TSTP Solution File: ITP083^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP083^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:47:41 EDT 2024
% Result : Theorem 76.87s 33.42s
% Output : Refutation 77.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 533
% Syntax : Number of formulae : 935 ( 394 unt; 183 typ; 0 def)
% Number of atoms : 1972 ( 582 equ; 3 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 6900 ( 278 ~; 57 |; 124 &;5720 @)
% ( 0 <=>; 721 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Number of types : 53 ( 52 usr)
% Number of type conns : 625 ( 625 >; 0 *; 0 +; 0 <<)
% Number of symbols : 137 ( 133 usr; 15 con; 0-8 aty)
% Number of variables : 1957 ( 243 ^1640 !; 74 ?;1957 :)
% Comments :
%------------------------------------------------------------------------------
thf(list_P88441325et_val_type,type,
list_P88441325et_val: $tType ).
thf(set_Pr1587248327et_val_type,type,
set_Pr1587248327et_val: $tType ).
thf(produc1904584935et_val_type,type,
produc1904584935et_val: $tType ).
thf(list_P729276995de_val_type,type,
list_P729276995de_val: $tType ).
thf(set_Pr819703837de_val_type,type,
set_Pr819703837de_val: $tType ).
thf(produc452075965de_val_type,type,
produc452075965de_val: $tType ).
thf(list_P1108777338de_val_type,type,
list_P1108777338de_val: $tType ).
thf(list_P844977291de_val_type,type,
list_P844977291de_val: $tType ).
thf(set_Pr1245322836de_val_type,type,
set_Pr1245322836de_val: $tType ).
thf(set_Pr701036849de_val_type,type,
set_Pr701036849de_val: $tType ).
thf(list_P2089461677et_val_type,type,
list_P2089461677et_val: $tType ).
thf(set_Pr1311924359et_val_type,type,
set_Pr1311924359et_val: $tType ).
thf(produc1615737844de_val_type,type,
produc1615737844de_val: $tType ).
thf(produc1664334075de_val_type,type,
produc1664334075de_val: $tType ).
thf(list_P12184414et_val_type,type,
list_P12184414et_val: $tType ).
thf(list_P1414038306l_node_type,type,
list_P1414038306l_node: $tType ).
thf(list_P761482893et_val_type,type,
list_P761482893et_val: $tType ).
thf(list_P940784845al_val_type,type,
list_P940784845al_val: $tType ).
thf(set_Pr1320419588et_val_type,type,
set_Pr1320419588et_val: $tType ).
thf(set_Pr574789832l_node_type,type,
set_Pr574789832l_node: $tType ).
thf(set_Pr978022247et_val_type,type,
set_Pr978022247et_val: $tType ).
thf(set_Pr1157324199al_val_type,type,
set_Pr1157324199al_val: $tType ).
thf(produc1324971431et_val_type,type,
produc1324971431et_val: $tType ).
thf(list_P561207620_edgeD_type,type,
list_P561207620_edgeD: $tType ).
thf(list_P1127016369e_node_type,type,
list_P1127016369e_node: $tType ).
thf(list_P1078858818l_node_type,type,
list_P1078858818l_node: $tType ).
thf(list_P1820443774de_val_type,type,
list_P1820443774de_val: $tType ).
thf(set_Pr9085835e_node_type,type,
set_Pr9085835e_node: $tType ).
thf(list_P1811375021al_val_type,type,
list_P1811375021al_val: $tType ).
thf(set_Pr2105655784l_node_type,type,
set_Pr2105655784l_node: $tType ).
thf(set_Pr699757092de_val_type,type,
set_Pr699757092de_val: $tType ).
thf(produc1062784462et_val_type,type,
produc1062784462et_val: $tType ).
thf(produc1013974930l_node_type,type,
produc1013974930l_node: $tType ).
thf(set_Pr700443783al_val_type,type,
set_Pr700443783al_val: $tType ).
thf(produc1858904199et_val_type,type,
produc1858904199et_val: $tType ).
thf(produc782216903al_val_type,type,
produc782216903al_val: $tType ).
thf(produc951622955e_node_type,type,
produc951622955e_node: $tType ).
thf(option_list_val_type,type,
option_list_val: $tType ).
thf(produc1946948786l_node_type,type,
produc1946948786l_node: $tType ).
thf(produc1432036078de_val_type,type,
produc1432036078de_val: $tType ).
thf(product_prod_val_val_type,type,
product_prod_val_val: $tType ).
thf(option_set_val_type,type,
option_set_val: $tType ).
thf(list_set_val_type,type,
list_set_val: $tType ).
thf(set_set_val_type,type,
set_set_val: $tType ).
thf(list_node_type,type,
list_node: $tType ).
thf(list_val_type,type,
list_val: $tType ).
thf(set_node_type,type,
set_node: $tType ).
thf(set_val_type,type,
set_val: $tType ).
thf(node_type,type,
node: $tType ).
thf(var_type,type,
var: $tType ).
thf(val_type,type,
val: $tType ).
thf(g_type,type,
g: $tType ).
thf(finite79836624et_val_type,type,
finite79836624et_val: set_Pr1311924359et_val > $o ).
thf(finite2056463621de_val_type,type,
finite2056463621de_val: set_Pr699757092de_val > $o ).
thf(finite781217938de_val_type,type,
finite781217938de_val: set_Pr701036849de_val > $o ).
thf(finite1581417648et_val_type,type,
finite1581417648et_val: set_Pr978022247et_val > $o ).
thf(finite423892681l_node_type,type,
finite423892681l_node: set_Pr2105655784l_node > $o ).
thf(finite759259600al_val_type,type,
finite759259600al_val: set_Pr700443783al_val > $o ).
thf(finite1265617511et_val_type,type,
finite1265617511et_val: set_set_val > $o ).
thf(finite_finite_node_type,type,
finite_finite_node: set_node > $o ).
thf(finite_finite_val_type,type,
finite_finite_val: set_val > $o ).
thf(graph_272749361_edgeD_type,type,
graph_272749361_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_node ).
thf(graph_1037173556_edgeD_type,type,
graph_1037173556_edgeD: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node ).
thf(irredu893086079de_val_type,type,
irredu893086079de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > set_val > set_Pr1311924359et_val ).
thf(irredu681226810de_val_type,type,
irredu681226810de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > set_val > set_set_val ).
thf(irredu1955035135eD_val_type,type,
irredu1955035135eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > node > set_val ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > set_val > set_val > $o ).
thf(irredu224829488eD_val_type,type,
irredu224829488eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > node > set_val ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > set_val > $o ).
thf(sup_su1487070040et_val_type,type,
sup_su1487070040et_val: option_set_val > option_set_val > option_set_val ).
thf(sup_su2005730907et_val_type,type,
sup_su2005730907et_val: set_Pr1311924359et_val > set_Pr1311924359et_val > set_Pr1311924359et_val ).
thf(sup_su2138939728de_val_type,type,
sup_su2138939728de_val: set_Pr699757092de_val > set_Pr699757092de_val > set_Pr699757092de_val ).
thf(sup_sup_set_set_val_type,type,
sup_sup_set_set_val: set_set_val > set_set_val > set_set_val ).
thf(sup_sup_set_node_type,type,
sup_sup_set_node: set_node > set_node > set_node ).
thf(sup_sup_set_val_type,type,
sup_sup_set_val: set_val > set_val > set_val ).
thf(set_Pr1006393724et_val_type,type,
set_Pr1006393724et_val: list_P88441325et_val > set_Pr1587248327et_val ).
thf(set_Pr482027474de_val_type,type,
set_Pr482027474de_val: list_P729276995de_val > set_Pr819703837de_val ).
thf(set_Pr284769596et_val_type,type,
set_Pr284769596et_val: list_P2089461677et_val > set_Pr1311924359et_val ).
thf(set_Pr1904955709l_node_type,type,
set_Pr1904955709l_node: list_P1414038306l_node > set_Pr574789832l_node ).
thf(set_Pr1027623516al_val_type,type,
set_Pr1027623516al_val: list_P940784845al_val > set_Pr1157324199al_val ).
thf(set_Pr1157337481de_val_type,type,
set_Pr1157337481de_val: list_P1108777338de_val > set_Pr1245322836de_val ).
thf(set_Pr1953765241et_val_type,type,
set_Pr1953765241et_val: list_P12184414et_val > set_Pr1320419588et_val ).
thf(set_Pr1085970585de_val_type,type,
set_Pr1085970585de_val: list_P1820443774de_val > set_Pr699757092de_val ).
thf(set_Pr434939430de_val_type,type,
set_Pr434939430de_val: list_P844977291de_val > set_Pr701036849de_val ).
thf(set_Pr2104310812et_val_type,type,
set_Pr2104310812et_val: list_P761482893et_val > set_Pr978022247et_val ).
thf(set_Pr1600883293l_node_type,type,
set_Pr1600883293l_node: list_P1078858818l_node > set_Pr2105655784l_node ).
thf(set_Pr102746428al_val_type,type,
set_Pr102746428al_val: list_P1811375021al_val > set_Pr700443783al_val ).
thf(set_set_val2_type,type,
set_set_val2: list_set_val > set_set_val ).
thf(set_node2_type,type,
set_node2: list_node > set_node ).
thf(set_val2_type,type,
set_val2: list_val > set_val ).
thf(zip_Pr21865079et_val_type,type,
zip_Pr21865079et_val: list_P2089461677et_val > list_P2089461677et_val > list_P88441325et_val ).
thf(zip_Pr1472086037de_val_type,type,
zip_Pr1472086037de_val: list_P1820443774de_val > list_P1820443774de_val > list_P729276995de_val ).
thf(zip_set_val_set_val_type,type,
zip_set_val_set_val: list_set_val > list_set_val > list_P2089461677et_val ).
thf(zip_set_val_node_type,type,
zip_set_val_node: list_set_val > list_node > list_P1414038306l_node ).
thf(zip_set_val_val_type,type,
zip_set_val_val: list_set_val > list_val > list_P940784845al_val ).
thf(zip_no263301324de_val_type,type,
zip_no263301324de_val: list_node > list_P1820443774de_val > list_P1108777338de_val ).
thf(zip_node_set_val_type,type,
zip_node_set_val: list_node > list_set_val > list_P12184414et_val ).
thf(zip_node_val_type,type,
zip_node_val: list_node > list_val > list_P1820443774de_val ).
thf(zip_va679686869de_val_type,type,
zip_va679686869de_val: list_val > list_P1820443774de_val > list_P844977291de_val ).
thf(zip_val_set_val_type,type,
zip_val_set_val: list_val > list_set_val > list_P761482893et_val ).
thf(zip_val_node_type,type,
zip_val_node: list_val > list_node > list_P1078858818l_node ).
thf(zip_val_val_type,type,
zip_val_val: list_val > list_val > list_P1811375021al_val ).
thf(dom_Pr729677986st_val_type,type,
dom_Pr729677986st_val: ( produc1432036078de_val > option_list_val ) > set_Pr699757092de_val ).
thf(dom_val_list_val_type,type,
dom_val_list_val: ( val > option_list_val ) > set_val ).
thf(none_list_val_type,type,
none_list_val: option_list_val ).
thf(some_list_val_type,type,
some_list_val: list_val > option_list_val ).
thf(some_set_val_type,type,
some_set_val: set_val > option_set_val ).
thf(bot_bo2078591731et_val_type,type,
bot_bo2078591731et_val: set_Pr1311924359et_val ).
thf(bot_bo404898488de_val_type,type,
bot_bo404898488de_val: set_Pr699757092de_val ).
thf(bot_bot_set_set_val_type,type,
bot_bot_set_set_val: set_set_val ).
thf(bot_bot_set_val_type,type,
bot_bot_set_val: set_val ).
thf(ord_le596993316et_val_type,type,
ord_le596993316et_val: option_set_val > option_set_val > $o ).
thf(ord_le299366439et_val_type,type,
ord_le299366439et_val: set_Pr1311924359et_val > set_Pr1311924359et_val > $o ).
thf(ord_le1643692676de_val_type,type,
ord_le1643692676de_val: set_Pr699757092de_val > set_Pr699757092de_val > $o ).
thf(ord_le1742111550et_val_type,type,
ord_le1742111550et_val: set_set_val > set_set_val > $o ).
thf(ord_less_eq_set_node_type,type,
ord_less_eq_set_node: set_node > set_node > $o ).
thf(ord_less_eq_set_val_type,type,
ord_less_eq_set_val: set_val > set_val > $o ).
thf(ord_less_eq_val_type,type,
ord_less_eq_val: val > val > $o ).
thf(produc1377626967et_val_type,type,
produc1377626967et_val: produc1324971431et_val > produc1324971431et_val > produc1904584935et_val ).
thf(produc453318901de_val_type,type,
produc453318901de_val: produc1432036078de_val > produc1432036078de_val > produc452075965de_val ).
thf(produc1041633943et_val_type,type,
produc1041633943et_val: set_val > set_val > produc1324971431et_val ).
thf(produc2052093836l_node_type,type,
produc2052093836l_node: set_val > node > produc1013974930l_node ).
thf(produc1337903031al_val_type,type,
produc1337903031al_val: set_val > val > produc782216903al_val ).
thf(produc1162531244de_val_type,type,
produc1162531244de_val: node > produc1432036078de_val > produc1615737844de_val ).
thf(produc2042994048et_val_type,type,
produc2042994048et_val: node > set_val > produc1062784462et_val ).
thf(produc1470527136de_val_type,type,
produc1470527136de_val: node > val > produc1432036078de_val ).
thf(produc1571934709de_val_type,type,
produc1571934709de_val: val > produc1432036078de_val > produc1664334075de_val ).
thf(produc1446164855et_val_type,type,
produc1446164855et_val: val > set_val > produc1858904199et_val ).
thf(produc1074923692l_node_type,type,
produc1074923692l_node: val > node > produc1946948786l_node ).
thf(product_Pair_val_val_type,type,
product_Pair_val_val: val > val > product_prod_val_val ).
thf(sSA_CF139593942de_val_type,type,
sSA_CF139593942de_val: ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(sSA_CF178745443eD_val_type,type,
sSA_CF178745443eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(sSA_CF1517915011eD_val_type,type,
sSA_CF1517915011eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > node > set_val ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > set_val ).
thf(sSA_CF370335846de_val_type,type,
sSA_CF370335846de_val: ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(sSA_CF848637139eD_val_type,type,
sSA_CF848637139eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(sSA_CF551432799de_val_type,type,
sSA_CF551432799de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > node ).
thf(sSA_CF1909049442de_val_type,type,
sSA_CF1909049442de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
thf(sSA_CF794421325de_val_type,type,
sSA_CF794421325de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > $o ).
thf(sSA_CF1252180629de_val_type,type,
sSA_CF1252180629de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
thf(sSA_CF262257161de_val_type,type,
sSA_CF262257161de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > option_list_val ).
thf(sSA_CF2074824714de_val_type,type,
sSA_CF2074824714de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > $o ).
thf(sSA_CF1660885746eD_val_type,type,
sSA_CF1660885746eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > node > set_val ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > $o ).
thf(sSA_CF1899243830eD_val_type,type,
sSA_CF1899243830eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > node > set_val ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > $o ).
thf(sSA_CF655860150de_val_type,type,
sSA_CF655860150de_val: ( g > list_node ) > ( g > node > set_val ) > g > set_val ).
thf(collec1117167378et_val_type,type,
collec1117167378et_val: ( produc1324971431et_val > $o ) > set_Pr1311924359et_val ).
thf(collec370342979de_val_type,type,
collec370342979de_val: ( produc1432036078de_val > $o ) > set_Pr699757092de_val ).
thf(collec885255687l_node_type,type,
collec885255687l_node: ( produc1946948786l_node > $o ) > set_Pr2105655784l_node ).
thf(collec52550418al_val_type,type,
collec52550418al_val: ( product_prod_val_val > $o ) > set_Pr700443783al_val ).
thf(collect_set_val_type,type,
collect_set_val: ( set_val > $o ) > set_set_val ).
thf(collect_node_type,type,
collect_node: ( node > $o ) > set_node ).
thf(collect_val_type,type,
collect_val: ( val > $o ) > set_val ).
thf(insert1846469495et_val_type,type,
insert1846469495et_val: produc1324971431et_val > set_Pr1311924359et_val > set_Pr1311924359et_val ).
thf(insert869443870de_val_type,type,
insert869443870de_val: produc1432036078de_val > set_Pr699757092de_val > set_Pr699757092de_val ).
thf(insert_set_val_type,type,
insert_set_val: set_val > set_set_val > set_set_val ).
thf(insert_node_type,type,
insert_node: node > set_node > set_node ).
thf(insert_val_type,type,
insert_val: val > set_val > set_val ).
thf(transi1953622797et_val_type,type,
transi1953622797et_val: set_Pr1311924359et_val > $o ).
thf(transi1991289355lp_val_type,type,
transi1991289355lp_val: ( val > val > $o ) > val > val > $o ).
thf(member1254968080et_val_type,type,
member1254968080et_val: produc1904584935et_val > set_Pr1587248327et_val > $o ).
thf(member698732390de_val_type,type,
member698732390de_val: produc452075965de_val > set_Pr819703837de_val > $o ).
thf(member1711426256et_val_type,type,
member1711426256et_val: produc1324971431et_val > set_Pr1311924359et_val > $o ).
thf(member76372137l_node_type,type,
member76372137l_node: produc1013974930l_node > set_Pr574789832l_node > $o ).
thf(member1110026224al_val_type,type,
member1110026224al_val: produc782216903al_val > set_Pr1157324199al_val > $o ).
thf(member562853661de_val_type,type,
member562853661de_val: produc1615737844de_val > set_Pr1245322836de_val > $o ).
thf(member125181669et_val_type,type,
member125181669et_val: produc1062784462et_val > set_Pr1320419588et_val > $o ).
thf(member313544709de_val_type,type,
member313544709de_val: produc1432036078de_val > set_Pr699757092de_val > $o ).
thf(member1894062994de_val_type,type,
member1894062994de_val: produc1664334075de_val > set_Pr701036849de_val > $o ).
thf(member39229872et_val_type,type,
member39229872et_val: produc1858904199et_val > set_Pr978022247et_val > $o ).
thf(member828457417l_node_type,type,
member828457417l_node: produc1946948786l_node > set_Pr2105655784l_node > $o ).
thf(member1680438992al_val_type,type,
member1680438992al_val: product_prod_val_val > set_Pr700443783al_val > $o ).
thf(member_set_val_type,type,
member_set_val: set_val > set_set_val > $o ).
thf(member_node_type,type,
member_node: node > set_node > $o ).
thf(member_val_type,type,
member_val: val > set_val > $o ).
thf(alpha_n_type,type,
alpha_n: g > list_node ).
thf(phi_type,type,
phi: val ).
thf(phi_s_type,type,
phi_s: val ).
thf(phi2_type,type,
phi2: val ).
thf(defs_type,type,
defs: g > node > set_val ).
thf(g2_type,type,
g2: g ).
thf(inEdges_type,type,
inEdges: g > node > list_P561207620_edgeD ).
thf(phis_type,type,
phis: g > produc1432036078de_val > option_list_val ).
thf(s_type,type,
s: val ).
thf(uses_type,type,
uses: g > node > set_val ).
thf(var2_type,type,
var2: g > val > var ).
thf(sk1_type,type,
sk1: set_set_val > set_set_val > set_val ).
thf(189,axiom,
irredu893086079de_val = irredu893086079de_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_CFG__SSA__Transformed_Ocondensation__edges_Ocong) ).
thf(892,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(335,axiom,
! [A: g,B: node] :
( ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ A @ B )
= ( sup_sup_set_val @ ( uses @ A @ B ) @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_allUses__def) ).
thf(1322,plain,
! [A: g,B: node] :
( ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ A @ B )
= ( sup_sup_set_val @ ( uses @ A @ B ) @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(339,axiom,
! [A: g,B: node,C: val,D: list_val,E: node,F: list_val] :
( ( ( phis @ A @ ( produc1470527136de_val @ B @ C ) )
= ( some_list_val @ D ) )
=> ( ( ( phis @ A @ ( produc1470527136de_val @ E @ C ) )
= ( some_list_val @ F ) )
=> ( D = F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_phis__disj_I2_J) ).
thf(1337,plain,
! [A: g,B: node,C: val,D: list_val,E: node,F: list_val] :
( ( ( phis @ A @ ( produc1470527136de_val @ B @ C ) )
= ( some_list_val @ D ) )
=> ( ( ( phis @ A @ ( produc1470527136de_val @ E @ C ) )
= ( some_list_val @ F ) )
=> ( D = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(100,axiom,
! [A: set_val,B: set_set_val,C: set_set_val] :
( ( member_set_val @ A @ ( sup_sup_set_set_val @ B @ C ) )
= ( ( member_set_val @ A @ B )
| ( member_set_val @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_Un__iff) ).
thf(629,plain,
! [A: set_val,B: set_set_val,C: set_set_val] :
( ( member_set_val @ A @ ( sup_sup_set_set_val @ B @ C ) )
= ( ( member_set_val @ A @ B )
| ( member_set_val @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(288,axiom,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( defs @ B @ C ) )
=> ( member_val @ A @ ( sSA_CF139593942de_val @ defs @ phis @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_defs__in__allDefs) ).
thf(1168,plain,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( defs @ B @ C ) )
=> ( member_val @ A @ ( sSA_CF139593942de_val @ defs @ phis @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(190,axiom,
( sup_sup_set_val
= ( ^ [A: set_val,B: set_val] : ( sup_sup_set_val @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_sup_Ocommute) ).
thf(893,plain,
( sup_sup_set_val
= ( ^ [A: set_val,B: set_val] : ( sup_sup_set_val @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(1,conjecture,
member_val @ phi_s @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( member_val @ phi_s @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(352,plain,
~ ( member_val @ phi_s @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
( ord_le299366439et_val
= ( ^ [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
! [C: produc1324971431et_val] :
( ( member1711426256et_val @ C @ A )
=> ( member1711426256et_val @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_subset__eq) ).
thf(365,plain,
( ord_le299366439et_val
= ( ^ [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
! [C: produc1324971431et_val] :
( ( member1711426256et_val @ C @ A )
=> ( member1711426256et_val @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(295,axiom,
sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi2 @ phi_s,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062phiArg_Ag_A_092_060phi_062_H_A_092_060phi_062_092_060_094sub_062s_092_060close_062) ).
thf(1190,plain,
sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi2 @ phi_s,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(261,axiom,
! [A: set_val,B: g,C: set_val] :
( ( member_set_val @ A @ ( irredu681226810de_val @ alpha_n @ defs @ phis @ B @ C ) )
=> ( ord_less_eq_set_val @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_scc__in__P) ).
thf(1083,plain,
! [A: set_val,B: g,C: set_val] :
( ( member_set_val @ A @ ( irredu681226810de_val @ alpha_n @ defs @ phis @ B @ C ) )
=> ( ord_less_eq_set_val @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(44,axiom,
sSA_CF139593942de_val = sSA_CF139593942de_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_CFG__SSA__base_OallDefs_Ocong) ).
thf(468,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(304,axiom,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( finite_finite_val @ ( sSA_CF139593942de_val @ defs @ phis @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_allDefs__finite) ).
thf(1211,plain,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( finite_finite_val @ ( sSA_CF139593942de_val @ defs @ phis @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(284,axiom,
! [A: g,B: val] :
( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ A @ B )
=> ( member_val @ B @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_liveVal__in__allVars) ).
thf(1158,plain,
! [A: g,B: val] :
( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ A @ B )
=> ( member_val @ B @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(256,axiom,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( uses @ B @ C ) )
=> ( member_val @ A @ ( sSA_CF655860150de_val @ alpha_n @ uses @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_uses__in__vars) ).
thf(1068,plain,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( uses @ B @ C ) )
=> ( member_val @ A @ ( sSA_CF655860150de_val @ alpha_n @ uses @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(178,axiom,
! [A: option_list_val] :
( ( ! [B: list_val] :
( A
!= ( some_list_val @ B ) ) )
= ( A = none_list_val ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_not__Some__eq) ).
thf(861,plain,
! [A: option_list_val] :
( ( ! [B: list_val] :
( A
!= ( some_list_val @ B ) ) )
= ( A = none_list_val ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(24,axiom,
! [A: produc1432036078de_val,B: set_Pr699757092de_val,C: set_Pr699757092de_val] :
( ( member313544709de_val @ A @ ( sup_su2138939728de_val @ B @ C ) )
=> ( ~ ( member313544709de_val @ A @ B )
=> ( member313544709de_val @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_UnE) ).
thf(408,plain,
! [A: produc1432036078de_val,B: set_Pr699757092de_val,C: set_Pr699757092de_val] :
( ( member313544709de_val @ A @ ( sup_su2138939728de_val @ B @ C ) )
=> ( ~ ( member313544709de_val @ A @ B )
=> ( member313544709de_val @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(223,axiom,
! [A: set_val,B: set_set_val,C: set_set_val] :
( ( ~ ( member_set_val @ A @ B )
=> ( member_set_val @ A @ C ) )
=> ( member_set_val @ A @ ( sup_sup_set_set_val @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_UnCI) ).
thf(977,plain,
! [A: set_val,B: set_set_val,C: set_set_val] :
( ( ~ ( member_set_val @ A @ B )
=> ( member_set_val @ A @ C ) )
=> ( member_set_val @ A @ ( sup_sup_set_set_val @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(15,axiom,
( ord_less_eq_set_node
= ( ^ [A: set_node,B: set_node] :
! [C: node] :
( ( member_node @ C @ A )
=> ( member_node @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_subset__iff) ).
thf(385,plain,
( ord_less_eq_set_node
= ( ^ [A: set_node,B: set_node] :
! [C: node] :
( ( member_node @ C @ A )
=> ( member_node @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(14,axiom,
( ord_less_eq_set_node
= ( ^ [A: set_node,B: set_node] :
! [C: node] :
( ( member_node @ C @ A )
=> ( member_node @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_subset__eq) ).
thf(383,plain,
( ord_less_eq_set_node
= ( ^ [A: set_node,B: set_node] :
! [C: node] :
( ( member_node @ C @ A )
=> ( member_node @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(384,plain,
( ord_less_eq_set_node
= ( ^ [A: set_node,B: set_node] :
! [C: node] :
( ( member_node @ C @ A )
=> ( member_node @ C @ B ) ) ) ),
inference(lifteq,[status(thm)],[383]) ).
thf(57,axiom,
! [A: node,B: set_node,C: set_node] :
( ( ~ ( member_node @ A @ B )
=> ( member_node @ A @ C ) )
=> ( member_node @ A @ ( sup_sup_set_node @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_UnCI) ).
thf(500,plain,
! [A: node,B: set_node,C: set_node] :
( ( ~ ( member_node @ A @ B )
=> ( member_node @ A @ C ) )
=> ( member_node @ A @ ( sup_sup_set_node @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(158,axiom,
! [A: produc1324971431et_val,B: produc1324971431et_val > $o] :
( ( member1711426256et_val @ A @ ( collec1117167378et_val @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_mem__Collect__eq) ).
thf(797,plain,
! [A: produc1324971431et_val,B: produc1324971431et_val > $o] :
( ( member1711426256et_val @ A @ ( collec1117167378et_val @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(318,axiom,
! [A: node,B: g,C: val] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_val @ C @ ( defs @ B @ A ) )
=> ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ B @ C )
= none_list_val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_simpleDef__not__phi) ).
thf(1260,plain,
! [A: node,B: g,C: val] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_val @ C @ ( defs @ B @ A ) )
=> ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ B @ C )
= none_list_val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(345,axiom,
! [A: set_val] :
( ( collect_val
@ ^ [B: val] : ( member_val @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Collect__mem__eq) ).
thf(1354,plain,
! [A: set_val] :
( ( collect_val
@ ^ [B: val] : ( member_val @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(205,axiom,
! [A: list_P1820443774de_val,B: set_Pr699757092de_val] :
( ( ord_le1643692676de_val @ ( set_Pr1085970585de_val @ A ) @ B )
= ( ! [C: produc1432036078de_val] :
( ( member313544709de_val @ C @ ( set_Pr1085970585de_val @ A ) )
=> ( member313544709de_val @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_subset__code_I1_J) ).
thf(930,plain,
! [A: list_P1820443774de_val,B: set_Pr699757092de_val] :
( ( ord_le1643692676de_val @ ( set_Pr1085970585de_val @ A ) @ B )
= ( ! [C: produc1432036078de_val] :
( ( member313544709de_val @ C @ ( set_Pr1085970585de_val @ A ) )
=> ( member313544709de_val @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(265,axiom,
! [A: g,B: val,C: val > $o] :
( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ A @ B )
=> ( ! [D: node,E: val] :
( ( member_node @ D @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ( ( member_val @ E @ ( uses @ A @ D ) )
=> ( C @ E ) ) )
=> ( ! [D: val,E: val] :
( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ A @ D )
=> ( ( C @ D )
=> ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ D @ E )
=> ( C @ E ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_liveVal_Oinducts) ).
thf(1095,plain,
! [A: g,B: val,C: val > $o] :
( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ A @ B )
=> ( ! [D: node,E: val] :
( ( member_node @ D @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ( ( member_val @ E @ ( uses @ A @ D ) )
=> ( C @ E ) ) )
=> ( ! [D: val,E: val] :
( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ A @ D )
=> ( ( C @ D )
=> ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ D @ E )
=> ( C @ E ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(232,axiom,
( ord_less_eq_set_val
= ( ^ [A: set_val,B: set_val] :
( ( sup_sup_set_val @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_subset__Un__eq) ).
thf(1001,plain,
( ord_less_eq_set_val
= ( ^ [A: set_val,B: set_val] :
( ( sup_sup_set_val @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(273,axiom,
! [A: g,B: val] :
( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A @ B )
= ( phis @ A @ ( produc1470527136de_val @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_phi__def) ).
thf(1127,plain,
! [A: g,B: val] :
( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A @ B )
= ( phis @ A @ ( produc1470527136de_val @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ A @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(151,axiom,
( ( (=) @ set_val )
= ( ^ [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
& ( ord_less_eq_set_val @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_set__eq__subset) ).
thf(782,plain,
( ( (=) @ set_val )
= ( ^ [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
& ( ord_less_eq_set_val @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(170,axiom,
! [A: set_Pr699757092de_val] :
( ( collec370342979de_val
@ ^ [B: produc1432036078de_val] : ( member313544709de_val @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Collect__mem__eq) ).
thf(841,plain,
! [A: set_Pr699757092de_val] :
( ( collec370342979de_val
@ ^ [B: produc1432036078de_val] : ( member313544709de_val @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(248,axiom,
! [A: val,B: set_val,C: list_val,D: list_set_val] :
( ( member39229872et_val @ ( produc1446164855et_val @ A @ B ) @ ( set_Pr2104310812et_val @ ( zip_val_set_val @ C @ D ) ) )
=> ~ ( ( member_val @ A @ ( set_val2 @ C ) )
=> ~ ( member_set_val @ B @ ( set_set_val2 @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_in__set__zipE) ).
thf(1046,plain,
! [A: val,B: set_val,C: list_val,D: list_set_val] :
( ( member39229872et_val @ ( produc1446164855et_val @ A @ B ) @ ( set_Pr2104310812et_val @ ( zip_val_set_val @ C @ D ) ) )
=> ~ ( ( member_val @ A @ ( set_val2 @ C ) )
=> ~ ( member_set_val @ B @ ( set_set_val2 @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(349,axiom,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ B @ C ) )
=> ~ ! [D: node] :
( ( member_node @ D @ ( set_node2 @ ( graph_1037173556_edgeD @ alpha_n @ inEdges @ B @ C ) ) )
=> ! [E: val,F: list_val] :
( ( member313544709de_val @ ( produc1470527136de_val @ C @ A ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ ( graph_272749361_edgeD @ inEdges @ B @ D ) @ F ) ) )
=> ( ( phis @ B @ ( produc1470527136de_val @ D @ E ) )
!= ( some_list_val @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_phiUsesE) ).
thf(1366,plain,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ B @ C ) )
=> ~ ! [D: node] :
( ( member_node @ D @ ( set_node2 @ ( graph_1037173556_edgeD @ alpha_n @ inEdges @ B @ C ) ) )
=> ! [E: val,F: list_val] :
( ( member313544709de_val @ ( produc1470527136de_val @ C @ A ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ ( graph_272749361_edgeD @ inEdges @ B @ D ) @ F ) ) )
=> ( ( phis @ B @ ( produc1470527136de_val @ D @ E ) )
!= ( some_list_val @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(34,axiom,
! [A: list_P2089461677et_val,B: set_Pr1311924359et_val] :
( ( ord_le299366439et_val @ ( set_Pr284769596et_val @ A ) @ B )
= ( ! [C: produc1324971431et_val] :
( ( member1711426256et_val @ C @ ( set_Pr284769596et_val @ A ) )
=> ( member1711426256et_val @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_subset__code_I1_J) ).
thf(436,plain,
! [A: list_P2089461677et_val,B: set_Pr1311924359et_val] :
( ( ord_le299366439et_val @ ( set_Pr284769596et_val @ A ) @ B )
= ( ! [C: produc1324971431et_val] :
( ( member1711426256et_val @ C @ ( set_Pr284769596et_val @ A ) )
=> ( member1711426256et_val @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(107,axiom,
! [A: val,B: set_val] :
( ( finite_finite_val @ ( insert_val @ A @ B ) )
= ( finite_finite_val @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_finite__insert) ).
thf(651,plain,
! [A: val,B: set_val] :
( ( finite_finite_val @ ( insert_val @ A @ B ) )
= ( finite_finite_val @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(17,axiom,
! [A: set_set_val,B: set_set_val,C: set_val] :
( ( ord_le1742111550et_val @ A @ B )
=> ( ( member_set_val @ C @ A )
=> ( member_set_val @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_in__mono) ).
thf(389,plain,
! [A: set_set_val,B: set_set_val,C: set_val] :
( ( ord_le1742111550et_val @ A @ B )
=> ( ( member_set_val @ C @ A )
=> ( member_set_val @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(130,axiom,
( ord_less_eq_set_val
= ( ^ [A: set_val,B: set_val] :
( ( sup_sup_set_val @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_sup_Oabsorb__iff1) ).
thf(721,plain,
( ord_less_eq_set_val
= ( ^ [A: set_val,B: set_val] :
( ( sup_sup_set_val @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(722,plain,
( ord_less_eq_set_val
= ( ^ [A: set_val,B: set_val] :
( ( sup_sup_set_val @ B @ A )
= B ) ) ),
inference(lifteq,[status(thm)],[721]) ).
thf(67,axiom,
( ord_less_eq_set_val
= ( ^ [A: set_val,B: set_val] :
( B
= ( sup_sup_set_val @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_sup_Oorder__iff) ).
thf(534,plain,
( ord_less_eq_set_val
= ( ^ [A: set_val,B: set_val] :
( B
= ( sup_sup_set_val @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(535,plain,
( ord_less_eq_set_val
= ( ^ [A: set_val,B: set_val] :
( B
= ( sup_sup_set_val @ B @ A ) ) ) ),
inference(lifteq,[status(thm)],[534]) ).
thf(1405,plain,
( ( ^ [A: set_val,B: set_val] :
( B
= ( sup_sup_set_val @ B @ A ) ) )
= ( ^ [A: set_val,B: set_val] :
( ( sup_sup_set_val @ B @ A )
= B ) ) ),
inference(rewrite,[status(thm)],[722,535]) ).
thf(103,axiom,
( ord_less_eq_set_val
= ( ^ [A: set_val,B: set_val] :
( ( sup_sup_set_val @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_sup_Oabsorb__iff2) ).
thf(638,plain,
( ord_less_eq_set_val
= ( ^ [A: set_val,B: set_val] :
( ( sup_sup_set_val @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(639,plain,
( ord_less_eq_set_val
= ( ^ [A: set_val,B: set_val] :
( ( sup_sup_set_val @ A @ B )
= B ) ) ),
inference(lifteq,[status(thm)],[638]) ).
thf(1396,plain,
( ( ^ [A: set_val,B: set_val] :
( B
= ( sup_sup_set_val @ B @ A ) ) )
= ( ^ [A: set_val,B: set_val] :
( ( sup_sup_set_val @ A @ B )
= B ) ) ),
inference(rewrite,[status(thm)],[639,535]) ).
thf(1408,plain,
( ( ( ^ [A: set_val,B: set_val] :
( ( sup_sup_set_val @ B @ A )
= B ) )
= ( ^ [A: set_val,B: set_val] :
( ( sup_sup_set_val @ A @ B )
= B ) ) )
| ( ( ^ [A: set_val,B: set_val] :
( B
= ( sup_sup_set_val @ B @ A ) ) )
!= ( ^ [A: set_val,B: set_val] :
( B
= ( sup_sup_set_val @ B @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1405,1396]) ).
thf(1409,plain,
( ( ^ [A: set_val,B: set_val] :
( ( sup_sup_set_val @ B @ A )
= B ) )
= ( ^ [A: set_val,B: set_val] :
( ( sup_sup_set_val @ A @ B )
= B ) ) ),
inference(pattern_uni,[status(thm)],[1408:[]]) ).
thf(129,axiom,
( ord_less_eq_set_val
= ( ^ [A: set_val,B: set_val] :
( ( sup_sup_set_val @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_le__iff__sup) ).
thf(719,plain,
( ord_less_eq_set_val
= ( ^ [A: set_val,B: set_val] :
( ( sup_sup_set_val @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(153,axiom,
! [A: set_val,B: set_val] :
( ( bot_bot_set_val
= ( sup_sup_set_val @ A @ B ) )
= ( ( A = bot_bot_set_val )
& ( B = bot_bot_set_val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_sup__bot_Oneutr__eq__iff) ).
thf(785,plain,
! [A: set_val,B: set_val] :
( ( bot_bot_set_val
= ( sup_sup_set_val @ A @ B ) )
= ( ( A = bot_bot_set_val )
& ( B = bot_bot_set_val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(319,axiom,
! [A: node,B: g,C: node] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_node @ A @ ( set_node2 @ ( graph_1037173556_edgeD @ alpha_n @ inEdges @ B @ C ) ) )
= ( member_node @ C @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_old_Osuccessors__predecessors) ).
thf(1264,plain,
! [A: node,B: g,C: node] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_node @ A @ ( set_node2 @ ( graph_1037173556_edgeD @ alpha_n @ inEdges @ B @ C ) ) )
= ( member_node @ C @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(324,axiom,
( sSA_CF2074824714de_val
= ( ^ [A: g > list_node,B: g > node > set_val,C: g > node > set_val,D: g > produc1432036078de_val > option_list_val,E: g] :
! [F: node] :
( ( member_node @ F @ ( set_node2 @ ( A @ E ) ) )
=> ! [G: val] :
( ( member_val @ G @ ( sSA_CF370335846de_val @ D @ E @ F ) )
=> ( sSA_CF794421325de_val @ A @ B @ C @ D @ E @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_CFG__SSA__wf__base_Opruned__def) ).
thf(1279,plain,
( sSA_CF2074824714de_val
= ( ^ [A: g > list_node,B: g > node > set_val,C: g > node > set_val,D: g > produc1432036078de_val > option_list_val,E: g] :
! [F: node] :
( ( member_node @ F @ ( set_node2 @ ( A @ E ) ) )
=> ! [G: val] :
( ( member_val @ G @ ( sSA_CF370335846de_val @ D @ E @ F ) )
=> ( sSA_CF794421325de_val @ A @ B @ C @ D @ E @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(70,axiom,
! [A: set_val,B: set_val] :
( ( sup_sup_set_val @ A @ ( sup_sup_set_val @ A @ B ) )
= ( sup_sup_set_val @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_sup_Oleft__idem) ).
thf(542,plain,
! [A: set_val,B: set_val] :
( ( sup_sup_set_val @ A @ ( sup_sup_set_val @ A @ B ) )
= ( sup_sup_set_val @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(85,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_sup_OcoboundedI2) ).
thf(587,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(169,axiom,
! [A: val > $o,B: val > $o] :
( ! [C: val] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_val @ ( collect_val @ A ) @ ( collect_val @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_Collect__mono) ).
thf(838,plain,
! [A: val > $o,B: val > $o] :
( ! [C: val] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_val @ ( collect_val @ A ) @ ( collect_val @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(200,axiom,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
( ( ord_le1643692676de_val @ A @ B )
=> ( ~ ( finite2056463621de_val @ A )
=> ~ ( finite2056463621de_val @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_infinite__super) ).
thf(917,plain,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
( ( ord_le1643692676de_val @ A @ B )
=> ( ~ ( finite2056463621de_val @ A )
=> ~ ( finite2056463621de_val @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(122,axiom,
! [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
( ( finite79836624et_val @ ( sup_su2005730907et_val @ A @ B ) )
= ( ( finite79836624et_val @ A )
& ( finite79836624et_val @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_finite__Un) ).
thf(702,plain,
! [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
( ( finite79836624et_val @ ( sup_su2005730907et_val @ A @ B ) )
= ( ( finite79836624et_val @ A )
& ( finite79836624et_val @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(4,axiom,
! [A: set_set_val,B: set_set_val] :
( ! [C: set_val] :
( ( member_set_val @ C @ A )
=> ( member_set_val @ C @ B ) )
=> ( ord_le1742111550et_val @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_subsetI) ).
thf(356,plain,
! [A: set_set_val,B: set_set_val] :
( ! [C: set_val] :
( ( member_set_val @ C @ A )
=> ( member_set_val @ C @ B ) )
=> ( ord_le1742111550et_val @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(357,plain,
! [B: set_set_val,A: set_set_val] :
( ( member_set_val @ ( sk1 @ B @ A ) @ A )
| ( ord_le1742111550et_val @ A @ B ) ),
inference(cnf,[status(esa)],[356]) ).
thf(296,axiom,
! [A: val,B: g] :
( ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) )
=> ( member_val @ A @ ( sSA_CF139593942de_val @ defs @ phis @ B @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_defNode_I2_J) ).
thf(1191,plain,
! [A: val,B: g] :
( ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) )
=> ( member_val @ A @ ( sSA_CF139593942de_val @ defs @ phis @ B @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(252,axiom,
! [A: val,B: g,C: list_val] :
( ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) )
=> ( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ B @ A )
= ( some_list_val @ C ) )
=> ( ( set_val2 @ C )
!= ( insert_val @ A @ bot_bot_set_val ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_phi__no__closed__loop) ).
thf(1056,plain,
! [A: val,B: g,C: list_val] :
( ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) )
=> ( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ B @ A )
= ( some_list_val @ C ) )
=> ( ( set_val2 @ C )
!= ( insert_val @ A @ bot_bot_set_val ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(1057,plain,
! [A: val,B: g] :
( ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) )
=> ! [C: list_val] :
( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ B @ A )
= ( some_list_val @ C ) )
=> ( ( set_val2 @ C )
!= ( insert_val @ A @ bot_bot_set_val ) ) ) ),
inference(miniscope,[status(thm)],[1056]) ).
thf(1058,plain,
! [C: list_val,B: g,A: val] :
( ~ ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) )
| ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ B @ A )
!= ( some_list_val @ C ) )
| ( ( set_val2 @ C )
!= ( insert_val @ A @ bot_bot_set_val ) ) ),
inference(cnf,[status(esa)],[1057]) ).
thf(1059,plain,
! [C: list_val,B: g,A: val] :
( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ B @ A )
!= ( some_list_val @ C ) )
| ( ( set_val2 @ C )
!= ( insert_val @ A @ bot_bot_set_val ) )
| ~ ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) ) ),
inference(lifteq,[status(thm)],[1058]) ).
thf(275,axiom,
! [A: g,B: val,C: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ B @ C )
=> ( member_val @ C @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_phiArg__in__allVars) ).
thf(1132,plain,
! [A: g,B: val,C: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ B @ C )
=> ( member_val @ C @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(194,axiom,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
( ( ord_le1643692676de_val @ A @ B )
=> ( ( finite2056463621de_val @ B )
=> ( finite2056463621de_val @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_finite__subset) ).
thf(902,plain,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
( ( ord_le1643692676de_val @ A @ B )
=> ( ( finite2056463621de_val @ B )
=> ( finite2056463621de_val @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(314,axiom,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( finite_finite_val @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_phiUses__finite) ).
thf(1247,plain,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( finite_finite_val @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(220,axiom,
( sup_sup_set_val
= ( ^ [A: set_val,B: set_val] : ( sup_sup_set_val @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_Un__commute) ).
thf(969,plain,
( sup_sup_set_val
= ( ^ [A: set_val,B: set_val] : ( sup_sup_set_val @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(237,axiom,
! [A: val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ ( insert_val @ A @ B ) @ C )
= ( ( member_val @ A @ C )
& ( ord_less_eq_set_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_insert__subset) ).
thf(1013,plain,
! [A: val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ ( insert_val @ A @ B ) @ C )
= ( ( member_val @ A @ C )
& ( ord_less_eq_set_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(39,axiom,
! [A: set_val > set_val > set_val,B: set_val,C: set_val] :
( ! [D: set_val,E: set_val] : ( ord_less_eq_set_val @ D @ ( A @ D @ E ) )
=> ( ! [D: set_val,E: set_val] : ( ord_less_eq_set_val @ E @ ( A @ D @ E ) )
=> ( ! [D: set_val,E: set_val,F: set_val] :
( ( ord_less_eq_set_val @ E @ D )
=> ( ( ord_less_eq_set_val @ F @ D )
=> ( ord_less_eq_set_val @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup_sup_set_val @ B @ C )
= ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_sup__unique) ).
thf(448,plain,
! [A: set_val > set_val > set_val,B: set_val,C: set_val] :
( ! [D: set_val,E: set_val] : ( ord_less_eq_set_val @ D @ ( A @ D @ E ) )
=> ( ! [D: set_val,E: set_val] : ( ord_less_eq_set_val @ E @ ( A @ D @ E ) )
=> ( ! [D: set_val,E: set_val,F: set_val] :
( ( ord_less_eq_set_val @ E @ D )
=> ( ( ord_less_eq_set_val @ F @ D )
=> ( ord_less_eq_set_val @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup_sup_set_val @ B @ C )
= ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(175,axiom,
! [A: node,B: set_node,C: set_node] :
( ( ord_less_eq_set_node @ ( insert_node @ A @ B ) @ C )
= ( ( member_node @ A @ C )
& ( ord_less_eq_set_node @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_insert__subset) ).
thf(853,plain,
! [A: node,B: set_node,C: set_node] :
( ( ord_less_eq_set_node @ ( insert_node @ A @ B ) @ C )
= ( ( member_node @ A @ C )
& ( ord_less_eq_set_node @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(29,axiom,
! [A: produc1324971431et_val,B: set_Pr1311924359et_val,C: set_Pr1311924359et_val] :
( ( ord_le299366439et_val @ ( insert1846469495et_val @ A @ B ) @ C )
= ( ( member1711426256et_val @ A @ C )
& ( ord_le299366439et_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_insert__subset) ).
thf(421,plain,
! [A: produc1324971431et_val,B: set_Pr1311924359et_val,C: set_Pr1311924359et_val] :
( ( ord_le299366439et_val @ ( insert1846469495et_val @ A @ B ) @ C )
= ( ( member1711426256et_val @ A @ C )
& ( ord_le299366439et_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(181,axiom,
( sup_sup_set_val
= ( ^ [A: set_val,B: set_val] : ( sup_sup_set_val @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_sup__commute) ).
thf(870,plain,
( sup_sup_set_val
= ( ^ [A: set_val,B: set_val] : ( sup_sup_set_val @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(203,axiom,
! [A: set_val] :
( ( sup_sup_set_val @ A @ bot_bot_set_val )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_sup__bot_Oright__neutral) ).
thf(924,plain,
! [A: set_val] :
( ( sup_sup_set_val @ A @ bot_bot_set_val )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(53,axiom,
sSA_CF655860150de_val = sSA_CF655860150de_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_CFG__base_Ovars_Ocong) ).
thf(492,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(87,axiom,
! [A: set_val,B: set_val] :
( ( sup_sup_set_val @ A @ ( sup_sup_set_val @ A @ B ) )
= ( sup_sup_set_val @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_sup__left__idem) ).
thf(591,plain,
! [A: set_val,B: set_val] :
( ( sup_sup_set_val @ A @ ( sup_sup_set_val @ A @ B ) )
= ( sup_sup_set_val @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(266,axiom,
! [A: set_val,B: set_val,C: val > $o] :
( ( ! [D: val] :
( ( member_val @ D @ ( sup_sup_set_val @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: val] :
( ( member_val @ D @ A )
=> ( C @ D ) )
& ! [D: val] :
( ( member_val @ D @ B )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_ball__Un) ).
thf(1109,plain,
! [A: set_val,B: set_val,C: val > $o] :
( ( ! [D: val] :
( ( member_val @ D @ ( sup_sup_set_val @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: val] :
( ( member_val @ D @ A )
=> ( C @ D ) )
& ! [D: val] :
( ( member_val @ D @ B )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(80,axiom,
! [A: node,B: produc1432036078de_val,C: list_node,D: list_P1820443774de_val] :
( ( member562853661de_val @ ( produc1162531244de_val @ A @ B ) @ ( set_Pr1157337481de_val @ ( zip_no263301324de_val @ C @ D ) ) )
=> ~ ( ( member_node @ A @ ( set_node2 @ C ) )
=> ~ ( member313544709de_val @ B @ ( set_Pr1085970585de_val @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_in__set__zipE) ).
thf(574,plain,
! [A: node,B: produc1432036078de_val,C: list_node,D: list_P1820443774de_val] :
( ( member562853661de_val @ ( produc1162531244de_val @ A @ B ) @ ( set_Pr1157337481de_val @ ( zip_no263301324de_val @ C @ D ) ) )
=> ~ ( ( member_node @ A @ ( set_node2 @ C ) )
=> ~ ( member313544709de_val @ B @ ( set_Pr1085970585de_val @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(161,axiom,
irredu1955035135eD_val = irredu1955035135eD_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_CFG__SSA__Transformed_Oredundant__scc_Ocong) ).
thf(806,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(250,axiom,
! [A: g,B: val] :
( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ A @ B )
= ( ? [C: node,D: val] :
( ( B = D )
& ( member_node @ C @ ( set_node2 @ ( alpha_n @ A ) ) )
& ( member_val @ D @ ( uses @ A @ C ) ) )
| ? [C: val,D: val] :
( ( B = D )
& ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ A @ C )
& ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_liveVal_Osimps) ).
thf(1051,plain,
! [A: g,B: val] :
( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ A @ B )
= ( ? [C: node,D: val] :
( ( B = D )
& ( member_node @ C @ ( set_node2 @ ( alpha_n @ A ) ) )
& ( member_val @ D @ ( uses @ A @ C ) ) )
| ? [C: val,D: val] :
( ( B = D )
& ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ A @ C )
& ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(49,axiom,
! [A: set_Pr699757092de_val] :
( ~ ( finite2056463621de_val @ A )
=> ( A != bot_bo404898488de_val ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_infinite__imp__nonempty) ).
thf(480,plain,
! [A: set_Pr699757092de_val] :
( ~ ( finite2056463621de_val @ A )
=> ( A != bot_bo404898488de_val ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(338,axiom,
! [A: g,B: val,C: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ B @ C )
=> ( ( member_val @ B @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A ) )
=> ~ ! [D: node] :
( ( member_val @ C @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ A @ D ) )
=> ~ ( member_node @ D @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_phiUses__exI_H) ).
thf(1334,plain,
! [A: g,B: val,C: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ B @ C )
=> ( ( member_val @ B @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A ) )
=> ~ ! [D: node] :
( ( member_val @ C @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ A @ D ) )
=> ~ ( member_node @ D @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ A @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(105,axiom,
! [A: list_set_val,B: set_set_val] :
( ( ord_le1742111550et_val @ ( set_set_val2 @ A ) @ B )
= ( ! [C: set_val] :
( ( member_set_val @ C @ ( set_set_val2 @ A ) )
=> ( member_set_val @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_subset__code_I1_J) ).
thf(646,plain,
! [A: list_set_val,B: set_set_val] :
( ( ord_le1742111550et_val @ ( set_set_val2 @ A ) @ B )
= ( ! [C: set_val] :
( ( member_set_val @ C @ ( set_set_val2 @ A ) )
=> ( member_set_val @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(50,axiom,
! [A: list_val] : ( finite_finite_val @ ( set_val2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_List_Ofinite__set) ).
thf(484,plain,
! [A: list_val] : ( finite_finite_val @ ( set_val2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(485,plain,
! [A: list_val] : ( finite_finite_val @ ( set_val2 @ A ) ),
inference(cnf,[status(esa)],[484]) ).
thf(167,axiom,
finite2056463621de_val @ bot_bo404898488de_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_finite_OemptyI) ).
thf(834,plain,
finite2056463621de_val @ bot_bo404898488de_val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(3,axiom,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val,C: produc1432036078de_val] :
( ( ord_le1643692676de_val @ A @ B )
=> ( ( member313544709de_val @ C @ A )
=> ( member313544709de_val @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_in__mono) ).
thf(353,plain,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val,C: produc1432036078de_val] :
( ( ord_le1643692676de_val @ A @ B )
=> ( ( member313544709de_val @ C @ A )
=> ( member313544709de_val @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(219,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ C )
= ( ( ord_less_eq_set_val @ A @ C )
& ( ord_less_eq_set_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_le__sup__iff) ).
thf(966,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ C )
= ( ( ord_less_eq_set_val @ A @ C )
& ( ord_less_eq_set_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(184,axiom,
! [A: set_val,B: set_val] :
( ( ord_le596993316et_val @ ( some_set_val @ A ) @ ( some_set_val @ B ) )
= ( ord_less_eq_set_val @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_less__eq__option__Some) ).
thf(877,plain,
! [A: set_val,B: set_val] :
( ( ord_le596993316et_val @ ( some_set_val @ A ) @ ( some_set_val @ B ) )
= ( ord_less_eq_set_val @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(269,axiom,
( ord_less_eq_set_val
= ( ^ [A: set_val,B: set_val] :
! [C: val] :
( ( member_val @ C @ A )
=> ( member_val @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_subset__eq) ).
thf(1119,plain,
( ord_less_eq_set_val
= ( ^ [A: set_val,B: set_val] :
! [C: val] :
( ( member_val @ C @ A )
=> ( member_val @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(231,axiom,
! [A: set_val,B: set_val,C: set_val,D: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( ord_less_eq_set_val @ C @ D )
=> ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ C ) @ ( sup_sup_set_val @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_sup_Omono) ).
thf(998,plain,
! [A: set_val,B: set_val,C: set_val,D: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( ord_less_eq_set_val @ C @ D )
=> ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ C ) @ ( sup_sup_set_val @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(227,axiom,
sSA_CF794421325de_val = sSA_CF794421325de_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_CFG__SSA__wf__base_OliveVal_Ocong) ).
thf(988,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(300,axiom,
! [A: g,B: node,C: val,D: list_val] :
( ( ( phis @ A @ ( produc1470527136de_val @ B @ C ) )
= ( some_list_val @ D ) )
=> ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A @ C )
= ( some_list_val @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_phis__phi) ).
thf(1201,plain,
! [A: g,B: node,C: val,D: list_val] :
( ( ( phis @ A @ ( produc1470527136de_val @ B @ C ) )
= ( some_list_val @ D ) )
=> ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A @ C )
= ( some_list_val @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(91,axiom,
! [A: set_val,B: set_val > $o] :
( ( member_set_val @ A @ ( collect_set_val @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_mem__Collect__eq) ).
thf(602,plain,
! [A: set_val,B: set_val > $o] :
( ( member_set_val @ A @ ( collect_set_val @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(147,axiom,
! [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
( ( ord_le299366439et_val @ A @ B )
=> ( ~ ( finite79836624et_val @ A )
=> ~ ( finite79836624et_val @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_infinite__super) ).
thf(766,plain,
! [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
( ( ord_le299366439et_val @ A @ B )
=> ( ~ ( finite79836624et_val @ A )
=> ~ ( finite79836624et_val @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(20,axiom,
! [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
( ! [C: produc1324971431et_val] :
( ( member1711426256et_val @ C @ A )
=> ( member1711426256et_val @ C @ B ) )
=> ( ord_le299366439et_val @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_subsetI) ).
thf(397,plain,
! [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
( ! [C: produc1324971431et_val] :
( ( member1711426256et_val @ C @ A )
=> ( member1711426256et_val @ C @ B ) )
=> ( ord_le299366439et_val @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(118,axiom,
! [A: set_val,B: set_val] :
( ( A = B )
=> ( ord_less_eq_set_val @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_equalityD1) ).
thf(687,plain,
! [A: set_val,B: set_val] :
( ( A = B )
=> ( ord_less_eq_set_val @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(258,axiom,
! [A: g,B: val,C: val] :
( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ A @ B )
=> ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ B @ C )
=> ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_livePhi) ).
thf(1074,plain,
! [A: g,B: val,C: val] :
( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ A @ B )
=> ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ B @ C )
=> ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(301,axiom,
phi != phi_s,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_False) ).
thf(1204,plain,
phi != phi_s,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(1205,plain,
phi != phi_s,
inference(polarity_switch,[status(thm)],[1204]) ).
thf(1206,plain,
phi_s != phi,
inference(lifteq,[status(thm)],[1205]) ).
thf(13,axiom,
! [A: produc1432036078de_val,B: set_Pr699757092de_val,C: set_Pr699757092de_val] :
( ( ord_le1643692676de_val @ ( insert869443870de_val @ A @ B ) @ C )
= ( ( member313544709de_val @ A @ C )
& ( ord_le1643692676de_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_insert__subset) ).
thf(380,plain,
! [A: produc1432036078de_val,B: set_Pr699757092de_val,C: set_Pr699757092de_val] :
( ( ord_le1643692676de_val @ ( insert869443870de_val @ A @ B ) @ C )
= ( ( member313544709de_val @ A @ C )
& ( ord_le1643692676de_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(35,axiom,
! [A: produc1324971431et_val,B: set_Pr1311924359et_val,C: set_Pr1311924359et_val] :
( ( member1711426256et_val @ A @ B )
=> ( member1711426256et_val @ A @ ( sup_su2005730907et_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_UnI1) ).
thf(439,plain,
! [A: produc1324971431et_val,B: set_Pr1311924359et_val,C: set_Pr1311924359et_val] :
( ( member1711426256et_val @ A @ B )
=> ( member1711426256et_val @ A @ ( sup_su2005730907et_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(145,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C ) )
= ( sup_sup_set_val @ B @ ( sup_sup_set_val @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_inf__sup__aci_I7_J) ).
thf(761,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C ) )
= ( sup_sup_set_val @ B @ ( sup_sup_set_val @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(366,plain,
( ord_le299366439et_val
= ( ^ [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
! [C: produc1324971431et_val] :
( ( member1711426256et_val @ C @ A )
=> ( member1711426256et_val @ C @ B ) ) ) ),
inference(lifteq,[status(thm)],[365]) ).
thf(126,axiom,
! [A: list_P761482893et_val] : ( finite1581417648et_val @ ( set_Pr2104310812et_val @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_List_Ofinite__set) ).
thf(714,plain,
! [A: list_P761482893et_val] : ( finite1581417648et_val @ ( set_Pr2104310812et_val @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(331,axiom,
! [A: val,B: g] :
( ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) )
=> ( ~ ( member_val @ A @ ( defs @ B @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ B @ A ) ) )
=> ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ B @ A )
!= none_list_val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_defNode__cases) ).
thf(1311,plain,
! [A: val,B: g] :
( ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) )
=> ( ~ ( member_val @ A @ ( defs @ B @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ B @ A ) ) )
=> ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ B @ A )
!= none_list_val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(321,axiom,
! [A: g,B: val] :
( ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B )
=> ( member_val @ B @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_trivial__in__allVars) ).
thf(1274,plain,
! [A: g,B: val] :
( ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B )
=> ( member_val @ B @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(215,axiom,
irredu681226810de_val = irredu681226810de_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_CFG__SSA__Transformed_Ocondensation__nodes_Ocong) ).
thf(957,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(263,axiom,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( uses @ B @ C ) )
=> ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_uses__in___092_060alpha_062n) ).
thf(1091,plain,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( uses @ B @ C ) )
=> ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(271,axiom,
! [A: val,B: g] :
( ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) )
=> ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ B @ A ) @ ( set_node2 @ ( alpha_n @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_defNode_I1_J) ).
thf(1123,plain,
! [A: val,B: g] :
( ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) )
=> ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ B @ A ) @ ( set_node2 @ ( alpha_n @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(75,axiom,
( ( '!' @ option_list_val )
= ( ^ [A: option_list_val > $o] :
( ( A @ none_list_val )
& ! [B: list_val] : ( A @ ( some_list_val @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_split__option__all) ).
thf(561,plain,
( ( '!' @ option_list_val )
= ( ^ [A: option_list_val > $o] :
( ( A @ none_list_val )
& ! [B: list_val] : ( A @ ( some_list_val @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(18,axiom,
( ord_le299366439et_val
= ( ^ [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
! [C: produc1324971431et_val] :
( ( member1711426256et_val @ C @ A )
=> ( member1711426256et_val @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_subset__iff) ).
thf(392,plain,
( ord_le299366439et_val
= ( ^ [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
! [C: produc1324971431et_val] :
( ( member1711426256et_val @ C @ A )
=> ( member1711426256et_val @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(30,axiom,
! [A: produc1432036078de_val,B: set_Pr699757092de_val,C: set_Pr699757092de_val] :
( ( member313544709de_val @ A @ ( sup_su2138939728de_val @ B @ C ) )
= ( ( member313544709de_val @ A @ B )
| ( member313544709de_val @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_Un__iff) ).
thf(424,plain,
! [A: produc1432036078de_val,B: set_Pr699757092de_val,C: set_Pr699757092de_val] :
( ( member313544709de_val @ A @ ( sup_su2138939728de_val @ B @ C ) )
= ( ( member313544709de_val @ A @ B )
| ( member313544709de_val @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(154,axiom,
! [A: set_val,B: set_val] : ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_inf__sup__ord_I3_J) ).
thf(788,plain,
! [A: set_val,B: set_val] : ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(312,axiom,
! [A: set_val,B: g] :
( ( A != bot_bot_set_val )
=> ? [C: set_val] :
( ( member_set_val @ C @ ( irredu681226810de_val @ alpha_n @ defs @ phis @ B @ A ) )
& ! [D: set_val] :
~ ( member1711426256et_val @ ( produc1041633943et_val @ C @ D ) @ ( irredu893086079de_val @ alpha_n @ defs @ phis @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_Ex__condensation__leaf) ).
thf(1238,plain,
! [A: set_val,B: g] :
( ( A != bot_bot_set_val )
=> ? [C: set_val] :
( ( member_set_val @ C @ ( irredu681226810de_val @ alpha_n @ defs @ phis @ B @ A ) )
& ! [D: set_val] :
~ ( member1711426256et_val @ ( produc1041633943et_val @ C @ D ) @ ( irredu893086079de_val @ alpha_n @ defs @ phis @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(164,axiom,
! [A: set_val] :
( ( sup_sup_set_val @ bot_bot_set_val @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_sup__bot_Oleft__neutral) ).
thf(825,plain,
! [A: set_val] :
( ( sup_sup_set_val @ bot_bot_set_val @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(341,axiom,
! [A: set_val,B: set_val,C: val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( member_val @ C @ A )
=> ( member_val @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_in__mono) ).
thf(1343,plain,
! [A: set_val,B: set_val,C: val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( member_val @ C @ A )
=> ( member_val @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(243,axiom,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ B @ C ) )
=> ( ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_allUses__in__allVars) ).
thf(1032,plain,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ B @ C ) )
=> ( ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(174,axiom,
finite_finite_val @ bot_bot_set_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_finite_OemptyI) ).
thf(852,plain,
finite_finite_val @ bot_bot_set_val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(111,axiom,
! [A: val > $o,B: val > $o] :
( ( ord_less_eq_set_val @ ( collect_val @ A ) @ ( collect_val @ B ) )
= ( ! [C: val] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_Collect__mono__iff) ).
thf(665,plain,
! [A: val > $o,B: val > $o] :
( ( ord_less_eq_set_val @ ( collect_val @ A ) @ ( collect_val @ B ) )
= ( ! [C: val] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(188,axiom,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
( ( finite2056463621de_val @ ( sup_su2138939728de_val @ A @ B ) )
= ( ( finite2056463621de_val @ A )
& ( finite2056463621de_val @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_finite__Un) ).
thf(889,plain,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
( ( finite2056463621de_val @ ( sup_su2138939728de_val @ A @ B ) )
= ( ( finite2056463621de_val @ A )
& ( finite2056463621de_val @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(54,axiom,
! [A: set_val,B: set_val] : ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_inf__sup__ord_I4_J) ).
thf(493,plain,
! [A: set_val,B: set_val] : ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(241,axiom,
! [A: node,B: val,C: list_node,D: list_val] :
( ( member313544709de_val @ ( produc1470527136de_val @ A @ B ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ C @ D ) ) )
=> ( member_val @ B @ ( set_val2 @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_set__zip__rightD) ).
thf(1027,plain,
! [A: node,B: val,C: list_node,D: list_val] :
( ( member313544709de_val @ ( produc1470527136de_val @ A @ B ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ C @ D ) ) )
=> ( member_val @ B @ ( set_val2 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(325,axiom,
! [A: g,B: node,C: val,D: list_val] :
( ( ( phis @ A @ ( produc1470527136de_val @ B @ C ) )
= ( some_list_val @ D ) )
=> ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_phis__in___092_060alpha_062n) ).
thf(1281,plain,
! [A: g,B: node,C: val,D: list_val] :
( ( ( phis @ A @ ( produc1470527136de_val @ B @ C ) )
= ( some_list_val @ D ) )
=> ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(40,axiom,
! [A: node,B: set_node,C: set_node] :
( ( member_node @ A @ B )
=> ( member_node @ A @ ( sup_sup_set_node @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_UnI1) ).
thf(456,plain,
! [A: node,B: set_node,C: set_node] :
( ( member_node @ A @ B )
=> ( member_node @ A @ ( sup_sup_set_node @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(222,axiom,
! [A: set_val,B: set_val,C: set_val,D: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( ord_less_eq_set_val @ C @ D )
=> ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ C ) @ ( sup_sup_set_val @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_Un__mono) ).
thf(974,plain,
! [A: set_val,B: set_val,C: set_val,D: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( ord_less_eq_set_val @ C @ D )
=> ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ C ) @ ( sup_sup_set_val @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(236,axiom,
! [A: g,B: set_val,C: set_val,D: val] :
( ( irredu224829488eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B )
=> ( ( member_set_val @ C @ ( irredu681226810de_val @ alpha_n @ defs @ phis @ A @ B ) )
=> ( ( member_val @ D @ C )
=> ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A @ D )
!= none_list_val ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_redundant__scc__phis) ).
thf(1009,plain,
! [A: g,B: set_val,C: set_val,D: val] :
( ( irredu224829488eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B )
=> ( ( member_set_val @ C @ ( irredu681226810de_val @ alpha_n @ defs @ phis @ A @ B ) )
=> ( ( member_val @ D @ C )
=> ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A @ D )
!= none_list_val ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(1010,plain,
! [A: g,B: set_val] :
( ( irredu224829488eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B )
=> ! [C: set_val] :
( ( member_set_val @ C @ ( irredu681226810de_val @ alpha_n @ defs @ phis @ A @ B ) )
=> ! [D: val] :
( ( member_val @ D @ C )
=> ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A @ D )
!= none_list_val ) ) ) ),
inference(miniscope,[status(thm)],[1009]) ).
thf(1011,plain,
! [D: val,C: set_val,B: set_val,A: g] :
( ~ ( irredu224829488eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B )
| ~ ( member_set_val @ C @ ( irredu681226810de_val @ alpha_n @ defs @ phis @ A @ B ) )
| ~ ( member_val @ D @ C )
| ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A @ D )
!= none_list_val ) ),
inference(cnf,[status(esa)],[1010]) ).
thf(1012,plain,
! [D: val,C: set_val,B: set_val,A: g] :
( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A @ D )
!= none_list_val )
| ~ ( irredu224829488eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B )
| ~ ( member_set_val @ C @ ( irredu681226810de_val @ alpha_n @ defs @ phis @ A @ B ) )
| ~ ( member_val @ D @ C ) ),
inference(lifteq,[status(thm)],[1011]) ).
thf(172,axiom,
! [A: set_val] :
( ( sup_sup_set_val @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_sup_Oidem) ).
thf(847,plain,
! [A: set_val] :
( ( sup_sup_set_val @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(77,axiom,
! [A: set_val,B: set_val,C: list_set_val,D: list_set_val] :
( ( member1711426256et_val @ ( produc1041633943et_val @ A @ B ) @ ( set_Pr284769596et_val @ ( zip_set_val_set_val @ C @ D ) ) )
=> ( member_set_val @ B @ ( set_set_val2 @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_set__zip__rightD) ).
thf(566,plain,
! [A: set_val,B: set_val,C: list_set_val,D: list_set_val] :
( ( member1711426256et_val @ ( produc1041633943et_val @ A @ B ) @ ( set_Pr284769596et_val @ ( zip_set_val_set_val @ C @ D ) ) )
=> ( member_set_val @ B @ ( set_set_val2 @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(83,axiom,
finite79836624et_val @ bot_bo2078591731et_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_finite_OemptyI) ).
thf(583,plain,
finite79836624et_val @ bot_bo2078591731et_val,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(63,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_le__supI1) ).
thf(522,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(117,axiom,
! [A: set_set_val] :
( ( finite1265617511et_val @ A )
=> ( ( A != bot_bot_set_set_val )
=> ? [B: set_val] :
( ( member_set_val @ B @ A )
& ! [C: set_val] :
( ( member_set_val @ C @ A )
=> ( ( ord_less_eq_set_val @ C @ B )
=> ( B = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_finite__has__minimal) ).
thf(682,plain,
! [A: set_set_val] :
( ( finite1265617511et_val @ A )
=> ( ( A != bot_bot_set_set_val )
=> ? [B: set_val] :
( ( member_set_val @ B @ A )
& ! [C: set_val] :
( ( member_set_val @ C @ A )
=> ( ( ord_less_eq_set_val @ C @ B )
=> ( B = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(298,axiom,
! [A: g,B: val,C: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ B @ C )
= ( ? [D: list_val] :
( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A @ B )
= ( some_list_val @ D ) )
& ( member_val @ C @ ( set_val2 @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_phiArg__def) ).
thf(1195,plain,
! [A: g,B: val,C: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ B @ C )
= ( ? [D: list_val] :
( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A @ B )
= ( some_list_val @ D ) )
& ( member_val @ C @ ( set_val2 @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(328,axiom,
! [A: list_val,B: set_val] :
( ( ord_less_eq_set_val @ ( set_val2 @ A ) @ B )
= ( ! [C: val] :
( ( member_val @ C @ ( set_val2 @ A ) )
=> ( member_val @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_subset__code_I1_J) ).
thf(1291,plain,
! [A: list_val,B: set_val] :
( ( ord_less_eq_set_val @ ( set_val2 @ A ) @ B )
= ( ! [C: val] :
( ( member_val @ C @ ( set_val2 @ A ) )
=> ( member_val @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(125,axiom,
! [A: set_val,B: set_val] :
( ( A = B )
=> ( ord_less_eq_set_val @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_equalityD2) ).
thf(710,plain,
! [A: set_val,B: set_val] :
( ( A = B )
=> ( ord_less_eq_set_val @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(280,axiom,
! [A: node,B: g,C: val] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_val @ C @ ( defs @ B @ A ) )
=> ~ ( member_val @ C @ ( uses @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_defs__uses__disjoint_H) ).
thf(1146,plain,
! [A: node,B: g,C: val] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_val @ C @ ( defs @ B @ A ) )
=> ~ ( member_val @ C @ ( uses @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(1147,plain,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ! [C: val] :
( ( member_val @ C @ ( defs @ B @ A ) )
=> ~ ( member_val @ C @ ( uses @ B @ A ) ) ) ),
inference(miniscope,[status(thm)],[1146]) ).
thf(1148,plain,
! [C: val,B: g,A: node] :
( ~ ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
| ~ ( member_val @ C @ ( defs @ B @ A ) )
| ~ ( member_val @ C @ ( uses @ B @ A ) ) ),
inference(cnf,[status(esa)],[1147]) ).
thf(1401,plain,
! [C: val,B: g,A: node] :
( ~ ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
| ~ ( member_val @ C @ ( defs @ B @ A ) )
| ( ( member_val @ C @ ( uses @ B @ A ) )
!= ( member_val @ C @ ( defs @ B @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1148]) ).
thf(1402,plain,
! [C: val,B: g,A: node] :
( ~ ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
| ~ ( member_val @ C @ ( defs @ B @ A ) )
| ( ( member_val @ C @ ( uses @ B @ A ) )
!= ( member_val @ C @ ( defs @ B @ A ) ) ) ),
inference(simp,[status(thm)],[1401]) ).
thf(347,axiom,
! [A: g,B: val,C: val,D: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ B @ C )
=> ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ B @ D )
=> ( ( C != D )
=> ( ( member_val @ B @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A ) )
=> ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ A @ C )
!= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_phiArgs__def__distinct) ).
thf(1360,plain,
! [A: g,B: val,C: val,D: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ B @ C )
=> ( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ B @ D )
=> ( ( C != D )
=> ( ( member_val @ B @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A ) )
=> ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ A @ C )
!= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(95,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_set_val @ A @ C )
=> ~ ( ord_less_eq_set_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_sup_OboundedE) ).
thf(615,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_set_val @ A @ C )
=> ~ ( ord_less_eq_set_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(337,axiom,
! [A: set_val,B: val] :
( ( finite_finite_val @ A )
=> ( ( member_val @ B @ A )
=> ? [C: val] :
( ( member_val @ C @ A )
& ( ord_less_eq_val @ B @ C )
& ! [D: val] :
( ( member_val @ D @ A )
=> ( ( ord_less_eq_val @ C @ D )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_finite__has__maximal2) ).
thf(1328,plain,
! [A: set_val,B: val] :
( ( finite_finite_val @ A )
=> ( ( member_val @ B @ A )
=> ? [C: val] :
( ( member_val @ C @ A )
& ( ord_less_eq_val @ B @ C )
& ! [D: val] :
( ( member_val @ D @ A )
=> ( ( ord_less_eq_val @ C @ D )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(270,axiom,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ B @ C ) )
=> ( member_val @ A @ ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_phiUses__in__allUses) ).
thf(1121,plain,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ B @ C ) )
=> ( member_val @ A @ ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(254,axiom,
phi_s != s,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I4_J) ).
thf(1062,plain,
phi_s != s,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(1063,plain,
phi_s != s,
inference(polarity_switch,[status(thm)],[1062]) ).
thf(1064,plain,
s != phi_s,
inference(lifteq,[status(thm)],[1063]) ).
thf(309,axiom,
! [A: g,B: val] :
( ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B )
= ( ? [C: val] :
( ( member_val @ C @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A ) )
& ( sSA_CF1909049442de_val @ alpha_n @ defs @ phis @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_trivial__def) ).
thf(1227,plain,
! [A: g,B: val] :
( ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B )
= ( ? [C: val] :
( ( member_val @ C @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A ) )
& ( sSA_CF1909049442de_val @ alpha_n @ defs @ phis @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(16,axiom,
( ord_le1742111550et_val
= ( ^ [A: set_set_val,B: set_set_val] :
! [C: set_val] :
( ( member_set_val @ C @ A )
=> ( member_set_val @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_subset__eq) ).
thf(387,plain,
( ord_le1742111550et_val
= ( ^ [A: set_set_val,B: set_set_val] :
! [C: set_val] :
( ( member_set_val @ C @ A )
=> ( member_set_val @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(388,plain,
( ord_le1742111550et_val
= ( ^ [A: set_set_val,B: set_set_val] :
! [C: set_val] :
( ( member_set_val @ C @ A )
=> ( member_set_val @ C @ B ) ) ) ),
inference(lifteq,[status(thm)],[387]) ).
thf(783,plain,
( ( ^ [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
& ( ord_less_eq_set_val @ B @ A ) ) )
= ( (=) @ set_val ) ),
inference(lifteq,[status(thm)],[782]) ).
thf(228,axiom,
! [A: set_val] :
( ~ ( finite_finite_val @ A )
=> ( A != bot_bot_set_val ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_infinite__imp__nonempty) ).
thf(989,plain,
! [A: set_val] :
( ~ ( finite_finite_val @ A )
=> ( A != bot_bot_set_val ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(62,axiom,
! [A: set_val,B: set_val] :
( ( ( sup_sup_set_val @ A @ B )
= bot_bot_set_val )
= ( ( A = bot_bot_set_val )
& ( B = bot_bot_set_val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_sup__bot_Oeq__neutr__iff) ).
thf(519,plain,
! [A: set_val,B: set_val] :
( ( ( sup_sup_set_val @ A @ B )
= bot_bot_set_val )
= ( ( A = bot_bot_set_val )
& ( B = bot_bot_set_val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(138,axiom,
! [A: set_val,B: set_set_val,C: set_set_val] :
( ( member_set_val @ A @ B )
=> ( member_set_val @ A @ ( sup_sup_set_set_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_UnI1) ).
thf(742,plain,
! [A: set_val,B: set_set_val,C: set_set_val] :
( ( member_set_val @ A @ B )
=> ( member_set_val @ A @ ( sup_sup_set_set_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(121,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ B @ C ) )
=> ~ ! [D: set_val] :
( ( ord_less_eq_set_val @ D @ B )
=> ! [E: set_val] :
( ( ord_less_eq_set_val @ E @ C )
=> ( A
!= ( sup_sup_set_val @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_subset__UnE) ).
thf(697,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ B @ C ) )
=> ~ ! [D: set_val] :
( ( ord_less_eq_set_val @ D @ B )
=> ! [E: set_val] :
( ( ord_less_eq_set_val @ E @ C )
=> ( A
!= ( sup_sup_set_val @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(311,axiom,
! [A: g,B: node,C: val,D: list_val,E: node,F: list_val] :
( ( ( phis @ A @ ( produc1470527136de_val @ B @ C ) )
= ( some_list_val @ D ) )
=> ( ( ( phis @ A @ ( produc1470527136de_val @ E @ C ) )
= ( some_list_val @ F ) )
=> ( B = E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_phis__disj_I1_J) ).
thf(1234,plain,
! [A: g,B: node,C: val,D: list_val,E: node,F: list_val] :
( ( ( phis @ A @ ( produc1470527136de_val @ B @ C ) )
= ( some_list_val @ D ) )
=> ( ( ( phis @ A @ ( produc1470527136de_val @ E @ C ) )
= ( some_list_val @ F ) )
=> ( B = E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(224,axiom,
! [A: set_val,B: set_val] : ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_Un__upper1) ).
thf(980,plain,
! [A: set_val,B: set_val] : ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(22,axiom,
! [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val,C: produc1324971431et_val] :
( ( ord_le299366439et_val @ A @ B )
=> ( ( member1711426256et_val @ C @ A )
=> ( member1711426256et_val @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_subsetD) ).
thf(403,plain,
! [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val,C: produc1324971431et_val] :
( ( ord_le299366439et_val @ A @ B )
=> ( ( member1711426256et_val @ C @ A )
=> ( member1711426256et_val @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(277,axiom,
! [A: set_val,B: set_val] :
( ! [C: val] :
( ( member_val @ C @ A )
=> ( member_val @ C @ B ) )
=> ( ord_less_eq_set_val @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_subsetI) ).
thf(1138,plain,
! [A: set_val,B: set_val] :
( ! [C: val] :
( ( member_val @ C @ A )
=> ( member_val @ C @ B ) )
=> ( ord_less_eq_set_val @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(46,axiom,
! [A: set_val,B: set_val] :
( ( finite_finite_val @ A )
=> ( ( ord_less_eq_set_val @ B @ A )
=> ( finite_finite_val @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_rev__finite__subset) ).
thf(471,plain,
! [A: set_val,B: set_val] :
( ( finite_finite_val @ A )
=> ( ( ord_less_eq_set_val @ B @ A )
=> ( finite_finite_val @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(285,axiom,
( ord_less_eq_set_val
= ( ^ [A: set_val,B: set_val] :
! [C: val] :
( ( member_val @ C @ A )
=> ( member_val @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_subset__iff) ).
thf(1160,plain,
( ord_less_eq_set_val
= ( ^ [A: set_val,B: set_val] :
! [C: val] :
( ( member_val @ C @ A )
=> ( member_val @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(206,axiom,
! [A: option_list_val,B: list_val] :
( ( A
= ( some_list_val @ B ) )
=> ( A != none_list_val ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_option_OdiscI) ).
thf(933,plain,
! [A: option_list_val,B: list_val] :
( ( A
= ( some_list_val @ B ) )
=> ( A != none_list_val ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(73,axiom,
! [A: node,B: set_node,C: set_node] :
( ( member_node @ A @ ( sup_sup_set_node @ B @ C ) )
=> ( ~ ( member_node @ A @ B )
=> ( member_node @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_UnE) ).
thf(554,plain,
! [A: node,B: set_node,C: set_node] :
( ( member_node @ A @ ( sup_sup_set_node @ B @ C ) )
=> ( ~ ( member_node @ A @ B )
=> ( member_node @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(293,axiom,
! [A: node,B: g,C: val] :
( ( member_node @ A @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ B @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ B @ C ) ) ) )
=> ( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ B @ C )
!= none_list_val )
=> ( ( member_val @ C @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) )
=> ~ ! [D: val] :
( ( member_val @ D @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ B @ A ) )
=> ~ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ B @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_phiArg__exI) ).
thf(1182,plain,
! [A: node,B: g,C: val] :
( ( member_node @ A @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ B @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ B @ C ) ) ) )
=> ( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ B @ C )
!= none_list_val )
=> ( ( member_val @ C @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) )
=> ~ ! [D: val] :
( ( member_val @ D @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ B @ A ) )
=> ~ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ B @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(52,axiom,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
( ~ ( finite2056463621de_val @ A )
=> ~ ( finite2056463621de_val @ ( sup_su2138939728de_val @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_Un__infinite) ).
thf(489,plain,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
( ~ ( finite2056463621de_val @ A )
=> ~ ( finite2056463621de_val @ ( sup_su2138939728de_val @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(283,axiom,
! [A: g,B: set_val] :
( ( irredu224829488eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B )
=> ? [C: set_val] :
( ( ord_less_eq_set_val @ C @ B )
& ( irredu1955035135eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149__C1_C) ).
thf(1155,plain,
! [A: g,B: set_val] :
( ( irredu224829488eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B )
=> ? [C: set_val] :
( ( ord_less_eq_set_val @ C @ B )
& ( irredu1955035135eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(238,axiom,
! [A: val,B: g] :
( ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) )
=> ? [C: node] :
( ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) )
& ( member_val @ A @ ( sSA_CF139593942de_val @ defs @ phis @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_allVars__in__allDefs) ).
thf(1016,plain,
! [A: val,B: g] :
( ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) )
=> ? [C: node] :
( ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) )
& ( member_val @ A @ ( sSA_CF139593942de_val @ defs @ phis @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(302,axiom,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( sSA_CF370335846de_val @ phis @ B @ C ) )
=> ( member_val @ A @ ( sSA_CF139593942de_val @ defs @ phis @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_phiDefs__in__allDefs) ).
thf(1207,plain,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( sSA_CF370335846de_val @ phis @ B @ C ) )
=> ( member_val @ A @ ( sSA_CF139593942de_val @ defs @ phis @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(86,axiom,
sSA_CF370335846de_val = sSA_CF370335846de_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_CFG__SSA__base_OphiDefs_Ocong) ).
thf(590,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(116,axiom,
! [A: g > list_node,B: g > node > set_val,C: g > node > set_val,D: g > produc1432036078de_val > option_list_val,E: g,F: val,G: val] :
( ( sSA_CF794421325de_val @ A @ B @ C @ D @ E @ F )
=> ( ( sSA_CF1252180629de_val @ A @ B @ D @ E @ F @ G )
=> ( sSA_CF794421325de_val @ A @ B @ C @ D @ E @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_CFG__SSA__wf__base_OlivePhi) ).
thf(679,plain,
! [A: g > list_node,B: g > node > set_val,C: g > node > set_val,D: g > produc1432036078de_val > option_list_val,E: g,F: val,G: val] :
( ( sSA_CF794421325de_val @ A @ B @ C @ D @ E @ F )
=> ( ( sSA_CF1252180629de_val @ A @ B @ D @ E @ F @ G )
=> ( sSA_CF794421325de_val @ A @ B @ C @ D @ E @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(245,axiom,
! [A: g,B: val,C: list_val] :
( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A @ B )
= ( some_list_val @ C ) )
=> ( member_val @ B @ ( sSA_CF370335846de_val @ phis @ A @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_phi__phiDefs) ).
thf(1039,plain,
! [A: g,B: val,C: list_val] :
( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A @ B )
= ( some_list_val @ C ) )
=> ( member_val @ B @ ( sSA_CF370335846de_val @ phis @ A @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(226,axiom,
! [A: set_val] :
( ( sup_sup_set_val @ A @ bot_bot_set_val )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_sup__bot__right) ).
thf(985,plain,
! [A: set_val] :
( ( sup_sup_set_val @ A @ bot_bot_set_val )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(108,axiom,
! [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( sup_sup_set_val @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_Un__absorb1) ).
thf(654,plain,
! [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( sup_sup_set_val @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(253,axiom,
! [A: g] : ( finite_finite_val @ ( dom_val_list_val @ ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_phi__finite) ).
thf(1060,plain,
! [A: g] : ( finite_finite_val @ ( dom_val_list_val @ ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(198,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_le__supI2) ).
thf(911,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(313,axiom,
! [A: g,B: val] :
( ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B )
=> ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A @ B )
!= none_list_val ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_trivial__phi) ).
thf(1244,plain,
! [A: g,B: val] :
( ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B )
=> ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A @ B )
!= none_list_val ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(1245,plain,
! [B: val,A: g] :
( ~ ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B )
| ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A @ B )
!= none_list_val ) ),
inference(cnf,[status(esa)],[1244]) ).
thf(1246,plain,
! [B: val,A: g] :
( ( ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A @ B )
!= none_list_val )
| ~ ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B ) ),
inference(lifteq,[status(thm)],[1245]) ).
thf(150,axiom,
! [A: set_val] :
( ( finite_finite_val @ A )
=> ? [B: list_val] :
( ( set_val2 @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_finite__list) ).
thf(779,plain,
! [A: set_val] :
( ( finite_finite_val @ A )
=> ? [B: list_val] :
( ( set_val2 @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(10,axiom,
! [A: set_node,B: set_node] :
( ! [C: node] :
( ( member_node @ C @ A )
=> ( member_node @ C @ B ) )
=> ( ord_less_eq_set_node @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_subsetI) ).
thf(371,plain,
! [A: set_node,B: set_node] :
( ! [C: node] :
( ( member_node @ C @ A )
=> ( member_node @ C @ B ) )
=> ( ord_less_eq_set_node @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(282,axiom,
! [A: g > list_node,B: g > node > set_val,C: g > node > set_val,D: g > produc1432036078de_val > option_list_val,E: g,F: val] :
( ( sSA_CF794421325de_val @ A @ B @ C @ D @ E @ F )
=> ( ! [G: node] :
( ( member_node @ G @ ( set_node2 @ ( A @ E ) ) )
=> ~ ( member_val @ F @ ( C @ E @ G ) ) )
=> ~ ! [G: val] :
( ( sSA_CF794421325de_val @ A @ B @ C @ D @ E @ G )
=> ~ ( sSA_CF1252180629de_val @ A @ B @ D @ E @ G @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_CFG__SSA__wf__base_OliveVal_Ocases) ).
thf(1150,plain,
! [A: g > list_node,B: g > node > set_val,C: g > node > set_val,D: g > produc1432036078de_val > option_list_val,E: g,F: val] :
( ( sSA_CF794421325de_val @ A @ B @ C @ D @ E @ F )
=> ( ! [G: node] :
( ( member_node @ G @ ( set_node2 @ ( A @ E ) ) )
=> ~ ( member_val @ F @ ( C @ E @ G ) ) )
=> ~ ! [G: val] :
( ( sSA_CF794421325de_val @ A @ B @ C @ D @ E @ G )
=> ~ ( sSA_CF1252180629de_val @ A @ B @ D @ E @ G @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(315,axiom,
! [A: val,B: g,C: val] :
( ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) )
=> ( ( member_val @ C @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) )
=> ( ( A != C )
=> ( ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ B @ A )
= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ B @ C ) )
=> ( ( var2 @ B @ A )
!= ( var2 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_defNode__var__disjoint) ).
thf(1249,plain,
! [A: val,B: g,C: val] :
( ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) )
=> ( ( member_val @ C @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) )
=> ( ( A != C )
=> ( ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ B @ A )
= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ B @ C ) )
=> ( ( var2 @ B @ A )
!= ( var2 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(58,axiom,
! [A: set_val] :
( ( sup_sup_set_val @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_sup__idem) ).
thf(503,plain,
! [A: set_val] :
( ( sup_sup_set_val @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(92,axiom,
! [A: set_Pr1311924359et_val] :
( ~ ( finite79836624et_val @ A )
=> ( A != bot_bo2078591731et_val ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_infinite__imp__nonempty) ).
thf(605,plain,
! [A: set_Pr1311924359et_val] :
( ~ ( finite79836624et_val @ A )
=> ( A != bot_bo2078591731et_val ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(333,axiom,
! [A: g] : ( finite_finite_val @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_allVars__finite) ).
thf(1318,plain,
! [A: g] : ( finite_finite_val @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(156,axiom,
! [A: set_val] :
( ( sup_sup_set_val @ bot_bot_set_val @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_Un__empty__left) ).
thf(792,plain,
! [A: set_val] :
( ( sup_sup_set_val @ bot_bot_set_val @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(207,axiom,
( sup_sup_set_val
= ( ^ [A: set_val,B: set_val] : ( sup_sup_set_val @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_inf__sup__aci_I5_J) ).
thf(938,plain,
( sup_sup_set_val
= ( ^ [A: set_val,B: set_val] : ( sup_sup_set_val @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(5,axiom,
! [A: produc1432036078de_val,B: set_Pr699757092de_val,C: set_Pr699757092de_val] :
( ( ~ ( member313544709de_val @ A @ B )
=> ( member313544709de_val @ A @ C ) )
=> ( member313544709de_val @ A @ ( sup_su2138939728de_val @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_UnCI) ).
thf(359,plain,
! [A: produc1432036078de_val,B: set_Pr699757092de_val,C: set_Pr699757092de_val] :
( ( ~ ( member313544709de_val @ A @ B )
=> ( member313544709de_val @ A @ C ) )
=> ( member313544709de_val @ A @ ( sup_su2138939728de_val @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(360,plain,
! [C: set_Pr699757092de_val,B: set_Pr699757092de_val,A: produc1432036078de_val] :
( ~ ( member313544709de_val @ A @ B )
| ( member313544709de_val @ A @ ( sup_su2138939728de_val @ C @ B ) ) ),
inference(cnf,[status(esa)],[359]) ).
thf(109,axiom,
( ( '?' @ option_list_val )
= ( ^ [A: option_list_val > $o] :
( ( A @ none_list_val )
| ? [B: list_val] : ( A @ ( some_list_val @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_split__option__ex) ).
thf(657,plain,
( ( '?' @ option_list_val )
= ( ^ [A: option_list_val > $o] :
( ( A @ none_list_val )
| ? [B: list_val] : ( A @ ( some_list_val @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(251,axiom,
! [A: g,B: node] : ( finite_finite_val @ ( uses @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_uses__finite) ).
thf(1054,plain,
! [A: g,B: node] : ( finite_finite_val @ ( uses @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(289,axiom,
( sSA_CF1660885746eD_val
= ( ^ [A: g > list_node,B: g > node > list_P561207620_edgeD,C: g > node > set_val,D: g > node > set_val,E: g > produc1432036078de_val > option_list_val,F: g] :
? [G: val] :
( ( member_val @ G @ ( sSA_CF1517915011eD_val @ A @ B @ C @ D @ E @ F ) )
& ( sSA_CF1899243830eD_val @ A @ B @ C @ D @ E @ F @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_CFG__SSA__wf__base_Oredundant__def) ).
thf(1170,plain,
( sSA_CF1660885746eD_val
= ( ^ [A: g > list_node,B: g > node > list_P561207620_edgeD,C: g > node > set_val,D: g > node > set_val,E: g > produc1432036078de_val > option_list_val,F: g] :
? [G: val] :
( ( member_val @ G @ ( sSA_CF1517915011eD_val @ A @ B @ C @ D @ E @ F ) )
& ( sSA_CF1899243830eD_val @ A @ B @ C @ D @ E @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(257,axiom,
! [A: val,B: set_val,C: set_val] :
( ( member_val @ A @ B )
=> ( member_val @ A @ ( sup_sup_set_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_UnI1) ).
thf(1071,plain,
! [A: val,B: set_val,C: set_val] :
( ( member_val @ A @ B )
=> ( member_val @ A @ ( sup_sup_set_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(294,axiom,
! [A: val,B: produc1432036078de_val,C: list_val,D: list_P1820443774de_val] :
( ( member1894062994de_val @ ( produc1571934709de_val @ A @ B ) @ ( set_Pr434939430de_val @ ( zip_va679686869de_val @ C @ D ) ) )
=> ~ ( ( member_val @ A @ ( set_val2 @ C ) )
=> ~ ( member313544709de_val @ B @ ( set_Pr1085970585de_val @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_in__set__zipE) ).
thf(1187,plain,
! [A: val,B: produc1432036078de_val,C: list_val,D: list_P1820443774de_val] :
( ( member1894062994de_val @ ( produc1571934709de_val @ A @ B ) @ ( set_Pr434939430de_val @ ( zip_va679686869de_val @ C @ D ) ) )
=> ~ ( ( member_val @ A @ ( set_val2 @ C ) )
=> ~ ( member313544709de_val @ B @ ( set_Pr1085970585de_val @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(149,axiom,
! [A: set_set_val,B: set_val] :
( ( finite1265617511et_val @ A )
=> ( ( member_set_val @ B @ A )
=> ? [C: set_val] :
( ( member_set_val @ C @ A )
& ( ord_less_eq_set_val @ B @ C )
& ! [D: set_val] :
( ( member_set_val @ D @ A )
=> ( ( ord_less_eq_set_val @ C @ D )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_finite__has__maximal2) ).
thf(773,plain,
! [A: set_set_val,B: set_val] :
( ( finite1265617511et_val @ A )
=> ( ( member_set_val @ B @ A )
=> ? [C: set_val] :
( ( member_set_val @ C @ A )
& ( ord_less_eq_set_val @ B @ C )
& ! [D: set_val] :
( ( member_set_val @ D @ A )
=> ( ( ord_less_eq_set_val @ C @ D )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(323,axiom,
member_val @ s @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_assms_I3_J) ).
thf(1278,plain,
member_val @ s @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(96,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ C )
= ( ( ord_less_eq_set_val @ A @ C )
& ( ord_less_eq_set_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_Un__subset__iff) ).
thf(618,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ C )
= ( ( ord_less_eq_set_val @ A @ C )
& ( ord_less_eq_set_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(307,axiom,
! [A: val,B: g] :
( ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) )
=> ? [C: node] :
( ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) )
& ( member_val @ A @ ( sSA_CF139593942de_val @ defs @ phis @ B @ C ) )
& ! [D: node] :
( ( ( member_node @ D @ ( set_node2 @ ( alpha_n @ B ) ) )
& ( member_val @ A @ ( sSA_CF139593942de_val @ defs @ phis @ B @ D ) ) )
=> ( D = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_defNode__ex1) ).
thf(1219,plain,
! [A: val,B: g] :
( ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) )
=> ? [C: node] :
( ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) )
& ( member_val @ A @ ( sSA_CF139593942de_val @ defs @ phis @ B @ C ) )
& ! [D: node] :
( ( ( member_node @ D @ ( set_node2 @ ( alpha_n @ B ) ) )
& ( member_val @ A @ ( sSA_CF139593942de_val @ defs @ phis @ B @ D ) ) )
=> ( D = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(176,axiom,
! [A: set_val,B: set_val] : ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_sup__ge1) ).
thf(856,plain,
! [A: set_val,B: set_val] : ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(139,axiom,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
( ( finite2056463621de_val @ A )
=> ( ( ord_le1643692676de_val @ B @ A )
=> ( finite2056463621de_val @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_rev__finite__subset) ).
thf(745,plain,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
( ( finite2056463621de_val @ A )
=> ( ( ord_le1643692676de_val @ B @ A )
=> ( finite2056463621de_val @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(351,axiom,
! [A: val,B: set_val,C: set_val] :
( ( member_val @ A @ ( sup_sup_set_val @ B @ C ) )
=> ( ~ ( member_val @ A @ B )
=> ( member_val @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_UnE) ).
thf(1374,plain,
! [A: val,B: set_val,C: set_val] :
( ( member_val @ A @ ( sup_sup_set_val @ B @ C ) )
=> ( ~ ( member_val @ A @ B )
=> ( member_val @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(135,axiom,
! [A: set_val,B: set_val] :
( ( ( sup_sup_set_val @ A @ B )
= bot_bot_set_val )
= ( ( A = bot_bot_set_val )
& ( B = bot_bot_set_val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_sup__eq__bot__iff) ).
thf(733,plain,
! [A: set_val,B: set_val] :
( ( ( sup_sup_set_val @ A @ B )
= bot_bot_set_val )
= ( ( A = bot_bot_set_val )
& ( B = bot_bot_set_val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(60,axiom,
! [A: node,B: set_node,C: set_node] :
( ( member_node @ A @ B )
=> ( member_node @ A @ ( sup_sup_set_node @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_UnI2) ).
thf(513,plain,
! [A: node,B: set_node,C: set_node] :
( ( member_node @ A @ B )
=> ( member_node @ A @ ( sup_sup_set_node @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(32,axiom,
! [A: set_set_val,B: set_set_val,C: set_val] :
( ( ord_le1742111550et_val @ A @ B )
=> ( ( member_set_val @ C @ A )
=> ( member_set_val @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_subsetD) ).
thf(430,plain,
! [A: set_set_val,B: set_set_val,C: set_val] :
( ( ord_le1742111550et_val @ A @ B )
=> ( ( member_set_val @ C @ A )
=> ( member_set_val @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(84,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C ) )
= ( sup_sup_set_val @ B @ ( sup_sup_set_val @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_Un__left__commute) ).
thf(584,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C ) )
= ( sup_sup_set_val @ B @ ( sup_sup_set_val @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(272,axiom,
( sSA_CF1252180629de_val
= ( ^ [A: g > list_node,B: g > node > set_val,C: g > produc1432036078de_val > option_list_val,D: g,E: val,F: val] :
? [G: list_val] :
( ( ( sSA_CF262257161de_val @ A @ B @ C @ D @ E )
= ( some_list_val @ G ) )
& ( member_val @ F @ ( set_val2 @ G ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_CFG__SSA__wf__base_OphiArg__def) ).
thf(1125,plain,
( sSA_CF1252180629de_val
= ( ^ [A: g > list_node,B: g > node > set_val,C: g > produc1432036078de_val > option_list_val,D: g,E: val,F: val] :
? [G: list_val] :
( ( ( sSA_CF262257161de_val @ A @ B @ C @ D @ E )
= ( some_list_val @ G ) )
& ( member_val @ F @ ( set_val2 @ G ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(216,axiom,
! [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
( ( ord_le299366439et_val @ A @ B )
=> ( ( finite79836624et_val @ B )
=> ( finite79836624et_val @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_finite__subset) ).
thf(958,plain,
! [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
( ( ord_le299366439et_val @ A @ B )
=> ( ( finite79836624et_val @ B )
=> ( finite79836624et_val @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(71,axiom,
! [A: list_val] :
( none_list_val
!= ( some_list_val @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_option_Odistinct_I1_J) ).
thf(545,plain,
! [A: list_val] :
( none_list_val
!= ( some_list_val @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(26,axiom,
( ord_le1643692676de_val
= ( ^ [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
! [C: produc1432036078de_val] :
( ( member313544709de_val @ C @ A )
=> ( member313544709de_val @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_subset__iff) ).
thf(413,plain,
( ord_le1643692676de_val
= ( ^ [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
! [C: produc1432036078de_val] :
( ( member313544709de_val @ C @ A )
=> ( member313544709de_val @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(562,plain,
( ( ^ [A: option_list_val > $o] :
( ( A @ none_list_val )
& ! [B: list_val] : ( A @ ( some_list_val @ B ) ) ) )
= ( '!' @ option_list_val ) ),
inference(lifteq,[status(thm)],[561]) ).
thf(195,axiom,
! [A: set_val] :
( ( sup_sup_set_val @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_Un__absorb) ).
thf(904,plain,
! [A: set_val] :
( ( sup_sup_set_val @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(235,axiom,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( finite_finite_val @ ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_allUses__finite) ).
thf(1007,plain,
! [A: node,B: g] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( finite_finite_val @ ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(120,axiom,
! [A: produc1432036078de_val,B: produc1432036078de_val,C: list_P1820443774de_val] :
( ( member698732390de_val @ ( produc453318901de_val @ A @ B ) @ ( set_Pr482027474de_val @ ( zip_Pr1472086037de_val @ C @ C ) ) )
= ( ( member313544709de_val @ A @ ( set_Pr1085970585de_val @ C ) )
& ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_zip__same) ).
thf(694,plain,
! [A: produc1432036078de_val,B: produc1432036078de_val,C: list_P1820443774de_val] :
( ( member698732390de_val @ ( produc453318901de_val @ A @ B ) @ ( set_Pr482027474de_val @ ( zip_Pr1472086037de_val @ C @ C ) ) )
= ( ( member313544709de_val @ A @ ( set_Pr1085970585de_val @ C ) )
& ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(183,axiom,
( sSA_CF262257161de_val
= ( ^ [A: g > list_node,B: g > node > set_val,C: g > produc1432036078de_val > option_list_val,D: g,E: val] : ( C @ D @ ( produc1470527136de_val @ ( sSA_CF551432799de_val @ A @ B @ C @ D @ E ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_CFG__SSA__wf__base_Ophi__def) ).
thf(875,plain,
( sSA_CF262257161de_val
= ( ^ [A: g > list_node,B: g > node > set_val,C: g > produc1432036078de_val > option_list_val,D: g,E: val] : ( C @ D @ ( produc1470527136de_val @ ( sSA_CF551432799de_val @ A @ B @ C @ D @ E ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(81,axiom,
! [A: option_list_val] :
( ( A != none_list_val )
= ( ? [B: list_val] :
( A
= ( some_list_val @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_not__None__eq) ).
thf(577,plain,
! [A: option_list_val] :
( ( A != none_list_val )
= ( ? [B: list_val] :
( A
= ( some_list_val @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(37,axiom,
sSA_CF2074824714de_val = sSA_CF2074824714de_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_CFG__SSA__wf__base_Opruned_Ocong) ).
thf(445,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(350,axiom,
! [A: set_val,B: val,C: list_set_val,D: list_val] :
( ( member1110026224al_val @ ( produc1337903031al_val @ A @ B ) @ ( set_Pr1027623516al_val @ ( zip_set_val_val @ C @ D ) ) )
=> ~ ( ( member_set_val @ A @ ( set_set_val2 @ C ) )
=> ~ ( member_val @ B @ ( set_val2 @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_in__set__zipE) ).
thf(1371,plain,
! [A: set_val,B: val,C: list_set_val,D: list_val] :
( ( member1110026224al_val @ ( produc1337903031al_val @ A @ B ) @ ( set_Pr1027623516al_val @ ( zip_set_val_val @ C @ D ) ) )
=> ~ ( ( member_set_val @ A @ ( set_set_val2 @ C ) )
=> ~ ( member_val @ B @ ( set_val2 @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(201,axiom,
! [A: set_val,B: set_val] :
( ( ( sup_sup_set_val @ A @ B )
= bot_bot_set_val )
= ( ( A = bot_bot_set_val )
& ( B = bot_bot_set_val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_Un__empty) ).
thf(919,plain,
! [A: set_val,B: set_val] :
( ( ( sup_sup_set_val @ A @ B )
= bot_bot_set_val )
= ( ( A = bot_bot_set_val )
& ( B = bot_bot_set_val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(211,axiom,
! [A: set_node] :
( ( finite_finite_node @ A )
=> ? [B: list_node] :
( ( set_node2 @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_finite__list) ).
thf(947,plain,
! [A: set_node] :
( ( finite_finite_node @ A )
=> ? [B: list_node] :
( ( set_node2 @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(308,axiom,
! [A: g] :
( ( sSA_CF2074824714de_val @ alpha_n @ defs @ uses @ phis @ A )
= ( ! [B: node] :
( ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ! [C: val] :
( ( member_val @ C @ ( sSA_CF370335846de_val @ phis @ A @ B ) )
=> ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_pruned__def) ).
thf(1224,plain,
! [A: g] :
( ( sSA_CF2074824714de_val @ alpha_n @ defs @ uses @ phis @ A )
= ( ! [B: node] :
( ( member_node @ B @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ! [C: val] :
( ( member_val @ C @ ( sSA_CF370335846de_val @ phis @ A @ B ) )
=> ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(114,axiom,
! [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( ord_less_eq_set_val @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_subset__antisym) ).
thf(672,plain,
! [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( ord_less_eq_set_val @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(146,axiom,
! [A: list_P1078858818l_node] : ( finite423892681l_node @ ( set_Pr1600883293l_node @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_List_Ofinite__set) ).
thf(764,plain,
! [A: list_P1078858818l_node] : ( finite423892681l_node @ ( set_Pr1600883293l_node @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(303,axiom,
! [A: g,B: set_val] : ( transi1953622797et_val @ ( irredu893086079de_val @ alpha_n @ defs @ phis @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_condensation__acyclic) ).
thf(1209,plain,
! [A: g,B: set_val] : ( transi1953622797et_val @ ( irredu893086079de_val @ alpha_n @ defs @ phis @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(166,axiom,
! [A: set_val,B: set_val] :
( ( sup_sup_set_val @ A @ ( sup_sup_set_val @ A @ B ) )
= ( sup_sup_set_val @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_Un__left__absorb) ).
thf(831,plain,
! [A: set_val,B: set_val] :
( ( sup_sup_set_val @ A @ ( sup_sup_set_val @ A @ B ) )
= ( sup_sup_set_val @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(136,axiom,
! [A: produc1324971431et_val,B: produc1324971431et_val,C: list_P2089461677et_val] :
( ( member1254968080et_val @ ( produc1377626967et_val @ A @ B ) @ ( set_Pr1006393724et_val @ ( zip_Pr21865079et_val @ C @ C ) ) )
= ( ( member1711426256et_val @ A @ ( set_Pr284769596et_val @ C ) )
& ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_zip__same) ).
thf(736,plain,
! [A: produc1324971431et_val,B: produc1324971431et_val,C: list_P2089461677et_val] :
( ( member1254968080et_val @ ( produc1377626967et_val @ A @ B ) @ ( set_Pr1006393724et_val @ ( zip_Pr21865079et_val @ C @ C ) ) )
= ( ( member1711426256et_val @ A @ ( set_Pr284769596et_val @ C ) )
& ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(343,axiom,
! [A: val,B: val > $o] :
( ( member_val @ A @ ( collect_val @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_mem__Collect__eq) ).
thf(1349,plain,
! [A: val,B: val > $o] :
( ( member_val @ A @ ( collect_val @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(6,axiom,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val,C: produc1432036078de_val] :
( ( ord_le1643692676de_val @ A @ B )
=> ( ( member313544709de_val @ C @ A )
=> ( member313544709de_val @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_subsetD) ).
thf(362,plain,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val,C: produc1432036078de_val] :
( ( ord_le1643692676de_val @ A @ B )
=> ( ( member313544709de_val @ C @ A )
=> ( member313544709de_val @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(279,axiom,
! [A: g,B: node] : ( finite_finite_val @ ( sSA_CF370335846de_val @ phis @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_phiDefs__finite) ).
thf(1144,plain,
! [A: g,B: node] : ( finite_finite_val @ ( sSA_CF370335846de_val @ phis @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(90,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( ord_less_eq_set_val @ C @ B )
=> ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_sup_OboundedI) ).
thf(599,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( ord_less_eq_set_val @ C @ B )
=> ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(291,axiom,
! [A: set_val] :
( ( finite_finite_val @ A )
=> ( ( A != bot_bot_set_val )
=> ? [B: val] :
( ( member_val @ B @ A )
& ! [C: val] :
( ( member_val @ C @ A )
=> ( ( ord_less_eq_val @ C @ B )
=> ( B = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_finite__has__minimal) ).
thf(1175,plain,
! [A: set_val] :
( ( finite_finite_val @ A )
=> ( ( A != bot_bot_set_val )
=> ? [B: val] :
( ( member_val @ B @ A )
& ! [C: val] :
( ( member_val @ C @ A )
=> ( ( ord_less_eq_val @ C @ B )
=> ( B = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(193,axiom,
! [A: set_val] : ( ord_less_eq_set_val @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_subset__refl) ).
thf(900,plain,
! [A: set_val] : ( ord_less_eq_set_val @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(23,axiom,
( ord_le1742111550et_val
= ( ^ [A: set_set_val,B: set_set_val] :
! [C: set_val] :
( ( member_set_val @ C @ A )
=> ( member_set_val @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_subset__iff) ).
thf(406,plain,
( ord_le1742111550et_val
= ( ^ [A: set_set_val,B: set_set_val] :
! [C: set_val] :
( ( member_set_val @ C @ A )
=> ( member_set_val @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(152,axiom,
sSA_CF848637139eD_val = sSA_CF848637139eD_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_CFG__SSA__base_OphiUses_Ocong) ).
thf(784,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(268,axiom,
( ( var2 @ g2 @ phi )
= ( var2 @ g2 @ s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_assms_I5_J) ).
thf(1117,plain,
( ( var2 @ g2 @ phi )
= ( var2 @ g2 @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(12,axiom,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
( ! [C: produc1432036078de_val] :
( ( member313544709de_val @ C @ A )
=> ( member313544709de_val @ C @ B ) )
=> ( ord_le1643692676de_val @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_subsetI) ).
thf(377,plain,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
( ! [C: produc1432036078de_val] :
( ( member313544709de_val @ C @ A )
=> ( member313544709de_val @ C @ B ) )
=> ( ord_le1643692676de_val @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(230,axiom,
! [A: list_P2089461677et_val] : ( finite79836624et_val @ ( set_Pr284769596et_val @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_List_Ofinite__set) ).
thf(996,plain,
! [A: list_P2089461677et_val] : ( finite79836624et_val @ ( set_Pr284769596et_val @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(185,axiom,
! [A: product_prod_val_val,B: product_prod_val_val > $o] :
( ( member1680438992al_val @ A @ ( collec52550418al_val @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_mem__Collect__eq) ).
thf(880,plain,
! [A: product_prod_val_val,B: product_prod_val_val > $o] :
( ( member1680438992al_val @ A @ ( collec52550418al_val @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(106,axiom,
! [A: set_val,B: set_val] : ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_sup_Ocobounded1) ).
thf(649,plain,
! [A: set_val,B: set_val] : ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(246,axiom,
! [A: g,B: node] : ( finite_finite_val @ ( defs @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_defs__finite) ).
thf(1043,plain,
! [A: g,B: node] : ( finite_finite_val @ ( defs @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(48,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( ord_less_eq_set_val @ B @ C )
=> ( ord_less_eq_set_val @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_subset__trans) ).
thf(477,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( ord_less_eq_set_val @ B @ C )
=> ( ord_less_eq_set_val @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(260,axiom,
! [A: node,B: val,C: list_node,D: list_val] :
( ( member313544709de_val @ ( produc1470527136de_val @ A @ B ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ C @ D ) ) )
=> ~ ( ( member_node @ A @ ( set_node2 @ C ) )
=> ~ ( member_val @ B @ ( set_val2 @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_in__set__zipE) ).
thf(1080,plain,
! [A: node,B: val,C: list_node,D: list_val] :
( ( member313544709de_val @ ( produc1470527136de_val @ A @ B ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ C @ D ) ) )
=> ~ ( ( member_node @ A @ ( set_node2 @ C ) )
=> ~ ( member_val @ B @ ( set_val2 @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(144,axiom,
! [A: list_val,B: list_val] :
( ( ( some_list_val @ A )
= ( some_list_val @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_option_Oinject) ).
thf(758,plain,
! [A: list_val,B: list_val] :
( ( ( some_list_val @ A )
= ( some_list_val @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(93,axiom,
! [A: set_val,B: set_set_val,C: set_set_val] :
( ( member_set_val @ A @ B )
=> ( member_set_val @ A @ ( sup_sup_set_set_val @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_UnI2) ).
thf(609,plain,
! [A: set_val,B: set_set_val,C: set_set_val] :
( ( member_set_val @ A @ B )
=> ( member_set_val @ A @ ( sup_sup_set_set_val @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(88,axiom,
! [A: list_set_val] : ( finite1265617511et_val @ ( set_set_val2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_List_Ofinite__set) ).
thf(594,plain,
! [A: list_set_val] : ( finite1265617511et_val @ ( set_set_val2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(97,axiom,
! [A: set_val,B: set_val,C: list_set_val,D: list_set_val] :
( ( member1711426256et_val @ ( produc1041633943et_val @ A @ B ) @ ( set_Pr284769596et_val @ ( zip_set_val_set_val @ C @ D ) ) )
=> ( member_set_val @ A @ ( set_set_val2 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_set__zip__leftD) ).
thf(621,plain,
! [A: set_val,B: set_val,C: list_set_val,D: list_set_val] :
( ( member1711426256et_val @ ( produc1041633943et_val @ A @ B ) @ ( set_Pr284769596et_val @ ( zip_set_val_set_val @ C @ D ) ) )
=> ( member_set_val @ A @ ( set_set_val2 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(481,plain,
! [A: set_Pr699757092de_val] :
( ( finite2056463621de_val @ A )
| ( A != bot_bo404898488de_val ) ),
inference(cnf,[status(esa)],[480]) ).
thf(482,plain,
! [A: set_Pr699757092de_val] :
( ( A != bot_bo404898488de_val )
| ( finite2056463621de_val @ A ) ),
inference(lifteq,[status(thm)],[481]) ).
thf(483,plain,
finite2056463621de_val @ bot_bo404898488de_val,
inference(simp,[status(thm)],[482]) ).
thf(336,axiom,
! [A: g,B: node] :
( ( sSA_CF139593942de_val @ defs @ phis @ A @ B )
= ( sup_sup_set_val @ ( defs @ A @ B ) @ ( sSA_CF370335846de_val @ phis @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_allDefs__def) ).
thf(1325,plain,
! [A: g,B: node] :
( ( sSA_CF139593942de_val @ defs @ phis @ A @ B )
= ( sup_sup_set_val @ ( defs @ A @ B ) @ ( sSA_CF370335846de_val @ phis @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(281,axiom,
member_val @ phi @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_assms_I2_J) ).
thf(1149,plain,
member_val @ phi @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ g2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(99,axiom,
! [A: set_val,B: set_val] :
( ( A
= ( sup_sup_set_val @ A @ B ) )
=> ( ord_less_eq_set_val @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_sup_OorderI) ).
thf(626,plain,
! [A: set_val,B: set_val] :
( ( A
= ( sup_sup_set_val @ A @ B ) )
=> ( ord_less_eq_set_val @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(209,axiom,
sSA_CF262257161de_val = sSA_CF262257161de_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_CFG__SSA__wf__base_Ophi_Ocong) ).
thf(943,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(112,axiom,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
( ( finite2056463621de_val @ A )
=> ( ( finite2056463621de_val @ B )
=> ( finite2056463621de_val @ ( sup_su2138939728de_val @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_finite__UnI) ).
thf(668,plain,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
( ( finite2056463621de_val @ A )
=> ( ( finite2056463621de_val @ B )
=> ( finite2056463621de_val @ ( sup_su2138939728de_val @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(42,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C ) )
= ( sup_sup_set_val @ B @ ( sup_sup_set_val @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_sup__left__commute) ).
thf(462,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C ) )
= ( sup_sup_set_val @ B @ ( sup_sup_set_val @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(267,axiom,
! [A: set_val] :
( ( finite_finite_val @ A )
=> ( ( A != bot_bot_set_val )
=> ? [B: val] :
( ( member_val @ B @ A )
& ! [C: val] :
( ( member_val @ C @ A )
=> ( ( ord_less_eq_val @ B @ C )
=> ( B = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_finite__has__maximal) ).
thf(1112,plain,
! [A: set_val] :
( ( finite_finite_val @ A )
=> ( ( A != bot_bot_set_val )
=> ? [B: val] :
( ( member_val @ B @ A )
& ! [C: val] :
( ( member_val @ C @ A )
=> ( ( ord_less_eq_val @ B @ C )
=> ( B = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(177,axiom,
! [A: set_val] :
( ( ord_less_eq_set_val @ A @ bot_bot_set_val )
= ( A = bot_bot_set_val ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_subset__empty) ).
thf(858,plain,
! [A: set_val] :
( ( ord_less_eq_set_val @ A @ bot_bot_set_val )
= ( A = bot_bot_set_val ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(8,axiom,
! [A: produc1324971431et_val,B: set_Pr1311924359et_val,C: set_Pr1311924359et_val] :
( ( member1711426256et_val @ A @ ( sup_su2005730907et_val @ B @ C ) )
=> ( ~ ( member1711426256et_val @ A @ B )
=> ( member1711426256et_val @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_UnE) ).
thf(367,plain,
! [A: produc1324971431et_val,B: set_Pr1311924359et_val,C: set_Pr1311924359et_val] :
( ( member1711426256et_val @ A @ ( sup_su2005730907et_val @ B @ C ) )
=> ( ~ ( member1711426256et_val @ A @ B )
=> ( member1711426256et_val @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(286,axiom,
! [A: val,B: val,C: list_val] :
( ( member1680438992al_val @ ( product_Pair_val_val @ A @ B ) @ ( set_Pr102746428al_val @ ( zip_val_val @ C @ C ) ) )
= ( ( member_val @ A @ ( set_val2 @ C ) )
& ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_zip__same) ).
thf(1162,plain,
! [A: val,B: val,C: list_val] :
( ( member1680438992al_val @ ( product_Pair_val_val @ A @ B ) @ ( set_Pr102746428al_val @ ( zip_val_val @ C @ C ) ) )
= ( ( member_val @ A @ ( set_val2 @ C ) )
& ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(132,axiom,
! [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( finite_finite_val @ B )
=> ( finite_finite_val @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_finite__subset) ).
thf(726,plain,
! [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( finite_finite_val @ B )
=> ( finite_finite_val @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(242,axiom,
! [A: g,B: val,C: val] :
( ( transi1991289355lp_val @ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A ) @ B @ C )
=> ( ( var2 @ A @ B )
= ( var2 @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_phiArg__trancl__same__var) ).
thf(1029,plain,
! [A: g,B: val,C: val] :
( ( transi1991289355lp_val @ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A ) @ B @ C )
=> ( ( var2 @ A @ B )
= ( var2 @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(191,axiom,
( sSA_CF178745443eD_val
= ( ^ [A: g > list_node,B: g > node > list_P561207620_edgeD,C: g > node > set_val,D: g > produc1432036078de_val > option_list_val,E: g,F: node] : ( sup_sup_set_val @ ( C @ E @ F ) @ ( sSA_CF848637139eD_val @ A @ B @ D @ E @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_CFG__SSA__base_OallUses__def) ).
thf(895,plain,
( sSA_CF178745443eD_val
= ( ^ [A: g > list_node,B: g > node > list_P561207620_edgeD,C: g > node > set_val,D: g > produc1432036078de_val > option_list_val,E: g,F: node] : ( sup_sup_set_val @ ( C @ E @ F ) @ ( sSA_CF848637139eD_val @ A @ B @ D @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(186,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( sup_sup_set_val @ ( sup_sup_set_val @ A @ B ) @ C )
= ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_inf__sup__aci_I6_J) ).
thf(883,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( sup_sup_set_val @ ( sup_sup_set_val @ A @ B ) @ C )
= ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(19,axiom,
! [A: produc1324971431et_val,B: set_Pr1311924359et_val,C: set_Pr1311924359et_val] :
( ( member1711426256et_val @ A @ ( sup_su2005730907et_val @ B @ C ) )
= ( ( member1711426256et_val @ A @ B )
| ( member1711426256et_val @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_Un__iff) ).
thf(394,plain,
! [A: produc1324971431et_val,B: set_Pr1311924359et_val,C: set_Pr1311924359et_val] :
( ( member1711426256et_val @ A @ ( sup_su2005730907et_val @ B @ C ) )
= ( ( member1711426256et_val @ A @ B )
| ( member1711426256et_val @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(76,axiom,
! [A: produc1946948786l_node,B: produc1946948786l_node > $o] :
( ( member828457417l_node @ A @ ( collec885255687l_node @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_mem__Collect__eq) ).
thf(563,plain,
! [A: produc1946948786l_node,B: produc1946948786l_node > $o] :
( ( member828457417l_node @ A @ ( collec885255687l_node @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(348,axiom,
( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_s )
= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_eq) ).
thf(1364,plain,
( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_s )
= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(202,axiom,
! [A: set_val,B: set_val] : ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_sup__ge2) ).
thf(922,plain,
! [A: set_val,B: set_val] : ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(658,plain,
( ( ^ [A: option_list_val > $o] :
( ( A @ none_list_val )
| ? [B: list_val] : ( A @ ( some_list_val @ B ) ) ) )
= ( '?' @ option_list_val ) ),
inference(lifteq,[status(thm)],[657]) ).
thf(299,axiom,
! [A: node,B: g,C: val] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_val @ C @ ( uses @ B @ A ) )
=> ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_liveSimple) ).
thf(1198,plain,
! [A: node,B: g,C: val] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_val @ C @ ( uses @ B @ A ) )
=> ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(305,axiom,
! [A: val,B: g] :
( ( member_val @ A @ ( sSA_CF655860150de_val @ alpha_n @ uses @ B ) )
=> ~ ! [C: node] :
( ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ~ ( member_val @ A @ ( uses @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_varsE) ).
thf(1213,plain,
! [A: val,B: g] :
( ( member_val @ A @ ( sSA_CF655860150de_val @ alpha_n @ uses @ B ) )
=> ~ ! [C: node] :
( ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ~ ( member_val @ A @ ( uses @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(148,axiom,
! [A: set_val,B: set_val,C: set_val,D: set_val] :
( ( A
= ( sup_sup_set_val @ B @ C ) )
=> ( ( sup_sup_set_val @ A @ D )
= ( sup_sup_set_val @ B @ ( sup_sup_set_val @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_boolean__algebra__cancel_Osup1) ).
thf(768,plain,
! [A: set_val,B: set_val,C: set_val,D: set_val] :
( ( A
= ( sup_sup_set_val @ B @ C ) )
=> ( ( sup_sup_set_val @ A @ D )
= ( sup_sup_set_val @ B @ ( sup_sup_set_val @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(244,axiom,
! [A: g,B: val] :
( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ A @ B )
=> ( ! [C: node] :
( ( member_node @ C @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ~ ( member_val @ B @ ( uses @ A @ C ) ) )
=> ~ ! [C: val] :
( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ A @ C )
=> ~ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_liveVal_Ocases) ).
thf(1034,plain,
! [A: g,B: val] :
( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ A @ B )
=> ( ! [C: node] :
( ( member_node @ C @ ( set_node2 @ ( alpha_n @ A ) ) )
=> ~ ( member_val @ B @ ( uses @ A @ C ) ) )
=> ~ ! [C: val] :
( ( sSA_CF794421325de_val @ alpha_n @ defs @ uses @ phis @ A @ C )
=> ~ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(115,axiom,
! [A: option_list_val] :
( ( A != none_list_val )
=> ~ ! [B: list_val] :
( A
!= ( some_list_val @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_option_Oexhaust) ).
thf(675,plain,
! [A: option_list_val] :
( ( A != none_list_val )
=> ~ ! [B: list_val] :
( A
!= ( some_list_val @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(157,axiom,
! [A: set_val,B: set_val] : ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_sup_Ocobounded2) ).
thf(795,plain,
! [A: set_val,B: set_val] : ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(546,plain,
~ ? [A: list_val] :
( none_list_val
= ( some_list_val @ A ) ),
inference(miniscope,[status(thm)],[545]) ).
thf(547,plain,
! [A: list_val] :
( none_list_val
!= ( some_list_val @ A ) ),
inference(cnf,[status(esa)],[546]) ).
thf(548,plain,
! [A: list_val] :
( ( some_list_val @ A )
!= none_list_val ),
inference(lifteq,[status(thm)],[547]) ).
thf(276,axiom,
! [A: node,B: g,C: val,D: list_val,E: node,F: val] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( ( phis @ B @ ( produc1470527136de_val @ A @ C ) )
= ( some_list_val @ D ) )
=> ( ( member313544709de_val @ ( produc1470527136de_val @ E @ F ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ ( graph_272749361_edgeD @ inEdges @ B @ A ) @ D ) ) )
=> ( member_val @ F @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ B @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_phiUsesI) ).
thf(1134,plain,
! [A: node,B: g,C: val,D: list_val,E: node,F: val] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( ( phis @ B @ ( produc1470527136de_val @ A @ C ) )
= ( some_list_val @ D ) )
=> ( ( member313544709de_val @ ( produc1470527136de_val @ E @ F ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ ( graph_272749361_edgeD @ inEdges @ B @ A ) @ D ) ) )
=> ( member_val @ F @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ B @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(141,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( ord_less_eq_set_val @ C @ B )
=> ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_Un__least) ).
thf(749,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( ord_less_eq_set_val @ C @ B )
=> ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(61,axiom,
! [A: node,B: set_val,C: list_node,D: list_set_val] :
( ( member125181669et_val @ ( produc2042994048et_val @ A @ B ) @ ( set_Pr1953765241et_val @ ( zip_node_set_val @ C @ D ) ) )
=> ~ ( ( member_node @ A @ ( set_node2 @ C ) )
=> ~ ( member_set_val @ B @ ( set_set_val2 @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_in__set__zipE) ).
thf(516,plain,
! [A: node,B: set_val,C: list_node,D: list_set_val] :
( ( member125181669et_val @ ( produc2042994048et_val @ A @ B ) @ ( set_Pr1953765241et_val @ ( zip_node_set_val @ C @ D ) ) )
=> ~ ( ( member_node @ A @ ( set_node2 @ C ) )
=> ~ ( member_set_val @ B @ ( set_set_val2 @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(354,plain,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
( ( ord_le1643692676de_val @ A @ B )
=> ! [C: produc1432036078de_val] :
( ( member313544709de_val @ C @ A )
=> ( member313544709de_val @ C @ B ) ) ),
inference(miniscope,[status(thm)],[353]) ).
thf(355,plain,
! [C: produc1432036078de_val,B: set_Pr699757092de_val,A: set_Pr699757092de_val] :
( ~ ( ord_le1643692676de_val @ A @ B )
| ~ ( member313544709de_val @ C @ A )
| ( member313544709de_val @ C @ B ) ),
inference(cnf,[status(esa)],[354]) ).
thf(249,axiom,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( sSA_CF139593942de_val @ defs @ phis @ B @ C ) )
=> ( ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_allDefs__in__allVars) ).
thf(1049,plain,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( sSA_CF139593942de_val @ defs @ phis @ B @ C ) )
=> ( ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( member_val @ A @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(66,axiom,
! [A: set_val,B: set_val,C: list_set_val] :
( ( member1711426256et_val @ ( produc1041633943et_val @ A @ B ) @ ( set_Pr284769596et_val @ ( zip_set_val_set_val @ C @ C ) ) )
= ( ( member_set_val @ A @ ( set_set_val2 @ C ) )
& ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_zip__same) ).
thf(531,plain,
! [A: set_val,B: set_val,C: list_set_val] :
( ( member1711426256et_val @ ( produc1041633943et_val @ A @ B ) @ ( set_Pr284769596et_val @ ( zip_set_val_set_val @ C @ C ) ) )
= ( ( member_set_val @ A @ ( set_set_val2 @ C ) )
& ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(210,axiom,
! [A: set_val,B: set_val] :
( ~ ( finite_finite_val @ A )
=> ~ ( finite_finite_val @ ( sup_sup_set_val @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_Un__infinite) ).
thf(944,plain,
! [A: set_val,B: set_val] :
( ~ ( finite_finite_val @ A )
=> ~ ( finite_finite_val @ ( sup_sup_set_val @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(204,axiom,
! [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( B
= ( sup_sup_set_val @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_sup_OorderE) ).
thf(927,plain,
! [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( B
= ( sup_sup_set_val @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(11,axiom,
! [A: produc1324971431et_val,B: set_Pr1311924359et_val,C: set_Pr1311924359et_val] :
( ( member1711426256et_val @ A @ B )
=> ( member1711426256et_val @ A @ ( sup_su2005730907et_val @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_UnI2) ).
thf(374,plain,
! [A: produc1324971431et_val,B: set_Pr1311924359et_val,C: set_Pr1311924359et_val] :
( ( member1711426256et_val @ A @ B )
=> ( member1711426256et_val @ A @ ( sup_su2005730907et_val @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(64,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ C )
= ( ( ord_less_eq_set_val @ A @ C )
& ( ord_less_eq_set_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_sup_Obounded__iff) ).
thf(525,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ C )
= ( ( ord_less_eq_set_val @ A @ C )
& ( ord_less_eq_set_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(233,axiom,
sSA_CF178745443eD_val = sSA_CF178745443eD_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_CFG__SSA__base_OallUses_Ocong) ).
thf(1003,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(82,axiom,
! [A: node,B: node > $o] :
( ( member_node @ A @ ( collect_node @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_mem__Collect__eq) ).
thf(580,plain,
! [A: node,B: node > $o] :
( ( member_node @ A @ ( collect_node @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(104,axiom,
! [A: set_set_val,B: set_val] :
( ( finite1265617511et_val @ A )
=> ( ( member_set_val @ B @ A )
=> ? [C: set_val] :
( ( member_set_val @ C @ A )
& ( ord_less_eq_set_val @ C @ B )
& ! [D: set_val] :
( ( member_set_val @ D @ A )
=> ( ( ord_less_eq_set_val @ D @ C )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_finite__has__minimal2) ).
thf(640,plain,
! [A: set_set_val,B: set_val] :
( ( finite1265617511et_val @ A )
=> ( ( member_set_val @ B @ A )
=> ? [C: set_val] :
( ( member_set_val @ C @ A )
& ( ord_less_eq_set_val @ C @ B )
& ! [D: set_val] :
( ( member_set_val @ D @ A )
=> ( ( ord_less_eq_set_val @ D @ C )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(182,axiom,
! [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
( ( finite79836624et_val @ A )
=> ( ( ord_le299366439et_val @ B @ A )
=> ( finite79836624et_val @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_rev__finite__subset) ).
thf(872,plain,
! [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
( ( finite79836624et_val @ A )
=> ( ( ord_le299366439et_val @ B @ A )
=> ( finite79836624et_val @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(123,axiom,
! [A: set_val,B: node,C: list_set_val,D: list_node] :
( ( member76372137l_node @ ( produc2052093836l_node @ A @ B ) @ ( set_Pr1904955709l_node @ ( zip_set_val_node @ C @ D ) ) )
=> ~ ( ( member_set_val @ A @ ( set_set_val2 @ C ) )
=> ~ ( member_node @ B @ ( set_node2 @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_in__set__zipE) ).
thf(705,plain,
! [A: set_val,B: node,C: list_set_val,D: list_node] :
( ( member76372137l_node @ ( produc2052093836l_node @ A @ B ) @ ( set_Pr1904955709l_node @ ( zip_set_val_node @ C @ D ) ) )
=> ~ ( ( member_set_val @ A @ ( set_set_val2 @ C ) )
=> ~ ( member_node @ B @ ( set_node2 @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(221,axiom,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
( ( ~ ( finite2056463621de_val @ ( sup_su2138939728de_val @ A @ B ) ) )
= ( ~ ( finite2056463621de_val @ A )
| ~ ( finite2056463621de_val @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_infinite__Un) ).
thf(971,plain,
! [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
( ( ~ ( finite2056463621de_val @ ( sup_su2138939728de_val @ A @ B ) ) )
= ( ~ ( finite2056463621de_val @ A )
| ~ ( finite2056463621de_val @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(214,axiom,
! [A: produc1324971431et_val,B: set_Pr1311924359et_val] :
( ( finite79836624et_val @ ( insert1846469495et_val @ A @ B ) )
= ( finite79836624et_val @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_finite__insert) ).
thf(954,plain,
! [A: produc1324971431et_val,B: set_Pr1311924359et_val] :
( ( finite79836624et_val @ ( insert1846469495et_val @ A @ B ) )
= ( finite79836624et_val @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(137,axiom,
! [A: set_Pr1311924359et_val] :
( ( collec1117167378et_val
@ ^ [B: produc1324971431et_val] : ( member1711426256et_val @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_Collect__mem__eq) ).
thf(739,plain,
! [A: set_Pr1311924359et_val] :
( ( collec1117167378et_val
@ ^ [B: produc1324971431et_val] : ( member1711426256et_val @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(310,axiom,
! [A: node,B: g,C: val,D: val] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_val @ C @ ( sSA_CF139593942de_val @ defs @ phis @ B @ A ) )
=> ( ( member_val @ D @ ( sSA_CF139593942de_val @ defs @ phis @ B @ A ) )
=> ( ( C != D )
=> ( ( var2 @ B @ D )
!= ( var2 @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_allDefs__var__disjoint) ).
thf(1230,plain,
! [A: node,B: g,C: val,D: val] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_val @ C @ ( sSA_CF139593942de_val @ defs @ phis @ B @ A ) )
=> ( ( member_val @ D @ ( sSA_CF139593942de_val @ defs @ phis @ B @ A ) )
=> ( ( C != D )
=> ( ( var2 @ B @ D )
!= ( var2 @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(229,axiom,
! [A: set_val,B: set_val] :
( ( sup_su1487070040et_val @ ( some_set_val @ A ) @ ( some_set_val @ B ) )
= ( some_set_val @ ( sup_sup_set_val @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_sup__Some) ).
thf(993,plain,
! [A: set_val,B: set_val] :
( ( sup_su1487070040et_val @ ( some_set_val @ A ) @ ( some_set_val @ B ) )
= ( some_set_val @ ( sup_sup_set_val @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(9,axiom,
( ord_le1643692676de_val
= ( ^ [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
! [C: produc1432036078de_val] :
( ( member313544709de_val @ C @ A )
=> ( member313544709de_val @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_subset__eq) ).
thf(369,plain,
( ord_le1643692676de_val
= ( ^ [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
! [C: produc1432036078de_val] :
( ( member313544709de_val @ C @ A )
=> ( member313544709de_val @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(370,plain,
( ord_le1643692676de_val
= ( ^ [A: set_Pr699757092de_val,B: set_Pr699757092de_val] :
! [C: produc1432036078de_val] :
( ( member313544709de_val @ C @ A )
=> ( member313544709de_val @ C @ B ) ) ) ),
inference(lifteq,[status(thm)],[369]) ).
thf(128,axiom,
! [A: list_node] : ( finite_finite_node @ ( set_node2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_List_Ofinite__set) ).
thf(717,plain,
! [A: list_node] : ( finite_finite_node @ ( set_node2 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(274,axiom,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( uses @ B @ C ) )
=> ( member_val @ A @ ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_uses__in__allUses) ).
thf(1130,plain,
! [A: val,B: g,C: node] :
( ( member_val @ A @ ( uses @ B @ C ) )
=> ( member_val @ A @ ( sSA_CF178745443eD_val @ alpha_n @ inEdges @ uses @ phis @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(326,axiom,
! [A: val,B: set_val,C: set_val] :
( ( member_val @ A @ ( sup_sup_set_val @ B @ C ) )
= ( ( member_val @ A @ B )
| ( member_val @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_Un__iff) ).
thf(1285,plain,
! [A: val,B: set_val,C: set_val] :
( ( member_val @ A @ ( sup_sup_set_val @ B @ C ) )
= ( ( member_val @ A @ B )
| ( member_val @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(196,axiom,
sSA_CF1660885746eD_val = sSA_CF1660885746eD_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_CFG__SSA__wf__base_Oredundant_Ocong) ).
thf(907,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(262,axiom,
! [A: node,B: g,C: node,D: val,E: list_val] :
( ( member_node @ A @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ B @ C ) ) )
=> ( ( ( phis @ B @ ( produc1470527136de_val @ C @ D ) )
= ( some_list_val @ E ) )
=> ( ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ~ ! [F: val] :
( ( member_val @ F @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ B @ A ) )
=> ~ ( member_val @ F @ ( set_val2 @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_phiUses__exI) ).
thf(1085,plain,
! [A: node,B: g,C: node,D: val,E: list_val] :
( ( member_node @ A @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ B @ C ) ) )
=> ( ( ( phis @ B @ ( produc1470527136de_val @ C @ D ) )
= ( some_list_val @ E ) )
=> ( ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ~ ! [F: val] :
( ( member_val @ F @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ B @ A ) )
=> ~ ( member_val @ F @ ( set_val2 @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(45,axiom,
( sSA_CF139593942de_val
= ( ^ [A: g > node > set_val,B: g > produc1432036078de_val > option_list_val,C: g,D: node] : ( sup_sup_set_val @ ( A @ C @ D ) @ ( sSA_CF370335846de_val @ B @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_CFG__SSA__base_OallDefs__def) ).
thf(469,plain,
( sSA_CF139593942de_val
= ( ^ [A: g > node > set_val,B: g > produc1432036078de_val > option_list_val,C: g,D: node] : ( sup_sup_set_val @ ( A @ C @ D ) @ ( sSA_CF370335846de_val @ B @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(470,plain,
( sSA_CF139593942de_val
= ( ^ [A: g > node > set_val,B: g > produc1432036078de_val > option_list_val,C: g,D: node] : ( sup_sup_set_val @ ( A @ C @ D ) @ ( sSA_CF370335846de_val @ B @ C @ D ) ) ) ),
inference(lifteq,[status(thm)],[469]) ).
thf(213,axiom,
! [A: set_val,B: set_val] :
( ( sup_sup_set_val @ A @ ( sup_sup_set_val @ A @ B ) )
= ( sup_sup_set_val @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_inf__sup__aci_I8_J) ).
thf(951,plain,
! [A: set_val,B: set_val] :
( ( sup_sup_set_val @ A @ ( sup_sup_set_val @ A @ B ) )
= ( sup_sup_set_val @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(163,axiom,
! [A: option_list_val,B: option_list_val > option_list_val > $o,C: option_list_val] :
( ( ( A = none_list_val )
=> ( B @ A @ C ) )
=> ( ( ( C = none_list_val )
=> ( B @ A @ C ) )
=> ( ! [D: list_val,E: list_val] :
( ( A
= ( some_list_val @ D ) )
=> ( ( C
= ( some_list_val @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_combine__options__cases) ).
thf(808,plain,
! [A: option_list_val,B: option_list_val > option_list_val > $o,C: option_list_val] :
( ( ( A = none_list_val )
=> ( B @ A @ C ) )
=> ( ( ( C = none_list_val )
=> ( B @ A @ C ) )
=> ( ! [D: list_val,E: list_val] :
( ( A
= ( some_list_val @ D ) )
=> ( ( C
= ( some_list_val @ E ) )
=> ( B @ A @ C ) ) )
=> ( B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(1403,plain,
! [C: val,B: g,A: node] :
( ~ ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
| ~ ( member_val @ C @ ( defs @ B @ A ) )
| ( C != C )
| ( ( uses @ B @ A )
!= ( defs @ B @ A ) ) ),
inference(simp,[status(thm)],[1401]) ).
thf(1404,plain,
! [C: val,B: g,A: node] :
( ~ ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
| ~ ( member_val @ C @ ( defs @ B @ A ) )
| ( ( uses @ B @ A )
!= ( defs @ B @ A ) ) ),
inference(simp,[status(thm)],[1403]) ).
thf(317,axiom,
! [A: set_val,B: set_val,C: val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( member_val @ C @ A )
=> ( member_val @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_subsetD) ).
thf(1257,plain,
! [A: set_val,B: set_val,C: val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( member_val @ C @ A )
=> ( member_val @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(278,axiom,
! [A: g,B: val,C: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ B @ C )
=> ( ( B != C )
=> ( ( member_val @ B @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A ) )
=> ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ A @ B )
!= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_phiArg__distinct__nodes) ).
thf(1141,plain,
! [A: g,B: val,C: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ B @ C )
=> ( ( B != C )
=> ( ( member_val @ B @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A ) )
=> ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ A @ B )
!= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(240,axiom,
~ ! [A: val] :
~ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ A @ phi_s ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062_092_060phi_062_H_O_AphiArg_Ag_A_092_060phi_062_H_A_092_060phi_062_092_060_094sub_062s_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(1023,plain,
~ ! [A: val] :
~ ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ A @ phi_s ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(179,axiom,
! [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
( ( ~ ( finite79836624et_val @ ( sup_su2005730907et_val @ A @ B ) ) )
= ( ~ ( finite79836624et_val @ A )
| ~ ( finite79836624et_val @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_infinite__Un) ).
thf(864,plain,
! [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
( ( ~ ( finite79836624et_val @ ( sup_su2005730907et_val @ A @ B ) ) )
= ( ~ ( finite79836624et_val @ A )
| ~ ( finite79836624et_val @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(94,axiom,
! [A: val > option_list_val] :
( ( ( dom_val_list_val @ A )
= bot_bot_set_val )
= ( A
= ( ^ [B: val] : none_list_val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_dom__eq__empty__conv) ).
thf(612,plain,
! [A: val > option_list_val] :
( ( ( dom_val_list_val @ A )
= bot_bot_set_val )
= ( A
= ( ^ [B: val] : none_list_val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(38,axiom,
! [A: list_P1811375021al_val] : ( finite759259600al_val @ ( set_Pr102746428al_val @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_List_Ofinite__set) ).
thf(446,plain,
! [A: list_P1811375021al_val] : ( finite759259600al_val @ ( set_Pr102746428al_val @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(79,axiom,
! [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
( ( finite79836624et_val @ A )
=> ( ( finite79836624et_val @ B )
=> ( finite79836624et_val @ ( sup_su2005730907et_val @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_finite__UnI) ).
thf(571,plain,
! [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
( ( finite79836624et_val @ A )
=> ( ( finite79836624et_val @ B )
=> ( finite79836624et_val @ ( sup_su2005730907et_val @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(56,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( ord_less_eq_set_val @ C @ B )
=> ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_le__supI) ).
thf(497,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( ord_less_eq_set_val @ C @ B )
=> ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(876,plain,
( sSA_CF262257161de_val
= ( ^ [A: g > list_node,B: g > node > set_val,C: g > produc1432036078de_val > option_list_val,D: g,E: val] : ( C @ D @ ( produc1470527136de_val @ ( sSA_CF551432799de_val @ A @ B @ C @ D @ E ) @ E ) ) ) ),
inference(lifteq,[status(thm)],[875]) ).
thf(43,axiom,
! [A: produc1432036078de_val,B: produc1432036078de_val > $o] :
( ( member313544709de_val @ A @ ( collec370342979de_val @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_mem__Collect__eq) ).
thf(465,plain,
! [A: produc1432036078de_val,B: produc1432036078de_val > $o] :
( ( member313544709de_val @ A @ ( collec370342979de_val @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(292,axiom,
! [A: g] : ( finite_finite_val @ ( sSA_CF655860150de_val @ alpha_n @ uses @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_vars__finite) ).
thf(1180,plain,
! [A: g] : ( finite_finite_val @ ( sSA_CF655860150de_val @ alpha_n @ uses @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(74,axiom,
! [A: set_set_val] :
( ( finite1265617511et_val @ A )
=> ( ( A != bot_bot_set_set_val )
=> ? [B: set_val] :
( ( member_set_val @ B @ A )
& ! [C: set_val] :
( ( member_set_val @ C @ A )
=> ( ( ord_less_eq_set_val @ B @ C )
=> ( B = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_finite__has__maximal) ).
thf(556,plain,
! [A: set_set_val] :
( ( finite1265617511et_val @ A )
=> ( ( A != bot_bot_set_set_val )
=> ? [B: set_val] :
( ( member_set_val @ B @ A )
& ! [C: set_val] :
( ( member_set_val @ C @ A )
=> ( ( ord_less_eq_set_val @ B @ C )
=> ( B = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(69,axiom,
! [A: set_val,B: set_set_val,C: set_set_val] :
( ( ord_le1742111550et_val @ ( insert_set_val @ A @ B ) @ C )
= ( ( member_set_val @ A @ C )
& ( ord_le1742111550et_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_insert__subset) ).
thf(539,plain,
! [A: set_val,B: set_set_val,C: set_set_val] :
( ( ord_le1742111550et_val @ ( insert_set_val @ A @ B ) @ C )
= ( ( member_set_val @ A @ C )
& ( ord_le1742111550et_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(113,axiom,
sSA_CF1899243830eD_val = sSA_CF1899243830eD_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_CFG__SSA__wf__base_Otrivial_Ocong) ).
thf(671,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(55,axiom,
! [A: list_P844977291de_val] : ( finite781217938de_val @ ( set_Pr434939430de_val @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_List_Ofinite__set) ).
thf(495,plain,
! [A: list_P844977291de_val] : ( finite781217938de_val @ ( set_Pr434939430de_val @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(306,axiom,
! [A: val,B: set_val,C: set_val] :
( ( ~ ( member_val @ A @ B )
=> ( member_val @ A @ C ) )
=> ( member_val @ A @ ( sup_sup_set_val @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_UnCI) ).
thf(1216,plain,
! [A: val,B: set_val,C: set_val] :
( ( ~ ( member_val @ A @ B )
=> ( member_val @ A @ C ) )
=> ( member_val @ A @ ( sup_sup_set_val @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(171,axiom,
! [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( sup_sup_set_val @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_sup_Oabsorb1) ).
thf(844,plain,
! [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( sup_sup_set_val @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(322,axiom,
( sSA_CF794421325de_val
= ( ^ [A: g > list_node,B: g > node > set_val,C: g > node > set_val,D: g > produc1432036078de_val > option_list_val,E: g,F: val] :
( ? [G: node,H: val] :
( ( F = H )
& ( member_node @ G @ ( set_node2 @ ( A @ E ) ) )
& ( member_val @ H @ ( C @ E @ G ) ) )
| ? [G: val,H: val] :
( ( F = H )
& ( sSA_CF794421325de_val @ A @ B @ C @ D @ E @ G )
& ( sSA_CF1252180629de_val @ A @ B @ D @ E @ G @ H ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_CFG__SSA__wf__base_OliveVal_Osimps) ).
thf(1276,plain,
( sSA_CF794421325de_val
= ( ^ [A: g > list_node,B: g > node > set_val,C: g > node > set_val,D: g > produc1432036078de_val > option_list_val,E: g,F: val] :
( ? [G: node,H: val] :
( ( F = H )
& ( member_node @ G @ ( set_node2 @ ( A @ E ) ) )
& ( member_val @ H @ ( C @ E @ G ) ) )
| ? [G: val,H: val] :
( ( F = H )
& ( sSA_CF794421325de_val @ A @ B @ C @ D @ E @ G )
& ( sSA_CF1252180629de_val @ A @ B @ D @ E @ G @ H ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(316,axiom,
! [A: node,B: g,C: val] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_val @ C @ ( sSA_CF139593942de_val @ defs @ phis @ B @ A ) )
=> ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ B @ C )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_defNode__eq) ).
thf(1253,plain,
! [A: node,B: g,C: val] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_val @ C @ ( sSA_CF139593942de_val @ defs @ phis @ B @ A ) )
=> ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ B @ C )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(218,axiom,
! [A: set_val,B: set_val] :
( ( finite_finite_val @ ( sup_sup_set_val @ A @ B ) )
= ( ( finite_finite_val @ A )
& ( finite_finite_val @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_finite__Un) ).
thf(963,plain,
! [A: set_val,B: set_val] :
( ( finite_finite_val @ ( sup_sup_set_val @ A @ B ) )
= ( ( finite_finite_val @ A )
& ( finite_finite_val @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(101,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_set_val @ A @ C )
=> ~ ( ord_less_eq_set_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_le__supE) ).
thf(632,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_set_val @ A @ C )
=> ~ ( ord_less_eq_set_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(340,axiom,
( sSA_CF1899243830eD_val
= ( ^ [A: g > list_node,B: g > node > list_P561207620_edgeD,C: g > node > set_val,D: g > node > set_val,E: g > produc1432036078de_val > option_list_val,F: g,G: val] :
? [H: val] :
( ( member_val @ H @ ( sSA_CF1517915011eD_val @ A @ B @ C @ D @ E @ F ) )
& ( sSA_CF1909049442de_val @ A @ C @ E @ F @ G @ H ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_CFG__SSA__wf__base_Otrivial__def) ).
thf(1341,plain,
( sSA_CF1899243830eD_val
= ( ^ [A: g > list_node,B: g > node > list_P561207620_edgeD,C: g > node > set_val,D: g > node > set_val,E: g > produc1432036078de_val > option_list_val,F: g,G: val] :
? [H: val] :
( ( member_val @ H @ ( sSA_CF1517915011eD_val @ A @ B @ C @ D @ E @ F ) )
& ( sSA_CF1909049442de_val @ A @ C @ E @ F @ G @ H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(896,plain,
( sSA_CF178745443eD_val
= ( ^ [A: g > list_node,B: g > node > list_P561207620_edgeD,C: g > node > set_val,D: g > produc1432036078de_val > option_list_val,E: g,F: node] : ( sup_sup_set_val @ ( C @ E @ F ) @ ( sSA_CF848637139eD_val @ A @ B @ D @ E @ F ) ) ) ),
inference(lifteq,[status(thm)],[895]) ).
thf(140,axiom,
sSA_CF1909049442de_val = sSA_CF1909049442de_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_CFG__SSA__wf__base_OisTrivialPhi_Ocong) ).
thf(748,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(134,axiom,
! [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ~ ( finite_finite_val @ A )
=> ~ ( finite_finite_val @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_infinite__super) ).
thf(731,plain,
! [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ~ ( finite_finite_val @ A )
=> ~ ( finite_finite_val @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(28,axiom,
! [A: produc1324971431et_val,B: set_Pr1311924359et_val,C: set_Pr1311924359et_val] :
( ( ~ ( member1711426256et_val @ A @ B )
=> ( member1711426256et_val @ A @ C ) )
=> ( member1711426256et_val @ A @ ( sup_su2005730907et_val @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_UnCI) ).
thf(418,plain,
! [A: produc1324971431et_val,B: set_Pr1311924359et_val,C: set_Pr1311924359et_val] :
( ( ~ ( member1711426256et_val @ A @ B )
=> ( member1711426256et_val @ A @ C ) )
=> ( member1711426256et_val @ A @ ( sup_su2005730907et_val @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(78,axiom,
! [A: list_node,B: set_node] :
( ( ord_less_eq_set_node @ ( set_node2 @ A ) @ B )
= ( ! [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
=> ( member_node @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_subset__code_I1_J) ).
thf(568,plain,
! [A: list_node,B: set_node] :
( ( ord_less_eq_set_node @ ( set_node2 @ A ) @ B )
= ( ! [C: node] :
( ( member_node @ C @ ( set_node2 @ A ) )
=> ( member_node @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(199,axiom,
! [A: node,B: val,C: list_node,D: list_val] :
( ( member313544709de_val @ ( produc1470527136de_val @ A @ B ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ C @ D ) ) )
=> ( member_node @ A @ ( set_node2 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_set__zip__leftD) ).
thf(914,plain,
! [A: node,B: val,C: list_node,D: list_val] :
( ( member313544709de_val @ ( produc1470527136de_val @ A @ B ) @ ( set_Pr1085970585de_val @ ( zip_node_val @ C @ D ) ) )
=> ( member_node @ A @ ( set_node2 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(33,axiom,
! [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val,C: produc1324971431et_val] :
( ( ord_le299366439et_val @ A @ B )
=> ( ( member1711426256et_val @ C @ A )
=> ( member1711426256et_val @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_in__mono) ).
thf(433,plain,
! [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val,C: produc1324971431et_val] :
( ( ord_le299366439et_val @ A @ B )
=> ( ( member1711426256et_val @ C @ A )
=> ( member1711426256et_val @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(329,axiom,
! [A: g > list_node,B: g > node > set_val,C: g > node > set_val,D: g > produc1432036078de_val > option_list_val,E: g,F: val,G: val > $o] :
( ( sSA_CF794421325de_val @ A @ B @ C @ D @ E @ F )
=> ( ! [H: node,I: val] :
( ( member_node @ H @ ( set_node2 @ ( A @ E ) ) )
=> ( ( member_val @ I @ ( C @ E @ H ) )
=> ( G @ I ) ) )
=> ( ! [H: val,I: val] :
( ( sSA_CF794421325de_val @ A @ B @ C @ D @ E @ H )
=> ( ( G @ H )
=> ( ( sSA_CF1252180629de_val @ A @ B @ D @ E @ H @ I )
=> ( G @ I ) ) ) )
=> ( G @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_CFG__SSA__wf__base_OliveVal_Oinducts) ).
thf(1294,plain,
! [A: g > list_node,B: g > node > set_val,C: g > node > set_val,D: g > produc1432036078de_val > option_list_val,E: g,F: val,G: val > $o] :
( ( sSA_CF794421325de_val @ A @ B @ C @ D @ E @ F )
=> ( ! [H: node,I: val] :
( ( member_node @ H @ ( set_node2 @ ( A @ E ) ) )
=> ( ( member_val @ I @ ( C @ E @ H ) )
=> ( G @ I ) ) )
=> ( ! [H: val,I: val] :
( ( sSA_CF794421325de_val @ A @ B @ C @ D @ E @ H )
=> ( ( G @ H )
=> ( ( sSA_CF1252180629de_val @ A @ B @ D @ E @ H @ I )
=> ( G @ I ) ) ) )
=> ( G @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(330,axiom,
! [A: g] :
( ( sSA_CF1660885746eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A )
= ( ? [B: val] :
( ( member_val @ B @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A ) )
& ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_redundant__def) ).
thf(1308,plain,
! [A: g] :
( ( sSA_CF1660885746eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A )
= ( ? [B: val] :
( ( member_val @ B @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A ) )
& ( sSA_CF1899243830eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(297,axiom,
! [A: g,B: set_val] : ( finite79836624et_val @ ( irredu893086079de_val @ alpha_n @ defs @ phis @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_condensation__finite) ).
thf(1193,plain,
! [A: g,B: set_val] : ( finite79836624et_val @ ( irredu893086079de_val @ alpha_n @ defs @ phis @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(259,axiom,
! [A: val,B: node,C: list_val,D: list_node] :
( ( member828457417l_node @ ( produc1074923692l_node @ A @ B ) @ ( set_Pr1600883293l_node @ ( zip_val_node @ C @ D ) ) )
=> ~ ( ( member_val @ A @ ( set_val2 @ C ) )
=> ~ ( member_node @ B @ ( set_node2 @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_in__set__zipE) ).
thf(1077,plain,
! [A: val,B: node,C: list_val,D: list_node] :
( ( member828457417l_node @ ( produc1074923692l_node @ A @ B ) @ ( set_Pr1600883293l_node @ ( zip_val_node @ C @ D ) ) )
=> ~ ( ( member_val @ A @ ( set_val2 @ C ) )
=> ~ ( member_node @ B @ ( set_node2 @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(72,axiom,
! [A: set_val,B: set_val,C: set_val,D: set_val] :
( ( A
= ( sup_sup_set_val @ B @ C ) )
=> ( ( sup_sup_set_val @ D @ A )
= ( sup_sup_set_val @ B @ ( sup_sup_set_val @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_boolean__algebra__cancel_Osup2) ).
thf(549,plain,
! [A: set_val,B: set_val,C: set_val,D: set_val] :
( ( A
= ( sup_sup_set_val @ B @ C ) )
=> ( ( sup_sup_set_val @ D @ A )
= ( sup_sup_set_val @ B @ ( sup_sup_set_val @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(68,axiom,
! [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
( ~ ( finite79836624et_val @ A )
=> ~ ( finite79836624et_val @ ( sup_su2005730907et_val @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_Un__infinite) ).
thf(536,plain,
! [A: set_Pr1311924359et_val,B: set_Pr1311924359et_val] :
( ~ ( finite79836624et_val @ A )
=> ~ ( finite79836624et_val @ ( sup_su2005730907et_val @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(247,axiom,
sSA_CF1517915011eD_val = sSA_CF1517915011eD_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_CFG__SSA__base_OallVars_Ocong) ).
thf(1045,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(127,axiom,
sSA_CF1252180629de_val = sSA_CF1252180629de_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_CFG__SSA__wf__base_OphiArg_Ocong) ).
thf(716,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(159,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C ) )
= ( sup_sup_set_val @ B @ ( sup_sup_set_val @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_sup_Oleft__commute) ).
thf(800,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C ) )
= ( sup_sup_set_val @ B @ ( sup_sup_set_val @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(142,axiom,
! [A: set_val,B: set_val] :
( ( finite_finite_val @ A )
=> ( ( finite_finite_val @ B )
=> ( finite_finite_val @ ( sup_sup_set_val @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_finite__UnI) ).
thf(752,plain,
! [A: set_val,B: set_val] :
( ( finite_finite_val @ A )
=> ( ( finite_finite_val @ B )
=> ( finite_finite_val @ ( sup_sup_set_val @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(447,plain,
! [A: list_P1811375021al_val] : ( finite759259600al_val @ ( set_Pr102746428al_val @ A ) ),
inference(cnf,[status(esa)],[446]) ).
thf(25,axiom,
! [A: set_node,B: set_node,C: node] :
( ( ord_less_eq_set_node @ A @ B )
=> ( ( member_node @ C @ A )
=> ( member_node @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_subsetD) ).
thf(410,plain,
! [A: set_node,B: set_node,C: node] :
( ( ord_less_eq_set_node @ A @ B )
=> ( ( member_node @ C @ A )
=> ( member_node @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(155,axiom,
! [A: list_P1820443774de_val] : ( finite2056463621de_val @ ( set_Pr1085970585de_val @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_List_Ofinite__set) ).
thf(790,plain,
! [A: list_P1820443774de_val] : ( finite2056463621de_val @ ( set_Pr1085970585de_val @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(180,axiom,
! [A: set_val,B: set_val] :
( ( sup_sup_set_val @ ( sup_sup_set_val @ A @ B ) @ B )
= ( sup_sup_set_val @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_sup_Oright__idem) ).
thf(867,plain,
! [A: set_val,B: set_val] :
( ( sup_sup_set_val @ ( sup_sup_set_val @ A @ B ) @ B )
= ( sup_sup_set_val @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(212,axiom,
irredu224829488eD_val = irredu224829488eD_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_CFG__SSA__Transformed_Oredundant__set_Ocong) ).
thf(950,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(168,axiom,
! [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( sup_sup_set_val @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_sup__absorb1) ).
thf(835,plain,
! [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( sup_sup_set_val @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(332,axiom,
! [A: g,B: node,C: val,D: list_val,E: val] :
( ( ( phis @ A @ ( produc1470527136de_val @ B @ C ) )
= ( some_list_val @ D ) )
=> ( ( member_val @ E @ ( set_val2 @ D ) )
=> ( ( var2 @ A @ E )
= ( var2 @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_phis__same__var) ).
thf(1314,plain,
! [A: g,B: node,C: val,D: list_val,E: val] :
( ( ( phis @ A @ ( produc1470527136de_val @ B @ C ) )
= ( some_list_val @ D ) )
=> ( ( member_val @ E @ ( set_val2 @ D ) )
=> ( ( var2 @ A @ E )
= ( var2 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(59,axiom,
! [A: set_val,B: set_val] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_val @ A @ B )
=> ~ ( ord_less_eq_set_val @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_equalityE) ).
thf(506,plain,
! [A: set_val,B: set_val] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_val @ A @ B )
=> ~ ( ord_less_eq_set_val @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(165,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( sup_sup_set_val @ ( sup_sup_set_val @ A @ B ) @ C )
= ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_sup__assoc) ).
thf(828,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( sup_sup_set_val @ ( sup_sup_set_val @ A @ B ) @ C )
= ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(255,axiom,
! [A: val,B: val,C: list_val,D: list_val] :
( ( member1680438992al_val @ ( product_Pair_val_val @ A @ B ) @ ( set_Pr102746428al_val @ ( zip_val_val @ C @ D ) ) )
=> ~ ( ( member_val @ A @ ( set_val2 @ C ) )
=> ~ ( member_val @ B @ ( set_val2 @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_in__set__zipE) ).
thf(1065,plain,
! [A: val,B: val,C: list_val,D: list_val] :
( ( member1680438992al_val @ ( product_Pair_val_val @ A @ B ) @ ( set_Pr102746428al_val @ ( zip_val_val @ C @ D ) ) )
=> ~ ( ( member_val @ A @ ( set_val2 @ C ) )
=> ~ ( member_val @ B @ ( set_val2 @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(287,axiom,
! [A: g,B: set_val] :
( ( irredu224829488eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B )
= ( ( B != bot_bot_set_val )
& ( ord_less_eq_set_val @ B @ ( dom_val_list_val @ ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A ) ) )
& ? [C: val] :
( ( member_val @ C @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A ) )
& ! [D: val] :
( ( member_val @ D @ B )
=> ! [E: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ D @ E )
=> ( member_val @ E @ ( sup_sup_set_val @ B @ ( insert_val @ C @ bot_bot_set_val ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_redundant__set__def) ).
thf(1165,plain,
! [A: g,B: set_val] :
( ( irredu224829488eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A @ B )
= ( ( B != bot_bot_set_val )
& ( ord_less_eq_set_val @ B @ ( dom_val_list_val @ ( sSA_CF262257161de_val @ alpha_n @ defs @ phis @ A ) ) )
& ? [C: val] :
( ( member_val @ C @ ( sSA_CF1517915011eD_val @ alpha_n @ inEdges @ defs @ uses @ phis @ A ) )
& ! [D: val] :
( ( member_val @ D @ B )
=> ! [E: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ D @ E )
=> ( member_val @ E @ ( sup_sup_set_val @ B @ ( insert_val @ C @ bot_bot_set_val ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(342,axiom,
! [A: g,B: val,C: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ B @ C )
=> ( ( var2 @ A @ C )
= ( var2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_phiArg__same__var) ).
thf(1346,plain,
! [A: g,B: val,C: val] :
( ( sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ A @ B @ C )
=> ( ( var2 @ A @ C )
= ( var2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(358,plain,
! [B: set_set_val,A: set_set_val] :
( ~ ( member_set_val @ ( sk1 @ B @ A ) @ B )
| ( ord_le1742111550et_val @ A @ B ) ),
inference(cnf,[status(esa)],[356]) ).
thf(162,axiom,
sSA_CF551432799de_val = sSA_CF551432799de_val,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_CFG__SSA__wf__base_OdefNode_Ocong) ).
thf(807,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(290,axiom,
! [A: set_val,B: set_val,C: val > $o] :
( ( ? [D: val] :
( ( member_val @ D @ ( sup_sup_set_val @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: val] :
( ( member_val @ D @ A )
& ( C @ D ) )
| ? [D: val] :
( ( member_val @ D @ B )
& ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_bex__Un) ).
thf(1172,plain,
! [A: set_val,B: set_val,C: val > $o] :
( ( ? [D: val] :
( ( member_val @ D @ ( sup_sup_set_val @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: val] :
( ( member_val @ D @ A )
& ( C @ D ) )
| ? [D: val] :
( ( member_val @ D @ B )
& ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(192,axiom,
! [A: set_val] :
( ( sup_sup_set_val @ A @ bot_bot_set_val )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_Un__empty__right) ).
thf(897,plain,
! [A: set_val] :
( ( sup_sup_set_val @ A @ bot_bot_set_val )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(47,axiom,
! [A: node,B: set_node,C: set_node] :
( ( member_node @ A @ ( sup_sup_set_node @ B @ C ) )
= ( ( member_node @ A @ B )
| ( member_node @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_Un__iff) ).
thf(474,plain,
! [A: node,B: set_node,C: set_node] :
( ( member_node @ A @ ( sup_sup_set_node @ B @ C ) )
= ( ( member_node @ A @ B )
| ( member_node @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(327,axiom,
! [A: node,B: g > list_node,C: g,D: val,E: g > node > set_val,F: g > node > set_val,G: g > produc1432036078de_val > option_list_val] :
( ( member_node @ A @ ( set_node2 @ ( B @ C ) ) )
=> ( ( member_val @ D @ ( E @ C @ A ) )
=> ( sSA_CF794421325de_val @ B @ F @ E @ G @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_CFG__SSA__wf__base_OliveSimple) ).
thf(1288,plain,
! [A: node,B: g > list_node,C: g,D: val,E: g > node > set_val,F: g > node > set_val,G: g > produc1432036078de_val > option_list_val] :
( ( member_node @ A @ ( set_node2 @ ( B @ C ) ) )
=> ( ( member_val @ D @ ( E @ C @ A ) )
=> ( sSA_CF794421325de_val @ B @ F @ E @ G @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(21,axiom,
! [A: produc1432036078de_val,B: set_Pr699757092de_val,C: set_Pr699757092de_val] :
( ( member313544709de_val @ A @ B )
=> ( member313544709de_val @ A @ ( sup_su2138939728de_val @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_UnI2) ).
thf(400,plain,
! [A: produc1432036078de_val,B: set_Pr699757092de_val,C: set_Pr699757092de_val] :
( ( member313544709de_val @ A @ B )
=> ( member313544709de_val @ A @ ( sup_su2138939728de_val @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(217,axiom,
! [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( sup_sup_set_val @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_sup_Oabsorb2) ).
thf(960,plain,
! [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( sup_sup_set_val @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(102,axiom,
! [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( sup_sup_set_val @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_sup__absorb2) ).
thf(635,plain,
! [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( sup_sup_set_val @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(187,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( sup_sup_set_val @ ( sup_sup_set_val @ A @ B ) @ C )
= ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_Un__assoc) ).
thf(886,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( sup_sup_set_val @ ( sup_sup_set_val @ A @ B ) @ C )
= ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(27,axiom,
! [A: set_node,B: set_node,C: node] :
( ( ord_less_eq_set_node @ A @ B )
=> ( ( member_node @ C @ A )
=> ( member_node @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_in__mono) ).
thf(415,plain,
! [A: set_node,B: set_node,C: node] :
( ( ord_less_eq_set_node @ A @ B )
=> ( ( member_node @ C @ A )
=> ( member_node @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(133,axiom,
! [A: set_val,B: set_val] :
( ( bot_bot_set_val
= ( sup_sup_set_val @ A @ B ) )
= ( ( A = bot_bot_set_val )
& ( B = bot_bot_set_val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_bot__eq__sup__iff) ).
thf(728,plain,
! [A: set_val,B: set_val] :
( ( bot_bot_set_val
= ( sup_sup_set_val @ A @ B ) )
= ( ( A = bot_bot_set_val )
& ( B = bot_bot_set_val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(344,axiom,
( ( var2 @ g2 @ phi )
= ( var2 @ g2 @ phi_s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_vars__eq) ).
thf(1352,plain,
( ( var2 @ g2 @ phi )
= ( var2 @ g2 @ phi_s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(320,axiom,
! [A: set_val,B: val] :
( ( finite_finite_val @ A )
=> ( ( member_val @ B @ A )
=> ? [C: val] :
( ( member_val @ C @ A )
& ( ord_less_eq_val @ C @ B )
& ! [D: val] :
( ( member_val @ D @ A )
=> ( ( ord_less_eq_val @ D @ C )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_finite__has__minimal2) ).
thf(1268,plain,
! [A: set_val,B: val] :
( ( finite_finite_val @ A )
=> ( ( member_val @ B @ A )
=> ? [C: val] :
( ( member_val @ C @ A )
& ( ord_less_eq_val @ C @ B )
& ! [D: val] :
( ( member_val @ D @ A )
=> ( ( ord_less_eq_val @ D @ C )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(31,axiom,
! [A: produc1432036078de_val,B: set_Pr699757092de_val,C: set_Pr699757092de_val] :
( ( member313544709de_val @ A @ B )
=> ( member313544709de_val @ A @ ( sup_su2138939728de_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_UnI1) ).
thf(427,plain,
! [A: produc1432036078de_val,B: set_Pr699757092de_val,C: set_Pr699757092de_val] :
( ( member313544709de_val @ A @ B )
=> ( member313544709de_val @ A @ ( sup_su2138939728de_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(89,axiom,
! [A: produc1432036078de_val > option_list_val] :
( ( ( dom_Pr729677986st_val @ A )
= bot_bo404898488de_val )
= ( A
= ( ^ [B: produc1432036078de_val] : none_list_val ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_dom__eq__empty__conv) ).
thf(596,plain,
! [A: produc1432036078de_val > option_list_val] :
( ( ( dom_Pr729677986st_val @ A )
= bot_bo404898488de_val )
= ( A
= ( ^ [B: produc1432036078de_val] : none_list_val ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(239,axiom,
! [A: node,B: g,C: node,D: val] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_val @ D @ ( sSA_CF139593942de_val @ defs @ phis @ B @ A ) )
=> ( ( member_val @ D @ ( sSA_CF139593942de_val @ defs @ phis @ B @ C ) )
=> ( A = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_allDefs__disjoint_H) ).
thf(1019,plain,
! [A: node,B: g,C: node,D: val] :
( ( member_node @ A @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_node @ C @ ( set_node2 @ ( alpha_n @ B ) ) )
=> ( ( member_val @ D @ ( sSA_CF139593942de_val @ defs @ phis @ B @ A ) )
=> ( ( member_val @ D @ ( sSA_CF139593942de_val @ defs @ phis @ B @ C ) )
=> ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(65,axiom,
! [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( sup_sup_set_val @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_Un__absorb2) ).
thf(528,plain,
! [A: set_val,B: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( sup_sup_set_val @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(197,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( ord_less_eq_set_val @ C @ B )
=> ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_sup__least) ).
thf(908,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( ord_less_eq_set_val @ C @ B )
=> ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(131,axiom,
! [A: set_Pr699757092de_val] :
( ( finite2056463621de_val @ A )
=> ? [B: list_P1820443774de_val] :
( ( set_Pr1085970585de_val @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_finite__list) ).
thf(723,plain,
! [A: set_Pr699757092de_val] :
( ( finite2056463621de_val @ A )
=> ? [B: list_P1820443774de_val] :
( ( set_Pr1085970585de_val @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(173,axiom,
! [A: set_val,B: set_set_val,C: set_set_val] :
( ( member_set_val @ A @ ( sup_sup_set_set_val @ B @ C ) )
=> ( ~ ( member_set_val @ A @ B )
=> ( member_set_val @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_UnE) ).
thf(850,plain,
! [A: set_val,B: set_set_val,C: set_set_val] :
( ( member_set_val @ A @ ( sup_sup_set_set_val @ B @ C ) )
=> ( ~ ( member_set_val @ A @ B )
=> ( member_set_val @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(119,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_sup_OcoboundedI1) ).
thf(691,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(36,axiom,
! [A: set_val,B: set_val] :
( ( ~ ( finite_finite_val @ ( sup_sup_set_val @ A @ B ) ) )
= ( ~ ( finite_finite_val @ A )
| ~ ( finite_finite_val @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_infinite__Un) ).
thf(442,plain,
! [A: set_val,B: set_val] :
( ( ~ ( finite_finite_val @ ( sup_sup_set_val @ A @ B ) ) )
= ( ~ ( finite_finite_val @ A )
| ~ ( finite_finite_val @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(871,plain,
( sup_sup_set_val
= ( ^ [A: set_val,B: set_val] : ( sup_sup_set_val @ B @ A ) ) ),
inference(lifteq,[status(thm)],[870]) ).
thf(264,axiom,
( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_s )
= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14__092_060open_062_092_060not_062_AdefNode_Ag_A_092_060phi_062_092_060_094sub_062s_A_092_060noteq_062_AdefNode_Ag_As_092_060close_062) ).
thf(1093,plain,
( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_s )
= ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(98,axiom,
! [A: set_val,B: set_val] : ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_Un__upper2) ).
thf(624,plain,
! [A: set_val,B: set_val] : ( ord_less_eq_set_val @ A @ ( sup_sup_set_val @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(346,axiom,
! [A: val,B: set_val,C: set_val] :
( ( member_val @ A @ B )
=> ( member_val @ A @ ( sup_sup_set_val @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_UnI2) ).
thf(1357,plain,
! [A: val,B: set_val,C: set_val] :
( ( member_val @ A @ B )
=> ( member_val @ A @ ( sup_sup_set_val @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(41,axiom,
! [A: set_val,B: set_val,C: set_val,D: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( ord_less_eq_set_val @ C @ D )
=> ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ C ) @ ( sup_sup_set_val @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_sup__mono) ).
thf(459,plain,
! [A: set_val,B: set_val,C: set_val,D: set_val] :
( ( ord_less_eq_set_val @ A @ B )
=> ( ( ord_less_eq_set_val @ C @ D )
=> ( ord_less_eq_set_val @ ( sup_sup_set_val @ A @ C ) @ ( sup_sup_set_val @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(225,axiom,
! [A: set_set_val] :
( ( collect_set_val
@ ^ [B: set_val] : ( member_set_val @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Collect__mem__eq) ).
thf(982,plain,
! [A: set_set_val] :
( ( collect_set_val
@ ^ [B: set_val] : ( member_set_val @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(234,axiom,
! [A: set_val,B: set_val,C: set_val] :
( ( sup_sup_set_val @ ( sup_sup_set_val @ A @ B ) @ C )
= ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_sup_Oassoc) ).
thf(1004,plain,
! [A: set_val,B: set_val,C: set_val] :
( ( sup_sup_set_val @ ( sup_sup_set_val @ A @ B ) @ C )
= ( sup_sup_set_val @ A @ ( sup_sup_set_val @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(51,axiom,
! [A: set_Pr1311924359et_val] :
( ( finite79836624et_val @ A )
=> ? [B: list_P2089461677et_val] :
( ( set_Pr284769596et_val @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_finite__list) ).
thf(486,plain,
! [A: set_Pr1311924359et_val] :
( ( finite79836624et_val @ A )
=> ? [B: list_P2089461677et_val] :
( ( set_Pr284769596et_val @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(160,axiom,
! [A: set_val] :
( ( sup_sup_set_val @ bot_bot_set_val @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_sup__bot__left) ).
thf(803,plain,
! [A: set_val] :
( ( sup_sup_set_val @ bot_bot_set_val @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(334,axiom,
! [A: g] : ( finite2056463621de_val @ ( dom_Pr729677986st_val @ ( phis @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_phis__finite) ).
thf(1320,plain,
! [A: g] : ( finite2056463621de_val @ ( dom_Pr729677986st_val @ ( phis @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(110,axiom,
! [A: option_list_val > $o,B: option_list_val] :
( ( A @ none_list_val )
=> ( ! [C: list_val] : ( A @ ( some_list_val @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_option_Oinducts) ).
thf(659,plain,
! [A: option_list_val > $o,B: option_list_val] :
( ( A @ none_list_val )
=> ( ! [C: list_val] : ( A @ ( some_list_val @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(143,axiom,
! [A: produc1432036078de_val,B: set_Pr699757092de_val] :
( ( finite2056463621de_val @ ( insert869443870de_val @ A @ B ) )
= ( finite2056463621de_val @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_finite__insert) ).
thf(755,plain,
! [A: produc1432036078de_val,B: set_Pr699757092de_val] :
( ( finite2056463621de_val @ ( insert869443870de_val @ A @ B ) )
= ( finite2056463621de_val @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(496,plain,
! [A: list_P844977291de_val] : ( finite781217938de_val @ ( set_Pr434939430de_val @ A ) ),
inference(cnf,[status(esa)],[495]) ).
thf(124,axiom,
! [A: set_val] : ( ord_less_eq_set_val @ bot_bot_set_val @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_empty__subsetI) ).
thf(708,plain,
! [A: set_val] : ( ord_less_eq_set_val @ bot_bot_set_val @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(208,axiom,
! [A: set_node] :
( ( collect_node
@ ^ [B: node] : ( member_node @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Collect__mem__eq) ).
thf(940,plain,
! [A: set_node] :
( ( collect_node
@ ^ [B: node] : ( member_node @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(3911,plain,
$false,
inference(cvc4,[status(thm)],[892,1322,1337,629,1168,893,352,365,1190,1083,468,1211,1158,1068,861,408,977,385,384,500,797,1260,1354,930,1095,1001,1127,782,841,1046,1366,436,651,389,1409,719,785,1264,1279,542,587,838,917,702,357,1191,1059,1132,902,1247,969,1013,448,638,853,421,870,924,492,591,1109,574,806,1051,480,1334,646,485,834,353,966,877,1119,998,988,1405,1201,602,766,397,687,1074,1206,380,439,761,366,714,1311,534,1274,957,1091,1123,561,392,424,788,1238,825,1343,1032,852,665,889,493,1027,1281,456,974,1012,847,566,484,583,522,682,1195,1291,710,1402,1360,615,1328,1121,1064,1227,388,783,989,519,742,697,1234,980,403,1138,356,471,1160,933,554,1182,489,1155,1016,1207,590,679,1039,985,654,1060,911,721,1246,779,371,1150,1249,503,605,1318,792,938,360,657,1054,1170,1071,1187,773,1278,618,1219,856,745,1374,733,513,1146,430,584,1125,958,545,413,562,904,1007,694,875,577,445,1371,919,947,1224,672,764,1209,831,736,1349,362,1144,599,1175,900,406,784,1117,377,996,880,649,1043,477,387,1080,758,535,609,594,621,483,1325,1149,626,943,668,462,1112,858,367,1162,726,1029,895,883,394,563,1364,922,658,1198,1396,1213,768,1034,675,795,548,1134,749,516,355,1049,531,944,927,374,525,1003,580,640,872,705,971,954,739,1230,993,370,717,359,1130,1285,907,1085,470,951,808,1404,1257,1141,1023,864,612,446,571,497,876,465,1180,556,539,671,495,1216,844,1276,1253,963,1062,632,1244,1341,896,748,731,418,568,914,433,1294,1308,1193,1077,383,549,536,1045,716,800,752,447,410,1148,790,867,950,835,1314,506,1056,828,1065,1165,1346,358,807,1172,897,474,1288,400,960,635,886,415,728,1352,1268,427,596,1019,528,908,723,850,691,442,871,369,1093,624,1357,459,982,1004,486,803,1320,1009,659,755,1204,496,708,469,940]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP083^1 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n018.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 14:38:24 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.00/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.07/1.19 % [INFO] Parsing done (303ms).
% 2.07/1.20 % [INFO] Running in sequential loop mode.
% 3.04/1.47 % [INFO] eprover registered as external prover.
% 3.04/1.47 % [INFO] cvc4 registered as external prover.
% 3.04/1.48 % [INFO] Scanning for conjecture ...
% 3.23/1.58 % [INFO] Found a conjecture and 353 axioms. Running axiom selection ...
% 3.74/1.76 % [INFO] Axiom selection finished. Selected 349 axioms (removed 4 axioms).
% 4.56/1.96 % [INFO] Problem is higher-order (TPTP THF).
% 4.56/1.98 % [INFO] Type checking passed.
% 4.56/1.98 % [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 ...
% 76.87/33.41 % External prover 'cvc4' found a proof!
% 76.87/33.41 % [INFO] Killing All external provers ...
% 76.87/33.42 % Time passed: 32891ms (effective reasoning time: 32210ms)
% 76.87/33.42 % 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)>
% 76.87/33.42 % Axioms used in derivation (349): fact_79_CFG__SSA__wf__base_OliveVal_Ocong, fact_39_List_Ofinite__set, fact_344_phis__finite, fact_120_CFG__SSA__base_OallUses__def, fact_91_CFG__SSA__wf__base_OliveVal_Osimps, fact_8_trivial__in__allVars, fact_37_List_Ofinite__set, fact_28_defNode_I1_J, fact_192_Ex__condensation__leaf, fact_266_in__mono, fact_269_in__mono, fact_340_redundant__set__def, fact_148_zip__same, fact_283_Un__left__absorb, fact_298_UnI1, fact_257_subset__eq, fact_73_CFG__SSA__base_OphiDefs_Ocong, fact_46_phiDefs__finite, fact_53_mem__Collect__eq, fact_98_allDefs__def, fact_71_pruned__def, fact_149__C1_C, fact_156_finite__has__maximal2, fact_245_Collect__mono, fact_217_subset__empty, fact_317_sup__unique, fact_235_finite_OemptyI, fact_161_subset__code_I1_J, fact_65_phiArg__same__var, fact_288_bex__Un, fact_115_finite__UnI, fact_224_sup__bot_Oleft__neutral, fact_6_phiArg__in__allVars, fact_193_Un__subset__iff, fact_331_inf__sup__ord_I4_J, fact_303_UnE, fact_116_finite__UnI, fact_89_CFG__SSA__wf__base_OlivePhi, fact_211_Un__iff, fact_311_sup_OboundedI, fact_138_scc__in__P, fact_170_finite__subset, fact_251_subset__iff, fact_337_Un__upper1, fact_343_dom__eq__empty__conv, fact_24_liveVal_Osimps, fact_85_finite__list, fact_1_False, fact_228_old_Osuccessors__predecessors, fact_242_Collect__mono__iff, fact_29_uses__finite, fact_335_Un__absorb1, fact_142_option_Oinject, fact_220_sup__bot__right, fact_169_finite__subset, fact_249_subset__iff, fact_313_sup__absorb2, fact_323_sup_Omono, fact_281_inf__sup__aci_I8_J, fact_49_CFG__SSA__wf__base_Oredundant__def, fact_236_finite_OemptyI, fact_11_uses__in__allUses, fact_191_option_Odistinct_I1_J, fact_198_subsetI, fact_207_Un__iff, fact_122_condensation__acyclic, fact_259_equalityE, fact_292_UnI2, fact_92_CFG__SSA__wf__base_OliveVal_Ocases, fact_200_subsetI, fact_127_phis__disj_I2_J, fact_271_sup_Oleft__commute, fact_48_assms_I5_J, fact_72_CFG__SSA__base_OphiUses_Ocong, fact_264_subsetD, fact_55_mem__Collect__eq, fact_263_subsetD, fact_327_sup__ge1, fact_261_subsetD, fact_237_CFG__SSA__Transformed_Oredundant__scc_Ocong, fact_99_CFG__SSA__wf__base_Opruned__def, fact_26_liveVal_Ocases, fact_32_phiUses__in__allUses, fact_267_in__mono, fact_108_infinite__Un, fact_111_Un__infinite, fact_0_assms_I4_J, fact_332_subset__Un__eq, fact_182_set__zip__leftD, fact_12_redundant__def, fact_208_Un__iff, fact_131_phis__phi, fact_17_phiArg__distinct__nodes, fact_44_List_Ofinite__set, fact_233_infinite__imp__nonempty, fact_59_mem__Collect__eq, fact_109_infinite__Un, fact_61_Collect__mem__eq, fact_199_subsetI, fact_184_set__zip__rightD, fact_294_UnI1, fact_183_set__zip__rightD, fact_336_Un__upper2, fact_60_Collect__mem__eq, fact_4_assms_I2_J, fact_155_finite__has__maximal2, fact_158_subset__code_I1_J, fact_341_phi__no__closed__loop, fact_77_CFG__SSA__wf__base_OphiArg_Ocong, fact_272_sup__commute, fact_196_subset__antisym, fact_69_defNode__eq, fact_173_in__set__zipE, 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% 76.87/33.42 % No. of inferences in proof: 752
% 76.87/33.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 32891 ms resp. 32210 ms w/o parsing
% 77.70/33.61 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 77.70/33.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------