= ( paraco2040174112le_Det @ $true ) )
=> ( ( A
!= ( paraco2040174112le_Det @ $false ) )
=> ~ ! [B: nat] :
( A
!= ( paraco676387099_Indet @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(249,axiom,
( ( paraco876059933e_eval @ ( paraco753463838ge_int @ f @ i ) @ p1 )
= ( paraco1920534163nge_tv @ f @ ( paraco876059933e_eval @ i @ p1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_ih1) ).
thf(1153,plain,
( ( paraco876059933e_eval @ ( paraco753463838ge_int @ f @ i ) @ p1 )
= ( paraco1920534163nge_tv @ f @ ( paraco876059933e_eval @ i @ p1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(148,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ! [B: TA,C: TA] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_injI) ).
thf(761,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ! [B: TA,C: TA] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(174,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_22_fm_Oinject_I4_J) ).
thf(894,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)],[174]) ).
thf(238,axiom,
( ( paraco876059933e_eval @ i @ p2 )
= ( paraco2040174112le_Det @ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_a) ).
thf(1091,plain,
( ( paraco876059933e_eval @ i @ p2 )
= ( paraco2040174112le_Det @ $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on @ TA @ TB @ B @ A )
= ( inj_on @ TA @ TB @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_inj__on__cong) ).
thf(561,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( inj_on @ TA @ TB @ B @ A )
= ( inj_on @ TA @ TB @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_swap @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_swap__swap) ).
thf(297,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_swap @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType] :
( ( inj_on @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ B )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_inj__on__def) ).
thf(275,plain,
! [TA: $tType,TB: $tType] :
( ( inj_on @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ B )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(138,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_iso__tuple__UNIV__I) ).
thf(729,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(214,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( member @ TB @ B @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
= ( ? [C: TA] :
( ( B
= ( A @ C ) )
& ! [D: TA] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_range__ex1__eq) ).
thf(1021,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( member @ TB @ B @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) )
= ( ? [C: TA] :
( ( B
= ( A @ C ) )
& ! [D: TA] :
( ( B
= ( A @ D ) )
=> ( D = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(152,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_60_UNIV__eq__I) ).
thf(778,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(4,axiom,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_5) ).
thf(260,plain,
! [TA: $tType] : ( preorder @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(243,axiom,
! [A: paraco415392788lle_tv > $o,B: paraco415392788lle_tv] :
( ! [C: $o] : ( A @ ( paraco2040174112le_Det @ C ) )
=> ( ! [C: nat] : ( A @ ( paraco676387099_Indet @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_tv_Oinduct) ).
thf(1123,plain,
! [A: paraco415392788lle_tv > $o,B: paraco415392788lle_tv] :
( ! [C: $o] : ( A @ ( paraco2040174112le_Det @ C ) )
=> ( ! [C: nat] : ( A @ ( paraco676387099_Indet @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TB] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ( A @ C )
= D )
=> ( ( member @ TA @ C @ B )
=> ( ( the_inv_into @ TA @ TB @ B @ A @ D )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_the__inv__into__f__eq) ).
thf(349,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TB] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ( A @ C )
= D )
=> ( ( member @ TA @ C @ B )
=> ( ( the_inv_into @ TA @ TB @ B @ A @ D )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(180,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( inj_on @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_subset__inj__on) ).
thf(916,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( inj_on @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(96,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_187_subset__image__iff) ).
thf(583,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)],[96]) ).
thf(216,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_prod__induct5) ).
thf(1027,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(244,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_12_tv_Osimps_I7_J) ).
thf(1128,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)],[244]) ).
thf(241,axiom,
( ( paraco876059933e_eval @ i @ p1 )
!= ( paraco876059933e_eval @ i @ p2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_a_H) ).
thf(1106,plain,
( ( paraco876059933e_eval @ i @ p1 )
!= ( paraco876059933e_eval @ i @ p2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(23,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_227_ord__le__eq__subst) ).
thf(324,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)],[23]) ).
thf(200,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_UNIV__I) ).
thf(974,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TC @ TD,B: TA > TC,C: TB > TD,D: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TC @ TD ) @ A @ ( image @ ( product_prod @ TA @ TB ) @ ( product_prod @ TC @ TD ) @ ( product_map_prod @ TA @ TC @ TB @ TD @ B @ C ) @ D ) )
=> ~ ! [E: TA,F: TB] :
( ( A
= ( product_Pair @ TC @ TD @ ( B @ E ) @ ( C @ F ) ) )
=> ~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ F ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_prod__fun__imageE) ).
thf(519,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TC @ TD,B: TA > TC,C: TB > TD,D: set @ ( product_prod @ TA @ TB )] :
( ( member @ ( product_prod @ TC @ TD ) @ A @ ( image @ ( product_prod @ TA @ TB ) @ ( product_prod @ TC @ TD ) @ ( product_map_prod @ TA @ TC @ TB @ TD @ B @ C ) @ D ) )
=> ~ ! [E: TA,F: TB] :
( ( A
= ( product_Pair @ TC @ TD @ ( B @ E ) @ ( C @ F ) ) )
=> ~ ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ E @ F ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(105,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_214_subset__iff) ).
thf(615,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)],[105]) ).
thf(230,axiom,
( ( paraco876059933e_eval @ i @ p1 )
!= ( paraco2040174112le_Det @ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_a_H_H) ).
thf(1064,plain,
( ( paraco876059933e_eval @ i @ p1 )
!= ( paraco2040174112le_Det @ $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(247,axiom,
! [A: $o,B: nat] :
( ( paraco2040174112le_Det @ A )
!= ( paraco676387099_Indet @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_tv_Odistinct_I1_J) ).
thf(1138,plain,
! [A: $o,B: nat] :
( ( paraco2040174112le_Det @ A )
!= ( paraco676387099_Indet @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TB,C: TD,D: TA] :
( ( product_map_prod @ TD @ TC @ TA @ TB @ A @ B @ ( product_Pair @ TD @ TA @ C @ D ) )
= ( product_Pair @ TC @ TB @ ( A @ C ) @ ( B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_map__prod__simp) ).
thf(499,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TC,B: TA > TB,C: TD,D: TA] :
( ( product_map_prod @ TD @ TC @ TA @ TB @ A @ B @ ( product_Pair @ TD @ TA @ C @ D ) )
= ( product_Pair @ TC @ TB @ ( A @ C ) @ ( B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(205,axiom,
! [TA: $tType,TB: $tType] :
( ( image @ ( product_prod @ TA @ TB ) @ TA @ ( product_fst @ TA @ TB ) @ ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_range__fst) ).
thf(989,plain,
! [TA: $tType,TB: $tType] :
( ( image @ ( product_prod @ TA @ TB ) @ TA @ ( product_fst @ TA @ TB ) @ ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(154,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_156_surjI) ).
thf(783,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)],[154]) ).
thf(51,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_221_set__eq__subset) ).
thf(420,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)],[51]) ).
thf(1,conjecture,
( ( paraco876059933e_eval @ ( paraco753463838ge_int @ f @ i ) @ p2 )
= ( paraco2040174112le_Det @ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( paraco876059933e_eval @ ( paraco753463838ge_int @ f @ i ) @ p2 )
!= ( paraco2040174112le_Det @ $true ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(256,plain,
( ( paraco876059933e_eval @ ( paraco753463838ge_int @ f @ i ) @ p2 )
!= ( paraco2040174112le_Det @ $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(171,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_23_fm_Odistinct_I29_J) ).
thf(884,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)],[171]) ).
thf(84,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_212_equalityD1) ).
thf(537,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)],[84]) ).
thf(82,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_210_equalityE) ).
thf(526,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)],[82]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB,D: product_prod @ TA @ TB] :
( ( A @ B @ C )
=> ( ( D
= ( product_Pair @ TA @ TB @ B @ C ) )
=> ( A @ ( product_fst @ TA @ TB @ D ) @ ( product_snd @ TA @ TB @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_BNF__Greatest__Fixpoint_Osubst__Pair) ).
thf(637,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB,D: product_prod @ TA @ TB] :
( ( A @ B @ C )
=> ( ( D
= ( product_Pair @ TA @ TB @ B @ C ) )
=> ( A @ ( product_fst @ TA @ TB @ D ) @ ( product_snd @ TA @ TB @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(250,axiom,
! [A: ( list @ char ) > paraco415392788lle_tv] :
( ( paraco876059933e_eval @ A @ paraco251304083_Truth )
= ( paraco2040174112le_Det @ $true ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_eval_Osimps_I2_J) ).
thf(1155,plain,
! [A: ( list @ char ) > paraco415392788lle_tv] :
( ( paraco876059933e_eval @ A @ paraco251304083_Truth )
= ( paraco2040174112le_Det @ $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType] :
( ( product_swap @ TA @ TB )
= ( ^ [A: product_prod @ TA @ TB] : ( product_Pair @ TB @ TA @ ( product_snd @ TA @ TB @ A ) @ ( product_fst @ TA @ TB @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_prod_Oswap__def) ).
thf(547,plain,
! [TA: $tType,TB: $tType] :
( ( product_swap @ TA @ TB )
= ( ^ [A: product_prod @ TA @ TB] : ( product_Pair @ TB @ TA @ ( product_snd @ TA @ TB @ A ) @ ( product_fst @ TA @ TB @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(204,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_26_fm_Odistinct_I23_J) ).
thf(985,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)],[204]) ).
thf(224,axiom,
inj_on @ nat @ nat @ f @ ( top_top @ ( set @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_assms) ).
thf(1050,plain,
inj_on @ nat @ nat @ f @ ( top_top @ ( set @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(37,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_222_le__fun__def) ).
thf(371,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)],[37]) ).
thf(245,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( product_case_bool @ TA @ A @ B @ $true )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_old_Obool_Osimps_I3_J) ).
thf(1131,plain,
! [TA: $tType,A: TA,B: TA] :
( ( product_case_bool @ TA @ A @ B @ $true )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(115,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_172_subsetI) ).
thf(654,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)],[115]) ).
thf(157,axiom,
linorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(792,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: product_prod @ TA @ TB,C: TB > TC] :
( ( ( product_apsnd @ TB @ TC @ TA @ A @ B )
= ( product_apsnd @ TB @ TC @ TA @ C @ B ) )
= ( ( A @ ( product_snd @ TA @ TB @ B ) )
= ( C @ ( product_snd @ TA @ TB @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_apsnd__eq__conv) ).
thf(541,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: product_prod @ TA @ TB,C: TB > TC] :
( ( ( product_apsnd @ TB @ TC @ TA @ A @ B )
= ( product_apsnd @ TB @ TC @ TA @ C @ B ) )
= ( ( A @ ( product_snd @ TA @ TB @ B ) )
= ( C @ ( product_snd @ TA @ TB @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(226,axiom,
( ( paraco876059933e_eval @ ( paraco753463838ge_int @ f @ i ) @ p2 )
= ( paraco1920534163nge_tv @ f @ ( paraco876059933e_eval @ i @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_ih2) ).
thf(1054,plain,
( ( paraco876059933e_eval @ ( paraco753463838ge_int @ f @ i ) @ p2 )
= ( paraco1920534163nge_tv @ f @ ( paraco876059933e_eval @ i @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(232,axiom,
( ( paraco876059933e_eval @ i @ ( paraco1628874225le_Eql @ p1 @ p2 ) )
= ( paraco876059933e_eval @ i @ p1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_yes) ).
thf(1071,plain,
( ( paraco876059933e_eval @ i @ ( paraco1628874225le_Eql @ p1 @ p2 ) )
= ( paraco876059933e_eval @ i @ p1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(193,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_prod_Oinject) ).
thf(953,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( image @ TB @ TA @ ( the_inv_into @ TA @ TB @ B @ A ) @ ( image @ TA @ TB @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_the__inv__into__onto) ).
thf(586,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( image @ TB @ TA @ ( the_inv_into @ TA @ TB @ B @ A ) @ ( image @ TA @ TB @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(172,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_20_fm_Oinject_I3_J) ).
thf(888,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)],[172]) ).
thf(46,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_238_ord__le__eq__trans) ).
thf(398,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)],[46]) ).
thf(218,axiom,
! [A: set @ nat,B: paraco414474393lle_fm] :
( ~ ( paraco2086025920lid_in @ A @ B )
=> ~ ( paraco769098683_valid @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_transfer) ).
thf(1035,plain,
! [A: set @ nat,B: paraco414474393lle_fm] :
( ~ ( paraco2086025920lid_in @ A @ B )
=> ~ ( paraco769098683_valid @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TB > TA,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on @ TA @ TB @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_inj__on__inverseI) ).
thf(618,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TB > TA,C: TA > TB] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( B @ ( C @ D ) )
= D ) )
=> ( inj_on @ TA @ TB @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(53,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_229_antisym) ).
thf(425,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)],[53]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > TC,B: TA > TD,C: product_prod @ TA @ TB] :
( ( product_apsnd @ TB @ TC @ TD @ A @ ( product_apfst @ TA @ TD @ TB @ B @ C ) )
= ( product_Pair @ TD @ TC @ ( B @ ( product_fst @ TA @ TB @ C ) ) @ ( A @ ( product_snd @ TA @ TB @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_apsnd__apfst) ).
thf(513,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > TC,B: TA > TD,C: product_prod @ TA @ TB] :
( ( product_apsnd @ TB @ TC @ TD @ A @ ( product_apfst @ TA @ TD @ TB @ B @ C ) )
= ( product_Pair @ TD @ TC @ ( B @ ( product_fst @ TA @ TB @ C ) ) @ ( A @ ( product_snd @ TA @ TB @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(6,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_149_image__cong) ).
thf(264,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)],[6]) ).
thf(197,axiom,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ paraco251304083_Truth )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_fm_Osimps_I37_J) ).
thf(965,plain,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ paraco251304083_Truth )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(144,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( inj_on @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_inj__on__subset) ).
thf(750,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( inj_on @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(166,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA,C: TA] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_inj__def) ).
thf(819,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA,C: TA] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(177,axiom,
! [A: paraco414474393lle_fm] :
( ( A != paraco251304083_Truth )
=> ( ! [B: list @ char] :
( A
!= ( paraco27778325le_Pro @ B ) )
=> ( ! [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_49_props_Ocases) ).
thf(904,plain,
! [A: paraco414474393lle_fm] :
( ( A != paraco251304083_Truth )
=> ( ! [B: list @ char] :
( A
!= ( paraco27778325le_Pro @ B ) )
=> ( ! [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)],[177]) ).
thf(52,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_230_linear) ).
thf(423,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)],[52]) ).
thf(210,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_56_fm_Odistinct_I7_J) ).
thf(1007,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)],[210]) ).
thf(47,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_231_eq__refl) ).
thf(402,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)],[47]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: product_prod @ TA @ TB] :
( ( product_fst @ TC @ TB @ ( product_apfst @ TA @ TC @ TB @ A @ B ) )
= ( A @ ( product_fst @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_fst__apfst) ).
thf(281,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: product_prod @ TA @ TB] :
( ( product_fst @ TC @ TB @ ( product_apfst @ TA @ TC @ TB @ A @ B ) )
= ( A @ ( product_fst @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(168,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_old_Oprod_Orec) ).
thf(875,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ( ( ( image @ TA @ TB @ A @ C )
= ( image @ TA @ TB @ A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_inj__on__image__eq__iff) ).
thf(577,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ D @ B )
=> ( ( ( image @ TA @ TB @ A @ C )
= ( image @ TA @ TB @ A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(132,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_UNIV__witness) ).
thf(711,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > $o,D: TA] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( product_fst @ TB @ TA @ ( product_Pair @ TB @ TA @ B @ D ) ) )
& ( C @ ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_conjI__realizer) ).
thf(641,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > $o,D: TA] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( product_fst @ TB @ TA @ ( product_Pair @ TB @ TA @ B @ D ) ) )
& ( C @ ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(43,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_245_dual__order_Oantisym) ).
thf(391,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)],[43]) ).
thf(133,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_25_fm_Odistinct_I25_J) ).
thf(713,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)],[133]) ).
thf(228,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_14_eval__equality__simplify) ).
thf(1058,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)],[228]) ).
thf(63,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_213_equalityD2) ).
thf(466,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)],[63]) ).
thf(25,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_order__refl) ).
thf(335,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(102,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_218_le__funD) ).
thf(604,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)],[102]) ).
thf(123,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_28_fm_Odistinct_I19_J) ).
thf(681,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)],[123]) ).
thf(211,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_33_conjunction) ).
thf(1011,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)],[211]) ).
thf(223,axiom,
( paraco753463838ge_int
= ( ^ [A: nat > nat,B: ( list @ char ) > paraco415392788lle_tv,C: list @ char] : ( paraco1920534163nge_tv @ A @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_change__int__def) ).
thf(1048,plain,
( paraco753463838ge_int
= ( ^ [A: nat > nat,B: ( list @ char ) > paraco415392788lle_tv,C: list @ char] : ( paraco1920534163nge_tv @ A @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(176,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_54_fm_Odistinct_I5_J) ).
thf(900,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)],[176]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TD,B: TB > TC,C: product_prod @ TA @ TB] :
( ( product_snd @ TD @ TC @ ( product_map_prod @ TA @ TD @ TB @ TC @ A @ B @ C ) )
= ( B @ ( product_snd @ TA @ TB @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_snd__map__prod) ).
thf(406,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TD,B: TB > TC,C: product_prod @ TA @ TB] :
( ( product_snd @ TD @ TC @ ( product_map_prod @ TA @ TD @ TB @ TC @ A @ B @ C ) )
= ( B @ ( product_snd @ TA @ TB @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: TA] :
( ( inj_on @ TB @ TA @ A @ B )
=> ( ( member @ TA @ C @ ( image @ TB @ TA @ A @ B ) )
=> ( ( A @ ( the_inv_into @ TB @ TA @ B @ A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_f__the__inv__into__f) ).
thf(377,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TB,C: TA] :
( ( inj_on @ TB @ TA @ A @ B )
=> ( ( member @ TA @ C @ ( image @ TB @ TA @ A @ B ) )
=> ( ( A @ ( the_inv_into @ TB @ TA @ B @ A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(208,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_injD) ).
thf(996,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(33,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_208_in__mono) ).
thf(362,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)],[33]) ).
thf(92,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_150_bex__imageD) ).
thf(567,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)],[92]) ).
thf(140,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_prod__cases6) ).
thf(737,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType] :
( ( (=) @ ( product_prod @ TA @ TB ) )
= ( ^ [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
& ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_prod__eq__iff) ).
thf(318,plain,
! [TA: $tType,TB: $tType] :
( ( (=) @ ( product_prod @ TA @ TB ) )
= ( ^ [A: product_prod @ TA @ TB,B: product_prod @ TA @ TB] :
( ( ( product_fst @ TA @ TB @ A )
= ( product_fst @ TA @ TB @ B ) )
& ( ( product_snd @ TA @ TB @ A )
= ( product_snd @ TA @ TB @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB] :
( ( A @ B @ C )
=> ( A @ ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ C @ B ) ) @ ( product_fst @ TB @ TA @ ( product_Pair @ TB @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_exI__realizer) ).
thf(509,plain,
! [TA: $tType,TB: $tType,A: TA > TB > $o,B: TA,C: TB] :
( ( A @ B @ C )
=> ( A @ ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ C @ B ) ) @ ( product_fst @ TB @ TA @ ( product_Pair @ TB @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TD,B: TB > TC,C: product_prod @ TA @ TB] :
( ( product_apfst @ TA @ TD @ TC @ A @ ( product_apsnd @ TB @ TC @ TA @ B @ C ) )
= ( product_Pair @ TD @ TC @ ( A @ ( product_fst @ TA @ TB @ C ) ) @ ( B @ ( product_snd @ TA @ TB @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_apfst__apsnd) ).
thf(434,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TD,B: TB > TC,C: product_prod @ TA @ TB] :
( ( product_apfst @ TA @ TD @ TC @ A @ ( product_apsnd @ TB @ TC @ TA @ B @ C ) )
= ( product_Pair @ TD @ TC @ ( A @ ( product_fst @ TA @ TB @ C ) ) @ ( B @ ( product_snd @ TA @ TB @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB] :
( ! [C: TA,D: TA] :
( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on @ TA @ TB @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_inj__onI) ).
thf(477,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB] :
( ! [C: TA,D: TA] :
( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( ( B @ C )
= ( B @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on @ TA @ TB @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(147,axiom,
! [A: set @ nat,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco2086025920lid_in @ A @ ( paraco2100061555le_Con @ B @ C ) )
= ( ( paraco2086025920lid_in @ A @ B )
& ( paraco2086025920lid_in @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_conjunction__in) ).
thf(758,plain,
! [A: set @ nat,B: paraco414474393lle_fm,C: paraco414474393lle_fm] :
( ( paraco2086025920lid_in @ A @ ( paraco2100061555le_Con @ B @ C ) )
= ( ( paraco2086025920lid_in @ A @ B )
& ( paraco2086025920lid_in @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(28,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_159_range__eqI) ).
thf(345,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)],[28]) ).
thf(165,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) @ ( image @ TA @ TB @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_inj__image__subset__iff) ).
thf(816,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ord_less_eq @ ( set @ TB ) @ ( image @ TA @ TB @ A @ B ) @ ( image @ TA @ TB @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(104,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_148_ball__imageD) ).
thf(609,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)],[104]) ).
thf(100,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_233_order_Otrans) ).
thf(594,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)],[100]) ).
thf(137,axiom,
! [TA: $tType] :
( ( product_case_bool @ TA )
= ( ^ [A: TA,B: TA,C: $o] : ( if @ TA @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_bool_Ocase__eq__if) ).
thf(726,plain,
! [TA: $tType] :
( ( product_case_bool @ TA )
= ( ^ [A: TA,B: TA,C: $o] : ( if @ TA @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(129,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( product_curry @ TA @ TB @ TC )
= ( ^ [A: ( product_prod @ TA @ TB ) > TC,B: TA,C: TB] : ( A @ ( product_Pair @ TA @ TB @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_curry__conv) ).
thf(700,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( product_curry @ TA @ TB @ TC )
= ( ^ [A: ( product_prod @ TA @ TB ) > TC,B: TA,C: TB] : ( A @ ( product_Pair @ TA @ TB @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_snd__conv) ).
thf(626,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(190,axiom,
! [A: nat > nat,B: nat] :
( ( paraco1920534163nge_tv @ A @ ( paraco676387099_Indet @ B ) )
= ( paraco676387099_Indet @ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_change__tv_Osimps_I2_J) ).
thf(943,plain,
! [A: nat > nat,B: nat] :
( ( paraco1920534163nge_tv @ A @ ( paraco676387099_Indet @ B ) )
= ( paraco676387099_Indet @ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(229,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(1061,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: product_prod @ TA @ TB] :
( ( product_snd @ TC @ TB @ ( product_apfst @ TA @ TC @ TB @ A @ B ) )
= ( product_snd @ TA @ TB @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_snd__apfst) ).
thf(494,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: product_prod @ TA @ TB] :
( ( product_snd @ TC @ TB @ ( product_apfst @ TA @ TC @ TB @ A @ B ) )
= ( product_snd @ TA @ TB @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
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 @ ( 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_13_eval_Osimps_I5_J) ).
thf(1080,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)],[236]) ).
thf(195,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_surj__pair) ).
thf(959,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(127,axiom,
! [A: paraco414474393lle_fm,B: set @ nat] :
( ( paraco769098683_valid @ A )
=> ( paraco2086025920lid_in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_valid__valid__in) ).
thf(695,plain,
! [A: paraco414474393lle_fm,B: set @ nat] :
( ( paraco769098683_valid @ A )
=> ( paraco2086025920lid_in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_snd @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= ( product_fst @ TA @ TB @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_snd__swap) ).
thf(278,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( ( product_snd @ TB @ TA @ ( product_swap @ TA @ TB @ A ) )
= ( product_fst @ TA @ TB @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(44,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(394,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(182,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ ( product_prod @ TB @ TB )] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( total_on @ TB @ ( top_top @ ( set @ TB ) ) @ B )
=> ( total_on @ TA @ ( top_top @ ( set @ TA ) ) @ ( inv_image @ TB @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_total__inv__image) ).
thf(922,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ ( product_prod @ TB @ TB )] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( total_on @ TB @ ( top_top @ ( set @ TB ) ) @ B )
=> ( total_on @ TA @ ( top_top @ ( set @ TA ) ) @ ( inv_image @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: product_prod @ TA @ TB] :
( ( product_fst @ TA @ TC @ ( product_apsnd @ TB @ TC @ TA @ A @ B ) )
= ( product_fst @ TA @ TB @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_fst__apsnd) ).
thf(658,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: product_prod @ TA @ TB] :
( ( product_fst @ TA @ TC @ ( product_apsnd @ TB @ TC @ TA @ A @ B ) )
= ( product_fst @ TA @ TB @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(179,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco1628874225le_Eql @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_fm_Odistinct_I17_J) ).
thf(912,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco1628874225le_Eql @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(124,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( product_case_bool @ TA @ A @ B @ $false )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_old_Obool_Osimps_I4_J) ).
thf(685,plain,
! [TA: $tType,A: TA,B: TA] :
( ( product_case_bool @ TA @ A @ B @ $false )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(65,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_237_ord__eq__le__trans) ).
thf(473,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)],[65]) ).
thf(79,axiom,
! [TA: $tType] :
( ( total_on @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_total__on__def) ).
thf(516,plain,
! [TA: $tType] :
( ( total_on @ TA )
= ( ^ [A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(188,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TC,B: TB > TD] :
( ( inj_on @ TA @ TC @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( inj_on @ TB @ TD @ B @ ( top_top @ ( set @ TB ) ) )
=> ( inj_on @ ( product_prod @ TA @ TB ) @ ( product_prod @ TC @ TD ) @ ( product_map_prod @ TA @ TC @ TB @ TD @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_prod_Oinj__map) ).
thf(939,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TC,B: TB > TD] :
( ( inj_on @ TA @ TC @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( inj_on @ TB @ TD @ B @ ( top_top @ ( set @ TB ) ) )
=> ( inj_on @ ( product_prod @ TA @ TB ) @ ( product_prod @ TC @ TD ) @ ( product_map_prod @ TA @ TC @ TB @ TD @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(213,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_internal__case__prod__conv) ).
thf(1018,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(89,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_225_order__subst2) ).
thf(553,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)],[89]) ).
thf(254,axiom,
! [A: nat > nat,B: paraco415392788lle_tv,C: paraco415392788lle_tv] :
( ( ( paraco1920534163nge_tv @ A @ B )
= C )
=> ( ( accp @ ( product_prod @ ( nat > nat ) @ paraco415392788lle_tv ) @ paraco2077297190tv_rel @ ( product_Pair @ ( nat > nat ) @ paraco415392788lle_tv @ A @ B ) )
=> ( ! [D: $o] :
( ( B
= ( paraco2040174112le_Det @ D ) )
=> ( ( C
= ( paraco2040174112le_Det @ D ) )
=> ~ ( accp @ ( product_prod @ ( nat > nat ) @ paraco415392788lle_tv ) @ paraco2077297190tv_rel @ ( product_Pair @ ( nat > nat ) @ paraco415392788lle_tv @ A @ ( paraco2040174112le_Det @ D ) ) ) ) )
=> ~ ! [D: nat] :
( ( B
= ( paraco676387099_Indet @ D ) )
=> ( ( C
= ( paraco676387099_Indet @ ( A @ D ) ) )
=> ~ ( accp @ ( product_prod @ ( nat > nat ) @ paraco415392788lle_tv ) @ paraco2077297190tv_rel @ ( product_Pair @ ( nat > nat ) @ paraco415392788lle_tv @ A @ ( paraco676387099_Indet @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_change__tv_Opelims) ).
thf(1203,plain,
! [A: nat > nat,B: paraco415392788lle_tv,C: paraco415392788lle_tv] :
( ( ( paraco1920534163nge_tv @ A @ B )
= C )
=> ( ( accp @ ( product_prod @ ( nat > nat ) @ paraco415392788lle_tv ) @ paraco2077297190tv_rel @ ( product_Pair @ ( nat > nat ) @ paraco415392788lle_tv @ A @ B ) )
=> ( ! [D: $o] :
( ( B
= ( paraco2040174112le_Det @ D ) )
=> ( ( C
= ( paraco2040174112le_Det @ D ) )
=> ~ ( accp @ ( product_prod @ ( nat > nat ) @ paraco415392788lle_tv ) @ paraco2077297190tv_rel @ ( product_Pair @ ( nat > nat ) @ paraco415392788lle_tv @ A @ ( paraco2040174112le_Det @ D ) ) ) ) )
=> ~ ! [D: nat] :
( ( B
= ( paraco676387099_Indet @ D ) )
=> ( ( C
= ( paraco676387099_Indet @ ( A @ D ) ) )
=> ~ ( accp @ ( product_prod @ ( nat > nat ) @ paraco415392788lle_tv ) @ paraco2077297190tv_rel @ ( product_Pair @ ( nat > nat ) @ paraco415392788lle_tv @ A @ ( paraco676387099_Indet @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( inj_on @ TB @ TA @ ( the_inv_into @ TA @ TB @ B @ A ) @ ( image @ TA @ TB @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_inj__on__the__inv__into) ).
thf(589,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( inj_on @ TB @ TA @ ( the_inv_into @ TA @ TB @ B @ A ) @ ( image @ TA @ TB @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(184,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB] :
( ( inj_on @ ( product_prod @ TA @ TC ) @ ( product_prod @ TB @ TC ) @ ( product_apfst @ TA @ TB @ TC @ A ) @ ( top_top @ ( set @ ( product_prod @ TA @ TC ) ) ) )
= ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_inj__apfst) ).
thf(927,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TB] :
( ( inj_on @ ( product_prod @ TA @ TC ) @ ( product_prod @ TB @ TC ) @ ( product_apfst @ TA @ TB @ TC @ A ) @ ( top_top @ ( set @ ( product_prod @ TA @ TC ) ) ) )
= ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(38,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_244_dual__order_Oeq__iff) ).
thf(374,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)],[38]) ).
thf(246,axiom,
! [A: paraco415392788lle_tv] :
( ! [B: $o] :
( A
!= ( paraco2040174112le_Det @ B ) )
=> ~ ! [B: nat] :
( A
!= ( paraco676387099_Indet @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_tv_Oexhaust) ).
thf(1134,plain,
! [A: paraco415392788lle_tv] :
( ! [B: $o] :
( A
!= ( paraco2040174112le_Det @ B ) )
=> ~ ! [B: nat] :
( A
!= ( paraco676387099_Indet @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(68,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_224_order__subst1) ).
thf(487,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)],[68]) ).
thf(198,axiom,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA,G: paraco414474393lle_fm] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco329115265le_Neg @ G ) )
= ( C @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_fm_Osimps_I38_J) ).
thf(968,plain,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA,G: paraco414474393lle_fm] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco329115265le_Neg @ G ) )
= ( C @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(60,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_157_rangeI) ).
thf(458,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)],[60]) ).
thf(90,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_147_rev__image__eqI) ).
thf(557,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)],[90]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > TC,B: TA > TD,C: product_prod @ TA @ TB] :
( ( product_apsnd @ TB @ TC @ TD @ A @ ( product_apfst @ TA @ TD @ TB @ B @ C ) )
= ( product_apfst @ TA @ TD @ TC @ B @ ( product_apsnd @ TB @ TC @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_apsnd__apfst__commute) ).
thf(580,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TB > TC,B: TA > TD,C: product_prod @ TA @ TB] :
( ( product_apsnd @ TB @ TC @ TD @ A @ ( product_apfst @ TA @ TD @ TB @ B @ C ) )
= ( product_apfst @ TA @ TD @ TC @ B @ ( product_apsnd @ TB @ TC @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(295,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(131,axiom,
! [A: list @ char,B: paraco414474393lle_fm] :
( ( paraco27778325le_Pro @ A )
!= ( paraco329115265le_Neg @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_fm_Odistinct_I3_J) ).
thf(707,plain,
! [A: list @ char,B: paraco414474393lle_fm] :
( ( paraco27778325le_Pro @ A )
!= ( paraco329115265le_Neg @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(199,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ C ) )
= ( member @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_inj__image__mem__iff) ).
thf(971,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ C ) )
= ( member @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(49,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_226_ord__eq__le__subst) ).
thf(409,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)],[49]) ).
thf(207,axiom,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA,G: paraco414474393lle_fm,H: paraco414474393lle_fm] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco2100061555le_Con @ G @ H ) )
= ( D @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_fm_Osimps_I39_J) ).
thf(993,plain,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA,G: paraco414474393lle_fm,H: paraco414474393lle_fm] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco2100061555le_Con @ G @ H ) )
= ( D @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(121,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco2084319816le_Eql @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_fm_Odistinct_I15_J) ).
thf(673,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco2084319816le_Eql @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(220,axiom,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA,G: list @ char] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco27778325le_Pro @ G ) )
= ( A @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_fm_Osimps_I36_J) ).
thf(1038,plain,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA,G: list @ char] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco27778325le_Pro @ G ) )
= ( A @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(134,axiom,
! [TA: $tType,TB: $tType] :
( ( image @ ( product_prod @ TB @ TA ) @ TA @ ( product_snd @ TB @ TA ) @ ( top_top @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_range__snd) ).
thf(717,plain,
! [TA: $tType,TB: $tType] :
( ( image @ ( product_prod @ TB @ TA ) @ TA @ ( product_snd @ TB @ TA ) @ ( top_top @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(73,axiom,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_8) ).
thf(502,plain,
! [TA: $tType] : ( ord @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(62,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_235_antisym__conv) ).
thf(463,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)],[62]) ).
thf(64,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_151_image__iff) ).
thf(470,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)],[64]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: product_prod @ TA @ TB,C: TA > TC] :
( ( ( product_apfst @ TA @ TC @ TB @ A @ B )
= ( product_apfst @ TA @ TC @ TB @ C @ B ) )
= ( ( A @ ( product_fst @ TA @ TB @ B ) )
= ( C @ ( product_fst @ TA @ TB @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_apfst__eq__conv) ).
thf(359,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > TC,B: product_prod @ TA @ TB,C: TA > TC] :
( ( ( product_apfst @ TA @ TC @ TB @ A @ B )
= ( product_apfst @ TA @ TC @ TB @ C @ B ) )
= ( ( A @ ( product_fst @ TA @ TB @ B ) )
= ( C @ ( product_fst @ TA @ TB @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(86,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_239_order__class_Oorder_Oantisym) ).
thf(544,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)],[86]) ).
thf(142,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(744,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(130,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_126_ssubst__Pair__rhs) ).
thf(703,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)],[130]) ).
thf(202,axiom,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_top__apply) ).
thf(978,plain,
! [TA: $tType,TB: $tType] :
( ( top @ TB )
=> ( ( top_top @ ( TA > TB ) )
= ( ^ [A: TA] : ( top_top @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(20,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_142_image__eqI) ).
thf(314,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)],[20]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TA > TC,E: TB > TD] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( member @ ( product_prod @ TC @ TD ) @ ( product_Pair @ TC @ TD @ ( D @ A ) @ ( E @ B ) ) @ ( image @ ( product_prod @ TA @ TB ) @ ( product_prod @ TC @ TD ) @ ( product_map_prod @ TA @ TC @ TB @ TD @ D @ E ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_map__prod__imageI) ).
thf(497,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA,B: TB,C: set @ ( product_prod @ TA @ TB ),D: TA > TC,E: TB > TD] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ A @ B ) @ C )
=> ( member @ ( product_prod @ TC @ TD ) @ ( product_Pair @ TC @ TD @ ( D @ A ) @ ( E @ B ) ) @ ( image @ ( product_prod @ TA @ TB ) @ ( product_prod @ TC @ TD ) @ ( product_map_prod @ TA @ TC @ TB @ TD @ D @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(81,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_209_subsetD) ).
thf(524,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)],[81]) ).
thf(173,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( image @ TA @ TB @ A @ B )
= ( image @ TA @ TB @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_inj__image__eq__iff) ).
thf(891,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: set @ TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( image @ TA @ TB @ A @ B )
= ( image @ TA @ TB @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(253,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_15_eval_Osimps_I4_J) ).
thf(1189,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)],[253]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( C != D )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_inj__on__contraD) ).
thf(368,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( C != D )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( A @ C )
!= ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(150,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_55_fm_Odistinct_I9_J) ).
thf(771,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)],[150]) ).
thf(201,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_subset__UNIV) ).
thf(976,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(125,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_prod__induct4) ).
thf(688,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(164,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_prod__cases7) ).
thf(813,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(18,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ! [C: TA,D: TA] :
( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) )
=> ( total_on @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_total__onI) ).
thf(304,plain,
! [TA: $tType,A: set @ TA,B: set @ ( product_prod @ TA @ TA )] :
( ! [C: TA,D: TA] :
( ( member @ TA @ C @ A )
=> ( ( member @ TA @ D @ A )
=> ( ( C != D )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ D ) @ B )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ C ) @ B ) ) ) ) )
=> ( total_on @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_inj__onD) ).
thf(632,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(153,axiom,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] : ( inj_on @ ( product_prod @ TA @ TB ) @ ( product_prod @ TB @ TA ) @ ( product_swap @ TA @ TB ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_inj__swap) ).
thf(781,plain,
! [TA: $tType,TB: $tType,A: set @ ( product_prod @ TA @ TB )] : ( inj_on @ ( product_prod @ TA @ TB ) @ ( product_prod @ TB @ TA ) @ ( product_swap @ TA @ TB ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(191,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_prod__cases3) ).
thf(946,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(3,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_220_le__funI) ).
thf(258,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)],[3]) ).
thf(139,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_Pair__inject) ).
thf(731,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(155,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA,B: TC > TB] :
( ( ( image @ TD @ TA @ A @ ( top_top @ ( set @ TD ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( ( image @ TC @ TB @ B @ ( top_top @ ( set @ TC ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ( ( image @ ( product_prod @ TD @ TC ) @ ( product_prod @ TA @ TB ) @ ( product_map_prod @ TD @ TA @ TC @ TB @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ TD @ TC ) ) ) )
= ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_map__prod__surj) ).
thf(786,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD > TA,B: TC > TB] :
( ( ( image @ TD @ TA @ A @ ( top_top @ ( set @ TD ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( ( image @ TC @ TB @ B @ ( top_top @ ( set @ TC ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ( ( image @ ( product_prod @ TD @ TC ) @ ( product_prod @ TA @ TB ) @ ( product_map_prod @ TD @ TA @ TC @ TB @ A @ B ) @ ( top_top @ ( set @ ( product_prod @ TD @ TC ) ) ) )
= ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(119,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( the_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A @ ( A @ B ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_the__inv__f__f) ).
thf(667,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( the_inv_into @ TA @ TB @ ( top_top @ ( set @ TA ) ) @ A @ ( A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(235,axiom,
! [TA: $tType,A: $o > TA,B: nat > TA,C: $o] :
( ( paraco490622181ase_tv @ TA @ A @ B @ ( paraco2040174112le_Det @ C ) )
= ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_tv_Osimps_I5_J) ).
thf(1077,plain,
! [TA: $tType,A: $o > TA,B: nat > TA,C: $o] :
( ( paraco490622181ase_tv @ TA @ A @ B @ ( paraco2040174112le_Det @ C ) )
= ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: product_prod @ TA @ TB] :
( ( product_snd @ TA @ TC @ ( product_apsnd @ TB @ TC @ TA @ A @ B ) )
= ( A @ ( product_snd @ TA @ TB @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_snd__apsnd) ).
thf(272,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: product_prod @ TA @ TB] :
( ( product_snd @ TA @ TC @ ( product_apsnd @ TB @ TC @ TA @ A @ B ) )
= ( A @ ( product_snd @ TA @ TB @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(41,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_242_linorder__wlog) ).
thf(383,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)],[41]) ).
thf(222,axiom,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm] :
( ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ B ) )
= ( paraco490622181ase_tv @ paraco415392788lle_tv @ ( product_case_bool @ paraco415392788lle_tv @ ( paraco2040174112le_Det @ $false ) @ ( paraco2040174112le_Det @ $true ) ) @ paraco676387099_Indet @ ( paraco876059933e_eval @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_eval_Osimps_I3_J) ).
thf(1045,plain,
! [A: ( list @ char ) > paraco415392788lle_tv,B: paraco414474393lle_fm] :
( ( paraco876059933e_eval @ A @ ( paraco329115265le_Neg @ B ) )
= ( paraco490622181ase_tv @ paraco415392788lle_tv @ ( product_case_bool @ paraco415392788lle_tv @ ( paraco2040174112le_Det @ $false ) @ ( paraco2040174112le_Det @ $true ) ) @ paraco676387099_Indet @ ( paraco876059933e_eval @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(160,axiom,
! [TA: $tType,TB: $tType] :
( ( image @ ( product_prod @ TB @ TA ) @ ( product_prod @ TA @ TB ) @ ( product_swap @ TB @ TA ) @ ( top_top @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_surj__swap) ).
thf(800,plain,
! [TA: $tType,TB: $tType] :
( ( image @ ( product_prod @ TB @ TA ) @ ( product_prod @ TA @ TB ) @ ( product_swap @ TB @ TA ) @ ( top_top @ ( set @ ( product_prod @ TB @ TA ) ) ) )
= ( top_top @ ( set @ ( product_prod @ TA @ TB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(12,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_152_imageI) ).
thf(287,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)],[12]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TA] :
( ( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= C )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_snd__eqD) ).
thf(300,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TA] :
( ( ( product_snd @ TB @ TA @ ( product_Pair @ TB @ TA @ A @ B ) )
= C )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(209,axiom,
! [A: paraco414474393lle_fm > $o,B: paraco414474393lle_fm] :
( ( A @ paraco251304083_Truth )
=> ( ! [C: list @ char] : ( A @ ( paraco27778325le_Pro @ C ) )
=> ( ! [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_68_props_Oinduct) ).
thf(999,plain,
! [A: paraco414474393lle_fm > $o,B: paraco414474393lle_fm] :
( ( A @ paraco251304083_Truth )
=> ( ! [C: list @ char] : ( A @ ( paraco27778325le_Pro @ C ) )
=> ( ! [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)],[209]) ).
thf(145,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_inj__eq) ).
thf(752,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA,C: TA] :
( ( inj_on @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(55,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_subset__refl) ).
thf(432,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(5,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_191_image__mono) ).
thf(262,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)],[5]) ).
thf(181,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco2100061555le_Con @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_fm_Odistinct_I13_J) ).
thf(918,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco2100061555le_Con @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_inj__on__eq__iff) ).
thf(506,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TA,D: TA] :
( ( inj_on @ TA @ TB @ A @ B )
=> ( ( member @ TA @ C @ B )
=> ( ( member @ TA @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
= ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(162,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA,D: $o] :
( ( A @ ( product_case_bool @ TA @ B @ C @ D ) )
= ( ~ ( ( D
& ~ ( A @ B ) )
| ( ~ D
& ~ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_bool_Osplit__sel__asm) ).
thf(807,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA,D: $o] :
( ( A @ ( product_case_bool @ TA @ B @ C @ D ) )
= ( ~ ( ( D
& ~ ( A @ B ) )
| ( ~ D
& ~ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TC,B: TB > TD,C: product_prod @ TA @ TB] :
( ( product_fst @ TC @ TD @ ( product_map_prod @ TA @ TC @ TB @ TD @ A @ B @ C ) )
= ( A @ ( product_fst @ TA @ TB @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_fst__map__prod) ).
thf(437,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA > TC,B: TB > TD,C: product_prod @ TA @ TB] :
( ( product_fst @ TC @ TD @ ( product_map_prod @ TA @ TC @ TB @ TD @ A @ B @ C ) )
= ( A @ ( product_fst @ TA @ TB @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(111,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_240_order__trans) ).
thf(635,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)],[111]) ).
thf(135,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_21_fm_Oinject_I5_J) ).
thf(720,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)],[135]) ).
thf(159,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_44_fm_Oexhaust) ).
thf(796,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)],[159]) ).
thf(175,axiom,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA,G: paraco414474393lle_fm,H: paraco414474393lle_fm] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco1628874225le_Eql @ G @ H ) )
= ( F @ G @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_fm_Osimps_I41_J) ).
thf(897,plain,
! [TA: $tType,A: ( list @ char ) > TA,B: TA,C: paraco414474393lle_fm > TA,D: paraco414474393lle_fm > paraco414474393lle_fm > TA,E: paraco414474393lle_fm > paraco414474393lle_fm > TA,F: paraco414474393lle_fm > paraco414474393lle_fm > TA,G: paraco414474393lle_fm,H: paraco414474393lle_fm] :
( ( paraco1246693743ase_fm @ TA @ A @ B @ C @ D @ E @ F @ ( paraco1628874225le_Eql @ G @ H ) )
= ( F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(149,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_prod__cases) ).
thf(767,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(227,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_10_valid__def) ).
thf(1056,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)],[227]) ).
thf(118,axiom,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( ( ( paraco329115265le_Neg @ A )
= ( paraco329115265le_Neg @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_fm_Oinject_I2_J) ).
thf(664,plain,
! [A: paraco414474393lle_fm,B: paraco414474393lle_fm] :
( ( ( paraco329115265le_Neg @ A )
= ( paraco329115265le_Neg @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(239,axiom,
! [A: $o,B: $o] :
( ( ( paraco2040174112le_Det @ A )
= ( paraco2040174112le_Det @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_tv_Oinject_I1_J) ).
thf(1093,plain,
! [A: $o,B: $o] :
( ( ( paraco2040174112le_Det @ A )
= ( paraco2040174112le_Det @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(141,axiom,
! [A: list @ char] :
( ( paraco27778325le_Pro @ A )
!= paraco251304083_Truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_fm_Odistinct_I1_J) ).
thf(740,plain,
! [A: list @ char] :
( ( paraco27778325le_Pro @ A )
!= paraco251304083_Truth ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_surjective__pairing) ).
thf(332,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TA @ TB] :
( A
= ( product_Pair @ TA @ TB @ ( product_fst @ TA @ TB @ A ) @ ( product_snd @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TA] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( ( B @ ( C @ D ) )
= ( B @ ( C @ E ) ) )
= ( ( B @ D )
= ( B @ E ) ) ) ) )
=> ( ( inj_on @ TA @ TA @ C @ A )
=> ( ( inj_on @ TA @ TB @ B @ ( image @ TA @ TA @ C @ A ) )
= ( inj_on @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_inj__on__image__iff) ).
thf(596,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TA] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( ( B @ ( C @ D ) )
= ( B @ ( C @ E ) ) )
= ( ( B @ D )
= ( B @ E ) ) ) ) )
=> ( ( inj_on @ TA @ TA @ C @ A )
=> ( ( inj_on @ TA @ TB @ B @ ( image @ TA @ TA @ C @ A ) )
= ( inj_on @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(136,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_158_surj__def) ).
thf(723,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)],[136]) ).
thf(167,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_43_fm_Oinduct) ).
thf(822,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)],[167]) ).
thf(178,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_199_subrelI) ).
thf(908,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)],[178]) ).
thf(206,axiom,
order @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_2) ).
thf(992,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(161,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_prod__induct6) ).
thf(803,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_fst__conv) ).
thf(337,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB] :
( ( product_fst @ TA @ TB @ ( product_Pair @ TA @ TB @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(187,axiom,
! [A: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco329115265le_Neg @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_fm_Odistinct_I11_J) ).
thf(935,plain,
! [A: paraco414474393lle_fm] :
( paraco251304083_Truth
!= ( paraco329115265le_Neg @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(146,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_154_surjD) ).
thf(755,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)],[146]) ).
thf(34,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_dual__order_Orefl) ).
thf(364,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(212,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_prod__induct7) ).
thf(1014,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(219,axiom,
ord @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_3) ).
thf(1037,plain,
ord @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(151,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_prod__cases4) ).
thf(775,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(69,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_188_image__subset__iff) ).
thf(491,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)],[69]) ).
thf(237,axiom,
! [A: nat > nat,B: $o] :
( ( paraco1920534163nge_tv @ A @ ( paraco2040174112le_Det @ B ) )
= ( paraco2040174112le_Det @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_change__tv_Osimps_I1_J) ).
thf(1088,plain,
! [A: nat > nat,B: $o] :
( ( paraco1920534163nge_tv @ A @ ( paraco2040174112le_Det @ B ) )
= ( paraco2040174112le_Det @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(1234,plain,
$false,
inference(e,[status(thm)],[629,1024,1031,962,941,1158,1073,677,1041,878,440,511,550,698,747,340,930,670,417,651,389,504,949,460,934,357,1147,606,284,881,289,1232,924,789,591,443,623,485,574,353,1051,1109,321,981,1169,692,956,396,428,1104,312,1074,292,380,661,793,810,366,534,1067,1153,761,894,1091,561,297,275,729,1021,778,260,1123,349,916,583,1027,1128,1106,324,974,519,615,1064,1138,499,989,783,420,256,884,537,526,637,1155,547,985,1050,371,1131,654,792,541,1054,1071,953,586,888,398,1035,618,425,513,264,965,750,819,904,423,1007,402,281,875,577,711,641,391,713,1058,466,335,604,681,1011,1048,900,406,377,996,362,567,737,318,509,434,477,758,345,816,609,594,726,700,626,943,1061,494,1080,959,695,278,394,922,658,912,685,473,516,939,1018,553,1203,589,927,374,1134,487,968,458,557,580,295,707,971,409,993,673,1038,717,502,463,470,359,544,744,703,978,314,497,524,891,1189,368,771,976,688,813,304,632,781,946,258,731,786,667,1077,272,383,1045,800,287,300,999,752,432,262,918,506,807,437,635,720,796,897,767,1056,664,1093,740,332,596,723,822,908,992,803,337,935,755,364,1014,1037,775,491,1088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP135^2 : 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
% 0.09/0.19 % Computer : n018.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 20:01:11 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 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
% 0.86/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.01/1.16 % [INFO] Parsing done (364ms).
% 2.01/1.17 % [INFO] Running in sequential loop mode.
% 3.40/1.62 % [INFO] eprover registered as external prover.
% 3.40/1.63 % [INFO] Scanning for conjecture ...
% 3.56/1.78 % [INFO] Found a conjecture (or negated_conjecture) and 279 axioms. Running axiom selection ...
% 4.07/1.93 % [INFO] Axiom selection finished. Selected 253 axioms (removed 26 axioms).
% 5.02/2.25 % [INFO] Problem is higher-order (TPTP THF).
% 5.02/2.28 % [INFO] Type checking passed.
% 5.02/2.29 % [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 ...
% 120.45/94.61 % External prover 'e' found a proof!
% 120.45/94.62 % [INFO] Killing All external provers ...
% 120.45/94.62 % Time passed: 94276ms (effective reasoning time: 93442ms)
% 120.45/94.62 % 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)>
% 120.45/94.62 % Axioms used in derivation (253): fact_147_rev__image__eqI, fact_206_total__onI, fact_195_fst__conv, fact_213_equalityD2, fact_26_fm_Odistinct_I23_J, fact_18_assms, fact_108_old_Oprod_Oinducts, fact_247_prod_Oexpand, fact_25_fm_Odistinct_I25_J, tcon_Nat_Onat___Orderings_Oorder_2, fact_82_tv_Oexhaust, fact_184_fst__swap, fact_255_subset__image__inj, fact_163_inj__image__mem__iff, fact_244_dual__order_Oeq__iff, fact_15_eval_Osimps_I4_J, fact_194_snd__eqD, fact_9_yes, fact_221_set__eq__subset, fact_74_the__inv__f__f, fact_129_apsnd__apfst__commute, fact_67_inj__onD, tcon_Nat_Onat___Orderings_Olinorder, fact_112_prod__induct5, fact_87_tv_Osimps_I6_J, fact_27_fm_Odistinct_I21_J, fact_72_valid__valid__in, fact_95_prod_Oinject, fact_212_equalityD1, fact_106_old_Obool_Osimps_I4_J, fact_41_inj__eq, fact_161_range__ex1__eq, fact_165_f__the__inv__into__f, fact_239_order__class_Oorder_Oantisym, fact_64_inj__on__cong, fact_38_top__apply, fact_154_surjD, fact_76_fm_Osimps_I37_J, fact_226_ord__eq__le__subst, tcon_fun___Orderings_Oord, fact_105_old_Obool_Osimps_I3_J, fact_40_injI, fact_234_le__cases3, fact_124_inj__apsnd, fact_4_a_H_H, fact_181_snd__apsnd, fact_92_fm_Osimps_I39_J, fact_156_surjI, fact_7_change__int__def, fact_116_prod__cases6, fact_43_fm_Oinduct, fact_245_dual__order_Oantisym, fact_219_le__funE, fact_249_inj__on__image__mem__iff, fact_24_fm_Odistinct_I27_J, fact_118_prod__cases4, fact_155_surjE, fact_248_prod__eq__iff, fact_1__092_060open_062change__tv_Af_A_Ieval_Ai_Ap2_J_A_061_ADet_ATrue_092_060close_062, fact_207_total__on__def, fact_3_tv_Oinject_I1_J, fact_210_equalityE, fact_110_prod__induct7, fact_58_change__tv__injection, fact_241_dual__order_Orefl, fact_54_fm_Odistinct_I5_J, fact_237_ord__eq__le__trans, fact_65_inj__on__def, fact_149_image__cong, fact_132_curry__conv, fact_29_fm_Odistinct_I17_J, fact_253_conjI__realizer, fact_122_old_Oprod_Orec, fact_197_prod_Oexhaust__sel, fact_166_inj__on__the__inv__into, fact_59_UNIV__witness, fact_229_antisym, fact_144_swap__simp, fact_84_tv_Odistinct_I1_J, fact_140_map__prod__imageI, fact_145_pair__in__swap__image, fact_186_apfst__apsnd, fact_170_the__inv__into__into, fact_30_fm_Odistinct_I15_J, fact_10_valid__def, fact_100_surj__pair, fact_204_inj__on__subset, fact_164_prod__fun__imageE, fact_114_prod__induct3, help_If_1_1_T, fact_62_inj__on__contraD, fact_120_Pair__inject, fact_111_prod__induct6, fact_16_tv_Osimps_I5_J, fact_153_inj__on__image__iff, fact_97_eval_Osimps_I3_J, fact_69_eval_Ocases, fact_71_change__tv_Oelims, fact_128_apsnd__conv, fact_86_the__inv__into__f__eq, fact_177_fst__apfst, fact_150_bex__imageD, fact_142_image__eqI, fact_5_a_H, fact_61_inj__on__inverseI, fact_42_inj__def, fact_88_change__tv_Osimps_I2_J, fact_203_subset__UNIV, fact_240_order__trans, fact_102_bool_Ocase__distrib, fact_19_fm_Oinject_I2_J, tcon_Set_Oset___Orderings_Oorder_6, fact_75_conjunction__in, fact_55_fm_Odistinct_I9_J, fact_77_tv_Oinject_I2_J, fact_37_iso__tuple__UNIV__I, fact_180_apsnd__eq__conv, fact_50_fm_Oinject_I1_J, fact_81_string__tv_Ocases, fact_172_subsetI, fact_2_ih2, fact_91_fm_Osimps_I38_J, fact_131_prod_Oinj__map, fact_39_injD, fact_17_eval__negation, fact_44_fm_Oexhaust, fact_160_map__prod__surj, fact_96_old_Oprod_Oinject, fact_243_dual__order_Otrans, fact_138_the__inv__into__onto, fact_209_subsetD, fact_121_prod__cases, fact_80_change__tv_Oinduct, fact_93_fm_Osimps_I41_J, fact_104_bool_Osplit__sel, fact_119_prod__cases3, fact_225_order__subst2, fact_250_inj__on__image__eq__iff, fact_198_surjective__pairing, fact_83_tv_Oinduct, fact_109_old_Oprod_Oexhaust, fact_173_subset__antisym, fact_254_BNF__Greatest__Fixpoint_Osubst__Pair, tcon_Nat_Onat___Orderings_Oord_3, fact_214_subset__iff, fact_192_prod_Oswap__def, fact_182_prod_Ocollapse, fact_90_tv_Osimps_I8_J, fact_146_surj__swap, fact_251_inj__image__subset__iff, fact_31_fm_Odistinct_I13_J, fact_125_inj__apfst, fact_178_snd__apfst, fact_33_conjunction, fact_66_inj__onI, fact_94_fm_Osimps_I40_J, fact_68_props_Oinduct, fact_127_apfst__conv, fact_227_ord__le__eq__subst, fact_126_ssubst__Pair__rhs, fact_224_order__subst1, fact_158_surj__def, fact_22_fm_Oinject_I4_J, fact_222_le__fun__def, help_If_2_1_T, tcon_Set_Oset___Orderings_Oord_8, fact_130_change__tv_Opelims, tcon_fun___Orderings_Otop, fact_13_eval_Osimps_I5_J, help_If_3_1_T, fact_233_order_Otrans, fact_242_linorder__wlog, fact_57_fm_Odistinct_I1_J, fact_211_subset__eq, fact_205_subset__inj__on, fact_56_fm_Odistinct_I7_J, fact_35_double__negation, fact_143_swap__swap, fact_12_tv_Osimps_I7_J, fact_179_fst__apsnd, fact_193_fst__eqD, fact_60_UNIV__eq__I, fact_113_prod__induct4, fact_188_image__subset__iff, fact_28_fm_Odistinct_I19_J, fact_183_snd__swap, fact_103_bool_Ocase__eq__if, fact_135_map__prod__simp, fact_11_eval_Osimps_I2_J, fact_85_the__inv__into__f__f, tcon_fun___Orderings_Opreorder, fact_117_prod__cases5, fact_141_inj__swap, fact_236_order__class_Oorder_Oeq__iff, fact_6_ih1, fact_157_rangeI, tcon_Nat_Onat___Orderings_Opreorder_1, fact_63_inj__on__eq__iff, fact_218_le__funD, fact_79_string__tv_Oinduct, fact_49_props_Ocases, fact_159_range__eqI, fact_220_le__funI, fact_73_transfer, fact_190_image__subsetI, tcon_fun___Orderings_Oorder, fact_151_image__iff, fact_171_order__refl, fact_32_fm_Odistinct_I11_J, fact_89_fm_Osimps_I36_J, fact_217_subset__trans, fact_107_change__tv_Ocases, fact_152_imageI, fact_20_fm_Oinject_I3_J, fact_115_prod__cases7, fact_175_snd__map__prod, fact_228_eq__iff, fact_235_antisym__conv, fact_176_apfst__eq__conv, fact_199_subrelI, fact_238_ord__le__eq__trans, fact_14_eval__equality__simplify, fact_246_prod__eqI, fact_230_linear, fact_34_eval__equality, fact_148_ball__imageD, tcon_Set_Oset___Orderings_Opreorder_5, fact_252_exI__realizer, fact_162_inj__image__eq__iff, fact_196_snd__conv, fact_189_subset__imageE, fact_101_bool_Osplit__sel__asm, fact_169_range__snd, fact_123_internal__case__prod__conv, fact_187_subset__image__iff, fact_139_in__inv__image, fact_21_fm_Oinject_I5_J, tcon_Set_Oset___Orderings_Otop_7, fact_174_fst__map__prod, fact_215_subset__refl, fact_23_fm_Odistinct_I29_J, fact_191_image__mono, fact_208_in__mono, fact_185_apsnd__apfst, fact_167_total__inv__image, fact_231_eq__refl, fact_0_a, fact_232_le__cases, fact_8_change__tv_Osimps_I1_J, fact_53_fm_Odistinct_I3_J, fact_36_UNIV__I, fact_52_eval_Osimps_I1_J, fact_168_range__fst
% 120.45/94.62 % No. of inferences in proof: 510
% 120.45/94.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 94276 ms resp. 93442 ms w/o parsing
% 121.16/94.88 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 121.16/94.88 % [INFO] Killing All external provers ...
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