%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP176^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:07:03 AM UTC 2026
% Result : Theorem 19.36s 5.64s
% Output : Refutation 20.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 312
% Syntax : Number of formulae : 626 ( 351 unt; 0 typ; 0 def)
% Number of atoms : 1643 ( 715 equ; 6 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 4623 ( 212 ~; 29 |; 130 &;3730 @)
% ( 0 <=>; 522 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 30 ( 29 usr)
% Number of type conns : 114 ( 114 >; 0 *; 0 +; 0 <<)
% Number of symbols : 88 ( 84 usr; 13 con; 0-3 aty)
% Number of variables : 1613 ( 176 ^;1385 !; 52 ?;1613 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr2109276827od_b_b_type,type,
set_Pr2109276827od_b_b: $tType ).
thf(produc970027067od_b_b_type,type,
produc970027067od_b_b: $tType ).
thf(set_Pr1071216121od_b_b_type,type,
set_Pr1071216121od_b_b: $tType ).
thf(set_Pr2134561957od_b_b_type,type,
set_Pr2134561957od_b_b: $tType ).
thf(set_Pr1021918435od_b_b_type,type,
set_Pr1021918435od_b_b: $tType ).
thf(produc1052326083od_b_b_type,type,
produc1052326083od_b_b: $tType ).
thf(produc1990339951od_b_b_type,type,
produc1990339951od_b_b: $tType ).
thf(set_Pr2060523537od_b_b_type,type,
set_Pr2060523537od_b_b: $tType ).
thf(set_Pr1906739389_b_b_b_type,type,
set_Pr1906739389_b_b_b: $tType ).
thf(produc1605346267od_b_b_type,type,
produc1605346267od_b_b: $tType ).
thf(produc276146823_b_b_b_type,type,
produc276146823_b_b_b: $tType ).
thf(set_Pr306736955tant_a_type,type,
set_Pr306736955tant_a: $tType ).
thf(set_Pr1324126435od_b_b_type,type,
set_Pr1324126435od_b_b: $tType ).
thf(labele1835558936od_b_b_type,type,
labele1835558936od_b_b: $tType ).
thf(set_Pr2007082183od_b_b_type,type,
set_Pr2007082183od_b_b: $tType ).
thf(produc1367125253tant_a_type,type,
produc1367125253tant_a: $tType ).
thf(produc1213276845od_b_b_type,type,
produc1213276845od_b_b: $tType ).
thf(produc1168037607od_b_b_type,type,
produc1168037607od_b_b: $tType ).
thf(labele1159362096nt_a_b_type,type,
labele1159362096nt_a_b: $tType ).
thf(set_Pr621705391od_b_b_type,type,
set_Pr621705391od_b_b: $tType ).
thf(set_Pr357419743_b_b_b_type,type,
set_Pr357419743_b_b_b: $tType ).
thf(produc255402447od_b_b_type,type,
produc255402447od_b_b: $tType ).
thf(produc2112523263_b_b_b_type,type,
produc2112523263_b_b_b: $tType ).
thf(set_St761939237tant_a_type,type,
set_St761939237tant_a: $tType ).
thf(set_Product_prod_b_b_type,type,
set_Product_prod_b_b: $tType ).
thf(standard_Constant_a_type,type,
standard_Constant_a: $tType ).
thf(product_prod_b_b_type,type,
product_prod_b_b: $tType ).
thf(set_b_type,type,
set_b: $tType ).
thf(b_type,type,
b: $tType ).
thf(equiv_1629197578_set_b_decl,type,
equiv_1629197578_set_b: set_Pr2109276827od_b_b > set_Product_prod_b_b > ( produc1213276845od_b_b > b > set_b ) > $o ).
thf(equiv_1036235914_set_b_decl,type,
equiv_1036235914_set_b: set_Pr2007082183od_b_b > set_Product_prod_b_b > ( product_prod_b_b > b > set_b ) > $o ).
thf(equiv_167626658_set_b_decl,type,
equiv_167626658_set_b: set_Product_prod_b_b > set_Product_prod_b_b > ( b > b > set_b ) > $o ).
thf(equiv_1821124534_set_b_decl,type,
equiv_1821124534_set_b: set_Product_prod_b_b > ( b > set_b ) > $o ).
thf(equiv_2048442231od_b_b_decl,type,
equiv_2048442231od_b_b: set_Pr1324126435od_b_b > set_Pr2109276827od_b_b > $o ).
thf(equiv_1125628061od_b_b_decl,type,
equiv_1125628061od_b_b: set_Product_prod_b_b > set_Pr2007082183od_b_b > $o ).
thf(equiv_equiv_b_decl,type,
equiv_equiv_b: set_b > set_Product_prod_b_b > $o ).
thf(equiv_proj_b_b_decl,type,
equiv_proj_b_b: set_Product_prod_b_b > b > set_b ).
thf(hilber46179633od_b_b_decl,type,
hilber46179633od_b_b: ( produc1213276845od_b_b > $o ) > produc1213276845od_b_b ).
thf(hilber620807523od_b_b_decl,type,
hilber620807523od_b_b: ( product_prod_b_b > $o ) > product_prod_b_b ).
thf(hilbert_Eps_b_decl,type,
hilbert_Eps_b: ( b > $o ) > b ).
thf(if_b_decl,type,
if_b: $o > b > b > b ).
thf(standard_S_Idt_a_decl,type,
standard_S_Idt_a: standard_Constant_a ).
thf(getRel904497637nt_a_b_decl,type,
getRel904497637nt_a_b: standard_Constant_a > labele1159362096nt_a_b > set_Product_prod_b_b ).
thf(graph_792023598_b_b_b_decl,type,
graph_792023598_b_b_b: labele1835558936od_b_b > labele1159362096nt_a_b > set_Pr357419743_b_b_b > $o ).
thf(graph_222606102_a_b_b_decl,type,
graph_222606102_a_b_b: labele1159362096nt_a_b > labele1159362096nt_a_b > set_Product_prod_b_b > $o ).
thf(labele170595300od_b_b_decl,type,
labele170595300od_b_b: set_Pr1021918435od_b_b > set_Product_prod_b_b > labele1835558936od_b_b ).
thf(labele1230159100nt_a_b_decl,type,
labele1230159100nt_a_b: set_Pr1324126435od_b_b > set_b > labele1159362096nt_a_b ).
thf(labele377702064od_b_b_decl,type,
labele377702064od_b_b: ( set_Pr1324126435od_b_b > set_b > set_Pr1324126435od_b_b ) > labele1159362096nt_a_b > set_Pr1324126435od_b_b ).
thf(labele1287464530_set_b_decl,type,
labele1287464530_set_b: ( set_Pr1324126435od_b_b > set_b > set_b ) > labele1159362096nt_a_b > set_b ).
thf(labele1741081071nt_a_b_decl,type,
labele1741081071nt_a_b: labele1159362096nt_a_b > set_Pr1324126435od_b_b ).
thf(labele1424214014nt_a_b_decl,type,
labele1424214014nt_a_b: labele1159362096nt_a_b > set_b ).
thf(restri446606278nt_a_b_decl,type,
restri446606278nt_a_b: labele1159362096nt_a_b > labele1159362096nt_a_b ).
thf(order_653178932r_on_b_decl,type,
order_653178932r_on_b: set_b > set_Product_prod_b_b > $o ).
thf(bot_bo1734638456_b_b_o_decl,type,
bot_bo1734638456_b_b_o: standard_Constant_a > product_prod_b_b > $o ).
thf(bot_bo1167600078_b_b_o_decl,type,
bot_bo1167600078_b_b_o: produc1213276845od_b_b > $o ).
thf(bot_bo1302443370_b_b_o_decl,type,
bot_bo1302443370_b_b_o: product_prod_b_b > $o ).
thf(bot_bot_b_b_o_decl,type,
bot_bot_b_b_o: b > b > $o ).
thf(bot_bot_b_o_decl,type,
bot_bot_b_o: b > $o ).
thf(bot_bo1160111033tant_a_decl,type,
bot_bo1160111033tant_a: set_St761939237tant_a ).
thf(bot_bo1964903287od_b_b_decl,type,
bot_bo1964903287od_b_b: set_Pr1021918435od_b_b ).
thf(bot_bo1664927607od_b_b_decl,type,
bot_bo1664927607od_b_b: set_Pr1324126435od_b_b ).
thf(bot_bo1124087115_b_b_b_decl,type,
bot_bo1124087115_b_b_b: set_Pr357419743_b_b_b ).
thf(bot_bo1343651123od_b_b_decl,type,
bot_bo1343651123od_b_b: set_Product_prod_b_b ).
thf(bot_bot_set_b_decl,type,
bot_bot_set_b: set_b ).
thf(ord_le123089219od_b_b_decl,type,
ord_le123089219od_b_b: set_Pr1324126435od_b_b > set_Pr1324126435od_b_b > $o ).
thf(ord_le1036320359od_b_b_decl,type,
ord_le1036320359od_b_b: set_Product_prod_b_b > set_Product_prod_b_b > $o ).
thf(ord_less_eq_set_b_decl,type,
ord_less_eq_set_b: set_b > set_b > $o ).
thf(produc1432590431od_b_b_decl,type,
produc1432590431od_b_b: standard_Constant_a > product_prod_b_b > produc1213276845od_b_b ).
thf(produc1580777273_b_b_b_decl,type,
produc1580777273_b_b_b: produc1213276845od_b_b > b > produc276146823_b_b_b ).
thf(produc732676669od_b_b_decl,type,
produc732676669od_b_b: product_prod_b_b > produc1213276845od_b_b > produc1052326083od_b_b ).
thf(produc1001682799_b_b_b_decl,type,
produc1001682799_b_b_b: product_prod_b_b > b > produc2112523263_b_b_b ).
thf(produc800495189od_b_b_decl,type,
produc800495189od_b_b: b > produc1213276845od_b_b > produc1605346267od_b_b ).
thf(produc1257047359od_b_b_decl,type,
produc1257047359od_b_b: b > product_prod_b_b > produc255402447od_b_b ).
thf(product_Pair_b_b_decl,type,
product_Pair_b_b: b > b > product_prod_b_b ).
thf(image_1916422435od_b_b_decl,type,
image_1916422435od_b_b: set_Pr1324126435od_b_b > set_St761939237tant_a > set_Product_prod_b_b ).
thf(image_763305007od_b_b_decl,type,
image_763305007od_b_b: set_Pr2109276827od_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b ).
thf(image_1764625405_b_b_b_decl,type,
image_1764625405_b_b_b: set_Pr1906739389_b_b_b > set_Pr1324126435od_b_b > set_b ).
thf(image_532916993od_b_b_decl,type,
image_532916993od_b_b: set_Pr1071216121od_b_b > set_Product_prod_b_b > set_Pr1324126435od_b_b ).
thf(image_1928024979od_b_b_decl,type,
image_1928024979od_b_b: set_Pr2007082183od_b_b > set_Product_prod_b_b > set_Product_prod_b_b ).
thf(image_921732011_b_b_b_decl,type,
image_921732011_b_b_b: set_Pr357419743_b_b_b > set_Product_prod_b_b > set_b ).
thf(image_984343321od_b_b_decl,type,
image_984343321od_b_b: set_Pr2060523537od_b_b > set_b > set_Pr1324126435od_b_b ).
thf(image_1177096571od_b_b_decl,type,
image_1177096571od_b_b: set_Pr621705391od_b_b > set_b > set_Product_prod_b_b ).
thf(image_b_b_decl,type,
image_b_b: set_Product_prod_b_b > set_b > set_b ).
thf(converse_b_b_decl,type,
converse_b_b: set_Product_prod_b_b > set_Product_prod_b_b ).
thf(refl_on_b_decl,type,
refl_on_b: set_b > set_Product_prod_b_b > $o ).
thf(total_178717291od_b_b_decl,type,
total_178717291od_b_b: set_Product_prod_b_b > set_Pr2007082183od_b_b > $o ).
thf(total_on_b_decl,type,
total_on_b: set_b > set_Product_prod_b_b > $o ).
thf(collec279084418od_b_b_decl,type,
collec279084418od_b_b: ( produc1213276845od_b_b > $o ) > set_Pr1324126435od_b_b ).
thf(collec1481886546od_b_b_decl,type,
collec1481886546od_b_b: ( product_prod_b_b > $o ) > set_Product_prod_b_b ).
thf(collect_b_decl,type,
collect_b: ( b > $o ) > set_b ).
thf(insert1909710879tant_a_decl,type,
insert1909710879tant_a: standard_Constant_a > set_St761939237tant_a > set_St761939237tant_a ).
thf(insert2037698781od_b_b_decl,type,
insert2037698781od_b_b: produc1213276845od_b_b > set_Pr1324126435od_b_b > set_Pr1324126435od_b_b ).
thf(insert1952693431od_b_b_decl,type,
insert1952693431od_b_b: product_prod_b_b > set_Product_prod_b_b > set_Product_prod_b_b ).
thf(insert_b_decl,type,
insert_b: b > set_b > set_b ).
thf(is_sin1465183929od_b_b_decl,type,
is_sin1465183929od_b_b: set_Pr1324126435od_b_b > $o ).
thf(is_sin1713057243od_b_b_decl,type,
is_sin1713057243od_b_b: set_Product_prod_b_b > $o ).
thf(is_singleton_b_decl,type,
is_singleton_b: set_b > $o ).
thf(the_el329196508od_b_b_decl,type,
the_el329196508od_b_b: set_Product_prod_b_b > product_prod_b_b ).
thf(the_elem_b_decl,type,
the_elem_b: set_b > b ).
thf(member1632892294tant_a_decl,type,
member1632892294tant_a: standard_Constant_a > set_St761939237tant_a > $o ).
thf(member1516365892od_b_b_decl,type,
member1516365892od_b_b: produc1213276845od_b_b > set_Pr1324126435od_b_b > $o ).
thf(member1417789726_b_b_b_decl,type,
member1417789726_b_b_b: produc276146823_b_b_b > set_Pr1906739389_b_b_b > $o ).
thf(member4694106od_b_b_decl,type,
member4694106od_b_b: produc1052326083od_b_b > set_Pr1071216121od_b_b > $o ).
thf(member351494440_b_b_b_decl,type,
member351494440_b_b_b: produc2112523263_b_b_b > set_Pr357419743_b_b_b > $o ).
thf(member599505522od_b_b_decl,type,
member599505522od_b_b: produc1605346267od_b_b > set_Pr2060523537od_b_b > $o ).
thf(member641857272od_b_b_decl,type,
member641857272od_b_b: produc255402447od_b_b > set_Pr621705391od_b_b > $o ).
thf(member1285940496od_b_b_decl,type,
member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o ).
thf(member_b_decl,type,
member_b: b > set_b > $o ).
thf(g_decl,type,
g: labele1159362096nt_a_b ).
thf(p_decl,type,
p: b > b > $o ).
thf(f_decl,type,
f: b > b ).
thf(x_decl,type,
x: b ).
thf(y_decl,type,
y: b ).
thf(170,axiom,
! [A: labele1159362096nt_a_b,B: b,C: b,D: standard_Constant_a] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ ( getRel904497637nt_a_b @ D @ A ) )
=> ( member_b @ B @ ( labele1424214014nt_a_b @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_getRel__dom_I1_J) ).
thf(892,plain,
! [A: labele1159362096nt_a_b,B: b,C: b,D: standard_Constant_a] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ ( getRel904497637nt_a_b @ D @ A ) )
=> ( member_b @ B @ ( labele1424214014nt_a_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(95,axiom,
! [A: labele1159362096nt_a_b,B: set_Pr357419743_b_b_b] :
( ( graph_792023598_b_b_b @ ( labele170595300od_b_b @ bot_bo1964903287od_b_b @ bot_bo1343651123od_b_b ) @ A @ B )
= ( ( B = bot_bo1124087115_b_b_b )
& ( A
= ( restri446606278nt_a_b @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_graph__homomorphism__empty) ).
thf(629,plain,
! [A: labele1159362096nt_a_b,B: set_Pr357419743_b_b_b] :
( ( graph_792023598_b_b_b @ ( labele170595300od_b_b @ bot_bo1964903287od_b_b @ bot_bo1343651123od_b_b ) @ A @ B )
= ( ( B = bot_bo1124087115_b_b_b )
& ( A
= ( restri446606278nt_a_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(14,axiom,
! [A: set_Pr2007082183od_b_b] :
( ( image_1928024979od_b_b @ A @ bot_bo1343651123od_b_b )
= bot_bo1343651123od_b_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_Image__empty2) ).
thf(347,plain,
! [A: set_Pr2007082183od_b_b] :
( ( image_1928024979od_b_b @ A @ bot_bo1343651123od_b_b )
= bot_bo1343651123od_b_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(157,axiom,
! [A: b,B: b,C: b,D: b] :
( ( ( product_Pair_b_b @ A @ B )
= ( product_Pair_b_b @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_Pair__inject) ).
thf(846,plain,
! [A: b,B: b,C: b,D: b] :
( ( ( product_Pair_b_b @ A @ B )
= ( product_Pair_b_b @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(60,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: set_Pr1324126435od_b_b] :
( ( ord_le123089219od_b_b @ ( insert2037698781od_b_b @ A @ B ) @ C )
= ( ( member1516365892od_b_b @ A @ C )
& ( ord_le123089219od_b_b @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_insert__subset) ).
thf(518,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: set_Pr1324126435od_b_b] :
( ( ord_le123089219od_b_b @ ( insert2037698781od_b_b @ A @ B ) @ C )
= ( ( member1516365892od_b_b @ A @ C )
& ( ord_le123089219od_b_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(290,axiom,
! [A: b,B: b] :
( ( collect_b
@ ^ [C: b] :
( ( C = A )
| ( C = B ) ) )
= ( insert_b @ A @ ( insert_b @ B @ bot_bot_set_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_tuple__disj) ).
thf(1295,plain,
! [A: b,B: b] :
( ( collect_b
@ ^ [C: b] :
( ( C = A )
| ( C = B ) ) )
= ( insert_b @ A @ ( insert_b @ B @ bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(20,axiom,
! [A: set_Product_prod_b_b] :
( ( ! [B: product_prod_b_b] :
~ ( member1285940496od_b_b @ B @ A ) )
= ( A = bot_bo1343651123od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_all__not__in__conv) ).
thf(365,plain,
! [A: set_Product_prod_b_b] :
( ( ! [B: product_prod_b_b] :
~ ( member1285940496od_b_b @ B @ A ) )
= ( A = bot_bo1343651123od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(313,axiom,
! [A: set_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b,D: b > b > set_b,E: b] :
( ( equiv_equiv_b @ A @ B )
=> ( ( equiv_167626658_set_b @ B @ C @ D )
=> ( ( member_b @ E @ A )
=> ( equiv_1821124534_set_b @ C @ ( D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_congruent2__implies__congruent) ).
thf(1369,plain,
! [A: set_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b,D: b > b > set_b,E: b] :
( ( equiv_equiv_b @ A @ B )
=> ( ( equiv_167626658_set_b @ B @ C @ D )
=> ( ( member_b @ E @ A )
=> ( equiv_1821124534_set_b @ C @ ( D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(176,axiom,
! [A: set_b,B: b > $o,C: b > $o] :
( ? [D: b] :
( ( member_b @ D @ A )
& ( B @ D ) )
=> ( ! [D: b] :
( ( ( member_b @ D @ A )
& ( B @ D ) )
=> ( C @ D ) )
=> ( C
@ ( hilbert_Eps_b
@ ^ [D: b] :
( ( member_b @ D @ A )
& ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_someI2__bex) ).
thf(909,plain,
! [A: set_b,B: b > $o,C: b > $o] :
( ? [D: b] :
( ( member_b @ D @ A )
& ( B @ D ) )
=> ( ! [D: b] :
( ( ( member_b @ D @ A )
& ( B @ D ) )
=> ( C @ D ) )
=> ( C
@ ( hilbert_Eps_b
@ ^ [D: b] :
( ( member_b @ D @ A )
& ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(213,axiom,
! [A: produc1213276845od_b_b,B: set_Pr2060523537od_b_b,C: set_b] :
( ( member1516365892od_b_b @ A @ ( image_984343321od_b_b @ B @ C ) )
=> ~ ! [D: b] :
( ( member599505522od_b_b @ ( produc800495189od_b_b @ D @ A ) @ B )
=> ~ ( member_b @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_ImageE) ).
thf(1031,plain,
! [A: produc1213276845od_b_b,B: set_Pr2060523537od_b_b,C: set_b] :
( ( member1516365892od_b_b @ A @ ( image_984343321od_b_b @ B @ C ) )
=> ~ ! [D: b] :
( ( member599505522od_b_b @ ( produc800495189od_b_b @ D @ A ) @ B )
=> ~ ( member_b @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(227,axiom,
! [A: b] : ( member_b @ A @ ( insert_b @ A @ bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_singletonI) ).
thf(1083,plain,
! [A: b] : ( member_b @ A @ ( insert_b @ A @ bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(46,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b,D: set_Product_prod_b_b] :
( ~ ( member1285940496od_b_b @ A @ B )
=> ( ~ ( member1285940496od_b_b @ C @ D )
=> ( ( ( insert1952693431od_b_b @ A @ B )
= ( insert1952693431od_b_b @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_Product_prod_b_b] :
( ( B
= ( insert1952693431od_b_b @ C @ E ) )
& ~ ( member1285940496od_b_b @ C @ E )
& ( D
= ( insert1952693431od_b_b @ A @ E ) )
& ~ ( member1285940496od_b_b @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_insert__eq__iff) ).
thf(468,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b,D: set_Product_prod_b_b] :
( ~ ( member1285940496od_b_b @ A @ B )
=> ( ~ ( member1285940496od_b_b @ C @ D )
=> ( ( ( insert1952693431od_b_b @ A @ B )
= ( insert1952693431od_b_b @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_Product_prod_b_b] :
( ( B
= ( insert1952693431od_b_b @ C @ E ) )
& ~ ( member1285940496od_b_b @ C @ E )
& ( D
= ( insert1952693431od_b_b @ A @ E ) )
& ~ ( member1285940496od_b_b @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(259,axiom,
! [A: set_b,B: b] : ( ord_less_eq_set_b @ A @ ( insert_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_subset__insertI) ).
thf(1200,plain,
! [A: set_b,B: b] : ( ord_less_eq_set_b @ A @ ( insert_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(192,axiom,
! [A: b] : ( total_on_b @ ( insert_b @ A @ bot_bot_set_b ) @ ( insert1952693431od_b_b @ ( product_Pair_b_b @ A @ A ) @ bot_bo1343651123od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_total__on__singleton) ).
thf(977,plain,
! [A: b] : ( total_on_b @ ( insert_b @ A @ bot_bot_set_b ) @ ( insert1952693431od_b_b @ ( product_Pair_b_b @ A @ A ) @ bot_bo1343651123od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(263,axiom,
! [A: set_b] : ( ord_less_eq_set_b @ bot_bot_set_b @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_bot_Oextremum) ).
thf(1211,plain,
! [A: set_b] : ( ord_less_eq_set_b @ bot_bot_set_b @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(126,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ? [C: set_Product_prod_b_b] :
( ( B
= ( insert1952693431od_b_b @ A @ C ) )
& ~ ( member1285940496od_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_mk__disjoint__insert) ).
thf(741,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ? [C: set_Product_prod_b_b] :
( ( B
= ( insert1952693431od_b_b @ A @ C ) )
& ~ ( member1285940496od_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(24,axiom,
! [A: produc1213276845od_b_b] :
~ ! [B: standard_Constant_a,C: b,D: b] :
( A
!= ( produc1432590431od_b_b @ B @ ( product_Pair_b_b @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_prod__cases3) ).
thf(379,plain,
! [A: produc1213276845od_b_b] :
~ ! [B: standard_Constant_a,C: b,D: b] :
( A
!= ( produc1432590431od_b_b @ B @ ( product_Pair_b_b @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(165,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_insertI2) ).
thf(878,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(109,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b @ A @ B )
=> ~ ! [C: set_Pr1324126435od_b_b] :
( ( B
= ( insert2037698781od_b_b @ A @ C ) )
=> ( member1516365892od_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_Set_Oset__insert) ).
thf(677,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b @ A @ B )
=> ~ ! [C: set_Pr1324126435od_b_b] :
( ( B
= ( insert2037698781od_b_b @ A @ C ) )
=> ( member1516365892od_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(86,axiom,
! [A: standard_Constant_a,B: product_prod_b_b,C: standard_Constant_a,D: product_prod_b_b] :
( ( ( produc1432590431od_b_b @ A @ B )
= ( produc1432590431od_b_b @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_old_Oprod_Oinject) ).
thf(597,plain,
! [A: standard_Constant_a,B: product_prod_b_b,C: standard_Constant_a,D: product_prod_b_b] :
( ( ( produc1432590431od_b_b @ A @ B )
= ( produc1432590431od_b_b @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(225,axiom,
! [A: set_b,B: set_Product_prod_b_b,C: b] :
( ( equiv_equiv_b @ A @ B )
=> ( ( member_b @ C @ A )
=> ( member_b @ C @ ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_equiv__class__self) ).
thf(1078,plain,
! [A: set_b,B: set_Product_prod_b_b,C: b] :
( ( equiv_equiv_b @ A @ B )
=> ( ( member_b @ C @ A )
=> ( member_b @ C @ ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(65,axiom,
( is_sin1713057243od_b_b
= ( ^ [A: set_Product_prod_b_b] :
( A
= ( insert1952693431od_b_b @ ( the_el329196508od_b_b @ A ) @ bot_bo1343651123od_b_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_is__singleton__the__elem) ).
thf(533,plain,
( is_sin1713057243od_b_b
= ( ^ [A: set_Product_prod_b_b] :
( A
= ( insert1952693431od_b_b @ ( the_el329196508od_b_b @ A ) @ bot_bo1343651123od_b_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(71,axiom,
! [A: labele1159362096nt_a_b] :
( ( labele1230159100nt_a_b @ ( labele1741081071nt_a_b @ A ) @ ( labele1424214014nt_a_b @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_labeled__graph_Ocollapse) ).
thf(550,plain,
! [A: labele1159362096nt_a_b] :
( ( labele1230159100nt_a_b @ ( labele1741081071nt_a_b @ A ) @ ( labele1424214014nt_a_b @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(56,axiom,
! [A: product_prod_b_b,B: product_prod_b_b] :
( ( collec1481886546od_b_b
@ ^ [C: product_prod_b_b] :
( ( C = A )
| ( C = B ) ) )
= ( insert1952693431od_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_tuple__disj) ).
thf(500,plain,
! [A: product_prod_b_b,B: product_prod_b_b] :
( ( collec1481886546od_b_b
@ ^ [C: product_prod_b_b] :
( ( C = A )
| ( C = B ) ) )
= ( insert1952693431od_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(47,axiom,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
( ( ord_le1036320359od_b_b @ A @ ( converse_b_b @ B ) )
= ( ord_le1036320359od_b_b @ ( converse_b_b @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_converse__subset__swap) ).
thf(472,plain,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
( ( ord_le1036320359od_b_b @ A @ ( converse_b_b @ B ) )
= ( ord_le1036320359od_b_b @ ( converse_b_b @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(271,axiom,
! [A: b,B: b,C: standard_Constant_a] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( getRel904497637nt_a_b @ C @ g ) )
=> ( equiv_1821124534_set_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g )
@ ^ [D: b] : ( image_b_b @ ( getRel904497637nt_a_b @ C @ g ) @ ( insert_b @ D @ bot_bot_set_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_congr_I1_J) ).
thf(1233,plain,
! [A: b,B: b,C: standard_Constant_a] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( getRel904497637nt_a_b @ C @ g ) )
=> ( equiv_1821124534_set_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g )
@ ^ [D: b] : ( image_b_b @ ( getRel904497637nt_a_b @ C @ g ) @ ( insert_b @ D @ bot_bot_set_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(298,axiom,
! [A: b] :
( ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
!= bot_bot_set_b )
=> ( ( hilbert_Eps_b @ ( p @ ( hilbert_Eps_b @ ( p @ A ) ) ) )
= ( hilbert_Eps_b @ ( p @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_P__eq) ).
thf(1327,plain,
! [A: b] :
( ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
!= bot_bot_set_b )
=> ( ( hilbert_Eps_b @ ( p @ ( hilbert_Eps_b @ ( p @ A ) ) ) )
= ( hilbert_Eps_b @ ( p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(67,axiom,
( bot_bot_b_b_o
= ( ^ [A: b,B: b] : ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ bot_bo1343651123od_b_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_bot__empty__eq2) ).
thf(538,plain,
( bot_bot_b_b_o
= ( ^ [A: b,B: b] : ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ bot_bo1343651123od_b_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(107,axiom,
! [A: set_Product_prod_b_b,B: b > set_b] :
( ! [C: b,D: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ A )
=> ( ( B @ C )
= ( B @ D ) ) )
=> ( equiv_1821124534_set_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_congruentI) ).
thf(670,plain,
! [A: set_Product_prod_b_b,B: b > set_b] :
( ! [C: b,D: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ A )
=> ( ( B @ C )
= ( B @ D ) ) )
=> ( equiv_1821124534_set_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(172,axiom,
( f
= ( ^ [A: b] :
( if_b
@ ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
= bot_bot_set_b )
@ A
@ ( hilbert_Eps_b @ ( p @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062f_A_092_060equiv_062_A_092_060lambda_062x_O_Aif_AgetRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_A_123_125_Athen_Ax_Aelse_AEps_A_IP_Ax_J_092_060close_062) ).
thf(898,plain,
( f
= ( ^ [A: b] :
( if_b
@ ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
= bot_bot_set_b )
@ A
@ ( hilbert_Eps_b @ ( p @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(238,axiom,
! [A: b] :
( ( member_b @ A @ ( labele1424214014nt_a_b @ g ) )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ ( hilbert_Eps_b @ ( p @ A ) ) ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_vert__P) ).
thf(1127,plain,
! [A: b] :
( ( member_b @ A @ ( labele1424214014nt_a_b @ g ) )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ ( hilbert_Eps_b @ ( p @ A ) ) ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(137,axiom,
! [A: labele1159362096nt_a_b] :
( A
= ( labele1230159100nt_a_b @ ( labele1741081071nt_a_b @ A ) @ ( labele1424214014nt_a_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_labeled__graph_Oexhaust__sel) ).
thf(782,plain,
! [A: labele1159362096nt_a_b] :
( A
= ( labele1230159100nt_a_b @ ( labele1741081071nt_a_b @ A ) @ ( labele1424214014nt_a_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(168,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b] :
( ~ ( member1285940496od_b_b @ A @ B )
=> ( ( ord_le1036320359od_b_b @ B @ ( insert1952693431od_b_b @ A @ C ) )
= ( ord_le1036320359od_b_b @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_subset__insert) ).
thf(885,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b] :
( ~ ( member1285940496od_b_b @ A @ B )
=> ( ( ord_le1036320359od_b_b @ B @ ( insert1952693431od_b_b @ A @ C ) )
= ( ord_le1036320359od_b_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(309,axiom,
! [A: b,B: b] :
( ( member_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_singleton__iff) ).
thf(1359,plain,
! [A: b,B: b] :
( ( member_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(38,axiom,
! [A: b,B: b] :
( ( if_b @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001tf__b_T) ).
thf(436,plain,
! [A: b,B: b] :
( ( if_b @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(280,axiom,
! [A: b,B: set_b,C: set_b] :
( ( ord_less_eq_set_b @ ( insert_b @ A @ B ) @ C )
= ( ( member_b @ A @ C )
& ( ord_less_eq_set_b @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_insert__subset) ).
thf(1265,plain,
! [A: b,B: set_b,C: set_b] :
( ( ord_less_eq_set_b @ ( insert_b @ A @ B ) @ C )
= ( ( member_b @ A @ C )
& ( ord_less_eq_set_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(102,axiom,
! [A: product_prod_b_b,B: product_prod_b_b] :
( ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_singleton__iff) ).
thf(651,plain,
! [A: product_prod_b_b,B: product_prod_b_b] :
( ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(4,axiom,
! [A: set_Pr1324126435od_b_b,B: produc1213276845od_b_b > $o] :
( ord_le123089219od_b_b
@ ( collec279084418od_b_b
@ ^ [C: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_Collect__subset) ).
thf(320,plain,
! [A: set_Pr1324126435od_b_b,B: produc1213276845od_b_b > $o] :
( ord_le123089219od_b_b
@ ( collec279084418od_b_b
@ ^ [C: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(76,axiom,
! [A: product_prod_b_b,B: set_Pr1324126435od_b_b,C: set_St761939237tant_a] :
( ( member1285940496od_b_b @ A @ ( image_1916422435od_b_b @ B @ C ) )
= ( ? [D: standard_Constant_a] :
( ( member1632892294tant_a @ D @ C )
& ( member1516365892od_b_b @ ( produc1432590431od_b_b @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Image__iff) ).
thf(565,plain,
! [A: product_prod_b_b,B: set_Pr1324126435od_b_b,C: set_St761939237tant_a] :
( ( member1285940496od_b_b @ A @ ( image_1916422435od_b_b @ B @ C ) )
= ( ? [D: standard_Constant_a] :
( ( member1632892294tant_a @ D @ C )
& ( member1516365892od_b_b @ ( produc1432590431od_b_b @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(291,axiom,
! [A: set_b] :
( ( ? [B: b] : ( member_b @ B @ A ) )
= ( A != bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_ex__in__conv) ).
thf(1298,plain,
! [A: set_b] :
( ( ? [B: b] : ( member_b @ B @ A ) )
= ( A != bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(138,axiom,
! [A: b,B: b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ C )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ A ) @ ( converse_b_b @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_converse_Ointros) ).
thf(785,plain,
! [A: b,B: b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ C )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ A ) @ ( converse_b_b @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(22,axiom,
! [A: b,B: b,C: b,D: b] :
( ( ( product_Pair_b_b @ A @ B )
= ( product_Pair_b_b @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_prod_Oinject) ).
thf(372,plain,
! [A: b,B: b,C: b,D: b] :
( ( ( product_Pair_b_b @ A @ B )
= ( product_Pair_b_b @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(299,axiom,
! [A: set_b] :
( ( ! [B: b] :
~ ( member_b @ B @ A ) )
= ( A = bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_all__not__in__conv) ).
thf(1330,plain,
! [A: set_b] :
( ( ! [B: b] :
~ ( member_b @ B @ A ) )
= ( A = bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(154,axiom,
! [A: product_prod_b_b] : ( is_sin1713057243od_b_b @ ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_is__singletonI) ).
thf(838,plain,
! [A: product_prod_b_b] : ( is_sin1713057243od_b_b @ ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(256,axiom,
! [A: set_b] :
( ( is_singleton_b @ A )
=> ~ ! [B: b] :
( A
!= ( insert_b @ B @ bot_bot_set_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_is__singletonE) ).
thf(1191,plain,
! [A: set_b] :
( ( is_singleton_b @ A )
=> ~ ! [B: b] :
( A
!= ( insert_b @ B @ bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(185,axiom,
( equiv_proj_b_b
= ( ^ [A: set_Product_prod_b_b,B: b] : ( image_b_b @ A @ ( insert_b @ B @ bot_bot_set_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_proj__def) ).
thf(949,plain,
( equiv_proj_b_b
= ( ^ [A: set_Product_prod_b_b,B: b] : ( image_b_b @ A @ ( insert_b @ B @ bot_bot_set_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(43,axiom,
! [A: produc1213276845od_b_b,B: produc1213276845od_b_b,C: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ B @ C ) )
=> ( ( A != B )
=> ( member1516365892od_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_insertE) ).
thf(460,plain,
! [A: produc1213276845od_b_b,B: produc1213276845od_b_b,C: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ B @ C ) )
=> ( ( A != B )
=> ( member1516365892od_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(220,axiom,
! [A: b > $o,B: b] :
( ( A @ B )
=> ( ! [C: b] :
( ( A @ C )
=> ( C = B ) )
=> ( ( hilbert_Eps_b @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_some__equality) ).
thf(1055,plain,
! [A: b > $o,B: b] :
( ( A @ B )
=> ( ! [C: b] :
( ( A @ C )
=> ( C = B ) )
=> ( ( hilbert_Eps_b @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(122,axiom,
! [A: product_prod_b_b,B: product_prod_b_b] :
( ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_singletonD) ).
thf(724,plain,
! [A: product_prod_b_b,B: product_prod_b_b] :
( ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(276,axiom,
! [A: set_b] :
( ( A != bot_bot_set_b )
=> ( ! [B: b,C: b] :
( ( member_b @ B @ A )
=> ( ( member_b @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_is__singletonI_H) ).
thf(1247,plain,
! [A: set_b] :
( ( A != bot_bot_set_b )
=> ( ! [B: b,C: b] :
( ( member_b @ B @ A )
=> ( ( member_b @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(36,axiom,
! [A: set_Pr1324126435od_b_b,B: produc1213276845od_b_b > $o,C: produc1213276845od_b_b > $o] :
( ? [D: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ D @ A )
& ( B @ D ) )
=> ( ! [D: produc1213276845od_b_b] :
( ( ( member1516365892od_b_b @ D @ A )
& ( B @ D ) )
=> ( C @ D ) )
=> ( C
@ ( hilber46179633od_b_b
@ ^ [D: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ D @ A )
& ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_someI2__bex) ).
thf(421,plain,
! [A: set_Pr1324126435od_b_b,B: produc1213276845od_b_b > $o,C: produc1213276845od_b_b > $o] :
( ? [D: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ D @ A )
& ( B @ D ) )
=> ( ! [D: produc1213276845od_b_b] :
( ( ( member1516365892od_b_b @ D @ A )
& ( B @ D ) )
=> ( C @ D ) )
=> ( C
@ ( hilber46179633od_b_b
@ ^ [D: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ D @ A )
& ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(205,axiom,
refl_on_b @ ( labele1424214014nt_a_b @ g ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_local_Orefl) ).
thf(1013,plain,
refl_on_b @ ( labele1424214014nt_a_b @ g ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(166,axiom,
( ord_le1036320359od_b_b
= ( ^ [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
! [C: product_prod_b_b] :
( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_subset__iff) ).
thf(881,plain,
( ord_le1036320359od_b_b
= ( ^ [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
! [C: product_prod_b_b] :
( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(3,axiom,
! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
( ! [C: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ B ) )
=> ( ord_le123089219od_b_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_subsetI) ).
thf(316,plain,
! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
( ! [C: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ B ) )
=> ( ord_le123089219od_b_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(310,axiom,
! [A: b,B: set_b] :
( ( insert_b @ A @ ( insert_b @ A @ B ) )
= ( insert_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_insert__absorb2) ).
thf(1362,plain,
! [A: b,B: set_b] :
( ( insert_b @ A @ ( insert_b @ A @ B ) )
= ( insert_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(48,axiom,
! [A: b,B: b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( converse_b_b @ C ) )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_converse_Ocases) ).
thf(475,plain,
! [A: b,B: b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( converse_b_b @ C ) )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(130,axiom,
! [A: b > $o,B: b > $o] :
( ! [C: b] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_b @ A )
= ( collect_b @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_Collect__cong) ).
thf(756,plain,
! [A: b > $o,B: b > $o] :
( ! [C: b] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_b @ A )
= ( collect_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(216,axiom,
! [A: labele1159362096nt_a_b,B: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ bot_bot_set_b ) @ A @ B )
= ( ( B = bot_bo1343651123od_b_b )
& ( A
= ( restri446606278nt_a_b @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_graph__homomorphism__empty) ).
thf(1040,plain,
! [A: labele1159362096nt_a_b,B: set_Product_prod_b_b] :
( ( graph_222606102_a_b_b @ ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ bot_bot_set_b ) @ A @ B )
= ( ( B = bot_bo1343651123od_b_b )
& ( A
= ( restri446606278nt_a_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(242,axiom,
! [A: b > $o,B: b,C: b > $o] :
( ( A @ B )
=> ( ! [D: b] :
( ( A @ D )
=> ( C @ D ) )
=> ( C @ ( hilbert_Eps_b @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_someI2) ).
thf(1136,plain,
! [A: b > $o,B: b,C: b > $o] :
( ( A @ B )
=> ( ! [D: b] :
( ( A @ D )
=> ( C @ D ) )
=> ( C @ ( hilbert_Eps_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(79,axiom,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
( ( ord_le1036320359od_b_b @ A @ B )
=> ( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_subsetD) ).
thf(574,plain,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
( ( ord_le1036320359od_b_b @ A @ B )
=> ( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(16,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: produc1213276845od_b_b,D: set_Pr1071216121od_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ( ( member4694106od_b_b @ ( produc732676669od_b_b @ A @ C ) @ D )
=> ( member1516365892od_b_b @ C @ ( image_532916993od_b_b @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_rev__ImageI) ).
thf(353,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: produc1213276845od_b_b,D: set_Pr1071216121od_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ( ( member4694106od_b_b @ ( produc732676669od_b_b @ A @ C ) @ D )
=> ( member1516365892od_b_b @ C @ ( image_532916993od_b_b @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(148,axiom,
! [A: labele1159362096nt_a_b] :
( ( labele1424214014nt_a_b @ ( restri446606278nt_a_b @ A ) )
= ( labele1424214014nt_a_b @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_vertices__restrict) ).
thf(821,plain,
! [A: labele1159362096nt_a_b] :
( ( labele1424214014nt_a_b @ ( restri446606278nt_a_b @ A ) )
= ( labele1424214014nt_a_b @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(50,axiom,
! [A: set_Product_prod_b_b,B: set_Pr2007082183od_b_b,C: set_Product_prod_b_b,D: product_prod_b_b > b > set_b,E: product_prod_b_b] :
( ( equiv_1125628061od_b_b @ A @ B )
=> ( ( equiv_1036235914_set_b @ B @ C @ D )
=> ( ( member1285940496od_b_b @ E @ A )
=> ( equiv_1821124534_set_b @ C @ ( D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_congruent2__implies__congruent) ).
thf(480,plain,
! [A: set_Product_prod_b_b,B: set_Pr2007082183od_b_b,C: set_Product_prod_b_b,D: product_prod_b_b > b > set_b,E: product_prod_b_b] :
( ( equiv_1125628061od_b_b @ A @ B )
=> ( ( equiv_1036235914_set_b @ B @ C @ D )
=> ( ( member1285940496od_b_b @ E @ A )
=> ( equiv_1821124534_set_b @ C @ ( D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(245,axiom,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ? [C: set_b] :
( ( B
= ( insert_b @ A @ C ) )
& ~ ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_mk__disjoint__insert) ).
thf(1151,plain,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ? [C: set_b] :
( ( B
= ( insert_b @ A @ C ) )
& ~ ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(181,axiom,
! [A: b,B: set_Product_prod_b_b,C: b] :
( ( member_b @ A @ ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
= ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_Image__singleton__iff) ).
thf(937,plain,
! [A: b,B: set_Product_prod_b_b,C: b] :
( ( member_b @ A @ ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
= ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(194,axiom,
! [A: b,B: set_b,C: produc1213276845od_b_b,D: set_Pr2060523537od_b_b] :
( ( member_b @ A @ B )
=> ( ( member599505522od_b_b @ ( produc800495189od_b_b @ A @ C ) @ D )
=> ( member1516365892od_b_b @ C @ ( image_984343321od_b_b @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_rev__ImageI) ).
thf(981,plain,
! [A: b,B: set_b,C: produc1213276845od_b_b,D: set_Pr2060523537od_b_b] :
( ( member_b @ A @ B )
=> ( ( member599505522od_b_b @ ( produc800495189od_b_b @ A @ C ) @ D )
=> ( member1516365892od_b_b @ C @ ( image_984343321od_b_b @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(97,axiom,
! [A: set_Pr1324126435od_b_b,B: set_b] :
( ( labele1741081071nt_a_b @ ( labele1230159100nt_a_b @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_labeled__graph_Osel_I1_J) ).
thf(634,plain,
! [A: set_Pr1324126435od_b_b,B: set_b] :
( ( labele1741081071nt_a_b @ ( labele1230159100nt_a_b @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(235,axiom,
! [A: b,B: b > $o] :
( ( member_b @ A @ ( collect_b @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_mem__Collect__eq) ).
thf(1119,plain,
! [A: b,B: b > $o] :
( ( member_b @ A @ ( collect_b @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(232,axiom,
! [A: b,B: set_b,C: set_b] :
( ~ ( member_b @ A @ B )
=> ( ( ord_less_eq_set_b @ B @ ( insert_b @ A @ C ) )
= ( ord_less_eq_set_b @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_subset__insert) ).
thf(1104,plain,
! [A: b,B: set_b,C: set_b] :
( ~ ( member_b @ A @ B )
=> ( ( ord_less_eq_set_b @ B @ ( insert_b @ A @ C ) )
= ( ord_less_eq_set_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(250,axiom,
! [A: b] :
~ ( member_b @ A @ bot_bot_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_empty__iff) ).
thf(1169,plain,
! [A: b] :
~ ( member_b @ A @ bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(111,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ A @ B )
=> ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_insertI2) ).
thf(687,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ A @ B )
=> ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(224,axiom,
! [A: b,B: set_b] :
( ( insert_b @ A @ B )
!= bot_bot_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_insert__not__empty) ).
thf(1074,plain,
! [A: b,B: set_b] :
( ( insert_b @ A @ B )
!= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(177,axiom,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( equiv_equiv_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
=> ( ord_less_eq_set_b @ ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) @ ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_equiv__class__subset) ).
thf(920,plain,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( equiv_equiv_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
=> ( ord_less_eq_set_b @ ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) @ ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(39,axiom,
! [A: set_Product_prod_b_b] :
( ( ord_le1036320359od_b_b @ A @ bot_bo1343651123od_b_b )
=> ( A = bot_bo1343651123od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_bot_Oextremum__uniqueI) ).
thf(439,plain,
! [A: set_Product_prod_b_b] :
( ( ord_le1036320359od_b_b @ A @ bot_bo1343651123od_b_b )
=> ( A = bot_bo1343651123od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(141,axiom,
( is_sin1713057243od_b_b
= ( ^ [A: set_Product_prod_b_b] :
? [B: product_prod_b_b] :
( A
= ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_is__singleton__def) ).
thf(793,plain,
( is_sin1713057243od_b_b
= ( ^ [A: set_Product_prod_b_b] :
? [B: product_prod_b_b] :
( A
= ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(293,axiom,
! [A: b > $o,B: b] :
( ( ( A @ B )
=> ( ( collect_b
@ ^ [C: b] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_b @ B @ bot_bot_set_b ) ) )
& ( ~ ( A @ B )
=> ( ( collect_b
@ ^ [C: b] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_set_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_Collect__conv__if2) ).
thf(1306,plain,
! [A: b > $o,B: b] :
( ( ( A @ B )
=> ( ( collect_b
@ ^ [C: b] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_b @ B @ bot_bot_set_b ) ) )
& ( ~ ( A @ B )
=> ( ( collect_b
@ ^ [C: b] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(258,axiom,
equiv_equiv_b @ ( labele1424214014nt_a_b @ g ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_equiv) ).
thf(1199,plain,
equiv_equiv_b @ ( labele1424214014nt_a_b @ g ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(147,axiom,
! [A: set_Product_prod_b_b,B: product_prod_b_b > $o,C: product_prod_b_b > $o] :
( ? [D: product_prod_b_b] :
( ( member1285940496od_b_b @ D @ A )
& ( B @ D ) )
=> ( ! [D: product_prod_b_b] :
( ( ( member1285940496od_b_b @ D @ A )
& ( B @ D ) )
=> ( C @ D ) )
=> ( C
@ ( hilber620807523od_b_b
@ ^ [D: product_prod_b_b] :
( ( member1285940496od_b_b @ D @ A )
& ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_someI2__bex) ).
thf(810,plain,
! [A: set_Product_prod_b_b,B: product_prod_b_b > $o,C: product_prod_b_b > $o] :
( ? [D: product_prod_b_b] :
( ( member1285940496od_b_b @ D @ A )
& ( B @ D ) )
=> ( ! [D: product_prod_b_b] :
( ( ( member1285940496od_b_b @ D @ A )
& ( B @ D ) )
=> ( C @ D ) )
=> ( C
@ ( hilber620807523od_b_b
@ ^ [D: product_prod_b_b] :
( ( member1285940496od_b_b @ D @ A )
& ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(302,axiom,
! [A: b,B: b,C: set_Product_prod_b_b,D: set_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ C )
=> ( ( member_b @ A @ D )
=> ( member_b @ B @ ( image_b_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_ImageI) ).
thf(1338,plain,
! [A: b,B: b,C: set_Product_prod_b_b,D: set_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ C )
=> ( ( member_b @ A @ D )
=> ( member_b @ B @ ( image_b_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(222,axiom,
! [A: b,B: set_b] : ( member_b @ A @ ( insert_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_insertI1) ).
thf(1067,plain,
! [A: b,B: set_b] : ( member_b @ A @ ( insert_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(143,axiom,
( ord_le1036320359od_b_b
= ( ^ [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
! [C: product_prod_b_b] :
( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_subset__eq) ).
thf(798,plain,
( ord_le1036320359od_b_b
= ( ^ [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
! [C: product_prod_b_b] :
( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(283,axiom,
! [A: b,B: set_Product_prod_b_b,C: set_b] :
( ( member_b @ A @ ( image_b_b @ B @ C ) )
=> ~ ! [D: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ A ) @ B )
=> ~ ( member_b @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_ImageE) ).
thf(1274,plain,
! [A: b,B: set_Product_prod_b_b,C: set_b] :
( ( member_b @ A @ ( image_b_b @ B @ C ) )
=> ~ ! [D: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ A ) @ B )
=> ~ ( member_b @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(127,axiom,
! [A: produc1213276845od_b_b] : ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ A @ bot_bo1664927607od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_singletonI) ).
thf(746,plain,
! [A: produc1213276845od_b_b] : ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ A @ bot_bo1664927607od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(304,axiom,
! [A: b,B: set_b,C: b] :
( ( member_b @ A @ B )
=> ( member_b @ A @ ( insert_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_insertI2) ).
thf(1343,plain,
! [A: b,B: set_b,C: b] :
( ( member_b @ A @ B )
=> ( member_b @ A @ ( insert_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(160,axiom,
! [A: set_Product_prod_b_b,B: product_prod_b_b] :
( ( A = bot_bo1343651123od_b_b )
=> ~ ( member1285940496od_b_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_equals0D) ).
thf(862,plain,
! [A: set_Product_prod_b_b,B: product_prod_b_b] :
( ( A = bot_bo1343651123od_b_b )
=> ~ ( member1285940496od_b_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(113,axiom,
! [A: set_Pr1324126435od_b_b] :
( ! [B: produc1213276845od_b_b] :
~ ( member1516365892od_b_b @ B @ A )
=> ( A = bot_bo1664927607od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_equals0I) ).
thf(693,plain,
! [A: set_Pr1324126435od_b_b] :
( ! [B: produc1213276845od_b_b] :
~ ( member1516365892od_b_b @ B @ A )
=> ( A = bot_bo1664927607od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(273,axiom,
! [A: b,B: b,C: standard_Constant_a] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( getRel904497637nt_a_b @ C @ g ) )
=> ( equiv_1821124534_set_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g )
@ ^ [D: b] : ( image_b_b @ ( converse_b_b @ ( getRel904497637nt_a_b @ C @ g ) ) @ ( insert_b @ D @ bot_bot_set_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_congr_I2_J) ).
thf(1238,plain,
! [A: b,B: b,C: standard_Constant_a] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( getRel904497637nt_a_b @ C @ g ) )
=> ( equiv_1821124534_set_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g )
@ ^ [D: b] : ( image_b_b @ ( converse_b_b @ ( getRel904497637nt_a_b @ C @ g ) ) @ ( insert_b @ D @ bot_bot_set_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(209,axiom,
( insert_b
= ( ^ [A: b,B: set_b] :
( collect_b
@ ^ [C: b] :
( ( C = A )
| ( member_b @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_insert__compr) ).
thf(1021,plain,
( insert_b
= ( ^ [A: b,B: set_b] :
( collect_b
@ ^ [C: b] :
( ( C = A )
| ( member_b @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(136,axiom,
! [A: product_prod_b_b] :
~ ! [B: b,C: b] :
( A
!= ( product_Pair_b_b @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_old_Oprod_Oexhaust) ).
thf(778,plain,
! [A: product_prod_b_b] :
~ ! [B: b,C: b] :
( A
!= ( product_Pair_b_b @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(311,axiom,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: set_b,D: set_b] :
( ( ord_le1036320359od_b_b @ A @ B )
=> ( ( ord_less_eq_set_b @ C @ D )
=> ( ord_less_eq_set_b @ ( image_b_b @ A @ C ) @ ( image_b_b @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_Image__mono) ).
thf(1365,plain,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: set_b,D: set_b] :
( ( ord_le1036320359od_b_b @ A @ B )
=> ( ( ord_less_eq_set_b @ C @ D )
=> ( ord_less_eq_set_b @ ( image_b_b @ A @ C ) @ ( image_b_b @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(169,axiom,
! [A: set_b] :
( ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ A )
= ( restri446606278nt_a_b @ ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_graph__empty__e) ).
thf(889,plain,
! [A: set_b] :
( ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ A )
= ( restri446606278nt_a_b @ ( labele1230159100nt_a_b @ bot_bo1664927607od_b_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(247,axiom,
order_653178932r_on_b @ bot_bot_set_b @ bot_bo1343651123od_b_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_lnear__order__on__empty) ).
thf(1159,plain,
order_653178932r_on_b @ bot_bot_set_b @ bot_bo1343651123od_b_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(54,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: set_Pr1324126435od_b_b] :
( ~ ( member1516365892od_b_b @ A @ B )
=> ( ( ord_le123089219od_b_b @ B @ ( insert2037698781od_b_b @ A @ C ) )
= ( ord_le123089219od_b_b @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_subset__insert) ).
thf(493,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: set_Pr1324126435od_b_b] :
( ~ ( member1516365892od_b_b @ A @ B )
=> ( ( ord_le123089219od_b_b @ B @ ( insert2037698781od_b_b @ A @ C ) )
= ( ord_le123089219od_b_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(285,axiom,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( refl_on_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
=> ( member_b @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_refl__onD2) ).
thf(1281,plain,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( refl_on_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
=> ( member_b @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(8,axiom,
! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
( ( ord_le123089219od_b_b @ A @ B )
=> ( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_subsetD) ).
thf(329,plain,
! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
( ( ord_le123089219od_b_b @ A @ B )
=> ( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(253,axiom,
! [A: b > $o,B: b] :
( ( ( A @ B )
=> ( ( collect_b
@ ^ [C: b] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_b @ B @ bot_bot_set_b ) ) )
& ( ~ ( A @ B )
=> ( ( collect_b
@ ^ [C: b] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_set_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_Collect__conv__if) ).
thf(1178,plain,
! [A: b > $o,B: b] :
( ( ( A @ B )
=> ( ( collect_b
@ ^ [C: b] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_b @ B @ bot_bot_set_b ) ) )
& ( ~ ( A @ B )
=> ( ( collect_b
@ ^ [C: b] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(82,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
( ( ~ ( member1516365892od_b_b @ A @ B )
=> ( A = C ) )
=> ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_insertCI) ).
thf(583,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
( ( ~ ( member1516365892od_b_b @ A @ B )
=> ( A = C ) )
=> ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(151,axiom,
! [A: produc1213276845od_b_b,B: produc1213276845od_b_b,C: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ B @ C ) )
= ( ( A = B )
| ( member1516365892od_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_insert__iff) ).
thf(830,plain,
! [A: produc1213276845od_b_b,B: produc1213276845od_b_b,C: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ B @ C ) )
= ( ( A = B )
| ( member1516365892od_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(110,axiom,
! [A: b,B: b,C: set_Product_prod_b_b,D: b > b > $o] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( converse_b_b @ C ) )
=> ( ! [E: b,F: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ E @ F ) @ C )
=> ( D @ F @ E ) )
=> ( D @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_converse_Oinducts) ).
thf(682,plain,
! [A: b,B: b,C: set_Product_prod_b_b,D: b > b > $o] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( converse_b_b @ C ) )
=> ( ! [E: b,F: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ E @ F ) @ C )
=> ( D @ F @ E ) )
=> ( D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(257,axiom,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( equiv_equiv_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
=> ( ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) )
= ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_equiv__class__eq) ).
thf(1195,plain,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( equiv_equiv_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
=> ( ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) )
= ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(6,axiom,
! [A: product_prod_b_b > $o] :
( ( ( collec1481886546od_b_b @ A )
= bot_bo1343651123od_b_b )
= ( ! [B: product_prod_b_b] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Collect__empty__eq) ).
thf(324,plain,
! [A: product_prod_b_b > $o] :
( ( ( collec1481886546od_b_b @ A )
= bot_bo1343651123od_b_b )
= ( ! [B: product_prod_b_b] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(191,axiom,
! [A: b > $o] :
( ( ( collect_b @ A )
= bot_bot_set_b )
= ( ! [B: b] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Collect__empty__eq) ).
thf(974,plain,
! [A: b > $o] :
( ( ( collect_b @ A )
= bot_bot_set_b )
= ( ! [B: b] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(114,axiom,
! [A: set_Pr1324126435od_b_b] :
( ( collec279084418od_b_b
@ ^ [B: produc1213276845od_b_b] : ( member1516365892od_b_b @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Collect__mem__eq) ).
thf(697,plain,
! [A: set_Pr1324126435od_b_b] :
( ( collec279084418od_b_b
@ ^ [B: produc1213276845od_b_b] : ( member1516365892od_b_b @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(278,axiom,
! [A: b,B: product_prod_b_b,C: set_Pr621705391od_b_b,D: set_b] :
( ( member641857272od_b_b @ ( produc1257047359od_b_b @ A @ B ) @ C )
=> ( ( member_b @ A @ D )
=> ( member1285940496od_b_b @ B @ ( image_1177096571od_b_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_ImageI) ).
thf(1259,plain,
! [A: b,B: product_prod_b_b,C: set_Pr621705391od_b_b,D: set_b] :
( ( member641857272od_b_b @ ( produc1257047359od_b_b @ A @ B ) @ C )
=> ( ( member_b @ A @ D )
=> ( member1285940496od_b_b @ B @ ( image_1177096571od_b_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(207,axiom,
! [A: b] : ( order_653178932r_on_b @ ( insert_b @ A @ bot_bot_set_b ) @ ( insert1952693431od_b_b @ ( product_Pair_b_b @ A @ A ) @ bot_bo1343651123od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_linear__order__on__singleton) ).
thf(1017,plain,
! [A: b] : ( order_653178932r_on_b @ ( insert_b @ A @ bot_bot_set_b ) @ ( insert1952693431od_b_b @ ( product_Pair_b_b @ A @ A ) @ bot_bo1343651123od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(221,axiom,
! [A: b > $o,B: b] :
( ( A @ B )
=> ( A @ ( hilbert_Eps_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_someI) ).
thf(1064,plain,
! [A: b > $o,B: b] :
( ( A @ B )
=> ( A @ ( hilbert_Eps_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(269,axiom,
! [A: set_Product_prod_b_b] :
( ( image_b_b @ A @ bot_bot_set_b )
= bot_bot_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Image__empty2) ).
thf(1227,plain,
! [A: set_Product_prod_b_b] :
( ( image_b_b @ A @ bot_bot_set_b )
= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(202,axiom,
! [A: set_b,B: set_b,C: b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ord_less_eq_set_b @ A @ ( insert_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_subset__insertI2) ).
thf(1006,plain,
! [A: set_b,B: set_b,C: b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ord_less_eq_set_b @ A @ ( insert_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(26,axiom,
! [A: set_b,B: set_Product_prod_b_b] :
( ( total_on_b @ A @ ( converse_b_b @ B ) )
= ( total_on_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_total__on__converse) ).
thf(388,plain,
! [A: set_b,B: set_Product_prod_b_b] :
( ( total_on_b @ A @ ( converse_b_b @ B ) )
= ( total_on_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(17,axiom,
! [A: product_prod_b_b,B: produc1213276845od_b_b,C: set_Pr1071216121od_b_b,D: set_Product_prod_b_b] :
( ( member4694106od_b_b @ ( produc732676669od_b_b @ A @ B ) @ C )
=> ( ( member1285940496od_b_b @ A @ D )
=> ( member1516365892od_b_b @ B @ ( image_532916993od_b_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_ImageI) ).
thf(356,plain,
! [A: product_prod_b_b,B: produc1213276845od_b_b,C: set_Pr1071216121od_b_b,D: set_Product_prod_b_b] :
( ( member4694106od_b_b @ ( produc732676669od_b_b @ A @ B ) @ C )
=> ( ( member1285940496od_b_b @ A @ D )
=> ( member1516365892od_b_b @ B @ ( image_532916993od_b_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(162,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] : ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_insertI1) ).
thf(869,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] : ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(248,axiom,
! [A: b,B: set_b,C: b] :
( ( ~ ( member_b @ A @ B )
=> ( A = C ) )
=> ( member_b @ A @ ( insert_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_insertCI) ).
thf(1160,plain,
! [A: b,B: set_b,C: b] :
( ( ~ ( member_b @ A @ B )
=> ( A = C ) )
=> ( member_b @ A @ ( insert_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(11,axiom,
! [A: product_prod_b_b,B: product_prod_b_b > $o] :
( ( member1285940496od_b_b @ A @ ( collec1481886546od_b_b @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_mem__Collect__eq) ).
thf(339,plain,
! [A: product_prod_b_b,B: product_prod_b_b > $o] :
( ( member1285940496od_b_b @ A @ ( collec1481886546od_b_b @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(289,axiom,
! [A: b,B: set_b,C: product_prod_b_b,D: set_Pr621705391od_b_b] :
( ( member_b @ A @ B )
=> ( ( member641857272od_b_b @ ( produc1257047359od_b_b @ A @ C ) @ D )
=> ( member1285940496od_b_b @ C @ ( image_1177096571od_b_b @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_rev__ImageI) ).
thf(1292,plain,
! [A: b,B: set_b,C: product_prod_b_b,D: set_Pr621705391od_b_b] :
( ( member_b @ A @ B )
=> ( ( member641857272od_b_b @ ( produc1257047359od_b_b @ A @ C ) @ D )
=> ( member1285940496od_b_b @ C @ ( image_1177096571od_b_b @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(129,axiom,
! [A: set_Pr1324126435od_b_b] :
( ( ? [B: produc1213276845od_b_b] : ( member1516365892od_b_b @ B @ A ) )
= ( A != bot_bo1664927607od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_ex__in__conv) ).
thf(753,plain,
! [A: set_Pr1324126435od_b_b] :
( ( ? [B: produc1213276845od_b_b] : ( member1516365892od_b_b @ B @ A ) )
= ( A != bot_bo1664927607od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(98,axiom,
! [A: standard_Constant_a,B: set_St761939237tant_a,C: product_prod_b_b,D: set_Pr1324126435od_b_b] :
( ( member1632892294tant_a @ A @ B )
=> ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ C ) @ D )
=> ( member1285940496od_b_b @ C @ ( image_1916422435od_b_b @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_rev__ImageI) ).
thf(637,plain,
! [A: standard_Constant_a,B: set_St761939237tant_a,C: product_prod_b_b,D: set_Pr1324126435od_b_b] :
( ( member1632892294tant_a @ A @ B )
=> ( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ C ) @ D )
=> ( member1285940496od_b_b @ C @ ( image_1916422435od_b_b @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(70,axiom,
! [A: set_Product_prod_b_b] :
( ( converse_b_b @ ( converse_b_b @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_converse__converse) ).
thf(547,plain,
! [A: set_Product_prod_b_b] :
( ( converse_b_b @ ( converse_b_b @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(297,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: b,D: set_Pr1906739389_b_b_b] :
( ( member1516365892od_b_b @ A @ B )
=> ( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ A @ C ) @ D )
=> ( member_b @ C @ ( image_1764625405_b_b_b @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_rev__ImageI) ).
thf(1324,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: b,D: set_Pr1906739389_b_b_b] :
( ( member1516365892od_b_b @ A @ B )
=> ( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ A @ C ) @ D )
=> ( member_b @ C @ ( image_1764625405_b_b_b @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(195,axiom,
! [A: b] :
~ ( member_b @ A @ bot_bot_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_emptyE) ).
thf(984,plain,
! [A: b] :
~ ( member_b @ A @ bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(121,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b @ A @ B )
=> ( ( insert2037698781od_b_b @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_insert__absorb) ).
thf(721,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b @ A @ B )
=> ( ( insert2037698781od_b_b @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(201,axiom,
! [A: set_Product_prod_b_b,B: b,C: b,D: set_b] :
( ( ( image_b_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
= ( image_b_b @ A @ ( insert_b @ C @ bot_bot_set_b ) ) )
=> ( ( equiv_equiv_b @ D @ A )
=> ( ( member_b @ C @ D )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_eq__equiv__class) ).
thf(1002,plain,
! [A: set_Product_prod_b_b,B: b,C: b,D: set_b] :
( ( ( image_b_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
= ( image_b_b @ A @ ( insert_b @ C @ bot_bot_set_b ) ) )
=> ( ( equiv_equiv_b @ D @ A )
=> ( ( member_b @ C @ D )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(57,axiom,
! [A: set_Product_prod_b_b] :
( ( ord_le1036320359od_b_b @ A @ bot_bo1343651123od_b_b )
= ( A = bot_bo1343651123od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_subset__empty) ).
thf(503,plain,
! [A: set_Product_prod_b_b] :
( ( ord_le1036320359od_b_b @ A @ bot_bo1343651123od_b_b )
= ( A = bot_bo1343651123od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(240,axiom,
! [A: product_prod_b_b,B: b,C: set_Pr357419743_b_b_b,D: set_Product_prod_b_b] :
( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ A @ B ) @ C )
=> ( ( member1285940496od_b_b @ A @ D )
=> ( member_b @ B @ ( image_921732011_b_b_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_ImageI) ).
thf(1131,plain,
! [A: product_prod_b_b,B: b,C: set_Pr357419743_b_b_b,D: set_Product_prod_b_b] :
( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ A @ B ) @ C )
=> ( ( member1285940496od_b_b @ A @ D )
=> ( member_b @ B @ ( image_921732011_b_b_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(103,axiom,
! [A: b,B: b,C: b,D: b] :
( ( ( product_Pair_b_b @ A @ B )
= ( product_Pair_b_b @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_old_Oprod_Oinject) ).
thf(654,plain,
! [A: b,B: b,C: b,D: b] :
( ( ( product_Pair_b_b @ A @ B )
= ( product_Pair_b_b @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(300,axiom,
! [A: b,B: b,C: set_b] :
( ( insert_b @ A @ ( insert_b @ B @ C ) )
= ( insert_b @ B @ ( insert_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_insert__commute) ).
thf(1333,plain,
! [A: b,B: b,C: set_b] :
( ( insert_b @ A @ ( insert_b @ B @ C ) )
= ( insert_b @ B @ ( insert_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(295,axiom,
! [A: b] :
( ( collect_b
@ ^ [B: b] : ( B = A ) )
= ( insert_b @ A @ bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_singleton__conv) ).
thf(1318,plain,
! [A: b] :
( ( collect_b
@ ^ [B: b] : ( B = A ) )
= ( insert_b @ A @ bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(260,axiom,
( is_singleton_b
= ( ^ [A: set_b] :
( A
= ( insert_b @ ( the_elem_b @ A ) @ bot_bot_set_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_is__singleton__the__elem) ).
thf(1202,plain,
( is_singleton_b
= ( ^ [A: set_b] :
( A
= ( insert_b @ ( the_elem_b @ A ) @ bot_bot_set_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(104,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b] : ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_insertI1) ).
thf(657,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b] : ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(74,axiom,
! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
( ! [C: standard_Constant_a,D: product_prod_b_b] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ D ) @ A )
=> ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ D ) @ B ) )
=> ( ord_le123089219od_b_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_subrelI) ).
thf(558,plain,
! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
( ! [C: standard_Constant_a,D: product_prod_b_b] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ D ) @ A )
=> ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ D ) @ B ) )
=> ( ord_le123089219od_b_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(179,axiom,
member1285940496od_b_b @ ( product_Pair_b_b @ x @ y ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__092_060open_062_Ix_M_Ay_J_A_092_060in_062_AgetRel_AS__Idt_AG_092_060close_062) ).
thf(926,plain,
member1285940496od_b_b @ ( product_Pair_b_b @ x @ y ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(287,axiom,
! [A: set_Pr621705391od_b_b] :
( ( image_1177096571od_b_b @ A @ bot_bot_set_b )
= bot_bo1343651123od_b_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Image__empty2) ).
thf(1286,plain,
! [A: set_Pr621705391od_b_b] :
( ( image_1177096571od_b_b @ A @ bot_bot_set_b )
= bot_bo1343651123od_b_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(214,axiom,
! [A: b > $o] :
( ( bot_bot_set_b
= ( collect_b @ A ) )
= ( ! [B: b] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_empty__Collect__eq) ).
thf(1035,plain,
! [A: b > $o] :
( ( bot_bot_set_b
= ( collect_b @ A ) )
= ( ! [B: b] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(106,axiom,
! [A: product_prod_b_b > $o,B: product_prod_b_b] :
( ( ( A @ B )
=> ( ( collec1481886546od_b_b
@ ^ [C: product_prod_b_b] :
( ( C = B )
& ( A @ C ) ) )
= ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) )
& ( ~ ( A @ B )
=> ( ( collec1481886546od_b_b
@ ^ [C: product_prod_b_b] :
( ( C = B )
& ( A @ C ) ) )
= bot_bo1343651123od_b_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_Collect__conv__if) ).
thf(662,plain,
! [A: product_prod_b_b > $o,B: product_prod_b_b] :
( ( ( A @ B )
=> ( ( collec1481886546od_b_b
@ ^ [C: product_prod_b_b] :
( ( C = B )
& ( A @ C ) ) )
= ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) )
& ( ~ ( A @ B )
=> ( ( collec1481886546od_b_b
@ ^ [C: product_prod_b_b] :
( ( C = B )
& ( A @ C ) ) )
= bot_bo1343651123od_b_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(120,axiom,
! [A: produc1213276845od_b_b,B: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ B @ bot_bo1664927607od_b_b ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_singleton__iff) ).
thf(718,plain,
! [A: produc1213276845od_b_b,B: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ B @ bot_bo1664927607od_b_b ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(175,axiom,
! [A: product_prod_b_b,B: set_Pr621705391od_b_b,C: b] :
( ( member1285940496od_b_b @ A @ ( image_1177096571od_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
= ( member641857272od_b_b @ ( produc1257047359od_b_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_Image__singleton__iff) ).
thf(906,plain,
! [A: product_prod_b_b,B: set_Pr621705391od_b_b,C: b] :
( ( member1285940496od_b_b @ A @ ( image_1177096571od_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
= ( member641857272od_b_b @ ( produc1257047359od_b_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(284,axiom,
! [A: produc1213276845od_b_b,B: set_Pr2060523537od_b_b,C: b] :
( ( member1516365892od_b_b @ A @ ( image_984343321od_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
= ( member599505522od_b_b @ ( produc800495189od_b_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_Image__singleton__iff) ).
thf(1278,plain,
! [A: produc1213276845od_b_b,B: set_Pr2060523537od_b_b,C: b] :
( ( member1516365892od_b_b @ A @ ( image_984343321od_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
= ( member599505522od_b_b @ ( produc800495189od_b_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(33,axiom,
! [A: product_prod_b_b] :
( ( collec1481886546od_b_b @ ( (=) @ product_prod_b_b @ A ) )
= ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_singleton__conv2) ).
thf(412,plain,
! [A: product_prod_b_b] :
( ( collec1481886546od_b_b @ ( (=) @ product_prod_b_b @ A ) )
= ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(92,axiom,
! [A: product_prod_b_b,B: product_prod_b_b,C: product_prod_b_b,D: product_prod_b_b] :
( ( ( insert1952693431od_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
= ( insert1952693431od_b_b @ C @ ( insert1952693431od_b_b @ D @ bot_bo1343651123od_b_b ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_doubleton__eq__iff) ).
thf(618,plain,
! [A: product_prod_b_b,B: product_prod_b_b,C: product_prod_b_b,D: product_prod_b_b] :
( ( ( insert1952693431od_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
= ( insert1952693431od_b_b @ C @ ( insert1952693431od_b_b @ D @ bot_bo1343651123od_b_b ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(243,axiom,
( bot_bot_set_b
= ( collect_b
@ ^ [A: b] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_empty__def) ).
thf(1146,plain,
( bot_bot_set_b
= ( collect_b
@ ^ [A: b] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(149,axiom,
! [A: set_Pr1324126435od_b_b] :
( ( ! [B: produc1213276845od_b_b] :
~ ( member1516365892od_b_b @ B @ A ) )
= ( A = bot_bo1664927607od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_all__not__in__conv) ).
thf(824,plain,
! [A: set_Pr1324126435od_b_b] :
( ( ! [B: produc1213276845od_b_b] :
~ ( member1516365892od_b_b @ B @ A ) )
= ( A = bot_bo1664927607od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(158,axiom,
! [A: set_Pr1324126435od_b_b,B: set_b] :
( ( labele1424214014nt_a_b @ ( labele1230159100nt_a_b @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_labeled__graph_Osel_I2_J) ).
thf(856,plain,
! [A: set_Pr1324126435od_b_b,B: set_b] :
( ( labele1424214014nt_a_b @ ( labele1230159100nt_a_b @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(292,axiom,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( refl_on_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
=> ( ( member_b @ C @ A )
& ( member_b @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_refl__on__domain) ).
thf(1301,plain,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( refl_on_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
=> ( ( member_b @ C @ A )
& ( member_b @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(23,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: set_Pr1324126435od_b_b] :
( ~ ( member1516365892od_b_b @ A @ B )
=> ( ~ ( member1516365892od_b_b @ A @ C )
=> ( ( ( insert2037698781od_b_b @ A @ B )
= ( insert2037698781od_b_b @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_insert__ident) ).
thf(375,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: set_Pr1324126435od_b_b] :
( ~ ( member1516365892od_b_b @ A @ B )
=> ( ~ ( member1516365892od_b_b @ A @ C )
=> ( ( ( insert2037698781od_b_b @ A @ B )
= ( insert2037698781od_b_b @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(75,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
( ( ( insert1952693431od_b_b @ A @ B )
= ( insert1952693431od_b_b @ C @ bot_bo1343651123od_b_b ) )
= ( ( A = C )
& ( ord_le1036320359od_b_b @ B @ ( insert1952693431od_b_b @ C @ bot_bo1343651123od_b_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_singleton__insert__inj__eq_H) ).
thf(562,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
( ( ( insert1952693431od_b_b @ A @ B )
= ( insert1952693431od_b_b @ C @ bot_bo1343651123od_b_b ) )
= ( ( A = C )
& ( ord_le1036320359od_b_b @ B @ ( insert1952693431od_b_b @ C @ bot_bo1343651123od_b_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(30,axiom,
! [A: set_Product_prod_b_b] :
( ( is_sin1713057243od_b_b @ A )
=> ~ ! [B: product_prod_b_b] :
( A
!= ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_is__singletonE) ).
thf(402,plain,
! [A: set_Product_prod_b_b] :
( ( is_sin1713057243od_b_b @ A )
=> ~ ! [B: product_prod_b_b] :
( A
!= ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(134,axiom,
! [A: standard_Constant_a,B: product_prod_b_b,C: set_Pr1324126435od_b_b,D: set_St761939237tant_a] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ B ) @ C )
=> ( ( member1632892294tant_a @ A @ D )
=> ( member1285940496od_b_b @ B @ ( image_1916422435od_b_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_ImageI) ).
thf(772,plain,
! [A: standard_Constant_a,B: product_prod_b_b,C: set_Pr1324126435od_b_b,D: set_St761939237tant_a] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ B ) @ C )
=> ( ( member1632892294tant_a @ A @ D )
=> ( member1285940496od_b_b @ B @ ( image_1916422435od_b_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(156,axiom,
! [A: set_Pr1324126435od_b_b,B: set_Pr2109276827od_b_b,C: produc1213276845od_b_b] :
( ( equiv_2048442231od_b_b @ A @ B )
=> ( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ ( image_763305007od_b_b @ B @ ( insert2037698781od_b_b @ C @ bot_bo1664927607od_b_b ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_equiv__class__self) ).
thf(843,plain,
! [A: set_Pr1324126435od_b_b,B: set_Pr2109276827od_b_b,C: produc1213276845od_b_b] :
( ( equiv_2048442231od_b_b @ A @ B )
=> ( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ ( image_763305007od_b_b @ B @ ( insert2037698781od_b_b @ C @ bot_bo1664927607od_b_b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(237,axiom,
( ord_less_eq_set_b
= ( ^ [A: set_b,B: set_b] :
! [C: b] :
( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_subset__iff) ).
thf(1125,plain,
( ord_less_eq_set_b
= ( ^ [A: set_b,B: set_b] :
! [C: b] :
( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(164,axiom,
! [A: product_prod_b_b] :
( ( collec1481886546od_b_b
@ ^ [B: product_prod_b_b] : ( B = A ) )
= ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_singleton__conv) ).
thf(875,plain,
! [A: product_prod_b_b] :
( ( collec1481886546od_b_b
@ ^ [B: product_prod_b_b] : ( B = A ) )
= ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(80,axiom,
! [A: product_prod_b_b,B: product_prod_b_b] :
( ( ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b )
= ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_singleton__inject) ).
thf(577,plain,
! [A: product_prod_b_b,B: product_prod_b_b] :
( ( ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b )
= ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(118,axiom,
( bot_bo1167600078_b_b_o
= ( ^ [A: produc1213276845od_b_b] : ( member1516365892od_b_b @ A @ bot_bo1664927607od_b_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_bot__empty__eq) ).
thf(711,plain,
( bot_bo1167600078_b_b_o
= ( ^ [A: produc1213276845od_b_b] : ( member1516365892od_b_b @ A @ bot_bo1664927607od_b_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(277,axiom,
! [A: b,B: b,C: set_b] :
( ( member_b @ A @ ( insert_b @ B @ C ) )
=> ( ( A != B )
=> ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_insertE) ).
thf(1256,plain,
! [A: b,B: b,C: set_b] :
( ( member_b @ A @ ( insert_b @ B @ C ) )
=> ( ( A != B )
=> ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(69,axiom,
( bot_bo1343651123od_b_b
= ( collec1481886546od_b_b
@ ^ [A: product_prod_b_b] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_empty__def) ).
thf(545,plain,
( bot_bo1343651123od_b_b
= ( collec1481886546od_b_b
@ ^ [A: product_prod_b_b] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(27,axiom,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
( ! [C: product_prod_b_b] :
( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ B ) )
=> ( ord_le1036320359od_b_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_subsetI) ).
thf(391,plain,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
( ! [C: product_prod_b_b] :
( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ B ) )
=> ( ord_le1036320359od_b_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(282,axiom,
! [A: set_b,B: set_b,C: b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_subsetD) ).
thf(1271,plain,
! [A: set_b,B: set_b,C: b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(139,axiom,
! [A: b > $o,B: b > $o] :
( ( ord_less_eq_set_b @ ( collect_b @ A ) @ ( collect_b @ B ) )
= ( ! [C: b] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_Collect__mono__iff) ).
thf(787,plain,
! [A: b > $o,B: b > $o] :
( ( ord_less_eq_set_b @ ( collect_b @ A ) @ ( collect_b @ B ) )
= ( ! [C: b] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(119,axiom,
! [A: product_prod_b_b > $o,B: product_prod_b_b] :
( ! [C: b,D: b] : ( A @ ( product_Pair_b_b @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_old_Oprod_Oinducts) ).
thf(713,plain,
! [A: product_prod_b_b > $o,B: product_prod_b_b] :
( ! [C: b,D: b] : ( A @ ( product_Pair_b_b @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(45,axiom,
! [A: set_Product_prod_b_b,B: product_prod_b_b > $o] :
( ord_le1036320359od_b_b
@ ( collec1481886546od_b_b
@ ^ [C: product_prod_b_b] :
( ( member1285940496od_b_b @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_Collect__subset) ).
thf(466,plain,
! [A: set_Product_prod_b_b,B: product_prod_b_b > $o] :
( ord_le1036320359od_b_b
@ ( collec1481886546od_b_b
@ ^ [C: product_prod_b_b] :
( ( member1285940496od_b_b @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(268,axiom,
! [A: b] :
( ( collect_b @ ( (=) @ b @ A ) )
= ( insert_b @ A @ bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_singleton__conv2) ).
thf(1224,plain,
! [A: b] :
( ( collect_b @ ( (=) @ b @ A ) )
= ( insert_b @ A @ bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(308,axiom,
! [A: set_b,B: set_b,C: b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_in__mono) ).
thf(1356,plain,
! [A: set_b,B: set_b,C: b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(15,axiom,
! [A: set_Pr1324126435od_b_b,B: standard_Constant_a] :
( ( image_1916422435od_b_b @ A @ ( insert1909710879tant_a @ B @ bot_bo1160111033tant_a ) )
= ( collec1481886546od_b_b
@ ^ [C: product_prod_b_b] : ( member1516365892od_b_b @ ( produc1432590431od_b_b @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_Image__singleton) ).
thf(350,plain,
! [A: set_Pr1324126435od_b_b,B: standard_Constant_a] :
( ( image_1916422435od_b_b @ A @ ( insert1909710879tant_a @ B @ bot_bo1160111033tant_a ) )
= ( collec1481886546od_b_b
@ ^ [C: product_prod_b_b] : ( member1516365892od_b_b @ ( produc1432590431od_b_b @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(68,axiom,
! [A: set_Pr1324126435od_b_b,B: produc1213276845od_b_b] :
( ( A = bot_bo1664927607od_b_b )
=> ~ ( member1516365892od_b_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_equals0D) ).
thf(540,plain,
! [A: set_Pr1324126435od_b_b,B: produc1213276845od_b_b] :
( ( A = bot_bo1664927607od_b_b )
=> ~ ( member1516365892od_b_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(19,axiom,
! [A: product_prod_b_b > $o] :
( ( ( collec1481886546od_b_b @ A )
= bot_bo1343651123od_b_b )
= ( A = bot_bo1302443370_b_b_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_Collect__empty__eq__bot) ).
thf(362,plain,
! [A: product_prod_b_b > $o] :
( ( ( collec1481886546od_b_b @ A )
= bot_bo1343651123od_b_b )
= ( A = bot_bo1302443370_b_b_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(217,axiom,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ~ ! [C: set_b] :
( ( B
= ( insert_b @ A @ C ) )
=> ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_Set_Oset__insert) ).
thf(1043,plain,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ~ ! [C: set_b] :
( ( B
= ( insert_b @ A @ C ) )
=> ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(236,axiom,
! [A: set_b] :
( ( ord_less_eq_set_b @ A @ bot_bot_set_b )
= ( A = bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_bot_Oextremum__unique) ).
thf(1122,plain,
! [A: set_b] :
( ( ord_less_eq_set_b @ A @ bot_bot_set_b )
= ( A = bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(252,axiom,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ( ( insert_b @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_insert__absorb) ).
thf(1175,plain,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ( ( insert_b @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(193,axiom,
( g
= ( restri446606278nt_a_b @ g ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_assms_I1_J) ).
thf(979,plain,
( g
= ( restri446606278nt_a_b @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(89,axiom,
! [A: b,B: b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( converse_b_b @ C ) )
= ( ? [D: b,E: b] :
( ( A = E )
& ( B = D )
& ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ E ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_converse_Osimps) ).
thf(604,plain,
! [A: b,B: b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( converse_b_b @ C ) )
= ( ? [D: b,E: b] :
( ( A = E )
& ( B = D )
& ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ E ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(173,axiom,
! [A: set_b] :
( ( ord_less_eq_set_b @ A @ bot_bot_set_b )
= ( A = bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_subset__empty) ).
thf(900,plain,
! [A: set_b] :
( ( ord_less_eq_set_b @ A @ bot_bot_set_b )
= ( A = bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(31,axiom,
! [A: product_prod_b_b] :
( ( the_el329196508od_b_b @ ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_the__elem__eq) ).
thf(406,plain,
! [A: product_prod_b_b] :
( ( the_el329196508od_b_b @ ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(218,axiom,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( equiv_equiv_b @ A @ B )
=> ( ( member_b @ C @ A )
=> ( ( member_b @ D @ A )
=> ( ( ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) )
= ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) )
= ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_eq__equiv__class__iff) ).
thf(1048,plain,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( equiv_equiv_b @ A @ B )
=> ( ( member_b @ C @ A )
=> ( ( member_b @ D @ A )
=> ( ( ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) )
= ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) )
= ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(124,axiom,
! [A: produc1213276845od_b_b] :
? [B: standard_Constant_a,C: product_prod_b_b] :
( A
= ( produc1432590431od_b_b @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_surj__pair) ).
thf(736,plain,
! [A: produc1213276845od_b_b] :
? [B: standard_Constant_a,C: product_prod_b_b] :
( A
= ( produc1432590431od_b_b @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(197,axiom,
! [A: set_b] :
( ( collect_b
@ ^ [B: b] : ( member_b @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_Collect__mem__eq) ).
thf(990,plain,
! [A: set_b] :
( ( collect_b
@ ^ [B: b] : ( member_b @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(199,axiom,
! [A: b,B: b,C: set_b] :
( ( member_b @ A @ ( insert_b @ B @ C ) )
= ( ( A = B )
| ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_insert__iff) ).
thf(996,plain,
! [A: b,B: b,C: set_b] :
( ( member_b @ A @ ( insert_b @ B @ C ) )
= ( ( A = B )
| ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(49,axiom,
! [A: produc1213276845od_b_b,B: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ B @ bot_bo1664927607od_b_b ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_singletonD) ).
thf(477,plain,
! [A: produc1213276845od_b_b,B: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ A @ ( insert2037698781od_b_b @ B @ bot_bo1664927607od_b_b ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(13,axiom,
( ord_le123089219od_b_b
= ( ^ [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
! [C: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_subset__iff) ).
thf(345,plain,
( ord_le123089219od_b_b
= ( ^ [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
! [C: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(66,axiom,
! [A: product_prod_b_b] :
~ ( member1285940496od_b_b @ A @ bot_bo1343651123od_b_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_empty__iff) ).
thf(535,plain,
! [A: product_prod_b_b] :
~ ( member1285940496od_b_b @ A @ bot_bo1343651123od_b_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(91,axiom,
! [A: set_Product_prod_b_b] :
( ( A != bot_bo1343651123od_b_b )
=> ( ! [B: product_prod_b_b,C: product_prod_b_b] :
( ( member1285940496od_b_b @ B @ A )
=> ( ( member1285940496od_b_b @ C @ A )
=> ( B = C ) ) )
=> ( is_sin1713057243od_b_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_is__singletonI_H) ).
thf(609,plain,
! [A: set_Product_prod_b_b] :
( ( A != bot_bo1343651123od_b_b )
=> ( ! [B: product_prod_b_b,C: product_prod_b_b] :
( ( member1285940496od_b_b @ B @ A )
=> ( ( member1285940496od_b_b @ C @ A )
=> ( B = C ) ) )
=> ( is_sin1713057243od_b_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(85,axiom,
! [A: set_Product_prod_b_b] :
( ( member1285940496od_b_b
@ ( hilber620807523od_b_b
@ ^ [B: product_prod_b_b] : ( member1285940496od_b_b @ B @ A ) )
@ A )
= ( A != bot_bo1343651123od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_some__in__eq) ).
thf(594,plain,
! [A: set_Product_prod_b_b] :
( ( member1285940496od_b_b
@ ( hilber620807523od_b_b
@ ^ [B: product_prod_b_b] : ( member1285940496od_b_b @ B @ A ) )
@ A )
= ( A != bot_bo1343651123od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(93,axiom,
! [A: produc1213276845od_b_b] :
~ ( member1516365892od_b_b @ A @ bot_bo1664927607od_b_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_emptyE) ).
thf(621,plain,
! [A: produc1213276845od_b_b] :
~ ( member1516365892od_b_b @ A @ bot_bo1664927607od_b_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(51,axiom,
! [A: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b
@ ( hilber46179633od_b_b
@ ^ [B: produc1213276845od_b_b] : ( member1516365892od_b_b @ B @ A ) )
@ A )
= ( A != bot_bo1664927607od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_some__in__eq) ).
thf(483,plain,
! [A: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b
@ ( hilber46179633od_b_b
@ ^ [B: produc1213276845od_b_b] : ( member1516365892od_b_b @ B @ A ) )
@ A )
= ( A != bot_bo1664927607od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(115,axiom,
! [A: product_prod_b_b > $o,B: product_prod_b_b] :
( ! [C: b,D: b] : ( A @ ( product_Pair_b_b @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_prod__cases) ).
thf(700,plain,
! [A: product_prod_b_b > $o,B: product_prod_b_b] :
( ! [C: b,D: b] : ( A @ ( product_Pair_b_b @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(212,axiom,
( total_on_b
= ( ^ [A: set_b,B: set_Product_prod_b_b] :
! [C: b] :
( ( member_b @ C @ A )
=> ! [D: b] :
( ( member_b @ D @ A )
=> ( ( C != D )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
| ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ C ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_total__on__def) ).
thf(1029,plain,
( total_on_b
= ( ^ [A: set_b,B: set_Product_prod_b_b] :
! [C: b] :
( ( member_b @ C @ A )
=> ! [D: b] :
( ( member_b @ D @ A )
=> ( ( C != D )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
| ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ C ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(188,axiom,
! [A: set_b] :
( ! [B: b] :
~ ( member_b @ B @ A )
=> ( A = bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_equals0I) ).
thf(964,plain,
! [A: set_b] :
( ! [B: b] :
~ ( member_b @ B @ A )
=> ( A = bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(133,axiom,
! [A: set_Product_prod_b_b,B: product_prod_b_b] :
( ( ord_le1036320359od_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
= ( ( A = bot_bo1343651123od_b_b )
| ( A
= ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_subset__singleton__iff) ).
thf(769,plain,
! [A: set_Product_prod_b_b,B: product_prod_b_b] :
( ( ord_le1036320359od_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
= ( ( A = bot_bo1343651123od_b_b )
| ( A
= ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(183,axiom,
! [A: standard_Constant_a,B: b,C: b] :
( ( labele1230159100nt_a_b @ ( insert2037698781od_b_b @ ( produc1432590431od_b_b @ A @ ( product_Pair_b_b @ B @ C ) ) @ bot_bo1664927607od_b_b ) @ ( insert_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
= ( restri446606278nt_a_b @ ( labele1230159100nt_a_b @ ( insert2037698781od_b_b @ ( produc1432590431od_b_b @ A @ ( product_Pair_b_b @ B @ C ) ) @ bot_bo1664927607od_b_b ) @ ( insert_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_graph__single) ).
thf(943,plain,
! [A: standard_Constant_a,B: b,C: b] :
( ( labele1230159100nt_a_b @ ( insert2037698781od_b_b @ ( produc1432590431od_b_b @ A @ ( product_Pair_b_b @ B @ C ) ) @ bot_bo1664927607od_b_b ) @ ( insert_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) )
= ( restri446606278nt_a_b @ ( labele1230159100nt_a_b @ ( insert2037698781od_b_b @ ( produc1432590431od_b_b @ A @ ( product_Pair_b_b @ B @ C ) ) @ bot_bo1664927607od_b_b ) @ ( insert_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(61,axiom,
! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
( ( ( ^ [C: standard_Constant_a,D: product_prod_b_b] : ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ D ) @ A ) )
= ( ^ [C: standard_Constant_a,D: product_prod_b_b] : ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ D ) @ B ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_pred__equals__eq2) ).
thf(521,plain,
! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
( ( ( ^ [C: standard_Constant_a,D: product_prod_b_b] : ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ D ) @ A ) )
= ( ^ [C: standard_Constant_a,D: product_prod_b_b] : ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ D ) @ B ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(29,axiom,
! [A: set_Product_prod_b_b] :
( ( ? [B: product_prod_b_b] : ( member1285940496od_b_b @ B @ A ) )
= ( A != bot_bo1343651123od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_ex__in__conv) ).
thf(399,plain,
! [A: set_Product_prod_b_b] :
( ( ? [B: product_prod_b_b] : ( member1285940496od_b_b @ B @ A ) )
= ( A != bot_bo1343651123od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(264,axiom,
! [A: set_b] :
( ( member_b
@ ( hilbert_Eps_b
@ ^ [B: b] : ( member_b @ B @ A ) )
@ A )
= ( A != bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_some__in__eq) ).
thf(1213,plain,
! [A: set_b] :
( ( member_b
@ ( hilbert_Eps_b
@ ^ [B: b] : ( member_b @ B @ A ) )
@ A )
= ( A != bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(150,axiom,
! [A: product_prod_b_b,B: product_prod_b_b,C: set_Product_prod_b_b] :
( ( ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b )
= ( insert1952693431od_b_b @ B @ C ) )
= ( ( B = A )
& ( ord_le1036320359od_b_b @ C @ ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_singleton__insert__inj__eq) ).
thf(827,plain,
! [A: product_prod_b_b,B: product_prod_b_b,C: set_Product_prod_b_b] :
( ( ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b )
= ( insert1952693431od_b_b @ B @ C ) )
= ( ( B = A )
& ( ord_le1036320359od_b_b @ C @ ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(42,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b @ A @ B )
=> ? [C: set_Pr1324126435od_b_b] :
( ( B
= ( insert2037698781od_b_b @ A @ C ) )
& ~ ( member1516365892od_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_mk__disjoint__insert) ).
thf(455,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
( ( member1516365892od_b_b @ A @ B )
=> ? [C: set_Pr1324126435od_b_b] :
( ( B
= ( insert2037698781od_b_b @ A @ C ) )
& ~ ( member1516365892od_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(167,axiom,
! [A: set_Product_prod_b_b] : ( ord_le1036320359od_b_b @ bot_bo1343651123od_b_b @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_empty__subsetI) ).
thf(883,plain,
! [A: set_Product_prod_b_b] : ( ord_le1036320359od_b_b @ bot_bo1343651123od_b_b @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(249,axiom,
! [A: b] :
( ( the_elem_b @ ( insert_b @ A @ bot_bot_set_b ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_the__elem__eq) ).
thf(1166,plain,
! [A: b] :
( ( the_elem_b @ ( insert_b @ A @ bot_bot_set_b ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(64,axiom,
( bot_bo1302443370_b_b_o
= ( ^ [A: product_prod_b_b] : ( member1285940496od_b_b @ A @ bot_bo1343651123od_b_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_bot__empty__eq) ).
thf(531,plain,
( bot_bo1302443370_b_b_o
= ( ^ [A: product_prod_b_b] : ( member1285940496od_b_b @ A @ bot_bo1343651123od_b_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(142,axiom,
! [A: product_prod_b_b,B: set_Pr1324126435od_b_b,C: standard_Constant_a] :
( ( member1285940496od_b_b @ A @ ( image_1916422435od_b_b @ B @ ( insert1909710879tant_a @ C @ bot_bo1160111033tant_a ) ) )
= ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Image__singleton__iff) ).
thf(795,plain,
! [A: product_prod_b_b,B: set_Pr1324126435od_b_b,C: standard_Constant_a] :
( ( member1285940496od_b_b @ A @ ( image_1916422435od_b_b @ B @ ( insert1909710879tant_a @ C @ bot_bo1160111033tant_a ) ) )
= ( member1516365892od_b_b @ ( produc1432590431od_b_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(180,axiom,
! [A: b > $o,B: b > $o] :
( ? [C: b] : ( A @ C )
=> ( ! [C: b] :
( ( A @ C )
=> ( B @ C ) )
=> ( B @ ( hilbert_Eps_b @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_someI2__ex) ).
thf(927,plain,
! [A: b > $o,B: b > $o] :
( ? [C: b] : ( A @ C )
=> ( ! [C: b] :
( ( A @ C )
=> ( B @ C ) )
=> ( B @ ( hilbert_Eps_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(226,axiom,
! [A: b] : ( refl_on_b @ ( insert_b @ A @ bot_bot_set_b ) @ ( insert1952693431od_b_b @ ( product_Pair_b_b @ A @ A ) @ bot_bo1343651123od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_refl__on__singleton) ).
thf(1081,plain,
! [A: b] : ( refl_on_b @ ( insert_b @ A @ bot_bot_set_b ) @ ( insert1952693431od_b_b @ ( product_Pair_b_b @ A @ A ) @ bot_bo1343651123od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(59,axiom,
! [A: set_Pr2007082183od_b_b] : ( total_178717291od_b_b @ bot_bo1343651123od_b_b @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_total__on__empty) ).
thf(516,plain,
! [A: set_Pr2007082183od_b_b] : ( total_178717291od_b_b @ bot_bo1343651123od_b_b @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(12,axiom,
! [A: product_prod_b_b > $o] :
( ( bot_bo1343651123od_b_b
= ( collec1481886546od_b_b @ A ) )
= ( ! [B: product_prod_b_b] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_empty__Collect__eq) ).
thf(342,plain,
! [A: product_prod_b_b > $o] :
( ( bot_bo1343651123od_b_b
= ( collec1481886546od_b_b @ A ) )
= ( ! [B: product_prod_b_b] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(72,axiom,
! [A: set_Product_prod_b_b,B: set_Pr2007082183od_b_b,C: product_prod_b_b] :
( ( equiv_1125628061od_b_b @ A @ B )
=> ( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ ( image_1928024979od_b_b @ B @ ( insert1952693431od_b_b @ C @ bot_bo1343651123od_b_b ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_equiv__class__self) ).
thf(553,plain,
! [A: set_Product_prod_b_b,B: set_Pr2007082183od_b_b,C: product_prod_b_b] :
( ( equiv_1125628061od_b_b @ A @ B )
=> ( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ ( image_1928024979od_b_b @ B @ ( insert1952693431od_b_b @ C @ bot_bo1343651123od_b_b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(189,axiom,
! [A: b] :
( ( member_b @ A @ ( labele1424214014nt_a_b @ g ) )
= ( p @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_r1) ).
thf(968,plain,
! [A: b] :
( ( member_b @ A @ ( labele1424214014nt_a_b @ g ) )
= ( p @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(153,axiom,
( ( converse_b_b @ bot_bo1343651123od_b_b )
= bot_bo1343651123od_b_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_converse__empty) ).
thf(836,plain,
( ( converse_b_b @ bot_bo1343651123od_b_b )
= bot_bo1343651123od_b_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(53,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1071216121od_b_b,C: product_prod_b_b] :
( ( member1516365892od_b_b @ A @ ( image_532916993od_b_b @ B @ ( insert1952693431od_b_b @ C @ bot_bo1343651123od_b_b ) ) )
= ( member4694106od_b_b @ ( produc732676669od_b_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_Image__singleton__iff) ).
thf(490,plain,
! [A: produc1213276845od_b_b,B: set_Pr1071216121od_b_b,C: product_prod_b_b] :
( ( member1516365892od_b_b @ A @ ( image_532916993od_b_b @ B @ ( insert1952693431od_b_b @ C @ bot_bo1343651123od_b_b ) ) )
= ( member4694106od_b_b @ ( produc732676669od_b_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(108,axiom,
! [A: b,B: b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( converse_b_b @ C ) )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_converseD) ).
thf(675,plain,
! [A: b,B: b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( converse_b_b @ C ) )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(262,axiom,
! [A: set_b] :
( ( ord_less_eq_set_b @ A @ bot_bot_set_b )
=> ( A = bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_bot_Oextremum__uniqueI) ).
thf(1208,plain,
! [A: set_b] :
( ( ord_less_eq_set_b @ A @ bot_bot_set_b )
=> ( A = bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(83,axiom,
! [A: produc1213276845od_b_b] :
~ ( member1516365892od_b_b @ A @ bot_bo1664927607od_b_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_empty__iff) ).
thf(589,plain,
! [A: produc1213276845od_b_b] :
~ ( member1516365892od_b_b @ A @ bot_bo1664927607od_b_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(241,axiom,
( p
= ( ^ [A: b,B: b] : ( member_b @ B @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_P) ).
thf(1134,plain,
( p
= ( ^ [A: b,B: b] : ( member_b @ B @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(101,axiom,
! [A: b,B: b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( converse_b_b @ C ) )
= ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_converse__iff) ).
thf(648,plain,
! [A: b,B: b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ B ) @ ( converse_b_b @ C ) )
= ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(81,axiom,
! [A: b,B: b] :
( ( if_b @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001tf__b_T) ).
thf(580,plain,
! [A: b,B: b] :
( ( if_b @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(112,axiom,
! [A: standard_Constant_a,B: product_prod_b_b,C: standard_Constant_a,D: product_prod_b_b] :
( ( ( produc1432590431od_b_b @ A @ B )
= ( produc1432590431od_b_b @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_prod_Oinject) ).
thf(690,plain,
! [A: standard_Constant_a,B: product_prod_b_b,C: standard_Constant_a,D: product_prod_b_b] :
( ( ( produc1432590431od_b_b @ A @ B )
= ( produc1432590431od_b_b @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(99,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b] :
( ~ ( member1285940496od_b_b @ A @ B )
=> ( ~ ( member1285940496od_b_b @ A @ C )
=> ( ( ( insert1952693431od_b_b @ A @ B )
= ( insert1952693431od_b_b @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_insert__ident) ).
thf(640,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b] :
( ~ ( member1285940496od_b_b @ A @ B )
=> ( ~ ( member1285940496od_b_b @ A @ C )
=> ( ( ( insert1952693431od_b_b @ A @ B )
= ( insert1952693431od_b_b @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(211,axiom,
! [A: b,B: set_Pr357419743_b_b_b,C: set_Product_prod_b_b] :
( ( member_b @ A @ ( image_921732011_b_b_b @ B @ C ) )
=> ~ ! [D: product_prod_b_b] :
( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ D @ A ) @ B )
=> ~ ( member1285940496od_b_b @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_ImageE) ).
thf(1025,plain,
! [A: b,B: set_Pr357419743_b_b_b,C: set_Product_prod_b_b] :
( ( member_b @ A @ ( image_921732011_b_b_b @ B @ C ) )
=> ~ ! [D: product_prod_b_b] :
( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ D @ A ) @ B )
=> ~ ( member1285940496od_b_b @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(190,axiom,
! [A: b,B: b,C: set_b] :
( ( ( insert_b @ A @ bot_bot_set_b )
= ( insert_b @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq_set_b @ C @ ( insert_b @ A @ bot_bot_set_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_singleton__insert__inj__eq) ).
thf(971,plain,
! [A: b,B: b,C: set_b] :
( ( ( insert_b @ A @ bot_bot_set_b )
= ( insert_b @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq_set_b @ C @ ( insert_b @ A @ bot_bot_set_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(7,axiom,
( ord_le123089219od_b_b
= ( ^ [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
! [C: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_subset__eq) ).
thf(327,plain,
( ord_le123089219od_b_b
= ( ^ [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b] :
! [C: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(187,axiom,
! [A: b > $o,B: b] :
( ? [C: b] :
( ( A @ C )
& ! [D: b] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ( A @ B )
=> ( ( hilbert_Eps_b @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_some1__equality) ).
thf(954,plain,
! [A: b > $o,B: b] :
( ? [C: b] :
( ( A @ C )
& ! [D: b] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ( A @ B )
=> ( ( hilbert_Eps_b @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(125,axiom,
! [A: set_Product_prod_b_b] : ( ord_le1036320359od_b_b @ bot_bo1343651123od_b_b @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_bot_Oextremum) ).
thf(739,plain,
! [A: set_Product_prod_b_b] : ( ord_le1036320359od_b_b @ bot_bo1343651123od_b_b @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(312,axiom,
member1516365892od_b_b @ ( produc1432590431od_b_b @ standard_S_Idt_a @ ( product_Pair_b_b @ x @ y ) ) @ ( labele1741081071nt_a_b @ g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168__092_060open_062_IS__Idt_M_Ax_M_Ay_J_A_092_060in_062_Aedges_AG_092_060close_062) ).
thf(1368,plain,
member1516365892od_b_b @ ( produc1432590431od_b_b @ standard_S_Idt_a @ ( product_Pair_b_b @ x @ y ) ) @ ( labele1741081071nt_a_b @ g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(230,axiom,
! [A: b] :
( ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
= bot_bot_set_b )
= ( ~ ( member_b @ A @ ( labele1424214014nt_a_b @ g ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_r2) ).
thf(1098,plain,
! [A: b] :
( ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
= bot_bot_set_b )
= ( ~ ( member_b @ A @ ( labele1424214014nt_a_b @ g ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(198,axiom,
! [A: b > $o,B: b] :
( ( A @ B )
=> ( A @ ( hilbert_Eps_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_tfl__some) ).
thf(993,plain,
! [A: b > $o,B: b] :
( ( A @ B )
=> ( A @ ( hilbert_Eps_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(116,axiom,
! [A: set_b,B: set_Product_prod_b_b] :
( ( order_653178932r_on_b @ A @ ( converse_b_b @ B ) )
= ( order_653178932r_on_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_linear__order__on__converse) ).
thf(705,plain,
! [A: set_b,B: set_Product_prod_b_b] :
( ( order_653178932r_on_b @ A @ ( converse_b_b @ B ) )
= ( order_653178932r_on_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(246,axiom,
! [A: set_b] :
( ( image_b_b @ bot_bo1343651123od_b_b @ A )
= bot_bot_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_Image__empty1) ).
thf(1156,plain,
! [A: set_b] :
( ( image_b_b @ bot_bo1343651123od_b_b @ A )
= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(32,axiom,
! [A: product_prod_b_b] :
? [B: b,C: b] :
( A
= ( product_Pair_b_b @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_surj__pair) ).
thf(409,plain,
! [A: product_prod_b_b] :
? [B: b,C: b] :
( A
= ( product_Pair_b_b @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(270,axiom,
! [A: b,B: b > $o] :
( ( insert_b @ A @ ( collect_b @ B ) )
= ( collect_b
@ ^ [C: b] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_insert__Collect) ).
thf(1230,plain,
! [A: b,B: b > $o] :
( ( insert_b @ A @ ( collect_b @ B ) )
= ( collect_b
@ ^ [C: b] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(254,axiom,
! [A: set_b,B: set_Product_prod_b_b,C: b] :
( ( refl_on_b @ A @ B )
=> ( ( member_b @ C @ A )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_refl__onD) ).
thf(1186,plain,
! [A: set_b,B: set_Product_prod_b_b,C: b] :
( ( refl_on_b @ A @ B )
=> ( ( member_b @ C @ A )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(215,axiom,
! [A: set_Product_prod_b_b] : ( total_on_b @ bot_bot_set_b @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_total__on__empty) ).
thf(1038,plain,
! [A: set_Product_prod_b_b] : ( total_on_b @ bot_bot_set_b @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(155,axiom,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( ( ( labele1741081071nt_a_b @ A )
= ( labele1741081071nt_a_b @ B ) )
& ( ( labele1424214014nt_a_b @ A )
= ( labele1424214014nt_a_b @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_labeled__graph_Oexpand) ).
thf(840,plain,
! [A: labele1159362096nt_a_b,B: labele1159362096nt_a_b] :
( ( ( ( labele1741081071nt_a_b @ A )
= ( labele1741081071nt_a_b @ B ) )
& ( ( labele1424214014nt_a_b @ A )
= ( labele1424214014nt_a_b @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(44,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b] :
( ( ord_le1036320359od_b_b @ ( insert1952693431od_b_b @ A @ B ) @ C )
= ( ( member1285940496od_b_b @ A @ C )
& ( ord_le1036320359od_b_b @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_insert__subset) ).
thf(463,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: set_Product_prod_b_b] :
( ( ord_le1036320359od_b_b @ ( insert1952693431od_b_b @ A @ B ) @ C )
= ( ( member1285940496od_b_b @ A @ C )
& ( ord_le1036320359od_b_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(228,axiom,
! [A: set_b,B: set_Product_prod_b_b] :
( ! [C: b,D: b] :
( ( member_b @ C @ A )
=> ( ( member_b @ D @ A )
=> ( ( C != D )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
| ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ C ) @ B ) ) ) ) )
=> ( total_on_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_total__onI) ).
thf(1085,plain,
! [A: set_b,B: set_Product_prod_b_b] :
( ! [C: b,D: b] :
( ( member_b @ C @ A )
=> ( ( member_b @ D @ A )
=> ( ( C != D )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
| ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ C ) @ B ) ) ) ) )
=> ( total_on_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(18,axiom,
! [A: set_Product_prod_b_b] :
( ( collec1481886546od_b_b
@ ^ [B: product_prod_b_b] : ( member1285940496od_b_b @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_Collect__mem__eq) ).
thf(359,plain,
! [A: set_Product_prod_b_b] :
( ( collec1481886546od_b_b
@ ^ [B: product_prod_b_b] : ( member1285940496od_b_b @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(266,axiom,
( is_singleton_b
= ( ^ [A: set_b] :
? [B: b] :
( A
= ( insert_b @ B @ bot_bot_set_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_is__singleton__def) ).
thf(1218,plain,
( is_singleton_b
= ( ^ [A: set_b] :
? [B: b] :
( A
= ( insert_b @ B @ bot_bot_set_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(301,axiom,
( bot_bot_set_b
= ( collect_b @ bot_bot_b_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_bot__set__def) ).
thf(1336,plain,
( bot_bot_set_b
= ( collect_b @ bot_bot_b_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(267,axiom,
! [A: b,B: set_b,C: b,D: set_b] :
( ~ ( member_b @ A @ B )
=> ( ~ ( member_b @ C @ D )
=> ( ( ( insert_b @ A @ B )
= ( insert_b @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_b] :
( ( B
= ( insert_b @ C @ E ) )
& ~ ( member_b @ C @ E )
& ( D
= ( insert_b @ A @ E ) )
& ~ ( member_b @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_insert__eq__iff) ).
thf(1220,plain,
! [A: b,B: set_b,C: b,D: set_b] :
( ~ ( member_b @ A @ B )
=> ( ~ ( member_b @ C @ D )
=> ( ( ( insert_b @ A @ B )
= ( insert_b @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_b] :
( ( B
= ( insert_b @ C @ E ) )
& ~ ( member_b @ C @ E )
& ( D
= ( insert_b @ A @ E ) )
& ~ ( member_b @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(279,axiom,
! [A: b > $o,B: b > $o] :
( ! [C: b] :
( ( A @ C )
= ( B @ C ) )
=> ( ( hilbert_Eps_b @ A )
= ( hilbert_Eps_b @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_Eps__cong) ).
thf(1262,plain,
! [A: b > $o,B: b > $o] :
( ! [C: b] :
( ( A @ C )
= ( B @ C ) )
=> ( ( hilbert_Eps_b @ A )
= ( hilbert_Eps_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(272,axiom,
! [A: b > $o] :
( ( ( collect_b @ A )
= bot_bot_set_b )
= ( A = bot_bot_b_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_Collect__empty__eq__bot) ).
thf(1235,plain,
! [A: b > $o] :
( ( ( collect_b @ A )
= bot_bot_set_b )
= ( A = bot_bot_b_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(186,axiom,
! [A: b,B: set_Product_prod_b_b,C: set_b] :
( ( member_b @ A @ ( image_b_b @ B @ C ) )
= ( ? [D: b] :
( ( member_b @ D @ C )
& ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_Image__iff) ).
thf(951,plain,
! [A: b,B: set_Product_prod_b_b,C: set_b] :
( ( member_b @ A @ ( image_b_b @ B @ C ) )
= ( ? [D: b] :
( ( member_b @ D @ C )
& ( member1285940496od_b_b @ ( product_Pair_b_b @ D @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(146,axiom,
( insert2037698781od_b_b
= ( ^ [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
( collec279084418od_b_b
@ ^ [C: produc1213276845od_b_b] :
( ( C = A )
| ( member1516365892od_b_b @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_insert__compr) ).
thf(808,plain,
( insert2037698781od_b_b
= ( ^ [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b] :
( collec279084418od_b_b
@ ^ [C: produc1213276845od_b_b] :
( ( C = A )
| ( member1516365892od_b_b @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(10,axiom,
! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
( ( ord_le123089219od_b_b @ A @ B )
=> ( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_in__mono) ).
thf(336,plain,
! [A: set_Pr1324126435od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b] :
( ( ord_le123089219od_b_b @ A @ B )
=> ( ( member1516365892od_b_b @ C @ A )
=> ( member1516365892od_b_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(210,axiom,
! [A: set_b,B: b > $o] :
( ord_less_eq_set_b
@ ( collect_b
@ ^ [C: b] :
( ( member_b @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_Collect__subset) ).
thf(1023,plain,
! [A: set_b,B: b > $o] :
( ord_less_eq_set_b
@ ( collect_b
@ ^ [C: b] :
( ( member_b @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(286,axiom,
! [A: b] : ( is_singleton_b @ ( insert_b @ A @ bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_is__singletonI) ).
thf(1284,plain,
! [A: b] : ( is_singleton_b @ ( insert_b @ A @ bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(87,axiom,
! [A: set_Pr1324126435od_b_b,B: set_Pr2109276827od_b_b,C: set_Product_prod_b_b,D: produc1213276845od_b_b > b > set_b,E: produc1213276845od_b_b] :
( ( equiv_2048442231od_b_b @ A @ B )
=> ( ( equiv_1629197578_set_b @ B @ C @ D )
=> ( ( member1516365892od_b_b @ E @ A )
=> ( equiv_1821124534_set_b @ C @ ( D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_congruent2__implies__congruent) ).
thf(600,plain,
! [A: set_Pr1324126435od_b_b,B: set_Pr2109276827od_b_b,C: set_Product_prod_b_b,D: produc1213276845od_b_b > b > set_b,E: produc1213276845od_b_b] :
( ( equiv_2048442231od_b_b @ A @ B )
=> ( ( equiv_1629197578_set_b @ B @ C @ D )
=> ( ( member1516365892od_b_b @ E @ A )
=> ( equiv_1821124534_set_b @ C @ ( D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(219,axiom,
! [A: b,B: set_b,C: b,D: set_Product_prod_b_b] :
( ( member_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ C ) @ D )
=> ( member_b @ C @ ( image_b_b @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_rev__ImageI) ).
thf(1052,plain,
! [A: b,B: set_b,C: b,D: set_Product_prod_b_b] :
( ( member_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ C ) @ D )
=> ( member_b @ C @ ( image_b_b @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(123,axiom,
! [A: set_Pr1324126435od_b_b] :
( ( A != bot_bo1664927607od_b_b )
=> ( ! [B: produc1213276845od_b_b,C: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ B @ A )
=> ( ( member1516365892od_b_b @ C @ A )
=> ( B = C ) ) )
=> ( is_sin1465183929od_b_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_is__singletonI_H) ).
thf(727,plain,
! [A: set_Pr1324126435od_b_b] :
( ( A != bot_bo1664927607od_b_b )
=> ( ! [B: produc1213276845od_b_b,C: produc1213276845od_b_b] :
( ( member1516365892od_b_b @ B @ A )
=> ( ( member1516365892od_b_b @ C @ A )
=> ( B = C ) ) )
=> ( is_sin1465183929od_b_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(229,axiom,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( equiv_equiv_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
= ( ( ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) )
= ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) )
& ( member_b @ C @ A )
& ( member_b @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_equiv__class__eq__iff) ).
thf(1094,plain,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( equiv_equiv_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
= ( ( ( image_b_b @ B @ ( insert_b @ C @ bot_bot_set_b ) )
= ( image_b_b @ B @ ( insert_b @ D @ bot_bot_set_b ) ) )
& ( member_b @ C @ A )
& ( member_b @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(1,conjecture,
( ( hilbert_Eps_b
@ ^ [A: b] : ( member_b @ A @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) ) ) )
= ( hilbert_Eps_b
@ ^ [A: b] : ( member_b @ A @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( hilbert_Eps_b
@ ^ [A: b] : ( member_b @ A @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) ) ) )
!= ( hilbert_Eps_b
@ ^ [A: b] : ( member_b @ A @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(314,plain,
( ( hilbert_Eps_b
@ ^ [A: b] : ( member_b @ A @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) ) ) )
!= ( hilbert_Eps_b
@ ^ [A: b] : ( member_b @ A @ ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(78,axiom,
! [A: set_b,B: set_Product_prod_b_b] :
( ( refl_on_b @ A @ ( converse_b_b @ B ) )
= ( refl_on_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_refl__on__converse) ).
thf(571,plain,
! [A: set_b,B: set_Product_prod_b_b] :
( ( refl_on_b @ A @ ( converse_b_b @ B ) )
= ( refl_on_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(55,axiom,
! [A: product_prod_b_b] :
~ ( member1285940496od_b_b @ A @ bot_bo1343651123od_b_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_emptyE) ).
thf(497,plain,
! [A: product_prod_b_b] :
~ ( member1285940496od_b_b @ A @ bot_bo1343651123od_b_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(159,axiom,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
( ( ord_le1036320359od_b_b @ ( converse_b_b @ A ) @ ( converse_b_b @ B ) )
= ( ord_le1036320359od_b_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_converse__mono) ).
thf(859,plain,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
( ( ord_le1036320359od_b_b @ ( converse_b_b @ A ) @ ( converse_b_b @ B ) )
= ( ord_le1036320359od_b_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(274,axiom,
! [A: labele1159362096nt_a_b,B: b,C: b,D: standard_Constant_a] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ ( getRel904497637nt_a_b @ D @ A ) )
=> ( member_b @ C @ ( labele1424214014nt_a_b @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_getRel__dom_I2_J) ).
thf(1240,plain,
! [A: labele1159362096nt_a_b,B: b,C: b,D: standard_Constant_a] :
( ( A
= ( restri446606278nt_a_b @ A ) )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ ( getRel904497637nt_a_b @ D @ A ) )
=> ( member_b @ C @ ( labele1424214014nt_a_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(41,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ ( converse_b_b @ B ) )
=> ~ ! [C: b,D: b] :
( ( A
= ( product_Pair_b_b @ D @ C ) )
=> ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_converseE) ).
thf(450,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ ( converse_b_b @ B ) )
=> ~ ! [C: b,D: b] :
( ( A
= ( product_Pair_b_b @ D @ C ) )
=> ~ ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(73,axiom,
( insert1952693431od_b_b
= ( ^ [A: product_prod_b_b,B: set_Product_prod_b_b] :
( collec1481886546od_b_b
@ ^ [C: product_prod_b_b] :
( ( C = A )
| ( member1285940496od_b_b @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_insert__compr) ).
thf(556,plain,
( insert1952693431od_b_b
= ( ^ [A: product_prod_b_b,B: set_Product_prod_b_b] :
( collec1481886546od_b_b
@ ^ [C: product_prod_b_b] :
( ( C = A )
| ( member1285940496od_b_b @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(296,axiom,
! [A: b] :
( ( hilbert_Eps_b @ ( (=) @ b @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_some__sym__eq__trivial) ).
thf(1321,plain,
! [A: b] :
( ( hilbert_Eps_b @ ( (=) @ b @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(174,axiom,
! [A: b,B: produc1213276845od_b_b,C: set_Pr2060523537od_b_b,D: set_b] :
( ( member599505522od_b_b @ ( produc800495189od_b_b @ A @ B ) @ C )
=> ( ( member_b @ A @ D )
=> ( member1516365892od_b_b @ B @ ( image_984343321od_b_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_ImageI) ).
thf(903,plain,
! [A: b,B: produc1213276845od_b_b,C: set_Pr2060523537od_b_b,D: set_b] :
( ( member599505522od_b_b @ ( produc800495189od_b_b @ A @ B ) @ C )
=> ( ( member_b @ A @ D )
=> ( member1516365892od_b_b @ B @ ( image_984343321od_b_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(62,axiom,
! [A: set_Product_prod_b_b] :
( ! [B: product_prod_b_b] :
~ ( member1285940496od_b_b @ B @ A )
=> ( A = bot_bo1343651123od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_equals0I) ).
thf(524,plain,
! [A: set_Product_prod_b_b] :
( ! [B: product_prod_b_b] :
~ ( member1285940496od_b_b @ B @ A )
=> ( A = bot_bo1343651123od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(131,axiom,
! [A: produc1213276845od_b_b] :
~ ! [B: standard_Constant_a,C: product_prod_b_b] :
( A
!= ( produc1432590431od_b_b @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_old_Oprod_Oexhaust) ).
thf(759,plain,
! [A: produc1213276845od_b_b] :
~ ! [B: standard_Constant_a,C: product_prod_b_b] :
( A
!= ( produc1432590431od_b_b @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(265,axiom,
! [A: b] :
( ( member_b @ A @ ( labele1424214014nt_a_b @ g ) )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ A ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_A_092_060Longrightarrow_062_A_Ix_M_Ax_J_A_092_060in_062_AgetRel_AS__Idt_AG_092_060close_062) ).
thf(1216,plain,
! [A: b] :
( ( member_b @ A @ ( labele1424214014nt_a_b @ g ) )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ A @ A ) @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(255,axiom,
( bot_bot_b_o
= ( ^ [A: b] : ( member_b @ A @ bot_bot_set_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_bot__empty__eq) ).
thf(1189,plain,
( bot_bot_b_o
= ( ^ [A: b] : ( member_b @ A @ bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(204,axiom,
! [A: b,B: b,C: b,D: b] :
( ( ( insert_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
= ( insert_b @ C @ ( insert_b @ D @ bot_bot_set_b ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_doubleton__eq__iff) ).
thf(1010,plain,
! [A: b,B: b,C: b,D: b] :
( ( ( insert_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
= ( insert_b @ C @ ( insert_b @ D @ bot_bot_set_b ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(233,axiom,
! [A: b > $o,B: b,C: b] :
( ( ( hilbert_Eps_b @ A )
= B )
=> ( ( A @ C )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_some__eq__imp) ).
thf(1108,plain,
! [A: b > $o,B: b,C: b] :
( ( ( hilbert_Eps_b @ A )
= B )
=> ( ( A @ C )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(288,axiom,
! [A: set_Product_prod_b_b,B: b] :
( ( image_b_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
= ( collect_b
@ ^ [C: b] : ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Image__singleton) ).
thf(1289,plain,
! [A: set_Product_prod_b_b,B: b] :
( ( image_b_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
= ( collect_b
@ ^ [C: b] : ( member1285940496od_b_b @ ( product_Pair_b_b @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(21,axiom,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
( ! [C: b,D: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ A )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B ) )
=> ( ord_le1036320359od_b_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_subrelI) ).
thf(368,plain,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
( ! [C: b,D: b] :
( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ A )
=> ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B ) )
=> ( ord_le1036320359od_b_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(96,axiom,
( labele1741081071nt_a_b
= ( labele377702064od_b_b
@ ^ [A: set_Pr1324126435od_b_b,B: set_b] : A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_edges__def) ).
thf(632,plain,
( labele1741081071nt_a_b
= ( labele377702064od_b_b
@ ^ [A: set_Pr1324126435od_b_b,B: set_b] : A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(275,axiom,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( refl_on_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
=> ( member_b @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_refl__onD1) ).
thf(1244,plain,
! [A: set_b,B: set_Product_prod_b_b,C: b,D: b] :
( ( refl_on_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B )
=> ( member_b @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(35,axiom,
! [A: set_Pr357419743_b_b_b,B: product_prod_b_b] :
( ( image_921732011_b_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
= ( collect_b
@ ^ [C: b] : ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_Image__singleton) ).
thf(418,plain,
! [A: set_Pr357419743_b_b_b,B: product_prod_b_b] :
( ( image_921732011_b_b_b @ A @ ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) )
= ( collect_b
@ ^ [C: b] : ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(303,axiom,
( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) )
= ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062getRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_AgetRel_AS__Idt_AG_A_096_096_A_123y_125_092_060close_062) ).
thf(1341,plain,
( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ x @ bot_bot_set_b ) )
= ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ y @ bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(171,axiom,
( ord_less_eq_set_b
= ( ^ [A: set_b,B: set_b] :
! [C: b] :
( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_subset__eq) ).
thf(896,plain,
( ord_less_eq_set_b
= ( ^ [A: set_b,B: set_b] :
! [C: b] :
( ( member_b @ C @ A )
=> ( member_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(128,axiom,
! [A: produc1213276845od_b_b > $o,B: produc1213276845od_b_b] :
( ! [C: standard_Constant_a,D: product_prod_b_b] : ( A @ ( produc1432590431od_b_b @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_old_Oprod_Oinducts) ).
thf(748,plain,
! [A: produc1213276845od_b_b > $o,B: produc1213276845od_b_b] :
( ! [C: standard_Constant_a,D: product_prod_b_b] : ( A @ ( produc1432590431od_b_b @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(184,axiom,
! [A: set_b,B: b] :
( ( ord_less_eq_set_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
= ( ( A = bot_bot_set_b )
| ( A
= ( insert_b @ B @ bot_bot_set_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_subset__singleton__iff) ).
thf(946,plain,
! [A: set_b,B: b] :
( ( ord_less_eq_set_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
= ( ( A = bot_bot_set_b )
| ( A
= ( insert_b @ B @ bot_bot_set_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(231,axiom,
! [A: b,B: b] :
( ( member_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_singletonD) ).
thf(1101,plain,
! [A: b,B: b] :
( ( member_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(77,axiom,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
( ( ( converse_b_b @ A )
= ( converse_b_b @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_converse__inject) ).
thf(568,plain,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
( ( ( converse_b_b @ A )
= ( converse_b_b @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(132,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
( ( ~ ( member1285940496od_b_b @ A @ B )
=> ( A = C ) )
=> ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_insertCI) ).
thf(763,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
( ( ~ ( member1285940496od_b_b @ A @ B )
=> ( A = C ) )
=> ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(25,axiom,
! [A: produc1213276845od_b_b > $o,B: produc1213276845od_b_b] :
( ! [C: standard_Constant_a,D: b,E: b] : ( A @ ( produc1432590431od_b_b @ C @ ( product_Pair_b_b @ D @ E ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_prod__induct3) ).
thf(383,plain,
! [A: produc1213276845od_b_b > $o,B: produc1213276845od_b_b] :
( ! [C: standard_Constant_a,D: b,E: b] : ( A @ ( produc1432590431od_b_b @ C @ ( product_Pair_b_b @ D @ E ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(144,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ( ( insert1952693431od_b_b @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_insert__absorb) ).
thf(800,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ( ( insert1952693431od_b_b @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(234,axiom,
! [A: set_b,B: set_b,C: b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ord_less_eq_set_b @ ( insert_b @ C @ A ) @ ( insert_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_insert__mono) ).
thf(1116,plain,
! [A: set_b,B: set_b,C: b] :
( ( ord_less_eq_set_b @ A @ B )
=> ( ord_less_eq_set_b @ ( insert_b @ C @ A ) @ ( insert_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(306,axiom,
! [A: b,B: set_b,C: set_b] :
( ~ ( member_b @ A @ B )
=> ( ~ ( member_b @ A @ C )
=> ( ( ( insert_b @ A @ B )
= ( insert_b @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_insert__ident) ).
thf(1348,plain,
! [A: b,B: set_b,C: set_b] :
( ~ ( member_b @ A @ B )
=> ( ~ ( member_b @ A @ C )
=> ( ( ( insert_b @ A @ B )
= ( insert_b @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(200,axiom,
! [A: b,B: set_Pr357419743_b_b_b,C: product_prod_b_b] :
( ( member_b @ A @ ( image_921732011_b_b_b @ B @ ( insert1952693431od_b_b @ C @ bot_bo1343651123od_b_b ) ) )
= ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_Image__singleton__iff) ).
thf(999,plain,
! [A: b,B: set_Pr357419743_b_b_b,C: product_prod_b_b] :
( ( member_b @ A @ ( image_921732011_b_b_b @ B @ ( insert1952693431od_b_b @ C @ bot_bo1343651123od_b_b ) ) )
= ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(37,axiom,
! [A: b > $o,B: b > $o] :
( ! [C: b] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_b @ ( collect_b @ A ) @ ( collect_b @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_Collect__mono) ).
thf(432,plain,
! [A: b > $o,B: b > $o] :
( ! [C: b] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_b @ ( collect_b @ A ) @ ( collect_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(152,axiom,
! [A: product_prod_b_b,B: product_prod_b_b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ B @ C ) )
=> ( ( A != B )
=> ( member1285940496od_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_insertE) ).
thf(833,plain,
! [A: product_prod_b_b,B: product_prod_b_b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ B @ C ) )
=> ( ( A != B )
=> ( member1285940496od_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(244,axiom,
! [A: b,B: b] :
( ( ( insert_b @ A @ bot_bot_set_b )
= ( insert_b @ B @ bot_bot_set_b ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_singleton__inject) ).
thf(1148,plain,
! [A: b,B: b] :
( ( ( insert_b @ A @ bot_bot_set_b )
= ( insert_b @ B @ bot_bot_set_b ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(140,axiom,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
( ( ( ^ [C: b,D: b] : ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ A ) )
= ( ^ [C: b,D: b] : ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_pred__equals__eq2) ).
thf(790,plain,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b] :
( ( ( ^ [C: b,D: b] : ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ A ) )
= ( ^ [C: b,D: b] : ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ B ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(161,axiom,
! [A: product_prod_b_b] : ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_singletonI) ).
thf(867,plain,
! [A: product_prod_b_b] : ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ A @ bot_bo1343651123od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(88,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001tf__b_T) ).
thf(603,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(294,axiom,
! [A: b,B: set_Pr1906739389_b_b_b,C: set_Pr1324126435od_b_b] :
( ( member_b @ A @ ( image_1764625405_b_b_b @ B @ C ) )
=> ~ ! [D: produc1213276845od_b_b] :
( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ D @ A ) @ B )
=> ~ ( member1516365892od_b_b @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_ImageE) ).
thf(1314,plain,
! [A: b,B: set_Pr1906739389_b_b_b,C: set_Pr1324126435od_b_b] :
( ( member_b @ A @ ( image_1764625405_b_b_b @ B @ C ) )
=> ~ ! [D: produc1213276845od_b_b] :
( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ D @ A ) @ B )
=> ~ ( member1516365892od_b_b @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(58,axiom,
! [A: standard_Constant_a,B: product_prod_b_b,C: standard_Constant_a,D: product_prod_b_b] :
( ( ( produc1432590431od_b_b @ A @ B )
= ( produc1432590431od_b_b @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_Pair__inject) ).
thf(506,plain,
! [A: standard_Constant_a,B: product_prod_b_b,C: standard_Constant_a,D: product_prod_b_b] :
( ( ( produc1432590431od_b_b @ A @ B )
= ( produc1432590431od_b_b @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(251,axiom,
! [A: b] :
( ( hilbert_Eps_b
@ ^ [B: b] : ( B = A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_some__eq__trivial) ).
thf(1172,plain,
! [A: b] :
( ( hilbert_Eps_b
@ ^ [B: b] : ( B = A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(305,axiom,
! [A: set_b] : ( ord_less_eq_set_b @ bot_bot_set_b @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_empty__subsetI) ).
thf(1346,plain,
! [A: set_b] : ( ord_less_eq_set_b @ bot_bot_set_b @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(34,axiom,
! [A: produc1213276845od_b_b,B: produc1213276845od_b_b > $o] :
( ( member1516365892od_b_b @ A @ ( collec279084418od_b_b @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_mem__Collect__eq) ).
thf(415,plain,
! [A: produc1213276845od_b_b,B: produc1213276845od_b_b > $o] :
( ( member1516365892od_b_b @ A @ ( collec279084418od_b_b @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(196,axiom,
! [A: b > $o] :
( ( A @ ( hilbert_Eps_b @ A ) )
= ( ? [B: b] : ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_some__eq__ex) ).
thf(987,plain,
! [A: b > $o] :
( ( A @ ( hilbert_Eps_b @ A ) )
= ( ? [B: b] : ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(307,axiom,
! [A: product_prod_b_b,B: set_Pr621705391od_b_b,C: set_b] :
( ( member1285940496od_b_b @ A @ ( image_1177096571od_b_b @ B @ C ) )
=> ~ ! [D: b] :
( ( member641857272od_b_b @ ( produc1257047359od_b_b @ D @ A ) @ B )
=> ~ ( member_b @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ImageE) ).
thf(1352,plain,
! [A: product_prod_b_b,B: set_Pr621705391od_b_b,C: set_b] :
( ( member1285940496od_b_b @ A @ ( image_1177096571od_b_b @ B @ C ) )
=> ~ ! [D: b] :
( ( member641857272od_b_b @ ( produc1257047359od_b_b @ D @ A ) @ B )
=> ~ ( member_b @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(281,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: b,D: set_Pr357419743_b_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ A @ C ) @ D )
=> ( member_b @ C @ ( image_921732011_b_b_b @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_rev__ImageI) ).
thf(1268,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b,C: b,D: set_Pr357419743_b_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ( ( member351494440_b_b_b @ ( produc1001682799_b_b_b @ A @ C ) @ D )
=> ( member_b @ C @ ( image_921732011_b_b_b @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(208,axiom,
! [A: b > $o] :
( ? [B: b] : ( A @ B )
=> ( A @ ( hilbert_Eps_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_someI__ex) ).
thf(1019,plain,
! [A: b > $o] :
( ? [B: b] : ( A @ B )
=> ( A @ ( hilbert_Eps_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(63,axiom,
! [A: labele1159362096nt_a_b] :
( ( restri446606278nt_a_b @ ( restri446606278nt_a_b @ A ) )
= ( restri446606278nt_a_b @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_restrict__idemp) ).
thf(528,plain,
! [A: labele1159362096nt_a_b] :
( ( restri446606278nt_a_b @ ( restri446606278nt_a_b @ A ) )
= ( restri446606278nt_a_b @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(100,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b,D: set_Pr1324126435od_b_b] :
( ~ ( member1516365892od_b_b @ A @ B )
=> ( ~ ( member1516365892od_b_b @ C @ D )
=> ( ( ( insert2037698781od_b_b @ A @ B )
= ( insert2037698781od_b_b @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_Pr1324126435od_b_b] :
( ( B
= ( insert2037698781od_b_b @ C @ E ) )
& ~ ( member1516365892od_b_b @ C @ E )
& ( D
= ( insert2037698781od_b_b @ A @ E ) )
& ~ ( member1516365892od_b_b @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_insert__eq__iff) ).
thf(644,plain,
! [A: produc1213276845od_b_b,B: set_Pr1324126435od_b_b,C: produc1213276845od_b_b,D: set_Pr1324126435od_b_b] :
( ~ ( member1516365892od_b_b @ A @ B )
=> ( ~ ( member1516365892od_b_b @ C @ D )
=> ( ( ( insert2037698781od_b_b @ A @ B )
= ( insert2037698781od_b_b @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_Pr1324126435od_b_b] :
( ( B
= ( insert2037698781od_b_b @ C @ E ) )
& ~ ( member1516365892od_b_b @ C @ E )
& ( D
= ( insert2037698781od_b_b @ A @ E ) )
& ~ ( member1516365892od_b_b @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(40,axiom,
! [A: product_prod_b_b > $o,B: product_prod_b_b] :
( ( ( A @ B )
=> ( ( collec1481886546od_b_b
@ ^ [C: product_prod_b_b] :
( ( B = C )
& ( A @ C ) ) )
= ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) )
& ( ~ ( A @ B )
=> ( ( collec1481886546od_b_b
@ ^ [C: product_prod_b_b] :
( ( B = C )
& ( A @ C ) ) )
= bot_bo1343651123od_b_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_Collect__conv__if2) ).
thf(442,plain,
! [A: product_prod_b_b > $o,B: product_prod_b_b] :
( ( ( A @ B )
=> ( ( collec1481886546od_b_b
@ ^ [C: product_prod_b_b] :
( ( B = C )
& ( A @ C ) ) )
= ( insert1952693431od_b_b @ B @ bot_bo1343651123od_b_b ) ) )
& ( ~ ( A @ B )
=> ( ( collec1481886546od_b_b
@ ^ [C: product_prod_b_b] :
( ( B = C )
& ( A @ C ) ) )
= bot_bo1343651123od_b_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(163,axiom,
! [A: product_prod_b_b,B: set_Pr1324126435od_b_b,C: set_St761939237tant_a] :
( ( member1285940496od_b_b @ A @ ( image_1916422435od_b_b @ B @ C ) )
=> ~ ! [D: standard_Constant_a] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ D @ A ) @ B )
=> ~ ( member1632892294tant_a @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_ImageE) ).
thf(871,plain,
! [A: product_prod_b_b,B: set_Pr1324126435od_b_b,C: set_St761939237tant_a] :
( ( member1285940496od_b_b @ A @ ( image_1916422435od_b_b @ B @ C ) )
=> ~ ! [D: standard_Constant_a] :
( ( member1516365892od_b_b @ ( produc1432590431od_b_b @ D @ A ) @ B )
=> ~ ( member1632892294tant_a @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(90,axiom,
( labele1424214014nt_a_b
= ( labele1287464530_set_b
@ ^ [A: set_Pr1324126435od_b_b,B: set_b] : B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_vertices__def) ).
thf(607,plain,
( labele1424214014nt_a_b
= ( labele1287464530_set_b
@ ^ [A: set_Pr1324126435od_b_b,B: set_b] : B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(28,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b] :
( ( insert1952693431od_b_b @ A @ B )
!= bot_bo1343651123od_b_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_insert__not__empty) ).
thf(395,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b] :
( ( insert1952693431od_b_b @ A @ B )
!= bot_bo1343651123od_b_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(94,axiom,
! [A: produc1213276845od_b_b > $o,B: produc1213276845od_b_b] :
( ! [C: standard_Constant_a,D: product_prod_b_b] : ( A @ ( produc1432590431od_b_b @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_prod__cases) ).
thf(624,plain,
! [A: produc1213276845od_b_b > $o,B: produc1213276845od_b_b] :
( ! [C: standard_Constant_a,D: product_prod_b_b] : ( A @ ( produc1432590431od_b_b @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(9,axiom,
! [A: produc1213276845od_b_b,B: set_Pr1071216121od_b_b,C: set_Product_prod_b_b] :
( ( member1516365892od_b_b @ A @ ( image_532916993od_b_b @ B @ C ) )
=> ~ ! [D: product_prod_b_b] :
( ( member4694106od_b_b @ ( produc732676669od_b_b @ D @ A ) @ B )
=> ~ ( member1285940496od_b_b @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_ImageE) ).
thf(332,plain,
! [A: produc1213276845od_b_b,B: set_Pr1071216121od_b_b,C: set_Product_prod_b_b] :
( ( member1516365892od_b_b @ A @ ( image_532916993od_b_b @ B @ C ) )
=> ~ ! [D: product_prod_b_b] :
( ( member4694106od_b_b @ ( produc732676669od_b_b @ D @ A ) @ B )
=> ~ ( member1285940496od_b_b @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(239,axiom,
( f
= ( ^ [A: b] :
( if_b
@ ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
= bot_bot_set_b )
@ A
@ ( hilbert_Eps_b @ ( p @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_f) ).
thf(1129,plain,
( f
= ( ^ [A: b] :
( if_b
@ ( ( image_b_b @ ( getRel904497637nt_a_b @ standard_S_Idt_a @ g ) @ ( insert_b @ A @ bot_bot_set_b ) )
= bot_bot_set_b )
@ A
@ ( hilbert_Eps_b @ ( p @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(5,axiom,
( bot_bo1343651123od_b_b
= ( collec1481886546od_b_b @ bot_bo1302443370_b_b_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_bot__set__def) ).
thf(322,plain,
( bot_bo1343651123od_b_b
= ( collec1481886546od_b_b @ bot_bo1302443370_b_b_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(52,axiom,
! [A: set_Product_prod_b_b,B: b > set_b,C: b,D: b] :
( ( equiv_1821124534_set_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ A )
=> ( ( B @ C )
= ( B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_congruentD) ).
thf(486,plain,
! [A: set_Product_prod_b_b,B: b > set_b,C: b,D: b] :
( ( equiv_1821124534_set_b @ A @ B )
=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ C @ D ) @ A )
=> ( ( B @ C )
= ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(145,axiom,
! [A: product_prod_b_b,B: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ~ ! [C: set_Product_prod_b_b] :
( ( B
= ( insert1952693431od_b_b @ A @ C ) )
=> ( member1285940496od_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_Set_Oset__insert) ).
thf(803,plain,
! [A: product_prod_b_b,B: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ B )
=> ~ ! [C: set_Product_prod_b_b] :
( ( B
= ( insert1952693431od_b_b @ A @ C ) )
=> ( member1285940496od_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(182,axiom,
! [A: set_Pr357419743_b_b_b] :
( ( image_921732011_b_b_b @ A @ bot_bo1343651123od_b_b )
= bot_bot_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Image__empty2) ).
thf(940,plain,
! [A: set_Pr357419743_b_b_b] :
( ( image_921732011_b_b_b @ A @ bot_bo1343651123od_b_b )
= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(203,axiom,
refl_on_b @ bot_bot_set_b @ bot_bo1343651123od_b_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_refl__on__empty) ).
thf(1009,plain,
refl_on_b @ bot_bot_set_b @ bot_bo1343651123od_b_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(178,axiom,
! [A: b,B: set_b,C: b] :
( ( ( insert_b @ A @ B )
= ( insert_b @ C @ bot_bot_set_b ) )
= ( ( A = C )
& ( ord_less_eq_set_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_singleton__insert__inj__eq_H) ).
thf(923,plain,
! [A: b,B: set_b,C: b] :
( ( ( insert_b @ A @ B )
= ( insert_b @ C @ bot_bot_set_b ) )
= ( ( A = C )
& ( ord_less_eq_set_b @ B @ ( insert_b @ C @ bot_bot_set_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(105,axiom,
! [A: set_Product_prod_b_b] :
( ( ord_le1036320359od_b_b @ A @ bot_bo1343651123od_b_b )
= ( A = bot_bo1343651123od_b_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_bot_Oextremum__unique) ).
thf(659,plain,
! [A: set_Product_prod_b_b] :
( ( ord_le1036320359od_b_b @ A @ bot_bo1343651123od_b_b )
= ( A = bot_bo1343651123od_b_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(135,axiom,
! [A: product_prod_b_b,B: product_prod_b_b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ B @ C ) )
= ( ( A = B )
| ( member1285940496od_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_insert__iff) ).
thf(775,plain,
! [A: product_prod_b_b,B: product_prod_b_b,C: set_Product_prod_b_b] :
( ( member1285940496od_b_b @ A @ ( insert1952693431od_b_b @ B @ C ) )
= ( ( A = B )
| ( member1285940496od_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(261,axiom,
! [A: set_b,B: set_b] :
( ! [C: b] :
( ( member_b @ C @ A )
=> ( member_b @ C @ B ) )
=> ( ord_less_eq_set_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_subsetI) ).
thf(1204,plain,
! [A: set_b,B: set_b] :
( ! [C: b] :
( ( member_b @ C @ A )
=> ( member_b @ C @ B ) )
=> ( ord_less_eq_set_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(84,axiom,
( bot_bo1734638456_b_b_o
= ( ^ [A: standard_Constant_a,B: product_prod_b_b] : ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ B ) @ bot_bo1664927607od_b_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_bot__empty__eq2) ).
thf(592,plain,
( bot_bo1734638456_b_b_o
= ( ^ [A: standard_Constant_a,B: product_prod_b_b] : ( member1516365892od_b_b @ ( produc1432590431od_b_b @ A @ B ) @ bot_bo1664927607od_b_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(223,axiom,
! [A: set_b,B: b] :
( ( A = bot_bot_set_b )
=> ~ ( member_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_equals0D) ).
thf(1069,plain,
! [A: set_b,B: b] :
( ( A = bot_bot_set_b )
=> ~ ( member_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(117,axiom,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
( ( ord_le1036320359od_b_b @ A @ B )
=> ( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_in__mono) ).
thf(708,plain,
! [A: set_Product_prod_b_b,B: set_Product_prod_b_b,C: product_prod_b_b] :
( ( ord_le1036320359od_b_b @ A @ B )
=> ( ( member1285940496od_b_b @ C @ A )
=> ( member1285940496od_b_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(206,axiom,
! [A: produc1213276845od_b_b,B: b,C: set_Pr1906739389_b_b_b,D: set_Pr1324126435od_b_b] :
( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ A @ B ) @ C )
=> ( ( member1516365892od_b_b @ A @ D )
=> ( member_b @ B @ ( image_1764625405_b_b_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_ImageI) ).
thf(1014,plain,
! [A: produc1213276845od_b_b,B: b,C: set_Pr1906739389_b_b_b,D: set_Pr1324126435od_b_b] :
( ( member1417789726_b_b_b @ ( produc1580777273_b_b_b @ A @ B ) @ C )
=> ( ( member1516365892od_b_b @ A @ D )
=> ( member_b @ B @ ( image_1764625405_b_b_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(1406,plain,
$false,
inference(e,[status(thm)],[892,629,347,846,518,1295,365,1369,909,1031,1083,468,1200,977,1211,741,379,878,677,597,1078,533,550,500,472,1233,1327,538,670,898,1127,782,885,1359,436,1265,651,320,565,1298,785,372,1330,838,1191,949,460,1055,724,1247,421,1013,881,316,1362,475,756,1040,1136,574,353,821,480,1151,937,981,634,1119,1104,1169,687,1074,920,439,793,1306,1199,810,1338,1067,798,1274,746,1343,862,693,1238,1021,778,1365,889,1159,493,1281,329,1178,583,830,682,1195,324,974,697,1259,1017,1064,1227,1006,388,356,869,1160,339,1292,753,637,547,1324,984,721,1002,503,1131,654,1333,1318,1202,657,558,926,1286,1035,662,718,906,1278,412,618,1146,824,856,1301,375,562,402,772,843,1125,875,577,711,1256,545,391,1271,787,713,466,1224,1356,350,540,362,1043,1122,1175,979,604,900,406,1048,736,990,996,477,345,535,609,594,621,483,700,1029,964,769,943,521,399,1213,827,455,883,1166,531,795,927,1081,516,342,553,968,836,490,675,1208,589,1134,648,580,690,640,1025,971,327,954,739,1368,1098,993,705,1156,409,1230,1186,1038,840,463,1085,359,1218,1336,1220,1262,1235,951,808,336,1023,1284,600,1052,727,1094,314,571,497,859,1240,450,556,1321,903,524,759,1216,1189,1010,1108,1289,368,632,1244,418,1341,896,748,946,1101,568,763,383,800,1116,1348,999,432,833,1148,790,867,603,1314,506,1172,1346,415,987,1352,1268,1019,528,644,442,871,607,395,624,332,1129,322,486,803,940,1009,923,659,775,1204,592,1069,708,1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP176^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.09/0.23 % Computer : n010.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 20:06:48 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.01/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.39/1.24 % [INFO] Parsing done (433ms).
% 2.39/1.25 % [INFO] Running in sequential loop mode.
% 3.51/1.64 % [INFO] eprover registered as external prover.
% 3.51/1.65 % [INFO] Scanning for conjecture ...
% 3.96/1.83 % [INFO] Found a conjecture (or negated_conjecture) and 358 axioms. Running axiom selection ...
% 4.20/2.00 % [INFO] Axiom selection finished. Selected 311 axioms (removed 47 axioms).
% 5.25/2.26 % [INFO] Problem is higher-order (TPTP THF).
% 5.25/2.29 % [INFO] Type checking passed.
% 5.25/2.30 % [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 ...
% 19.36/5.63 % External prover 'e' found a proof!
% 19.36/5.63 % [INFO] Killing All external provers ...
% 19.36/5.63 % Time passed: 5265ms (effective reasoning time: 4371ms)
% 19.36/5.63 % 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)>
% 19.36/5.64 % Axioms used in derivation (311): fact_205_converseD, fact_58_pred__equals__eq2, fact_172_congr_I2_J, fact_116_insertI1, fact_14_Image__empty2, fact_309_empty__subsetI, fact_343_bot_Oextremum__unique, fact_117_insertI1, fact_127_Collect__mem__eq, fact_176_prod_Oinject, fact_41_ImageI, fact_281_total__on__def, fact_5__092_060open_062f_A_092_060equiv_062_A_092_060lambda_062x_O_Aif_AgetRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_A_123_125_Athen_Ax_Aelse_AEps_A_IP_Ax_J_092_060close_062, fact_322_Collect__subset, fact_231_refl__on__converse, fact_59_pred__equals__eq2, fact_318_singleton__insert__inj__eq, fact_292_graph__homomorphism__empty, fact_265_congruentI, fact_8_singleton__conv2, fact_342_bot_Oextremum__uniqueI, fact_187_labeled__graph_Oexpand, fact_268_equiv__class__self, fact_107_insert__ident, fact_285_total__on__empty, fact_202_converseE, fact_348_subset__insert, fact_310_empty__subsetI, fact_336_in__mono, fact_226_equiv, fact_115_insertI2, fact_140_some__eq__ex, fact_299_congruent2__implies__congruent, fact_239_refl__onD1, fact_104_insert__absorb, fact_351_subset__insertI, fact_158_singletonD, fact_174_the__elem__eq, fact_207_bot__set__def, fact_232_is__singletonI, fact_114_insertI2, fact_294_linear__order__on__converse, fact_149_insert__not__empty, fact_216_old_Oprod_Oexhaust, fact_350_subset__insert, fact_110_Set_Oset__insert, fact_225_local_Orefl, fact_217_prod__induct3, fact_70_Image__iff, fact_165_some__in__eq, fact_60_rev__ImageI, fact_50_f, fact_141_someI2__bex, fact_186__092_060open_062_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_A_092_060Longrightarrow_062_A_Ix_M_Ax_J_A_092_060in_062_AgetRel_AS__Idt_AG_092_060close_062, fact_15_Image__empty2, fact_106_insert__absorb, fact_24_Collect__empty__eq, fact_130_Collect__cong, fact_86_ex__in__conv, fact_96_emptyE, fact_228_getRel__dom_I2_J, fact_236_refl__onD, fact_1_assms_I1_J, fact_51_Image__singleton__iff, fact_48_ImageI, fact_148_singleton__inject, fact_284_total__onI, fact_199_converse_Ocases, fact_331_subset__eq, fact_276_total__on__singleton, fact_45_ImageI, fact_180_converse__converse, fact_3_P, fact_16_Image__empty2, fact_301_congruent2__implies__congruent, fact_296_vertices__def, fact_252_is__singletonE, fact_326_subset__iff, fact_71_Image__iff, fact_266_congruentD, fact_168__092_060open_062_IS__Idt_M_Ax_M_Ay_J_A_092_060in_062_Aedges_AG_092_060close_062, fact_251_is__singleton__def, fact_317_singleton__insert__inj__eq_H, fact_329_subset__eq, fact_352_subset__insertI2, fact_53_Image__singleton__iff, fact_157_singletonD, help_If_1_1_If_001tf__b_T, fact_155_singleton__iff, fact_105_insert__absorb, fact_100_insert__commute, fact_354_subset__singleton__iff, fact_316_singleton__insert__inj__eq_H, fact_2_P__eq, fact_223_surj__pair, fact_29_empty__iff, fact_311_subset__empty, fact_338_converse__subset__swap, fact_170_r2, fact_26_all__not__in__conv, fact_325_Collect__mono, fact_221_prod__cases, fact_98_mk__disjoint__insert, fact_339_subrelI, fact_253_is__singletonE, fact_4__092_060open_062_Ix_M_Ay_J_A_092_060in_062_AgetRel_AS__Idt_AG_092_060close_062, fact_89_equals0I, fact_143_someI2__bex, fact_209_bot__empty__eq, fact_30_empty__iff, fact_295_edges__def, fact_255_equiv__class__eq__iff, fact_345_bot_Oextremum, fact_335_in__mono, fact_328_subset__iff, fact_150_insert__not__empty, fact_128_Collect__mem__eq, fact_113_insertI2, fact_138_insert__compr, fact_177_old_Oprod_Oinject, fact_83_Image__singleton, fact_269_equiv__class__self, fact_278_total__on__converse, fact_6_singleton__conv, fact_344_bot_Oextremum__unique, fact_349_subset__insert, fact_146_someI2, fact_103_insert__eq__iff, fact_190_converse_Oinducts, fact_208_bot__empty__eq, fact_315_insert__subset, fact_289_labeled__graph_Oexhaust__sel, fact_287_labeled__graph_Osel_I2_J, fact_333_subsetD, fact_125_mem__Collect__eq, fact_81_ImageE, fact_12_Image__empty1, fact_229_is__singleton__the__elem, fact_163_some__in__eq, fact_175_prod_Oinject, fact_27_all__not__in__conv, fact_95_emptyE, fact_22_empty__Collect__eq, fact_133_empty__def, fact_13_Image__empty2, fact_139_some1__equality, fact_144_someI2__ex, fact_243_refl__on__empty, fact_290_linear__order__on__singleton, fact_247_is__singletonI_H, fact_78_ImageE, fact_49_ImageI, fact_111_Set_Oset__insert, fact_68_rev__ImageI, fact_72_ImageE, fact_227_getRel__dom_I1_J, fact_82_Image__singleton, fact_314_insert__subset, fact_64_rev__ImageI, fact_320_Image__mono, fact_33_insert__iff, fact_25_Collect__empty__eq, fact_90_equals0I, fact_93_equals0D, fact_39_some__sym__eq__trivial, fact_302_proj__def, fact_65_rev__ImageI, fact_34_insert__iff, fact_222_prod__cases, fact_32_insert__absorb2, fact_323_Collect__subset, fact_74_ImageE, fact_260_equiv__class__eq, fact_122_some__eq__imp, fact_20_some__equality, fact_94_emptyE, fact_288_labeled__graph_Osel_I1_J, fact_87_ex__in__conv, fact_270_Collect__empty__eq__bot, fact_118_insertI1, fact_215_old_Oprod_Oexhaust, fact_250_is__singleton__def, fact_156_singletonD, fact_160_Collect__conv__if2, fact_263_eq__equiv__class, fact_126_mem__Collect__eq, fact_330_subset__eq, fact_136_insert__compr, fact_212_bot__empty__eq2, fact_233_is__singletonI, fact_28_all__not__in__conv, fact_280_graph__empty__e, fact_17_singletonI, fact_246_is__singletonI_H, fact_321_Collect__subset, fact_38_insertCI, fact_196_converse_Osimps, fact_142_someI2__bex, fact_11_tuple__disj, fact_334_subsetD, fact_91_equals0D, fact_40_ImageI, fact_319_singleton__insert__inj__eq, fact_230_is__singleton__the__elem, fact_80_ImageE, fact_62_rev__ImageI, fact_31_empty__iff, fact_213_old_Oprod_Oinducts, fact_286_total__on__empty, fact_183_converse__iff, fact_145_someI__ex, fact_88_equals0I, fact_324_Collect__mono__iff, fact_97_mk__disjoint__insert, fact_99_mk__disjoint__insert, fact_137_insert__compr, fact_305_subsetI, fact_275_refl__on__domain, fact_341_bot_Oextremum__uniqueI, fact_0__092_060open_062getRel_AS__Idt_AG_A_096_096_A_123x_125_A_061_AgetRel_AS__Idt_AG_A_096_096_A_123y_125_092_060close_062, fact_173_the__elem__eq, fact_123_tfl__some, fact_211_bot__empty__eq2, fact_52_Image__singleton__iff, fact_35_insert__iff, fact_124_mem__Collect__eq, fact_193_converse_Ointros, fact_184_vertices__restrict, fact_164_some__in__eq, fact_178_old_Oprod_Oinject, fact_220_Pair__inject, fact_23_empty__Collect__eq, fact_353_subset__singleton__iff, fact_279_labeled__graph_Ocollapse, fact_57_Image__singleton__iff, fact_248_refl__on__singleton, fact_109_insert__ident, fact_337_in__mono, fact_108_insert__ident, fact_293_graph__homomorphism__empty, fact_169_restrict__idemp, fact_54_Image__singleton__iff, fact_242_refl__onD2, fact_152_doubleton__eq__iff, fact_73_ImageE, fact_271_Collect__empty__eq__bot, fact_327_subset__iff, fact_312_subset__empty, fact_119_insertE, fact_300_congruent2__implies__congruent, fact_224_surj__pair, fact_132_someI, fact_308_converse__mono, fact_210_bot__empty__eq, fact_112_Set_Oset__insert, fact_77_ImageE, fact_161_Collect__conv__if, fact_267_equiv__class__self, fact_129_Collect__mem__eq, fact_7_singleton__conv, fact_346_bot_Oextremum, fact_121_insertE, fact_307_subsetI, fact_61_rev__ImageI, fact_214_old_Oprod_Oinducts, fact_134_empty__def, fact_36_insertCI, fact_131_Eps__cong, fact_18_singletonI, fact_102_insert__eq__iff, fact_135_insert__Collect, fact_147_singleton__inject, fact_151_doubleton__eq__iff, fact_218_prod__cases3, fact_120_insertE, fact_159_Collect__conv__if2, fact_258_eq__equiv__class__iff, fact_154_singleton__iff, fact_44_ImageI, fact_10_tuple__disj, fact_332_subsetD, fact_162_Collect__conv__if, help_If_3_1_If_001tf__b_T, fact_306_subsetI, fact_37_insertCI, fact_171_r1, fact_55_Image__singleton__iff, fact_185_converse__empty, fact_21_some__eq__trivial, fact_166_congr_I1_J, fact_19_singletonI, fact_297_lnear__order__on__empty, fact_69_rev__ImageI, fact_153_singleton__iff, fact_85_ex__in__conv, help_If_2_1_If_001tf__b_T, fact_92_equals0D, fact_219_Pair__inject, fact_179_converse__inject, fact_84_Image__singleton, fact_347_insert__mono, fact_272_graph__single, fact_101_insert__eq__iff, fact_206_bot__set__def, fact_245_is__singletonI_H, fact_167_vert__P, fact_9_singleton__conv2, fact_340_subrelI, fact_313_insert__subset, fact_303_equiv__class__subset, fact_42_ImageI
% 19.36/5.64 % No. of inferences in proof: 626
% 19.36/5.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5265 ms resp. 4371 ms w/o parsing
% 20.69/5.90 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.69/5.91 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------