TSTP Solution File: ITP152^1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP152^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:48:17 EDT 2024
% Result : Theorem 31.56s 9.52s
% Output : Refutation 32.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 474
% Syntax : Number of formulae : 802 ( 253 unt; 148 typ; 0 def)
% Number of atoms : 1929 ( 520 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 6789 ( 234 ~; 43 |; 168 &;5516 @)
% ( 0 <=>; 828 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 23 ( 22 usr)
% Number of type conns : 504 ( 504 >; 0 *; 0 +; 0 <<)
% Number of symbols : 128 ( 126 usr; 9 con; 0-3 aty)
% Number of variables : 2102 ( 102 ^1952 !; 48 ?;2102 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr1930443975od_a_a_type,type,
set_Pr1930443975od_a_a: $tType ).
thf(produc562496743od_a_a_type,type,
produc562496743od_a_a: $tType ).
thf(set_Pr1295299783od_a_a_type,type,
set_Pr1295299783od_a_a: $tType ).
thf(produc1990712039od_a_a_type,type,
produc1990712039od_a_a: $tType ).
thf(set_Pr146455751iset_a_type,type,
set_Pr146455751iset_a: $tType ).
thf(produc558600423iset_a_type,type,
produc558600423iset_a: $tType ).
thf(set_Pr1821581383od_a_a_type,type,
set_Pr1821581383od_a_a: $tType ).
thf(produc2061001575od_a_a_type,type,
produc2061001575od_a_a: $tType ).
thf(set_Pr1948701895od_a_a_type,type,
set_Pr1948701895od_a_a: $tType ).
thf(produc1572603623od_a_a_type,type,
produc1572603623od_a_a: $tType ).
thf(set_Pr158363655iset_a_type,type,
set_Pr158363655iset_a: $tType ).
thf(produc1127127335iset_a_type,type,
produc1127127335iset_a: $tType ).
thf(multis1735859763od_a_a_type,type,
multis1735859763od_a_a: $tType ).
thf(set_mu1281098573od_a_a_type,type,
set_mu1281098573od_a_a: $tType ).
thf(multis599418605od_a_a_type,type,
multis599418605od_a_a: $tType ).
thf(set_Product_prod_a_a_type,type,
set_Product_prod_a_a: $tType ).
thf(multiset_multiset_a_type,type,
multiset_multiset_a: $tType ).
thf(set_multiset_a_type,type,
set_multiset_a: $tType ).
thf(product_prod_a_a_type,type,
product_prod_a_a: $tType ).
thf(multiset_a_type,type,
multiset_a: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(a_type,type,
a: $tType ).
thf(minus_1257885652od_a_a_type,type,
minus_1257885652od_a_a: multis599418605od_a_a > multis599418605od_a_a > multis599418605od_a_a ).
thf(minus_1649712171iset_a_type,type,
minus_1649712171iset_a: multiset_a > multiset_a > multiset_a ).
thf(plus_p404985124od_a_a_type,type,
plus_p404985124od_a_a: multis599418605od_a_a > multis599418605od_a_a > multis599418605od_a_a ).
thf(plus_plus_multiset_a_type,type,
plus_plus_multiset_a: multiset_a > multiset_a > multiset_a ).
thf(zero_z160849828od_a_a_type,type,
zero_z160849828od_a_a: multis599418605od_a_a ).
thf(zero_zero_multiset_a_type,type,
zero_zero_multiset_a: multiset_a ).
thf(add_ms1725977093od_a_a_type,type,
add_ms1725977093od_a_a: product_prod_a_a > multis599418605od_a_a > multis599418605od_a_a ).
thf(add_mset_a_type,type,
add_mset_a: a > multiset_a > multiset_a ).
thf(fold_m773816523od_a_a_type,type,
fold_m773816523od_a_a: ( multis599418605od_a_a > multis599418605od_a_a > multis599418605od_a_a ) > multis599418605od_a_a > multis1735859763od_a_a > multis599418605od_a_a ).
thf(fold_m382157835iset_a_type,type,
fold_m382157835iset_a: ( multiset_a > multiset_a > multiset_a ) > multiset_a > multiset_multiset_a > multiset_a ).
thf(mult1_1719650714od_a_a_type,type,
mult1_1719650714od_a_a: set_Pr1948701895od_a_a > set_Pr1821581383od_a_a ).
thf(mult1_a_type,type,
mult1_a: set_Product_prod_a_a > set_Pr158363655iset_a ).
thf(mult_a_type,type,
mult_a: set_Product_prod_a_a > set_Pr158363655iset_a ).
thf(multp_a_type,type,
multp_a: ( a > a > $o ) > multiset_a > multiset_a > $o ).
thf(set_ms1869569194od_a_a_type,type,
set_ms1869569194od_a_a: multis1735859763od_a_a > set_mu1281098573od_a_a ).
thf(set_mset_multiset_a_type,type,
set_mset_multiset_a: multiset_multiset_a > set_multiset_a ).
thf(set_ms1818337124od_a_a_type,type,
set_ms1818337124od_a_a: multis599418605od_a_a > set_Product_prod_a_a ).
thf(set_mset_a_type,type,
set_mset_a: multiset_a > set_a ).
thf(order_1040740996od_a_a_type,type,
order_1040740996od_a_a: set_mu1281098573od_a_a > set_Pr1821581383od_a_a > $o ).
thf(order_750350043iset_a_type,type,
order_750350043iset_a: set_multiset_a > set_Pr158363655iset_a > $o ).
thf(order_359341630od_a_a_type,type,
order_359341630od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(order_preorder_on_a_type,type,
order_preorder_on_a: set_a > set_Product_prod_a_a > $o ).
thf(order_1505515173od_a_a_type,type,
order_1505515173od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(order_1558116988r_on_a_type,type,
order_1558116988r_on_a: set_a > set_Product_prod_a_a > $o ).
thf(ord_le1824328871od_a_a_type,type,
ord_le1824328871od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o ).
thf(ord_less_eq_set_a_type,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(top_to1483957574_a_a_o_type,type,
top_to1483957574_a_a_o: product_prod_a_a > $o ).
thf(top_top_a_o_type,type,
top_top_a_o: a > $o ).
thf(top_to398455383od_a_a_type,type,
top_to398455383od_a_a: set_Product_prod_a_a ).
thf(top_top_set_a_type,type,
top_top_set_a: set_a ).
thf(prefer1191731497od_a_a_type,type,
prefer1191731497od_a_a: multis599418605od_a_a > set_mu1281098573od_a_a > set_Pr1821581383od_a_a > set_mu1281098573od_a_a ).
thf(prefer2130004608iset_a_type,type,
prefer2130004608iset_a: multiset_a > set_multiset_a > set_Pr158363655iset_a > set_multiset_a ).
thf(prefer477097315od_a_a_type,type,
prefer477097315od_a_a: product_prod_a_a > set_Product_prod_a_a > set_Pr1948701895od_a_a > set_Product_prod_a_a ).
thf(prefer161218362good_a_type,type,
prefer161218362good_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(prefer1340910575od_a_a_type,type,
prefer1340910575od_a_a: set_mu1281098573od_a_a > set_Pr1821581383od_a_a > $o ).
thf(prefer1571048262iset_a_type,type,
prefer1571048262iset_a: set_multiset_a > set_Pr158363655iset_a > $o ).
thf(prefer1338892073od_a_a_type,type,
prefer1338892073od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(prefer1292084992ence_a_type,type,
prefer1292084992ence_a: set_a > set_Product_prod_a_a > $o ).
thf(prefer1669415233od_a_a_type,type,
prefer1669415233od_a_a: set_mu1281098573od_a_a > set_Pr1821581383od_a_a > $o ).
thf(prefer1779827352iset_a_type,type,
prefer1779827352iset_a: set_multiset_a > set_Pr158363655iset_a > $o ).
thf(prefer697821563od_a_a_type,type,
prefer697821563od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(prefer719835986ence_a_type,type,
prefer719835986ence_a: set_a > set_Product_prod_a_a > $o ).
thf(prefer1064779160od_a_a_type,type,
prefer1064779160od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(prefer580340847ioms_a_type,type,
prefer580340847ioms_a: set_a > set_Product_prod_a_a > $o ).
thf(produc1859144151od_a_a_type,type,
produc1859144151od_a_a: multis599418605od_a_a > multis599418605od_a_a > produc2061001575od_a_a ).
thf(produc2037245207iset_a_type,type,
produc2037245207iset_a: multiset_a > multiset_a > produc1127127335iset_a ).
thf(produc1474507607od_a_a_type,type,
produc1474507607od_a_a: product_prod_a_a > product_prod_a_a > produc1572603623od_a_a ).
thf(product_Pair_a_a_type,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(produc1548936141_a_a_o_type,type,
produc1548936141_a_a_o: ( produc2061001575od_a_a > $o ) > multis599418605od_a_a > multis599418605od_a_a > $o ).
thf(produc1530159757et_a_o_type,type,
produc1530159757et_a_o: ( produc1127127335iset_a > $o ) > multiset_a > multiset_a > $o ).
thf(produc94438221_a_a_o_type,type,
produc94438221_a_a_o: ( produc1572603623od_a_a > $o ) > product_prod_a_a > product_prod_a_a > $o ).
thf(product_curry_a_a_o_type,type,
product_curry_a_a_o: ( product_prod_a_a > $o ) > a > a > $o ).
thf(produc143372156od_a_a_type,type,
produc143372156od_a_a: ( product_prod_a_a > set_Product_prod_a_a ) > a > a > set_Product_prod_a_a ).
thf(produc580150227_set_a_type,type,
produc580150227_set_a: ( product_prod_a_a > set_a ) > a > a > set_a ).
thf(produc748978966_a_a_o_type,type,
produc748978966_a_a_o: ( a > a > $o ) > product_prod_a_a > $o ).
thf(produc1653225349od_a_a_type,type,
produc1653225349od_a_a: ( a > a > set_Product_prod_a_a ) > product_prod_a_a > set_Product_prod_a_a ).
thf(produc694541532_set_a_type,type,
produc694541532_set_a: ( a > a > set_a ) > product_prod_a_a > set_a ).
thf(produc700022774_a_a_a_type,type,
produc700022774_a_a_a: ( a > a ) > ( a > a ) > product_prod_a_a > product_prod_a_a ).
thf(produc429414904iset_a_type,type,
produc429414904iset_a: ( multiset_a > multiset_a > set_multiset_a ) > produc1127127335iset_a > set_multiset_a ).
thf(produc2041367259od_a_a_type,type,
produc2041367259od_a_a: ( multiset_a > multiset_a > set_Product_prod_a_a ) > produc1127127335iset_a > set_Product_prod_a_a ).
thf(produc747255346_set_a_type,type,
produc747255346_set_a: ( multiset_a > multiset_a > set_a ) > produc1127127335iset_a > set_a ).
thf(produc734625720iset_a_type,type,
produc734625720iset_a: ( product_prod_a_a > product_prod_a_a > set_multiset_a ) > produc1572603623od_a_a > set_multiset_a ).
thf(produc869579762_set_a_type,type,
produc869579762_set_a: ( product_prod_a_a > product_prod_a_a > set_a ) > produc1572603623od_a_a > set_a ).
thf(produc1833107820_a_a_o_type,type,
produc1833107820_a_a_o: ( a > a > $o ) > product_prod_a_a > $o ).
thf(produc1121147169od_a_a_type,type,
produc1121147169od_a_a: ( a > a > set_mu1281098573od_a_a ) > product_prod_a_a > set_mu1281098573od_a_a ).
thf(produc1828150264iset_a_type,type,
produc1828150264iset_a: ( a > a > set_multiset_a ) > product_prod_a_a > set_multiset_a ).
thf(produc93594587iset_a_type,type,
produc93594587iset_a: ( a > a > set_Pr158363655iset_a ) > product_prod_a_a > set_Pr158363655iset_a ).
thf(produc1093061851od_a_a_type,type,
produc1093061851od_a_a: ( a > a > set_Product_prod_a_a ) > product_prod_a_a > set_Product_prod_a_a ).
thf(produc961951794_set_a_type,type,
produc961951794_set_a: ( a > a > set_a ) > product_prod_a_a > set_a ).
thf(product_fst_a_a_type,type,
product_fst_a_a: product_prod_a_a > a ).
thf(product_snd_a_a_type,type,
product_snd_a_a: product_prod_a_a > a ).
thf(produc1913956215od_a_a_type,type,
produc1913956215od_a_a: produc2061001575od_a_a > produc2061001575od_a_a ).
thf(produc506430135iset_a_type,type,
produc506430135iset_a: produc1127127335iset_a > produc1127127335iset_a ).
thf(produc1641853175od_a_a_type,type,
produc1641853175od_a_a: produc1572603623od_a_a > produc1572603623od_a_a ).
thf(product_swap_a_a_type,type,
product_swap_a_a: product_prod_a_a > product_prod_a_a ).
thf(asym_a_type,type,
asym_a: set_Product_prod_a_a > $o ).
thf(inv_im1681759523_a_a_a_type,type,
inv_im1681759523_a_a_a: set_Pr1821581383od_a_a > ( a > multis599418605od_a_a ) > set_Product_prod_a_a ).
thf(inv_im343774418iset_a_type,type,
inv_im343774418iset_a: set_Pr158363655iset_a > ( multiset_a > multiset_a ) > set_Pr158363655iset_a ).
thf(inv_im1716587189od_a_a_type,type,
inv_im1716587189od_a_a: set_Pr158363655iset_a > ( product_prod_a_a > multiset_a ) > set_Pr1948701895od_a_a ).
thf(inv_im975322764et_a_a_type,type,
inv_im975322764et_a_a: set_Pr158363655iset_a > ( a > multiset_a ) > set_Product_prod_a_a ).
thf(inv_im184450735iset_a_type,type,
inv_im184450735iset_a: set_Pr1948701895od_a_a > ( multiset_a > product_prod_a_a ) > set_Pr158363655iset_a ).
thf(inv_im777352425_a_a_a_type,type,
inv_im777352425_a_a_a: set_Pr1948701895od_a_a > ( a > product_prod_a_a ) > set_Product_prod_a_a ).
thf(inv_im941243329od_a_a_type,type,
inv_im941243329od_a_a: set_Product_prod_a_a > ( multis599418605od_a_a > a ) > set_Pr1821581383od_a_a ).
thf(inv_im479034648iset_a_type,type,
inv_im479034648iset_a: set_Product_prod_a_a > ( multiset_a > a ) > set_Pr158363655iset_a ).
thf(inv_im15016955od_a_a_type,type,
inv_im15016955od_a_a: set_Product_prod_a_a > ( product_prod_a_a > a ) > set_Pr1948701895od_a_a ).
thf(inv_image_a_a_type,type,
inv_image_a_a: set_Product_prod_a_a > ( a > a ) > set_Product_prod_a_a ).
thf(irrefl1672195874od_a_a_type,type,
irrefl1672195874od_a_a: set_Pr1821581383od_a_a > $o ).
thf(irrefl_multiset_a_type,type,
irrefl_multiset_a: set_Pr158363655iset_a > $o ).
thf(irrefl76447196od_a_a_type,type,
irrefl76447196od_a_a: set_Pr1948701895od_a_a > $o ).
thf(irrefl_a_type,type,
irrefl_a: set_Product_prod_a_a > $o ).
thf(refl_o581572716od_a_a_type,type,
refl_o581572716od_a_a: set_mu1281098573od_a_a > set_Pr1821581383od_a_a > $o ).
thf(refl_on_multiset_a_type,type,
refl_on_multiset_a: set_multiset_a > set_Pr158363655iset_a > $o ).
thf(refl_o1298442278od_a_a_type,type,
refl_o1298442278od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(refl_on_a_type,type,
refl_on_a: set_a > set_Product_prod_a_a > $o ).
thf(total_1024184433od_a_a_type,type,
total_1024184433od_a_a: set_mu1281098573od_a_a > set_Pr1821581383od_a_a > $o ).
thf(total_on_multiset_a_type,type,
total_on_multiset_a: set_multiset_a > set_Pr158363655iset_a > $o ).
thf(total_1490170027od_a_a_type,type,
total_1490170027od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > $o ).
thf(total_on_a_type,type,
total_on_a: set_a > set_Product_prod_a_a > $o ).
thf(trans_1520871884od_a_a_type,type,
trans_1520871884od_a_a: set_Pr1821581383od_a_a > $o ).
thf(trans_multiset_a_type,type,
trans_multiset_a: set_Pr158363655iset_a > $o ).
thf(trans_972827014od_a_a_type,type,
trans_972827014od_a_a: set_Pr1948701895od_a_a > $o ).
thf(trans_a_type,type,
trans_a: set_Product_prod_a_a > $o ).
thf(collec1948052440od_a_a_type,type,
collec1948052440od_a_a: ( multis599418605od_a_a > $o ) > set_mu1281098573od_a_a ).
thf(collect_multiset_a_type,type,
collect_multiset_a: ( multiset_a > $o ) > set_multiset_a ).
thf(collec8264402od_a_a_type,type,
collec8264402od_a_a: ( produc2061001575od_a_a > $o ) > set_Pr1821581383od_a_a ).
thf(collec1104713362iset_a_type,type,
collec1104713362iset_a: ( produc1127127335iset_a > $o ) > set_Pr158363655iset_a ).
thf(collec1635618130od_a_a_type,type,
collec1635618130od_a_a: ( produc1572603623od_a_a > $o ) > set_Pr1948701895od_a_a ).
thf(collec645855634od_a_a_type,type,
collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
thf(collect_a_type,type,
collect_a: ( a > $o ) > set_a ).
thf(image_794773445od_a_a_type,type,
image_794773445od_a_a: ( product_prod_a_a > product_prod_a_a ) > set_Product_prod_a_a > set_Product_prod_a_a ).
thf(image_340790172_a_a_a_type,type,
image_340790172_a_a_a: ( product_prod_a_a > a ) > set_Product_prod_a_a > set_a ).
thf(image_1725938350od_a_a_type,type,
image_1725938350od_a_a: ( a > product_prod_a_a ) > set_a > set_Product_prod_a_a ).
thf(image_a_a_type,type,
image_a_a: ( a > a ) > set_a > set_a ).
thf(lex_prod_a_a_type,type,
lex_prod_a_a: set_Product_prod_a_a > set_Product_prod_a_a > set_Pr1948701895od_a_a ).
thf(same_fst_a_a_type,type,
same_fst_a_a: ( a > $o ) > ( a > set_Product_prod_a_a ) > set_Pr1948701895od_a_a ).
thf(member1755255446od_a_a_type,type,
member1755255446od_a_a: multis599418605od_a_a > set_mu1281098573od_a_a > $o ).
thf(member_multiset_a_type,type,
member_multiset_a: multiset_a > set_multiset_a > $o ).
thf(member1349055120od_a_a_type,type,
member1349055120od_a_a: produc2061001575od_a_a > set_Pr1821581383od_a_a > $o ).
thf(member340150864iset_a_type,type,
member340150864iset_a: produc1127127335iset_a > set_Pr158363655iset_a > $o ).
thf(member2057358096od_a_a_type,type,
member2057358096od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > $o ).
thf(member449909584od_a_a_type,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(member_a_type,type,
member_a: a > set_a > $o ).
thf(carrier_type,type,
carrier: set_a ).
thf(relation_type,type,
relation: set_Product_prod_a_a ).
thf(x_type,type,
x: a ).
thf(y_type,type,
y: a ).
thf(183,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a,D: set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ A @ ( prefer477097315od_a_a @ B @ C @ D ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_at__least__as__goodD) ).
thf(892,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a,D: set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ A @ ( prefer477097315od_a_a @ B @ C @ D ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(304,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a,D: set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ A @ ( prefer477097315od_a_a @ B @ C @ D ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_at__lst__asgd__ge) ).
thf(1322,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a,D: set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ A @ ( prefer477097315od_a_a @ B @ C @ D ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(219,axiom,
! [A: a > a > set_Product_prod_a_a,B: a,C: a] :
( ( produc1093061851od_a_a @ A @ ( product_Pair_a_a @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_old_Oprod_Ocase) ).
thf(1036,plain,
! [A: a > a > set_Product_prod_a_a,B: a,C: a] :
( ( produc1093061851od_a_a @ A @ ( product_Pair_a_a @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(153,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( ( produc1474507607od_a_a @ A @ B )
= ( produc1474507607od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_prod_Oinject) ).
thf(809,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( ( produc1474507607od_a_a @ A @ B )
= ( produc1474507607od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(140,axiom,
! [A: set_Pr158363655iset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( trans_multiset_a @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ B @ C ) @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ A )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_transD) ).
thf(760,plain,
! [A: set_Pr158363655iset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( trans_multiset_a @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ B @ C ) @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ A )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ B @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(241,axiom,
prefer719835986ence_a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_rational__preference__axioms) ).
thf(1105,plain,
prefer719835986ence_a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(279,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( prefer1338892073od_a_a @ A @ B )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
=> ( member449909584od_a_a @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_preference_Onot__outside) ).
thf(1237,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( prefer1338892073od_a_a @ A @ B )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
=> ( member449909584od_a_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(4,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_Collect__cong) ).
thf(333,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(197,axiom,
! [A: a > $o,B: a,C: a,D: a,E: a > set_Product_prod_a_a] :
( ( A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ ( E @ B ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ B @ C ) @ ( product_Pair_a_a @ B @ D ) ) @ ( same_fst_a_a @ A @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_same__fstI) ).
thf(941,plain,
! [A: a > $o,B: a,C: a,D: a,E: a > set_Product_prod_a_a] :
( ( A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ ( E @ B ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ B @ C ) @ ( product_Pair_a_a @ B @ D ) ) @ ( same_fst_a_a @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(110,axiom,
! [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a,E: multis599418605od_a_a] :
( ( prefer1669415233od_a_a @ A @ B )
=> ( ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
& ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ D @ C ) @ B ) )
=> ( ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ D @ E ) @ B )
& ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ E @ D ) @ B ) )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ E ) @ B )
& ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ E @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_rational__preference_Ostrict__trans) ).
thf(666,plain,
! [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a,E: multis599418605od_a_a] :
( ( prefer1669415233od_a_a @ A @ B )
=> ( ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
& ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ D @ C ) @ B ) )
=> ( ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ D @ E ) @ B )
& ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ E @ D ) @ B ) )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ E ) @ B )
& ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ E @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(243,axiom,
( prefer1338892073od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ! [C: product_prod_a_a,D: product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
=> ( member449909584od_a_a @ C @ A ) )
& ! [C: product_prod_a_a,D: product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
=> ( member449909584od_a_a @ D @ A ) )
& ( order_359341630od_a_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_preference__def) ).
thf(1110,plain,
( prefer1338892073od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ! [C: product_prod_a_a,D: product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
=> ( member449909584od_a_a @ C @ A ) )
& ! [C: product_prod_a_a,D: product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
=> ( member449909584od_a_a @ D @ A ) )
& ( order_359341630od_a_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(49,axiom,
! [A: a,B: multiset_a,C: a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( C != A )
=> ( ( add_mset_a @ C @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) )
= ( minus_1649712171iset_a @ ( add_mset_a @ C @ B ) @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_multiset__add__sub__el__shuffle) ).
thf(481,plain,
! [A: a,B: multiset_a,C: a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( C != A )
=> ( ( add_mset_a @ C @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) )
= ( minus_1649712171iset_a @ ( add_mset_a @ C @ B ) @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(9,axiom,
! [A: set_Pr1821581383od_a_a] :
( ! [B: multis599418605od_a_a] :
~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ B @ B ) @ A )
=> ( irrefl1672195874od_a_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_irreflI) ).
thf(352,plain,
! [A: set_Pr1821581383od_a_a] :
( ! [B: multis599418605od_a_a] :
~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ B @ B ) @ A )
=> ( irrefl1672195874od_a_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(295,axiom,
! [A: set_Product_prod_a_a,B: a > a > $o,C: multiset_a,D: multiset_a] :
( ( irrefl_a @ A )
=> ( ( trans_a @ A )
=> ( ! [E: a,F: a] :
( ( B @ E @ F )
= ( member449909584od_a_a @ ( product_Pair_a_a @ E @ F ) @ A ) )
=> ( ( multp_a @ B @ C @ D )
= ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ ( mult_a @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_multp__iff) ).
thf(1290,plain,
! [A: set_Product_prod_a_a,B: a > a > $o,C: multiset_a,D: multiset_a] :
( ( irrefl_a @ A )
=> ( ( trans_a @ A )
=> ( ! [E: a,F: a] :
( ( B @ E @ F )
= ( member449909584od_a_a @ ( product_Pair_a_a @ E @ F ) @ A ) )
=> ( ( multp_a @ B @ C @ D )
= ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ ( mult_a @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(134,axiom,
! [A: multiset_a,B: multiset_a,C: set_Pr158363655iset_a,D: multiset_a > multiset_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ A @ B ) @ ( inv_im343774418iset_a @ C @ D ) )
= ( member340150864iset_a @ ( produc2037245207iset_a @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_in__inv__image) ).
thf(741,plain,
! [A: multiset_a,B: multiset_a,C: set_Pr158363655iset_a,D: multiset_a > multiset_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ A @ B ) @ ( inv_im343774418iset_a @ C @ D ) )
= ( member340150864iset_a @ ( produc2037245207iset_a @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(176,axiom,
! [A: multis599418605od_a_a,B: multis599418605od_a_a,C: set_Product_prod_a_a,D: multis599418605od_a_a > a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ A @ B ) @ ( inv_im941243329od_a_a @ C @ D ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_in__inv__image) ).
thf(873,plain,
! [A: multis599418605od_a_a,B: multis599418605od_a_a,C: set_Product_prod_a_a,D: multis599418605od_a_a > a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ A @ B ) @ ( inv_im941243329od_a_a @ C @ D ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(113,axiom,
! [A: a,B: set_a,C: a,D: a > a] :
( ( member_a @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_a @ C @ ( image_a_a @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_rev__image__eqI) ).
thf(677,plain,
! [A: a,B: set_a,C: a,D: a > a] :
( ( member_a @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_a @ C @ ( image_a_a @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(35,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer1338892073od_a_a @ A @ B )
=> ( order_359341630od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_preference_Otrans__refl) ).
thf(440,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer1338892073od_a_a @ A @ B )
=> ( order_359341630od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(106,axiom,
! [A: a,B: multiset_a,C: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ ( plus_plus_multiset_a @ B @ C ) ) )
= ( ( member_a @ A @ ( set_mset_a @ B ) )
| ( member_a @ A @ ( set_mset_a @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_union__iff) ).
thf(655,plain,
! [A: a,B: multiset_a,C: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ ( plus_plus_multiset_a @ B @ C ) ) )
= ( ( member_a @ A @ ( set_mset_a @ B ) )
| ( member_a @ A @ ( set_mset_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(66,axiom,
! [A: set_multiset_a,B: set_Pr158363655iset_a,C: multiset_a,D: multiset_a] :
( ( refl_on_multiset_a @ A @ B )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
=> ( member_multiset_a @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_refl__onD2) ).
thf(533,plain,
! [A: set_multiset_a,B: set_Pr158363655iset_a,C: multiset_a,D: multiset_a] :
( ( refl_on_multiset_a @ A @ B )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
=> ( member_multiset_a @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(55,axiom,
! [A: a,B: multiset_a,C: multiset_a] :
( ( ( add_mset_a @ A @ B )
= C )
=> ( member_a @ A @ ( set_mset_a @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_union__single__eq__member) ).
thf(500,plain,
! [A: a,B: multiset_a,C: multiset_a] :
( ( ( add_mset_a @ A @ B )
= C )
=> ( member_a @ A @ ( set_mset_a @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(149,axiom,
! [A: set_Pr1948701895od_a_a] :
( ( collec1635618130od_a_a
@ ^ [B: produc1572603623od_a_a] : ( member2057358096od_a_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_Collect__mem__eq) ).
thf(797,plain,
! [A: set_Pr1948701895od_a_a] :
( ( collec1635618130od_a_a
@ ^ [B: produc1572603623od_a_a] : ( member2057358096od_a_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(278,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( refl_on_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( ( member_a @ C @ A )
& ( member_a @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_refl__on__domain) ).
thf(1233,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( refl_on_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( ( member_a @ C @ A )
& ( member_a @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(228,axiom,
! [A: a,B: a] :
( ( ( member_a @ A @ carrier )
& ( member_a @ B @ carrier ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_strict__not__refl__weak) ).
thf(1063,plain,
! [A: a,B: a] :
( ( ( member_a @ A @ carrier )
& ( member_a @ B @ carrier ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(111,axiom,
! [A: set_multiset_a,B: set_Pr158363655iset_a,C: multiset_a,D: multiset_a] :
( ( refl_on_multiset_a @ A @ B )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
=> ( member_multiset_a @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_refl__onD1) ).
thf(670,plain,
! [A: set_multiset_a,B: set_Pr158363655iset_a,C: multiset_a,D: multiset_a] :
( ( refl_on_multiset_a @ A @ B )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
=> ( member_multiset_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(136,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Pr1948701895od_a_a,D: product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ C )
=> ( ( D = B )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_ssubst__Pair__rhs) ).
thf(747,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Pr1948701895od_a_a,D: product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ C )
=> ( ( D = B )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(189,axiom,
! [A: product_prod_a_a,B: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ? [C: multis599418605od_a_a] :
( B
= ( add_ms1725977093od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_multi__member__split) ).
thf(913,plain,
! [A: product_prod_a_a,B: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ? [C: multis599418605od_a_a] :
( B
= ( add_ms1725977093od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(164,axiom,
produc748978966_a_a_o = produc1833107820_a_a_o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_internal__case__prod__def) ).
thf(841,plain,
produc748978966_a_a_o = produc1833107820_a_a_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(313,axiom,
! [A: product_prod_a_a,B: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) ) )
=> ( ( set_ms1818337124od_a_a @ ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) )
= ( set_ms1818337124od_a_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_more__than__one__mset__mset__diff) ).
thf(1359,plain,
! [A: product_prod_a_a,B: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) ) )
=> ( ( set_ms1818337124od_a_a @ ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) )
= ( set_ms1818337124od_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(78,axiom,
! [A: a,B: multiset_a > multiset_a > set_a,C: produc1127127335iset_a] :
( ( member_a @ A @ ( produc747255346_set_a @ B @ C ) )
=> ~ ! [D: multiset_a,E: multiset_a] :
( ( C
= ( produc2037245207iset_a @ D @ E ) )
=> ~ ( member_a @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_mem__case__prodE) ).
thf(565,plain,
! [A: a,B: multiset_a > multiset_a > set_a,C: produc1127127335iset_a] :
( ( member_a @ A @ ( produc747255346_set_a @ B @ C ) )
=> ~ ! [D: multiset_a,E: multiset_a] :
( ( C
= ( produc2037245207iset_a @ D @ E ) )
=> ~ ( member_a @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(34,axiom,
! [A: set_Product_prod_a_a,B: a,C: multiset_a,D: multiset_a] :
( ( trans_a @ A )
=> ( ( irrefl_a @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ ( add_mset_a @ B @ C ) @ ( add_mset_a @ B @ D ) ) @ ( mult_a @ A ) )
= ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ ( mult_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_mult__cancel__add__mset) ).
thf(436,plain,
! [A: set_Product_prod_a_a,B: a,C: multiset_a,D: multiset_a] :
( ( trans_a @ A )
=> ( ( irrefl_a @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ ( add_mset_a @ B @ C ) @ ( add_mset_a @ B @ D ) ) @ ( mult_a @ A ) )
= ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ ( mult_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(160,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( total_1490170027od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_rational__preference_Ototal) ).
thf(829,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( total_1490170027od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(25,axiom,
! [A: set_Pr1948701895od_a_a] :
( ! [B: product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ C ) @ A )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ A )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ D ) @ A ) ) )
=> ( trans_972827014od_a_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_transI) ).
thf(404,plain,
! [A: set_Pr1948701895od_a_a] :
( ! [B: product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ C ) @ A )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ A )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ D ) @ A ) ) )
=> ( trans_972827014od_a_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(297,axiom,
! [A: a] :
( ( member_a @ A @ carrier )
=> ! [B: a] :
( ( member_a @ B @ carrier )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_compl) ).
thf(1298,plain,
! [A: a] :
( ( member_a @ A @ carrier )
=> ! [B: a] :
( ( member_a @ B @ carrier )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(15,axiom,
! [A: produc1127127335iset_a] :
~ ! [B: multiset_a,C: multiset_a] :
( A
!= ( produc2037245207iset_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_old_Oprod_Oexhaust) ).
thf(372,plain,
! [A: produc1127127335iset_a] :
~ ! [B: multiset_a,C: multiset_a] :
( A
!= ( produc2037245207iset_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(56,axiom,
( prefer719835986ence_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
& ( prefer580340847ioms_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_rational__preference__def) ).
thf(504,plain,
( prefer719835986ence_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
& ( prefer580340847ioms_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(287,axiom,
! [A: product_prod_a_a] :
( ( product_Pair_a_a @ ( product_fst_a_a @ A ) @ ( product_snd_a_a @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_prod_Ocollapse) ).
thf(1264,plain,
! [A: product_prod_a_a] :
( ( product_Pair_a_a @ ( product_fst_a_a @ A ) @ ( product_snd_a_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(121,axiom,
! [A: produc2061001575od_a_a] :
? [B: multis599418605od_a_a,C: multis599418605od_a_a] :
( A
= ( produc1859144151od_a_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_surj__pair) ).
thf(702,plain,
! [A: produc2061001575od_a_a] :
? [B: multis599418605od_a_a,C: multis599418605od_a_a] :
( A
= ( produc1859144151od_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(293,axiom,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) )
= C )
= ( B
= ( add_ms1725977093od_a_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_diff__single__eq__union) ).
thf(1279,plain,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) )
= C )
= ( B
= ( add_ms1725977093od_a_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(267,axiom,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a] :
( ( ( add_ms1725977093od_a_a @ A @ B )
= C )
=> ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_union__single__eq__member) ).
thf(1191,plain,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a] :
( ( ( add_ms1725977093od_a_a @ A @ B )
= C )
=> ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(69,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( trans_a @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_preference_Otransitivity) ).
thf(542,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( trans_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(227,axiom,
! [A: product_prod_a_a] :
~ ! [B: a,C: a] :
( A
!= ( product_Pair_a_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_old_Oprod_Oexhaust) ).
thf(1059,plain,
! [A: product_prod_a_a] :
~ ! [B: a,C: a] :
( A
!= ( product_Pair_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(251,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( refl_o1298442278od_a_a @ A @ B )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
=> ( member449909584od_a_a @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_refl__onD1) ).
thf(1132,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( refl_o1298442278od_a_a @ A @ B )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
=> ( member449909584od_a_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(310,axiom,
! [A: multiset_a,B: multiset_a,C: set_Product_prod_a_a,D: multiset_a > a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ A @ B ) @ ( inv_im479034648iset_a @ C @ D ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_in__inv__image) ).
thf(1347,plain,
! [A: multiset_a,B: multiset_a,C: set_Product_prod_a_a,D: multiset_a > a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ A @ B ) @ ( inv_im479034648iset_a @ C @ D ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(28,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( prefer1338892073od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_rational__preference_Oaxioms_I1_J) ).
thf(416,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( prefer1338892073od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(245,axiom,
( trans_a
= ( ^ [A: set_Product_prod_a_a] :
! [B: a,C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_trans__def) ).
thf(1115,plain,
( trans_a
= ( ^ [A: set_Product_prod_a_a] :
! [B: a,C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(314,axiom,
! [A: produc1572603623od_a_a > $o,B: produc1572603623od_a_a] :
( ! [C: product_prod_a_a,D: a,E: a] : ( A @ ( produc1474507607od_a_a @ C @ ( product_Pair_a_a @ D @ E ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_prod__induct3) ).
thf(1362,plain,
! [A: produc1572603623od_a_a > $o,B: produc1572603623od_a_a] :
( ! [C: product_prod_a_a,D: a,E: a] : ( A @ ( produc1474507607od_a_a @ C @ ( product_Pair_a_a @ D @ E ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(239,axiom,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ B @ C ) ) )
= ( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
| ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_union__iff) ).
thf(1100,plain,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ B @ C ) ) )
= ( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
| ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(156,axiom,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( add_mset_a @ A @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_insert__DiffM) ).
thf(817,plain,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( add_mset_a @ A @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(187,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_preference_Onot__outside) ).
thf(902,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(303,axiom,
! [A: a,B: a,C: set_Pr158363655iset_a,D: a > multiset_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( inv_im975322764et_a_a @ C @ D ) )
= ( member340150864iset_a @ ( produc2037245207iset_a @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_in__inv__image) ).
thf(1319,plain,
! [A: a,B: a,C: set_Pr158363655iset_a,D: a > multiset_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( inv_im975322764et_a_a @ C @ D ) )
= ( member340150864iset_a @ ( produc2037245207iset_a @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(175,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( refl_on_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_refl__onD1) ).
thf(870,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( refl_on_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(87,axiom,
! [A: produc1127127335iset_a,B: produc1127127335iset_a > $o] :
( ( member340150864iset_a @ A @ ( collec1104713362iset_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_mem__Collect__eq) ).
thf(591,plain,
! [A: produc1127127335iset_a,B: produc1127127335iset_a > $o] :
( ( member340150864iset_a @ A @ ( collec1104713362iset_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(16,axiom,
! [A: multiset_a,B: multiset_a,C: set_multiset_a,D: set_Pr158363655iset_a] :
( ( member_multiset_a @ A @ ( prefer2130004608iset_a @ B @ C @ D ) )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_at__lst__asgd__ge) ).
thf(376,plain,
! [A: multiset_a,B: multiset_a,C: set_multiset_a,D: set_Pr158363655iset_a] :
( ( member_multiset_a @ A @ ( prefer2130004608iset_a @ B @ C @ D ) )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(103,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( order_preorder_on_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_preference_Otrans__refl) ).
thf(646,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( order_preorder_on_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(60,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( total_on_a @ top_top_set_a @ A )
=> ( ( total_on_a @ top_top_set_a @ B )
=> ( total_1490170027od_a_a @ top_to398455383od_a_a @ ( lex_prod_a_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_total__lex__prod) ).
thf(514,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( total_on_a @ top_top_set_a @ A )
=> ( ( total_on_a @ top_top_set_a @ B )
=> ( total_1490170027od_a_a @ top_to398455383od_a_a @ ( lex_prod_a_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(81,axiom,
! [A: produc1127127335iset_a > $o,B: multiset_a,C: multiset_a] :
( ( A @ ( produc2037245207iset_a @ B @ C ) )
=> ( produc1530159757et_a_o @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_curryI) ).
thf(574,plain,
! [A: produc1127127335iset_a > $o,B: multiset_a,C: multiset_a] :
( ( A @ ( produc2037245207iset_a @ B @ C ) )
=> ( produc1530159757et_a_o @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(152,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_mem__Collect__eq) ).
thf(806,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(205,axiom,
! [A: set_Product_prod_a_a,B: multiset_a,C: multiset_a] :
( ( trans_a @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ B @ C ) @ ( mult_a @ A ) )
=> ? [D: multiset_a,E: multiset_a] :
( ( C
= ( plus_plus_multiset_a @ D @ E ) )
& ? [F: multiset_a] :
( ( B
= ( plus_plus_multiset_a @ D @ F ) )
& ( E != zero_zero_multiset_a )
& ! [G: a] :
( ( member_a @ G @ ( set_mset_a @ F ) )
=> ? [H: a] :
( ( member_a @ H @ ( set_mset_a @ E ) )
& ( member449909584od_a_a @ ( product_Pair_a_a @ G @ H ) @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_mult__implies__one__step) ).
thf(966,plain,
! [A: set_Product_prod_a_a,B: multiset_a,C: multiset_a] :
( ( trans_a @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ B @ C ) @ ( mult_a @ A ) )
=> ? [D: multiset_a,E: multiset_a] :
( ( C
= ( plus_plus_multiset_a @ D @ E ) )
& ? [F: multiset_a] :
( ( B
= ( plus_plus_multiset_a @ D @ F ) )
& ( E != zero_zero_multiset_a )
& ! [G: a] :
( ( member_a @ G @ ( set_mset_a @ F ) )
=> ? [H: a] :
( ( member_a @ H @ ( set_mset_a @ E ) )
& ( member449909584od_a_a @ ( product_Pair_a_a @ G @ H ) @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(294,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_Pair__inject) ).
thf(1283,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(188,axiom,
! [A: multiset_a,B: a,C: multiset_a,D: multiset_a,E: multiset_a,F: set_Product_prod_a_a] :
( ( A
= ( add_mset_a @ B @ C ) )
=> ( ( D
= ( plus_plus_multiset_a @ C @ E ) )
=> ( ! [G: a] :
( ( member_a @ G @ ( set_mset_a @ E ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ G @ B ) @ F ) )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ D @ A ) @ ( mult1_a @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_mult1I) ).
thf(905,plain,
! [A: multiset_a,B: a,C: multiset_a,D: multiset_a,E: multiset_a,F: set_Product_prod_a_a] :
( ( A
= ( add_mset_a @ B @ C ) )
=> ( ( D
= ( plus_plus_multiset_a @ C @ E ) )
=> ( ! [G: a] :
( ( member_a @ G @ ( set_mset_a @ E ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ G @ B ) @ F ) )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ D @ A ) @ ( mult1_a @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(47,axiom,
! [A: a > a > set_a] :
( ( produc580150227_set_a @ ( produc961951794_set_a @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_curry__case__prod) ).
thf(475,plain,
! [A: a > a > set_a] :
( ( produc580150227_set_a @ ( produc961951794_set_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(192,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( ( ( member449909584od_a_a @ C @ A )
& ( member449909584od_a_a @ D @ A ) )
=> ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ C ) @ B ) )
= ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
& ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_rational__preference_Ostrict__not__refl__weak) ).
thf(924,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( ( ( member449909584od_a_a @ C @ A )
& ( member449909584od_a_a @ D @ A ) )
=> ( ( ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ C ) @ B ) )
= ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
& ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(50,axiom,
! [A: set_Pr1821581383od_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( trans_1520871884od_a_a @ A )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ B @ C ) @ A )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ A )
=> ( member1349055120od_a_a @ ( produc1859144151od_a_a @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_transD) ).
thf(485,plain,
! [A: set_Pr1821581383od_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( trans_1520871884od_a_a @ A )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ B @ C ) @ A )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ A )
=> ( member1349055120od_a_a @ ( produc1859144151od_a_a @ B @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(162,axiom,
! [A: produc2061001575od_a_a,B: produc2061001575od_a_a > $o] :
( ( member1349055120od_a_a @ A @ ( collec8264402od_a_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_mem__Collect__eq) ).
thf(834,plain,
! [A: produc2061001575od_a_a,B: produc2061001575od_a_a > $o] :
( ( member1349055120od_a_a @ A @ ( collec8264402od_a_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(142,axiom,
! [A: a,B: multiset_a] :
( ( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( add_mset_a @ A @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) )
= B ) )
& ( ~ ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( add_mset_a @ A @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) )
= ( add_mset_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_add__mset__remove__trivial__If) ).
thf(766,plain,
! [A: a,B: multiset_a] :
( ( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( add_mset_a @ A @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) )
= B ) )
& ( ~ ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( add_mset_a @ A @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) )
= ( add_mset_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(23,axiom,
! [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( refl_o581572716od_a_a @ A @ B )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
=> ( member1755255446od_a_a @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_refl__onD1) ).
thf(397,plain,
! [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( refl_o581572716od_a_a @ A @ B )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
=> ( member1755255446od_a_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(132,axiom,
! [A: set_multiset_a,B: set_Pr158363655iset_a,C: multiset_a,D: multiset_a,E: multiset_a] :
( ( prefer1571048262iset_a @ A @ B )
=> ( ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
& ( member340150864iset_a @ ( produc2037245207iset_a @ D @ C ) @ B ) )
=> ( ( ( member340150864iset_a @ ( produc2037245207iset_a @ D @ E ) @ B )
& ( member340150864iset_a @ ( produc2037245207iset_a @ E @ D ) @ B ) )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ E ) @ B )
& ( member340150864iset_a @ ( produc2037245207iset_a @ E @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_preference_Oindiff__trans) ).
thf(734,plain,
! [A: set_multiset_a,B: set_Pr158363655iset_a,C: multiset_a,D: multiset_a,E: multiset_a] :
( ( prefer1571048262iset_a @ A @ B )
=> ( ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
& ( member340150864iset_a @ ( produc2037245207iset_a @ D @ C ) @ B ) )
=> ( ( ( member340150864iset_a @ ( produc2037245207iset_a @ D @ E ) @ B )
& ( member340150864iset_a @ ( produc2037245207iset_a @ E @ D ) @ B ) )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ E ) @ B )
& ( member340150864iset_a @ ( produc2037245207iset_a @ E @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(173,axiom,
! [A: a,B: a,C: set_Pr1821581383od_a_a,D: a > multis599418605od_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( inv_im1681759523_a_a_a @ C @ D ) )
= ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_in__inv__image) ).
thf(866,plain,
! [A: a,B: a,C: set_Pr1821581383od_a_a,D: a > multis599418605od_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( inv_im1681759523_a_a_a @ C @ D ) )
= ( member1349055120od_a_a @ ( produc1859144151od_a_a @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(231,axiom,
! [A: product_prod_a_a] :
( A
= ( product_Pair_a_a @ ( product_fst_a_a @ A ) @ ( product_snd_a_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_surjective__pairing) ).
thf(1072,plain,
! [A: product_prod_a_a] :
( A
= ( product_Pair_a_a @ ( product_fst_a_a @ A ) @ ( product_snd_a_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(326,axiom,
( prefer1292084992ence_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
( ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ C @ A ) )
& ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ D @ A ) )
& ( order_preorder_on_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_preference__def) ).
thf(1405,plain,
( prefer1292084992ence_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
( ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ C @ A ) )
& ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ D @ A ) )
& ( order_preorder_on_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(270,axiom,
! [A: multiset_a,B: a,C: multiset_a,D: set_Product_prod_a_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ A @ ( add_mset_a @ B @ C ) ) @ ( mult1_a @ D ) )
=> ( ? [E: multiset_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ E @ C ) @ ( mult1_a @ D ) )
& ( A
= ( add_mset_a @ B @ E ) ) )
| ? [E: multiset_a] :
( ! [F: a] :
( ( member_a @ F @ ( set_mset_a @ E ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ F @ B ) @ D ) )
& ( A
= ( plus_plus_multiset_a @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_less__add) ).
thf(1201,plain,
! [A: multiset_a,B: a,C: multiset_a,D: set_Product_prod_a_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ A @ ( add_mset_a @ B @ C ) ) @ ( mult1_a @ D ) )
=> ( ? [E: multiset_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ E @ C ) @ ( mult1_a @ D ) )
& ( A
= ( add_mset_a @ B @ E ) ) )
| ? [E: multiset_a] :
( ! [F: a] :
( ( member_a @ F @ ( set_mset_a @ E ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ F @ B ) @ D ) )
& ( A
= ( plus_plus_multiset_a @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(38,axiom,
! [A: produc1572603623od_a_a > $o,B: product_prod_a_a,C: product_prod_a_a] :
( ( A @ ( produc1474507607od_a_a @ B @ C ) )
=> ( produc94438221_a_a_o @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_curryI) ).
thf(452,plain,
! [A: produc1572603623od_a_a > $o,B: product_prod_a_a,C: product_prod_a_a] :
( ( A @ ( produc1474507607od_a_a @ B @ C ) )
=> ( produc94438221_a_a_o @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(191,axiom,
! [A: product_prod_a_a,B: a > a,C: a > a,D: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ B @ C ) @ D ) )
=> ~ ! [E: a,F: a] :
( ( A
= ( product_Pair_a_a @ ( B @ E ) @ ( C @ F ) ) )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ E @ F ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_prod__fun__imageE) ).
thf(920,plain,
! [A: product_prod_a_a,B: a > a,C: a > a,D: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ B @ C ) @ D ) )
=> ~ ! [E: a,F: a] :
( ( A
= ( product_Pair_a_a @ ( B @ E ) @ ( C @ F ) ) )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ E @ F ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(18,axiom,
! [A: set_Pr158363655iset_a,B: set_multiset_a] :
( ! [C: multiset_a,D: multiset_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ A )
=> ( member_multiset_a @ C @ B ) )
=> ( ! [C: multiset_a,D: multiset_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ A )
=> ( member_multiset_a @ D @ B ) )
=> ( ( order_750350043iset_a @ B @ A )
=> ( prefer1571048262iset_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_preference_Ointro) ).
thf(380,plain,
! [A: set_Pr158363655iset_a,B: set_multiset_a] :
( ! [C: multiset_a,D: multiset_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ A )
=> ( member_multiset_a @ C @ B ) )
=> ( ! [C: multiset_a,D: multiset_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ A )
=> ( member_multiset_a @ D @ B ) )
=> ( ( order_750350043iset_a @ B @ A )
=> ( prefer1571048262iset_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(59,axiom,
( trans_multiset_a
= ( ^ [A: set_Pr158363655iset_a] :
! [B: multiset_a,C: multiset_a,D: multiset_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ B @ C ) @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ A )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ B @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_trans__def) ).
thf(512,plain,
( trans_multiset_a
= ( ^ [A: set_Pr158363655iset_a] :
! [B: multiset_a,C: multiset_a,D: multiset_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ B @ C ) @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ A )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(301,axiom,
! [A: set_Product_prod_a_a] :
( ! [B: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ B ) @ A )
=> ( irrefl_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_irreflI) ).
thf(1311,plain,
! [A: set_Product_prod_a_a] :
( ! [B: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ B ) @ A )
=> ( irrefl_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(291,axiom,
( top_to1483957574_a_a_o
= ( ^ [A: product_prod_a_a] : ( member449909584od_a_a @ A @ top_to398455383od_a_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_top__empty__eq) ).
thf(1274,plain,
( top_to1483957574_a_a_o
= ( ^ [A: product_prod_a_a] : ( member449909584od_a_a @ A @ top_to398455383od_a_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(184,axiom,
! [A: a,B: a,C: a,D: a,E: set_Product_prod_a_a,F: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( product_Pair_a_a @ C @ D ) ) @ ( lex_prod_a_a @ E @ F ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ E )
| ( ( A = C )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_in__lex__prod) ).
thf(894,plain,
! [A: a,B: a,C: a,D: a,E: set_Product_prod_a_a,F: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( product_Pair_a_a @ C @ D ) ) @ ( lex_prod_a_a @ E @ F ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ E )
| ( ( A = C )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(309,axiom,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a] :
( ~ ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( minus_1257885652od_a_a @ ( add_ms1725977093od_a_a @ A @ C ) @ B )
= ( add_ms1725977093od_a_a @ A @ ( minus_1257885652od_a_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_diff__add__mset__swap) ).
thf(1343,plain,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a] :
( ~ ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( minus_1257885652od_a_a @ ( add_ms1725977093od_a_a @ A @ C ) @ B )
= ( add_ms1725977093od_a_a @ A @ ( minus_1257885652od_a_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(221,axiom,
! [A: a > a > set_a,B: a,C: a] :
( ( produc961951794_set_a @ A @ ( product_Pair_a_a @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_old_Oprod_Ocase) ).
thf(1042,plain,
! [A: a > a > set_a,B: a,C: a] :
( ( produc961951794_set_a @ A @ ( product_Pair_a_a @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(284,axiom,
! [A: produc1572603623od_a_a] :
~ ! [B: product_prod_a_a,C: a,D: a] :
( A
!= ( produc1474507607od_a_a @ B @ ( product_Pair_a_a @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_prod__cases3) ).
thf(1255,plain,
! [A: produc1572603623od_a_a] :
~ ! [B: product_prod_a_a,C: a,D: a] :
( A
!= ( produc1474507607od_a_a @ B @ ( product_Pair_a_a @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(157,axiom,
! [A: multis599418605od_a_a,B: multis599418605od_a_a > $o] :
( ( member1755255446od_a_a @ A @ ( collec1948052440od_a_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_mem__Collect__eq) ).
thf(820,plain,
! [A: multis599418605od_a_a,B: multis599418605od_a_a > $o] :
( ( member1755255446od_a_a @ A @ ( collec1948052440od_a_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(317,axiom,
! [A: product_prod_a_a,B: product_prod_a_a > product_prod_a_a,C: product_prod_a_a,D: set_Product_prod_a_a] :
( ( A
= ( B @ C ) )
=> ( ( member449909584od_a_a @ C @ D )
=> ( member449909584od_a_a @ A @ ( image_794773445od_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_image__eqI) ).
thf(1370,plain,
! [A: product_prod_a_a,B: product_prod_a_a > product_prod_a_a,C: product_prod_a_a,D: set_Product_prod_a_a] :
( ( A
= ( B @ C ) )
=> ( ( member449909584od_a_a @ C @ D )
=> ( member449909584od_a_a @ A @ ( image_794773445od_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(155,axiom,
! [A: produc2061001575od_a_a > $o,B: multis599418605od_a_a,C: multis599418605od_a_a] :
( ( A @ ( produc1859144151od_a_a @ B @ C ) )
=> ( produc1548936141_a_a_o @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_curryI) ).
thf(815,plain,
! [A: produc2061001575od_a_a > $o,B: multis599418605od_a_a,C: multis599418605od_a_a] :
( ( A @ ( produc1859144151od_a_a @ B @ C ) )
=> ( produc1548936141_a_a_o @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(273,axiom,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( minus_1257885652od_a_a @ ( add_ms1725977093od_a_a @ C @ B ) @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) )
= ( add_ms1725977093od_a_a @ C @ ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_diff__union__swap2) ).
thf(1217,plain,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( minus_1257885652od_a_a @ ( add_ms1725977093od_a_a @ C @ B ) @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) )
= ( add_ms1725977093od_a_a @ C @ ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(89,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ( produc2037245207iset_a @ A @ B )
= ( produc2037245207iset_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_Pair__inject) ).
thf(598,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ( produc2037245207iset_a @ A @ B )
= ( produc2037245207iset_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(118,axiom,
! [A: produc2061001575od_a_a] :
~ ! [B: multis599418605od_a_a,C: multis599418605od_a_a] :
( A
!= ( produc1859144151od_a_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_old_Oprod_Oexhaust) ).
thf(693,plain,
! [A: produc2061001575od_a_a] :
~ ! [B: multis599418605od_a_a,C: multis599418605od_a_a] :
( A
!= ( produc1859144151od_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(97,axiom,
! [A: multis599418605od_a_a,B: multis599418605od_a_a,C: set_mu1281098573od_a_a,D: set_Pr1821581383od_a_a] :
( ( member1755255446od_a_a @ A @ ( prefer1191731497od_a_a @ B @ C @ D ) )
=> ( member1349055120od_a_a @ ( produc1859144151od_a_a @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_at__lst__asgd__ge) ).
thf(630,plain,
! [A: multis599418605od_a_a,B: multis599418605od_a_a,C: set_mu1281098573od_a_a,D: set_Pr1821581383od_a_a] :
( ( member1755255446od_a_a @ A @ ( prefer1191731497od_a_a @ B @ C @ D ) )
=> ( member1349055120od_a_a @ ( produc1859144151od_a_a @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(167,axiom,
! [A: set_Product_prod_a_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( trans_a @ A )
=> ( ( irrefl_a @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ ( plus_plus_multiset_a @ B @ C ) @ ( plus_plus_multiset_a @ D @ C ) ) @ ( mult_a @ A ) )
= ( member340150864iset_a @ ( produc2037245207iset_a @ B @ D ) @ ( mult_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_mult__cancel) ).
thf(847,plain,
! [A: set_Product_prod_a_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( trans_a @ A )
=> ( ( irrefl_a @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ ( plus_plus_multiset_a @ B @ C ) @ ( plus_plus_multiset_a @ D @ C ) ) @ ( mult_a @ A ) )
= ( member340150864iset_a @ ( produc2037245207iset_a @ B @ D ) @ ( mult_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(315,axiom,
! [A: product_prod_a_a,B: multis599418605od_a_a] : ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_multi__member__this) ).
thf(1365,plain,
! [A: product_prod_a_a,B: multis599418605od_a_a] : ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(178,axiom,
! [A: product_prod_a_a] :
( A
= ( product_Pair_a_a @ ( product_fst_a_a @ A ) @ ( product_snd_a_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_prod_Oexhaust__sel) ).
thf(879,plain,
! [A: product_prod_a_a] :
( A
= ( product_Pair_a_a @ ( product_fst_a_a @ A ) @ ( product_snd_a_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(62,axiom,
( order_preorder_on_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
( ( refl_on_a @ A @ B )
& ( trans_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_preorder__on__def) ).
thf(522,plain,
( order_preorder_on_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
( ( refl_on_a @ A @ B )
& ( trans_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(260,axiom,
! [A: product_prod_a_a,B: multis599418605od_a_a] :
( ( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( add_ms1725977093od_a_a @ A @ ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) )
= B ) )
& ( ~ ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( add_ms1725977093od_a_a @ A @ ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) )
= ( add_ms1725977093od_a_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_add__mset__remove__trivial__If) ).
thf(1159,plain,
! [A: product_prod_a_a,B: multis599418605od_a_a] :
( ( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( add_ms1725977093od_a_a @ A @ ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) )
= B ) )
& ( ~ ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( add_ms1725977093od_a_a @ A @ ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) )
= ( add_ms1725977093od_a_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(53,axiom,
! [A: product_prod_a_a > set_Product_prod_a_a] :
( ( produc1093061851od_a_a @ ( produc143372156od_a_a @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_case__prod__curry) ).
thf(493,plain,
! [A: product_prod_a_a > set_Product_prod_a_a] :
( ( produc1093061851od_a_a @ ( produc143372156od_a_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(139,axiom,
! [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( prefer1340910575od_a_a @ A @ B )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
=> ( member1755255446od_a_a @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_preference_Onot__outside) ).
thf(757,plain,
! [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( prefer1340910575od_a_a @ A @ B )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
=> ( member1755255446od_a_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(73,axiom,
! [A: set_mu1281098573od_a_a] :
( ( collec1948052440od_a_a
@ ^ [B: multis599418605od_a_a] : ( member1755255446od_a_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_Collect__mem__eq) ).
thf(551,plain,
! [A: set_mu1281098573od_a_a] :
( ( collec1948052440od_a_a
@ ^ [B: multis599418605od_a_a] : ( member1755255446od_a_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(322,axiom,
! [A: a > a,B: a > a,C: a,D: a] :
( ( produc700022774_a_a_a @ A @ B @ ( product_Pair_a_a @ C @ D ) )
= ( product_Pair_a_a @ ( A @ C ) @ ( B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_map__prod__simp) ).
thf(1392,plain,
! [A: a > a,B: a > a,C: a,D: a] :
( ( produc700022774_a_a_a @ A @ B @ ( product_Pair_a_a @ C @ D ) )
= ( product_Pair_a_a @ ( A @ C ) @ ( B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(40,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ( produc2037245207iset_a @ A @ B )
= ( produc2037245207iset_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_old_Oprod_Oinject) ).
thf(456,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ( produc2037245207iset_a @ A @ B )
= ( produc2037245207iset_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(213,axiom,
! [A: a > a > $o,B: a,C: a,D: product_prod_a_a] :
( ( A @ B @ C )
=> ( ( D
= ( product_Pair_a_a @ B @ C ) )
=> ( A @ ( product_fst_a_a @ D ) @ ( product_snd_a_a @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_BNF__Greatest__Fixpoint_Osubst__Pair) ).
thf(1012,plain,
! [A: a > a > $o,B: a,C: a,D: product_prod_a_a] :
( ( A @ B @ C )
=> ( ( D
= ( product_Pair_a_a @ B @ C ) )
=> ( A @ ( product_fst_a_a @ D ) @ ( product_snd_a_a @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(242,axiom,
! [A: product_prod_a_a,B: a,C: a] :
( ( A
= ( product_Pair_a_a @ B @ C ) )
=> ( ( product_snd_a_a @ A )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_sndI) ).
thf(1106,plain,
! [A: product_prod_a_a,B: a,C: a] :
( ( A
= ( product_Pair_a_a @ B @ C ) )
=> ( ( product_snd_a_a @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(190,axiom,
! [A: product_prod_a_a,B: a > a > set_Product_prod_a_a,C: product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( produc1093061851od_a_a @ B @ C ) )
=> ~ ! [D: a,E: a] :
( ( C
= ( product_Pair_a_a @ D @ E ) )
=> ~ ( member449909584od_a_a @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_mem__case__prodE) ).
thf(916,plain,
! [A: product_prod_a_a,B: a > a > set_Product_prod_a_a,C: product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( produc1093061851od_a_a @ B @ C ) )
=> ~ ! [D: a,E: a] :
( ( C
= ( product_Pair_a_a @ D @ E ) )
=> ~ ( member449909584od_a_a @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(44,axiom,
! [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( prefer1669415233od_a_a @ A @ B )
=> ( ( ( member1755255446od_a_a @ C @ A )
& ( member1755255446od_a_a @ D @ A ) )
=> ( ( ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ D @ C ) @ B ) )
= ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
& ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ D @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_rational__preference_Ostrict__not__refl__weak) ).
thf(467,plain,
! [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( prefer1669415233od_a_a @ A @ B )
=> ( ( ( member1755255446od_a_a @ C @ A )
& ( member1755255446od_a_a @ D @ A ) )
=> ( ( ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ D @ C ) @ B ) )
= ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
& ~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ D @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(114,axiom,
! [A: set_multiset_a,B: set_Pr158363655iset_a,C: multiset_a] :
( ( refl_on_multiset_a @ A @ B )
=> ( ( member_multiset_a @ C @ A )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ C @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_refl__onD) ).
thf(682,plain,
! [A: set_multiset_a,B: set_Pr158363655iset_a,C: multiset_a] :
( ( refl_on_multiset_a @ A @ B )
=> ( ( member_multiset_a @ C @ A )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ C @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(268,axiom,
! [A: a,B: a,C: set_a,D: set_Product_prod_a_a] :
( ( member_a @ A @ ( prefer161218362good_a @ B @ C @ D ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_at__least__as__goodD) ).
thf(1195,plain,
! [A: a,B: a,C: set_a,D: set_Product_prod_a_a] :
( ( member_a @ A @ ( prefer161218362good_a @ B @ C @ D ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(327,axiom,
order_preorder_on_a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_trans__refl) ).
thf(1407,plain,
order_preorder_on_a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(311,axiom,
! [A: multiset_a,B: multiset_a,C: set_Product_prod_a_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ A @ B ) @ ( mult1_a @ C ) )
=> ~ ! [D: a,E: multiset_a] :
( ( B
= ( add_mset_a @ D @ E ) )
=> ! [F: multiset_a] :
( ( A
= ( plus_plus_multiset_a @ E @ F ) )
=> ~ ! [G: a] :
( ( member_a @ G @ ( set_mset_a @ F ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ G @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_mult1E) ).
thf(1350,plain,
! [A: multiset_a,B: multiset_a,C: set_Product_prod_a_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ A @ B ) @ ( mult1_a @ C ) )
=> ~ ! [D: a,E: multiset_a] :
( ( B
= ( add_mset_a @ D @ E ) )
=> ! [F: multiset_a] :
( ( A
= ( plus_plus_multiset_a @ E @ F ) )
=> ~ ! [G: a] :
( ( member_a @ G @ ( set_mset_a @ F ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ G @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(285,axiom,
! [A: set_Product_prod_a_a] :
( ( asym_a @ A )
=> ! [B: a,C: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_asym_Ocases) ).
thf(1259,plain,
! [A: set_Product_prod_a_a] :
( ( asym_a @ A )
=> ! [B: a,C: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(105,axiom,
! [A: multis599418605od_a_a,B: multis599418605od_a_a,C: set_Pr1821581383od_a_a,D: multis599418605od_a_a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ A @ B ) @ C )
=> ( ( D = B )
=> ( member1349055120od_a_a @ ( produc1859144151od_a_a @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_ssubst__Pair__rhs) ).
thf(650,plain,
! [A: multis599418605od_a_a,B: multis599418605od_a_a,C: set_Pr1821581383od_a_a,D: multis599418605od_a_a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ A @ B ) @ C )
=> ( ( D = B )
=> ( member1349055120od_a_a @ ( produc1859144151od_a_a @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(214,axiom,
( total_on_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ! [D: a] :
( ( member_a @ D @ A )
=> ( ( C != D )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
| ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_total__on__def) ).
thf(1017,plain,
( total_on_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ! [D: a] :
( ( member_a @ D @ A )
=> ( ( C != D )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
| ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(306,axiom,
! [A: multiset_a,B: multiset_a,C: set_Product_prod_a_a,D: multiset_a] :
( ( A != zero_zero_multiset_a )
=> ( ! [E: a] :
( ( member_a @ E @ ( set_mset_a @ B ) )
=> ? [F: a] :
( ( member_a @ F @ ( set_mset_a @ A ) )
& ( member449909584od_a_a @ ( product_Pair_a_a @ E @ F ) @ C ) ) )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ ( plus_plus_multiset_a @ D @ B ) @ ( plus_plus_multiset_a @ D @ A ) ) @ ( mult_a @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_one__step__implies__mult) ).
thf(1328,plain,
! [A: multiset_a,B: multiset_a,C: set_Product_prod_a_a,D: multiset_a] :
( ( A != zero_zero_multiset_a )
=> ( ! [E: a] :
( ( member_a @ E @ ( set_mset_a @ B ) )
=> ? [F: a] :
( ( member_a @ F @ ( set_mset_a @ A ) )
& ( member449909584od_a_a @ ( product_Pair_a_a @ E @ F ) @ C ) ) )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ ( plus_plus_multiset_a @ D @ B ) @ ( plus_plus_multiset_a @ D @ A ) ) @ ( mult_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(318,axiom,
! [A: set_Product_prod_a_a] :
( ! [B: a,C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ A ) ) )
=> ( trans_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_transI) ).
thf(1375,plain,
! [A: set_Product_prod_a_a] :
( ! [B: a,C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ A ) ) )
=> ( trans_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(253,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( member449909584od_a_a @ ( C @ A ) @ ( image_794773445od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_imageI) ).
thf(1138,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( member449909584od_a_a @ ( C @ A ) @ ( image_794773445od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(174,axiom,
member_a @ y @ carrier,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(869,plain,
member_a @ y @ carrier,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(92,axiom,
! [A: multis599418605od_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( ( produc1859144151od_a_a @ A @ B )
= ( produc1859144151od_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_Pair__inject) ).
thf(610,plain,
! [A: multis599418605od_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( ( produc1859144151od_a_a @ A @ B )
= ( produc1859144151od_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(324,axiom,
! [A: product_prod_a_a] : ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_multi__member__last) ).
thf(1397,plain,
! [A: product_prod_a_a] : ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(119,axiom,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ( produc2037245207iset_a @ A @ B )
= ( produc2037245207iset_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_prod_Oinject) ).
thf(697,plain,
! [A: multiset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( ( produc2037245207iset_a @ A @ B )
= ( produc2037245207iset_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(236,axiom,
! [A: a,B: a] :
( ( product_fst_a_a @ ( product_Pair_a_a @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_fst__conv) ).
thf(1089,plain,
! [A: a,B: a] :
( ( product_fst_a_a @ ( product_Pair_a_a @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(146,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: product_prod_a_a,E: product_prod_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
& ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ C ) @ B ) )
=> ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ E ) @ B )
& ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ E @ D ) @ B ) )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ E ) @ B )
& ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ E @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_rational__preference_Ostrict__trans) ).
thf(783,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: product_prod_a_a,E: product_prod_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
& ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ C ) @ B ) )
=> ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ E ) @ B )
& ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ E @ D ) @ B ) )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ E ) @ B )
& ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ E @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(30,axiom,
! [A: set_Pr1948701895od_a_a,B: product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( trans_972827014od_a_a @ A )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ C ) @ A )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ A )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_transE) ).
thf(420,plain,
! [A: set_Pr1948701895od_a_a,B: product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( trans_972827014od_a_a @ A )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ C ) @ A )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ A )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(180,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a] :
( ( refl_on_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ C @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_refl__onD) ).
thf(884,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a] :
( ( refl_on_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ C @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(234,axiom,
! [A: multis599418605od_a_a,B: a > a > set_mu1281098573od_a_a,C: product_prod_a_a] :
( ( member1755255446od_a_a @ A @ ( produc1121147169od_a_a @ B @ C ) )
=> ~ ! [D: a,E: a] :
( ( C
= ( product_Pair_a_a @ D @ E ) )
=> ~ ( member1755255446od_a_a @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_mem__case__prodE) ).
thf(1082,plain,
! [A: multis599418605od_a_a,B: a > a > set_mu1281098573od_a_a,C: product_prod_a_a] :
( ( member1755255446od_a_a @ A @ ( produc1121147169od_a_a @ B @ C ) )
=> ~ ! [D: a,E: a] :
( ( C
= ( product_Pair_a_a @ D @ E ) )
=> ~ ( member1755255446od_a_a @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(51,axiom,
( order_1558116988r_on_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
( ( trans_a @ B )
& ( irrefl_a @ B )
& ( total_on_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_strict__linear__order__on__def) ).
thf(488,plain,
( order_1558116988r_on_a
= ( ^ [A: set_a,B: set_Product_prod_a_a] :
( ( trans_a @ B )
& ( irrefl_a @ B )
& ( total_on_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(74,axiom,
! [A: set_Pr1821581383od_a_a] :
( ( collec8264402od_a_a
@ ^ [B: produc2061001575od_a_a] : ( member1349055120od_a_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_Collect__mem__eq) ).
thf(554,plain,
! [A: set_Pr1821581383od_a_a] :
( ( collec8264402od_a_a
@ ^ [B: produc2061001575od_a_a] : ( member1349055120od_a_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(232,axiom,
( product_curry_a_a_o
= ( ^ [A: product_prod_a_a > $o,B: a,C: a] : ( A @ ( product_Pair_a_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_curry__conv) ).
thf(1075,plain,
( product_curry_a_a_o
= ( ^ [A: product_prod_a_a > $o,B: a,C: a] : ( A @ ( product_Pair_a_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(100,axiom,
! [A: multiset_a,B: product_prod_a_a > product_prod_a_a > set_multiset_a,C: produc1572603623od_a_a] :
( ( member_multiset_a @ A @ ( produc734625720iset_a @ B @ C ) )
=> ~ ! [D: product_prod_a_a,E: product_prod_a_a] :
( ( C
= ( produc1474507607od_a_a @ D @ E ) )
=> ~ ( member_multiset_a @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_mem__case__prodE) ).
thf(637,plain,
! [A: multiset_a,B: product_prod_a_a > product_prod_a_a > set_multiset_a,C: produc1572603623od_a_a] :
( ( member_multiset_a @ A @ ( produc734625720iset_a @ B @ C ) )
=> ~ ! [D: product_prod_a_a,E: product_prod_a_a] :
( ( C
= ( produc1474507607od_a_a @ D @ E ) )
=> ~ ( member_multiset_a @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(220,axiom,
! [A: multis599418605od_a_a,B: product_prod_a_a] :
( ( A
= ( add_ms1725977093od_a_a @ B @ ( minus_1257885652od_a_a @ A @ ( add_ms1725977093od_a_a @ B @ zero_z160849828od_a_a ) ) ) )
= ( member449909584od_a_a @ B @ ( set_ms1818337124od_a_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_add__mset__remove__trivial__eq) ).
thf(1039,plain,
! [A: multis599418605od_a_a,B: product_prod_a_a] :
( ( A
= ( add_ms1725977093od_a_a @ B @ ( minus_1257885652od_a_a @ A @ ( add_ms1725977093od_a_a @ B @ zero_z160849828od_a_a ) ) ) )
= ( member449909584od_a_a @ B @ ( set_ms1818337124od_a_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(71,axiom,
( total_1024184433od_a_a
= ( ^ [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a] :
! [C: multis599418605od_a_a] :
( ( member1755255446od_a_a @ C @ A )
=> ! [D: multis599418605od_a_a] :
( ( member1755255446od_a_a @ D @ A )
=> ( ( C != D )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
| ( member1349055120od_a_a @ ( produc1859144151od_a_a @ D @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_total__on__def) ).
thf(547,plain,
( total_1024184433od_a_a
= ( ^ [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a] :
! [C: multis599418605od_a_a] :
( ( member1755255446od_a_a @ C @ A )
=> ! [D: multis599418605od_a_a] :
( ( member1755255446od_a_a @ D @ A )
=> ( ( C != D )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
| ( member1349055120od_a_a @ ( produc1859144151od_a_a @ D @ C ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(1,conjecture,
( ( member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ y @ x ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(2,negated_conjecture,
~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ y @ x ) @ relation ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(328,plain,
~ ( ( member449909584od_a_a @ ( product_Pair_a_a @ x @ y ) @ relation )
| ( member449909584od_a_a @ ( product_Pair_a_a @ y @ x ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(45,axiom,
( prefer697821563od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer1338892073od_a_a @ A @ B )
& ( prefer1064779160od_a_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_rational__preference__def) ).
thf(471,plain,
( prefer697821563od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer1338892073od_a_a @ A @ B )
& ( prefer1064779160od_a_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(163,axiom,
! [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a,E: multis599418605od_a_a] :
( ( prefer1340910575od_a_a @ A @ B )
=> ( ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
& ( member1349055120od_a_a @ ( produc1859144151od_a_a @ D @ C ) @ B ) )
=> ( ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ D @ E ) @ B )
& ( member1349055120od_a_a @ ( produc1859144151od_a_a @ E @ D ) @ B ) )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ E ) @ B )
& ( member1349055120od_a_a @ ( produc1859144151od_a_a @ E @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_preference_Oindiff__trans) ).
thf(837,plain,
! [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a,E: multis599418605od_a_a] :
( ( prefer1340910575od_a_a @ A @ B )
=> ( ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
& ( member1349055120od_a_a @ ( produc1859144151od_a_a @ D @ C ) @ B ) )
=> ( ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ D @ E ) @ B )
& ( member1349055120od_a_a @ ( produc1859144151od_a_a @ E @ D ) @ B ) )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ E ) @ B )
& ( member1349055120od_a_a @ ( produc1859144151od_a_a @ E @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(133,axiom,
! [A: set_Pr158363655iset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( trans_multiset_a @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ B @ C ) @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ A )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_transE) ).
thf(738,plain,
! [A: set_Pr158363655iset_a,B: multiset_a,C: multiset_a,D: multiset_a] :
( ( trans_multiset_a @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ B @ C ) @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ A )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ B @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(224,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_prod_Oinject) ).
thf(1050,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(79,axiom,
! [A: multiset_a,B: multiset_a > $o] :
( ( member_multiset_a @ A @ ( collect_multiset_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_mem__Collect__eq) ).
thf(569,plain,
! [A: multiset_a,B: multiset_a > $o] :
( ( member_multiset_a @ A @ ( collect_multiset_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(281,axiom,
! [A: a,B: a,C: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_indiff__trans) ).
thf(1246,plain,
! [A: a,B: a,C: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ relation )
& ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(90,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( ( produc1474507607od_a_a @ A @ B )
= ( produc1474507607od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_old_Oprod_Oinject) ).
thf(605,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( ( produc1474507607od_a_a @ A @ B )
= ( produc1474507607od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(305,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( ( member_a @ C @ A )
& ( member_a @ D @ A ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_rational__preference_Ostrict__not__refl__weak) ).
thf(1324,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( ( member_a @ C @ A )
& ( member_a @ D @ A ) )
=> ( ( ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(21,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer1338892073od_a_a @ A @ B )
=> ( trans_972827014od_a_a @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_preference_Otransitivity) ).
thf(393,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer1338892073od_a_a @ A @ B )
=> ( trans_972827014od_a_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(6,axiom,
( prefer1340910575od_a_a
= ( ^ [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a] :
( ! [C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
=> ( member1755255446od_a_a @ C @ A ) )
& ! [C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
=> ( member1755255446od_a_a @ D @ A ) )
& ( order_1040740996od_a_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_preference__def) ).
thf(343,plain,
( prefer1340910575od_a_a
= ( ^ [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a] :
( ! [C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
=> ( member1755255446od_a_a @ C @ A ) )
& ! [C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
=> ( member1755255446od_a_a @ D @ A ) )
& ( order_1040740996od_a_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(262,axiom,
prefer1292084992ence_a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_preference__axioms) ).
thf(1170,plain,
prefer1292084992ence_a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(65,axiom,
! [A: a,B: multiset_a,C: multiset_multiset_a] :
( ( member_a @ A @ ( set_mset_a @ ( fold_m382157835iset_a @ plus_plus_multiset_a @ B @ C ) ) )
= ( ( member_a @ A @ ( set_mset_a @ B ) )
| ? [D: multiset_a] :
( ( member_multiset_a @ D @ ( set_mset_multiset_a @ C ) )
& ( member_a @ A @ ( set_mset_a @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_in__mset__fold__plus__iff) ).
thf(530,plain,
! [A: a,B: multiset_a,C: multiset_multiset_a] :
( ( member_a @ A @ ( set_mset_a @ ( fold_m382157835iset_a @ plus_plus_multiset_a @ B @ C ) ) )
= ( ( member_a @ A @ ( set_mset_a @ B ) )
| ? [D: multiset_a] :
( ( member_multiset_a @ D @ ( set_mset_multiset_a @ C ) )
& ( member_a @ A @ ( set_mset_a @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(201,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a > product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member449909584od_a_a @ C @ ( image_794773445od_a_a @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_rev__image__eqI) ).
thf(953,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a > product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member449909584od_a_a @ C @ ( image_794773445od_a_a @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(143,axiom,
! [A: product_prod_a_a] :
( ( product_swap_a_a @ ( product_swap_a_a @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_swap__swap) ).
thf(773,plain,
! [A: product_prod_a_a] :
( ( product_swap_a_a @ ( product_swap_a_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(235,axiom,
! [A: a,B: a] :
( ( product_snd_a_a @ ( product_Pair_a_a @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_snd__conv) ).
thf(1086,plain,
! [A: a,B: a] :
( ( product_snd_a_a @ ( product_Pair_a_a @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(196,axiom,
! [A: product_prod_a_a,B: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( add_ms1725977093od_a_a @ A @ ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_insert__DiffM) ).
thf(938,plain,
! [A: product_prod_a_a,B: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( add_ms1725977093od_a_a @ A @ ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(108,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( ( prefer580340847ioms_a @ A @ B )
=> ( prefer719835986ence_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_rational__preference_Ointro) ).
thf(662,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( ( prefer580340847ioms_a @ A @ B )
=> ( prefer719835986ence_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(126,axiom,
! [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a] :
( ( prefer1669415233od_a_a @ A @ B )
=> ! [C: multis599418605od_a_a] :
( ( member1755255446od_a_a @ C @ A )
=> ! [D: multis599418605od_a_a] :
( ( member1755255446od_a_a @ D @ A )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
| ( member1349055120od_a_a @ ( produc1859144151od_a_a @ D @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_rational__preference_Ocompl) ).
thf(718,plain,
! [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a] :
( ( prefer1669415233od_a_a @ A @ B )
=> ! [C: multis599418605od_a_a] :
( ( member1755255446od_a_a @ C @ A )
=> ! [D: multis599418605od_a_a] :
( ( member1755255446od_a_a @ D @ A )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
| ( member1349055120od_a_a @ ( produc1859144151od_a_a @ D @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(240,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ! [C: a] :
( ( member_a @ C @ A )
=> ! [D: a] :
( ( member_a @ D @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
| ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_rational__preference_Ocompl) ).
thf(1103,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ! [C: a] :
( ( member_a @ C @ A )
=> ! [D: a] :
( ( member_a @ D @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
| ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(170,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Pr158363655iset_a,D: product_prod_a_a > multiset_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ ( inv_im1716587189od_a_a @ C @ D ) )
= ( member340150864iset_a @ ( produc2037245207iset_a @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_in__inv__image) ).
thf(856,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Pr158363655iset_a,D: product_prod_a_a > multiset_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ ( inv_im1716587189od_a_a @ C @ D ) )
= ( member340150864iset_a @ ( produc2037245207iset_a @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(299,axiom,
( asym_a
= ( ^ [A: set_Product_prod_a_a] :
? [B: set_Product_prod_a_a] :
( ( A = B )
& ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_asym_Osimps) ).
thf(1301,plain,
( asym_a
= ( ^ [A: set_Product_prod_a_a] :
? [B: set_Product_prod_a_a] :
( ( A = B )
& ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(252,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_old_Oprod_Oinject) ).
thf(1135,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( product_Pair_a_a @ A @ B )
= ( product_Pair_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(27,axiom,
! [A: set_multiset_a,B: set_Pr158363655iset_a,C: multiset_a,D: multiset_a,E: multiset_a] :
( ( prefer1779827352iset_a @ A @ B )
=> ( ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
& ~ ( member340150864iset_a @ ( produc2037245207iset_a @ D @ C ) @ B ) )
=> ( ( ( member340150864iset_a @ ( produc2037245207iset_a @ D @ E ) @ B )
& ~ ( member340150864iset_a @ ( produc2037245207iset_a @ E @ D ) @ B ) )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ E ) @ B )
& ~ ( member340150864iset_a @ ( produc2037245207iset_a @ E @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_rational__preference_Ostrict__trans) ).
thf(412,plain,
! [A: set_multiset_a,B: set_Pr158363655iset_a,C: multiset_a,D: multiset_a,E: multiset_a] :
( ( prefer1779827352iset_a @ A @ B )
=> ( ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
& ~ ( member340150864iset_a @ ( produc2037245207iset_a @ D @ C ) @ B ) )
=> ( ( ( member340150864iset_a @ ( produc2037245207iset_a @ D @ E ) @ B )
& ~ ( member340150864iset_a @ ( produc2037245207iset_a @ E @ D ) @ B ) )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ E ) @ B )
& ~ ( member340150864iset_a @ ( produc2037245207iset_a @ E @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(85,axiom,
! [A: a,B: multiset_a,C: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( minus_1649712171iset_a @ ( plus_plus_multiset_a @ C @ B ) @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
= ( plus_plus_multiset_a @ C @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_diff__union__single__conv) ).
thf(584,plain,
! [A: a,B: multiset_a,C: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( minus_1649712171iset_a @ ( plus_plus_multiset_a @ C @ B ) @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
= ( plus_plus_multiset_a @ C @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(77,axiom,
! [A: produc2061001575od_a_a > $o,B: produc2061001575od_a_a] :
( ! [C: multis599418605od_a_a,D: multis599418605od_a_a] : ( A @ ( produc1859144151od_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_old_Oprod_Oinducts) ).
thf(562,plain,
! [A: produc2061001575od_a_a > $o,B: produc2061001575od_a_a] :
( ! [C: multis599418605od_a_a,D: multis599418605od_a_a] : ( A @ ( produc1859144151od_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(31,axiom,
! [A: set_multiset_a,B: set_Pr158363655iset_a] :
( ! [C: multiset_a,D: multiset_a] :
( ( member_multiset_a @ C @ A )
=> ( ( member_multiset_a @ D @ A )
=> ( ( C != D )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
| ( member340150864iset_a @ ( produc2037245207iset_a @ D @ C ) @ B ) ) ) ) )
=> ( total_on_multiset_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_total__onI) ).
thf(423,plain,
! [A: set_multiset_a,B: set_Pr158363655iset_a] :
( ! [C: multiset_a,D: multiset_a] :
( ( member_multiset_a @ C @ A )
=> ( ( member_multiset_a @ D @ A )
=> ( ( C != D )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
| ( member340150864iset_a @ ( produc2037245207iset_a @ D @ C ) @ B ) ) ) ) )
=> ( total_on_multiset_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(321,axiom,
! [A: set_Product_prod_a_a,B: product_prod_a_a > a,C: set_a] :
( ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
=> ( member_a @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_image__subsetI) ).
thf(1389,plain,
! [A: set_Product_prod_a_a,B: product_prod_a_a > a,C: set_a] :
( ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
=> ( member_a @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_a @ ( image_340790172_a_a_a @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(165,axiom,
( order_359341630od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( refl_o1298442278od_a_a @ A @ B )
& ( trans_972827014od_a_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_preorder__on__def) ).
thf(843,plain,
( order_359341630od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( refl_o1298442278od_a_a @ A @ B )
& ( trans_972827014od_a_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(124,axiom,
! [A: multiset_a,B: multiset_a,C: set_Pr158363655iset_a,D: multiset_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ A @ B ) @ C )
=> ( ( D = B )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_ssubst__Pair__rhs) ).
thf(711,plain,
! [A: multiset_a,B: multiset_a,C: set_Pr158363655iset_a,D: multiset_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ A @ B ) @ C )
=> ( ( D = B )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(83,axiom,
! [A: a,B: multiset_a] : ( member_a @ A @ ( set_mset_a @ ( plus_plus_multiset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_multi__member__this) ).
thf(579,plain,
! [A: a,B: multiset_a] : ( member_a @ A @ ( set_mset_a @ ( plus_plus_multiset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(202,axiom,
! [A: product_prod_a_a,B: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( plus_p404985124od_a_a @ ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_insert__DiffM2) ).
thf(958,plain,
! [A: product_prod_a_a,B: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( plus_p404985124od_a_a @ ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(248,axiom,
! [A: a,B: a,C: set_a,D: set_Product_prod_a_a] :
( ( member_a @ A @ ( prefer161218362good_a @ B @ C @ D ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_at__lst__asgd__ge) ).
thf(1124,plain,
! [A: a,B: a,C: set_a,D: set_Product_prod_a_a] :
( ( member_a @ A @ ( prefer161218362good_a @ B @ C @ D ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(101,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( prefer580340847ioms_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_rational__preference_Oaxioms_I2_J) ).
thf(641,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( prefer580340847ioms_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(80,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( total_1490170027od_a_a @ A @ B )
=> ( prefer1064779160od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_rational__preference__axioms_Ointro) ).
thf(572,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( total_1490170027od_a_a @ A @ B )
=> ( prefer1064779160od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(290,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ ( inv_im15016955od_a_a @ C @ D ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_in__inv__image) ).
thf(1271,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ ( inv_im15016955od_a_a @ C @ D ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(147,axiom,
! [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a] :
( ! [C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( member1755255446od_a_a @ C @ A )
=> ( ( member1755255446od_a_a @ D @ A )
=> ( ( C != D )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
| ( member1349055120od_a_a @ ( produc1859144151od_a_a @ D @ C ) @ B ) ) ) ) )
=> ( total_1024184433od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_total__onI) ).
thf(787,plain,
! [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a] :
( ! [C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( member1755255446od_a_a @ C @ A )
=> ( ( member1755255446od_a_a @ D @ A )
=> ( ( C != D )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
| ( member1349055120od_a_a @ ( produc1859144151od_a_a @ D @ C ) @ B ) ) ) ) )
=> ( total_1024184433od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(237,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: a,D: product_prod_a_a > a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_a @ C @ ( image_340790172_a_a_a @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_rev__image__eqI) ).
thf(1092,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: a,D: product_prod_a_a > a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_a @ C @ ( image_340790172_a_a_a @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(199,axiom,
! [A: a,B: product_prod_a_a] :
( ( A
= ( product_snd_a_a @ B ) )
= ( ? [C: a] :
( B
= ( product_Pair_a_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_eq__snd__iff) ).
thf(947,plain,
! [A: a,B: product_prod_a_a] :
( ( A
= ( product_snd_a_a @ B ) )
= ( ? [C: a] :
( B
= ( product_Pair_a_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(275,axiom,
! [A: a,B: product_prod_a_a > a,C: product_prod_a_a,D: set_Product_prod_a_a] :
( ( A
= ( B @ C ) )
=> ( ( member449909584od_a_a @ C @ D )
=> ( member_a @ A @ ( image_340790172_a_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_image__eqI) ).
thf(1224,plain,
! [A: a,B: product_prod_a_a > a,C: product_prod_a_a,D: set_Product_prod_a_a] :
( ( A
= ( B @ C ) )
=> ( ( member449909584od_a_a @ C @ D )
=> ( member_a @ A @ ( image_340790172_a_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(312,axiom,
! [A: set_Product_prod_a_a] :
( ! [B: a,C: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ A ) )
=> ( asym_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_asym_Ointros) ).
thf(1356,plain,
! [A: set_Product_prod_a_a] :
( ! [B: a,C: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ A ) )
=> ( asym_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(8,axiom,
( irrefl1672195874od_a_a
= ( ^ [A: set_Pr1821581383od_a_a] :
! [B: multis599418605od_a_a] :
~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ B @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_irrefl__def) ).
thf(350,plain,
( irrefl1672195874od_a_a
= ( ^ [A: set_Pr1821581383od_a_a] :
! [B: multis599418605od_a_a] :
~ ( member1349055120od_a_a @ ( produc1859144151od_a_a @ B @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(271,axiom,
! [A: a,B: a,C: a] :
( ( ( product_fst_a_a @ ( product_Pair_a_a @ A @ B ) )
= C )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_fst__eqD) ).
thf(1209,plain,
! [A: a,B: a,C: a] :
( ( ( product_fst_a_a @ ( product_Pair_a_a @ A @ B ) )
= C )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(186,axiom,
! [A: product_prod_a_a > $o,B: a,C: a] :
( ( A @ ( product_Pair_a_a @ B @ C ) )
=> ( product_curry_a_a_o @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_curryI) ).
thf(900,plain,
! [A: product_prod_a_a > $o,B: a,C: a] :
( ( A @ ( product_Pair_a_a @ B @ C ) )
=> ( product_curry_a_a_o @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(161,axiom,
! [A: multis599418605od_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( ( produc1859144151od_a_a @ A @ B )
= ( produc1859144151od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_prod_Oinject) ).
thf(831,plain,
! [A: multis599418605od_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( ( produc1859144151od_a_a @ A @ B )
= ( produc1859144151od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(246,axiom,
! [A: a,B: set_a,C: product_prod_a_a,D: a > product_prod_a_a] :
( ( member_a @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member449909584od_a_a @ C @ ( image_1725938350od_a_a @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_rev__image__eqI) ).
thf(1117,plain,
! [A: a,B: set_a,C: product_prod_a_a,D: a > product_prod_a_a] :
( ( member_a @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member449909584od_a_a @ C @ ( image_1725938350od_a_a @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(223,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_rational__preference_Ocompl) ).
thf(1048,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(210,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a,E: a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ E @ D ) @ B ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ E ) @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ E @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_preference_Oindiff__trans) ).
thf(996,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a,E: a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ E @ D ) @ B ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ E ) @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ E @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(12,axiom,
( trans_1520871884od_a_a
= ( ^ [A: set_Pr1821581383od_a_a] :
! [B: multis599418605od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ B @ C ) @ A )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ A )
=> ( member1349055120od_a_a @ ( produc1859144151od_a_a @ B @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_trans__def) ).
thf(362,plain,
( trans_1520871884od_a_a
= ( ^ [A: set_Pr1821581383od_a_a] :
! [B: multis599418605od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ B @ C ) @ A )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ A )
=> ( member1349055120od_a_a @ ( produc1859144151od_a_a @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(247,axiom,
( irrefl_a
= ( ^ [A: set_Product_prod_a_a] :
! [B: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_irrefl__def) ).
thf(1122,plain,
( irrefl_a
= ( ^ [A: set_Product_prod_a_a] :
! [B: a] :
~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(58,axiom,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) )
=> ( ( set_mset_a @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) )
= ( set_mset_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_more__than__one__mset__mset__diff) ).
thf(509,plain,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) )
=> ( ( set_mset_a @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) )
= ( set_mset_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(33,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( prefer1064779160od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_rational__preference_Oaxioms_I2_J) ).
thf(434,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer697821563od_a_a @ A @ B )
=> ( prefer1064779160od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(172,axiom,
! [A: multis599418605od_a_a,B: multis599418605od_a_a] :
( ( produc1913956215od_a_a @ ( produc1859144151od_a_a @ A @ B ) )
= ( produc1859144151od_a_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_swap__simp) ).
thf(863,plain,
! [A: multis599418605od_a_a,B: multis599418605od_a_a] :
( ( produc1913956215od_a_a @ ( produc1859144151od_a_a @ A @ B ) )
= ( produc1859144151od_a_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(264,axiom,
! [A: set_Product_prod_a_a,B: set_a] :
( ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member_a @ C @ B ) )
=> ( ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member_a @ D @ B ) )
=> ( ( order_preorder_on_a @ B @ A )
=> ( prefer1292084992ence_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_preference_Ointro) ).
thf(1175,plain,
! [A: set_Product_prod_a_a,B: set_a] :
( ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member_a @ C @ B ) )
=> ( ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member_a @ D @ B ) )
=> ( ( order_preorder_on_a @ B @ A )
=> ( prefer1292084992ence_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(182,axiom,
! [A: product_prod_a_a,B: a > a > $o] :
( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ ( produc1833107820_a_a_o @ B ) ) )
=> ( B @ ( product_fst_a_a @ A ) @ ( product_snd_a_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_Product__Type_OCollect__case__prodD) ).
thf(890,plain,
! [A: product_prod_a_a,B: a > a > $o] :
( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ ( produc1833107820_a_a_o @ B ) ) )
=> ( B @ ( product_fst_a_a @ A ) @ ( product_snd_a_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(308,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a > $o] :
( ( asym_a @ A )
=> ( ! [C: set_Product_prod_a_a] :
( ! [D: a,E: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ C )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ E @ D ) @ C ) )
=> ( B @ C ) )
=> ( B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_asym_Oinducts) ).
thf(1339,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a > $o] :
( ( asym_a @ A )
=> ( ! [C: set_Product_prod_a_a] :
( ! [D: a,E: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ C )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ E @ D ) @ C ) )
=> ( B @ C ) )
=> ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(88,axiom,
! [A: a,B: multiset_a,C: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
= C )
= ( B
= ( add_mset_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_diff__single__eq__union) ).
thf(594,plain,
! [A: a,B: multiset_a,C: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
= C )
= ( B
= ( add_mset_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(129,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( total_on_a @ A @ B )
=> ( prefer580340847ioms_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_rational__preference__axioms_Ointro) ).
thf(726,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( total_on_a @ A @ B )
=> ( prefer580340847ioms_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(120,axiom,
( trans_972827014od_a_a
= ( ^ [A: set_Pr1948701895od_a_a] :
! [B: product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ C ) @ A )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ A )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_trans__def) ).
thf(700,plain,
( trans_972827014od_a_a
= ( ^ [A: set_Pr1948701895od_a_a] :
! [B: product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ C ) @ A )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ A )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(257,axiom,
! [A: product_prod_a_a,B: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_multi__drop__mem__not__eq) ).
thf(1149,plain,
! [A: product_prod_a_a,B: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(216,axiom,
! [A: multis599418605od_a_a,B: product_prod_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a,E: multis599418605od_a_a,F: set_Pr1948701895od_a_a] :
( ( A
= ( add_ms1725977093od_a_a @ B @ C ) )
=> ( ( D
= ( plus_p404985124od_a_a @ C @ E ) )
=> ( ! [G: product_prod_a_a] :
( ( member449909584od_a_a @ G @ ( set_ms1818337124od_a_a @ E ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ G @ B ) @ F ) )
=> ( member1349055120od_a_a @ ( produc1859144151od_a_a @ D @ A ) @ ( mult1_1719650714od_a_a @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_mult1I) ).
thf(1022,plain,
! [A: multis599418605od_a_a,B: product_prod_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a,E: multis599418605od_a_a,F: set_Pr1948701895od_a_a] :
( ( A
= ( add_ms1725977093od_a_a @ B @ C ) )
=> ( ( D
= ( plus_p404985124od_a_a @ C @ E ) )
=> ( ! [G: product_prod_a_a] :
( ( member449909584od_a_a @ G @ ( set_ms1818337124od_a_a @ E ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ G @ B ) @ F ) )
=> ( member1349055120od_a_a @ ( produc1859144151od_a_a @ D @ A ) @ ( mult1_1719650714od_a_a @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(244,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a] :
( ( refl_o1298442278od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_refl__onD) ).
thf(1112,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a] :
( ( refl_o1298442278od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(7,axiom,
! [A: a,B: a > a,C: a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( member_a @ C @ D )
=> ( member_a @ A @ ( image_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_image__eqI) ).
thf(345,plain,
! [A: a,B: a > a,C: a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( member_a @ C @ D )
=> ( member_a @ A @ ( image_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(14,axiom,
! [A: set_Pr1821581383od_a_a] :
( ! [B: multis599418605od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ B @ C ) @ A )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ A )
=> ( member1349055120od_a_a @ ( produc1859144151od_a_a @ B @ D ) @ A ) ) )
=> ( trans_1520871884od_a_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_transI) ).
thf(367,plain,
! [A: set_Pr1821581383od_a_a] :
( ! [B: multis599418605od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ B @ C ) @ A )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ A )
=> ( member1349055120od_a_a @ ( produc1859144151od_a_a @ B @ D ) @ A ) ) )
=> ( trans_1520871884od_a_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(42,axiom,
! [A: produc1572603623od_a_a] :
? [B: product_prod_a_a,C: product_prod_a_a] :
( A
= ( produc1474507607od_a_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_surj__pair) ).
thf(462,plain,
! [A: produc1572603623od_a_a] :
? [B: product_prod_a_a,C: product_prod_a_a] :
( A
= ( produc1474507607od_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(194,axiom,
! [A: a,B: product_prod_a_a] :
( ( A
= ( product_fst_a_a @ B ) )
= ( ? [C: a] :
( B
= ( product_Pair_a_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_eq__fst__iff) ).
thf(932,plain,
! [A: a,B: product_prod_a_a] :
( ( A
= ( product_fst_a_a @ B ) )
= ( ? [C: a] :
( B
= ( product_Pair_a_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(229,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > a] :
( ( member449909584od_a_a @ A @ B )
=> ( member_a @ ( C @ A ) @ ( image_340790172_a_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_imageI) ).
thf(1066,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > a] :
( ( member449909584od_a_a @ A @ B )
=> ( member_a @ ( C @ A ) @ ( image_340790172_a_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(145,axiom,
! [A: produc1127127335iset_a] :
? [B: multiset_a,C: multiset_a] :
( A
= ( produc2037245207iset_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_surj__pair) ).
thf(780,plain,
! [A: produc1127127335iset_a] :
? [B: multiset_a,C: multiset_a] :
( A
= ( produc2037245207iset_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(91,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer1338892073od_a_a @ A @ B )
=> ( ( prefer1064779160od_a_a @ A @ B )
=> ( prefer697821563od_a_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_rational__preference_Ointro) ).
thf(608,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer1338892073od_a_a @ A @ B )
=> ( ( prefer1064779160od_a_a @ A @ B )
=> ( prefer697821563od_a_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(209,axiom,
! [A: a > $o,B: a,C: a > $o,D: a] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( product_fst_a_a @ ( product_Pair_a_a @ B @ D ) ) )
& ( C @ ( product_snd_a_a @ ( product_Pair_a_a @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_conjI__realizer) ).
thf(986,plain,
! [A: a > $o,B: a,C: a > $o,D: a] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( product_fst_a_a @ ( product_Pair_a_a @ B @ D ) ) )
& ( C @ ( product_snd_a_a @ ( product_Pair_a_a @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(211,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ! [C: a,D: a] :
( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ( C != D )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
| ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) )
=> ( total_on_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_total__onI) ).
thf(1000,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ! [C: a,D: a] :
( ( member_a @ C @ A )
=> ( ( member_a @ D @ A )
=> ( ( C != D )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
| ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) ) ) ) )
=> ( total_on_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(282,axiom,
( asym_a
= ( ^ [A: set_Product_prod_a_a] :
! [B: a,C: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_asym__iff) ).
thf(1250,plain,
( asym_a
= ( ^ [A: set_Product_prod_a_a] :
! [B: a,C: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(168,axiom,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( plus_plus_multiset_a @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_insert__DiffM2) ).
thf(851,plain,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( plus_plus_multiset_a @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(32,axiom,
! [A: produc1572603623od_a_a > $o,B: produc1572603623od_a_a] :
( ! [C: product_prod_a_a,D: product_prod_a_a] : ( A @ ( produc1474507607od_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_prod__cases) ).
thf(431,plain,
! [A: produc1572603623od_a_a > $o,B: produc1572603623od_a_a] :
( ! [C: product_prod_a_a,D: product_prod_a_a] : ( A @ ( produc1474507607od_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(107,axiom,
! [A: set_multiset_a,B: set_Pr158363655iset_a,C: multiset_a,D: multiset_a] :
( ( prefer1779827352iset_a @ A @ B )
=> ( ( ( member_multiset_a @ C @ A )
& ( member_multiset_a @ D @ A ) )
=> ( ( ~ ( member340150864iset_a @ ( produc2037245207iset_a @ D @ C ) @ B ) )
= ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
& ~ ( member340150864iset_a @ ( produc2037245207iset_a @ D @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_rational__preference_Ostrict__not__refl__weak) ).
thf(658,plain,
! [A: set_multiset_a,B: set_Pr158363655iset_a,C: multiset_a,D: multiset_a] :
( ( prefer1779827352iset_a @ A @ B )
=> ( ( ( member_multiset_a @ C @ A )
& ( member_multiset_a @ D @ A ) )
=> ( ( ~ ( member340150864iset_a @ ( produc2037245207iset_a @ D @ C ) @ B ) )
= ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
& ~ ( member340150864iset_a @ ( produc2037245207iset_a @ D @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(115,axiom,
! [A: a > a > set_Product_prod_a_a] :
( ( produc143372156od_a_a @ ( produc1093061851od_a_a @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_curry__case__prod) ).
thf(685,plain,
! [A: a > a > set_Product_prod_a_a] :
( ( produc143372156od_a_a @ ( produc1093061851od_a_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(263,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( refl_o1298442278od_a_a @ A @ B )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
=> ( ( member449909584od_a_a @ C @ A )
& ( member449909584od_a_a @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_refl__on__domain) ).
thf(1171,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( refl_o1298442278od_a_a @ A @ B )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
=> ( ( member449909584od_a_a @ C @ A )
& ( member449909584od_a_a @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(272,axiom,
! [A: a,B: a,C: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ relation ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_strict__trans) ).
thf(1213,plain,
! [A: a,B: a,C: a] :
( ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ relation ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ relation ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ relation )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ A ) @ relation ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(159,axiom,
! [A: a] : ( member_a @ A @ ( set_mset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_multi__member__last) ).
thf(827,plain,
! [A: a] : ( member_a @ A @ ( set_mset_a @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(46,axiom,
! [A: set_multiset_a,B: set_Pr158363655iset_a] :
( ( prefer1779827352iset_a @ A @ B )
=> ! [C: multiset_a] :
( ( member_multiset_a @ C @ A )
=> ! [D: multiset_a] :
( ( member_multiset_a @ D @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
| ( member340150864iset_a @ ( produc2037245207iset_a @ D @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_rational__preference_Ocompl) ).
thf(473,plain,
! [A: set_multiset_a,B: set_Pr158363655iset_a] :
( ( prefer1779827352iset_a @ A @ B )
=> ! [C: multiset_a] :
( ( member_multiset_a @ C @ A )
=> ! [D: multiset_a] :
( ( member_multiset_a @ D @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
| ( member340150864iset_a @ ( produc2037245207iset_a @ D @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(52,axiom,
! [A: produc1127127335iset_a > $o,B: produc1127127335iset_a] :
( ! [C: multiset_a,D: multiset_a] : ( A @ ( produc2037245207iset_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_old_Oprod_Oinducts) ).
thf(490,plain,
! [A: produc1127127335iset_a > $o,B: produc1127127335iset_a] :
( ! [C: multiset_a,D: multiset_a] : ( A @ ( produc2037245207iset_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(261,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a,E: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ E @ D ) @ B ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ E ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ E @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_rational__preference_Ostrict__trans) ).
thf(1166,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a,E: a] :
( ( prefer719835986ence_a @ A @ B )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ D @ C ) @ B ) )
=> ( ( ( member449909584od_a_a @ ( product_Pair_a_a @ D @ E ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ E @ D ) @ B ) )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ E ) @ B )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ E @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(198,axiom,
! [A: a,B: a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( image_794773445od_a_a @ product_swap_a_a @ C ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_pair__in__swap__image) ).
thf(944,plain,
! [A: a,B: a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( image_794773445od_a_a @ product_swap_a_a @ C ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(148,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( prefer1292084992ence_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_rational__preference_Oaxioms_I1_J) ).
thf(795,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( prefer1292084992ence_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(104,axiom,
! [A: produc2061001575od_a_a > $o,B: multis599418605od_a_a,C: multis599418605od_a_a] :
( ( produc1548936141_a_a_o @ A @ B @ C )
=> ( A @ ( produc1859144151od_a_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_curryD) ).
thf(648,plain,
! [A: produc2061001575od_a_a > $o,B: multis599418605od_a_a,C: multis599418605od_a_a] :
( ( produc1548936141_a_a_o @ A @ B @ C )
=> ( A @ ( produc1859144151od_a_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(154,axiom,
! [A: produc1127127335iset_a > $o,B: produc1127127335iset_a] :
( ! [C: multiset_a,D: multiset_a] : ( A @ ( produc2037245207iset_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_prod__cases) ).
thf(812,plain,
! [A: produc1127127335iset_a > $o,B: produc1127127335iset_a] :
( ! [C: multiset_a,D: multiset_a] : ( A @ ( produc2037245207iset_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(93,axiom,
! [A: set_a,B: a > a,C: set_a] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ( member_a @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_a @ ( image_a_a @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_image__subsetI) ).
thf(617,plain,
! [A: set_a,B: a > a,C: set_a] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ( member_a @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_a @ ( image_a_a @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(255,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a] :
( ! [C: a,D: a] : ( A @ ( product_Pair_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_old_Oprod_Oinducts) ).
thf(1145,plain,
! [A: product_prod_a_a > $o,B: product_prod_a_a] :
( ! [C: a,D: a] : ( A @ ( product_Pair_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(10,axiom,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_multi__drop__mem__not__eq) ).
thf(355,plain,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(138,axiom,
! [A: a,B: set_a,C: a > a] :
( ( member_a @ A @ B )
=> ( member_a @ ( C @ A ) @ ( image_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_imageI) ).
thf(754,plain,
! [A: a,B: set_a,C: a > a] :
( ( member_a @ A @ B )
=> ( member_a @ ( C @ A ) @ ( image_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(265,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ! [C: product_prod_a_a,D: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( ( member449909584od_a_a @ D @ A )
=> ( ( C != D )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ C ) @ B ) ) ) ) )
=> ( total_1490170027od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_total__onI) ).
thf(1181,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ! [C: product_prod_a_a,D: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( ( member449909584od_a_a @ D @ A )
=> ( ( C != D )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ C ) @ B ) ) ) ) )
=> ( total_1490170027od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(158,axiom,
! [A: multiset_a,B: multiset_a > multiset_a > set_multiset_a,C: produc1127127335iset_a] :
( ( member_multiset_a @ A @ ( produc429414904iset_a @ B @ C ) )
=> ~ ! [D: multiset_a,E: multiset_a] :
( ( C
= ( produc2037245207iset_a @ D @ E ) )
=> ~ ( member_multiset_a @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_mem__case__prodE) ).
thf(823,plain,
! [A: multiset_a,B: multiset_a > multiset_a > set_multiset_a,C: produc1127127335iset_a] :
( ( member_multiset_a @ A @ ( produc429414904iset_a @ B @ C ) )
=> ~ ! [D: multiset_a,E: multiset_a] :
( ( C
= ( produc2037245207iset_a @ D @ E ) )
=> ~ ( member_multiset_a @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(144,axiom,
! [A: a,B: multiset_a,C: a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( minus_1649712171iset_a @ ( add_mset_a @ C @ B ) @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
= ( add_mset_a @ C @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_diff__union__swap2) ).
thf(776,plain,
! [A: a,B: multiset_a,C: a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( minus_1649712171iset_a @ ( add_mset_a @ C @ B ) @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
= ( add_mset_a @ C @ ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(75,axiom,
! [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a,C: multis599418605od_a_a] :
( ( refl_o581572716od_a_a @ A @ B )
=> ( ( member1755255446od_a_a @ C @ A )
=> ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_refl__onD) ).
thf(557,plain,
! [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a,C: multis599418605od_a_a] :
( ( refl_o581572716od_a_a @ A @ B )
=> ( ( member1755255446od_a_a @ C @ A )
=> ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(181,axiom,
! [A: set_a,B: a > product_prod_a_a,C: set_Product_prod_a_a] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ( member449909584od_a_a @ ( B @ D ) @ C ) )
=> ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_image__subsetI) ).
thf(887,plain,
! [A: set_a,B: a > product_prod_a_a,C: set_Product_prod_a_a] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ( member449909584od_a_a @ ( B @ D ) @ C ) )
=> ( ord_le1824328871od_a_a @ ( image_1725938350od_a_a @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(283,axiom,
! [A: a,B: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
=> ( member_a @ A @ carrier ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_not__outside) ).
thf(1252,plain,
! [A: a,B: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ relation )
=> ( member_a @ A @ carrier ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(288,axiom,
member_a @ x @ carrier,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(1267,plain,
member_a @ x @ carrier,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(122,axiom,
! [A: produc1572603623od_a_a > $o,B: produc1572603623od_a_a] :
( ! [C: product_prod_a_a,D: product_prod_a_a] : ( A @ ( produc1474507607od_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_old_Oprod_Oinducts) ).
thf(705,plain,
! [A: produc1572603623od_a_a > $o,B: produc1572603623od_a_a] :
( ! [C: product_prod_a_a,D: product_prod_a_a] : ( A @ ( produc1474507607od_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(259,axiom,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ ( minus_1257885652od_a_a @ B @ C ) ) )
=> ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_in__diffD) ).
thf(1156,plain,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ ( minus_1257885652od_a_a @ B @ C ) ) )
=> ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(26,axiom,
! [A: product_prod_a_a > $o] :
( ( produc1833107820_a_a_o @ ( product_curry_a_a_o @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_case__prod__curry) ).
thf(409,plain,
! [A: product_prod_a_a > $o] :
( ( produc1833107820_a_a_o @ ( product_curry_a_a_o @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(277,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B ) )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_subrelI) ).
thf(1230,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ! [C: a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B ) )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(225,axiom,
! [A: a,B: a,C: set_Pr1948701895od_a_a,D: a > product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( inv_im777352425_a_a_a @ C @ D ) )
= ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_in__inv__image) ).
thf(1053,plain,
! [A: a,B: a,C: set_Pr1948701895od_a_a,D: a > product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( inv_im777352425_a_a_a @ C @ D ) )
= ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(112,axiom,
! [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( refl_o581572716od_a_a @ A @ B )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
=> ( ( member1755255446od_a_a @ C @ A )
& ( member1755255446od_a_a @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_refl__on__domain) ).
thf(673,plain,
! [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( refl_o581572716od_a_a @ A @ B )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
=> ( ( member1755255446od_a_a @ C @ A )
& ( member1755255446od_a_a @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(298,axiom,
refl_on_a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_reflexivity) ).
thf(1300,plain,
refl_on_a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(3,axiom,
( order_1505515173od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( trans_972827014od_a_a @ B )
& ( irrefl76447196od_a_a @ B )
& ( total_1490170027od_a_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_strict__linear__order__on__def) ).
thf(331,plain,
( order_1505515173od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( trans_972827014od_a_a @ B )
& ( irrefl76447196od_a_a @ B )
& ( total_1490170027od_a_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(82,axiom,
! [A: set_Pr158363655iset_a] :
( ( collec1104713362iset_a
@ ^ [B: produc1127127335iset_a] : ( member340150864iset_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Collect__mem__eq) ).
thf(576,plain,
! [A: set_Pr158363655iset_a] :
( ( collec1104713362iset_a
@ ^ [B: produc1127127335iset_a] : ( member340150864iset_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(102,axiom,
! [A: produc2061001575od_a_a > $o,B: produc2061001575od_a_a] :
( ! [C: multis599418605od_a_a,D: multis599418605od_a_a] : ( A @ ( produc1859144151od_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_prod__cases) ).
thf(643,plain,
! [A: produc2061001575od_a_a > $o,B: produc2061001575od_a_a] :
( ! [C: multis599418605od_a_a,D: multis599418605od_a_a] : ( A @ ( produc1859144151od_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(70,axiom,
! [A: set_Pr1948701895od_a_a,B: product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( trans_972827014od_a_a @ A )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ C ) @ A )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ A )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_transD) ).
thf(544,plain,
! [A: set_Pr1948701895od_a_a,B: product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( trans_972827014od_a_a @ A )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ C ) @ A )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ A )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(135,axiom,
! [A: produc1572603623od_a_a,B: produc1572603623od_a_a > $o] :
( ( member2057358096od_a_a @ A @ ( collec1635618130od_a_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_mem__Collect__eq) ).
thf(744,plain,
! [A: produc1572603623od_a_a,B: produc1572603623od_a_a > $o] :
( ( member2057358096od_a_a @ A @ ( collec1635618130od_a_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(5,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( ( produc1474507607od_a_a @ A @ B )
= ( produc1474507607od_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_Pair__inject) ).
thf(336,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( ( produc1474507607od_a_a @ A @ B )
= ( produc1474507607od_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(254,axiom,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( minus_1257885652od_a_a @ ( plus_p404985124od_a_a @ C @ B ) @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) )
= ( plus_p404985124od_a_a @ C @ ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_diff__union__single__conv) ).
thf(1141,plain,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( minus_1257885652od_a_a @ ( plus_p404985124od_a_a @ C @ B ) @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) )
= ( plus_p404985124od_a_a @ C @ ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(274,axiom,
! [A: a,B: a] :
( ( product_swap_a_a @ ( product_Pair_a_a @ A @ B ) )
= ( product_Pair_a_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_swap__simp) ).
thf(1221,plain,
! [A: a,B: a] :
( ( product_swap_a_a @ ( product_Pair_a_a @ A @ B ) )
= ( product_Pair_a_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(212,axiom,
! [A: produc1127127335iset_a,B: a > a > set_Pr158363655iset_a,C: product_prod_a_a] :
( ( member340150864iset_a @ A @ ( produc93594587iset_a @ B @ C ) )
=> ~ ! [D: a,E: a] :
( ( C
= ( product_Pair_a_a @ D @ E ) )
=> ~ ( member340150864iset_a @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_mem__case__prodE) ).
thf(1008,plain,
! [A: produc1127127335iset_a,B: a > a > set_Pr158363655iset_a,C: product_prod_a_a] :
( ( member340150864iset_a @ A @ ( produc93594587iset_a @ B @ C ) )
=> ~ ! [D: a,E: a] :
( ( C
= ( product_Pair_a_a @ D @ E ) )
=> ~ ( member340150864iset_a @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(37,axiom,
! [A: set_Pr1821581383od_a_a,B: set_mu1281098573od_a_a] :
( ! [C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ A )
=> ( member1755255446od_a_a @ C @ B ) )
=> ( ! [C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ A )
=> ( member1755255446od_a_a @ D @ B ) )
=> ( ( order_1040740996od_a_a @ B @ A )
=> ( prefer1340910575od_a_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_preference_Ointro) ).
thf(446,plain,
! [A: set_Pr1821581383od_a_a,B: set_mu1281098573od_a_a] :
( ! [C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ A )
=> ( member1755255446od_a_a @ C @ B ) )
=> ( ! [C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ A )
=> ( member1755255446od_a_a @ D @ B ) )
=> ( ( order_1040740996od_a_a @ B @ A )
=> ( prefer1340910575od_a_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(177,axiom,
! [A: set_Product_prod_a_a,B: a,C: a,D: a] :
( ( trans_a @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_transD) ).
thf(876,plain,
! [A: set_Product_prod_a_a,B: a,C: a,D: a] :
( ( trans_a @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(171,axiom,
! [A: set_multiset_a,B: set_Pr158363655iset_a,C: multiset_a,D: multiset_a] :
( ( refl_on_multiset_a @ A @ B )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
=> ( ( member_multiset_a @ C @ A )
& ( member_multiset_a @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_refl__on__domain) ).
thf(859,plain,
! [A: set_multiset_a,B: set_Pr158363655iset_a,C: multiset_a,D: multiset_a] :
( ( refl_on_multiset_a @ A @ B )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
=> ( ( member_multiset_a @ C @ A )
& ( member_multiset_a @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(280,axiom,
! [A: multis599418605od_a_a,B: multis599418605od_a_a,C: set_Pr1948701895od_a_a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ A @ B ) @ ( mult1_1719650714od_a_a @ C ) )
=> ~ ! [D: product_prod_a_a,E: multis599418605od_a_a] :
( ( B
= ( add_ms1725977093od_a_a @ D @ E ) )
=> ! [F: multis599418605od_a_a] :
( ( A
= ( plus_p404985124od_a_a @ E @ F ) )
=> ~ ! [G: product_prod_a_a] :
( ( member449909584od_a_a @ G @ ( set_ms1818337124od_a_a @ F ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ G @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_mult1E) ).
thf(1240,plain,
! [A: multis599418605od_a_a,B: multis599418605od_a_a,C: set_Pr1948701895od_a_a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ A @ B ) @ ( mult1_1719650714od_a_a @ C ) )
=> ~ ! [D: product_prod_a_a,E: multis599418605od_a_a] :
( ( B
= ( add_ms1725977093od_a_a @ D @ E ) )
=> ! [F: multis599418605od_a_a] :
( ( A
= ( plus_p404985124od_a_a @ E @ F ) )
=> ~ ! [G: product_prod_a_a] :
( ( member449909584od_a_a @ G @ ( set_ms1818337124od_a_a @ F ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ G @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(207,axiom,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: product_prod_a_a,D: multis599418605od_a_a] :
( ( ( add_ms1725977093od_a_a @ A @ B )
= ( add_ms1725977093od_a_a @ C @ D ) )
=> ( ( A != C )
=> ( member449909584od_a_a @ C @ ( set_ms1818337124od_a_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_insert__noteq__member) ).
thf(978,plain,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: product_prod_a_a,D: multis599418605od_a_a] :
( ( ( add_ms1725977093od_a_a @ A @ B )
= ( add_ms1725977093od_a_a @ C @ D ) )
=> ( ( A != C )
=> ( member449909584od_a_a @ C @ ( set_ms1818337124od_a_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(19,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: product_prod_a_a,E: product_prod_a_a] :
( ( prefer1338892073od_a_a @ A @ B )
=> ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
& ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ C ) @ B ) )
=> ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ E ) @ B )
& ( member2057358096od_a_a @ ( produc1474507607od_a_a @ E @ D ) @ B ) )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ E ) @ B )
& ( member2057358096od_a_a @ ( produc1474507607od_a_a @ E @ C ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_preference_Oindiff__trans) ).
thf(386,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: product_prod_a_a,E: product_prod_a_a] :
( ( prefer1338892073od_a_a @ A @ B )
=> ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
& ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ C ) @ B ) )
=> ( ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ E ) @ B )
& ( member2057358096od_a_a @ ( produc1474507607od_a_a @ E @ D ) @ B ) )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ E ) @ B )
& ( member2057358096od_a_a @ ( produc1474507607od_a_a @ E @ C ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(166,axiom,
( prefer1571048262iset_a
= ( ^ [A: set_multiset_a,B: set_Pr158363655iset_a] :
( ! [C: multiset_a,D: multiset_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
=> ( member_multiset_a @ C @ A ) )
& ! [C: multiset_a,D: multiset_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
=> ( member_multiset_a @ D @ A ) )
& ( order_750350043iset_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_preference__def) ).
thf(845,plain,
( prefer1571048262iset_a
= ( ^ [A: set_multiset_a,B: set_Pr158363655iset_a] :
( ! [C: multiset_a,D: multiset_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
=> ( member_multiset_a @ C @ A ) )
& ! [C: multiset_a,D: multiset_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
=> ( member_multiset_a @ D @ A ) )
& ( order_750350043iset_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(43,axiom,
! [A: multiset_a,B: multiset_a,C: set_multiset_a,D: set_Pr158363655iset_a] :
( ( member_multiset_a @ A @ ( prefer2130004608iset_a @ B @ C @ D ) )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_at__least__as__goodD) ).
thf(465,plain,
! [A: multiset_a,B: multiset_a,C: set_multiset_a,D: set_Pr158363655iset_a] :
( ( member_multiset_a @ A @ ( prefer2130004608iset_a @ B @ C @ D ) )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(96,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_Collect__mem__eq) ).
thf(627,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(68,axiom,
! [A: multiset_a,B: a] :
( ( A
= ( add_mset_a @ B @ ( minus_1649712171iset_a @ A @ ( add_mset_a @ B @ zero_zero_multiset_a ) ) ) )
= ( member_a @ B @ ( set_mset_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_add__mset__remove__trivial__eq) ).
thf(539,plain,
! [A: multiset_a,B: a] :
( ( A
= ( add_mset_a @ B @ ( minus_1649712171iset_a @ A @ ( add_mset_a @ B @ zero_zero_multiset_a ) ) ) )
= ( member_a @ B @ ( set_mset_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(249,axiom,
! [A: set_Product_prod_a_a,B: product_prod_a_a > product_prod_a_a,C: set_Product_prod_a_a] :
( ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
=> ( member449909584od_a_a @ ( B @ D ) @ C ) )
=> ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_image__subsetI) ).
thf(1126,plain,
! [A: set_Product_prod_a_a,B: product_prod_a_a > product_prod_a_a,C: set_Product_prod_a_a] :
( ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
=> ( member449909584od_a_a @ ( B @ D ) @ C ) )
=> ( ord_le1824328871od_a_a @ ( image_794773445od_a_a @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(266,axiom,
( total_1490170027od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
=> ( ( C != D )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_total__on__def) ).
thf(1189,plain,
( total_1490170027od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
=> ( ( C != D )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
| ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ C ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(206,axiom,
! [A: product_prod_a_a > $o,B: a,C: a] :
( ( product_curry_a_a_o @ A @ B @ C )
=> ( A @ ( product_Pair_a_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_curryE) ).
thf(976,plain,
! [A: product_prod_a_a > $o,B: a,C: a] :
( ( product_curry_a_a_o @ A @ B @ C )
=> ( A @ ( product_Pair_a_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(116,axiom,
! [A: set_multiset_a,B: set_Pr158363655iset_a,C: multiset_a,D: multiset_a] :
( ( prefer1571048262iset_a @ A @ B )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
=> ( member_multiset_a @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_preference_Onot__outside) ).
thf(688,plain,
! [A: set_multiset_a,B: set_Pr158363655iset_a,C: multiset_a,D: multiset_a] :
( ( prefer1571048262iset_a @ A @ B )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
=> ( member_multiset_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(63,axiom,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ~ ! [C: multiset_a] :
( B
!= ( add_mset_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_mset__add) ).
thf(524,plain,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ~ ! [C: multiset_a] :
( B
!= ( add_mset_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(84,axiom,
! [A: set_Product_prod_a_a,B: a > a] :
( ( trans_a @ A )
=> ( trans_a @ ( inv_image_a_a @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_trans__inv__image) ).
thf(581,plain,
! [A: set_Product_prod_a_a,B: a > a] :
( ( trans_a @ A )
=> ( trans_a @ ( inv_image_a_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(292,axiom,
! [A: product_prod_a_a] :
? [B: a,C: a] :
( A
= ( product_Pair_a_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_surj__pair) ).
thf(1276,plain,
! [A: product_prod_a_a] :
? [B: a,C: a] :
( A
= ( product_Pair_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(86,axiom,
! [A: multiset_a,B: multiset_a] :
( ( produc506430135iset_a @ ( produc2037245207iset_a @ A @ B ) )
= ( produc2037245207iset_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_swap__simp) ).
thf(588,plain,
! [A: multiset_a,B: multiset_a] :
( ( produc506430135iset_a @ ( produc2037245207iset_a @ A @ B ) )
= ( produc2037245207iset_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(203,axiom,
( product_swap_a_a
= ( ^ [A: product_prod_a_a] : ( product_Pair_a_a @ ( product_snd_a_a @ A ) @ ( product_fst_a_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_prod_Oswap__def) ).
thf(961,plain,
( product_swap_a_a
= ( ^ [A: product_prod_a_a] : ( product_Pair_a_a @ ( product_snd_a_a @ A ) @ ( product_fst_a_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(20,axiom,
! [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( refl_o581572716od_a_a @ A @ B )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
=> ( member1755255446od_a_a @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_refl__onD2) ).
thf(390,plain,
! [A: set_mu1281098573od_a_a,B: set_Pr1821581383od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( refl_o581572716od_a_a @ A @ B )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ B )
=> ( member1755255446od_a_a @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(98,axiom,
! [A: multis599418605od_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( ( produc1859144151od_a_a @ A @ B )
= ( produc1859144151od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_old_Oprod_Oinject) ).
thf(632,plain,
! [A: multis599418605od_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( ( produc1859144151od_a_a @ A @ B )
= ( produc1859144151od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(204,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( refl_on_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_refl__onD2) ).
thf(963,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a,D: a] :
( ( refl_on_a @ A @ B )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B )
=> ( member_a @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(61,axiom,
! [A: set_Pr158363655iset_a] :
( ! [B: multiset_a,C: multiset_a,D: multiset_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ B @ C ) @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ A )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ B @ D ) @ A ) ) )
=> ( trans_multiset_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_transI) ).
thf(517,plain,
! [A: set_Pr158363655iset_a] :
( ! [B: multiset_a,C: multiset_a,D: multiset_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ B @ C ) @ A )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ A )
=> ( member340150864iset_a @ ( produc2037245207iset_a @ B @ D ) @ A ) ) )
=> ( trans_multiset_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(131,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a > $o] :
( ! [C: product_prod_a_a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec645855634od_a_a @ A )
= ( collec645855634od_a_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_Collect__cong) ).
thf(731,plain,
! [A: product_prod_a_a > $o,B: product_prod_a_a > $o] :
( ! [C: product_prod_a_a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec645855634od_a_a @ A )
= ( collec645855634od_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(29,axiom,
( top_top_a_o
= ( ^ [A: a] : ( member_a @ A @ top_top_set_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_top__empty__eq) ).
thf(418,plain,
( top_top_a_o
= ( ^ [A: a] : ( member_a @ A @ top_top_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(217,axiom,
! [A: a > a > $o,B: a,C: a] :
( ( produc1833107820_a_a_o @ A @ ( product_Pair_a_a @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_old_Oprod_Ocase) ).
thf(1030,plain,
! [A: a > a > $o,B: a,C: a] :
( ( produc1833107820_a_a_o @ A @ ( product_Pair_a_a @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(17,axiom,
produc694541532_set_a = produc961951794_set_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_internal__case__prod__def) ).
thf(378,plain,
produc694541532_set_a = produc961951794_set_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(296,axiom,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( C != A )
=> ( ( add_ms1725977093od_a_a @ C @ ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) )
= ( minus_1257885652od_a_a @ ( add_ms1725977093od_a_a @ C @ B ) @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_multiset__add__sub__el__shuffle) ).
thf(1294,plain,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( C != A )
=> ( ( add_ms1725977093od_a_a @ C @ ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) )
= ( minus_1257885652od_a_a @ ( add_ms1725977093od_a_a @ C @ B ) @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(141,axiom,
! [A: a > a > $o] :
( ( product_curry_a_a_o @ ( produc1833107820_a_a_o @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_curry__case__prod) ).
thf(763,plain,
! [A: a > a > $o] :
( ( product_curry_a_a_o @ ( produc1833107820_a_a_o @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(72,axiom,
produc1653225349od_a_a = produc1093061851od_a_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_internal__case__prod__def) ).
thf(549,plain,
produc1653225349od_a_a = produc1093061851od_a_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(67,axiom,
! [A: a,B: multiset_a] :
( ~ ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_diff__single__trivial) ).
thf(536,plain,
! [A: a,B: multiset_a] :
( ~ ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( minus_1649712171iset_a @ B @ ( add_mset_a @ A @ zero_zero_multiset_a ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(222,axiom,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ ( add_ms1725977093od_a_a @ C @ zero_z160849828od_a_a ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_multi__member__skip) ).
thf(1045,plain,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ ( plus_p404985124od_a_a @ ( add_ms1725977093od_a_a @ C @ zero_z160849828od_a_a ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(233,axiom,
! [A: a,B: a,C: set_Product_prod_a_a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ C )
=> ( ( D = B )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_ssubst__Pair__rhs) ).
thf(1077,plain,
! [A: a,B: a,C: set_Product_prod_a_a,D: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ C )
=> ( ( D = B )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(48,axiom,
! [A: product_prod_a_a > set_a] :
( ( produc961951794_set_a @ ( produc580150227_set_a @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_case__prod__curry) ).
thf(478,plain,
! [A: product_prod_a_a > set_a] :
( ( produc961951794_set_a @ ( produc580150227_set_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(125,axiom,
prefer1064779160od_a_a = total_1490170027od_a_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_rational__preference__axioms__def) ).
thf(716,plain,
prefer1064779160od_a_a = total_1490170027od_a_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(150,axiom,
! [A: a,B: multiset_a,C: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ ( minus_1649712171iset_a @ B @ C ) ) )
=> ( member_a @ A @ ( set_mset_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_in__diffD) ).
thf(800,plain,
! [A: a,B: multiset_a,C: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ ( minus_1649712171iset_a @ B @ C ) ) )
=> ( member_a @ A @ ( set_mset_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(94,axiom,
! [A: a,B: product_prod_a_a > product_prod_a_a > set_a,C: produc1572603623od_a_a] :
( ( member_a @ A @ ( produc869579762_set_a @ B @ C ) )
=> ~ ! [D: product_prod_a_a,E: product_prod_a_a] :
( ( C
= ( produc1474507607od_a_a @ D @ E ) )
=> ~ ( member_a @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_mem__case__prodE) ).
thf(620,plain,
! [A: a,B: product_prod_a_a > product_prod_a_a > set_a,C: produc1572603623od_a_a] :
( ( member_a @ A @ ( produc869579762_set_a @ B @ C ) )
=> ~ ! [D: product_prod_a_a,E: product_prod_a_a] :
( ( C
= ( produc1474507607od_a_a @ D @ E ) )
=> ~ ( member_a @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(137,axiom,
( total_on_multiset_a
= ( ^ [A: set_multiset_a,B: set_Pr158363655iset_a] :
! [C: multiset_a] :
( ( member_multiset_a @ C @ A )
=> ! [D: multiset_a] :
( ( member_multiset_a @ D @ A )
=> ( ( C != D )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
| ( member340150864iset_a @ ( produc2037245207iset_a @ D @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_total__on__def) ).
thf(752,plain,
( total_on_multiset_a
= ( ^ [A: set_multiset_a,B: set_Pr158363655iset_a] :
! [C: multiset_a] :
( ( member_multiset_a @ C @ A )
=> ! [D: multiset_a] :
( ( member_multiset_a @ D @ A )
=> ( ( C != D )
=> ( ( member340150864iset_a @ ( produc2037245207iset_a @ C @ D ) @ B )
| ( member340150864iset_a @ ( produc2037245207iset_a @ D @ C ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(276,axiom,
total_on_a @ carrier @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_total) ).
thf(1229,plain,
total_on_a @ carrier @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(323,axiom,
! [A: product_prod_a_a > $o,B: a,C: a] :
( ( product_curry_a_a_o @ A @ B @ C )
=> ( A @ ( product_Pair_a_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_curryD) ).
thf(1395,plain,
! [A: product_prod_a_a > $o,B: a,C: a] :
( ( product_curry_a_a_o @ A @ B @ C )
=> ( A @ ( product_Pair_a_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(319,axiom,
! [A: a,B: a,C: a] :
( ( ( product_snd_a_a @ ( product_Pair_a_a @ A @ B ) )
= C )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_snd__eqD) ).
thf(1380,plain,
! [A: a,B: a,C: a] :
( ( ( product_snd_a_a @ ( product_Pair_a_a @ A @ B ) )
= C )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(256,axiom,
trans_a @ relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_transitivity) ).
thf(1148,plain,
trans_a @ relation,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(200,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a] :
( ! [C: a,D: a] : ( A @ ( product_Pair_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_prod__cases) ).
thf(950,plain,
! [A: product_prod_a_a > $o,B: product_prod_a_a] :
( ! [C: a,D: a] : ( A @ ( product_Pair_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(238,axiom,
! [A: set_Product_prod_a_a,B: a,C: a] :
( ( asym_a @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_asymD) ).
thf(1097,plain,
! [A: set_Product_prod_a_a,B: a,C: a] :
( ( asym_a @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(169,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( total_on_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_rational__preference_Ototal) ).
thf(854,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer719835986ence_a @ A @ B )
=> ( total_on_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(300,axiom,
! [A: multis599418605od_a_a,B: product_prod_a_a,C: multis599418605od_a_a,D: set_Pr1948701895od_a_a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ A @ ( add_ms1725977093od_a_a @ B @ C ) ) @ ( mult1_1719650714od_a_a @ D ) )
=> ( ? [E: multis599418605od_a_a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ E @ C ) @ ( mult1_1719650714od_a_a @ D ) )
& ( A
= ( add_ms1725977093od_a_a @ B @ E ) ) )
| ? [E: multis599418605od_a_a] :
( ! [F: product_prod_a_a] :
( ( member449909584od_a_a @ F @ ( set_ms1818337124od_a_a @ E ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ F @ B ) @ D ) )
& ( A
= ( plus_p404985124od_a_a @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_less__add) ).
thf(1303,plain,
! [A: multis599418605od_a_a,B: product_prod_a_a,C: multis599418605od_a_a,D: set_Pr1948701895od_a_a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ A @ ( add_ms1725977093od_a_a @ B @ C ) ) @ ( mult1_1719650714od_a_a @ D ) )
=> ( ? [E: multis599418605od_a_a] :
( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ E @ C ) @ ( mult1_1719650714od_a_a @ D ) )
& ( A
= ( add_ms1725977093od_a_a @ B @ E ) ) )
| ? [E: multis599418605od_a_a] :
( ! [F: product_prod_a_a] :
( ( member449909584od_a_a @ F @ ( set_ms1818337124od_a_a @ E ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ F @ B ) @ D ) )
& ( A
= ( plus_p404985124od_a_a @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(302,axiom,
! [A: product_prod_a_a,B: a,C: a] :
( ( A
= ( product_Pair_a_a @ B @ C ) )
=> ( ( product_fst_a_a @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_fstI) ).
thf(1314,plain,
! [A: product_prod_a_a,B: a,C: a] :
( ( A
= ( product_Pair_a_a @ B @ C ) )
=> ( ( product_fst_a_a @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(57,axiom,
! [A: set_Pr158363655iset_a] :
( ! [B: multiset_a] :
~ ( member340150864iset_a @ ( produc2037245207iset_a @ B @ B ) @ A )
=> ( irrefl_multiset_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_irreflI) ).
thf(506,plain,
! [A: set_Pr158363655iset_a] :
( ! [B: multiset_a] :
~ ( member340150864iset_a @ ( produc2037245207iset_a @ B @ B ) @ A )
=> ( irrefl_multiset_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(11,axiom,
! [A: a,B: multiset_a,C: a,D: multiset_a] :
( ( ( add_mset_a @ A @ B )
= ( add_mset_a @ C @ D ) )
=> ( ( A != C )
=> ( member_a @ C @ ( set_mset_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_insert__noteq__member) ).
thf(358,plain,
! [A: a,B: multiset_a,C: a,D: multiset_a] :
( ( ( add_mset_a @ A @ B )
= ( add_mset_a @ C @ D ) )
=> ( ( A != C )
=> ( member_a @ C @ ( set_mset_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(307,axiom,
! [A: multis599418605od_a_a] :
( ( A != zero_z160849828od_a_a )
=> ~ ! [B: product_prod_a_a] :
~ ( member449909584od_a_a @ B @ ( set_ms1818337124od_a_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_multiset__nonemptyE) ).
thf(1335,plain,
! [A: multis599418605od_a_a] :
( ( A != zero_z160849828od_a_a )
=> ~ ! [B: product_prod_a_a] :
~ ( member449909584od_a_a @ B @ ( set_ms1818337124od_a_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(185,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( refl_o1298442278od_a_a @ A @ B )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
=> ( member449909584od_a_a @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_refl__onD2) ).
thf(897,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( refl_o1298442278od_a_a @ A @ B )
=> ( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B )
=> ( member449909584od_a_a @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(99,axiom,
! [A: multis599418605od_a_a,B: multis599418605od_a_a,C: set_mu1281098573od_a_a,D: set_Pr1821581383od_a_a] :
( ( member1755255446od_a_a @ A @ ( prefer1191731497od_a_a @ B @ C @ D ) )
=> ( member1349055120od_a_a @ ( produc1859144151od_a_a @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_at__least__as__goodD) ).
thf(635,plain,
! [A: multis599418605od_a_a,B: multis599418605od_a_a,C: set_mu1281098573od_a_a,D: set_Pr1821581383od_a_a] :
( ( member1755255446od_a_a @ A @ ( prefer1191731497od_a_a @ B @ C @ D ) )
=> ( member1349055120od_a_a @ ( produc1859144151od_a_a @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(127,axiom,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( produc1641853175od_a_a @ ( produc1474507607od_a_a @ A @ B ) )
= ( produc1474507607od_a_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_swap__simp) ).
thf(720,plain,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( produc1641853175od_a_a @ ( produc1474507607od_a_a @ A @ B ) )
= ( produc1474507607od_a_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(193,axiom,
! [A: multiset_a,B: a > a > set_multiset_a,C: product_prod_a_a] :
( ( member_multiset_a @ A @ ( produc1828150264iset_a @ B @ C ) )
=> ~ ! [D: a,E: a] :
( ( C
= ( product_Pair_a_a @ D @ E ) )
=> ~ ( member_multiset_a @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_mem__case__prodE) ).
thf(928,plain,
! [A: multiset_a,B: a > a > set_multiset_a,C: product_prod_a_a] :
( ( member_multiset_a @ A @ ( produc1828150264iset_a @ B @ C ) )
=> ~ ! [D: a,E: a] :
( ( C
= ( product_Pair_a_a @ D @ E ) )
=> ~ ( member_multiset_a @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(226,axiom,
x != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(1056,plain,
x != y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(109,axiom,
( irrefl76447196od_a_a
= ( ^ [A: set_Pr1948701895od_a_a] :
! [B: product_prod_a_a] :
~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_irrefl__def) ).
thf(664,plain,
( irrefl76447196od_a_a
= ( ^ [A: set_Pr1948701895od_a_a] :
! [B: product_prod_a_a] :
~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(218,axiom,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: multis1735859763od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ ( fold_m773816523od_a_a @ plus_p404985124od_a_a @ B @ C ) ) )
= ( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
| ? [D: multis599418605od_a_a] :
( ( member1755255446od_a_a @ D @ ( set_ms1869569194od_a_a @ C ) )
& ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_in__mset__fold__plus__iff) ).
thf(1033,plain,
! [A: product_prod_a_a,B: multis599418605od_a_a,C: multis1735859763od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ ( fold_m773816523od_a_a @ plus_p404985124od_a_a @ B @ C ) ) )
= ( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
| ? [D: multis599418605od_a_a] :
( ( member1755255446od_a_a @ D @ ( set_ms1869569194od_a_a @ C ) )
& ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(24,axiom,
! [A: a,B: multiset_a,C: multiset_a] :
( ~ ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( minus_1649712171iset_a @ ( add_mset_a @ A @ C ) @ B )
= ( add_mset_a @ A @ ( minus_1649712171iset_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_diff__add__mset__swap) ).
thf(400,plain,
! [A: a,B: multiset_a,C: multiset_a] :
( ~ ( member_a @ A @ ( set_mset_a @ B ) )
=> ( ( minus_1649712171iset_a @ ( add_mset_a @ A @ C ) @ B )
= ( add_mset_a @ A @ ( minus_1649712171iset_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(269,axiom,
! [A: product_prod_a_a,B: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ~ ! [C: multis599418605od_a_a] :
( B
!= ( add_ms1725977093od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_mset__add) ).
thf(1197,plain,
! [A: product_prod_a_a,B: multis599418605od_a_a] :
( ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ~ ! [C: multis599418605od_a_a] :
( B
!= ( add_ms1725977093od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(130,axiom,
! [A: set_multiset_a] :
( ( collect_multiset_a
@ ^ [B: multiset_a] : ( member_multiset_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_Collect__mem__eq) ).
thf(728,plain,
! [A: set_multiset_a] :
( ( collect_multiset_a
@ ^ [B: multiset_a] : ( member_multiset_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(250,axiom,
! [A: a,B: set_a,C: a > product_prod_a_a] :
( ( member_a @ A @ B )
=> ( member449909584od_a_a @ ( C @ A ) @ ( image_1725938350od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_imageI) ).
thf(1129,plain,
! [A: a,B: set_a,C: a > product_prod_a_a] :
( ( member_a @ A @ B )
=> ( member449909584od_a_a @ ( C @ A ) @ ( image_1725938350od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(286,axiom,
! [A: a,B: a,C: set_Product_prod_a_a,D: a > a,E: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ C )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( D @ A ) @ ( E @ B ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ D @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_map__prod__imageI) ).
thf(1261,plain,
! [A: a,B: a,C: set_Product_prod_a_a,D: a > a,E: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ C )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( D @ A ) @ ( E @ B ) ) @ ( image_794773445od_a_a @ ( produc700022774_a_a_a @ D @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(289,axiom,
! [A: set_Product_prod_a_a] :
( ( collec645855634od_a_a
@ ^ [B: product_prod_a_a] : ( member449909584od_a_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_Collect__mem__eq) ).
thf(1268,plain,
! [A: set_Product_prod_a_a] :
( ( collec645855634od_a_a
@ ^ [B: product_prod_a_a] : ( member449909584od_a_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(258,axiom,
! [A: a,B: a > a > set_a,C: product_prod_a_a] :
( ( member_a @ A @ ( produc961951794_set_a @ B @ C ) )
=> ~ ! [D: a,E: a] :
( ( C
= ( product_Pair_a_a @ D @ E ) )
=> ~ ( member_a @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_mem__case__prodE) ).
thf(1152,plain,
! [A: a,B: a > a > set_a,C: product_prod_a_a] :
( ( member_a @ A @ ( produc961951794_set_a @ B @ C ) )
=> ~ ! [D: a,E: a] :
( ( C
= ( product_Pair_a_a @ D @ E ) )
=> ~ ( member_a @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(320,axiom,
! [A: product_prod_a_a,B: a > product_prod_a_a,C: a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( member_a @ C @ D )
=> ( member449909584od_a_a @ A @ ( image_1725938350od_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_image__eqI) ).
thf(1384,plain,
! [A: product_prod_a_a,B: a > product_prod_a_a,C: a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( member_a @ C @ D )
=> ( member449909584od_a_a @ A @ ( image_1725938350od_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(215,axiom,
! [A: product_prod_a_a,B: product_prod_a_a > $o] :
( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_mem__Collect__eq) ).
thf(1019,plain,
! [A: product_prod_a_a,B: product_prod_a_a > $o] :
( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(64,axiom,
prefer580340847ioms_a = total_on_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_rational__preference__axioms__def) ).
thf(528,plain,
prefer580340847ioms_a = total_on_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(41,axiom,
! [A: a,B: multiset_a,C: a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( member_a @ A @ ( set_mset_a @ ( plus_plus_multiset_a @ ( add_mset_a @ C @ zero_zero_multiset_a ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_multi__member__skip) ).
thf(459,plain,
! [A: a,B: multiset_a,C: a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ( member_a @ A @ ( set_mset_a @ ( plus_plus_multiset_a @ ( add_mset_a @ C @ zero_zero_multiset_a ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(128,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( trans_a @ A )
=> ( ( trans_a @ B )
=> ( trans_972827014od_a_a @ ( lex_prod_a_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_trans__lex__prod) ).
thf(723,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( trans_a @ A )
=> ( ( trans_a @ B )
=> ( trans_972827014od_a_a @ ( lex_prod_a_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(208,axiom,
! [A: product_prod_a_a,B: multiset_a > multiset_a > set_Product_prod_a_a,C: produc1127127335iset_a] :
( ( member449909584od_a_a @ A @ ( produc2041367259od_a_a @ B @ C ) )
=> ~ ! [D: multiset_a,E: multiset_a] :
( ( C
= ( produc2037245207iset_a @ D @ E ) )
=> ~ ( member449909584od_a_a @ A @ ( B @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_mem__case__prodE) ).
thf(982,plain,
! [A: product_prod_a_a,B: multiset_a > multiset_a > set_Product_prod_a_a,C: produc1127127335iset_a] :
( ( member449909584od_a_a @ A @ ( produc2041367259od_a_a @ B @ C ) )
=> ~ ! [D: multiset_a,E: multiset_a] :
( ( C
= ( produc2037245207iset_a @ D @ E ) )
=> ~ ( member449909584od_a_a @ A @ ( B @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(117,axiom,
( irrefl_multiset_a
= ( ^ [A: set_Pr158363655iset_a] :
! [B: multiset_a] :
~ ( member340150864iset_a @ ( produc2037245207iset_a @ B @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_irrefl__def) ).
thf(691,plain,
( irrefl_multiset_a
= ( ^ [A: set_Pr158363655iset_a] :
! [B: multiset_a] :
~ ( member340150864iset_a @ ( produc2037245207iset_a @ B @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(36,axiom,
! [A: produc1572603623od_a_a] :
~ ! [B: product_prod_a_a,C: product_prod_a_a] :
( A
!= ( produc1474507607od_a_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_old_Oprod_Oexhaust) ).
thf(442,plain,
! [A: produc1572603623od_a_a] :
~ ! [B: product_prod_a_a,C: product_prod_a_a] :
( A
!= ( produc1474507607od_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(325,axiom,
! [A: set_Pr1948701895od_a_a,B: set_Product_prod_a_a] :
( ! [C: product_prod_a_a,D: product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ C @ B ) )
=> ( ! [C: product_prod_a_a,D: product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ D @ B ) )
=> ( ( order_359341630od_a_a @ B @ A )
=> ( prefer1338892073od_a_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_preference_Ointro) ).
thf(1399,plain,
! [A: set_Pr1948701895od_a_a,B: set_Product_prod_a_a] :
( ! [C: product_prod_a_a,D: product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ C @ B ) )
=> ( ! [C: product_prod_a_a,D: product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ D @ B ) )
=> ( ( order_359341630od_a_a @ B @ A )
=> ( prefer1338892073od_a_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(22,axiom,
! [A: produc1127127335iset_a > $o,B: multiset_a,C: multiset_a] :
( ( produc1530159757et_a_o @ A @ B @ C )
=> ( A @ ( produc2037245207iset_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_curryD) ).
thf(395,plain,
! [A: produc1127127335iset_a > $o,B: multiset_a,C: multiset_a] :
( ( produc1530159757et_a_o @ A @ B @ C )
=> ( A @ ( produc2037245207iset_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(95,axiom,
! [A: set_Pr1821581383od_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( trans_1520871884od_a_a @ A )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ B @ C ) @ A )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ A )
=> ( member1349055120od_a_a @ ( produc1859144151od_a_a @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_transE) ).
thf(624,plain,
! [A: set_Pr1821581383od_a_a,B: multis599418605od_a_a,C: multis599418605od_a_a,D: multis599418605od_a_a] :
( ( trans_1520871884od_a_a @ A )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ B @ C ) @ A )
=> ( ( member1349055120od_a_a @ ( produc1859144151od_a_a @ C @ D ) @ A )
=> ( member1349055120od_a_a @ ( produc1859144151od_a_a @ B @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(151,axiom,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ? [C: multiset_a] :
( B
= ( add_mset_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_multi__member__split) ).
thf(803,plain,
! [A: a,B: multiset_a] :
( ( member_a @ A @ ( set_mset_a @ B ) )
=> ? [C: multiset_a] :
( B
= ( add_mset_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(316,axiom,
! [A: set_Product_prod_a_a,B: a,C: a,D: a] :
( ( trans_a @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_transE) ).
thf(1367,plain,
! [A: set_Product_prod_a_a,B: a,C: a,D: a] :
( ( trans_a @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ B @ C ) @ A )
=> ( ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(195,axiom,
! [A: product_prod_a_a,B: multis599418605od_a_a] :
( ~ ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_diff__single__trivial) ).
thf(935,plain,
! [A: product_prod_a_a,B: multis599418605od_a_a] :
( ~ ( member449909584od_a_a @ A @ ( set_ms1818337124od_a_a @ B ) )
=> ( ( minus_1257885652od_a_a @ B @ ( add_ms1725977093od_a_a @ A @ zero_z160849828od_a_a ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(76,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( refl_on_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_preference_Oreflexivity) ).
thf(560,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( prefer1292084992ence_a @ A @ B )
=> ( refl_on_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(13,axiom,
! [A: multiset_a,B: multiset_a,C: set_Pr1948701895od_a_a,D: multiset_a > product_prod_a_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ A @ B ) @ ( inv_im184450735iset_a @ C @ D ) )
= ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_in__inv__image) ).
thf(364,plain,
! [A: multiset_a,B: multiset_a,C: set_Pr1948701895od_a_a,D: multiset_a > product_prod_a_a] :
( ( member340150864iset_a @ ( produc2037245207iset_a @ A @ B ) @ ( inv_im184450735iset_a @ C @ D ) )
= ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(123,axiom,
! [A: set_Pr1948701895od_a_a] :
( ! [B: product_prod_a_a] :
~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ B ) @ A )
=> ( irrefl76447196od_a_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_irreflI) ).
thf(708,plain,
! [A: set_Pr1948701895od_a_a] :
( ! [B: product_prod_a_a] :
~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ B ) @ A )
=> ( irrefl76447196od_a_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(179,axiom,
! [A: a > a > $o,B: a,C: a] :
( ( A @ B @ C )
=> ( A @ ( product_snd_a_a @ ( product_Pair_a_a @ C @ B ) ) @ ( product_fst_a_a @ ( product_Pair_a_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_exI__realizer) ).
thf(882,plain,
! [A: a > a > $o,B: a,C: a] :
( ( A @ B @ C )
=> ( A @ ( product_snd_a_a @ ( product_Pair_a_a @ C @ B ) ) @ ( product_fst_a_a @ ( product_Pair_a_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(54,axiom,
! [A: multiset_a] :
( ( A != zero_zero_multiset_a )
=> ~ ! [B: a] :
~ ( member_a @ B @ ( set_mset_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_multiset__nonemptyE) ).
thf(496,plain,
! [A: multiset_a] :
( ( A != zero_zero_multiset_a )
=> ~ ! [B: a] :
~ ( member_a @ B @ ( set_mset_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(39,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer1338892073od_a_a @ A @ B )
=> ( refl_o1298442278od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_preference_Oreflexivity) ).
thf(454,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a] :
( ( prefer1338892073od_a_a @ A @ B )
=> ( refl_o1298442278od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(230,axiom,
! [A: a,B: a,C: set_Product_prod_a_a,D: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( inv_image_a_a @ C @ D ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_in__inv__image) ).
thf(1069,plain,
! [A: a,B: a,C: set_Product_prod_a_a,D: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( inv_image_a_a @ C @ D ) )
= ( member449909584od_a_a @ ( product_Pair_a_a @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(1494,plain,
$false,
inference(e,[status(thm)],[892,1322,1036,809,760,1105,1237,333,941,666,1110,481,352,1290,741,873,677,440,655,533,500,797,1233,1063,670,747,913,841,1359,565,436,829,404,1298,372,504,1264,702,1279,1191,542,1059,1132,1347,416,1115,1362,1100,817,902,1319,870,591,376,646,514,574,806,966,1283,905,475,924,485,834,766,397,734,866,1072,1405,1201,452,920,380,512,1311,1274,894,1343,1042,1255,820,1370,815,1217,598,693,630,847,1365,879,522,1159,493,757,551,1392,456,1012,1106,916,467,682,1195,1407,1350,1259,650,1017,1328,1375,1138,869,610,1397,697,1089,783,420,884,1082,488,554,1075,637,1039,547,328,471,837,738,1050,569,1246,605,1324,393,343,1170,530,953,773,1086,938,662,718,1103,856,1301,1135,412,584,562,423,1389,843,711,579,958,1124,641,572,1271,787,1092,947,1224,1356,350,1209,900,831,1117,1048,996,362,1122,509,434,863,1175,890,1339,594,726,700,1149,1022,1112,345,367,462,932,1066,780,608,986,1000,1250,851,431,658,685,1171,1213,827,473,490,1166,944,795,648,812,617,1145,355,754,1181,823,776,557,887,1252,1267,705,1156,409,1230,1053,673,1300,331,576,643,544,744,336,1141,1221,1008,446,876,859,1240,978,386,845,465,627,539,1126,1189,976,688,524,581,1276,588,961,390,632,963,517,731,418,1030,378,1294,763,549,536,1045,1077,478,716,800,620,752,1229,1395,1380,1148,950,1097,854,1303,1314,506,358,1335,897,635,720,928,1056,664,1033,400,1197,728,1129,1261,1268,1152,1384,1019,528,459,723,982,691,442,1399,395,624,803,1367,935,560,364,708,882,496,454,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP152^1 : TPTP v8.1.2. Released v7.5.0.
% 0.06/0.14 % Command : run_Leo-III %s %d
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 6 14:36:24 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.94/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.58/1.15 % [INFO] Parsing done (260ms).
% 1.58/1.16 % [INFO] Running in sequential loop mode.
% 2.58/1.39 % [INFO] eprover registered as external prover.
% 2.58/1.39 % [INFO] cvc4 registered as external prover.
% 2.58/1.40 % [INFO] Scanning for conjecture ...
% 2.87/1.52 % [INFO] Found a conjecture and 358 axioms. Running axiom selection ...
% 3.26/1.64 % [INFO] Axiom selection finished. Selected 325 axioms (removed 33 axioms).
% 4.11/1.85 % [INFO] Problem is higher-order (TPTP THF).
% 4.11/1.88 % [INFO] Type checking passed.
% 4.11/1.88 % [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 ...
% 31.56/9.51 % External prover 'e' found a proof!
% 31.56/9.52 % [INFO] Killing All external provers ...
% 31.56/9.52 % Time passed: 9004ms (effective reasoning time: 8359ms)
% 31.56/9.52 % 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)>
% 31.56/9.52 % Axioms used in derivation (325): fact_300_same__fstI, fact_90_prod__induct3, fact_6_preference__axioms, fact_21_surj__pair, fact_195_curryI, fact_350_multiset__add__sub__el__shuffle, fact_254_asym_Ocases, fact_305_less__add, fact_139_refl__onD1, fact_48_preference_Ointro, fact_177_ssubst__Pair__rhs, fact_17_old_Oprod_Oinject, fact_193_curryI, fact_332_diff__add__mset__swap, fact_37_preference_Oreflexivity, fact_250_multp__iff, fact_303_mult1I, fact_312_insert__noteq__member, fact_152_transI, fact_119_Collect__mem__eq, fact_276_trans__lex__prod, fact_273_total__lex__prod, fact_218_case__prod__curry, fact_59_preference_Oindiff__trans, fact_7_trans__refl, fact_217_case__prod__curry, fact_125_Collect__cong, fact_271_top__empty__eq, fact_81_rational__preference_Ocompl, fact_163_transE, fact_4_not__outside, fact_88_old_Oprod_Oexhaust, fact_168_rational__preference_Oaxioms_I2_J, fact_210_swap__simp, fact_206_in__inv__image, fact_338_in__diffD, fact_22_surj__pair, fact_302_mult1E, fact_323_multi__member__skip, fact_331_diff__add__mset__swap, fact_15_old_Oprod_Oinject, fact_29_Pair__inject, fact_247_curryE, fact_251_asym_Oinducts, fact_12_prod_Oinject, fact_288_exI__realizer, fact_224_mem__case__prodE, fact_299_image__subsetI, fact_123_Collect__mem__eq, fact_306_less__add, fact_91_preorder__on__def, fact_257_image__eqI, fact_241_irrefl__def, fact_111_mem__Collect__eq, fact_83_old_Oprod_Oinducts, fact_188_at__least__as__goodD, fact_112_mem__Collect__eq, fact_41_rational__preference_Ototal, fact_340_diff__single__trivial, fact_311_insert__noteq__member, fact_295_subrelI, fact_213_internal__case__prod__def, fact_304_mult1I, fact_92_preorder__on__def, fact_258_image__eqI, fact_110_refl__on__domain, fact_297_image__subsetI, fact_70_rational__preference_Ostrict__not__refl__weak, fact_78_rational__preference_Ocompl, fact_57_preference_Oindiff__trans, fact_86_old_Oprod_Oexhaust, fact_183_at__lst__asgd__ge, fact_56_preference_Oindiff__trans, fact_268_rev__image__eqI, fact_353_diff__union__single__conv, fact_329_insert__DiffM2, fact_14_old_Oprod_Oinject, fact_223_mem__case__prodE, fact_192_curry__conv, fact_115_mem__Collect__eq, fact_253_asym_Osimps, fact_283_fst__eqD, fact_232_mem__case__prodE, fact_286_prod_Oswap__def, fact_8_total, fact_155_transI, fact_114_mem__Collect__eq, fact_138_refl__onD1, fact_285_snd__eqD, fact_320_multiset__nonemptyE, fact_73_rational__preference_Ostrict__not__refl__weak, fact_225_mem__case__prodE, fact_35_preference_Otrans__refl, fact_287_prod__fun__imageE, fact_352_more__than__one__mset__mset__diff, fact_167_rational__preference__def, fact_343_multi__drop__mem__not__eq, fact_282_fst__conv, fact_234_old_Oprod_Ocase, fact_243_irrefl__def, fact_118_Collect__mem__eq, fact_108_refl__on__domain, fact_13_prod_Oinject, fact_0_indiff__trans, fact_202_in__inv__image, fact_197_in__inv__image, fact_238_irreflI, fact_19_surj__pair, fact_264_imageI, fact_79_rational__preference_Ocompl, fact_144_refl__onD, fact_165_rational__preference_Ointro, fact_194_curryI, fact_153_transI, fact_66_preference_Onot__outside, fact_348_add__mset__remove__trivial__eq, fact_298_image__subsetI, fact_308_mset__add, fact_45_preference_Ointro, fact_175_ssubst__Pair__rhs, fact_256_asymD, fact_291_sndI, fact_93_total__on__def, fact_293_eq__snd__iff, fact_2_rational__preference__axioms, fact_89_old_Oprod_Oexhaust, fact_166_rational__preference__def, fact_265_imageI, fact_149_trans__def, fact_31_prod__cases3, fact_277_prod_Ocollapse, fact_52_preference__def, fact_270_rev__image__eqI, fact_294_eq__fst__iff, fact_279_Product__Type_OCollect__case__prodD, fact_333_insert__DiffM, fact_274_map__prod__simp, fact_345_add__mset__remove__trivial__If, fact_219_case__prod__curry, fact_220_curry__case__prod, conj_2, fact_18_transitivity, fact_148_trans__def, fact_33_rational__preference_Oaxioms_I1_J, fact_351_more__than__one__mset__mset__diff, fact_281_surjective__pairing, fact_208_strict__linear__order__on__def, fact_126_Collect__cong, fact_132_refl__onD2, fact_75_rational__preference_Ostrict__trans, fact_328_in__mset__fold__plus__iff, fact_242_irrefl__def, fact_172_rational__preference__axioms__def, fact_227_mem__case__prodE, fact_190_at__least__as__goodD, fact_120_Collect__mem__eq, fact_337_in__diffD, fact_321_multi__member__last, fact_249_pair__in__swap__image, fact_226_mem__case__prodE, fact_20_surj__pair, fact_344_multi__drop__mem__not__eq, fact_301_mult1E, fact_346_add__mset__remove__trivial__If, fact_131_refl__onD2, fact_174_ssubst__Pair__rhs, fact_261_mult__cancel, fact_84_old_Oprod_Oinducts, fact_204_in__inv__image, fact_339_diff__single__trivial, fact_58_preference_Oindiff__trans, fact_266_imageI, fact_215_internal__case__prod__def, fact_95_total__on__def, fact_212_swap__simp, fact_196_curryI, fact_146_refl__onD, fact_11_prod_Oinject, fact_207_strict__linear__order__on__def, fact_147_refl__onD, fact_38_preference_Otransitivity, fact_171_rational__preference__axioms_Ointro, fact_327_in__mset__fold__plus__iff, fact_347_add__mset__remove__trivial__eq, fact_55_preference__def, fact_309_multi__member__split, fact_317_mult__implies__one__step, fact_205_in__inv__image, fact_96_total__on__def, fact_330_insert__DiffM2, fact_280_prod_Oexhaust__sel, fact_239_irreflI, fact_248_trans__inv__image, fact_39_preference_Otransitivity, fact_170_rational__preference__axioms_Ointro, fact_32_rational__preference_Oaxioms_I1_J, fact_246_curryD, fact_116_mem__Collect__eq, fact_211_swap__simp, fact_151_trans__def, fact_1_strict__trans, fact_87_old_Oprod_Oexhaust, fact_140_refl__onD1, fact_318_one__step__implies__mult, fact_262_mult__cancel__add__mset, fact_159_transD, fact_222_curry__case__prod, fact_23_prod__cases, fact_145_refl__onD, fact_36_preference_Oreflexivity, fact_184_at__lst__asgd__ge, fact_169_rational__preference_Oaxioms_I2_J, fact_272_top__empty__eq, fact_85_old_Oprod_Oinducts, fact_130_refl__onD2, fact_5_strict__not__refl__weak, fact_237_irreflI, fact_290_BNF__Greatest__Fixpoint_Osubst__Pair, fact_71_rational__preference_Ostrict__not__refl__weak, fact_113_mem__Collect__eq, fact_231_mem__case__prodE, fact_137_refl__onD1, fact_162_transE, fact_121_Collect__mem__eq, fact_296_image__subsetI, fact_133_refl__onD2, fact_354_diff__union__single__conv, fact_74_rational__preference_Ostrict__trans, fact_53_preference__def, fact_230_mem__case__prodE, fact_216_swap__swap, fact_260_image__eqI, fact_267_rev__image__eqI, fact_349_multiset__add__sub__el__shuffle, fact_336_diff__union__swap2, fact_16_old_Oprod_Oinject, fact_72_rational__preference_Ostrict__not__refl__weak, fact_191_at__least__as__goodD, fact_64_preference_Onot__outside, fact_3_compl, fact_307_mset__add, conj_1, fact_117_mem__Collect__eq, fact_24_prod__cases, fact_109_refl__on__domain, fact_94_total__on__def, fact_199_in__inv__image, fact_235_old_Oprod_Ocase, fact_245_curryD, fact_313_union__single__eq__member, fact_252_asym_Ointros, fact_156_transD, fact_161_transE, fact_34_preference_Otrans__refl, fact_275_in__lex__prod, fact_342_diff__single__eq__union, fact_160_transE, fact_40_rational__preference_Ototal, fact_124_Collect__mem__eq, fact_26_prod__cases, fact_25_prod__cases, fact_228_mem__case__prodE, fact_319_multiset__nonemptyE, fact_181_at__lst__asgd__ge, fact_164_rational__preference_Ointro, fact_103_total__onI, fact_107_refl__on__domain, fact_310_multi__member__split, fact_63_preference_Onot__outside, fact_236_irreflI, fact_263_imageI, fact_324_multi__member__skip, fact_9_reflexivity, fact_229_mem__case__prodE, fact_173_rational__preference__axioms__def, fact_28_Pair__inject, fact_269_rev__image__eqI, fact_214_internal__case__prod__def, fact_122_Collect__mem__eq, fact_289_conjI__realizer, fact_30_Pair__inject, fact_292_fstI, fact_80_rational__preference_Ocompl, fact_47_preference_Ointro, fact_101_total__onI, fact_27_Pair__inject, fact_157_transD, fact_240_irrefl__def, fact_150_trans__def, fact_278_map__prod__imageI, fact_158_transD, fact_10_prod_Oinject, fact_255_asym__iff, fact_76_rational__preference_Ostrict__trans, fact_203_in__inv__image, fact_46_preference_Ointro, fact_100_total__onI, fact_326_multi__member__this, fact_54_preference__def, fact_284_snd__conv, fact_182_at__lst__asgd__ge, conj_0, fact_176_ssubst__Pair__rhs, fact_198_in__inv__image, fact_325_multi__member__this, fact_200_in__inv__image, fact_77_rational__preference_Ostrict__trans, fact_82_old_Oprod_Oinducts, fact_233_old_Oprod_Ocase, fact_322_multi__member__last, fact_189_at__least__as__goodD, fact_341_diff__single__eq__union, fact_65_preference_Onot__outside, fact_314_union__single__eq__member, fact_334_insert__DiffM, fact_315_union__iff, fact_244_curryD, fact_335_diff__union__swap2, fact_102_total__onI, fact_259_image__eqI, fact_154_transI, fact_209_swap__simp, fact_316_union__iff, fact_201_in__inv__image, fact_221_curry__case__prod
% 31.56/9.52 % No. of inferences in proof: 654
% 31.56/9.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9004 ms resp. 8359 ms w/o parsing
% 32.32/9.72 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 32.32/9.73 % [INFO] Killing All external provers ...
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