TSTP Solution File: ITP157^1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP157^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.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 07:48:19 EDT 2024
% Result : Theorem 17.61s 5.24s
% Output : Refutation 18.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 482
% Syntax : Number of formulae : 812 ( 302 unt; 154 typ; 0 def)
% Number of atoms : 1800 ( 580 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 5976 ( 216 ~; 6 |; 198 &;4888 @)
% ( 0 <=>; 668 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 31 ( 30 usr)
% Number of type conns : 679 ( 679 >; 0 *; 0 +; 0 <<)
% Number of symbols : 126 ( 124 usr; 9 con; 0-3 aty)
% Number of variables : 2398 ( 310 ^2044 !; 44 ?;2398 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr2081559751od_a_a_type,type,
set_Pr2081559751od_a_a: $tType ).
thf(set_Pr532616391od_a_a_type,type,
set_Pr532616391od_a_a: $tType ).
thf(produc1423126247od_a_a_type,type,
produc1423126247od_a_a: $tType ).
thf(produc1056976615od_a_a_type,type,
produc1056976615od_a_a: $tType ).
thf(set_Pr660101255od_a_a_type,type,
set_Pr660101255od_a_a: $tType ).
thf(produc1546279079od_a_a_type,type,
produc1546279079od_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_Pr1194146439od_a_a_type,type,
set_Pr1194146439od_a_a: $tType ).
thf(set_Pr231806599od_a_a_type,type,
set_Pr231806599od_a_a: $tType ).
thf(set_Pr729215751_a_a_a_type,type,
set_Pr729215751_a_a_a: $tType ).
thf(set_Pr173461255od_a_a_type,type,
set_Pr173461255od_a_a: $tType ).
thf(produc772425383od_a_a_type,type,
produc772425383od_a_a: $tType ).
thf(produc2010915495od_a_a_type,type,
produc2010915495od_a_a: $tType ).
thf(produc1120419623_a_a_a_type,type,
produc1120419623_a_a_a: $tType ).
thf(produc47586087od_a_a_type,type,
produc47586087od_a_a: $tType ).
thf(set_Pr195866352od_a_a_type,type,
set_Pr195866352od_a_a: $tType ).
thf(set_Pr6137822_a_a_a_type,type,
set_Pr6137822_a_a_a: $tType ).
thf(produc1555800720od_a_a_type,type,
produc1555800720od_a_a: $tType ).
thf(produc1683075710_a_a_a_type,type,
produc1683075710_a_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_Pr681306928od_a_a_type,type,
set_Pr681306928od_a_a: $tType ).
thf(set_Pr1689873822_a_a_a_type,type,
set_Pr1689873822_a_a_a: $tType ).
thf(produc1921647824od_a_a_type,type,
produc1921647824od_a_a: $tType ).
thf(produc1016684094_a_a_a_type,type,
produc1016684094_a_a_a: $tType ).
thf(set_Product_prod_a_a_type,type,
set_Product_prod_a_a: $tType ).
thf(product_prod_a_a_type,type,
product_prod_a_a: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(a_type,type,
a: $tType ).
thf(bNF_Gr1372473186od_a_a_type,type,
bNF_Gr1372473186od_a_a: set_Product_prod_a_a > ( product_prod_a_a > product_prod_a_a ) > set_Pr1948701895od_a_a ).
thf(bNF_Gr_a_a_type,type,
bNF_Gr_a_a: set_a > ( a > a ) > set_Product_prod_a_a ).
thf(bNF_Gr533818957od_a_a_type,type,
bNF_Gr533818957od_a_a: set_Pr1948701895od_a_a > ( produc1572603623od_a_a > product_prod_a_a ) > ( produc1572603623od_a_a > product_prod_a_a ) > set_Pr1948701895od_a_a ).
thf(bNF_Gr356189709_a_a_a_type,type,
bNF_Gr356189709_a_a_a: set_Pr1948701895od_a_a > ( produc1572603623od_a_a > a ) > ( produc1572603623od_a_a > a ) > set_Product_prod_a_a ).
thf(bNF_Gr200450189od_a_a_type,type,
bNF_Gr200450189od_a_a: set_Product_prod_a_a > ( product_prod_a_a > product_prod_a_a ) > ( product_prod_a_a > product_prod_a_a ) > set_Pr1948701895od_a_a ).
thf(bNF_Gr1853143117_a_a_a_type,type,
bNF_Gr1853143117_a_a_a: set_Product_prod_a_a > ( product_prod_a_a > a ) > ( product_prod_a_a > a ) > set_Product_prod_a_a ).
thf(bNF_Gr1715025636od_a_a_type,type,
bNF_Gr1715025636od_a_a: set_a > ( a > product_prod_a_a ) > ( a > product_prod_a_a ) > set_Pr1948701895od_a_a ).
thf(bNF_Gr423046308_a_a_a_type,type,
bNF_Gr423046308_a_a_a: set_a > ( a > a ) > ( a > a ) > set_Product_prod_a_a ).
thf(minus_107310383_a_a_o_type,type,
minus_107310383_a_a_o: ( produc1572603623od_a_a > $o ) > ( produc1572603623od_a_a > $o ) > produc1572603623od_a_a > $o ).
thf(minus_1797478127_a_a_o_type,type,
minus_1797478127_a_a_o: ( product_prod_a_a > $o ) > ( product_prod_a_a > $o ) > product_prod_a_a > $o ).
thf(minus_minus_a_o_type,type,
minus_minus_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
thf(minus_1034916142od_a_a_type,type,
minus_1034916142od_a_a: set_Pr1948701895od_a_a > set_Pr1948701895od_a_a > set_Pr1948701895od_a_a ).
thf(minus_1507102574od_a_a_type,type,
minus_1507102574od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > set_Product_prod_a_a ).
thf(minus_minus_set_a_type,type,
minus_minus_set_a: set_a > set_a > set_a ).
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(bot_bo2131659635od_a_a_type,type,
bot_bo2131659635od_a_a: set_Product_prod_a_a ).
thf(ord_le1525442358_a_a_o_type,type,
ord_le1525442358_a_a_o: ( produc1572603623od_a_a > $o ) > ( produc1572603623od_a_a > $o ) > $o ).
thf(ord_le252190158_a_a_o_type,type,
ord_le252190158_a_a_o: ( product_prod_a_a > product_prod_a_a > $o ) > ( product_prod_a_a > product_prod_a_a > $o ) > $o ).
thf(ord_le1347718902_a_a_o_type,type,
ord_le1347718902_a_a_o: ( product_prod_a_a > $o ) > ( product_prod_a_a > $o ) > $o ).
thf(ord_less_eq_a_a_o_type,type,
ord_less_eq_a_a_o: ( a > a > $o ) > ( a > a > $o ) > $o ).
thf(ord_less_eq_a_o_type,type,
ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(ord_le456379495od_a_a_type,type,
ord_le456379495od_a_a: set_Pr1948701895od_a_a > set_Pr1948701895od_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_to2011536774_a_a_o_type,type,
top_to2011536774_a_a_o: produc1572603623od_a_a > $o ).
thf(top_to993969022_a_a_o_type,type,
top_to993969022_a_a_o: product_prod_a_a > product_prod_a_a > $o ).
thf(top_to1483957574_a_a_o_type,type,
top_to1483957574_a_a_o: product_prod_a_a > $o ).
thf(top_top_a_a_o_type,type,
top_top_a_a_o: a > a > $o ).
thf(top_top_a_o_type,type,
top_top_a_o: a > $o ).
thf(top_to52711959od_a_a_type,type,
top_to52711959od_a_a: set_Pr1948701895od_a_a ).
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(prefer74720675od_a_a_type,type,
prefer74720675od_a_a: product_prod_a_a > set_Product_prod_a_a > set_Pr1948701895od_a_a > set_Product_prod_a_a ).
thf(prefer436369274d_as_a_type,type,
prefer436369274d_as_a: a > set_a > set_Product_prod_a_a > set_a ).
thf(prefer468349667od_a_a_type,type,
prefer468349667od_a_a: produc2010915495od_a_a > set_Pr231806599od_a_a > set_Pr532616391od_a_a > set_Pr231806599od_a_a ).
thf(prefer1377343203od_a_a_type,type,
prefer1377343203od_a_a: produc772425383od_a_a > set_Pr1194146439od_a_a > set_Pr2081559751od_a_a > set_Pr1194146439od_a_a ).
thf(prefer1944486522_a_a_a_type,type,
prefer1944486522_a_a_a: produc1016684094_a_a_a > set_Pr1689873822_a_a_a > set_Pr729215751_a_a_a > set_Pr1689873822_a_a_a ).
thf(prefer701966604od_a_a_type,type,
prefer701966604od_a_a: produc1921647824od_a_a > set_Pr681306928od_a_a > set_Pr231806599od_a_a > set_Pr681306928od_a_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(prefer1498087410od_a_a_type,type,
prefer1498087410od_a_a: product_prod_a_a > set_Product_prod_a_a > set_Pr1948701895od_a_a > set_Product_prod_a_a ).
thf(prefer1676310729than_a_type,type,
prefer1676310729than_a: a > set_a > set_Product_prod_a_a > set_a ).
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(produc539587415od_a_a_type,type,
produc539587415od_a_a: produc2010915495od_a_a > produc2010915495od_a_a > produc1056976615od_a_a ).
thf(produc852390743od_a_a_type,type,
produc852390743od_a_a: produc772425383od_a_a > produc772425383od_a_a > produc1423126247od_a_a ).
thf(produc524982679od_a_a_type,type,
produc524982679od_a_a: produc1572603623od_a_a > product_prod_a_a > produc47586087od_a_a ).
thf(produc436797294_a_a_a_type,type,
produc436797294_a_a_a: produc1572603623od_a_a > a > produc1683075710_a_a_a ).
thf(produc2054708503_a_a_a_type,type,
produc2054708503_a_a_a: produc1016684094_a_a_a > produc1016684094_a_a_a > produc1120419623_a_a_a ).
thf(produc563767703od_a_a_type,type,
produc563767703od_a_a: produc1921647824od_a_a > produc1921647824od_a_a > produc2010915495od_a_a ).
thf(produc1555606807od_a_a_type,type,
produc1555606807od_a_a: product_prod_a_a > produc1572603623od_a_a > produc772425383od_a_a ).
thf(produc1474507607od_a_a_type,type,
produc1474507607od_a_a: product_prod_a_a > product_prod_a_a > produc1572603623od_a_a ).
thf(produc2061588782_a_a_a_type,type,
produc2061588782_a_a_a: product_prod_a_a > a > produc1016684094_a_a_a ).
thf(produc1095491584od_a_a_type,type,
produc1095491584od_a_a: a > produc1572603623od_a_a > produc1555800720od_a_a ).
thf(produc1299253312od_a_a_type,type,
produc1299253312od_a_a: a > product_prod_a_a > produc1921647824od_a_a ).
thf(product_Pair_a_a_type,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(produc197318472od_a_a_type,type,
produc197318472od_a_a: set_Pr1948701895od_a_a > ( produc1572603623od_a_a > set_Product_prod_a_a ) > set_Pr173461255od_a_a ).
thf(produc4724255_a_a_a_type,type,
produc4724255_a_a_a: set_Pr1948701895od_a_a > ( produc1572603623od_a_a > set_a ) > set_Pr6137822_a_a_a ).
thf(produc1227942600od_a_a_type,type,
produc1227942600od_a_a: set_Product_prod_a_a > ( product_prod_a_a > set_Pr1948701895od_a_a ) > set_Pr1194146439od_a_a ).
thf(produc304751368od_a_a_type,type,
produc304751368od_a_a: set_Product_prod_a_a > ( product_prod_a_a > set_Product_prod_a_a ) > set_Pr1948701895od_a_a ).
thf(produc1282482655_a_a_a_type,type,
produc1282482655_a_a_a: set_Product_prod_a_a > ( product_prod_a_a > set_a ) > set_Pr1689873822_a_a_a ).
thf(produc663418545od_a_a_type,type,
produc663418545od_a_a: set_a > ( a > set_Pr1948701895od_a_a ) > set_Pr195866352od_a_a ).
thf(produc520147185od_a_a_type,type,
produc520147185od_a_a: set_a > ( a > set_Product_prod_a_a ) > set_Pr681306928od_a_a ).
thf(product_Sigma_a_a_type,type,
product_Sigma_a_a: set_a > ( a > set_a ) > set_Product_prod_a_a ).
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(produc1779756150od_a_a_type,type,
produc1779756150od_a_a: ( product_prod_a_a > product_prod_a_a ) > ( product_prod_a_a > product_prod_a_a ) > produc1572603623od_a_a > produc1572603623od_a_a ).
thf(produc363290532_a_a_a_type,type,
produc363290532_a_a_a: ( product_prod_a_a > a ) > ( product_prod_a_a > a ) > produc1572603623od_a_a > product_prod_a_a ).
thf(produc2012818120od_a_a_type,type,
produc2012818120od_a_a: ( a > product_prod_a_a ) > ( a > product_prod_a_a ) > product_prod_a_a > produc1572603623od_a_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(produc745123715od_a_a_type,type,
produc745123715od_a_a: produc47586087od_a_a > produc1572603623od_a_a ).
thf(produc2019352922_a_a_a_type,type,
produc2019352922_a_a_a: produc1683075710_a_a_a > produc1572603623od_a_a ).
thf(produc1775747843od_a_a_type,type,
produc1775747843od_a_a: produc772425383od_a_a > product_prod_a_a ).
thf(produc2115494211od_a_a_type,type,
produc2115494211od_a_a: produc1572603623od_a_a > product_prod_a_a ).
thf(produc1805832986_a_a_a_type,type,
produc1805832986_a_a_a: produc1016684094_a_a_a > product_prod_a_a ).
thf(produc530563564od_a_a_type,type,
produc530563564od_a_a: produc1555800720od_a_a > a ).
thf(produc1043497516od_a_a_type,type,
produc1043497516od_a_a: produc1921647824od_a_a > a ).
thf(product_fst_a_a_type,type,
product_fst_a_a: product_prod_a_a > a ).
thf(produc24848069od_a_a_type,type,
produc24848069od_a_a: produc47586087od_a_a > product_prod_a_a ).
thf(produc262335132_a_a_a_type,type,
produc262335132_a_a_a: produc1683075710_a_a_a > a ).
thf(produc1055472197od_a_a_type,type,
produc1055472197od_a_a: produc772425383od_a_a > produc1572603623od_a_a ).
thf(produc368344197od_a_a_type,type,
produc368344197od_a_a: produc1572603623od_a_a > product_prod_a_a ).
thf(produc1954021468_a_a_a_type,type,
produc1954021468_a_a_a: produc1016684094_a_a_a > a ).
thf(produc921029422od_a_a_type,type,
produc921029422od_a_a: produc1555800720od_a_a > produc1572603623od_a_a ).
thf(produc1191685998od_a_a_type,type,
produc1191685998od_a_a: produc1921647824od_a_a > product_prod_a_a ).
thf(product_snd_a_a_type,type,
product_snd_a_a: product_prod_a_a > 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(produc905674258od_a_a_type,type,
produc905674258od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > set_Pr1948701895od_a_a ).
thf(product_product_a_a_type,type,
product_product_a_a: set_a > set_a > set_Product_prod_a_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_236793797od_a_a_type,type,
image_236793797od_a_a: ( produc1572603623od_a_a > produc1572603623od_a_a ) > set_Pr1948701895od_a_a > set_Pr1948701895od_a_a ).
thf(image_734753285od_a_a_type,type,
image_734753285od_a_a: ( produc1572603623od_a_a > product_prod_a_a ) > set_Pr1948701895od_a_a > set_Product_prod_a_a ).
thf(image_1105229276_a_a_a_type,type,
image_1105229276_a_a_a: ( produc1572603623od_a_a > a ) > set_Pr1948701895od_a_a > set_a ).
thf(image_1765377413od_a_a_type,type,
image_1765377413od_a_a: ( product_prod_a_a > produc1572603623od_a_a ) > set_Product_prod_a_a > set_Pr1948701895od_a_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_1763923566od_a_a_type,type,
image_1763923566od_a_a: ( a > produc1572603623od_a_a ) > set_a > set_Pr1948701895od_a_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_pr2084296006_a_a_a_type,type,
lex_pr2084296006_a_a_a: set_Pr1948701895od_a_a > set_Product_prod_a_a > set_Pr729215751_a_a_a ).
thf(lex_pr1321960536od_a_a_type,type,
lex_pr1321960536od_a_a: set_Product_prod_a_a > set_Pr1948701895od_a_a > set_Pr231806599od_a_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(member180906768od_a_a_type,type,
member180906768od_a_a: produc1056976615od_a_a > set_Pr532616391od_a_a > $o ).
thf(member547056400od_a_a_type,type,
member547056400od_a_a: produc1423126247od_a_a > set_Pr2081559751od_a_a > $o ).
thf(member1545452880od_a_a_type,type,
member1545452880od_a_a: produc47586087od_a_a > set_Pr173461255od_a_a > $o ).
thf(member575366567_a_a_a_type,type,
member575366567_a_a_a: produc1683075710_a_a_a > set_Pr6137822_a_a_a > $o ).
thf(member470802768_a_a_a_type,type,
member470802768_a_a_a: produc1120419623_a_a_a > set_Pr729215751_a_a_a > $o ).
thf(member1361298640od_a_a_type,type,
member1361298640od_a_a: produc2010915495od_a_a > set_Pr231806599od_a_a > $o ).
thf(member122808528od_a_a_type,type,
member122808528od_a_a: produc772425383od_a_a > set_Pr1194146439od_a_a > $o ).
thf(member2057358096od_a_a_type,type,
member2057358096od_a_a: produc1572603623od_a_a > set_Pr1948701895od_a_a > $o ).
thf(member1403138919_a_a_a_type,type,
member1403138919_a_a_a: produc1016684094_a_a_a > set_Pr1689873822_a_a_a > $o ).
thf(member448091577od_a_a_type,type,
member448091577od_a_a: produc1555800720od_a_a > set_Pr195866352od_a_a > $o ).
thf(member160619001od_a_a_type,type,
member160619001od_a_a: produc1921647824od_a_a > set_Pr681306928od_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(b_type,type,
b: set_a ).
thf(pr_type,type,
pr: set_Product_prod_a_a ).
thf(y_type,type,
y: a ).
thf(z_type,type,
z: a ).
thf(214,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_84_preference_Ointro) ).
thf(1024,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)],[214]) ).
thf(260,axiom,
! [A: produc772425383od_a_a,B: set_Product_prod_a_a,C: set_Pr1948701895od_a_a] :
( ( member122808528od_a_a @ A
@ ( produc1227942600od_a_a @ B
@ ^ [D: product_prod_a_a] : C ) )
= ( ( member449909584od_a_a @ ( produc1775747843od_a_a @ A ) @ B )
& ( member2057358096od_a_a @ ( produc1055472197od_a_a @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_mem__Times__iff) ).
thf(1190,plain,
! [A: produc772425383od_a_a,B: set_Product_prod_a_a,C: set_Pr1948701895od_a_a] :
( ( member122808528od_a_a @ A
@ ( produc1227942600od_a_a @ B
@ ^ [D: product_prod_a_a] : C ) )
= ( ( member449909584od_a_a @ ( produc1775747843od_a_a @ A ) @ B )
& ( member2057358096od_a_a @ ( produc1055472197od_a_a @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(255,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_83_preference_Ointro) ).
thf(1168,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)],[255]) ).
thf(275,axiom,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: produc1572603623od_a_a > product_prod_a_a] :
( ( member2057358096od_a_a @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member449909584od_a_a @ C @ ( image_734753285od_a_a @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_rev__image__eqI) ).
thf(1237,plain,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: produc1572603623od_a_a > product_prod_a_a] :
( ( member2057358096od_a_a @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member449909584od_a_a @ C @ ( image_734753285od_a_a @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(216,axiom,
! [A: produc1572603623od_a_a,B: product_prod_a_a > produc1572603623od_a_a,C: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ A @ ( image_1765377413od_a_a @ B @ C ) )
=> ~ ! [D: product_prod_a_a] :
( ( A
= ( B @ D ) )
=> ~ ( member449909584od_a_a @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_imageE) ).
thf(1031,plain,
! [A: produc1572603623od_a_a,B: product_prod_a_a > produc1572603623od_a_a,C: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ A @ ( image_1765377413od_a_a @ B @ C ) )
=> ~ ! [D: product_prod_a_a] :
( ( A
= ( B @ D ) )
=> ~ ( member449909584od_a_a @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(139,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_66_swap__simp) ).
thf(777,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)],[139]) ).
thf(47,axiom,
! [A: produc772425383od_a_a] :
~ ! [B: product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( A
!= ( produc1555606807od_a_a @ B @ ( produc1474507607od_a_a @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_prod__cases3) ).
thf(479,plain,
! [A: produc772425383od_a_a] :
~ ! [B: product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( A
!= ( produc1555606807od_a_a @ B @ ( produc1474507607od_a_a @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(238,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_51_old_Oprod_Oexhaust) ).
thf(1105,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)],[238]) ).
thf(78,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_21_old_Oprod_Oinject) ).
thf(582,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)],[78]) ).
thf(207,axiom,
! [A: a,B: a,C: set_a,D: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( bNF_Gr_a_a @ C @ D ) )
=> ( ( D @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_GrD2) ).
thf(1005,plain,
! [A: a,B: a,C: set_a,D: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( bNF_Gr_a_a @ C @ D ) )
=> ( ( D @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(329,axiom,
! [A: produc1572603623od_a_a,B: product_prod_a_a,C: set_Pr1948701895od_a_a,D: produc1572603623od_a_a > set_Product_prod_a_a] :
( ( member1545452880od_a_a @ ( produc524982679od_a_a @ A @ B ) @ ( produc197318472od_a_a @ C @ D ) )
=> ~ ( ( member2057358096od_a_a @ A @ C )
=> ~ ( member449909584od_a_a @ B @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_SigmaE2) ).
thf(1406,plain,
! [A: produc1572603623od_a_a,B: product_prod_a_a,C: set_Pr1948701895od_a_a,D: produc1572603623od_a_a > set_Product_prod_a_a] :
( ( member1545452880od_a_a @ ( produc524982679od_a_a @ A @ B ) @ ( produc197318472od_a_a @ C @ D ) )
=> ~ ( ( member2057358096od_a_a @ A @ C )
=> ~ ( member449909584od_a_a @ B @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(227,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_43_Pair__inject) ).
thf(1068,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)],[227]) ).
thf(167,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_199_fstI) ).
thf(873,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)],[167]) ).
thf(87,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Pr1948701895od_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ ( image_236793797od_a_a @ produc1641853175od_a_a @ C ) )
= ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_pair__in__swap__image) ).
thf(614,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Pr1948701895od_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ ( image_236793797od_a_a @ produc1641853175od_a_a @ C ) )
= ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(123,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_subsetD) ).
thf(730,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(293,axiom,
! [A: a > product_prod_a_a,B: a > product_prod_a_a,C: a,D: a] :
( ( produc2012818120od_a_a @ A @ B @ ( product_Pair_a_a @ C @ D ) )
= ( produc1474507607od_a_a @ ( A @ C ) @ ( B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_map__prod__simp) ).
thf(1290,plain,
! [A: a > product_prod_a_a,B: a > product_prod_a_a,C: a,D: a] :
( ( produc2012818120od_a_a @ A @ B @ ( product_Pair_a_a @ C @ D ) )
= ( produc1474507607od_a_a @ ( A @ C ) @ ( B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(168,axiom,
! [A: produc1921647824od_a_a,B: set_a,C: a > set_Product_prod_a_a] :
( ( member160619001od_a_a @ A @ ( produc520147185od_a_a @ B @ C ) )
=> ~ ! [D: a] :
( ( member_a @ D @ B )
=> ! [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ ( C @ D ) )
=> ( A
!= ( produc1299253312od_a_a @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_SigmaE) ).
thf(878,plain,
! [A: produc1921647824od_a_a,B: set_a,C: a > set_Product_prod_a_a] :
( ( member160619001od_a_a @ A @ ( produc520147185od_a_a @ B @ C ) )
=> ~ ! [D: a] :
( ( member_a @ D @ B )
=> ! [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ ( C @ D ) )
=> ( A
!= ( produc1299253312od_a_a @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(101,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_57_ssubst__Pair__rhs) ).
thf(655,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)],[101]) ).
thf(57,axiom,
! [A: produc1572603623od_a_a] :
( A
= ( produc1474507607od_a_a @ ( produc2115494211od_a_a @ A ) @ ( produc368344197od_a_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_prod_Oexhaust__sel) ).
thf(511,plain,
! [A: produc1572603623od_a_a] :
( A
= ( produc1474507607od_a_a @ ( produc2115494211od_a_a @ A ) @ ( produc368344197od_a_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(298,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_less_eq_a_a_o
@ ^ [C: a,D: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
@ ^ [C: a,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_331_pred__subset__eq2) ).
thf(1305,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_less_eq_a_a_o
@ ^ [C: a,D: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ A )
@ ^ [C: a,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)],[298]) ).
thf(81,axiom,
( ord_le456379495od_a_a
= ( ^ [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
( ord_le1525442358_a_a_o
@ ^ [C: produc1572603623od_a_a] : ( member2057358096od_a_a @ C @ A )
@ ^ [C: produc1572603623od_a_a] : ( member2057358096od_a_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_less__eq__set__def) ).
thf(597,plain,
( ord_le456379495od_a_a
= ( ^ [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
( ord_le1525442358_a_a_o
@ ^ [C: produc1572603623od_a_a] : ( member2057358096od_a_a @ C @ A )
@ ^ [C: produc1572603623od_a_a] : ( member2057358096od_a_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(229,axiom,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ord_le1347718902_a_a_o
@ ^ [C: product_prod_a_a] : ( member449909584od_a_a @ C @ A )
@ ^ [C: product_prod_a_a] : ( member449909584od_a_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_less__eq__set__def) ).
thf(1078,plain,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ord_le1347718902_a_a_o
@ ^ [C: product_prod_a_a] : ( member449909584od_a_a @ C @ A )
@ ^ [C: product_prod_a_a] : ( member449909584od_a_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(247,axiom,
! [A: a,B: a,C: set_a,D: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( product_Sigma_a_a @ C @ D ) )
= ( ( member_a @ A @ C )
& ( member_a @ B @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_mem__Sigma__iff) ).
thf(1137,plain,
! [A: a,B: a,C: set_a,D: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( product_Sigma_a_a @ C @ D ) )
= ( ( member_a @ A @ C )
& ( member_a @ B @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(64,axiom,
! [A: produc1572603623od_a_a > $o,B: product_prod_a_a,C: product_prod_a_a] :
( ( produc94438221_a_a_o @ A @ B @ C )
=> ( A @ ( produc1474507607od_a_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_curryD) ).
thf(533,plain,
! [A: produc1572603623od_a_a > $o,B: product_prod_a_a,C: product_prod_a_a] :
( ( produc94438221_a_a_o @ A @ B @ C )
=> ( A @ ( produc1474507607od_a_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(144,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
=> ~ ( ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_DiffE) ).
thf(797,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
=> ~ ( ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(66,axiom,
! [A: a,B: produc1572603623od_a_a > a,C: set_Pr1948701895od_a_a] :
( ( member_a @ A @ ( image_1105229276_a_a_a @ B @ C ) )
=> ~ ! [D: produc1572603623od_a_a] :
( ( A
= ( B @ D ) )
=> ~ ( member2057358096od_a_a @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_imageE) ).
thf(538,plain,
! [A: a,B: produc1572603623od_a_a > a,C: set_Pr1948701895od_a_a] :
( ( member_a @ A @ ( image_1105229276_a_a_a @ B @ C ) )
=> ~ ! [D: produc1572603623od_a_a] :
( ( A
= ( B @ D ) )
=> ~ ( member2057358096od_a_a @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(270,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_211_surjective__pairing) ).
thf(1222,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)],[270]) ).
thf(262,axiom,
! [A: product_prod_a_a,B: set_a,C: a > set_a] :
( ( member449909584od_a_a @ A @ ( product_Sigma_a_a @ B @ C ) )
=> ~ ! [D: a] :
( ( member_a @ D @ B )
=> ! [E: a] :
( ( member_a @ E @ ( C @ D ) )
=> ( A
!= ( product_Pair_a_a @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_SigmaE) ).
thf(1196,plain,
! [A: product_prod_a_a,B: set_a,C: a > set_a] :
( ( member449909584od_a_a @ A @ ( product_Sigma_a_a @ B @ C ) )
=> ~ ! [D: a] :
( ( member_a @ D @ B )
=> ! [E: a] :
( ( member_a @ E @ ( C @ D ) )
=> ( A
!= ( product_Pair_a_a @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(244,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_subsetD) ).
thf(1127,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(325,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_15_prod_Oinject) ).
thf(1391,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)],[325]) ).
thf(158,axiom,
! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
( ( ord_le1525442358_a_a_o
@ ^ [C: produc1572603623od_a_a] : ( member2057358096od_a_a @ C @ A )
@ ^ [C: produc1572603623od_a_a] : ( member2057358096od_a_a @ C @ B ) )
= ( ord_le456379495od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_pred__subset__eq) ).
thf(841,plain,
! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
( ( ord_le1525442358_a_a_o
@ ^ [C: produc1572603623od_a_a] : ( member2057358096od_a_a @ C @ A )
@ ^ [C: produc1572603623od_a_a] : ( member2057358096od_a_a @ C @ B ) )
= ( ord_le456379495od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(170,axiom,
! [A: set_Product_prod_a_a] :
( ( ? [B: product_prod_a_a] : ( member449909584od_a_a @ B @ A ) )
= ( A != bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_ex__in__conv) ).
thf(885,plain,
! [A: set_Product_prod_a_a] :
( ( ? [B: product_prod_a_a] : ( member449909584od_a_a @ B @ A ) )
= ( A != bot_bo2131659635od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(323,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_180_map__prod__imageI) ).
thf(1386,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)],[323]) ).
thf(284,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_176_map__prod__simp) ).
thf(1265,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)],[284]) ).
thf(272,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a > set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ ( D @ A ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ C ) @ ( produc304751368od_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_SigmaI) ).
thf(1228,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a > set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ ( D @ A ) )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ C ) @ ( produc304751368od_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(280,axiom,
( prefer74720675od_a_a
= ( ^ [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Pr1948701895od_a_a] :
( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
& ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ D ) @ C )
& ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_as__good__as__def) ).
thf(1254,plain,
( prefer74720675od_a_a
= ( ^ [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Pr1948701895od_a_a] :
( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
& ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ D ) @ C )
& ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(121,axiom,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( produc2115494211od_a_a @ ( produc1474507607od_a_a @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_fst__conv) ).
thf(724,plain,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( produc2115494211od_a_a @ ( produc1474507607od_a_a @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(292,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_126_imageI) ).
thf(1287,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)],[292]) ).
thf(15,axiom,
! [A: produc1555800720od_a_a,B: set_a,C: a > set_Pr1948701895od_a_a] :
( ( member448091577od_a_a @ A @ ( produc663418545od_a_a @ B @ C ) )
=> ~ ! [D: a] :
( ( member_a @ D @ B )
=> ! [E: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ E @ ( C @ D ) )
=> ( A
!= ( produc1095491584od_a_a @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_SigmaE) ).
thf(372,plain,
! [A: produc1555800720od_a_a,B: set_a,C: a > set_Pr1948701895od_a_a] :
( ( member448091577od_a_a @ A @ ( produc663418545od_a_a @ B @ C ) )
=> ~ ! [D: a] :
( ( member_a @ D @ B )
=> ! [E: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ E @ ( C @ D ) )
=> ( A
!= ( produc1095491584od_a_a @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(289,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_29_surj__pair) ).
thf(1279,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)],[289]) ).
thf(184,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_69_curryE) ).
thf(934,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)],[184]) ).
thf(67,axiom,
( minus_1034916142od_a_a
= ( ^ [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
( collec1635618130od_a_a
@ ^ [C: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ C @ A )
& ~ ( member2057358096od_a_a @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_set__diff__eq) ).
thf(542,plain,
( minus_1034916142od_a_a
= ( ^ [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
( collec1635618130od_a_a
@ ^ [C: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ C @ A )
& ~ ( member2057358096od_a_a @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(89,axiom,
! [A: produc1572603623od_a_a] :
( ( produc1474507607od_a_a @ ( produc2115494211od_a_a @ A ) @ ( produc368344197od_a_a @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_prod_Ocollapse) ).
thf(619,plain,
! [A: produc1572603623od_a_a] :
( ( produc1474507607od_a_a @ ( produc2115494211od_a_a @ A ) @ ( produc368344197od_a_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(157,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_28_surj__pair) ).
thf(838,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)],[157]) ).
thf(179,axiom,
! [A: product_prod_a_a] : ( member449909584od_a_a @ A @ top_to398455383od_a_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_iso__tuple__UNIV__I) ).
thf(917,plain,
! [A: product_prod_a_a] : ( member449909584od_a_a @ A @ top_to398455383od_a_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(130,axiom,
( minus_minus_set_a
= ( ^ [A: set_a,B: set_a] :
( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
& ~ ( member_a @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_set__diff__eq) ).
thf(751,plain,
( minus_minus_set_a
= ( ^ [A: set_a,B: set_a] :
( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
& ~ ( member_a @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(175,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_115_rev__image__eqI) ).
thf(902,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)],[175]) ).
thf(96,axiom,
! [A: produc772425383od_a_a,B: produc772425383od_a_a,C: set_Pr1194146439od_a_a,D: set_Pr2081559751od_a_a] :
( ( member122808528od_a_a @ A @ ( prefer1377343203od_a_a @ B @ C @ D ) )
=> ( member547056400od_a_a @ ( produc852390743od_a_a @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_at__lst__asgd__ge) ).
thf(638,plain,
! [A: produc772425383od_a_a,B: produc772425383od_a_a,C: set_Pr1194146439od_a_a,D: set_Pr2081559751od_a_a] :
( ( member122808528od_a_a @ A @ ( prefer1377343203od_a_a @ B @ C @ D ) )
=> ( member547056400od_a_a @ ( produc852390743od_a_a @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(232,axiom,
! [A: a,B: a,C: set_a,D: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( bNF_Gr_a_a @ C @ D ) )
=> ( member_a @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_GrD1) ).
thf(1087,plain,
! [A: a,B: a,C: set_a,D: a > a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( bNF_Gr_a_a @ C @ D ) )
=> ( member_a @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(210,axiom,
! [A: product_prod_a_a > a,B: product_prod_a_a > a,C: product_prod_a_a,D: product_prod_a_a] :
( ( produc363290532_a_a_a @ A @ B @ ( produc1474507607od_a_a @ C @ D ) )
= ( product_Pair_a_a @ ( A @ C ) @ ( B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_map__prod__simp) ).
thf(1013,plain,
! [A: product_prod_a_a > a,B: product_prod_a_a > a,C: product_prod_a_a,D: product_prod_a_a] :
( ( produc363290532_a_a_a @ A @ B @ ( produc1474507607od_a_a @ C @ D ) )
= ( product_Pair_a_a @ ( A @ C ) @ ( B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(38,axiom,
! [A: set_a,B: set_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_subsetI) ).
thf(448,plain,
! [A: set_a,B: set_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(196,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Pr1948701895od_a_a,D: product_prod_a_a > a,E: product_prod_a_a > a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ C )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( D @ A ) @ ( E @ B ) ) @ ( image_734753285od_a_a @ ( produc363290532_a_a_a @ D @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_map__prod__imageI) ).
thf(969,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Pr1948701895od_a_a,D: product_prod_a_a > a,E: product_prod_a_a > a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ C )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ ( D @ A ) @ ( E @ B ) ) @ ( image_734753285od_a_a @ ( produc363290532_a_a_a @ D @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(311,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_184_top__empty__eq) ).
thf(1347,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)],[311]) ).
thf(49,axiom,
! [A: set_Pr1948701895od_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 ) @ A )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B ) )
=> ( ord_le456379495od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_subrelI) ).
thf(485,plain,
! [A: set_Pr1948701895od_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 ) @ A )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B ) )
=> ( ord_le456379495od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(58,axiom,
! [A: a,B: set_a,C: produc1572603623od_a_a,D: a > produc1572603623od_a_a] :
( ( member_a @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member2057358096od_a_a @ C @ ( image_1763923566od_a_a @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_rev__image__eqI) ).
thf(514,plain,
! [A: a,B: set_a,C: produc1572603623od_a_a,D: a > produc1572603623od_a_a] :
( ( member_a @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member2057358096od_a_a @ C @ ( image_1763923566od_a_a @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(7,axiom,
! [A: produc1555800720od_a_a] :
? [B: a,C: produc1572603623od_a_a] :
( A
= ( produc1095491584od_a_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_surj__pair) ).
thf(348,plain,
! [A: produc1555800720od_a_a] :
? [B: a,C: produc1572603623od_a_a] :
( A
= ( produc1095491584od_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(195,axiom,
! [A: product_prod_a_a > produc1572603623od_a_a,B: set_Product_prod_a_a,C: produc1572603623od_a_a > $o] :
( ( collec1635618130od_a_a
@ ^ [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ ( image_1765377413od_a_a @ A @ B ) )
& ( C @ D ) ) )
= ( image_1765377413od_a_a @ A
@ ( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_Compr__image__eq) ).
thf(966,plain,
! [A: product_prod_a_a > produc1572603623od_a_a,B: set_Product_prod_a_a,C: produc1572603623od_a_a > $o] :
( ( collec1635618130od_a_a
@ ^ [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ ( image_1765377413od_a_a @ A @ B ) )
& ( C @ D ) ) )
= ( image_1765377413od_a_a @ A
@ ( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(151,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_92_mem__Collect__eq) ).
thf(821,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)],[151]) ).
thf(297,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_203_eq__snd__iff) ).
thf(1302,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)],[297]) ).
thf(132,axiom,
! [A: set_a,B: a > $o] :
( ord_less_eq_set_a
@ ( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_Collect__subset) ).
thf(756,plain,
! [A: set_a,B: a > $o] :
( ord_less_eq_set_a
@ ( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(218,axiom,
! [A: product_prod_a_a,B: a > product_prod_a_a,C: set_a] :
( ( member449909584od_a_a @ A @ ( image_1725938350od_a_a @ B @ C ) )
=> ~ ! [D: a] :
( ( A
= ( B @ D ) )
=> ~ ( member_a @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_imageE) ).
thf(1040,plain,
! [A: product_prod_a_a,B: a > product_prod_a_a,C: set_a] :
( ( member449909584od_a_a @ A @ ( image_1725938350od_a_a @ B @ C ) )
=> ~ ! [D: a] :
( ( A
= ( B @ D ) )
=> ~ ( member_a @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(239,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_22_old_Oprod_Oinject) ).
thf(1109,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)],[239]) ).
thf(135,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ ( bNF_Gr1372473186od_a_a @ C @ D ) )
=> ( ( D @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_GrD2) ).
thf(766,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ ( bNF_Gr1372473186od_a_a @ C @ D ) )
=> ( ( D @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(110,axiom,
! [A: produc1572603623od_a_a,B: a > produc1572603623od_a_a,C: a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( member_a @ C @ D )
=> ( member2057358096od_a_a @ A @ ( image_1763923566od_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_image__eqI) ).
thf(687,plain,
! [A: produc1572603623od_a_a,B: a > produc1572603623od_a_a,C: a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( member_a @ C @ D )
=> ( member2057358096od_a_a @ A @ ( image_1763923566od_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(320,axiom,
! [A: produc1921647824od_a_a] :
~ ! [B: a,C: a,D: a] :
( A
!= ( produc1299253312od_a_a @ B @ ( product_Pair_a_a @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_prod__cases3) ).
thf(1377,plain,
! [A: produc1921647824od_a_a] :
~ ! [B: a,C: a,D: a] :
( A
!= ( produc1299253312od_a_a @ B @ ( product_Pair_a_a @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(111,axiom,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a > a] :
( ( member2057358096od_a_a @ A @ B )
=> ( member_a @ ( C @ A ) @ ( image_1105229276_a_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_imageI) ).
thf(692,plain,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a > a] :
( ( member2057358096od_a_a @ A @ B )
=> ( member_a @ ( C @ A ) @ ( image_1105229276_a_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(326,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: produc1572603623od_a_a,D: product_prod_a_a > produc1572603623od_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member2057358096od_a_a @ C @ ( image_1765377413od_a_a @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_rev__image__eqI) ).
thf(1394,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: produc1572603623od_a_a,D: product_prod_a_a > produc1572603623od_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member2057358096od_a_a @ C @ ( image_1765377413od_a_a @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(22,axiom,
! [A: a,B: produc1572603623od_a_a,C: set_a,D: a > set_Pr1948701895od_a_a] :
( ( member448091577od_a_a @ ( produc1095491584od_a_a @ A @ B ) @ ( produc663418545od_a_a @ C @ D ) )
=> ~ ( ( member_a @ A @ C )
=> ~ ( member2057358096od_a_a @ B @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_SigmaE2) ).
thf(396,plain,
! [A: a,B: produc1572603623od_a_a,C: set_a,D: a > set_Pr1948701895od_a_a] :
( ( member448091577od_a_a @ ( produc1095491584od_a_a @ A @ B ) @ ( produc663418545od_a_a @ C @ D ) )
=> ~ ( ( member_a @ A @ C )
=> ~ ( member2057358096od_a_a @ B @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(313,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_7_at__lst__asgd__ge) ).
thf(1351,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)],[313]) ).
thf(102,axiom,
! [A: product_prod_a_a,B: a,C: product_prod_a_a,D: a] :
( ( ( produc2061588782_a_a_a @ A @ B )
= ( produc2061588782_a_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_old_Oprod_Oinject) ).
thf(660,plain,
! [A: product_prod_a_a,B: a,C: product_prod_a_a,D: a] :
( ( ( produc2061588782_a_a_a @ A @ B )
= ( produc2061588782_a_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(276,axiom,
! [A: set_a,B: a,C: set_Product_prod_a_a] :
( ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ A )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ B ) @ C )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ C ) ) )
= ( minus_minus_set_a @ ( prefer161218362good_a @ B @ A @ C ) @ ( prefer436369274d_as_a @ B @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_strict__contour__is__diff) ).
thf(1242,plain,
! [A: set_a,B: a,C: set_Product_prod_a_a] :
( ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ A )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ B ) @ C )
& ~ ( member449909584od_a_a @ ( product_Pair_a_a @ B @ D ) @ C ) ) )
= ( minus_minus_set_a @ ( prefer161218362good_a @ B @ A @ C ) @ ( prefer436369274d_as_a @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(62,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_in__mono) ).
thf(527,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(242,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_64_preference_Onot__outside) ).
thf(1119,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)],[242]) ).
thf(138,axiom,
! [A: set_Pr1948701895od_a_a,B: produc1572603623od_a_a > a,C: set_a] :
( ! [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ A )
=> ( member_a @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_a @ ( image_1105229276_a_a_a @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_image__subsetI) ).
thf(774,plain,
! [A: set_Pr1948701895od_a_a,B: produc1572603623od_a_a > a,C: set_a] :
( ! [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ A )
=> ( member_a @ ( B @ D ) @ C ) )
=> ( ord_less_eq_set_a @ ( image_1105229276_a_a_a @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(26,axiom,
? [A: a] : ( member_a @ A @ top_top_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_UNIV__witness) ).
thf(411,plain,
? [A: a] : ( member_a @ A @ top_top_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(201,axiom,
( minus_1507102574od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( collec645855634od_a_a
@ ^ [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
& ~ ( member449909584od_a_a @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_set__diff__eq) ).
thf(988,plain,
( minus_1507102574od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( collec645855634od_a_a
@ ^ [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
& ~ ( member449909584od_a_a @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(32,axiom,
! [A: a,B: produc1572603623od_a_a,C: set_a,D: a > set_Pr1948701895od_a_a] :
( ( member448091577od_a_a @ ( produc1095491584od_a_a @ A @ B ) @ ( produc663418545od_a_a @ C @ D ) )
= ( ( member_a @ A @ C )
& ( member2057358096od_a_a @ B @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_mem__Sigma__iff) ).
thf(428,plain,
! [A: a,B: produc1572603623od_a_a,C: set_a,D: a > set_Pr1948701895od_a_a] :
( ( member448091577od_a_a @ ( produc1095491584od_a_a @ A @ B ) @ ( produc663418545od_a_a @ C @ D ) )
= ( ( member_a @ A @ C )
& ( member2057358096od_a_a @ B @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(263,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: a,D: product_prod_a_a > set_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( member_a @ C @ ( D @ A ) )
=> ( member1403138919_a_a_a @ ( produc2061588782_a_a_a @ A @ C ) @ ( produc1282482655_a_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_SigmaI) ).
thf(1201,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: a,D: product_prod_a_a > set_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( member_a @ C @ ( D @ A ) )
=> ( member1403138919_a_a_a @ ( produc2061588782_a_a_a @ A @ C ) @ ( produc1282482655_a_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(17,axiom,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: a,D: produc1572603623od_a_a > set_a] :
( ( member2057358096od_a_a @ A @ B )
=> ( ( member_a @ C @ ( D @ A ) )
=> ( member575366567_a_a_a @ ( produc436797294_a_a_a @ A @ C ) @ ( produc4724255_a_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_SigmaI) ).
thf(380,plain,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: a,D: produc1572603623od_a_a > set_a] :
( ( member2057358096od_a_a @ A @ B )
=> ( ( member_a @ C @ ( D @ A ) )
=> ( member575366567_a_a_a @ ( produc436797294_a_a_a @ A @ C ) @ ( produc4724255_a_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(35,axiom,
! [A: set_a] :
( ! [B: a] : ( member_a @ B @ A )
=> ( top_top_set_a = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_UNIV__eq__I) ).
thf(439,plain,
! [A: set_a] :
( ! [B: a] : ( member_a @ B @ A )
=> ( top_top_set_a = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(107,axiom,
! [A: a,B: product_prod_a_a,C: a,D: product_prod_a_a] :
( ( ( produc1299253312od_a_a @ A @ B )
= ( produc1299253312od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_prod_Oinject) ).
thf(678,plain,
! [A: a,B: product_prod_a_a,C: a,D: product_prod_a_a] :
( ( ( produc1299253312od_a_a @ A @ B )
= ( produc1299253312od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(134,axiom,
! [A: set_a,B: set_a,C: a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ! [E: a] :
( ( member_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq_set_a
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ A )
& ( C @ E ) ) )
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_subset__CollectI) ).
thf(761,plain,
! [A: set_a,B: set_a,C: a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ! [E: a] :
( ( member_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq_set_a
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ A )
& ( C @ E ) ) )
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(308,axiom,
! [A: produc1016684094_a_a_a,B: set_Product_prod_a_a,C: set_a] :
( ( member1403138919_a_a_a @ A
@ ( produc1282482655_a_a_a @ B
@ ^ [D: product_prod_a_a] : C ) )
= ( ( member449909584od_a_a @ ( produc1805832986_a_a_a @ A ) @ B )
& ( member_a @ ( produc1954021468_a_a_a @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_mem__Times__iff) ).
thf(1338,plain,
! [A: produc1016684094_a_a_a,B: set_Product_prod_a_a,C: set_a] :
( ( member1403138919_a_a_a @ A
@ ( produc1282482655_a_a_a @ B
@ ^ [D: product_prod_a_a] : C ) )
= ( ( member449909584od_a_a @ ( produc1805832986_a_a_a @ A ) @ B )
& ( member_a @ ( produc1954021468_a_a_a @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(13,axiom,
! [A: a] : ( member_a @ A @ top_top_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_iso__tuple__UNIV__I) ).
thf(366,plain,
! [A: a] : ( member_a @ A @ top_top_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(300,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: produc1572603623od_a_a,D: product_prod_a_a > set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( member2057358096od_a_a @ C @ ( D @ A ) )
=> ( member122808528od_a_a @ ( produc1555606807od_a_a @ A @ C ) @ ( produc1227942600od_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_SigmaI) ).
thf(1311,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: produc1572603623od_a_a,D: product_prod_a_a > set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( member2057358096od_a_a @ C @ ( D @ A ) )
=> ( member122808528od_a_a @ ( produc1555606807od_a_a @ A @ C ) @ ( produc1227942600od_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(220,axiom,
( prefer1676310729than_a
= ( ^ [A: a,B: set_a,C: set_Product_prod_a_a] :
( collect_a
@ ^ [D: a] :
( ( member_a @ D @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ A @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_no__better__than__def) ).
thf(1047,plain,
( prefer1676310729than_a
= ( ^ [A: a,B: set_a,C: set_Product_prod_a_a] :
( collect_a
@ ^ [D: a] :
( ( member_a @ D @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ A @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(224,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_102_image__eqI) ).
thf(1057,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)],[224]) ).
thf(287,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_215_prod_Oswap__def) ).
thf(1274,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)],[287]) ).
thf(177,axiom,
! [A: a,B: product_prod_a_a > a,C: set_Product_prod_a_a] :
( ( member_a @ A @ ( image_340790172_a_a_a @ B @ C ) )
=> ~ ! [D: product_prod_a_a] :
( ( A
= ( B @ D ) )
=> ~ ( member449909584od_a_a @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_imageE) ).
thf(910,plain,
! [A: a,B: product_prod_a_a > a,C: set_Product_prod_a_a] :
( ( member_a @ A @ ( image_340790172_a_a_a @ B @ C ) )
=> ~ ! [D: product_prod_a_a] :
( ( A
= ( B @ D ) )
=> ~ ( member449909584od_a_a @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(173,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_114_rev__image__eqI) ).
thf(894,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)],[173]) ).
thf(190,axiom,
! [A: set_Product_prod_a_a] :
( ( ! [B: product_prod_a_a] :
~ ( member449909584od_a_a @ B @ A ) )
= ( A = bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_all__not__in__conv) ).
thf(952,plain,
! [A: set_Product_prod_a_a] :
( ( ! [B: product_prod_a_a] :
~ ( member449909584od_a_a @ B @ A ) )
= ( A = bot_bo2131659635od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(315,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_232_in__lex__prod) ).
thf(1355,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)],[315]) ).
thf(256,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_288_image__subsetI) ).
thf(1174,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)],[256]) ).
thf(73,axiom,
! [A: produc1683075710_a_a_a,B: set_Pr1948701895od_a_a,C: set_a] :
( ( member575366567_a_a_a @ A
@ ( produc4724255_a_a_a @ B
@ ^ [D: produc1572603623od_a_a] : C ) )
= ( ( member2057358096od_a_a @ ( produc2019352922_a_a_a @ A ) @ B )
& ( member_a @ ( produc262335132_a_a_a @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_mem__Times__iff) ).
thf(561,plain,
! [A: produc1683075710_a_a_a,B: set_Pr1948701895od_a_a,C: set_a] :
( ( member575366567_a_a_a @ A
@ ( produc4724255_a_a_a @ B
@ ^ [D: produc1572603623od_a_a] : C ) )
= ( ( member2057358096od_a_a @ ( produc2019352922_a_a_a @ A ) @ B )
& ( member_a @ ( produc262335132_a_a_a @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(93,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ B )
=> ( ~ ( member_a @ A @ C )
=> ( member_a @ A @ ( minus_minus_set_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_DiffI) ).
thf(630,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ B )
=> ( ~ ( member_a @ A @ C )
=> ( member_a @ A @ ( minus_minus_set_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(160,axiom,
! [A: a,B: a > a,C: a,D: a,E: a > a,F: set_a] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member_a @ C @ F )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ D ) @ ( bNF_Gr423046308_a_a_a @ F @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_image2__eqI) ).
thf(847,plain,
! [A: a,B: a > a,C: a,D: a,E: a > a,F: set_a] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member_a @ C @ F )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ D ) @ ( bNF_Gr423046308_a_a_a @ F @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(12,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_103_image__eqI) ).
thf(361,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)],[12]) ).
thf(91,axiom,
( ord_le456379495od_a_a
= ( ^ [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
! [C: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ C @ A )
=> ( member2057358096od_a_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_subset__iff) ).
thf(625,plain,
( ord_le456379495od_a_a
= ( ^ [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
! [C: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ C @ A )
=> ( member2057358096od_a_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(161,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_48_prod__induct3) ).
thf(852,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)],[161]) ).
thf(154,axiom,
! [A: set_Pr1948701895od_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 ) @ A ) )
= ( ^ [C: product_prod_a_a,D: product_prod_a_a] : ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_pred__equals__eq2) ).
thf(830,plain,
! [A: set_Pr1948701895od_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 ) @ A ) )
= ( ^ [C: product_prod_a_a,D: product_prod_a_a] : ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(70,axiom,
! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
( ( ord_le252190158_a_a_o
@ ^ [C: product_prod_a_a,D: product_prod_a_a] : ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ A )
@ ^ [C: product_prod_a_a,D: product_prod_a_a] : ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B ) )
= ( ord_le456379495od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_pred__subset__eq2) ).
thf(551,plain,
! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
( ( ord_le252190158_a_a_o
@ ^ [C: product_prod_a_a,D: product_prod_a_a] : ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ A )
@ ^ [C: product_prod_a_a,D: product_prod_a_a] : ( member2057358096od_a_a @ ( produc1474507607od_a_a @ C @ D ) @ B ) )
= ( ord_le456379495od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(116,axiom,
! [A: product_prod_a_a,B: produc1572603623od_a_a,C: product_prod_a_a,D: produc1572603623od_a_a] :
( ( ( produc1555606807od_a_a @ A @ B )
= ( produc1555606807od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_prod_Oinject) ).
thf(710,plain,
! [A: product_prod_a_a,B: produc1572603623od_a_a,C: product_prod_a_a,D: produc1572603623od_a_a] :
( ( ( produc1555606807od_a_a @ A @ B )
= ( produc1555606807od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(252,axiom,
! [A: a,B: product_prod_a_a,C: a,D: product_prod_a_a,E: set_Product_prod_a_a,F: set_Pr1948701895od_a_a] :
( ( member1361298640od_a_a @ ( produc563767703od_a_a @ ( produc1299253312od_a_a @ A @ B ) @ ( produc1299253312od_a_a @ C @ D ) ) @ ( lex_pr1321960536od_a_a @ E @ F ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ E )
| ( ( A = C )
& ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ D ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_in__lex__prod) ).
thf(1159,plain,
! [A: a,B: product_prod_a_a,C: a,D: product_prod_a_a,E: set_Product_prod_a_a,F: set_Pr1948701895od_a_a] :
( ( member1361298640od_a_a @ ( produc563767703od_a_a @ ( produc1299253312od_a_a @ A @ B ) @ ( produc1299253312od_a_a @ C @ D ) ) @ ( lex_pr1321960536od_a_a @ E @ F ) )
= ( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ E )
| ( ( A = C )
& ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ D ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(42,axiom,
! [A: produc1572603623od_a_a] :
( A
= ( produc1474507607od_a_a @ ( produc2115494211od_a_a @ A ) @ ( produc368344197od_a_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_surjective__pairing) ).
thf(461,plain,
! [A: produc1572603623od_a_a] :
( A
= ( produc1474507607od_a_a @ ( produc2115494211od_a_a @ A ) @ ( produc368344197od_a_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(51,axiom,
( minus_minus_set_a
= ( ^ [A: set_a,B: set_a] :
( collect_a
@ ( minus_minus_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_minus__set__def) ).
thf(493,plain,
( minus_minus_set_a
= ( ^ [A: set_a,B: set_a] :
( collect_a
@ ( minus_minus_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(266,axiom,
! [A: produc1921647824od_a_a,B: set_a,C: set_Product_prod_a_a] :
( ( member160619001od_a_a @ A
@ ( produc520147185od_a_a @ B
@ ^ [D: a] : C ) )
= ( ( member_a @ ( produc1043497516od_a_a @ A ) @ B )
& ( member449909584od_a_a @ ( produc1191685998od_a_a @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_mem__Times__iff) ).
thf(1210,plain,
! [A: produc1921647824od_a_a,B: set_a,C: set_Product_prod_a_a] :
( ( member160619001od_a_a @ A
@ ( produc520147185od_a_a @ B
@ ^ [D: a] : C ) )
= ( ( member_a @ ( produc1043497516od_a_a @ A ) @ B )
& ( member449909584od_a_a @ ( produc1191685998od_a_a @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(59,axiom,
( produc1641853175od_a_a
= ( ^ [A: produc1572603623od_a_a] : ( produc1474507607od_a_a @ ( produc368344197od_a_a @ A ) @ ( produc2115494211od_a_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_prod_Oswap__def) ).
thf(519,plain,
( produc1641853175od_a_a
= ( ^ [A: produc1572603623od_a_a] : ( produc1474507607od_a_a @ ( produc368344197od_a_a @ A ) @ ( produc2115494211od_a_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(282,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_174_same__fstI) ).
thf(1259,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)],[282]) ).
thf(189,axiom,
! [A: set_Product_prod_a_a] :
( ! [B: product_prod_a_a] :
~ ( member449909584od_a_a @ B @ A )
=> ( A = bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_equals0I) ).
thf(948,plain,
! [A: set_Product_prod_a_a] :
( ! [B: product_prod_a_a] :
~ ( member449909584od_a_a @ B @ A )
=> ( A = bot_bo2131659635od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(235,axiom,
! [A: set_Product_prod_a_a,B: product_prod_a_a > $o] :
( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_Collect__restrict) ).
thf(1096,plain,
! [A: set_Product_prod_a_a,B: product_prod_a_a > $o] :
( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(19,axiom,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a > produc1572603623od_a_a] :
( ( member2057358096od_a_a @ A @ B )
=> ( member2057358096od_a_a @ ( C @ A ) @ ( image_236793797od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_imageI) ).
thf(388,plain,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a > produc1572603623od_a_a] :
( ( member2057358096od_a_a @ A @ B )
=> ( member2057358096od_a_a @ ( C @ A ) @ ( image_236793797od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(10,axiom,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: set_Pr1948701895od_a_a] :
( ( member2057358096od_a_a @ A @ ( minus_1034916142od_a_a @ B @ C ) )
=> ( member2057358096od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_DiffD1) ).
thf(356,plain,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: set_Pr1948701895od_a_a] :
( ( member2057358096od_a_a @ A @ ( minus_1034916142od_a_a @ B @ C ) )
=> ( member2057358096od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(85,axiom,
! [A: produc2010915495od_a_a,B: produc2010915495od_a_a,C: set_Pr231806599od_a_a,D: set_Pr532616391od_a_a] :
( ( member1361298640od_a_a @ A @ ( prefer468349667od_a_a @ B @ C @ D ) )
=> ( member180906768od_a_a @ ( produc539587415od_a_a @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_at__lst__asgd__ge) ).
thf(610,plain,
! [A: produc2010915495od_a_a,B: produc2010915495od_a_a,C: set_Pr231806599od_a_a,D: set_Pr532616391od_a_a] :
( ( member1361298640od_a_a @ A @ ( prefer468349667od_a_a @ B @ C @ D ) )
=> ( member180906768od_a_a @ ( produc539587415od_a_a @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(163,axiom,
( top_top_a_a_o
= ( ^ [A: a,B: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ top_to398455383od_a_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_top__empty__eq2) ).
thf(857,plain,
( top_top_a_a_o
= ( ^ [A: a,B: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ top_to398455383od_a_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(113,axiom,
! [A: set_Pr1948701895od_a_a,B: produc1572603623od_a_a > produc1572603623od_a_a,C: set_Pr1948701895od_a_a] :
( ! [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ A )
=> ( member2057358096od_a_a @ ( B @ D ) @ C ) )
=> ( ord_le456379495od_a_a @ ( image_236793797od_a_a @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_image__subsetI) ).
thf(697,plain,
! [A: set_Pr1948701895od_a_a,B: produc1572603623od_a_a > produc1572603623od_a_a,C: set_Pr1948701895od_a_a] :
( ! [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ A )
=> ( member2057358096od_a_a @ ( B @ D ) @ C ) )
=> ( ord_le456379495od_a_a @ ( image_236793797od_a_a @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(274,axiom,
! [A: set_Product_prod_a_a,B: product_prod_a_a > produc1572603623od_a_a,C: set_Pr1948701895od_a_a] :
( ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
=> ( member2057358096od_a_a @ ( B @ D ) @ C ) )
=> ( ord_le456379495od_a_a @ ( image_1765377413od_a_a @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_image__subsetI) ).
thf(1234,plain,
! [A: set_Product_prod_a_a,B: product_prod_a_a > produc1572603623od_a_a,C: set_Pr1948701895od_a_a] :
( ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
=> ( member2057358096od_a_a @ ( B @ D ) @ C ) )
=> ( ord_le456379495od_a_a @ ( image_1765377413od_a_a @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(199,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_100_image__eqI) ).
thf(980,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)],[199]) ).
thf(24,axiom,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: set_Pr1948701895od_a_a] :
( ( member2057358096od_a_a @ A @ B )
=> ( ~ ( member2057358096od_a_a @ A @ C )
=> ( member2057358096od_a_a @ A @ ( minus_1034916142od_a_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_DiffI) ).
thf(403,plain,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: set_Pr1948701895od_a_a] :
( ( member2057358096od_a_a @ A @ B )
=> ( ~ ( member2057358096od_a_a @ A @ C )
=> ( member2057358096od_a_a @ A @ ( minus_1034916142od_a_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(141,axiom,
! [A: product_prod_a_a > product_prod_a_a,B: product_prod_a_a > product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( produc1779756150od_a_a @ A @ B @ ( produc1474507607od_a_a @ C @ D ) )
= ( produc1474507607od_a_a @ ( A @ C ) @ ( B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_map__prod__simp) ).
thf(783,plain,
! [A: product_prod_a_a > product_prod_a_a,B: product_prod_a_a > product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a] :
( ( produc1779756150od_a_a @ A @ B @ ( produc1474507607od_a_a @ C @ D ) )
= ( produc1474507607od_a_a @ ( A @ C ) @ ( B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(29,axiom,
! [A: produc1572603623od_a_a] : ( member2057358096od_a_a @ A @ top_to52711959od_a_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_UNIV__I) ).
thf(420,plain,
! [A: produc1572603623od_a_a] : ( member2057358096od_a_a @ A @ top_to52711959od_a_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(44,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
= ( ( member_a @ A @ B )
& ~ ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_Diff__iff) ).
thf(471,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
= ( ( member_a @ A @ B )
& ~ ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(305,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ ( produc304751368od_a_a @ C @ D ) )
=> ( member449909584od_a_a @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_SigmaD1) ).
thf(1329,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ ( produc304751368od_a_a @ C @ D ) )
=> ( member449909584od_a_a @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(231,axiom,
! [A: set_Product_prod_a_a,B: product_prod_a_a] :
( ( A = bot_bo2131659635od_a_a )
=> ~ ( member449909584od_a_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_equals0D) ).
thf(1082,plain,
! [A: set_Product_prod_a_a,B: product_prod_a_a] :
( ( A = bot_bo2131659635od_a_a )
=> ~ ( member449909584od_a_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(50,axiom,
! [A: product_prod_a_a,B: produc1572603623od_a_a > product_prod_a_a,C: produc1572603623od_a_a,D: product_prod_a_a,E: produc1572603623od_a_a > product_prod_a_a,F: set_Pr1948701895od_a_a] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member2057358096od_a_a @ C @ F )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ D ) @ ( bNF_Gr533818957od_a_a @ F @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_image2__eqI) ).
thf(488,plain,
! [A: product_prod_a_a,B: produc1572603623od_a_a > product_prod_a_a,C: produc1572603623od_a_a,D: product_prod_a_a,E: produc1572603623od_a_a > product_prod_a_a,F: set_Pr1948701895od_a_a] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member2057358096od_a_a @ C @ F )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ D ) @ ( bNF_Gr533818957od_a_a @ F @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(317,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_219_conjI__realizer) ).
thf(1361,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)],[317]) ).
thf(258,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ~ ( member449909584od_a_a @ A @ C )
=> ( member449909584od_a_a @ A @ ( minus_1507102574od_a_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_DiffI) ).
thf(1182,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ~ ( member449909584od_a_a @ A @ C )
=> ( member449909584od_a_a @ A @ ( minus_1507102574od_a_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(228,axiom,
! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_emptyE) ).
thf(1075,plain,
! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(98,axiom,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: a,D: produc1572603623od_a_a > a] :
( ( member2057358096od_a_a @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_a @ C @ ( image_1105229276_a_a_a @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_rev__image__eqI) ).
thf(642,plain,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: a,D: produc1572603623od_a_a > a] :
( ( member2057358096od_a_a @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_a @ C @ ( image_1105229276_a_a_a @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(69,axiom,
! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a > $o] :
( ( ord_le456379495od_a_a @ A @ B )
=> ( ( ord_le456379495od_a_a @ A
@ ( collec1635618130od_a_a
@ ^ [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_subset__Collect__iff) ).
thf(547,plain,
! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a > $o] :
( ( ord_le456379495od_a_a @ A @ B )
=> ( ( ord_le456379495od_a_a @ A
@ ( collec1635618130od_a_a
@ ^ [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(71,axiom,
( top_to2011536774_a_a_o
= ( ^ [A: produc1572603623od_a_a] : ( member2057358096od_a_a @ A @ top_to52711959od_a_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_top__empty__eq) ).
thf(554,plain,
( top_to2011536774_a_a_o
= ( ^ [A: produc1572603623od_a_a] : ( member2057358096od_a_a @ A @ top_to52711959od_a_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(131,axiom,
! [A: product_prod_a_a,B: a,C: product_prod_a_a,D: a] :
( ( ( produc2061588782_a_a_a @ A @ B )
= ( produc2061588782_a_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_prod_Oinject) ).
thf(753,plain,
! [A: product_prod_a_a,B: a,C: product_prod_a_a,D: a] :
( ( ( produc2061588782_a_a_a @ A @ B )
= ( produc2061588782_a_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(211,axiom,
( prefer161218362good_a
= ( ^ [A: a,B: set_a,C: set_Product_prod_a_a] :
( collect_a
@ ^ [D: a] :
( ( member_a @ D @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_at__least__as__good__def) ).
thf(1016,plain,
( prefer161218362good_a
= ( ^ [A: a,B: set_a,C: set_Product_prod_a_a] :
( collect_a
@ ^ [D: a] :
( ( member_a @ D @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(265,axiom,
! [A: a,B: set_a,C: product_prod_a_a,D: a > set_Product_prod_a_a] :
( ( member_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ ( D @ A ) )
=> ( member160619001od_a_a @ ( produc1299253312od_a_a @ A @ C ) @ ( produc520147185od_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_SigmaI) ).
thf(1207,plain,
! [A: a,B: set_a,C: product_prod_a_a,D: a > set_Product_prod_a_a] :
( ( member_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ ( D @ A ) )
=> ( member160619001od_a_a @ ( produc1299253312od_a_a @ A @ C ) @ ( produc520147185od_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(80,axiom,
! [A: produc1921647824od_a_a,B: produc1921647824od_a_a,C: produc1921647824od_a_a,D: produc1921647824od_a_a] :
( ( ( produc563767703od_a_a @ A @ B )
= ( produc563767703od_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_Pair__inject) ).
thf(590,plain,
! [A: produc1921647824od_a_a,B: produc1921647824od_a_a,C: produc1921647824od_a_a,D: produc1921647824od_a_a] :
( ( ( produc563767703od_a_a @ A @ B )
= ( produc563767703od_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(90,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_mem__Collect__eq) ).
thf(622,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(200,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_65_swap__simp) ).
thf(985,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)],[200]) ).
thf(295,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ ( produc304751368od_a_a @ C @ D ) )
= ( ( member449909584od_a_a @ A @ C )
& ( member449909584od_a_a @ B @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_mem__Sigma__iff) ).
thf(1297,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ ( produc304751368od_a_a @ C @ D ) )
= ( ( member449909584od_a_a @ A @ C )
& ( member449909584od_a_a @ B @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(126,axiom,
! [A: set_a,B: a > $o] :
( ord_less_eq_set_a
@ ( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_Collect__restrict) ).
thf(738,plain,
! [A: set_a,B: a > $o] :
( ord_less_eq_set_a
@ ( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(273,axiom,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: produc1572603623od_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ ( D @ A ) )
=> ( member1545452880od_a_a @ ( produc524982679od_a_a @ A @ C ) @ ( produc197318472od_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_SigmaI) ).
thf(1231,plain,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a,D: produc1572603623od_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ ( D @ A ) )
=> ( member1545452880od_a_a @ ( produc524982679od_a_a @ A @ C ) @ ( produc197318472od_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(41,axiom,
! [A: produc1572603623od_a_a,B: product_prod_a_a,C: product_prod_a_a] :
( ( A
= ( produc1474507607od_a_a @ B @ C ) )
=> ( ( produc368344197od_a_a @ A )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_sndI) ).
thf(457,plain,
! [A: produc1572603623od_a_a,B: product_prod_a_a,C: product_prod_a_a] :
( ( A
= ( produc1474507607od_a_a @ B @ C ) )
=> ( ( produc368344197od_a_a @ A )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(120,axiom,
! [A: produc1016684094_a_a_a > $o,B: produc1016684094_a_a_a] :
( ! [C: product_prod_a_a,D: a] : ( A @ ( produc2061588782_a_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_prod__cases) ).
thf(721,plain,
! [A: produc1016684094_a_a_a > $o,B: produc1016684094_a_a_a] :
( ! [C: product_prod_a_a,D: a] : ( A @ ( produc2061588782_a_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(206,axiom,
! [A: produc1572603623od_a_a,B: product_prod_a_a,C: set_Pr1948701895od_a_a,D: produc1572603623od_a_a > set_Product_prod_a_a] :
( ( member1545452880od_a_a @ ( produc524982679od_a_a @ A @ B ) @ ( produc197318472od_a_a @ C @ D ) )
= ( ( member2057358096od_a_a @ A @ C )
& ( member449909584od_a_a @ B @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_mem__Sigma__iff) ).
thf(1002,plain,
! [A: produc1572603623od_a_a,B: product_prod_a_a,C: set_Pr1948701895od_a_a,D: produc1572603623od_a_a > set_Product_prod_a_a] :
( ( member1545452880od_a_a @ ( produc524982679od_a_a @ A @ B ) @ ( produc197318472od_a_a @ C @ D ) )
= ( ( member2057358096od_a_a @ A @ C )
& ( member449909584od_a_a @ B @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(304,axiom,
! [A: product_prod_a_a,B: product_prod_a_a > product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a,E: product_prod_a_a > product_prod_a_a,F: set_Product_prod_a_a] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member449909584od_a_a @ C @ F )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ D ) @ ( bNF_Gr200450189od_a_a @ F @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_image2__eqI) ).
thf(1324,plain,
! [A: product_prod_a_a,B: product_prod_a_a > product_prod_a_a,C: product_prod_a_a,D: product_prod_a_a,E: product_prod_a_a > product_prod_a_a,F: set_Product_prod_a_a] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member449909584od_a_a @ C @ F )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ D ) @ ( bNF_Gr200450189od_a_a @ F @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(21,axiom,
! [A: a,B: set_a,C: produc1572603623od_a_a,D: a > set_Pr1948701895od_a_a] :
( ( member_a @ A @ B )
=> ( ( member2057358096od_a_a @ C @ ( D @ A ) )
=> ( member448091577od_a_a @ ( produc1095491584od_a_a @ A @ C ) @ ( produc663418545od_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_SigmaI) ).
thf(393,plain,
! [A: a,B: set_a,C: produc1572603623od_a_a,D: a > set_Pr1948701895od_a_a] :
( ( member_a @ A @ B )
=> ( ( member2057358096od_a_a @ C @ ( D @ A ) )
=> ( member448091577od_a_a @ ( produc1095491584od_a_a @ A @ C ) @ ( produc663418545od_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(99,axiom,
! [A: a,B: produc1572603623od_a_a > a,C: produc1572603623od_a_a,D: set_Pr1948701895od_a_a] :
( ( A
= ( B @ C ) )
=> ( ( member2057358096od_a_a @ C @ D )
=> ( member_a @ A @ ( image_1105229276_a_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_image__eqI) ).
thf(647,plain,
! [A: a,B: produc1572603623od_a_a > a,C: produc1572603623od_a_a,D: set_Pr1948701895od_a_a] :
( ( A
= ( B @ C ) )
=> ( ( member2057358096od_a_a @ C @ D )
=> ( member_a @ A @ ( image_1105229276_a_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(204,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_81_preference__def) ).
thf(997,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)],[204]) ).
thf(94,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_subset__iff) ).
thf(633,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(223,axiom,
! [A: product_prod_a_a,B: a,C: set_Product_prod_a_a,D: product_prod_a_a > set_a] :
( ( member1403138919_a_a_a @ ( produc2061588782_a_a_a @ A @ B ) @ ( produc1282482655_a_a_a @ C @ D ) )
= ( ( member449909584od_a_a @ A @ C )
& ( member_a @ B @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_mem__Sigma__iff) ).
thf(1054,plain,
! [A: product_prod_a_a,B: a,C: set_Product_prod_a_a,D: product_prod_a_a > set_a] :
( ( member1403138919_a_a_a @ ( produc2061588782_a_a_a @ A @ B ) @ ( produc1282482655_a_a_a @ C @ D ) )
= ( ( member449909584od_a_a @ A @ C )
& ( member_a @ B @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(217,axiom,
! [A: produc772425383od_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > set_Pr1948701895od_a_a] :
( ( member122808528od_a_a @ A @ ( produc1227942600od_a_a @ B @ C ) )
=> ~ ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
=> ! [E: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ E @ ( C @ D ) )
=> ( A
!= ( produc1555606807od_a_a @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_SigmaE) ).
thf(1035,plain,
! [A: produc772425383od_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > set_Pr1948701895od_a_a] :
( ( member122808528od_a_a @ A @ ( produc1227942600od_a_a @ B @ C ) )
=> ~ ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
=> ! [E: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ E @ ( C @ D ) )
=> ( A
!= ( produc1555606807od_a_a @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(106,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: product_prod_a_a] :
( ( ( produc2115494211od_a_a @ ( produc1474507607od_a_a @ A @ B ) )
= C )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_fst__eqD) ).
thf(674,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: product_prod_a_a] :
( ( ( produc2115494211od_a_a @ ( produc1474507607od_a_a @ A @ B ) )
= C )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(63,axiom,
! [A: produc1921647824od_a_a > $o,B: produc1921647824od_a_a] :
( ! [C: a,D: product_prod_a_a] : ( A @ ( produc1299253312od_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_prod__cases) ).
thf(530,plain,
! [A: produc1921647824od_a_a > $o,B: produc1921647824od_a_a] :
( ! [C: a,D: product_prod_a_a] : ( A @ ( produc1299253312od_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(259,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_56_ssubst__Pair__rhs) ).
thf(1185,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)],[259]) ).
thf(182,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 ) )
= ( ^ [C: a,D: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_pred__equals__eq2) ).
thf(926,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 ) )
= ( ^ [C: a,D: a] : ( member449909584od_a_a @ ( product_Pair_a_a @ C @ D ) @ B ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(119,axiom,
! [A: a > a,B: set_a,C: a > $o] :
( ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ ( image_a_a @ A @ B ) )
& ( C @ D ) ) )
= ( image_a_a @ A
@ ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_Compr__image__eq) ).
thf(718,plain,
! [A: a > a,B: set_a,C: a > $o] :
( ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ ( image_a_a @ A @ B ) )
& ( C @ D ) ) )
= ( image_a_a @ A
@ ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(171,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_80_preference__def) ).
thf(888,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)],[171]) ).
thf(279,axiom,
! [A: product_prod_a_a,B: produc1572603623od_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > set_Pr1948701895od_a_a] :
( ( member122808528od_a_a @ ( produc1555606807od_a_a @ A @ B ) @ ( produc1227942600od_a_a @ C @ D ) )
= ( ( member449909584od_a_a @ A @ C )
& ( member2057358096od_a_a @ B @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_mem__Sigma__iff) ).
thf(1251,plain,
! [A: product_prod_a_a,B: produc1572603623od_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > set_Pr1948701895od_a_a] :
( ( member122808528od_a_a @ ( produc1555606807od_a_a @ A @ B ) @ ( produc1227942600od_a_a @ C @ D ) )
= ( ( member449909584od_a_a @ A @ C )
& ( member2057358096od_a_a @ B @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(31,axiom,
! [A: set_Pr1948701895od_a_a] :
( ! [B: produc1572603623od_a_a] : ( member2057358096od_a_a @ B @ A )
=> ( top_to52711959od_a_a = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_UNIV__eq__I) ).
thf(425,plain,
! [A: set_Pr1948701895od_a_a] :
( ! [B: produc1572603623od_a_a] : ( member2057358096od_a_a @ B @ A )
=> ( top_to52711959od_a_a = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(319,axiom,
! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_empty__iff) ).
thf(1374,plain,
! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(124,axiom,
! [A: a > produc1572603623od_a_a,B: set_a,C: produc1572603623od_a_a > $o] :
( ( collec1635618130od_a_a
@ ^ [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ ( image_1763923566od_a_a @ A @ B ) )
& ( C @ D ) ) )
= ( image_1763923566od_a_a @ A
@ ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_Compr__image__eq) ).
thf(733,plain,
! [A: a > produc1572603623od_a_a,B: set_a,C: produc1572603623od_a_a > $o] :
( ( collec1635618130od_a_a
@ ^ [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ ( image_1763923566od_a_a @ A @ B ) )
& ( C @ D ) ) )
= ( image_1763923566od_a_a @ A
@ ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(269,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > produc1572603623od_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( member2057358096od_a_a @ ( C @ A ) @ ( image_1765377413od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_imageI) ).
thf(1219,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > produc1572603623od_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( member2057358096od_a_a @ ( C @ A ) @ ( image_1765377413od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(152,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_291_image__subsetI) ).
thf(824,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)],[152]) ).
thf(251,axiom,
! [A: a,B: produc1572603623od_a_a > a,C: produc1572603623od_a_a,D: a,E: produc1572603623od_a_a > a,F: set_Pr1948701895od_a_a] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member2057358096od_a_a @ C @ F )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ D ) @ ( bNF_Gr356189709_a_a_a @ F @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_image2__eqI) ).
thf(1154,plain,
! [A: a,B: produc1572603623od_a_a > a,C: produc1572603623od_a_a,D: a,E: produc1572603623od_a_a > a,F: set_Pr1948701895od_a_a] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member2057358096od_a_a @ C @ F )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ D ) @ ( bNF_Gr356189709_a_a_a @ F @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(198,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_99_image__eqI) ).
thf(975,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)],[198]) ).
thf(324,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_67_curryD) ).
thf(1389,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)],[324]) ).
thf(76,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_50_old_Oprod_Oinducts) ).
thf(577,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)],[76]) ).
thf(192,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ ( produc304751368od_a_a @ C @ D ) )
=> ~ ( ( member449909584od_a_a @ A @ C )
=> ~ ( member449909584od_a_a @ B @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_SigmaE2) ).
thf(958,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ ( produc304751368od_a_a @ C @ D ) )
=> ~ ( ( member449909584od_a_a @ A @ C )
=> ~ ( member449909584od_a_a @ B @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(281,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( minus_1507102574od_a_a @ B @ C ) )
= ( ( member449909584od_a_a @ A @ B )
& ~ ( member449909584od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_Diff__iff) ).
thf(1256,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( minus_1507102574od_a_a @ B @ C ) )
= ( ( member449909584od_a_a @ A @ B )
& ~ ( member449909584od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(27,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_118_rev__image__eqI) ).
thf(413,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)],[27]) ).
thf(20,axiom,
? [A: produc1572603623od_a_a] : ( member2057358096od_a_a @ A @ top_to52711959od_a_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_UNIV__witness) ).
thf(391,plain,
? [A: produc1572603623od_a_a] : ( member2057358096od_a_a @ A @ top_to52711959od_a_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(306,axiom,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a > product_prod_a_a] :
( ( member2057358096od_a_a @ A @ B )
=> ( member449909584od_a_a @ ( C @ A ) @ ( image_734753285od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_imageI) ).
thf(1332,plain,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a > product_prod_a_a] :
( ( member2057358096od_a_a @ A @ B )
=> ( member449909584od_a_a @ ( C @ A ) @ ( image_734753285od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(233,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_290_image__subsetI) ).
thf(1090,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)],[233]) ).
thf(37,axiom,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: set_Pr1948701895od_a_a] :
( ( member2057358096od_a_a @ A @ ( minus_1034916142od_a_a @ B @ C ) )
=> ~ ( ( member2057358096od_a_a @ A @ B )
=> ( member2057358096od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_DiffE) ).
thf(445,plain,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: set_Pr1948701895od_a_a] :
( ( member2057358096od_a_a @ A @ ( minus_1034916142od_a_a @ B @ C ) )
=> ~ ( ( member2057358096od_a_a @ A @ B )
=> ( member2057358096od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(185,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_49_old_Oprod_Oinducts) ).
thf(936,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)],[185]) ).
thf(286,axiom,
! [A: a,B: a,C: set_a,D: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( product_Sigma_a_a @ C @ D ) )
=> ( member_a @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_SigmaD1) ).
thf(1271,plain,
! [A: a,B: a,C: set_a,D: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( product_Sigma_a_a @ C @ D ) )
=> ( member_a @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(318,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_85_pair__in__swap__image) ).
thf(1371,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)],[318]) ).
thf(117,axiom,
! [A: produc1921647824od_a_a,B: produc1921647824od_a_a,C: produc1921647824od_a_a,D: produc1921647824od_a_a] :
( ( ( produc563767703od_a_a @ A @ B )
= ( produc563767703od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_old_Oprod_Oinject) ).
thf(713,plain,
! [A: produc1921647824od_a_a,B: produc1921647824od_a_a,C: produc1921647824od_a_a,D: produc1921647824od_a_a] :
( ( ( produc563767703od_a_a @ A @ B )
= ( produc563767703od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(53,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_95_Collect__mem__eq) ).
thf(498,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)],[53]) ).
thf(180,axiom,
! [A: a,B: product_prod_a_a,C: set_a,D: a > set_Product_prod_a_a] :
( ( member160619001od_a_a @ ( produc1299253312od_a_a @ A @ B ) @ ( produc520147185od_a_a @ C @ D ) )
= ( ( member_a @ A @ C )
& ( member449909584od_a_a @ B @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_mem__Sigma__iff) ).
thf(919,plain,
! [A: a,B: product_prod_a_a,C: set_a,D: a > set_Product_prod_a_a] :
( ( member160619001od_a_a @ ( produc1299253312od_a_a @ A @ B ) @ ( produc520147185od_a_a @ C @ D ) )
= ( ( member_a @ A @ C )
& ( member449909584od_a_a @ B @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(146,axiom,
! [A: a,B: product_prod_a_a,C: a,D: product_prod_a_a] :
( ( ( produc1299253312od_a_a @ A @ B )
= ( produc1299253312od_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_Pair__inject) ).
thf(804,plain,
! [A: a,B: product_prod_a_a,C: a,D: product_prod_a_a] :
( ( ( produc1299253312od_a_a @ A @ B )
= ( produc1299253312od_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(25,axiom,
! [A: produc1572603623od_a_a,B: produc1572603623od_a_a > produc1572603623od_a_a,C: produc1572603623od_a_a,D: set_Pr1948701895od_a_a] :
( ( A
= ( B @ C ) )
=> ( ( member2057358096od_a_a @ C @ D )
=> ( member2057358096od_a_a @ A @ ( image_236793797od_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_image__eqI) ).
thf(406,plain,
! [A: produc1572603623od_a_a,B: produc1572603623od_a_a > produc1572603623od_a_a,C: produc1572603623od_a_a,D: set_Pr1948701895od_a_a] :
( ( A
= ( B @ C ) )
=> ( ( member2057358096od_a_a @ C @ D )
=> ( member2057358096od_a_a @ A @ ( image_236793797od_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(108,axiom,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: set_Pr1948701895od_a_a,D: produc1572603623od_a_a > $o] :
( ( member2057358096od_a_a @ A @ B )
=> ( ( ord_le456379495od_a_a @ B
@ ( collec1635618130od_a_a
@ ^ [E: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_prop__restrict) ).
thf(681,plain,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: set_Pr1948701895od_a_a,D: produc1572603623od_a_a > $o] :
( ( member2057358096od_a_a @ A @ B )
=> ( ( ord_le456379495od_a_a @ B
@ ( collec1635618130od_a_a
@ ^ [E: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(290,axiom,
! [A: a,B: a] :
( ( product_fst_a_a @ ( product_Pair_a_a @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_fst__conv) ).
thf(1282,plain,
! [A: a,B: a] :
( ( product_fst_a_a @ ( product_Pair_a_a @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(125,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
=> ~ ( member_a @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_DiffD2) ).
thf(736,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
=> ~ ( member_a @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(312,axiom,
( prefer477097315od_a_a
= ( ^ [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Pr1948701895od_a_a] :
( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
& ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_at__least__as__good__def) ).
thf(1349,plain,
( prefer477097315od_a_a
= ( ^ [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Pr1948701895od_a_a] :
( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
& ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(249,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_217_BNF__Greatest__Fixpoint_Osubst__Pair) ).
thf(1144,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)],[249]) ).
thf(243,axiom,
! [A: produc47586087od_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a > set_Product_prod_a_a] :
( ( member1545452880od_a_a @ A @ ( produc197318472od_a_a @ B @ C ) )
=> ~ ! [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ B )
=> ! [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ ( C @ D ) )
=> ( A
!= ( produc524982679od_a_a @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_SigmaE) ).
thf(1122,plain,
! [A: produc47586087od_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a > set_Product_prod_a_a] :
( ( member1545452880od_a_a @ A @ ( produc197318472od_a_a @ B @ C ) )
=> ~ ! [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ B )
=> ! [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ ( C @ D ) )
=> ( A
!= ( produc524982679od_a_a @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(82,axiom,
! [A: produc1572603623od_a_a,B: product_prod_a_a > product_prod_a_a,C: product_prod_a_a > product_prod_a_a,D: set_Pr1948701895od_a_a] :
( ( member2057358096od_a_a @ A @ ( image_236793797od_a_a @ ( produc1779756150od_a_a @ B @ C ) @ D ) )
=> ~ ! [E: product_prod_a_a,F: product_prod_a_a] :
( ( A
= ( produc1474507607od_a_a @ ( B @ E ) @ ( C @ F ) ) )
=> ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ E @ F ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_prod__fun__imageE) ).
thf(599,plain,
! [A: produc1572603623od_a_a,B: product_prod_a_a > product_prod_a_a,C: product_prod_a_a > product_prod_a_a,D: set_Pr1948701895od_a_a] :
( ( member2057358096od_a_a @ A @ ( image_236793797od_a_a @ ( produc1779756150od_a_a @ B @ C ) @ D ) )
=> ~ ! [E: product_prod_a_a,F: product_prod_a_a] :
( ( A
= ( produc1474507607od_a_a @ ( B @ E ) @ ( C @ F ) ) )
=> ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ E @ F ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(165,axiom,
! [A: produc1016684094_a_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > set_a] :
( ( member1403138919_a_a_a @ A @ ( produc1282482655_a_a_a @ B @ C ) )
=> ~ ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
=> ! [E: a] :
( ( member_a @ E @ ( C @ D ) )
=> ( A
!= ( produc2061588782_a_a_a @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_SigmaE) ).
thf(863,plain,
! [A: produc1016684094_a_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > set_a] :
( ( member1403138919_a_a_a @ A @ ( produc1282482655_a_a_a @ B @ C ) )
=> ~ ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
=> ! [E: a] :
( ( member_a @ E @ ( C @ D ) )
=> ( A
!= ( produc2061588782_a_a_a @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(16,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_127_imageI) ).
thf(377,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)],[16]) ).
thf(202,axiom,
! [A: product_prod_a_a,B: produc1572603623od_a_a > product_prod_a_a,C: produc1572603623od_a_a,D: set_Pr1948701895od_a_a] :
( ( A
= ( B @ C ) )
=> ( ( member2057358096od_a_a @ C @ D )
=> ( member449909584od_a_a @ A @ ( image_734753285od_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_image__eqI) ).
thf(990,plain,
! [A: product_prod_a_a,B: produc1572603623od_a_a > product_prod_a_a,C: produc1572603623od_a_a,D: set_Pr1948701895od_a_a] :
( ( A
= ( B @ C ) )
=> ( ( member2057358096od_a_a @ C @ D )
=> ( member449909584od_a_a @ A @ ( image_734753285od_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(39,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_35_prod__cases) ).
thf(451,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)],[39]) ).
thf(75,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a,C: product_prod_a_a > $o,D: product_prod_a_a] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( produc2115494211od_a_a @ ( produc1474507607od_a_a @ B @ D ) ) )
& ( C @ ( produc368344197od_a_a @ ( produc1474507607od_a_a @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_conjI__realizer) ).
thf(567,plain,
! [A: product_prod_a_a > $o,B: product_prod_a_a,C: product_prod_a_a > $o,D: product_prod_a_a] :
( ( A @ B )
=> ( ( C @ D )
=> ( ( A @ ( produc2115494211od_a_a @ ( produc1474507607od_a_a @ B @ D ) ) )
& ( C @ ( produc368344197od_a_a @ ( produc1474507607od_a_a @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(56,axiom,
( minus_1034916142od_a_a
= ( ^ [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
( collec1635618130od_a_a
@ ( minus_107310383_a_a_o
@ ^ [C: produc1572603623od_a_a] : ( member2057358096od_a_a @ C @ A )
@ ^ [C: produc1572603623od_a_a] : ( member2057358096od_a_a @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_minus__set__def) ).
thf(509,plain,
( minus_1034916142od_a_a
= ( ^ [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
( collec1635618130od_a_a
@ ( minus_107310383_a_a_o
@ ^ [C: produc1572603623od_a_a] : ( member2057358096od_a_a @ C @ A )
@ ^ [C: produc1572603623od_a_a] : ( member2057358096od_a_a @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(34,axiom,
! [A: produc1683075710_a_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a > set_a] :
( ( member575366567_a_a_a @ A @ ( produc4724255_a_a_a @ B @ C ) )
=> ~ ! [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ B )
=> ! [E: a] :
( ( member_a @ E @ ( C @ D ) )
=> ( A
!= ( produc436797294_a_a_a @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_SigmaE) ).
thf(434,plain,
! [A: produc1683075710_a_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a > set_a] :
( ( member575366567_a_a_a @ A @ ( produc4724255_a_a_a @ B @ C ) )
=> ~ ! [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ B )
=> ! [E: a] :
( ( member_a @ E @ ( C @ D ) )
=> ( A
!= ( produc436797294_a_a_a @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(172,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ A
@ ( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_subset__Collect__iff) ).
thf(890,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ A
@ ( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(46,axiom,
! [A: set_Pr1948701895od_a_a,B: produc1572603623od_a_a > $o] :
( ord_le456379495od_a_a
@ ( collec1635618130od_a_a
@ ^ [C: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_Collect__restrict) ).
thf(477,plain,
! [A: set_Pr1948701895od_a_a,B: produc1572603623od_a_a > $o] :
( ord_le456379495od_a_a
@ ( collec1635618130od_a_a
@ ^ [C: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(147,axiom,
( top_to993969022_a_a_o
= ( ^ [A: product_prod_a_a,B: product_prod_a_a] : ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ top_to52711959od_a_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_top__empty__eq2) ).
thf(811,plain,
( top_to993969022_a_a_o
= ( ^ [A: product_prod_a_a,B: product_prod_a_a] : ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ top_to52711959od_a_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(230,axiom,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_subset__eq) ).
thf(1080,plain,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(133,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
=> ( member_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_DiffD1) ).
thf(758,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
=> ( member_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(6,axiom,
! [A: a,B: produc1572603623od_a_a,C: a,D: produc1572603623od_a_a] :
( ( ( produc1095491584od_a_a @ A @ B )
= ( produc1095491584od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_prod_Oinject) ).
thf(345,plain,
! [A: a,B: produc1572603623od_a_a,C: a,D: produc1572603623od_a_a] :
( ( ( produc1095491584od_a_a @ A @ B )
= ( produc1095491584od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(65,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Pr1948701895od_a_a,D: product_prod_a_a > product_prod_a_a,E: product_prod_a_a > product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ C )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( D @ A ) @ ( E @ B ) ) @ ( image_236793797od_a_a @ ( produc1779756150od_a_a @ D @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_map__prod__imageI) ).
thf(535,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Pr1948701895od_a_a,D: product_prod_a_a > product_prod_a_a,E: product_prod_a_a > product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ C )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( D @ A ) @ ( E @ B ) ) @ ( image_236793797od_a_a @ ( produc1779756150od_a_a @ D @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(149,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_subset__eq) ).
thf(816,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(253,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_201_prod_Ocollapse) ).
thf(1162,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)],[253]) ).
thf(48,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_less__eq__set__def) ).
thf(483,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(114,axiom,
! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
( ! [C: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ C @ A )
=> ( member2057358096od_a_a @ C @ B ) )
=> ( ord_le456379495od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_subsetI) ).
thf(700,plain,
! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
( ! [C: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ C @ A )
=> ( member2057358096od_a_a @ C @ B ) )
=> ( ord_le456379495od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(310,axiom,
! [A: a,B: a,C: set_a,D: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( product_Sigma_a_a @ C @ D ) )
=> ~ ( ( member_a @ A @ C )
=> ~ ( member_a @ B @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_SigmaE2) ).
thf(1344,plain,
! [A: a,B: a,C: set_a,D: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( product_Sigma_a_a @ C @ D ) )
=> ~ ( ( member_a @ A @ C )
=> ~ ( member_a @ B @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(136,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_59_curryI) ).
thf(769,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)],[136]) ).
thf(1,conjecture,
member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ pr,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ pr ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(330,plain,
~ ( member449909584od_a_a @ ( product_Pair_a_a @ z @ y ) @ pr ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(240,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_207_snd__eqD) ).
thf(1112,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)],[240]) ).
thf(250,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_117_rev__image__eqI) ).
thf(1149,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)],[250]) ).
thf(194,axiom,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_subset__iff) ).
thf(964,plain,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(187,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_90_mem__Collect__eq) ).
thf(943,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)],[187]) ).
thf(213,axiom,
( prefer436369274d_as_a
= ( ^ [A: a,B: set_a,C: set_Product_prod_a_a] :
( collect_a
@ ^ [D: a] :
( ( member_a @ D @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ A @ D ) @ C )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_as__good__as__def) ).
thf(1022,plain,
( prefer436369274d_as_a
= ( ^ [A: a,B: set_a,C: set_Product_prod_a_a] :
( collect_a
@ ^ [D: a] :
( ( member_a @ D @ B )
& ( member449909584od_a_a @ ( product_Pair_a_a @ A @ D ) @ C )
& ( member449909584od_a_a @ ( product_Pair_a_a @ D @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(294,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_47_prod__cases3) ).
thf(1293,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)],[294]) ).
thf(104,axiom,
! [A: produc1921647824od_a_a,B: produc1921647824od_a_a,C: produc1921647824od_a_a,D: produc1921647824od_a_a] :
( ( ( produc563767703od_a_a @ A @ B )
= ( produc563767703od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_prod_Oinject) ).
thf(668,plain,
! [A: produc1921647824od_a_a,B: produc1921647824od_a_a,C: produc1921647824od_a_a,D: produc1921647824od_a_a] :
( ( ( produc563767703od_a_a @ A @ B )
= ( produc563767703od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(257,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > $o,D: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ! [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
& ( C @ E ) ) )
@ ( collec645855634od_a_a
@ ^ [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_subset__CollectI) ).
thf(1177,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > $o,D: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ! [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
& ( C @ E ) ) )
@ ( collec645855634od_a_a
@ ^ [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(321,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_123_imageI) ).
thf(1381,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)],[321]) ).
thf(60,axiom,
! [A: product_prod_a_a,B: produc1572603623od_a_a] :
( ( A
= ( produc2115494211od_a_a @ B ) )
= ( ? [C: product_prod_a_a] :
( B
= ( produc1474507607od_a_a @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_eq__fst__iff) ).
thf(521,plain,
! [A: product_prod_a_a,B: produc1572603623od_a_a] :
( ( A
= ( produc2115494211od_a_a @ B ) )
= ( ? [C: product_prod_a_a] :
( B
= ( produc1474507607od_a_a @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(23,axiom,
! [A: produc1572603623od_a_a,B: produc1572603623od_a_a > produc1572603623od_a_a,C: set_Pr1948701895od_a_a] :
( ( member2057358096od_a_a @ A @ ( image_236793797od_a_a @ B @ C ) )
=> ~ ! [D: produc1572603623od_a_a] :
( ( A
= ( B @ D ) )
=> ~ ( member2057358096od_a_a @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_imageE) ).
thf(399,plain,
! [A: produc1572603623od_a_a,B: produc1572603623od_a_a > produc1572603623od_a_a,C: set_Pr1948701895od_a_a] :
( ( member2057358096od_a_a @ A @ ( image_236793797od_a_a @ B @ C ) )
=> ~ ! [D: produc1572603623od_a_a] :
( ( A
= ( B @ D ) )
=> ~ ( member2057358096od_a_a @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(166,axiom,
! [A: produc1572603623od_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ A @ ( produc304751368od_a_a @ B @ C ) )
=> ~ ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
=> ! [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ ( C @ D ) )
=> ( A
!= ( produc1474507607od_a_a @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_SigmaE) ).
thf(868,plain,
! [A: produc1572603623od_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ A @ ( produc304751368od_a_a @ B @ C ) )
=> ~ ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
=> ! [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ ( C @ D ) )
=> ( A
!= ( produc1474507607od_a_a @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(140,axiom,
! [A: product_prod_a_a,B: produc1572603623od_a_a] :
( ( A
= ( produc368344197od_a_a @ B ) )
= ( ? [C: product_prod_a_a] :
( B
= ( produc1474507607od_a_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_eq__snd__iff) ).
thf(780,plain,
! [A: product_prod_a_a,B: produc1572603623od_a_a] :
( ( A
= ( produc368344197od_a_a @ B ) )
= ( ? [C: product_prod_a_a] :
( B
= ( produc1474507607od_a_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(169,axiom,
( prefer1498087410od_a_a
= ( ^ [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Pr1948701895od_a_a] :
( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
& ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_no__better__than__def) ).
thf(883,plain,
( prefer1498087410od_a_a
= ( ^ [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Pr1948701895od_a_a] :
( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
& ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(237,axiom,
! [A: produc1572603623od_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ A
@ ( produc304751368od_a_a @ B
@ ^ [D: product_prod_a_a] : C ) )
= ( ( member449909584od_a_a @ ( produc2115494211od_a_a @ A ) @ B )
& ( member449909584od_a_a @ ( produc368344197od_a_a @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_mem__Times__iff) ).
thf(1102,plain,
! [A: produc1572603623od_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ A
@ ( produc304751368od_a_a @ B
@ ^ [D: product_prod_a_a] : C ) )
= ( ( member449909584od_a_a @ ( produc2115494211od_a_a @ A ) @ B )
& ( member449909584od_a_a @ ( produc368344197od_a_a @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(33,axiom,
! [A: produc1572603623od_a_a,B: a,C: set_Pr1948701895od_a_a,D: produc1572603623od_a_a > set_a] :
( ( member575366567_a_a_a @ ( produc436797294_a_a_a @ A @ B ) @ ( produc4724255_a_a_a @ C @ D ) )
= ( ( member2057358096od_a_a @ A @ C )
& ( member_a @ B @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_mem__Sigma__iff) ).
thf(431,plain,
! [A: produc1572603623od_a_a,B: a,C: set_Pr1948701895od_a_a,D: produc1572603623od_a_a > set_a] :
( ( member575366567_a_a_a @ ( produc436797294_a_a_a @ A @ B ) @ ( produc4724255_a_a_a @ C @ D ) )
= ( ( member2057358096od_a_a @ A @ C )
& ( member_a @ B @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(181,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_60_preference_Oindiff__trans) ).
thf(922,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)],[181]) ).
thf(267,axiom,
! [A: product_prod_a_a,B: set_a,C: set_a] :
( ( member449909584od_a_a @ A @ ( product_product_a_a @ B @ C ) )
= ( member449909584od_a_a @ A
@ ( product_Sigma_a_a @ B
@ ^ [D: a] : C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_member__product) ).
thf(1213,plain,
! [A: product_prod_a_a,B: set_a,C: set_a] :
( ( member449909584od_a_a @ A @ ( product_product_a_a @ B @ C ) )
= ( member449909584od_a_a @ A
@ ( product_Sigma_a_a @ B
@ ^ [D: a] : C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(153,axiom,
! [A: produc1016684094_a_a_a] :
? [B: product_prod_a_a,C: a] :
( A
= ( produc2061588782_a_a_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_surj__pair) ).
thf(827,plain,
! [A: produc1016684094_a_a_a] :
? [B: product_prod_a_a,C: a] :
( A
= ( produc2061588782_a_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(219,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_287_image__subsetI) ).
thf(1044,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)],[219]) ).
thf(112,axiom,
! [A: produc1016684094_a_a_a,B: produc1016684094_a_a_a,C: set_Pr1689873822_a_a_a,D: set_Pr729215751_a_a_a] :
( ( member1403138919_a_a_a @ A @ ( prefer1944486522_a_a_a @ B @ C @ D ) )
=> ( member470802768_a_a_a @ ( produc2054708503_a_a_a @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_at__lst__asgd__ge) ).
thf(695,plain,
! [A: produc1016684094_a_a_a,B: produc1016684094_a_a_a,C: set_Pr1689873822_a_a_a,D: set_Pr729215751_a_a_a] :
( ( member1403138919_a_a_a @ A @ ( prefer1944486522_a_a_a @ B @ C @ D ) )
=> ( member470802768_a_a_a @ ( produc2054708503_a_a_a @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(277,axiom,
! [A: a,B: a,C: set_Product_prod_a_a,D: a > product_prod_a_a,E: a > product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ C )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( D @ A ) @ ( E @ B ) ) @ ( image_1765377413od_a_a @ ( produc2012818120od_a_a @ D @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_map__prod__imageI) ).
thf(1245,plain,
! [A: a,B: a,C: set_Product_prod_a_a,D: a > product_prod_a_a,E: a > product_prod_a_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ C )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ ( D @ A ) @ ( E @ B ) ) @ ( image_1765377413od_a_a @ ( produc2012818120od_a_a @ D @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(103,axiom,
! [A: product_prod_a_a > product_prod_a_a > $o,B: product_prod_a_a,C: product_prod_a_a,D: produc1572603623od_a_a] :
( ( A @ B @ C )
=> ( ( D
= ( produc1474507607od_a_a @ B @ C ) )
=> ( A @ ( produc2115494211od_a_a @ D ) @ ( produc368344197od_a_a @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_BNF__Greatest__Fixpoint_Osubst__Pair) ).
thf(663,plain,
! [A: product_prod_a_a > product_prod_a_a > $o,B: product_prod_a_a,C: product_prod_a_a,D: produc1572603623od_a_a] :
( ( A @ B @ C )
=> ( ( D
= ( produc1474507607od_a_a @ B @ C ) )
=> ( A @ ( produc2115494211od_a_a @ D ) @ ( produc368344197od_a_a @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(88,axiom,
( top_top_a_o
= ( ^ [A: a] : ( member_a @ A @ top_top_set_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_top__empty__eq) ).
thf(617,plain,
( top_top_a_o
= ( ^ [A: a] : ( member_a @ A @ top_top_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(186,axiom,
! [A: produc1572603623od_a_a,B: a > product_prod_a_a,C: a > product_prod_a_a,D: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ A @ ( image_1765377413od_a_a @ ( produc2012818120od_a_a @ B @ C ) @ D ) )
=> ~ ! [E: a,F: a] :
( ( A
= ( produc1474507607od_a_a @ ( B @ E ) @ ( C @ F ) ) )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ E @ F ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_prod__fun__imageE) ).
thf(939,plain,
! [A: produc1572603623od_a_a,B: a > product_prod_a_a,C: a > product_prod_a_a,D: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ A @ ( image_1765377413od_a_a @ ( produc2012818120od_a_a @ B @ C ) @ D ) )
=> ~ ! [E: a,F: a] :
( ( A
= ( produc1474507607od_a_a @ ( B @ E ) @ ( C @ F ) ) )
=> ~ ( member449909584od_a_a @ ( product_Pair_a_a @ E @ F ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(212,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_187_fst__eqD) ).
thf(1018,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)],[212]) ).
thf(156,axiom,
! [A: product_prod_a_a > product_prod_a_a > $o,B: product_prod_a_a,C: product_prod_a_a] :
( ( A @ B @ C )
=> ( A @ ( produc368344197od_a_a @ ( produc1474507607od_a_a @ C @ B ) ) @ ( produc2115494211od_a_a @ ( produc1474507607od_a_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_exI__realizer) ).
thf(836,plain,
! [A: product_prod_a_a > product_prod_a_a > $o,B: product_prod_a_a,C: product_prod_a_a] :
( ( A @ B @ C )
=> ( A @ ( produc368344197od_a_a @ ( produc1474507607od_a_a @ C @ B ) ) @ ( produc2115494211od_a_a @ ( produc1474507607od_a_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(221,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_213_prod_Oexhaust__sel) ).
thf(1049,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)],[221]) ).
thf(97,axiom,
! [A: produc1921647824od_a_a,B: produc1921647824od_a_a,C: set_Pr681306928od_a_a,D: set_Pr231806599od_a_a] :
( ( member160619001od_a_a @ A @ ( prefer701966604od_a_a @ B @ C @ D ) )
=> ( member1361298640od_a_a @ ( produc563767703od_a_a @ A @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_at__lst__asgd__ge) ).
thf(640,plain,
! [A: produc1921647824od_a_a,B: produc1921647824od_a_a,C: set_Pr681306928od_a_a,D: set_Pr231806599od_a_a] :
( ( member160619001od_a_a @ A @ ( prefer701966604od_a_a @ B @ C @ D ) )
=> ( member1361298640od_a_a @ ( produc563767703od_a_a @ A @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(271,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_197_eq__fst__iff) ).
thf(1225,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)],[271]) ).
thf(236,axiom,
! [A: product_prod_a_a,B: produc1572603623od_a_a > product_prod_a_a,C: set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ A @ ( image_734753285od_a_a @ B @ C ) )
=> ~ ! [D: produc1572603623od_a_a] :
( ( A
= ( B @ D ) )
=> ~ ( member2057358096od_a_a @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_imageE) ).
thf(1098,plain,
! [A: product_prod_a_a,B: produc1572603623od_a_a > product_prod_a_a,C: set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ A @ ( image_734753285od_a_a @ B @ C ) )
=> ~ ! [D: produc1572603623od_a_a] :
( ( A
= ( B @ D ) )
=> ~ ( member2057358096od_a_a @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(77,axiom,
( ord_le456379495od_a_a
= ( ^ [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
! [C: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ C @ A )
=> ( member2057358096od_a_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_subset__eq) ).
thf(580,plain,
( ord_le456379495od_a_a
= ( ^ [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
! [C: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ C @ A )
=> ( member2057358096od_a_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(162,axiom,
! [A: a,B: a,C: set_a,D: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( product_Sigma_a_a @ C @ D ) )
=> ( member_a @ B @ ( D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_SigmaD2) ).
thf(855,plain,
! [A: a,B: a,C: set_a,D: a > set_a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B ) @ ( product_Sigma_a_a @ C @ D ) )
=> ( member_a @ B @ ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(296,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_221_exI__realizer) ).
thf(1300,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)],[296]) ).
thf(3,axiom,
! [A: a,B: produc1572603623od_a_a,C: a,D: produc1572603623od_a_a] :
( ( ( produc1095491584od_a_a @ A @ B )
= ( produc1095491584od_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_Pair__inject) ).
thf(331,plain,
! [A: a,B: produc1572603623od_a_a,C: a,D: produc1572603623od_a_a] :
( ( ( produc1095491584od_a_a @ A @ B )
= ( produc1095491584od_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(79,axiom,
! [A: produc1572603623od_a_a,B: product_prod_a_a,C: product_prod_a_a] :
( ( A
= ( produc1474507607od_a_a @ B @ C ) )
=> ( ( produc2115494211od_a_a @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_fstI) ).
thf(585,plain,
! [A: produc1572603623od_a_a,B: product_prod_a_a,C: product_prod_a_a] :
( ( A
= ( produc1474507607od_a_a @ B @ C ) )
=> ( ( produc2115494211od_a_a @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(283,axiom,
! [A: product_prod_a_a,B: set_a,C: set_a] :
( ( member449909584od_a_a @ A
@ ( product_Sigma_a_a @ B
@ ^ [D: a] : C ) )
= ( ( member_a @ ( product_fst_a_a @ A ) @ B )
& ( member_a @ ( product_snd_a_a @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_mem__Times__iff) ).
thf(1262,plain,
! [A: product_prod_a_a,B: set_a,C: set_a] :
( ( member449909584od_a_a @ A
@ ( product_Sigma_a_a @ B
@ ^ [D: a] : C ) )
= ( ( member_a @ ( product_fst_a_a @ A ) @ B )
& ( member_a @ ( product_snd_a_a @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(302,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_205_sndI) ).
thf(1317,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)],[302]) ).
thf(4,axiom,
! [A: produc1555800720od_a_a > $o,B: produc1555800720od_a_a] :
( ! [C: a,D: produc1572603623od_a_a] : ( A @ ( produc1095491584od_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_prod__cases) ).
thf(338,plain,
! [A: produc1555800720od_a_a > $o,B: produc1555800720od_a_a] :
( ! [C: a,D: produc1572603623od_a_a] : ( A @ ( produc1095491584od_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
! [A: a] : ( member_a @ A @ top_top_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_UNIV__I) ).
thf(359,plain,
! [A: a] : ( member_a @ A @ top_top_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(245,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_36_prod__cases) ).
thf(1130,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)],[245]) ).
thf(291,axiom,
! [A: product_prod_a_a] : ( member449909584od_a_a @ A @ top_to398455383od_a_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_UNIV__I) ).
thf(1285,plain,
! [A: product_prod_a_a] : ( member449909584od_a_a @ A @ top_to398455383od_a_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(68,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_prod_Oinject) ).
thf(544,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)],[68]) ).
thf(176,axiom,
! [A: product_prod_a_a > a,B: set_Product_prod_a_a,C: a > $o] :
( ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ ( image_340790172_a_a_a @ A @ B ) )
& ( C @ D ) ) )
= ( image_340790172_a_a_a @ A
@ ( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_Compr__image__eq) ).
thf(907,plain,
! [A: product_prod_a_a > a,B: set_Product_prod_a_a,C: a > $o] :
( ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ ( image_340790172_a_a_a @ A @ B ) )
& ( C @ D ) ) )
= ( image_340790172_a_a_a @ A
@ ( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(128,axiom,
! [A: set_a,B: set_a,C: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ A
@ ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: a] :
( ( member_a @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_subset__Collect__iff) ).
thf(744,plain,
! [A: set_a,B: set_a,C: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ A
@ ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: a] :
( ( member_a @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(115,axiom,
! [A: product_prod_a_a,B: produc1572603623od_a_a,C: product_prod_a_a,D: produc1572603623od_a_a] :
( ( ( produc1555606807od_a_a @ A @ B )
= ( produc1555606807od_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_Pair__inject) ).
thf(703,plain,
! [A: product_prod_a_a,B: produc1572603623od_a_a,C: product_prod_a_a,D: produc1572603623od_a_a] :
( ( ( produc1555606807od_a_a @ A @ B )
= ( produc1555606807od_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(314,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ ( produc304751368od_a_a @ C @ D ) )
=> ( member449909584od_a_a @ B @ ( D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_SigmaD2) ).
thf(1353,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > set_Product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ ( produc304751368od_a_a @ C @ D ) )
=> ( member449909584od_a_a @ B @ ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(222,axiom,
( minus_1507102574od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( collec645855634od_a_a
@ ( minus_1797478127_a_a_o
@ ^ [C: product_prod_a_a] : ( member449909584od_a_a @ C @ A )
@ ^ [C: product_prod_a_a] : ( member449909584od_a_a @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_minus__set__def) ).
thf(1052,plain,
( minus_1507102574od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( collec645855634od_a_a
@ ( minus_1797478127_a_a_o
@ ^ [C: product_prod_a_a] : ( member449909584od_a_a @ C @ A )
@ ^ [C: product_prod_a_a] : ( member449909584od_a_a @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(122,axiom,
! [A: produc772425383od_a_a > $o,B: produc772425383od_a_a] :
( ! [C: product_prod_a_a,D: produc1572603623od_a_a] : ( A @ ( produc1555606807od_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_prod__cases) ).
thf(727,plain,
! [A: produc772425383od_a_a > $o,B: produc772425383od_a_a] :
( ! [C: product_prod_a_a,D: produc1572603623od_a_a] : ( A @ ( produc1555606807od_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(248,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_191_prod__fun__imageE) ).
thf(1140,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)],[248]) ).
thf(208,axiom,
! [A: set_Product_prod_a_a,B: product_prod_a_a > $o] :
( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_Collect__subset) ).
thf(1008,plain,
! [A: set_Product_prod_a_a,B: product_prod_a_a > $o] :
( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(86,axiom,
! [A: set_Pr1948701895od_a_a,B: produc1572603623od_a_a > $o] :
( ord_le456379495od_a_a
@ ( collec1635618130od_a_a
@ ^ [C: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_Collect__subset) ).
thf(612,plain,
! [A: set_Pr1948701895od_a_a,B: produc1572603623od_a_a > $o] :
( ord_le456379495od_a_a
@ ( collec1635618130od_a_a
@ ^ [C: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(164,axiom,
! [A: product_prod_a_a,B: product_prod_a_a > product_prod_a_a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( image_794773445od_a_a @ B @ C ) )
=> ~ ! [D: product_prod_a_a] :
( ( A
= ( B @ D ) )
=> ~ ( member449909584od_a_a @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_imageE) ).
thf(859,plain,
! [A: product_prod_a_a,B: product_prod_a_a > product_prod_a_a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( image_794773445od_a_a @ B @ C ) )
=> ~ ! [D: product_prod_a_a] :
( ( A
= ( B @ D ) )
=> ~ ( member449909584od_a_a @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(328,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_58_curryI) ).
thf(1404,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)],[328]) ).
thf(316,axiom,
! [A: a,B: a] :
( ( product_snd_a_a @ ( product_Pair_a_a @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_snd__conv) ).
thf(1358,plain,
! [A: a,B: a] :
( ( product_snd_a_a @ ( product_Pair_a_a @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(92,axiom,
! [A: produc1572603623od_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ A @ ( produc905674258od_a_a @ B @ C ) )
= ( member2057358096od_a_a @ A
@ ( produc304751368od_a_a @ B
@ ^ [D: product_prod_a_a] : C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_member__product) ).
thf(627,plain,
! [A: produc1572603623od_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( member2057358096od_a_a @ A @ ( produc905674258od_a_a @ B @ C ) )
= ( member2057358096od_a_a @ A
@ ( produc304751368od_a_a @ B
@ ^ [D: product_prod_a_a] : C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(72,axiom,
! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a > $o,D: produc1572603623od_a_a > $o] :
( ( ord_le456379495od_a_a @ A @ B )
=> ( ! [E: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_le456379495od_a_a
@ ( collec1635618130od_a_a
@ ^ [E: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ E @ A )
& ( C @ E ) ) )
@ ( collec1635618130od_a_a
@ ^ [E: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_subset__CollectI) ).
thf(556,plain,
! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a > $o,D: produc1572603623od_a_a > $o] :
( ( ord_le456379495od_a_a @ A @ B )
=> ( ! [E: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_le456379495od_a_a
@ ( collec1635618130od_a_a
@ ^ [E: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ E @ A )
& ( C @ E ) ) )
@ ( collec1635618130od_a_a
@ ^ [E: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(105,axiom,
! [A: a,B: set_a,C: a > produc1572603623od_a_a] :
( ( member_a @ A @ B )
=> ( member2057358096od_a_a @ ( C @ A ) @ ( image_1763923566od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_imageI) ).
thf(671,plain,
! [A: a,B: set_a,C: a > produc1572603623od_a_a] :
( ( member_a @ A @ B )
=> ( member2057358096od_a_a @ ( C @ A ) @ ( image_1763923566od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(303,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_in__mono) ).
thf(1321,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(61,axiom,
! [A: set_a,B: a > produc1572603623od_a_a,C: set_Pr1948701895od_a_a] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ( member2057358096od_a_a @ ( B @ D ) @ C ) )
=> ( ord_le456379495od_a_a @ ( image_1763923566od_a_a @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_image__subsetI) ).
thf(524,plain,
! [A: set_a,B: a > produc1572603623od_a_a,C: set_Pr1948701895od_a_a] :
( ! [D: a] :
( ( member_a @ D @ A )
=> ( member2057358096od_a_a @ ( B @ D ) @ C ) )
=> ( ord_le456379495od_a_a @ ( image_1763923566od_a_a @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(52,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_Collect__mem__eq) ).
thf(495,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(268,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ ( bNF_Gr1372473186od_a_a @ C @ D ) )
=> ( member449909584od_a_a @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_GrD1) ).
thf(1216,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > product_prod_a_a] :
( ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ B ) @ ( bNF_Gr1372473186od_a_a @ C @ D ) )
=> ( member449909584od_a_a @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(209,axiom,
! [A: produc47586087od_a_a,B: set_Pr1948701895od_a_a,C: set_Product_prod_a_a] :
( ( member1545452880od_a_a @ A
@ ( produc197318472od_a_a @ B
@ ^ [D: produc1572603623od_a_a] : C ) )
= ( ( member2057358096od_a_a @ ( produc745123715od_a_a @ A ) @ B )
& ( member449909584od_a_a @ ( produc24848069od_a_a @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_mem__Times__iff) ).
thf(1010,plain,
! [A: produc47586087od_a_a,B: set_Pr1948701895od_a_a,C: set_Product_prod_a_a] :
( ( member1545452880od_a_a @ A
@ ( produc197318472od_a_a @ B
@ ^ [D: produc1572603623od_a_a] : C ) )
= ( ( member2057358096od_a_a @ ( produc745123715od_a_a @ A ) @ B )
& ( member449909584od_a_a @ ( produc24848069od_a_a @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(137,axiom,
! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a] :
( ( ord_le456379495od_a_a @ A @ B )
=> ( ( member2057358096od_a_a @ C @ A )
=> ( member2057358096od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_in__mono) ).
thf(771,plain,
! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a] :
( ( ord_le456379495od_a_a @ A @ B )
=> ( ( member2057358096od_a_a @ C @ A )
=> ( member2057358096od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(14,axiom,
! [A: a,B: a > a,C: set_a] :
( ( member_a @ A @ ( image_a_a @ B @ C ) )
=> ~ ! [D: a] :
( ( A
= ( B @ D ) )
=> ~ ( member_a @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_imageE) ).
thf(368,plain,
! [A: a,B: a > a,C: set_a] :
( ( member_a @ A @ ( image_a_a @ B @ C ) )
=> ~ ! [D: a] :
( ( A
= ( B @ D ) )
=> ~ ( member_a @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(159,axiom,
! [A: produc1921647824od_a_a] :
? [B: a,C: product_prod_a_a] :
( A
= ( produc1299253312od_a_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_surj__pair) ).
thf(844,plain,
! [A: produc1921647824od_a_a] :
? [B: a,C: product_prod_a_a] :
( A
= ( produc1299253312od_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(288,axiom,
! [A: a,B: set_a,C: a,D: a > set_a] :
( ( member_a @ A @ B )
=> ( ( member_a @ C @ ( D @ A ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ ( product_Sigma_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_SigmaI) ).
thf(1276,plain,
! [A: a,B: set_a,C: a,D: a > set_a] :
( ( member_a @ A @ B )
=> ( ( member_a @ C @ ( D @ A ) )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ C ) @ ( product_Sigma_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(225,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_63_preference_Onot__outside) ).
thf(1062,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)],[225]) ).
thf(188,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_8_at__lst__asgd__ge) ).
thf(946,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)],[188]) ).
thf(203,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( minus_1507102574od_a_a @ B @ C ) )
=> ~ ( member449909584od_a_a @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_DiffD2) ).
thf(995,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( minus_1507102574od_a_a @ B @ C ) )
=> ~ ( member449909584od_a_a @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(193,axiom,
! [A: product_prod_a_a,B: produc1572603623od_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > set_Pr1948701895od_a_a] :
( ( member122808528od_a_a @ ( produc1555606807od_a_a @ A @ B ) @ ( produc1227942600od_a_a @ C @ D ) )
=> ~ ( ( member449909584od_a_a @ A @ C )
=> ~ ( member2057358096od_a_a @ B @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_SigmaE2) ).
thf(961,plain,
! [A: product_prod_a_a,B: produc1572603623od_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > set_Pr1948701895od_a_a] :
( ( member122808528od_a_a @ ( produc1555606807od_a_a @ A @ B ) @ ( produc1227942600od_a_a @ C @ D ) )
=> ~ ( ( member449909584od_a_a @ A @ C )
=> ~ ( member2057358096od_a_a @ B @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(148,axiom,
! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a] :
( ( ord_le456379495od_a_a @ A @ B )
=> ( ( member2057358096od_a_a @ C @ A )
=> ( member2057358096od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_subsetD) ).
thf(813,plain,
! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a] :
( ( ord_le456379495od_a_a @ A @ B )
=> ( ( member2057358096od_a_a @ C @ A )
=> ( member2057358096od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(309,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( minus_1507102574od_a_a @ B @ C ) )
=> ( member449909584od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_DiffD1) ).
thf(1341,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( minus_1507102574od_a_a @ B @ C ) )
=> ( member449909584od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(129,axiom,
! [A: produc1555800720od_a_a,B: set_a,C: set_Pr1948701895od_a_a] :
( ( member448091577od_a_a @ A
@ ( produc663418545od_a_a @ B
@ ^ [D: a] : C ) )
= ( ( member_a @ ( produc530563564od_a_a @ A ) @ B )
& ( member2057358096od_a_a @ ( produc921029422od_a_a @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_mem__Times__iff) ).
thf(748,plain,
! [A: produc1555800720od_a_a,B: set_a,C: set_Pr1948701895od_a_a] :
( ( member448091577od_a_a @ A
@ ( produc663418545od_a_a @ B
@ ^ [D: a] : C ) )
= ( ( member_a @ ( produc530563564od_a_a @ A ) @ B )
& ( member2057358096od_a_a @ ( produc921029422od_a_a @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(100,axiom,
! [A: produc2010915495od_a_a] :
? [B: produc1921647824od_a_a,C: produc1921647824od_a_a] :
( A
= ( produc563767703od_a_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_surj__pair) ).
thf(652,plain,
! [A: produc2010915495od_a_a] :
? [B: produc1921647824od_a_a,C: produc1921647824od_a_a] :
( A
= ( produc563767703od_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(8,axiom,
! [A: a,B: produc1572603623od_a_a,C: a,D: produc1572603623od_a_a] :
( ( ( produc1095491584od_a_a @ A @ B )
= ( produc1095491584od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_old_Oprod_Oinject) ).
thf(351,plain,
! [A: a,B: produc1572603623od_a_a,C: a,D: produc1572603623od_a_a] :
( ( ( produc1095491584od_a_a @ A @ B )
= ( produc1095491584od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(28,axiom,
! [A: produc1572603623od_a_a] : ( member2057358096od_a_a @ A @ top_to52711959od_a_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_iso__tuple__UNIV__I) ).
thf(418,plain,
! [A: produc1572603623od_a_a] : ( member2057358096od_a_a @ A @ top_to52711959od_a_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(142,axiom,
! [A: product_prod_a_a,B: product_prod_a_a,C: product_prod_a_a] :
( ( ( produc368344197od_a_a @ ( produc1474507607od_a_a @ A @ B ) )
= C )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_snd__eqD) ).
thf(786,plain,
! [A: product_prod_a_a,B: product_prod_a_a,C: product_prod_a_a] :
( ( ( produc368344197od_a_a @ ( produc1474507607od_a_a @ A @ B ) )
= C )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(215,axiom,
member_a @ z @ ( prefer161218362good_a @ y @ b @ pr ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms) ).
thf(1030,plain,
member_a @ z @ ( prefer161218362good_a @ y @ b @ pr ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(178,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_296_subrelI) ).
thf(914,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)],[178]) ).
thf(183,axiom,
! [A: a,B: product_prod_a_a > a,C: product_prod_a_a,D: a,E: product_prod_a_a > a,F: set_Product_prod_a_a] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member449909584od_a_a @ C @ F )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ D ) @ ( bNF_Gr1853143117_a_a_a @ F @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_image2__eqI) ).
thf(929,plain,
! [A: a,B: product_prod_a_a > a,C: product_prod_a_a,D: a,E: product_prod_a_a > a,F: set_Product_prod_a_a] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member449909584od_a_a @ C @ F )
=> ( member449909584od_a_a @ ( product_Pair_a_a @ A @ D ) @ ( bNF_Gr1853143117_a_a_a @ F @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(299,axiom,
! [A: product_prod_a_a,B: a,C: set_Product_prod_a_a,D: product_prod_a_a > set_a] :
( ( member1403138919_a_a_a @ ( produc2061588782_a_a_a @ A @ B ) @ ( produc1282482655_a_a_a @ C @ D ) )
=> ~ ( ( member449909584od_a_a @ A @ C )
=> ~ ( member_a @ B @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_SigmaE2) ).
thf(1308,plain,
! [A: product_prod_a_a,B: a,C: set_Product_prod_a_a,D: product_prod_a_a > set_a] :
( ( member1403138919_a_a_a @ ( produc2061588782_a_a_a @ A @ B ) @ ( produc1282482655_a_a_a @ C @ D ) )
=> ~ ( ( member449909584od_a_a @ A @ C )
=> ~ ( member_a @ B @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(261,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1347718902_a_a_o
@ ^ [C: product_prod_a_a] : ( member449909584od_a_a @ C @ A )
@ ^ [C: product_prod_a_a] : ( member449909584od_a_a @ C @ B ) )
= ( ord_le1824328871od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_pred__subset__eq) ).
thf(1193,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1347718902_a_a_o
@ ^ [C: product_prod_a_a] : ( member449909584od_a_a @ C @ A )
@ ^ [C: product_prod_a_a] : ( member449909584od_a_a @ C @ B ) )
= ( ord_le1824328871od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(18,axiom,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a,D: produc1572603623od_a_a > produc1572603623od_a_a] :
( ( member2057358096od_a_a @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member2057358096od_a_a @ C @ ( image_236793797od_a_a @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_rev__image__eqI) ).
thf(383,plain,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a,D: produc1572603623od_a_a > produc1572603623od_a_a] :
( ( member2057358096od_a_a @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member2057358096od_a_a @ C @ ( image_236793797od_a_a @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(174,axiom,
! [A: set_Product_prod_a_a,B: product_prod_a_a,C: set_Pr1948701895od_a_a] :
( ( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
& ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ B ) @ C )
& ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ D ) @ C ) ) )
= ( minus_1507102574od_a_a @ ( prefer477097315od_a_a @ B @ A @ C ) @ ( prefer74720675od_a_a @ B @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_strict__contour__is__diff) ).
thf(899,plain,
! [A: set_Product_prod_a_a,B: product_prod_a_a,C: set_Pr1948701895od_a_a] :
( ( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
& ( member2057358096od_a_a @ ( produc1474507607od_a_a @ D @ B ) @ C )
& ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ B @ D ) @ C ) ) )
= ( minus_1507102574od_a_a @ ( prefer477097315od_a_a @ B @ A @ C ) @ ( prefer74720675od_a_a @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(109,axiom,
! [A: a,B: set_a,C: set_a,D: a > $o] :
( ( member_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_prop__restrict) ).
thf(684,plain,
! [A: a,B: set_a,C: set_a,D: a > $o] :
( ( member_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(118,axiom,
! [A: produc1572603623od_a_a > $o,B: product_prod_a_a,C: product_prod_a_a] :
( ( produc94438221_a_a_o @ A @ B @ C )
=> ( A @ ( produc1474507607od_a_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_curryE) ).
thf(716,plain,
! [A: produc1572603623od_a_a > $o,B: product_prod_a_a,C: product_prod_a_a] :
( ( produc94438221_a_a_o @ A @ B @ C )
=> ( A @ ( produc1474507607od_a_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(145,axiom,
! [A: produc1572603623od_a_a,B: a > produc1572603623od_a_a,C: set_a] :
( ( member2057358096od_a_a @ A @ ( image_1763923566od_a_a @ B @ C ) )
=> ~ ! [D: a] :
( ( A
= ( B @ D ) )
=> ~ ( member_a @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_imageE) ).
thf(800,plain,
! [A: produc1572603623od_a_a,B: a > produc1572603623od_a_a,C: set_a] :
( ( member2057358096od_a_a @ A @ ( image_1763923566od_a_a @ B @ C ) )
=> ~ ! [D: a] :
( ( A
= ( B @ D ) )
=> ~ ( member_a @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(241,axiom,
! [A: produc1572603623od_a_a > product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a > $o] :
( ( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ ( image_734753285od_a_a @ A @ B ) )
& ( C @ D ) ) )
= ( image_734753285od_a_a @ A
@ ( collec1635618130od_a_a
@ ^ [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_Compr__image__eq) ).
thf(1116,plain,
! [A: produc1572603623od_a_a > product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_prod_a_a > $o] :
( ( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ ( image_734753285od_a_a @ A @ B ) )
& ( C @ D ) ) )
= ( image_734753285od_a_a @ A
@ ( collec1635618130od_a_a
@ ^ [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(246,axiom,
! [A: product_prod_a_a,B: product_prod_a_a > a,C: product_prod_a_a > a,D: set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ A @ ( image_734753285od_a_a @ ( produc363290532_a_a_a @ B @ C ) @ D ) )
=> ~ ! [E: product_prod_a_a,F: product_prod_a_a] :
( ( A
= ( product_Pair_a_a @ ( B @ E ) @ ( C @ F ) ) )
=> ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ E @ F ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_prod__fun__imageE) ).
thf(1133,plain,
! [A: product_prod_a_a,B: product_prod_a_a > a,C: product_prod_a_a > a,D: set_Pr1948701895od_a_a] :
( ( member449909584od_a_a @ A @ ( image_734753285od_a_a @ ( produc363290532_a_a_a @ B @ C ) @ D ) )
=> ~ ! [E: product_prod_a_a,F: product_prod_a_a] :
( ( A
= ( product_Pair_a_a @ ( B @ E ) @ ( C @ F ) ) )
=> ~ ( member2057358096od_a_a @ ( produc1474507607od_a_a @ E @ F ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(205,axiom,
! [A: a,B: product_prod_a_a,C: set_a,D: a > set_Product_prod_a_a] :
( ( member160619001od_a_a @ ( produc1299253312od_a_a @ A @ B ) @ ( produc520147185od_a_a @ C @ D ) )
=> ~ ( ( member_a @ A @ C )
=> ~ ( member449909584od_a_a @ B @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_SigmaE2) ).
thf(999,plain,
! [A: a,B: product_prod_a_a,C: set_a,D: a > set_Product_prod_a_a] :
( ( member160619001od_a_a @ ( produc1299253312od_a_a @ A @ B ) @ ( produc520147185od_a_a @ C @ D ) )
=> ~ ( ( member_a @ A @ C )
=> ~ ( member449909584od_a_a @ B @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(155,axiom,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( produc368344197od_a_a @ ( produc1474507607od_a_a @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_snd__conv) ).
thf(833,plain,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( produc368344197od_a_a @ ( produc1474507607od_a_a @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(150,axiom,
! [A: product_prod_a_a,B: produc1572603623od_a_a,C: product_prod_a_a,D: produc1572603623od_a_a] :
( ( ( produc1555606807od_a_a @ A @ B )
= ( produc1555606807od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_old_Oprod_Oinject) ).
thf(818,plain,
! [A: product_prod_a_a,B: produc1572603623od_a_a,C: product_prod_a_a,D: produc1572603623od_a_a] :
( ( ( produc1555606807od_a_a @ A @ B )
= ( produc1555606807od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(83,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_52_old_Oprod_Oexhaust) ).
thf(603,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)],[83]) ).
thf(30,axiom,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: set_Pr1948701895od_a_a] :
( ( member2057358096od_a_a @ A @ ( minus_1034916142od_a_a @ B @ C ) )
= ( ( member2057358096od_a_a @ A @ B )
& ~ ( member2057358096od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_Diff__iff) ).
thf(422,plain,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: set_Pr1948701895od_a_a] :
( ( member2057358096od_a_a @ A @ ( minus_1034916142od_a_a @ B @ C ) )
= ( ( member2057358096od_a_a @ A @ B )
& ~ ( member2057358096od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(278,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( minus_1507102574od_a_a @ B @ C ) )
=> ~ ( ( member449909584od_a_a @ A @ B )
=> ( member449909584od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_DiffE) ).
thf(1248,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ ( minus_1507102574od_a_a @ B @ C ) )
=> ~ ( ( member449909584od_a_a @ A @ B )
=> ( member449909584od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(143,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_42_Pair__inject) ).
thf(790,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)],[143]) ).
thf(74,axiom,
! [A: a,B: product_prod_a_a,C: a,D: product_prod_a_a] :
( ( ( produc1299253312od_a_a @ A @ B )
= ( produc1299253312od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_old_Oprod_Oinject) ).
thf(564,plain,
! [A: a,B: product_prod_a_a,C: a,D: product_prod_a_a] :
( ( ( produc1299253312od_a_a @ A @ B )
= ( produc1299253312od_a_a @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(301,axiom,
! [A: a > product_prod_a_a,B: set_a,C: product_prod_a_a > $o] :
( ( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ ( image_1725938350od_a_a @ A @ B ) )
& ( C @ D ) ) )
= ( image_1725938350od_a_a @ A
@ ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_Compr__image__eq) ).
thf(1314,plain,
! [A: a > product_prod_a_a,B: set_a,C: product_prod_a_a > $o] :
( ( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ ( image_1725938350od_a_a @ A @ B ) )
& ( C @ D ) ) )
= ( image_1725938350od_a_a @ A
@ ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(5,axiom,
! [A: produc1555800720od_a_a] :
~ ! [B: a,C: product_prod_a_a,D: product_prod_a_a] :
( A
!= ( produc1095491584od_a_a @ B @ ( produc1474507607od_a_a @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_prod__cases3) ).
thf(341,plain,
! [A: produc1555800720od_a_a] :
~ ! [B: a,C: product_prod_a_a,D: product_prod_a_a] :
( A
!= ( produc1095491584od_a_a @ B @ ( produc1474507607od_a_a @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(55,axiom,
! [A: produc1572603623od_a_a > a,B: set_Pr1948701895od_a_a,C: a > $o] :
( ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ ( image_1105229276_a_a_a @ A @ B ) )
& ( C @ D ) ) )
= ( image_1105229276_a_a_a @ A
@ ( collec1635618130od_a_a
@ ^ [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_Compr__image__eq) ).
thf(506,plain,
! [A: produc1572603623od_a_a > a,B: set_Pr1948701895od_a_a,C: a > $o] :
( ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ ( image_1105229276_a_a_a @ A @ B ) )
& ( C @ D ) ) )
= ( image_1105229276_a_a_a @ A
@ ( collec1635618130od_a_a
@ ^ [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(307,axiom,
! [A: product_prod_a_a,B: a,C: product_prod_a_a,D: a,E: set_Pr1948701895od_a_a,F: set_Product_prod_a_a] :
( ( member470802768_a_a_a @ ( produc2054708503_a_a_a @ ( produc2061588782_a_a_a @ A @ B ) @ ( produc2061588782_a_a_a @ C @ D ) ) @ ( lex_pr2084296006_a_a_a @ E @ F ) )
= ( ( member2057358096od_a_a @ ( produc1474507607od_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_230_in__lex__prod) ).
thf(1335,plain,
! [A: product_prod_a_a,B: a,C: product_prod_a_a,D: a,E: set_Pr1948701895od_a_a,F: set_Product_prod_a_a] :
( ( member470802768_a_a_a @ ( produc2054708503_a_a_a @ ( produc2061588782_a_a_a @ A @ B ) @ ( produc2061588782_a_a_a @ C @ D ) ) @ ( lex_pr2084296006_a_a_a @ E @ F ) )
= ( ( member2057358096od_a_a @ ( produc1474507607od_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)],[307]) ).
thf(45,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_pred__subset__eq) ).
thf(474,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(95,axiom,
! [A: produc2010915495od_a_a > $o,B: produc2010915495od_a_a] :
( ! [C: produc1921647824od_a_a,D: produc1921647824od_a_a] : ( A @ ( produc563767703od_a_a @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_prod__cases) ).
thf(635,plain,
! [A: produc2010915495od_a_a > $o,B: produc2010915495od_a_a] :
( ! [C: produc1921647824od_a_a,D: produc1921647824od_a_a] : ( A @ ( produc563767703od_a_a @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(226,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_93_Collect__mem__eq) ).
thf(1065,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)],[226]) ).
thf(254,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > $o] :
( ( member449909584od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B
@ ( collec645855634od_a_a
@ ^ [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_prop__restrict) ).
thf(1165,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > $o] :
( ( member449909584od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B
@ ( collec645855634od_a_a
@ ^ [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(191,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_124_imageI) ).
thf(955,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)],[191]) ).
thf(234,axiom,
! [A: product_prod_a_a > product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > $o] :
( ( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ ( image_794773445od_a_a @ A @ B ) )
& ( C @ D ) ) )
= ( image_794773445od_a_a @ A
@ ( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_Compr__image__eq) ).
thf(1093,plain,
! [A: product_prod_a_a > product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > $o] :
( ( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ ( image_794773445od_a_a @ A @ B ) )
& ( C @ D ) ) )
= ( image_794773445od_a_a @ A
@ ( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(127,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_61_preference_Oindiff__trans) ).
thf(740,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)],[127]) ).
thf(43,axiom,
! [A: product_prod_a_a,B: a,C: product_prod_a_a,D: a] :
( ( ( produc2061588782_a_a_a @ A @ B )
= ( produc2061588782_a_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_Pair__inject) ).
thf(464,plain,
! [A: product_prod_a_a,B: a,C: product_prod_a_a,D: a] :
( ( ( produc2061588782_a_a_a @ A @ B )
= ( produc2061588782_a_a_a @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(285,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_subsetI) ).
thf(1268,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(322,axiom,
? [A: product_prod_a_a] : ( member449909584od_a_a @ A @ top_to398455383od_a_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_UNIV__witness) ).
thf(1384,plain,
? [A: product_prod_a_a] : ( member449909584od_a_a @ A @ top_to398455383od_a_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(36,axiom,
! [A: produc1572603623od_a_a,B: a,C: set_Pr1948701895od_a_a,D: produc1572603623od_a_a > set_a] :
( ( member575366567_a_a_a @ ( produc436797294_a_a_a @ A @ B ) @ ( produc4724255_a_a_a @ C @ D ) )
=> ~ ( ( member2057358096od_a_a @ A @ C )
=> ~ ( member_a @ B @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_SigmaE2) ).
thf(442,plain,
! [A: produc1572603623od_a_a,B: a,C: set_Pr1948701895od_a_a,D: produc1572603623od_a_a > set_a] :
( ( member575366567_a_a_a @ ( produc436797294_a_a_a @ A @ B ) @ ( produc4724255_a_a_a @ C @ D ) )
=> ~ ( ( member2057358096od_a_a @ A @ C )
=> ~ ( member_a @ B @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(327,axiom,
! [A: produc1572603623od_a_a,B: product_prod_a_a > produc1572603623od_a_a,C: product_prod_a_a,D: set_Product_prod_a_a] :
( ( A
= ( B @ C ) )
=> ( ( member449909584od_a_a @ C @ D )
=> ( member2057358096od_a_a @ A @ ( image_1765377413od_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_image__eqI) ).
thf(1399,plain,
! [A: produc1572603623od_a_a,B: product_prod_a_a > produc1572603623od_a_a,C: product_prod_a_a,D: set_Product_prod_a_a] :
( ( A
= ( B @ C ) )
=> ( ( member449909584od_a_a @ C @ D )
=> ( member2057358096od_a_a @ A @ ( image_1765377413od_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(54,axiom,
! [A: product_prod_a_a,B: a > product_prod_a_a,C: a,D: product_prod_a_a,E: a > product_prod_a_a,F: set_a] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member_a @ C @ F )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ D ) @ ( bNF_Gr1715025636od_a_a @ F @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_image2__eqI) ).
thf(501,plain,
! [A: product_prod_a_a,B: a > product_prod_a_a,C: a,D: product_prod_a_a,E: a > product_prod_a_a,F: set_a] :
( ( A
= ( B @ C ) )
=> ( ( D
= ( E @ C ) )
=> ( ( member_a @ C @ F )
=> ( member2057358096od_a_a @ ( produc1474507607od_a_a @ A @ D ) @ ( bNF_Gr1715025636od_a_a @ F @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(84,axiom,
! [A: produc772425383od_a_a] :
? [B: product_prod_a_a,C: produc1572603623od_a_a] :
( A
= ( produc1555606807od_a_a @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_surj__pair) ).
thf(607,plain,
! [A: produc772425383od_a_a] :
? [B: product_prod_a_a,C: produc1572603623od_a_a] :
( A
= ( produc1555606807od_a_a @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(9,axiom,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: set_Pr1948701895od_a_a] :
( ( member2057358096od_a_a @ A @ ( minus_1034916142od_a_a @ B @ C ) )
=> ~ ( member2057358096od_a_a @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_DiffD2) ).
thf(354,plain,
! [A: produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: set_Pr1948701895od_a_a] :
( ( member2057358096od_a_a @ A @ ( minus_1034916142od_a_a @ B @ C ) )
=> ~ ( member2057358096od_a_a @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(264,axiom,
! [A: set_Product_prod_a_a] :
( ! [B: product_prod_a_a] : ( member449909584od_a_a @ B @ A )
=> ( top_to398455383od_a_a = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_UNIV__eq__I) ).
thf(1204,plain,
! [A: set_Product_prod_a_a] :
( ! [B: product_prod_a_a] : ( member449909584od_a_a @ B @ A )
=> ( top_to398455383od_a_a = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(40,axiom,
! [A: produc1572603623od_a_a > produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a > $o] :
( ( collec1635618130od_a_a
@ ^ [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ ( image_236793797od_a_a @ A @ B ) )
& ( C @ D ) ) )
= ( image_236793797od_a_a @ A
@ ( collec1635618130od_a_a
@ ^ [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_Compr__image__eq) ).
thf(454,plain,
! [A: produc1572603623od_a_a > produc1572603623od_a_a,B: set_Pr1948701895od_a_a,C: produc1572603623od_a_a > $o] :
( ( collec1635618130od_a_a
@ ^ [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ ( image_236793797od_a_a @ A @ B ) )
& ( C @ D ) ) )
= ( image_236793797od_a_a @ A
@ ( collec1635618130od_a_a
@ ^ [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(197,axiom,
! [A: set_Pr1948701895od_a_a,B: produc1572603623od_a_a > product_prod_a_a,C: set_Product_prod_a_a] :
( ! [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ A )
=> ( member449909584od_a_a @ ( B @ D ) @ C ) )
=> ( ord_le1824328871od_a_a @ ( image_734753285od_a_a @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_image__subsetI) ).
thf(972,plain,
! [A: set_Pr1948701895od_a_a,B: produc1572603623od_a_a > product_prod_a_a,C: set_Product_prod_a_a] :
( ! [D: produc1572603623od_a_a] :
( ( member2057358096od_a_a @ D @ A )
=> ( member449909584od_a_a @ ( B @ D ) @ C ) )
=> ( ord_le1824328871od_a_a @ ( image_734753285od_a_a @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(1409,plain,
$false,
inference(e,[status(thm)],[1024,1190,1168,1237,1031,777,479,1105,582,1005,1406,1068,873,614,730,1290,878,655,511,1305,597,1078,1137,533,797,538,1222,1196,1127,1391,841,885,1386,1265,1228,1254,724,1287,372,1279,934,542,619,838,917,751,902,638,1087,1013,448,969,1347,485,514,348,966,821,1302,756,1040,1109,766,687,1377,692,1394,396,1351,660,1242,527,1119,774,411,988,428,1201,380,439,678,761,1338,366,1311,1047,1057,1274,910,894,952,1355,1174,561,630,847,361,625,852,830,551,710,1159,461,493,1210,519,1259,948,1096,388,356,610,857,697,1234,980,403,783,420,471,1329,1082,488,1361,1182,1075,642,547,554,753,1016,1207,590,622,985,1297,738,1231,457,721,1002,1324,393,647,997,633,1054,1035,674,530,1185,926,718,888,1251,425,1374,733,1219,824,1154,975,1389,577,958,1256,413,391,1332,1090,445,936,1271,1371,713,498,919,804,406,681,1282,736,1349,1144,1122,599,863,377,990,451,567,509,434,890,477,811,1080,758,345,535,816,1162,483,700,1344,769,330,1112,1149,964,943,1022,1293,668,1177,1381,521,399,868,780,883,1102,431,922,1213,827,1044,695,1245,663,617,939,1018,836,1049,640,1225,1098,580,855,1300,331,585,1262,1317,338,359,1130,1285,544,907,744,703,1353,1052,727,1140,1008,612,859,1404,1358,627,556,671,1321,524,495,1216,1010,771,368,844,1276,1062,946,995,961,813,1341,748,652,351,418,786,1030,914,929,1308,1193,383,899,684,716,800,1116,1133,999,833,818,603,422,1248,790,564,1314,341,506,1335,474,635,1065,1165,955,1093,740,464,1268,1384,442,1399,501,607,354,1204,454,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP157^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n011.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 6 14:19:24 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.95/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.03/1.19 % [INFO] Parsing done (306ms).
% 2.03/1.20 % [INFO] Running in sequential loop mode.
% 2.82/1.42 % [INFO] eprover registered as external prover.
% 2.82/1.43 % [INFO] cvc4 registered as external prover.
% 2.82/1.43 % [INFO] Scanning for conjecture ...
% 3.13/1.54 % [INFO] Found a conjecture and 355 axioms. Running axiom selection ...
% 3.50/1.66 % [INFO] Axiom selection finished. Selected 327 axioms (removed 28 axioms).
% 4.17/1.85 % [INFO] Problem is higher-order (TPTP THF).
% 4.17/1.87 % [INFO] Type checking passed.
% 4.17/1.87 % [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 ...
% 17.61/5.23 % External prover 'e' found a proof!
% 17.61/5.23 % [INFO] Killing All external provers ...
% 17.61/5.24 % Time passed: 4688ms (effective reasoning time: 4035ms)
% 17.61/5.24 % 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)>
% 17.61/5.24 % Axioms used in derivation (327): fact_259_SigmaE2, fact_84_preference_Ointro, fact_192_prod__fun__imageE, fact_286_subsetI, fact_201_prod_Ocollapse, fact_214_prod_Oexhaust__sel, fact_111_minus__set__def, fact_86_pair__in__swap__image, fact_325_pred__subset__eq, fact_92_mem__Collect__eq, fact_298_subset__iff, fact_148_imageE, fact_134_DiffD2, fact_311_prop__restrict, fact_228_image2__eqI, fact_223_image2__eqI, fact_17_old_Oprod_Oinject, fact_25_surj__pair, fact_69_curryE, fact_262_SigmaD1, fact_183_map__prod__imageI, fact_56_ssubst__Pair__rhs, fact_109_Diff__iff, fact_65_swap__simp, fact_21_old_Oprod_Oinject, fact_295_image__subsetI, fact_221_exI__realizer, fact_335_GrD2, fact_211_surjective__pairing, fact_281_mem__Times__iff, fact_28_surj__pair, fact_36_prod__cases, fact_112_minus__set__def, fact_153_Compr__image__eq, fact_313_Collect__restrict, fact_120_rev__image__eqI, fact_226_image2__eqI, fact_299_subset__iff, fact_265_SigmaE, fact_287_image__subsetI, fact_256_SigmaE2, fact_125_imageI, fact_12_prod_Oinject, fact_49_old_Oprod_Oinducts, fact_48_prod__induct3, fact_274_mem__Times__iff, fact_296_subrelI, fact_101_image__eqI, fact_51_old_Oprod_Oexhaust, fact_346_equals0I, fact_238_mem__Sigma__iff, fact_263_SigmaD1, fact_269_SigmaE, fact_235_mem__Sigma__iff, fact_151_Compr__image__eq, fact_143_imageE, fact_266_SigmaE, fact_288_image__subsetI, fact_205_sndI, fact_186_top__empty__eq, fact_292_image__subsetI, fact_349_equals0D, fact_320_subset__Collect__iff, fact_224_image2__eqI, fact_330_less__eq__set__def, fact_129_imageI, fact_316_Collect__subset, fact_240_mem__Sigma__iff, fact_18_old_Oprod_Oinject, fact_246_SigmaI, fact_123_imageI, fact_159_set__diff__eq, fact_88_strict__contour__is__diff, fact_203_eq__snd__iff, fact_206_sndI, fact_326_pred__subset__eq, fact_30_prod__cases, fact_319_subset__Collect__iff, fact_191_prod__fun__imageE, fact_5_at__lst__asgd__ge, fact_58_curryI, fact_119_rev__image__eqI, fact_318_Collect__subset, fact_199_fstI, fact_310_prop__restrict, fact_76_as__good__as__def, fact_106_image__eqI, fact_312_prop__restrict, fact_93_Collect__mem__eq, fact_114_rev__image__eqI, fact_7_at__lst__asgd__ge, fact_121_rev__image__eqI, fact_3_at__lst__asgd__ge, fact_13_prod_Oinject, fact_172_iso__tuple__UNIV__I, fact_72_no__better__than__def, fact_133_DiffD2, fact_55_at__least__as__good__def, fact_35_prod__cases, fact_244_SigmaI, fact_304_subsetD, fact_251_SigmaE2, fact_152_Compr__image__eq, fact_140_DiffE, fact_89_strict__contour__is__diff, fact_323_subset__CollectI, fact_181_map__prod__imageI, fact_124_imageI, fact_343_ex__in__conv, fact_155_Compr__image__eq, fact_156_Compr__image__eq, fact_209_snd__conv, fact_46_prod__cases3, fact_301_subset__eq, fact_213_prod_Oexhaust__sel, fact_180_map__prod__imageI, fact_290_image__subsetI, fact_158_Compr__image__eq, fact_54_at__least__as__good__def, fact_293_image__subsetI, fact_305_subsetD, fact_161_set__diff__eq, fact_61_preference_Oindiff__trans, fact_166_UNIV__witness, fact_149_imageE, fact_188_fst__eqD, fact_122_rev__image__eqI, fact_170_UNIV__eq__I, fact_169_UNIV__eq__I, fact_189_fst__conv, fact_142_imageE, fact_204_eq__snd__iff, fact_241_mem__Sigma__iff, fact_302_subset__eq, fact_208_snd__eqD, fact_219_conjI__realizer, fact_29_surj__pair, fact_45_prod__cases3, fact_102_image__eqI, fact_268_SigmaE, fact_81_preference__def, fact_215_prod_Oswap__def, fact_210_snd__conv, fact_60_preference_Oindiff__trans, fact_254_SigmaE2, fact_285_subsetI, fact_277_mem__Times__iff, fact_98_DiffI, fact_47_prod__cases3, fact_194_prod__fun__imageE, fact_104_image__eqI, fact_105_image__eqI, fact_115_rev__image__eqI, fact_43_Pair__inject, fact_113_minus__set__def, fact_11_prod_Oinject, fact_195_top__empty__eq2, fact_234_mem__Sigma__iff, fact_127_imageI, fact_164_UNIV__I, fact_230_in__lex__prod, fact_327_pred__subset__eq, fact_136_DiffD1, fact_137_DiffD1, fact_52_old_Oprod_Oexhaust, fact_173_iso__tuple__UNIV__I, fact_212_surjective__pairing, fact_103_image__eqI, fact_303_subset__eq, fact_67_curryD, fact_321_subset__Collect__iff, fact_32_prod__cases, fact_135_DiffD1, fact_178_map__prod__simp, fact_233_mem__Sigma__iff, fact_222_exI__realizer, fact_255_SigmaE2, fact_284_subsetI, fact_83_preference_Ointro, fact_249_SigmaI, fact_261_SigmaD2, fact_324_subset__CollectI, fact_154_Compr__image__eq, fact_291_image__subsetI, fact_144_imageE, fact_99_image__eqI, fact_165_UNIV__witness, fact_329_less__eq__set__def, fact_66_swap__simp, fact_147_imageE, fact_80_preference__def, fact_116_rev__image__eqI, fact_334_GrD1, fact_243_SigmaI, fact_314_Collect__restrict, fact_308_in__mono, fact_34_prod__cases, fact_264_SigmaE, fact_26_surj__pair, fact_42_Pair__inject, fact_200_fstI, fact_260_SigmaD2, fact_27_surj__pair, fact_220_conjI__realizer, fact_73_no__better__than__def, fact_2_at__lst__asgd__ge, fact_50_old_Oprod_Oinducts, fact_184_top__empty__eq, fact_275_mem__Times__iff, fact_14_prod_Oinject, fact_282_member__product, fact_272_SigmaE, fact_97_DiffI, fact_130_imageI, fact_227_image2__eqI, fact_96_DiffI, fact_41_Pair__inject, fact_193_prod__fun__imageE, fact_332_pred__subset__eq2, fact_132_DiffD2, fact_177_map__prod__simp, fact_182_map__prod__imageI, fact_40_Pair__inject, fact_90_mem__Collect__eq, fact_95_Collect__mem__eq, fact_22_old_Oprod_Oinject, fact_131_imageI, fact_64_preference_Onot__outside, fact_16_old_Oprod_Oinject, fact_229_in__lex__prod, fact_141_imageE, fact_145_imageE, fact_75_as__good__as__def, fact_190_fst__conv, fact_237_mem__Sigma__iff, fact_70_curryE, fact_300_subset__iff, fact_171_iso__tuple__UNIV__I, fact_306_subsetD, fact_24_surj__pair, fact_139_DiffE, fact_118_rev__image__eqI, fact_197_eq__fst__iff, fact_352_emptyE, fact_94_Collect__mem__eq, fact_77_pred__equals__eq2, fact_160_set__diff__eq, fact_280_mem__Times__iff, fact_242_SigmaI, fact_207_snd__eqD, fact_317_Collect__subset, fact_337_all__not__in__conv, fact_108_Diff__iff, fact_340_empty__iff, fact_162_UNIV__I, fact_33_prod__cases, fact_59_curryI, fact_117_rev__image__eqI, fact_63_preference_Onot__outside, fact_294_image__subsetI, fact_15_prod_Oinject, fact_174_same__fstI, fact_283_member__product, fact_179_map__prod__simp, fact_252_SigmaE2, fact_271_SigmaE, fact_9_prod_Oinject, fact_328_less__eq__set__def, fact_38_Pair__inject, fact_168_UNIV__eq__I, fact_185_top__empty__eq, fact_39_Pair__inject, fact_336_GrD2, fact_253_SigmaE2, fact_297_subrelI, fact_146_imageE, fact_167_UNIV__witness, fact_107_image__eqI, fact_276_mem__Times__iff, fact_85_pair__in__swap__image, fact_20_old_Oprod_Oinject, fact_44_prod__cases3, fact_309_in__mono, fact_273_mem__Times__iff, fact_225_image2__eqI, fact_19_old_Oprod_Oinject, fact_247_SigmaI, fact_217_BNF__Greatest__Fixpoint_Osubst__Pair, fact_176_map__prod__simp, fact_110_Diff__iff, fact_198_eq__fst__iff, fact_68_curryD, fact_245_SigmaI, fact_267_SigmaE, fact_10_prod_Oinject, fact_236_mem__Sigma__iff, fact_322_subset__CollectI, fact_78_pred__equals__eq2, fact_218_BNF__Greatest__Fixpoint_Osubst__Pair, fact_37_Pair__inject, fact_23_surj__pair, fact_289_image__subsetI, fact_307_in__mono, fact_100_image__eqI, fact_91_mem__Collect__eq, fact_196_top__empty__eq2, fact_331_pred__subset__eq2, fact_187_fst__eqD, fact_150_Compr__image__eq, fact_0_assms, fact_333_GrD1, fact_216_prod_Oswap__def, fact_31_prod__cases, fact_250_SigmaI, fact_138_DiffE, fact_8_at__lst__asgd__ge, fact_202_prod_Ocollapse, fact_128_imageI, fact_232_in__lex__prod, fact_278_mem__Times__iff, fact_157_Compr__image__eq, fact_1_at__lst__asgd__ge, fact_258_SigmaE2, fact_57_ssubst__Pair__rhs, fact_315_Collect__restrict, fact_126_imageI, fact_163_UNIV__I
% 17.61/5.24 % No. of inferences in proof: 658
% 17.61/5.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4688 ms resp. 4035 ms w/o parsing
% 18.44/5.42 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.44/5.42 % [INFO] Killing All external provers ...
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