TSTP Solution File: ITP093^1 by Leo-III---1.7.10
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP093^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 07:47:45 EDT 2024
% Result : Theorem 16.27s 4.71s
% Output : Refutation 17.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 402
% Syntax : Number of formulae : 707 ( 189 unt; 99 typ; 0 def)
% Number of atoms : 2097 ( 400 equ; 30 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 5633 ( 160 ~; 46 |; 202 &;4162 @)
% ( 0 <=>;1063 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 32 ( 31 usr)
% Number of type conns : 422 ( 422 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 68 usr; 8 con; 0-3 aty)
% Number of variables : 1985 ( 286 ^1639 !; 60 ?;1985 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr1295299783od_a_a_type,type,
set_Pr1295299783od_a_a: $tType ).
thf(pair_p1593840546t_unit_type,type,
pair_p1593840546t_unit: $tType ).
thf(pair_p2041852168t_unit_type,type,
pair_p2041852168t_unit: $tType ).
thf(set_Pr1490359111at_nat_type,type,
set_Pr1490359111at_nat: $tType ).
thf(pair_p1765063010t_unit_type,type,
pair_p1765063010t_unit: $tType ).
thf(set_se958357159od_a_a_type,type,
set_se958357159od_a_a: $tType ).
thf(set_Pr1948701895od_a_a_type,type,
set_Pr1948701895od_a_a: $tType ).
thf(pair_p1914262621t_unit_type,type,
pair_p1914262621t_unit: $tType ).
thf(set_Pr1746169692at_nat_type,type,
set_Pr1746169692at_nat: $tType ).
thf(produc1572603623od_a_a_type,type,
produc1572603623od_a_a: $tType ).
thf(pair_p125712459t_unit_type,type,
pair_p125712459t_unit: $tType ).
thf(set_Pr7688842at_nat_type,type,
set_Pr7688842at_nat: $tType ).
thf(set_Pr894832732_a_nat_type,type,
set_Pr894832732_a_nat: $tType ).
thf(set_Pr339609346od_a_a_type,type,
set_Pr339609346od_a_a: $tType ).
thf(set_Pr681306928od_a_a_type,type,
set_Pr681306928od_a_a: $tType ).
thf(set_Pr1689873822_a_a_a_type,type,
set_Pr1689873822_a_a_a: $tType ).
thf(set_se1612935105at_nat_type,type,
set_se1612935105at_nat: $tType ).
thf(set_se1596668135od_a_a_type,type,
set_se1596668135od_a_a: $tType ).
thf(set_Pr1986765409at_nat_type,type,
set_Pr1986765409at_nat: $tType ).
thf(set_Pr548851891_a_nat_type,type,
set_Pr548851891_a_nat: $tType ).
thf(set_Pr967348953_nat_a_type,type,
set_Pr967348953_nat_a: $tType ).
thf(set_Product_prod_a_a_type,type,
set_Product_prod_a_a: $tType ).
thf(product_prod_nat_nat_type,type,
product_prod_nat_nat: $tType ).
thf(set_set_nat_type,type,
set_set_nat: $tType ).
thf(product_prod_a_a_type,type,
product_prod_a_a: $tType ).
thf(set_set_a_type,type,
set_set_a: $tType ).
thf(set_nat_type,type,
set_nat: $tType ).
thf(product_unit_type,type,
product_unit: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(finite351630733od_a_a_type,type,
finite351630733od_a_a: set_Product_prod_a_a > set_se1596668135od_a_a ).
thf(finite_card_a_type,type,
finite_card_a: set_a > nat ).
thf(finite_finite_nat_type,type,
finite_finite_nat: set_nat > $o ).
thf(finite772653738at_nat_type,type,
finite772653738at_nat: set_Pr1986765409at_nat > $o ).
thf(finite1297454819od_a_a_type,type,
finite1297454819od_a_a: set_Pr339609346od_a_a > $o ).
thf(finite1808550458_nat_a_type,type,
finite1808550458_nat_a: set_Pr967348953_nat_a > $o ).
thf(finite1837575485_a_nat_type,type,
finite1837575485_a_nat: set_Pr894832732_a_nat > $o ).
thf(finite1664988688od_a_a_type,type,
finite1664988688od_a_a: set_Pr1948701895od_a_a > $o ).
thf(finite1919032935_a_a_a_type,type,
finite1919032935_a_a_a: set_Pr1689873822_a_a_a > $o ).
thf(finite1743148308_a_nat_type,type,
finite1743148308_a_nat: set_Pr548851891_a_nat > $o ).
thf(finite676513017od_a_a_type,type,
finite676513017od_a_a: set_Pr681306928od_a_a > $o ).
thf(finite179568208od_a_a_type,type,
finite179568208od_a_a: set_Product_prod_a_a > $o ).
thf(finite1145471536od_a_a_type,type,
finite1145471536od_a_a: set_se1596668135od_a_a > $o ).
thf(finite_finite_a_type,type,
finite_finite_a: set_a > $o ).
thf(bot_bot_set_nat_type,type,
bot_bot_set_nat: set_nat ).
thf(bot_bo2131659635od_a_a_type,type,
bot_bo2131659635od_a_a: set_Product_prod_a_a ).
thf(bot_bot_set_a_type,type,
bot_bot_set_a: set_a ).
thf(ord_le1347718902_a_a_o_type,type,
ord_le1347718902_a_a_o: ( product_prod_a_a > $o ) > ( product_prod_a_a > $o ) > $o ).
thf(ord_less_eq_nat_type,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ord_less_eq_set_nat_type,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(ord_le2084554594od_a_a_type,type,
ord_le2084554594od_a_a: set_Pr339609346od_a_a > set_Pr339609346od_a_a > $o ).
thf(ord_le344568633_nat_a_type,type,
ord_le344568633_nat_a: set_Pr967348953_nat_a > set_Pr967348953_nat_a > $o ).
thf(ord_le492294332_a_nat_type,type,
ord_le492294332_a_nat: set_Pr894832732_a_nat > set_Pr894832732_a_nat > $o ).
thf(ord_le456379495od_a_a_type,type,
ord_le456379495od_a_a: set_Pr1948701895od_a_a > set_Pr1948701895od_a_a > $o ).
thf(ord_le677315902_a_a_a_type,type,
ord_le677315902_a_a_a: set_Pr1689873822_a_a_a > set_Pr1689873822_a_a_a > $o ).
thf(ord_le2073555219_a_nat_type,type,
ord_le2073555219_a_nat: set_Pr548851891_a_nat > set_Pr548851891_a_nat > $o ).
thf(ord_le1816232656od_a_a_type,type,
ord_le1816232656od_a_a: set_Pr681306928od_a_a > set_Pr681306928od_a_a > $o ).
thf(ord_le1824328871od_a_a_type,type,
ord_le1824328871od_a_a: set_Product_prod_a_a > set_Product_prod_a_a > $o ).
thf(ord_less_eq_set_a_type,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(pair_p159207083od_a_a_type,type,
pair_p159207083od_a_a: pair_p1593840546t_unit > $o ).
thf(pair_p374947051od_a_a_type,type,
pair_p374947051od_a_a: pair_p1765063010t_unit > $o ).
thf(pair_p1802376898raph_a_type,type,
pair_p1802376898raph_a: pair_p125712459t_unit > $o ).
thf(pair_p504738056od_a_a_type,type,
pair_p504738056od_a_a: pair_p1765063010t_unit > $o ).
thf(pair_p1864019935ioms_a_type,type,
pair_p1864019935ioms_a: pair_p125712459t_unit > $o ).
thf(pair_p1984658862t_unit_type,type,
pair_p1984658862t_unit: pair_p1765063010t_unit > product_unit ).
thf(pair_p1896222615t_unit_type,type,
pair_p1896222615t_unit: pair_p125712459t_unit > product_unit ).
thf(pair_p398687508t_unit_type,type,
pair_p398687508t_unit: set_Product_prod_a_a > set_Pr1948701895od_a_a > product_unit > pair_p1765063010t_unit ).
thf(pair_p1621517565t_unit_type,type,
pair_p1621517565t_unit: set_a > set_Product_prod_a_a > product_unit > pair_p125712459t_unit ).
thf(pair_p1783210148t_unit_type,type,
pair_p1783210148t_unit: pair_p1765063010t_unit > set_Pr1948701895od_a_a ).
thf(pair_p133601421t_unit_type,type,
pair_p133601421t_unit: pair_p125712459t_unit > set_Product_prod_a_a ).
thf(pair_p1652294923t_unit_type,type,
pair_p1652294923t_unit: pair_p1593840546t_unit > set_Pr1948701895od_a_a ).
thf(pair_p447552203t_unit_type,type,
pair_p447552203t_unit: pair_p1765063010t_unit > set_Product_prod_a_a ).
thf(pair_p1047056820t_unit_type,type,
pair_p1047056820t_unit: pair_p125712459t_unit > set_a ).
thf(pair_p646030121od_a_a_type,type,
pair_p646030121od_a_a: pair_p1765063010t_unit > $o ).
thf(pair_p68905728raph_a_type,type,
pair_p68905728raph_a: pair_p125712459t_unit > $o ).
thf(product_Pair_a_a_type,type,
product_Pair_a_a: a > a > product_prod_a_a ).
thf(produc1182842125od_a_a_type,type,
produc1182842125od_a_a: set_nat > ( nat > set_Product_prod_a_a ) > set_Pr339609346od_a_a ).
thf(product_Sigma_nat_a_type,type,
product_Sigma_nat_a: set_nat > ( nat > set_a ) > set_Pr967348953_nat_a ).
thf(produc931712687_a_nat_type,type,
produc931712687_a_nat: set_Product_prod_a_a > ( product_prod_a_a > set_nat ) > set_Pr894832732_a_nat ).
thf(produc304751368od_a_a_type,type,
produc304751368od_a_a: set_Product_prod_a_a > ( product_prod_a_a > set_Product_prod_a_a ) > set_Pr1948701895od_a_a ).
thf(produc1282482655_a_a_a_type,type,
produc1282482655_a_a_a: set_Product_prod_a_a > ( product_prod_a_a > set_a ) > set_Pr1689873822_a_a_a ).
thf(product_Sigma_a_nat_type,type,
product_Sigma_a_nat: set_a > ( a > set_nat ) > set_Pr548851891_a_nat ).
thf(produc520147185od_a_a_type,type,
produc520147185od_a_a: set_a > ( a > set_Product_prod_a_a ) > set_Pr681306928od_a_a ).
thf(product_Sigma_a_a_type,type,
product_Sigma_a_a: set_a > ( a > set_a ) > set_Product_prod_a_a ).
thf(produc1833107820_a_a_o_type,type,
produc1833107820_a_a_o: ( a > a > $o ) > product_prod_a_a > $o ).
thf(product_product_a_a_type,type,
product_product_a_a: set_a > set_a > set_Product_prod_a_a ).
thf(collect_nat_type,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(collec1635618130od_a_a_type,type,
collec1635618130od_a_a: ( produc1572603623od_a_a > $o ) > set_Pr1948701895od_a_a ).
thf(collec645855634od_a_a_type,type,
collec645855634od_a_a: ( product_prod_a_a > $o ) > set_Product_prod_a_a ).
thf(collec183727474od_a_a_type,type,
collec183727474od_a_a: ( set_Product_prod_a_a > $o ) > set_se1596668135od_a_a ).
thf(collect_a_type,type,
collect_a: ( a > $o ) > set_a ).
thf(member_nat_type,type,
member_nat: nat > set_nat > $o ).
thf(member701585322at_nat_type,type,
member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
thf(member449909584od_a_a_type,type,
member449909584od_a_a: product_prod_a_a > set_Product_prod_a_a > $o ).
thf(member1838126896od_a_a_type,type,
member1838126896od_a_a: set_Product_prod_a_a > set_se1596668135od_a_a > $o ).
thf(member_a_type,type,
member_a: a > set_a > $o ).
thf(g_type,type,
g: pair_p125712459t_unit ).
thf(n_type,type,
n: nat ).
thf(150,axiom,
! [A: pair_p125712459t_unit] :
( ( pair_p1802376898raph_a @ A )
=> ( finite_finite_a @ ( pair_p1047056820t_unit @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_pair__fin__digraph_Opair__finite__verts) ).
thf(892,plain,
! [A: pair_p125712459t_unit] :
( ( pair_p1802376898raph_a @ A )
=> ( finite_finite_a @ ( pair_p1047056820t_unit @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(193,axiom,
( ( (=) @ set_Product_prod_a_a )
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
& ( ord_le1824328871od_a_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_eq__iff) ).
thf(1024,plain,
( ( (=) @ set_Product_prod_a_a )
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
& ( ord_le1824328871od_a_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(15,axiom,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_subset__antisym) ).
thf(365,plain,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(43,axiom,
( ord_less_eq_set_nat
= ( ^ [A: set_nat,B: set_nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_subset__iff) ).
thf(479,plain,
( ord_less_eq_set_nat
= ( ^ [A: set_nat,B: set_nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(11,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_order__subst1) ).
thf(347,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(175,axiom,
! [A: a > $o,B: a > $o] :
( ( ( finite_finite_a @ ( collect_a @ A ) )
| ( finite_finite_a @ ( collect_a @ B ) ) )
=> ( finite_finite_a
@ ( collect_a
@ ^ [C: a] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_finite__Collect__conjI) ).
thf(962,plain,
! [A: a > $o,B: a > $o] :
( ( ( finite_finite_a @ ( collect_a @ A ) )
| ( finite_finite_a @ ( collect_a @ B ) ) )
=> ( finite_finite_a
@ ( collect_a
@ ^ [C: a] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(44,axiom,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_ord__le__eq__trans) ).
thf(481,plain,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(7,axiom,
( ord_less_eq_set_nat
= ( ^ [A: set_nat,B: set_nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_subset__eq) ).
thf(333,plain,
( ord_less_eq_set_nat
= ( ^ [A: set_nat,B: set_nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(196,axiom,
! [A: set_a,B: set_a,C: a > set_a,D: a > set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ! [E: a] :
( ( member_a @ E @ A )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le1824328871od_a_a @ ( product_Sigma_a_a @ A @ C ) @ ( product_Sigma_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_Sigma__mono) ).
thf(1031,plain,
! [A: set_a,B: set_a,C: a > set_a,D: a > set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ! [E: a] :
( ( member_a @ E @ A )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le1824328871od_a_a @ ( product_Sigma_a_a @ A @ C ) @ ( product_Sigma_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(246,axiom,
! [A: pair_p125712459t_unit] :
( ( pair_p1802376898raph_a @ A )
=> ( pair_p1864019935ioms_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_pair__fin__digraph_Oaxioms_I2_J) ).
thf(1200,plain,
! [A: pair_p125712459t_unit] :
( ( pair_p1802376898raph_a @ A )
=> ( pair_p1864019935ioms_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(249,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > set_nat,D: product_prod_a_a > set_nat] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ! [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le492294332_a_nat @ ( produc931712687_a_nat @ A @ C ) @ ( produc931712687_a_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_Sigma__mono) ).
thf(1211,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > set_nat,D: product_prod_a_a > set_nat] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ! [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le492294332_a_nat @ ( produc931712687_a_nat @ A @ C ) @ ( produc931712687_a_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(208,axiom,
! [A: set_Product_prod_a_a] :
( ( collec645855634od_a_a
@ ^ [B: product_prod_a_a] : ( member449909584od_a_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_Collect__mem__eq) ).
thf(1068,plain,
! [A: set_Product_prod_a_a] :
( ( collec645855634od_a_a
@ ^ [B: product_prod_a_a] : ( member449909584od_a_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(36,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_set__eq__subset) ).
thf(449,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(92,axiom,
! [A: set_a,B: set_a] :
( ( finite_finite_a @ A )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( finite_finite_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_rev__finite__subset) ).
thf(655,plain,
! [A: set_a,B: set_a] :
( ( finite_finite_a @ A )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( finite_finite_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(96,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_ord__le__eq__trans) ).
thf(677,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(199,axiom,
! [A: set_a,B: set_a,C: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ A
@ ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: a] :
( ( member_a @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_subset__Collect__iff) ).
thf(1041,plain,
! [A: set_a,B: set_a,C: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ A
@ ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: a] :
( ( member_a @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(238,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > $o,D: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ! [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
& ( C @ E ) ) )
@ ( collec645855634od_a_a
@ ^ [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_subset__CollectI) ).
thf(1173,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > $o,D: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ! [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
& ( C @ E ) ) )
@ ( collec645855634od_a_a
@ ^ [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(56,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_order__subst1) ).
thf(523,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(234,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > $o] :
( ( member449909584od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B
@ ( collec645855634od_a_a
@ ^ [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_prop__restrict) ).
thf(1158,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a,D: product_prod_a_a > $o] :
( ( member449909584od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B
@ ( collec645855634od_a_a
@ ^ [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(72,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ~ ( finite_finite_a @ A )
=> ~ ( finite_finite_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_infinite__super) ).
thf(582,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ~ ( finite_finite_a @ A )
=> ~ ( finite_finite_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(114,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_dual__order_Orefl) ).
thf(762,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(107,axiom,
! [A: set_a,B: set_a,C: set_a > nat,D: nat] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_ord__le__eq__subst) ).
thf(730,plain,
! [A: set_a,B: set_a,C: set_a > nat,D: nat] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(274,axiom,
! [A: set_Product_prod_a_a,B: set_nat] :
( ( finite179568208od_a_a @ A )
=> ( ( finite_finite_nat @ B )
=> ( finite1837575485_a_nat
@ ( produc931712687_a_nat @ A
@ ^ [C: product_prod_a_a] : B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_finite__cartesian__product) ).
thf(1290,plain,
! [A: set_Product_prod_a_a,B: set_nat] :
( ( finite179568208od_a_a @ A )
=> ( ( finite_finite_nat @ B )
=> ( finite1837575485_a_nat
@ ( produc931712687_a_nat @ A
@ ^ [C: product_prod_a_a] : B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(279,axiom,
! [A: pair_p1765063010t_unit] :
( ( finite179568208od_a_a @ ( pair_p447552203t_unit @ A ) )
=> ( ( finite1664988688od_a_a @ ( pair_p1783210148t_unit @ A ) )
=> ( pair_p504738056od_a_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_pair__fin__digraph__axioms_Ointro) ).
thf(1305,plain,
! [A: pair_p1765063010t_unit] :
( ( finite179568208od_a_a @ ( pair_p447552203t_unit @ A ) )
=> ( ( finite1664988688od_a_a @ ( pair_p1783210148t_unit @ A ) )
=> ( pair_p504738056od_a_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(76,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_antisym) ).
thf(597,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(211,axiom,
! [A: set_nat,B: set_nat,C: nat > nat > $o] :
( ~ ( finite_finite_nat @ A )
=> ( ( finite_finite_nat @ B )
=> ( ! [D: nat] :
( ( member_nat @ D @ A )
=> ? [E: nat] :
( ( member_nat @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: nat] :
( ( member_nat @ D @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_pigeonhole__infinite__rel) ).
thf(1078,plain,
! [A: set_nat,B: set_nat,C: nat > nat > $o] :
( ~ ( finite_finite_nat @ A )
=> ( ( finite_finite_nat @ B )
=> ( ! [D: nat] :
( ( member_nat @ D @ A )
=> ? [E: nat] :
( ( member_nat @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: nat] :
( ( member_nat @ D @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(281,axiom,
! [A: set_Product_prod_a_a,B: set_nat] :
( ~ ( finite179568208od_a_a @ A )
=> ( ~ ( finite_finite_nat @ B )
=> ~ ( finite1837575485_a_nat
@ ( produc931712687_a_nat @ A
@ ^ [C: product_prod_a_a] : B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_infinite__cartesian__product) ).
thf(1310,plain,
! [A: set_Product_prod_a_a,B: set_nat] :
( ~ ( finite179568208od_a_a @ A )
=> ( ~ ( finite_finite_nat @ B )
=> ~ ( finite1837575485_a_nat
@ ( produc931712687_a_nat @ A
@ ^ [C: product_prod_a_a] : B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(236,axiom,
! [A: set_a,B: set_a,C: a > a > $o] :
( ~ ( finite_finite_a @ A )
=> ( ( finite_finite_a @ B )
=> ( ! [D: a] :
( ( member_a @ D @ A )
=> ? [E: a] :
( ( member_a @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: a] :
( ( member_a @ D @ B )
& ~ ( finite_finite_a
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_pigeonhole__infinite__rel) ).
thf(1164,plain,
! [A: set_a,B: set_a,C: a > a > $o] :
( ~ ( finite_finite_a @ A )
=> ( ( finite_finite_a @ B )
=> ( ! [D: a] :
( ( member_a @ D @ A )
=> ? [E: a] :
( ( member_a @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: a] :
( ( member_a @ D @ B )
& ~ ( finite_finite_a
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(285,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: product_unit] :
( ( pair_p133601421t_unit @ ( pair_p1621517565t_unit @ A @ B @ C ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_pair__pre__digraph_Oselect__convs_I2_J) ).
thf(1327,plain,
! [A: set_a,B: set_Product_prod_a_a,C: product_unit] :
( ( pair_p133601421t_unit @ ( pair_p1621517565t_unit @ A @ B @ C ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(157,axiom,
! [A: pair_p1765063010t_unit] :
( ( pair_p374947051od_a_a @ A )
=> ( finite1664988688od_a_a @ ( pair_p1783210148t_unit @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_pair__fin__digraph_Opair__finite__arcs) ).
thf(913,plain,
! [A: pair_p1765063010t_unit] :
( ( pair_p374947051od_a_a @ A )
=> ( finite1664988688od_a_a @ ( pair_p1783210148t_unit @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(253,axiom,
! [A: set_nat,B: set_a,C: nat > a > $o] :
( ~ ( finite_finite_nat @ A )
=> ( ( finite_finite_a @ B )
=> ( ! [D: nat] :
( ( member_nat @ D @ A )
=> ? [E: a] :
( ( member_a @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: a] :
( ( member_a @ D @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_pigeonhole__infinite__rel) ).
thf(1222,plain,
! [A: set_nat,B: set_a,C: nat > a > $o] :
( ~ ( finite_finite_nat @ A )
=> ( ( finite_finite_a @ B )
=> ( ! [D: nat] :
( ( member_nat @ D @ A )
=> ? [E: a] :
( ( member_a @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: a] :
( ( member_a @ D @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(132,axiom,
! [A: set_nat,B: set_nat,C: set_nat > set_a,D: set_a] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_order__subst2) ).
thf(829,plain,
! [A: set_nat,B: set_nat,C: set_nat > set_a,D: set_a] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(224,axiom,
! [A: nat,B: set_nat,C: set_Product_prod_a_a,D: set_Product_prod_a_a] :
( ( member_nat @ A @ B )
=> ( ( ord_le492294332_a_nat
@ ( produc931712687_a_nat @ C
@ ^ [E: product_prod_a_a] : B )
@ ( produc931712687_a_nat @ D
@ ^ [E: product_prod_a_a] : B ) )
= ( ord_le1824328871od_a_a @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_Times__subset__cancel2) ).
thf(1127,plain,
! [A: nat,B: set_nat,C: set_Product_prod_a_a,D: set_Product_prod_a_a] :
( ( member_nat @ A @ B )
=> ( ( ord_le492294332_a_nat
@ ( produc931712687_a_nat @ C
@ ^ [E: product_prod_a_a] : B )
@ ( produc931712687_a_nat @ D
@ ^ [E: product_prod_a_a] : B ) )
= ( ord_le1824328871od_a_a @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(103,axiom,
! [A: nat,B: nat,C: nat > set_a,D: set_a] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_ord__le__eq__subst) ).
thf(709,plain,
! [A: nat,B: nat,C: nat > set_a,D: set_a] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(296,axiom,
! [A: pair_p125712459t_unit] :
( ( pair_p1802376898raph_a @ A )
=> ( finite179568208od_a_a @ ( pair_p133601421t_unit @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_pair__fin__digraph_Opair__finite__arcs) ).
thf(1359,plain,
! [A: pair_p125712459t_unit] :
( ( pair_p1802376898raph_a @ A )
=> ( finite179568208od_a_a @ ( pair_p133601421t_unit @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(265,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( finite179568208od_a_a @ A )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( finite179568208od_a_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_rev__finite__subset) ).
thf(1265,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( finite179568208od_a_a @ A )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( finite179568208od_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(254,axiom,
( finite_finite_nat
= ( ^ [A: set_nat] :
? [B: nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_finite__nat__set__iff__bounded__le) ).
thf(1228,plain,
( finite_finite_nat
= ( ^ [A: set_nat] :
? [B: nat] :
! [C: nat] :
( ( member_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(91,axiom,
! [A: set_a,B: set_a,C: set_a > set_nat,D: set_nat] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_nat @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_order__subst2) ).
thf(651,plain,
! [A: set_a,B: set_a,C: set_a > set_nat,D: set_nat] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_nat @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(120,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_subset__eq) ).
thf(785,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(17,axiom,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ~ ( finite_finite_nat @ A )
=> ~ ( finite_finite_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_infinite__super) ).
thf(372,plain,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ~ ( finite_finite_nat @ A )
=> ~ ( finite_finite_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(50,axiom,
! [A: set_nat,B: set_nat,C: set_nat > nat,D: nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_order__subst2) ).
thf(504,plain,
! [A: set_nat,B: set_nat,C: set_nat > nat,D: nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(286,axiom,
! [A: pair_p125712459t_unit,B: pair_p125712459t_unit] :
( ( ( pair_p1047056820t_unit @ A )
= ( pair_p1047056820t_unit @ B ) )
=> ( ( ( pair_p133601421t_unit @ A )
= ( pair_p133601421t_unit @ B ) )
=> ( ( ( pair_p1896222615t_unit @ A )
= ( pair_p1896222615t_unit @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_pair__pre__digraph_Oequality) ).
thf(1330,plain,
! [A: pair_p125712459t_unit,B: pair_p125712459t_unit] :
( ( ( pair_p1047056820t_unit @ A )
= ( pair_p1047056820t_unit @ B ) )
=> ( ( ( pair_p133601421t_unit @ A )
= ( pair_p133601421t_unit @ B ) )
=> ( ( ( pair_p1896222615t_unit @ A )
= ( pair_p1896222615t_unit @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(282,axiom,
! [A: set_Product_prod_a_a,B: set_nat,C: product_prod_a_a > nat > $o] :
( ~ ( finite179568208od_a_a @ A )
=> ( ( finite_finite_nat @ B )
=> ( ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
=> ? [E: nat] :
( ( member_nat @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: nat] :
( ( member_nat @ D @ B )
& ~ ( finite179568208od_a_a
@ ( collec645855634od_a_a
@ ^ [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_pigeonhole__infinite__rel) ).
thf(1313,plain,
! [A: set_Product_prod_a_a,B: set_nat,C: product_prod_a_a > nat > $o] :
( ~ ( finite179568208od_a_a @ A )
=> ( ( finite_finite_nat @ B )
=> ( ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
=> ? [E: nat] :
( ( member_nat @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: nat] :
( ( member_nat @ D @ B )
& ~ ( finite179568208od_a_a
@ ( collec645855634od_a_a
@ ^ [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(243,axiom,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ ( collect_nat @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_mem__Collect__eq) ).
thf(1191,plain,
! [A: nat,B: nat > $o] :
( ( member_nat @ A @ ( collect_nat @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(170,axiom,
! [A: nat,B: set_nat,C: set_nat,D: nat > $o] :
( ( member_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_prop__restrict) ).
thf(949,plain,
! [A: nat,B: set_nat,C: set_nat,D: nat > $o] :
( ( member_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(61,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_order__class_Oorder_Oantisym) ).
thf(542,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(125,axiom,
! [A: nat,B: set_a > nat,C: set_a,D: set_a] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_order__subst1) ).
thf(802,plain,
! [A: nat,B: set_a > nat,C: set_a,D: set_a] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(10,axiom,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ord_less_eq_set_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_order__trans) ).
thf(344,plain,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ord_less_eq_set_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(129,axiom,
! [A: set_Product_prod_a_a,B: nat > set_Product_prod_a_a,C: nat,D: nat] :
( ( ord_le1824328871od_a_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_le1824328871od_a_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1824328871od_a_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_order__subst1) ).
thf(817,plain,
! [A: set_Product_prod_a_a,B: nat > set_Product_prod_a_a,C: nat,D: nat] :
( ( ord_le1824328871od_a_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_le1824328871od_a_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1824328871od_a_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(66,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_order__refl) ).
thf(559,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(138,axiom,
! [A: set_nat,B: set_a] :
( ~ ( finite_finite_nat @ A )
=> ( ~ ( finite_finite_a @ B )
=> ~ ( finite1808550458_nat_a
@ ( product_Sigma_nat_a @ A
@ ^ [C: nat] : B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_infinite__cartesian__product) ).
thf(853,plain,
! [A: set_nat,B: set_a] :
( ~ ( finite_finite_nat @ A )
=> ( ~ ( finite_finite_a @ B )
=> ~ ( finite1808550458_nat_a
@ ( product_Sigma_nat_a @ A
@ ^ [C: nat] : B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(302,axiom,
( pair_p1864019935ioms_a
= ( ^ [A: pair_p125712459t_unit] :
( ( finite_finite_a @ ( pair_p1047056820t_unit @ A ) )
& ( finite179568208od_a_a @ ( pair_p133601421t_unit @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_pair__fin__digraph__axioms__def) ).
thf(1379,plain,
( pair_p1864019935ioms_a
= ( ^ [A: pair_p125712459t_unit] :
( ( finite_finite_a @ ( pair_p1047056820t_unit @ A ) )
& ( finite179568208od_a_a @ ( pair_p133601421t_unit @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(213,axiom,
! [A: set_nat] :
( ( collect_nat
@ ^ [B: nat] : ( member_nat @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_Collect__mem__eq) ).
thf(1087,plain,
! [A: set_nat] :
( ( collect_nat
@ ^ [B: nat] : ( member_nat @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(229,axiom,
! [A: produc1572603623od_a_a > $o] :
( ~ ( finite1664988688od_a_a @ ( collec1635618130od_a_a @ A ) )
=> ? [B: produc1572603623od_a_a] : ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_not__finite__existsD) ).
thf(1147,plain,
! [A: produc1572603623od_a_a > $o] :
( ~ ( finite1664988688od_a_a @ ( collec1635618130od_a_a @ A ) )
=> ? [B: produc1572603623od_a_a] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(260,axiom,
! [A: set_nat,B: set_a] :
( ( finite1808550458_nat_a
@ ( product_Sigma_nat_a @ A
@ ^ [C: nat] : B ) )
= ( ( A = bot_bot_set_nat )
| ( B = bot_bot_set_a )
| ( ( finite_finite_nat @ A )
& ( finite_finite_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_finite__cartesian__product__iff) ).
thf(1247,plain,
! [A: set_nat,B: set_a] :
( ( finite1808550458_nat_a
@ ( product_Sigma_nat_a @ A
@ ^ [C: nat] : B ) )
= ( ( A = bot_bot_set_nat )
| ( B = bot_bot_set_a )
| ( ( finite_finite_nat @ A )
& ( finite_finite_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(190,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > set_Product_prod_a_a,D: product_prod_a_a > set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ! [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
=> ( ord_le1824328871od_a_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le456379495od_a_a @ ( produc304751368od_a_a @ A @ C ) @ ( produc304751368od_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_Sigma__mono) ).
thf(1013,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > set_Product_prod_a_a,D: product_prod_a_a > set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ! [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
=> ( ord_le1824328871od_a_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le456379495od_a_a @ ( produc304751368od_a_a @ A @ C ) @ ( produc304751368od_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(6,axiom,
! [A: set_nat,B: nat > set_nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_ord__eq__le__subst) ).
thf(325,plain,
! [A: set_nat,B: nat > set_nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(283,axiom,
! [A: set_Product_prod_a_a,B: set_a,C: product_prod_a_a > a > $o] :
( ~ ( finite179568208od_a_a @ A )
=> ( ( finite_finite_a @ B )
=> ( ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
=> ? [E: a] :
( ( member_a @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: a] :
( ( member_a @ D @ B )
& ~ ( finite179568208od_a_a
@ ( collec645855634od_a_a
@ ^ [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_pigeonhole__infinite__rel) ).
thf(1319,plain,
! [A: set_Product_prod_a_a,B: set_a,C: product_prod_a_a > a > $o] :
( ~ ( finite179568208od_a_a @ A )
=> ( ( finite_finite_a @ B )
=> ( ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
=> ? [E: a] :
( ( member_a @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: a] :
( ( member_a @ D @ B )
& ~ ( finite179568208od_a_a
@ ( collec645855634od_a_a
@ ^ [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(143,axiom,
! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ bot_bo2131659635od_a_a @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_empty__subsetI) ).
thf(870,plain,
! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ bot_bo2131659635od_a_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(177,axiom,
! [A: set_Product_prod_a_a] :
( ( ! [B: product_prod_a_a] :
~ ( member449909584od_a_a @ B @ A ) )
= ( A = bot_bo2131659635od_a_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_all__not__in__conv) ).
thf(969,plain,
! [A: set_Product_prod_a_a] :
( ( ! [B: product_prod_a_a] :
~ ( member449909584od_a_a @ B @ A ) )
= ( A = bot_bo2131659635od_a_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(292,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ~ ( finite_finite_a @ A )
=> ( ~ ( finite179568208od_a_a @ B )
=> ~ ( finite676513017od_a_a
@ ( produc520147185od_a_a @ A
@ ^ [C: a] : B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_infinite__cartesian__product) ).
thf(1347,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ~ ( finite_finite_a @ A )
=> ( ~ ( finite179568208od_a_a @ B )
=> ~ ( finite676513017od_a_a
@ ( produc520147185od_a_a @ A
@ ^ [C: a] : B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(161,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a > $o] :
( ! [C: product_prod_a_a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le1824328871od_a_a @ ( collec645855634od_a_a @ A ) @ ( collec645855634od_a_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_Collect__mono) ).
thf(924,plain,
! [A: product_prod_a_a > $o,B: product_prod_a_a > $o] :
( ! [C: product_prod_a_a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le1824328871od_a_a @ ( collec645855634od_a_a @ A ) @ ( collec645855634od_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(278,axiom,
! [A: set_a,B: set_a] :
( ( finite179568208od_a_a
@ ( product_Sigma_a_a @ A
@ ^ [C: a] : B ) )
= ( ( A = bot_bot_set_a )
| ( B = bot_bot_set_a )
| ( ( finite_finite_a @ A )
& ( finite_finite_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_finite__cartesian__product__iff) ).
thf(1302,plain,
! [A: set_a,B: set_a] :
( ( finite179568208od_a_a
@ ( product_Sigma_a_a @ A
@ ^ [C: a] : B ) )
= ( ( A = bot_bot_set_a )
| ( B = bot_bot_set_a )
| ( ( finite_finite_a @ A )
& ( finite_finite_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(300,axiom,
! [A: set_a,B: a > set_Product_prod_a_a] :
( ( finite_finite_a @ A )
=> ( ! [C: a] :
( ( member_a @ C @ A )
=> ( finite179568208od_a_a @ ( B @ C ) ) )
=> ( finite676513017od_a_a @ ( produc520147185od_a_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_finite__SigmaI) ).
thf(1373,plain,
! [A: set_a,B: a > set_Product_prod_a_a] :
( ( finite_finite_a @ A )
=> ( ! [C: a] :
( ( member_a @ C @ A )
=> ( finite179568208od_a_a @ ( B @ C ) ) )
=> ( finite676513017od_a_a @ ( produc520147185od_a_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(231,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_subsetI) ).
thf(1151,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(126,axiom,
! [A: set_a,B: set_a,C: a > set_nat,D: a > set_nat] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ! [E: a] :
( ( member_a @ E @ A )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le2073555219_a_nat @ ( product_Sigma_a_nat @ A @ C ) @ ( product_Sigma_a_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_Sigma__mono) ).
thf(806,plain,
! [A: set_a,B: set_a,C: a > set_nat,D: a > set_nat] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ! [E: a] :
( ( member_a @ E @ A )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le2073555219_a_nat @ ( product_Sigma_a_nat @ A @ C ) @ ( product_Sigma_a_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(304,axiom,
! [A: set_a,B: a > set_a] :
( ( finite_finite_a @ A )
=> ( ! [C: a] :
( ( member_a @ C @ A )
=> ( finite_finite_a @ ( B @ C ) ) )
=> ( finite179568208od_a_a @ ( product_Sigma_a_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_finite__SigmaI) ).
thf(1383,plain,
! [A: set_a,B: a > set_a] :
( ( finite_finite_a @ A )
=> ( ! [C: a] :
( ( member_a @ C @ A )
=> ( finite_finite_a @ ( B @ C ) ) )
=> ( finite179568208od_a_a @ ( product_Sigma_a_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(192,axiom,
! [A: a,B: set_a,C: set_a,D: set_a] :
( ( member_a @ A @ B )
=> ( ( ( product_Sigma_a_a @ C
@ ^ [E: a] : B )
= ( product_Sigma_a_a @ D
@ ^ [E: a] : B ) )
= ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_Times__eq__cancel2) ).
thf(1020,plain,
! [A: a,B: set_a,C: set_a,D: set_a] :
( ( member_a @ A @ B )
=> ( ( ( product_Sigma_a_a @ C
@ ^ [E: a] : B )
= ( product_Sigma_a_a @ D
@ ^ [E: a] : B ) )
= ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(202,axiom,
! [A: produc1572603623od_a_a > $o,B: produc1572603623od_a_a > $o] :
( ( ( finite1664988688od_a_a @ ( collec1635618130od_a_a @ A ) )
| ( finite1664988688od_a_a @ ( collec1635618130od_a_a @ B ) ) )
=> ( finite1664988688od_a_a
@ ( collec1635618130od_a_a
@ ^ [C: produc1572603623od_a_a] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_finite__Collect__conjI) ).
thf(1051,plain,
! [A: produc1572603623od_a_a > $o,B: produc1572603623od_a_a > $o] :
( ( ( finite1664988688od_a_a @ ( collec1635618130od_a_a @ A ) )
| ( finite1664988688od_a_a @ ( collec1635618130od_a_a @ B ) ) )
=> ( finite1664988688od_a_a
@ ( collec1635618130od_a_a
@ ^ [C: produc1572603623od_a_a] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(130,axiom,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ord_less_eq_set_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_order_Otrans) ).
thf(821,plain,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ord_less_eq_set_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(301,axiom,
! [A: product_prod_a_a > $o] :
( ~ ( finite179568208od_a_a @ ( collec645855634od_a_a @ A ) )
=> ? [B: product_prod_a_a] : ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_not__finite__existsD) ).
thf(1377,plain,
! [A: product_prod_a_a > $o] :
( ~ ( finite179568208od_a_a @ ( collec645855634od_a_a @ A ) )
=> ? [B: product_prod_a_a] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(250,axiom,
! [A: nat > $o] :
( ( bot_bot_set_nat
= ( collect_nat @ A ) )
= ( ! [B: nat] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_empty__Collect__eq) ).
thf(1215,plain,
! [A: nat > $o] :
( ( bot_bot_set_nat
= ( collect_nat @ A ) )
= ( ! [B: nat] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(146,axiom,
! [A: product_prod_a_a > $o] :
( ( bot_bo2131659635od_a_a
= ( collec645855634od_a_a @ A ) )
= ( ! [B: product_prod_a_a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_empty__Collect__eq) ).
thf(877,plain,
! [A: product_prod_a_a > $o] :
( ( bot_bo2131659635od_a_a
= ( collec645855634od_a_a @ A ) )
= ( ! [B: product_prod_a_a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(24,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_linear) ).
thf(396,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(294,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ~ ( finite179568208od_a_a @ A )
=> ~ ( finite179568208od_a_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_infinite__super) ).
thf(1351,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ~ ( finite179568208od_a_a @ A )
=> ~ ( finite179568208od_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(29,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( ord_less_eq_nat @ A @ B )
=> ~ ( ord_less_eq_nat @ B @ C ) )
=> ( ( ( ord_less_eq_nat @ B @ A )
=> ~ ( ord_less_eq_nat @ A @ C ) )
=> ( ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ C @ B ) )
=> ( ( ( ord_less_eq_nat @ C @ B )
=> ~ ( ord_less_eq_nat @ B @ A ) )
=> ( ( ( ord_less_eq_nat @ B @ C )
=> ~ ( ord_less_eq_nat @ C @ A ) )
=> ~ ( ( ord_less_eq_nat @ C @ A )
=> ~ ( ord_less_eq_nat @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_le__cases3) ).
thf(411,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ord_less_eq_nat @ A @ B )
=> ~ ( ord_less_eq_nat @ B @ C ) )
=> ( ( ( ord_less_eq_nat @ B @ A )
=> ~ ( ord_less_eq_nat @ A @ C ) )
=> ( ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ C @ B ) )
=> ( ( ( ord_less_eq_nat @ C @ B )
=> ~ ( ord_less_eq_nat @ B @ A ) )
=> ( ( ( ord_less_eq_nat @ B @ C )
=> ~ ( ord_less_eq_nat @ C @ A ) )
=> ~ ( ( ord_less_eq_nat @ C @ A )
=> ~ ( ord_less_eq_nat @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(258,axiom,
! [A: nat > nat,B: nat] :
( ! [C: nat] : ( ord_less_eq_nat @ C @ ( A @ C ) )
=> ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] : ( ord_less_eq_nat @ ( A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_finite__less__ub) ).
thf(1242,plain,
! [A: nat > nat,B: nat] :
( ! [C: nat] : ( ord_less_eq_nat @ C @ ( A @ C ) )
=> ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] : ( ord_less_eq_nat @ ( A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(57,axiom,
! [A: set_nat,B: set_nat,C: nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_subsetD) ).
thf(527,plain,
! [A: set_nat,B: set_nat,C: nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(20,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ B @ A )
& ( ord_less_eq_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_dual__order_Oeq__iff) ).
thf(380,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ B @ A )
& ( ord_less_eq_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(94,axiom,
! [A: set_a,B: set_a,C: set_a > set_nat,D: set_nat] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_ord__le__eq__subst) ).
thf(661,plain,
! [A: set_a,B: set_a,C: set_a > set_nat,D: set_nat] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(127,axiom,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_antisym__conv) ).
thf(810,plain,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(289,axiom,
! [A: set_Product_prod_a_a,B: set_a] :
( ( finite179568208od_a_a @ A )
=> ( ( finite_finite_a @ B )
=> ( finite1919032935_a_a_a
@ ( produc1282482655_a_a_a @ A
@ ^ [C: product_prod_a_a] : B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_finite__cartesian__product) ).
thf(1338,plain,
! [A: set_Product_prod_a_a,B: set_a] :
( ( finite179568208od_a_a @ A )
=> ( ( finite_finite_a @ B )
=> ( finite1919032935_a_a_a
@ ( produc1282482655_a_a_a @ A
@ ^ [C: product_prod_a_a] : B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(168,axiom,
! [A: a,B: set_a,C: set_a,D: set_a] :
( ( member_a @ A @ B )
=> ( ( ord_le1824328871od_a_a
@ ( product_Sigma_a_a @ C
@ ^ [E: a] : B )
@ ( product_Sigma_a_a @ D
@ ^ [E: a] : B ) )
= ( ord_less_eq_set_a @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_Times__subset__cancel2) ).
thf(942,plain,
! [A: a,B: set_a,C: set_a,D: set_a] :
( ( member_a @ A @ B )
=> ( ( ord_le1824328871od_a_a
@ ( product_Sigma_a_a @ C
@ ^ [E: a] : B )
@ ( product_Sigma_a_a @ D
@ ^ [E: a] : B ) )
= ( ord_less_eq_set_a @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(34,axiom,
! [A: set_nat,B: set_nat,C: set_nat > nat,D: nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_ord__le__eq__subst) ).
thf(439,plain,
! [A: set_nat,B: set_nat,C: set_nat > nat,D: nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(269,axiom,
! [A: set_a,B: set_a] :
( ( finite_finite_a @ A )
=> ( ( finite_finite_a @ B )
=> ( finite179568208od_a_a
@ ( product_Sigma_a_a @ A
@ ^ [C: a] : B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_finite__cartesian__product) ).
thf(1274,plain,
! [A: set_a,B: set_a] :
( ( finite_finite_a @ A )
=> ( ( finite_finite_a @ B )
=> ( finite179568208od_a_a
@ ( product_Sigma_a_a @ A
@ ^ [C: a] : B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(156,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_unit] :
( ( pair_p1783210148t_unit @ ( pair_p398687508t_unit @ A @ B @ C ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_pair__pre__digraph_Oselect__convs_I2_J) ).
thf(910,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_unit] :
( ( pair_p1783210148t_unit @ ( pair_p398687508t_unit @ A @ B @ C ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(109,axiom,
! [A: nat,B: nat,C: nat > set_a,D: set_a] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_order__subst2) ).
thf(746,plain,
! [A: nat,B: nat,C: nat > set_a,D: set_a] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(118,axiom,
! [A: set_nat,B: set_nat] :
( ! [C: nat] :
( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) )
=> ( ord_less_eq_set_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_subsetI) ).
thf(778,plain,
! [A: set_nat,B: set_nat] :
( ! [C: nat] :
( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) )
=> ( ord_less_eq_set_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(171,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_subsetD) ).
thf(952,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(222,axiom,
! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_dual__order_Orefl) ).
thf(1123,plain,
! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(67,axiom,
! [A: nat,B: set_nat > nat,C: set_nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_ord__eq__le__subst) ).
thf(561,plain,
! [A: nat,B: set_nat > nat,C: set_nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(299,axiom,
! [A: set_nat,B: set_Product_prod_a_a] :
( ( finite1297454819od_a_a
@ ( produc1182842125od_a_a @ A
@ ^ [C: nat] : B ) )
= ( ( A = bot_bot_set_nat )
| ( B = bot_bo2131659635od_a_a )
| ( ( finite_finite_nat @ A )
& ( finite179568208od_a_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_finite__cartesian__product__iff) ).
thf(1370,plain,
! [A: set_nat,B: set_Product_prod_a_a] :
( ( finite1297454819od_a_a
@ ( produc1182842125od_a_a @ A
@ ^ [C: nat] : B ) )
= ( ( A = bot_bot_set_nat )
| ( B = bot_bo2131659635od_a_a )
| ( ( finite_finite_nat @ A )
& ( finite179568208od_a_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(257,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a,D: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( ord_le456379495od_a_a
@ ( produc304751368od_a_a @ C
@ ^ [E: product_prod_a_a] : B )
@ ( produc304751368od_a_a @ D
@ ^ [E: product_prod_a_a] : B ) )
= ( ord_le1824328871od_a_a @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_Times__subset__cancel2) ).
thf(1238,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a,D: set_Product_prod_a_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( ord_le456379495od_a_a
@ ( produc304751368od_a_a @ C
@ ^ [E: product_prod_a_a] : B )
@ ( produc304751368od_a_a @ D
@ ^ [E: product_prod_a_a] : B ) )
= ( ord_le1824328871od_a_a @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(173,axiom,
! [A: set_Product_prod_a_a,B: product_prod_a_a > $o] :
( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_Collect__restrict) ).
thf(957,plain,
! [A: set_Product_prod_a_a,B: product_prod_a_a > $o] :
( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(151,axiom,
! [A: pair_p1765063010t_unit] :
( A
= ( pair_p398687508t_unit @ ( pair_p447552203t_unit @ A ) @ ( pair_p1783210148t_unit @ A ) @ ( pair_p1984658862t_unit @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_pair__pre__digraph_Osurjective) ).
thf(894,plain,
! [A: pair_p1765063010t_unit] :
( A
= ( pair_p398687508t_unit @ ( pair_p447552203t_unit @ A ) @ ( pair_p1783210148t_unit @ A ) @ ( pair_p1984658862t_unit @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(33,axiom,
! [A: set_nat,B: set_nat,C: set_nat > set_nat,D: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ ( C @ B ) @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_order__subst2) ).
thf(435,plain,
! [A: set_nat,B: set_nat,C: set_nat > set_nat,D: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ ( C @ B ) @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(239,axiom,
! [A: set_a,B: a > set_nat] :
( ( finite_finite_a @ A )
=> ( ! [C: a] :
( ( member_a @ C @ A )
=> ( finite_finite_nat @ ( B @ C ) ) )
=> ( finite1743148308_a_nat @ ( product_Sigma_a_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_finite__SigmaI) ).
thf(1178,plain,
! [A: set_a,B: a > set_nat] :
( ( finite_finite_a @ A )
=> ( ! [C: a] :
( ( member_a @ C @ A )
=> ( finite_finite_nat @ ( B @ C ) ) )
=> ( finite1743148308_a_nat @ ( product_Sigma_a_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(276,axiom,
! [A: set_nat,B: set_Product_prod_a_a] :
( ~ ( finite_finite_nat @ A )
=> ( ~ ( finite179568208od_a_a @ B )
=> ~ ( finite1297454819od_a_a
@ ( produc1182842125od_a_a @ A
@ ^ [C: nat] : B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_infinite__cartesian__product) ).
thf(1296,plain,
! [A: set_nat,B: set_Product_prod_a_a] :
( ~ ( finite_finite_nat @ A )
=> ( ~ ( finite179568208od_a_a @ B )
=> ~ ( finite1297454819od_a_a
@ ( produc1182842125od_a_a @ A
@ ^ [C: nat] : B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(97,axiom,
! [A: set_nat,B: set_nat,C: nat > set_a,D: nat > set_a] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ! [E: nat] :
( ( member_nat @ E @ A )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le344568633_nat_a @ ( product_Sigma_nat_a @ A @ C ) @ ( product_Sigma_nat_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Sigma__mono) ).
thf(682,plain,
! [A: set_nat,B: set_nat,C: nat > set_a,D: nat > set_a] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ! [E: nat] :
( ( member_nat @ E @ A )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le344568633_nat_a @ ( product_Sigma_nat_a @ A @ C ) @ ( product_Sigma_nat_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(64,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_antisym) ).
thf(551,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(136,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_antisym) ).
thf(842,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(179,axiom,
! [A: set_a,B: set_Pr1986765409at_nat,C: a > product_prod_nat_nat > $o] :
( ~ ( finite_finite_a @ A )
=> ( ( finite772653738at_nat @ B )
=> ( ! [D: a] :
( ( member_a @ D @ A )
=> ? [E: product_prod_nat_nat] :
( ( member701585322at_nat @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: product_prod_nat_nat] :
( ( member701585322at_nat @ D @ B )
& ~ ( finite_finite_a
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_pigeonhole__infinite__rel) ).
thf(974,plain,
! [A: set_a,B: set_Pr1986765409at_nat,C: a > product_prod_nat_nat > $o] :
( ~ ( finite_finite_a @ A )
=> ( ( finite772653738at_nat @ B )
=> ( ! [D: a] :
( ( member_a @ D @ A )
=> ? [E: product_prod_nat_nat] :
( ( member701585322at_nat @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: product_prod_nat_nat] :
( ( member701585322at_nat @ D @ B )
& ~ ( finite_finite_a
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(293,axiom,
( finite179568208od_a_a
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [A: a] : ( pair_p1047056820t_unit @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062finite_A_Ipverts_AG_A_092_060times_062_Apverts_AG_J_092_060close_062) ).
thf(1350,plain,
( finite179568208od_a_a
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [A: a] : ( pair_p1047056820t_unit @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(267,axiom,
( ord_le1824328871od_a_a @ ( pair_p133601421t_unit @ g )
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [A: a] : ( pair_p1047056820t_unit @ g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062parcs_AG_A_092_060subseteq_062_Apverts_AG_A_092_060times_062_Apverts_AG_092_060close_062) ).
thf(1270,plain,
( ord_le1824328871od_a_a @ ( pair_p133601421t_unit @ g )
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [A: a] : ( pair_p1047056820t_unit @ g ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(191,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_order_Otrans) ).
thf(1017,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(180,axiom,
! [A: set_Product_prod_a_a,B: product_prod_a_a > $o] :
( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_Collect__subset) ).
thf(980,plain,
! [A: set_Product_prod_a_a,B: product_prod_a_a > $o] :
( ord_le1824328871od_a_a
@ ( collec645855634od_a_a
@ ^ [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(227,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( B = C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_ord__le__eq__trans) ).
thf(1138,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( B = C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(145,axiom,
! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
( ( finite1664988688od_a_a @ A )
=> ( ( ord_le456379495od_a_a @ B @ A )
=> ( finite1664988688od_a_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_rev__finite__subset) ).
thf(874,plain,
! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
( ( finite1664988688od_a_a @ A )
=> ( ( ord_le456379495od_a_a @ B @ A )
=> ( finite1664988688od_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(228,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( A = B )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_eq__refl) ).
thf(1143,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( A = B )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(46,axiom,
! [A: nat,B: set_a > nat,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_ord__eq__le__subst) ).
thf(488,plain,
! [A: nat,B: set_a > nat,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(297,axiom,
( ( finite_finite_a @ ( pair_p1047056820t_unit @ g ) )
& ( ( finite_card_a @ ( pair_p1047056820t_unit @ g ) )
= n )
& ( ( pair_p133601421t_unit @ g )
= ( collec645855634od_a_a
@ ( produc1833107820_a_a_o
@ ^ [A: a,B: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B )
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [C: a] : ( pair_p1047056820t_unit @ g ) ) )
& ( A != B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_calculation) ).
thf(1361,plain,
( ( finite_finite_a @ ( pair_p1047056820t_unit @ g ) )
& ( ( finite_card_a @ ( pair_p1047056820t_unit @ g ) )
= n )
& ( ( pair_p133601421t_unit @ g )
= ( collec645855634od_a_a
@ ( produc1833107820_a_a_o
@ ^ [A: a,B: a] :
( ( member449909584od_a_a @ ( product_Pair_a_a @ A @ B )
@ ( product_Sigma_a_a @ ( pair_p1047056820t_unit @ g )
@ ^ [C: a] : ( pair_p1047056820t_unit @ g ) ) )
& ( A != B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(240,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ A
@ ( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_subset__Collect__iff) ).
thf(1182,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ A
@ ( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(95,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_ord__eq__le__subst) ).
thf(669,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(86,axiom,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ord_less_eq_set_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_subset__trans) ).
thf(637,plain,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ord_less_eq_set_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(233,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_in__mono) ).
thf(1155,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(65,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_ord__le__eq__trans) ).
thf(554,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(111,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_eq__iff) ).
thf(753,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(98,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_subset__refl) ).
thf(686,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(210,axiom,
! [A: pair_p1765063010t_unit,B: pair_p1765063010t_unit] :
( ( ( pair_p447552203t_unit @ A )
= ( pair_p447552203t_unit @ B ) )
=> ( ( ( pair_p1783210148t_unit @ A )
= ( pair_p1783210148t_unit @ B ) )
=> ( ( ( pair_p1984658862t_unit @ A )
= ( pair_p1984658862t_unit @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_pair__pre__digraph_Oequality) ).
thf(1075,plain,
! [A: pair_p1765063010t_unit,B: pair_p1765063010t_unit] :
( ( ( pair_p447552203t_unit @ A )
= ( pair_p447552203t_unit @ B ) )
=> ( ( ( pair_p1783210148t_unit @ A )
= ( pair_p1783210148t_unit @ B ) )
=> ( ( ( pair_p1984658862t_unit @ A )
= ( pair_p1984658862t_unit @ B ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(42,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_order__trans) ).
thf(476,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(82,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_dual__order_Orefl) ).
thf(622,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(216,axiom,
! [A: a > $o,B: a > $o] :
( ( finite_finite_a
@ ( collect_a
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_a @ ( collect_a @ A ) )
& ( finite_finite_a @ ( collect_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_finite__Collect__disjI) ).
thf(1099,plain,
! [A: a > $o,B: a > $o] :
( ( finite_finite_a
@ ( collect_a
@ ^ [C: a] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_a @ ( collect_a @ A ) )
& ( finite_finite_a @ ( collect_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(108,axiom,
! [A: nat,B: nat,C: nat > set_nat,D: set_nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_ord__le__eq__subst) ).
thf(738,plain,
! [A: nat,B: nat,C: nat > set_nat,D: set_nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(225,axiom,
! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_subset__refl) ).
thf(1131,plain,
! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(182,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( A = B )
=> ~ ( ( ord_le1824328871od_a_a @ A @ B )
=> ~ ( ord_le1824328871od_a_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_equalityE) ).
thf(984,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( A = B )
=> ~ ( ( ord_le1824328871od_a_a @ A @ B )
=> ~ ( ord_le1824328871od_a_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(68,axiom,
! [A: set_nat,B: nat > set_nat,C: nat,D: nat] :
( ( ord_less_eq_set_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_order__subst1) ).
thf(569,plain,
! [A: set_nat,B: nat > set_nat,C: nat,D: nat] :
( ( ord_less_eq_set_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(79,axiom,
! [A: set_a,B: nat > set_a,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_ord__eq__le__subst) ).
thf(605,plain,
! [A: set_a,B: nat > set_a,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(23,axiom,
! [A: nat > $o,B: nat > $o] :
( ! [C: nat] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_nat @ ( collect_nat @ A ) @ ( collect_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_Collect__mono) ).
thf(393,plain,
! [A: nat > $o,B: nat > $o] :
( ! [C: nat] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_nat @ ( collect_nat @ A ) @ ( collect_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(219,axiom,
! [A: product_prod_a_a,B: set_a,C: set_a] :
( ( member449909584od_a_a @ A @ ( product_product_a_a @ B @ C ) )
= ( member449909584od_a_a @ A
@ ( product_Sigma_a_a @ B
@ ^ [D: a] : C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_member__product) ).
thf(1114,plain,
! [A: product_prod_a_a,B: set_a,C: set_a] :
( ( member449909584od_a_a @ A @ ( product_product_a_a @ B @ C ) )
= ( member449909584od_a_a @ A
@ ( product_Sigma_a_a @ B
@ ^ [D: a] : C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(89,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_empty__subsetI) ).
thf(647,plain,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(185,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ( finite_finite_nat @ ( collect_nat @ A ) )
| ( finite_finite_nat @ ( collect_nat @ B ) ) )
=> ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_finite__Collect__conjI) ).
thf(997,plain,
! [A: nat > $o,B: nat > $o] :
( ( ( finite_finite_nat @ ( collect_nat @ A ) )
| ( finite_finite_nat @ ( collect_nat @ B ) ) )
=> ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(287,axiom,
! [A: set_nat,B: set_Product_prod_a_a] :
( ( finite_finite_nat @ A )
=> ( ( finite179568208od_a_a @ B )
=> ( finite1297454819od_a_a
@ ( produc1182842125od_a_a @ A
@ ^ [C: nat] : B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_finite__cartesian__product) ).
thf(1333,plain,
! [A: set_nat,B: set_Product_prod_a_a] :
( ( finite_finite_nat @ A )
=> ( ( finite179568208od_a_a @ B )
=> ( finite1297454819od_a_a
@ ( produc1182842125od_a_a @ A
@ ^ [C: nat] : B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(247,axiom,
! [A: set_se1596668135od_a_a,B: set_Product_prod_a_a] :
( ( finite1145471536od_a_a @ A )
=> ( ( member1838126896od_a_a @ B @ A )
=> ? [C: set_Product_prod_a_a] :
( ( member1838126896od_a_a @ C @ A )
& ( ord_le1824328871od_a_a @ C @ B )
& ! [D: set_Product_prod_a_a] :
( ( member1838126896od_a_a @ D @ A )
=> ( ( ord_le1824328871od_a_a @ D @ C )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_finite__has__minimal2) ).
thf(1202,plain,
! [A: set_se1596668135od_a_a,B: set_Product_prod_a_a] :
( ( finite1145471536od_a_a @ A )
=> ( ( member1838126896od_a_a @ B @ A )
=> ? [C: set_Product_prod_a_a] :
( ( member1838126896od_a_a @ C @ A )
& ( ord_le1824328871od_a_a @ C @ B )
& ! [D: set_Product_prod_a_a] :
( ( member1838126896od_a_a @ D @ A )
=> ( ( ord_le1824328871od_a_a @ D @ C )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(166,axiom,
( ( (=) @ set_Product_prod_a_a )
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
& ( ord_le1824328871od_a_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_order__class_Oorder_Oeq__iff) ).
thf(938,plain,
( ( (=) @ set_Product_prod_a_a )
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
& ( ord_le1824328871od_a_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(51,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_le__cases) ).
thf(508,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(160,axiom,
! [A: set_nat] :
( ( ! [B: nat] :
~ ( member_nat @ B @ A ) )
= ( A = bot_bot_set_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_all__not__in__conv) ).
thf(921,plain,
! [A: set_nat] :
( ( ! [B: nat] :
~ ( member_nat @ B @ A ) )
= ( A = bot_bot_set_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(203,axiom,
! [A: pair_p1765063010t_unit] :
( ( pair_p646030121od_a_a @ A )
=> ( ( pair_p504738056od_a_a @ A )
=> ( pair_p374947051od_a_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_pair__fin__digraph_Ointro) ).
thf(1054,plain,
! [A: pair_p1765063010t_unit] :
( ( pair_p646030121od_a_a @ A )
=> ( ( pair_p504738056od_a_a @ A )
=> ( pair_p374947051od_a_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(237,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: product_unit] :
( ( pair_p1047056820t_unit @ ( pair_p1621517565t_unit @ A @ B @ C ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_pair__pre__digraph_Oselect__convs_I1_J) ).
thf(1170,plain,
! [A: set_a,B: set_Product_prod_a_a,C: product_unit] :
( ( pair_p1047056820t_unit @ ( pair_p1621517565t_unit @ A @ B @ C ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(209,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_nat,D: set_nat] :
( ( member449909584od_a_a @ A @ B )
=> ( ( ord_le2084554594od_a_a
@ ( produc1182842125od_a_a @ C
@ ^ [E: nat] : B )
@ ( produc1182842125od_a_a @ D
@ ^ [E: nat] : B ) )
= ( ord_less_eq_set_nat @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_Times__subset__cancel2) ).
thf(1071,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_nat,D: set_nat] :
( ( member449909584od_a_a @ A @ B )
=> ( ( ord_le2084554594od_a_a
@ ( produc1182842125od_a_a @ C
@ ^ [E: nat] : B )
@ ( produc1182842125od_a_a @ D
@ ^ [E: nat] : B ) )
= ( ord_less_eq_set_nat @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(194,axiom,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_nat @ ( collect_nat @ A ) )
& ( finite_finite_nat @ ( collect_nat @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_finite__Collect__disjI) ).
thf(1026,plain,
! [A: nat > $o,B: nat > $o] :
( ( finite_finite_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite_finite_nat @ ( collect_nat @ A ) )
& ( finite_finite_nat @ ( collect_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(58,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: nat,E: nat] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_linorder__wlog) ).
thf(530,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less_eq_nat @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: nat,E: nat] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(25,axiom,
! [A: set_a,B: set_nat > set_a,C: set_nat,D: set_nat] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_order__subst1) ).
thf(398,plain,
! [A: set_a,B: set_nat > set_a,C: set_nat,D: set_nat] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(197,axiom,
! [A: nat > $o] :
( ( ( collect_nat @ A )
= bot_bot_set_nat )
= ( ! [B: nat] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_Collect__empty__eq) ).
thf(1035,plain,
! [A: nat > $o] :
( ( ( collect_nat @ A )
= bot_bot_set_nat )
= ( ! [B: nat] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(154,axiom,
! [A: nat] :
( finite_finite_nat
@ ( collect_nat
@ ^ [B: nat] : ( ord_less_eq_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_finite__Collect__le__nat) ).
thf(906,plain,
! [A: nat] :
( finite_finite_nat
@ ( collect_nat
@ ^ [B: nat] : ( ord_less_eq_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(81,axiom,
! [A: nat,B: set_nat,C: set_a,D: set_a] :
( ( member_nat @ A @ B )
=> ( ( ord_le2073555219_a_nat
@ ( product_Sigma_a_nat @ C
@ ^ [E: a] : B )
@ ( product_Sigma_a_nat @ D
@ ^ [E: a] : B ) )
= ( ord_less_eq_set_a @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_Times__subset__cancel2) ).
thf(618,plain,
! [A: nat,B: set_nat,C: set_a,D: set_a] :
( ( member_nat @ A @ B )
=> ( ( ord_le2073555219_a_nat
@ ( product_Sigma_a_nat @ C
@ ^ [E: a] : B )
@ ( product_Sigma_a_nat @ D
@ ^ [E: a] : B ) )
= ( ord_less_eq_set_a @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(30,axiom,
( ( (=) @ set_nat )
= ( ^ [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
& ( ord_less_eq_set_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_order__class_Oorder_Oeq__iff) ).
thf(425,plain,
( ( (=) @ set_nat )
= ( ^ [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
& ( ord_less_eq_set_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(53,axiom,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_order__subst2) ).
thf(513,plain,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(131,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_ord__eq__le__trans) ).
thf(824,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(139,axiom,
! [A: a,B: set_a,C: set_a,D: a > $o] :
( ( member_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_prop__restrict) ).
thf(856,plain,
! [A: a,B: set_a,C: set_a,D: a > $o] :
( ( member_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(69,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ B @ A )
& ( ord_less_eq_set_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_dual__order_Oeq__iff) ).
thf(573,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ B @ A )
& ( ord_less_eq_set_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(176,axiom,
! [A: set_nat,B: nat > set_a] :
( ( finite_finite_nat @ A )
=> ( ! [C: nat] :
( ( member_nat @ C @ A )
=> ( finite_finite_a @ ( B @ C ) ) )
=> ( finite1808550458_nat_a @ ( product_Sigma_nat_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_finite__SigmaI) ).
thf(965,plain,
! [A: set_nat,B: nat > set_a] :
( ( finite_finite_nat @ A )
=> ( ! [C: nat] :
( ( member_nat @ C @ A )
=> ( finite_finite_a @ ( B @ C ) ) )
=> ( finite1808550458_nat_a @ ( product_Sigma_nat_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(110,axiom,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ C @ A )
=> ( ord_less_eq_set_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_dual__order_Otrans) ).
thf(750,plain,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ C @ A )
=> ( ord_less_eq_set_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(188,axiom,
! [A: set_a,B: set_nat] :
( ~ ( finite_finite_a @ A )
=> ( ~ ( finite_finite_nat @ B )
=> ~ ( finite1743148308_a_nat
@ ( product_Sigma_a_nat @ A
@ ^ [C: a] : B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_infinite__cartesian__product) ).
thf(1007,plain,
! [A: set_a,B: set_nat] :
( ~ ( finite_finite_a @ A )
=> ( ~ ( finite_finite_nat @ B )
=> ~ ( finite1743148308_a_nat
@ ( product_Sigma_a_nat @ A
@ ^ [C: a] : B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(26,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_Collect__mono) ).
thf(402,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(223,axiom,
! [A: set_a,B: a > $o] :
( ord_less_eq_set_a
@ ( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_Collect__restrict) ).
thf(1125,plain,
! [A: set_a,B: a > $o] :
( ord_less_eq_set_a
@ ( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(116,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_eq__refl) ).
thf(772,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(71,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_order_Otrans) ).
thf(579,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(62,axiom,
! [A: set_a,B: nat > set_a,C: nat,D: nat] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_order__subst1) ).
thf(545,plain,
! [A: set_a,B: nat > set_a,C: nat,D: nat] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(73,axiom,
! [A: nat,B: set_Product_prod_a_a > nat,C: set_Product_prod_a_a,D: set_Product_prod_a_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_le1824328871od_a_a @ C @ D )
=> ( ! [E: set_Product_prod_a_a,F: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_ord__eq__le__subst) ).
thf(584,plain,
! [A: nat,B: set_Product_prod_a_a > nat,C: set_Product_prod_a_a,D: set_Product_prod_a_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_le1824328871od_a_a @ C @ D )
=> ( ! [E: set_Product_prod_a_a,F: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(232,axiom,
! [A: pair_p125712459t_unit] :
( ( pair_p1802376898raph_a @ A )
=> ( pair_p1802376898raph_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_pair__fin__digraph_Opair__fin__digraph) ).
thf(1154,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(165,axiom,
( ( (=) @ set_Product_prod_a_a )
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ B @ A )
& ( ord_le1824328871od_a_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_dual__order_Oeq__iff) ).
thf(936,plain,
( ( (=) @ set_Product_prod_a_a )
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ B @ A )
& ( ord_le1824328871od_a_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(21,axiom,
! [A: set_nat,B: set_nat,C: set_nat > set_a,D: set_a] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_ord__le__eq__subst) ).
thf(382,plain,
! [A: set_nat,B: set_nat,C: set_nat > set_a,D: set_a] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(268,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a > $o] :
( ( finite179568208od_a_a
@ ( collec645855634od_a_a
@ ^ [C: product_prod_a_a] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite179568208od_a_a @ ( collec645855634od_a_a @ A ) )
& ( finite179568208od_a_a @ ( collec645855634od_a_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_finite__Collect__disjI) ).
thf(1271,plain,
! [A: product_prod_a_a > $o,B: product_prod_a_a > $o] :
( ( finite179568208od_a_a
@ ( collec645855634od_a_a
@ ^ [C: product_prod_a_a] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite179568208od_a_a @ ( collec645855634od_a_a @ A ) )
& ( finite179568208od_a_a @ ( collec645855634od_a_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(121,axiom,
! [A: set_nat,B: set_a > set_nat,C: set_a,D: set_a] :
( ( ord_less_eq_set_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_order__subst1) ).
thf(787,plain,
! [A: set_nat,B: set_a > set_nat,C: set_a,D: set_a] :
( ( ord_less_eq_set_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(48,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_subset__trans) ).
thf(498,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(205,axiom,
! [A: set_nat] :
( ( ~ ( finite_finite_nat @ A ) )
= ( ! [B: nat] :
? [C: nat] :
( ( ord_less_eq_nat @ B @ C )
& ( member_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_infinite__nat__iff__unbounded__le) ).
thf(1058,plain,
! [A: set_nat] :
( ( ~ ( finite_finite_nat @ A ) )
= ( ! [B: nat] :
? [C: nat] :
( ( ord_less_eq_nat @ B @ C )
& ( member_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(8,axiom,
! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_subset__refl) ).
thf(335,plain,
! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(214,axiom,
! [A: nat] :
~ ( member_nat @ A @ bot_bot_set_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_empty__iff) ).
thf(1090,plain,
! [A: nat] :
~ ( member_nat @ A @ bot_bot_set_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(115,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a > nat,D: nat] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_Product_prod_a_a,F: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_ord__le__eq__subst) ).
thf(764,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a > nat,D: nat] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_Product_prod_a_a,F: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(244,axiom,
! [A: set_a,B: set_a,C: a > set_Product_prod_a_a,D: a > set_Product_prod_a_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ! [E: a] :
( ( member_a @ E @ A )
=> ( ord_le1824328871od_a_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le1816232656od_a_a @ ( produc520147185od_a_a @ A @ C ) @ ( produc520147185od_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_Sigma__mono) ).
thf(1194,plain,
! [A: set_a,B: set_a,C: a > set_Product_prod_a_a,D: a > set_Product_prod_a_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ! [E: a] :
( ( member_a @ E @ A )
=> ( ord_le1824328871od_a_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le1816232656od_a_a @ ( produc520147185od_a_a @ A @ C ) @ ( produc520147185od_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(272,axiom,
! [A: pair_p125712459t_unit] :
( ( finite_finite_a @ ( pair_p1047056820t_unit @ A ) )
=> ( ( finite179568208od_a_a @ ( pair_p133601421t_unit @ A ) )
=> ( pair_p1864019935ioms_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_pair__fin__digraph__axioms_Ointro) ).
thf(1282,plain,
! [A: pair_p125712459t_unit] :
( ( finite_finite_a @ ( pair_p1047056820t_unit @ A ) )
=> ( ( finite179568208od_a_a @ ( pair_p133601421t_unit @ A ) )
=> ( pair_p1864019935ioms_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(220,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a > $o] :
( ! [C: product_prod_a_a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec645855634od_a_a @ A )
= ( collec645855634od_a_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_Collect__cong) ).
thf(1117,plain,
! [A: product_prod_a_a > $o,B: product_prod_a_a > $o] :
( ! [C: product_prod_a_a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec645855634od_a_a @ A )
= ( collec645855634od_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(19,axiom,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_order__class_Oorder_Oantisym) ).
thf(377,plain,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
! [A: set_nat,B: set_nat] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_nat @ A @ B )
=> ~ ( ord_less_eq_set_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_equalityE) ).
thf(318,plain,
! [A: set_nat,B: set_nat] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_nat @ A @ B )
=> ~ ( ord_less_eq_set_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(280,axiom,
! [A: set_a,B: set_a] :
( ~ ( finite_finite_a @ A )
=> ( ~ ( finite_finite_a @ B )
=> ~ ( finite179568208od_a_a
@ ( product_Sigma_a_a @ A
@ ^ [C: a] : B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_infinite__cartesian__product) ).
thf(1307,plain,
! [A: set_a,B: set_a] :
( ~ ( finite_finite_a @ A )
=> ( ~ ( finite_finite_a @ B )
=> ~ ( finite179568208od_a_a
@ ( product_Sigma_a_a @ A
@ ^ [C: a] : B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(141,axiom,
! [A: set_a,B: a > $o] :
( ord_less_eq_set_a
@ ( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_Collect__subset) ).
thf(863,plain,
! [A: set_a,B: a > $o] :
( ord_less_eq_set_a
@ ( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(14,axiom,
! [A: set_a,B: set_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_subsetI) ).
thf(362,plain,
! [A: set_a,B: set_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(37,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_order__trans) ).
thf(451,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(147,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ ( collec645855634od_a_a @ A ) @ ( collec645855634od_a_a @ B ) )
= ( ! [C: product_prod_a_a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_Collect__mono__iff) ).
thf(880,plain,
! [A: product_prod_a_a > $o,B: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ ( collec645855634od_a_a @ A ) @ ( collec645855634od_a_a @ B ) )
= ( ! [C: product_prod_a_a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(90,axiom,
( ( (=) @ set_nat )
= ( ^ [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ B @ A )
& ( ord_less_eq_set_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_dual__order_Oeq__iff) ).
thf(649,plain,
( ( (=) @ set_nat )
= ( ^ [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ B @ A )
& ( ord_less_eq_set_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(55,axiom,
! [A: set_nat,B: set_nat] :
( ( finite_finite_nat @ A )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( finite_finite_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_rev__finite__subset) ).
thf(520,plain,
! [A: set_nat,B: set_nat] :
( ( finite_finite_nat @ A )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( finite_finite_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(284,axiom,
! [A: pair_p1765063010t_unit] :
( ( pair_p374947051od_a_a @ A )
=> ( finite179568208od_a_a @ ( pair_p447552203t_unit @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_pair__fin__digraph_Opair__finite__verts) ).
thf(1325,plain,
! [A: pair_p1765063010t_unit] :
( ( pair_p374947051od_a_a @ A )
=> ( finite179568208od_a_a @ ( pair_p447552203t_unit @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(195,axiom,
! [A: pair_p125712459t_unit] :
( ( pair_p68905728raph_a @ A )
=> ( ( pair_p1864019935ioms_a @ A )
=> ( pair_p1802376898raph_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_pair__fin__digraph_Ointro) ).
thf(1029,plain,
! [A: pair_p125712459t_unit] :
( ( pair_p68905728raph_a @ A )
=> ( ( pair_p1864019935ioms_a @ A )
=> ( pair_p1802376898raph_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(230,axiom,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ord_le1347718902_a_a_o
@ ^ [C: product_prod_a_a] : ( member449909584od_a_a @ C @ A )
@ ^ [C: product_prod_a_a] : ( member449909584od_a_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_less__eq__set__def) ).
thf(1149,plain,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ord_le1347718902_a_a_o
@ ^ [C: product_prod_a_a] : ( member449909584od_a_a @ C @ A )
@ ^ [C: product_prod_a_a] : ( member449909584od_a_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(158,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_order__trans) ).
thf(915,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(291,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( finite676513017od_a_a
@ ( produc520147185od_a_a @ A
@ ^ [C: a] : B ) )
= ( ( A = bot_bot_set_a )
| ( B = bot_bo2131659635od_a_a )
| ( ( finite_finite_a @ A )
& ( finite179568208od_a_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_finite__cartesian__product__iff) ).
thf(1344,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( finite676513017od_a_a
@ ( produc520147185od_a_a @ A
@ ^ [C: a] : B ) )
= ( ( A = bot_bot_set_a )
| ( B = bot_bo2131659635od_a_a )
| ( ( finite_finite_a @ A )
& ( finite179568208od_a_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(275,axiom,
! [A: set_Product_prod_a_a,B: set_nat] :
( ( finite1837575485_a_nat
@ ( produc931712687_a_nat @ A
@ ^ [C: product_prod_a_a] : B ) )
= ( ( A = bot_bo2131659635od_a_a )
| ( B = bot_bot_set_nat )
| ( ( finite179568208od_a_a @ A )
& ( finite_finite_nat @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_finite__cartesian__product__iff) ).
thf(1293,plain,
! [A: set_Product_prod_a_a,B: set_nat] :
( ( finite1837575485_a_nat
@ ( produc931712687_a_nat @ A
@ ^ [C: product_prod_a_a] : B ) )
= ( ( A = bot_bo2131659635od_a_a )
| ( B = bot_bot_set_nat )
| ( ( finite179568208od_a_a @ A )
& ( finite_finite_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(303,axiom,
! [A: set_Product_prod_a_a] :
( ( finite179568208od_a_a @ A )
=> ( finite1145471536od_a_a
@ ( collec183727474od_a_a
@ ^ [B: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_finite__Collect__subsets) ).
thf(1381,plain,
! [A: set_Product_prod_a_a] :
( ( finite179568208od_a_a @ A )
=> ( finite1145471536od_a_a
@ ( collec183727474od_a_a
@ ^ [B: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(164,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > set_a,D: product_prod_a_a > set_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ! [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le677315902_a_a_a @ ( produc1282482655_a_a_a @ A @ C ) @ ( produc1282482655_a_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_Sigma__mono) ).
thf(932,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: product_prod_a_a > set_a,D: product_prod_a_a > set_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ! [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ A )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le677315902_a_a_a @ ( produc1282482655_a_a_a @ A @ C ) @ ( produc1282482655_a_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(206,axiom,
! [A: set_nat,B: set_nat,C: nat > $o] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ A
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: nat] :
( ( member_nat @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_subset__Collect__iff) ).
thf(1061,plain,
! [A: set_nat,B: set_nat,C: nat > $o] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ A
@ ( collect_nat
@ ^ [D: nat] :
( ( member_nat @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: nat] :
( ( member_nat @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(245,axiom,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_subset__iff) ).
thf(1198,plain,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(174,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_order__class_Oorder_Oantisym) ).
thf(959,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(259,axiom,
! [A: nat > $o] :
( ~ ( finite_finite_nat @ ( collect_nat @ A ) )
=> ? [B: nat] : ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_not__finite__existsD) ).
thf(1245,plain,
! [A: nat > $o] :
( ~ ( finite_finite_nat @ ( collect_nat @ A ) )
=> ? [B: nat] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(148,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_dual__order_Oantisym) ).
thf(883,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(3,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_ord__eq__le__subst) ).
thf(306,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(186,axiom,
! [A: set_Product_prod_a_a,B: product_prod_a_a > $o,C: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ A
@ ( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_le1824328871od_a_a @ A @ ( collec645855634od_a_a @ B ) )
& ( ord_le1824328871od_a_a @ A @ ( collec645855634od_a_a @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_conj__subset__def) ).
thf(1000,plain,
! [A: set_Product_prod_a_a,B: product_prod_a_a > $o,C: product_prod_a_a > $o] :
( ( ord_le1824328871od_a_a @ A
@ ( collec645855634od_a_a
@ ^ [D: product_prod_a_a] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_le1824328871od_a_a @ A @ ( collec645855634od_a_a @ B ) )
& ( ord_le1824328871od_a_a @ A @ ( collec645855634od_a_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(261,axiom,
! [A: set_Product_prod_a_a,B: set_a] :
( ( finite1919032935_a_a_a
@ ( produc1282482655_a_a_a @ A
@ ^ [C: product_prod_a_a] : B ) )
= ( ( A = bot_bo2131659635od_a_a )
| ( B = bot_bot_set_a )
| ( ( finite179568208od_a_a @ A )
& ( finite_finite_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_finite__cartesian__product__iff) ).
thf(1250,plain,
! [A: set_Product_prod_a_a,B: set_a] :
( ( finite1919032935_a_a_a
@ ( produc1282482655_a_a_a @ A
@ ^ [C: product_prod_a_a] : B ) )
= ( ( A = bot_bo2131659635od_a_a )
| ( B = bot_bot_set_a )
| ( ( finite179568208od_a_a @ A )
& ( finite_finite_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(217,axiom,
! [A: set_a,B: set_nat,C: a > nat > $o] :
( ~ ( finite_finite_a @ A )
=> ( ( finite_finite_nat @ B )
=> ( ! [D: a] :
( ( member_a @ D @ A )
=> ? [E: nat] :
( ( member_nat @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: nat] :
( ( member_nat @ D @ B )
& ~ ( finite_finite_a
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_pigeonhole__infinite__rel) ).
thf(1102,plain,
! [A: set_a,B: set_nat,C: a > nat > $o] :
( ~ ( finite_finite_a @ A )
=> ( ( finite_finite_nat @ B )
=> ( ! [D: a] :
( ( member_a @ D @ A )
=> ? [E: nat] :
( ( member_nat @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: nat] :
( ( member_nat @ D @ B )
& ~ ( finite_finite_a
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(32,axiom,
! [A: nat,B: nat,C: nat > set_nat,D: set_nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_order__subst2) ).
thf(431,plain,
! [A: nat,B: nat,C: nat > set_nat,D: set_nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(93,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_antisym__conv) ).
thf(658,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(41,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_dual__order_Otrans) ).
thf(473,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(248,axiom,
! [A: nat > $o,B: nat > $o] :
( ! [C: nat] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_nat @ A )
= ( collect_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_Collect__cong) ).
thf(1208,plain,
! [A: nat > $o,B: nat > $o] :
( ! [C: nat] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_nat @ A )
= ( collect_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(123,axiom,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_ord__eq__le__trans) ).
thf(795,plain,
! [A: nat,B: nat,C: nat] :
( ( A = B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(270,axiom,
! [A: set_a,B: set_Product_prod_a_a] :
( ( finite_finite_a @ A )
=> ( ( finite179568208od_a_a @ B )
=> ( finite676513017od_a_a
@ ( produc520147185od_a_a @ A
@ ^ [C: a] : B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_finite__cartesian__product) ).
thf(1277,plain,
! [A: set_a,B: set_Product_prod_a_a] :
( ( finite_finite_a @ A )
=> ( ( finite179568208od_a_a @ B )
=> ( finite676513017od_a_a
@ ( produc520147185od_a_a @ A
@ ^ [C: a] : B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(39,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ~ ! [D: nat] :
( ( A @ D )
=> ~ ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_bounded__Max__nat) ).
thf(458,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ~ ! [D: nat] :
( ( A @ D )
=> ~ ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(134,axiom,
! [A: set_nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_set_nat @ A
@ ( collect_nat
@ ^ [D: nat] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq_set_nat @ A @ ( collect_nat @ B ) )
& ( ord_less_eq_set_nat @ A @ ( collect_nat @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_conj__subset__def) ).
thf(836,plain,
! [A: set_nat,B: nat > $o,C: nat > $o] :
( ( ord_less_eq_set_nat @ A
@ ( collect_nat
@ ^ [D: nat] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq_set_nat @ A @ ( collect_nat @ B ) )
& ( ord_less_eq_set_nat @ A @ ( collect_nat @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(201,axiom,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_subset__eq) ).
thf(1049,plain,
( ord_le1824328871od_a_a
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( member449909584od_a_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(162,axiom,
! [A: set_nat,B: nat > $o] :
( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( member_nat @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_Collect__subset) ).
thf(927,plain,
! [A: set_nat,B: nat > $o] :
( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( member_nat @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(18,axiom,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_set_nat @ ( collect_nat @ A ) @ ( collect_nat @ B ) )
= ( ! [C: nat] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_Collect__mono__iff) ).
thf(374,plain,
! [A: nat > $o,B: nat > $o] :
( ( ord_less_eq_set_nat @ ( collect_nat @ A ) @ ( collect_nat @ B ) )
= ( ! [C: nat] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(117,axiom,
! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_dual__order_Orefl) ).
thf(776,plain,
! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(187,axiom,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_a,D: set_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( ord_le1816232656od_a_a
@ ( produc520147185od_a_a @ C
@ ^ [E: a] : B )
@ ( produc520147185od_a_a @ D
@ ^ [E: a] : B ) )
= ( ord_less_eq_set_a @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_Times__subset__cancel2) ).
thf(1003,plain,
! [A: product_prod_a_a,B: set_Product_prod_a_a,C: set_a,D: set_a] :
( ( member449909584od_a_a @ A @ B )
=> ( ( ord_le1816232656od_a_a
@ ( produc520147185od_a_a @ C
@ ^ [E: a] : B )
@ ( produc520147185od_a_a @ D
@ ^ [E: a] : B ) )
= ( ord_less_eq_set_a @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(87,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_order__class_Oorder_Oantisym) ).
thf(640,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(144,axiom,
! [A: pair_p1593840546t_unit] :
( ( pair_p159207083od_a_a @ A )
=> ( finite1664988688od_a_a @ ( pair_p1652294923t_unit @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_pair__fin__digraph_Opair__finite__verts) ).
thf(872,plain,
! [A: pair_p1593840546t_unit] :
( ( pair_p159207083od_a_a @ A )
=> ( finite1664988688od_a_a @ ( pair_p1652294923t_unit @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(102,axiom,
( ( (=) @ set_nat )
= ( ^ [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
& ( ord_less_eq_set_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_set__eq__subset) ).
thf(707,plain,
( ( (=) @ set_nat )
= ( ^ [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
& ( ord_less_eq_set_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(184,axiom,
! [A: set_nat,B: set_nat,C: nat > set_Product_prod_a_a,D: nat > set_Product_prod_a_a] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ! [E: nat] :
( ( member_nat @ E @ A )
=> ( ord_le1824328871od_a_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le2084554594od_a_a @ ( produc1182842125od_a_a @ A @ C ) @ ( produc1182842125od_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_Sigma__mono) ).
thf(993,plain,
! [A: set_nat,B: set_nat,C: nat > set_Product_prod_a_a,D: nat > set_Product_prod_a_a] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ! [E: nat] :
( ( member_nat @ E @ A )
=> ( ord_le1824328871od_a_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le2084554594od_a_a @ ( produc1182842125od_a_a @ A @ C ) @ ( produc1182842125od_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(28,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_order__refl) ).
thf(409,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(255,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( A = B )
=> ( ( ord_le1824328871od_a_a @ B @ C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_ord__eq__le__trans) ).
thf(1230,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( A = B )
=> ( ( ord_le1824328871od_a_a @ B @ C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(122,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_equalityD1) ).
thf(791,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(198,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1347718902_a_a_o
@ ^ [C: product_prod_a_a] : ( member449909584od_a_a @ C @ A )
@ ^ [C: product_prod_a_a] : ( member449909584od_a_a @ C @ B ) )
= ( ord_le1824328871od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_pred__subset__eq) ).
thf(1038,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1347718902_a_a_o
@ ^ [C: product_prod_a_a] : ( member449909584od_a_a @ C @ A )
@ ^ [C: product_prod_a_a] : ( member449909584od_a_a @ C @ B ) )
= ( ord_le1824328871od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(104,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_dual__order_Oantisym) ).
thf(717,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(256,axiom,
! [A: set_a,B: set_nat] :
( ( finite1743148308_a_nat
@ ( product_Sigma_a_nat @ A
@ ^ [C: a] : B ) )
= ( ( A = bot_bot_set_a )
| ( B = bot_bot_set_nat )
| ( ( finite_finite_a @ A )
& ( finite_finite_nat @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_finite__cartesian__product__iff) ).
thf(1235,plain,
! [A: set_a,B: set_nat] :
( ( finite1743148308_a_nat
@ ( product_Sigma_a_nat @ A
@ ^ [C: a] : B ) )
= ( ( A = bot_bot_set_a )
| ( B = bot_bot_set_nat )
| ( ( finite_finite_a @ A )
& ( finite_finite_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(251,axiom,
( product_product_a_a
= ( ^ [A: set_a,B: set_a] :
( product_Sigma_a_a @ A
@ ^ [C: a] : B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_Product__Type_Oproduct__def) ).
thf(1218,plain,
( product_product_a_a
= ( ^ [A: set_a,B: set_a] :
( product_Sigma_a_a @ A
@ ^ [C: a] : B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(252,axiom,
( ( (=) @ set_Product_prod_a_a )
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
& ( ord_le1824328871od_a_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_set__eq__subset) ).
thf(1220,plain,
( ( (=) @ set_Product_prod_a_a )
= ( ^ [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
& ( ord_le1824328871od_a_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(242,axiom,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_unit] :
( ( pair_p447552203t_unit @ ( pair_p398687508t_unit @ A @ B @ C ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_pair__pre__digraph_Oselect__convs_I1_J) ).
thf(1188,plain,
! [A: set_Product_prod_a_a,B: set_Pr1948701895od_a_a,C: product_unit] :
( ( pair_p447552203t_unit @ ( pair_p398687508t_unit @ A @ B @ C ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(241,axiom,
( pair_p374947051od_a_a
= ( ^ [A: pair_p1765063010t_unit] :
( ( pair_p646030121od_a_a @ A )
& ( pair_p504738056od_a_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_pair__fin__digraph__def) ).
thf(1186,plain,
( pair_p374947051od_a_a
= ( ^ [A: pair_p1765063010t_unit] :
( ( pair_p646030121od_a_a @ A )
& ( pair_p504738056od_a_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(288,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( finite179568208od_a_a @ B )
=> ( finite179568208od_a_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_finite__subset) ).
thf(1336,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( finite179568208od_a_a @ B )
=> ( finite179568208od_a_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(88,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_order__subst2) ).
thf(643,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(263,axiom,
! [A: set_Product_prod_a_a,B: product_prod_a_a > set_nat] :
( ( finite179568208od_a_a @ A )
=> ( ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( finite_finite_nat @ ( B @ C ) ) )
=> ( finite1837575485_a_nat @ ( produc931712687_a_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_finite__SigmaI) ).
thf(1257,plain,
! [A: set_Product_prod_a_a,B: product_prod_a_a > set_nat] :
( ( finite179568208od_a_a @ A )
=> ( ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( finite_finite_nat @ ( B @ C ) ) )
=> ( finite1837575485_a_nat @ ( produc931712687_a_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(80,axiom,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( A = B )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ord_less_eq_set_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_ord__eq__le__trans) ).
thf(613,plain,
! [A: set_nat,B: set_nat,C: set_nat] :
( ( A = B )
=> ( ( ord_less_eq_set_nat @ B @ C )
=> ( ord_less_eq_set_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(273,axiom,
! [A: set_a,B: set_Product_prod_a_a,C: a > product_prod_a_a > $o] :
( ~ ( finite_finite_a @ A )
=> ( ( finite179568208od_a_a @ B )
=> ( ! [D: a] :
( ( member_a @ D @ A )
=> ? [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
& ~ ( finite_finite_a
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_pigeonhole__infinite__rel) ).
thf(1284,plain,
! [A: set_a,B: set_Product_prod_a_a,C: a > product_prod_a_a > $o] :
( ~ ( finite_finite_a @ A )
=> ( ( finite179568208od_a_a @ B )
=> ( ! [D: a] :
( ( member_a @ D @ A )
=> ? [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
& ~ ( finite_finite_a
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(4,axiom,
! [A: set_nat,B: set_nat] :
( ( A = B )
=> ( ord_less_eq_set_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_equalityD2) ).
thf(314,plain,
! [A: set_nat,B: set_nat] :
( ( A = B )
=> ( ord_less_eq_set_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(75,axiom,
! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_order__refl) ).
thf(595,plain,
! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(140,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( A = B )
=> ( ord_le1824328871od_a_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_equalityD2) ).
thf(859,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( A = B )
=> ( ord_le1824328871od_a_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(183,axiom,
! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
( ( ord_le456379495od_a_a @ A @ B )
=> ( ~ ( finite1664988688od_a_a @ A )
=> ~ ( finite1664988688od_a_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_infinite__super) ).
thf(991,plain,
! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
( ( ord_le456379495od_a_a @ A @ B )
=> ( ~ ( finite1664988688od_a_a @ A )
=> ~ ( finite1664988688od_a_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(295,axiom,
! [A: set_nat,B: set_Product_prod_a_a,C: nat > product_prod_a_a > $o] :
( ~ ( finite_finite_nat @ A )
=> ( ( finite179568208od_a_a @ B )
=> ( ! [D: nat] :
( ( member_nat @ D @ A )
=> ? [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_pigeonhole__infinite__rel) ).
thf(1353,plain,
! [A: set_nat,B: set_Product_prod_a_a,C: nat > product_prod_a_a > $o] :
( ~ ( finite_finite_nat @ A )
=> ( ( finite179568208od_a_a @ B )
=> ( ! [D: nat] :
( ( member_nat @ D @ A )
=> ? [E: product_prod_a_a] :
( ( member449909584od_a_a @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: product_prod_a_a] :
( ( member449909584od_a_a @ D @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(77,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_antisym__conv) ).
thf(600,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(137,axiom,
! [A: set_a,B: set_a,C: a > set_a,D: a > set_a] :
( ( A = B )
=> ( ! [E: a] :
( ( member_a @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( product_Sigma_a_a @ A @ C )
= ( product_Sigma_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_Sigma__cong) ).
thf(845,plain,
! [A: set_a,B: set_a,C: a > set_a,D: a > set_a] :
( ( A = B )
=> ( ! [E: a] :
( ( member_a @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( product_Sigma_a_a @ A @ C )
= ( product_Sigma_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(40,axiom,
! [A: set_nat,B: set_a > set_nat,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_ord__eq__le__subst) ).
thf(465,plain,
! [A: set_nat,B: set_a > set_nat,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(212,axiom,
! [A: product_prod_a_a,B: product_prod_a_a > $o] :
( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_mem__Collect__eq) ).
thf(1084,plain,
! [A: product_prod_a_a,B: product_prod_a_a > $o] :
( ( member449909584od_a_a @ A @ ( collec645855634od_a_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(60,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_dual__order_Oantisym) ).
thf(539,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(113,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_in__mono) ).
thf(759,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(189,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_subset__antisym) ).
thf(1010,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(16,axiom,
! [A: set_nat,B: set_nat] :
( ( A = B )
=> ( ord_less_eq_set_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_equalityD1) ).
thf(368,plain,
! [A: set_nat,B: set_nat] :
( ( A = B )
=> ( ord_less_eq_set_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(218,axiom,
! [A: set_se1596668135od_a_a,B: set_Product_prod_a_a] :
( ( finite1145471536od_a_a @ A )
=> ( ( member1838126896od_a_a @ B @ A )
=> ? [C: set_Product_prod_a_a] :
( ( member1838126896od_a_a @ C @ A )
& ( ord_le1824328871od_a_a @ B @ C )
& ! [D: set_Product_prod_a_a] :
( ( member1838126896od_a_a @ D @ A )
=> ( ( ord_le1824328871od_a_a @ C @ D )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_finite__has__maximal2) ).
thf(1108,plain,
! [A: set_se1596668135od_a_a,B: set_Product_prod_a_a] :
( ( finite1145471536od_a_a @ A )
=> ( ( member1838126896od_a_a @ B @ A )
=> ? [C: set_Product_prod_a_a] :
( ( member1838126896od_a_a @ C @ A )
& ( ord_le1824328871od_a_a @ B @ C )
& ! [D: set_Product_prod_a_a] :
( ( member1838126896od_a_a @ D @ A )
=> ( ( ord_le1824328871od_a_a @ C @ D )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(99,axiom,
! [A: set_nat,B: set_nat,C: nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_in__mono) ).
thf(688,plain,
! [A: set_nat,B: set_nat,C: nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( member_nat @ C @ A )
=> ( member_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(153,axiom,
! [A: set_nat,B: set_a] :
( ( finite_finite_nat @ A )
=> ( ( finite_finite_a @ B )
=> ( finite1808550458_nat_a
@ ( product_Sigma_nat_a @ A
@ ^ [C: nat] : B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_finite__cartesian__product) ).
thf(903,plain,
! [A: set_nat,B: set_a] :
( ( finite_finite_nat @ A )
=> ( ( finite_finite_a @ B )
=> ( finite1808550458_nat_a
@ ( product_Sigma_nat_a @ A
@ ^ [C: nat] : B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(128,axiom,
! [A: set_nat,B: set_nat > set_nat,C: set_nat,D: set_nat] :
( ( ord_less_eq_set_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_order__subst1) ).
thf(813,plain,
! [A: set_nat,B: set_nat > set_nat,C: set_nat,D: set_nat] :
( ( ord_less_eq_set_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(54,axiom,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_antisym) ).
thf(517,plain,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(290,axiom,
! [A: pair_p125712459t_unit] :
( A
= ( pair_p1621517565t_unit @ ( pair_p1047056820t_unit @ A ) @ ( pair_p133601421t_unit @ A ) @ ( pair_p1896222615t_unit @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_pair__pre__digraph_Osurjective) ).
thf(1341,plain,
! [A: pair_p125712459t_unit] :
( A
= ( pair_p1621517565t_unit @ ( pair_p1047056820t_unit @ A ) @ ( pair_p133601421t_unit @ A ) @ ( pair_p1896222615t_unit @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(169,axiom,
! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_empty__iff) ).
thf(946,plain,
! [A: product_prod_a_a] :
~ ( member449909584od_a_a @ A @ bot_bo2131659635od_a_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(12,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_order_Otrans) ).
thf(351,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(22,axiom,
! [A: set_a,B: a > $o,C: a > $o] :
( ( ord_less_eq_set_a @ A
@ ( collect_a
@ ^ [D: a] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq_set_a @ A @ ( collect_a @ B ) )
& ( ord_less_eq_set_a @ A @ ( collect_a @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_conj__subset__def) ).
thf(390,plain,
! [A: set_a,B: a > $o,C: a > $o] :
( ( ord_less_eq_set_a @ A
@ ( collect_a
@ ^ [D: a] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq_set_a @ A @ ( collect_a @ B ) )
& ( ord_less_eq_set_a @ A @ ( collect_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(84,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_subset__empty) ).
thf(632,plain,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(119,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_equalityD2) ).
thf(781,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(262,axiom,
! [A: set_Product_prod_a_a,B: product_prod_a_a > set_a] :
( ( finite179568208od_a_a @ A )
=> ( ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( finite_finite_a @ ( B @ C ) ) )
=> ( finite1919032935_a_a_a @ ( produc1282482655_a_a_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_finite__SigmaI) ).
thf(1253,plain,
! [A: set_Product_prod_a_a,B: product_prod_a_a > set_a] :
( ( finite179568208od_a_a @ A )
=> ( ! [C: product_prod_a_a] :
( ( member449909584od_a_a @ C @ A )
=> ( finite_finite_a @ ( B @ C ) ) )
=> ( finite1919032935_a_a_a @ ( produc1282482655_a_a_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(101,axiom,
! [A: set_nat,B: set_nat,C: set_nat > set_nat,D: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_ord__le__eq__subst) ).
thf(699,plain,
! [A: set_nat,B: set_nat,C: set_nat > set_nat,D: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(52,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_subset__antisym) ).
thf(510,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(163,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_antisym__conv) ).
thf(929,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(63,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_subset__iff) ).
thf(549,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(59,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_Collect__mono__iff) ).
thf(536,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(200,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( A = B )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_equalityD1) ).
thf(1045,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a] :
( ( A = B )
=> ( ord_le1824328871od_a_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(235,axiom,
! [A: product_prod_a_a > $o] :
( ( ( collec645855634od_a_a @ A )
= bot_bo2131659635od_a_a )
= ( ! [B: product_prod_a_a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_Collect__empty__eq) ).
thf(1161,plain,
! [A: product_prod_a_a > $o] :
( ( ( collec645855634od_a_a @ A )
= bot_bo2131659635od_a_a )
= ( ! [B: product_prod_a_a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(124,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( finite_finite_a @ B )
=> ( finite_finite_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_finite__subset) ).
thf(800,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( finite_finite_a @ B )
=> ( finite_finite_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(226,axiom,
! [A: set_nat,B: set_nat,C: nat > $o,D: nat > $o] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ! [E: nat] :
( ( member_nat @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ A )
& ( C @ E ) ) )
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_subset__CollectI) ).
thf(1133,plain,
! [A: set_nat,B: set_nat,C: nat > $o,D: nat > $o] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ! [E: nat] :
( ( member_nat @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ A )
& ( C @ E ) ) )
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(35,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_order__class_Oorder_Oeq__iff) ).
thf(447,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(271,axiom,
( finite351630733od_a_a
= ( ^ [A: set_Product_prod_a_a] :
( collec183727474od_a_a
@ ^ [B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ B @ A )
& ( finite179568208od_a_a @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_Fpow__def) ).
thf(1280,plain,
( finite351630733od_a_a
= ( ^ [A: set_Product_prod_a_a] :
( collec183727474od_a_a
@ ^ [B: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ B @ A )
& ( finite179568208od_a_a @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(133,axiom,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_dual__order_Oantisym) ).
thf(833,plain,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( ord_less_eq_set_nat @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(27,axiom,
! [A: nat,B: set_nat > nat,C: set_nat,D: set_nat] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_order__subst1) ).
thf(405,plain,
! [A: nat,B: set_nat > nat,C: set_nat,D: set_nat] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(142,axiom,
! [A: set_a,B: set_a,C: a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ! [E: a] :
( ( member_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq_set_a
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ A )
& ( C @ E ) ) )
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_subset__CollectI) ).
thf(865,plain,
! [A: set_a,B: set_a,C: a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ! [E: a] :
( ( member_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq_set_a
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ A )
& ( C @ E ) ) )
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(78,axiom,
( ( (=) @ set_nat )
= ( ^ [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
& ( ord_less_eq_set_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_eq__iff) ).
thf(603,plain,
( ( (=) @ set_nat )
= ( ^ [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
& ( ord_less_eq_set_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(1,conjecture,
finite179568208od_a_a @ ( pair_p133601421t_unit @ g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(305,plain,
~ ( finite179568208od_a_a @ ( pair_p133601421t_unit @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(159,axiom,
! [A: set_a,B: set_nat] :
( ( finite_finite_a @ A )
=> ( ( finite_finite_nat @ B )
=> ( finite1743148308_a_nat
@ ( product_Sigma_a_nat @ A
@ ^ [C: a] : B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_finite__cartesian__product) ).
thf(918,plain,
! [A: set_a,B: set_nat] :
( ( finite_finite_a @ A )
=> ( ( finite_finite_nat @ B )
=> ( finite1743148308_a_nat
@ ( product_Sigma_a_nat @ A
@ ^ [C: a] : B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(152,axiom,
! [A: set_nat,B: nat] :
( ( finite_finite_nat @ A )
=> ( ( member_nat @ B @ A )
=> ? [C: nat] :
( ( member_nat @ C @ A )
& ( ord_less_eq_nat @ B @ C )
& ! [D: nat] :
( ( member_nat @ D @ A )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_finite__has__maximal2) ).
thf(897,plain,
! [A: set_nat,B: nat] :
( ( finite_finite_nat @ A )
=> ( ( member_nat @ B @ A )
=> ? [C: nat] :
( ( member_nat @ C @ A )
& ( ord_less_eq_nat @ B @ C )
& ! [D: nat] :
( ( member_nat @ D @ A )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(204,axiom,
! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_order__refl) ).
thf(1056,plain,
! [A: set_Product_prod_a_a] : ( ord_le1824328871od_a_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(85,axiom,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( finite_finite_nat @ B )
=> ( finite_finite_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_finite__subset) ).
thf(635,plain,
! [A: set_nat,B: set_nat] :
( ( ord_less_eq_set_nat @ A @ B )
=> ( ( finite_finite_nat @ B )
=> ( finite_finite_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(207,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_subset__trans) ).
thf(1065,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ B @ C )
=> ( ord_le1824328871od_a_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(105,axiom,
! [A: set_a,B: set_nat > set_a,C: set_nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_ord__eq__le__subst) ).
thf(720,plain,
! [A: set_a,B: set_nat > set_a,C: set_nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(172,axiom,
! [A: a > $o] :
( ~ ( finite_finite_a @ ( collect_a @ A ) )
=> ? [B: a] : ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_not__finite__existsD) ).
thf(955,plain,
! [A: a > $o] :
( ~ ( finite_finite_a @ ( collect_a @ A ) )
=> ? [B: a] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(149,axiom,
! [A: set_nat,B: set_Pr1986765409at_nat,C: nat > product_prod_nat_nat > $o] :
( ~ ( finite_finite_nat @ A )
=> ( ( finite772653738at_nat @ B )
=> ( ! [D: nat] :
( ( member_nat @ D @ A )
=> ? [E: product_prod_nat_nat] :
( ( member701585322at_nat @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: product_prod_nat_nat] :
( ( member701585322at_nat @ D @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_pigeonhole__infinite__rel) ).
thf(886,plain,
! [A: set_nat,B: set_Pr1986765409at_nat,C: nat > product_prod_nat_nat > $o] :
( ~ ( finite_finite_nat @ A )
=> ( ( finite772653738at_nat @ B )
=> ( ! [D: nat] :
( ( member_nat @ D @ A )
=> ? [E: product_prod_nat_nat] :
( ( member701585322at_nat @ E @ B )
& ( C @ D @ E ) ) )
=> ? [D: product_prod_nat_nat] :
( ( member701585322at_nat @ D @ B )
& ~ ( finite_finite_nat
@ ( collect_nat
@ ^ [E: nat] :
( ( member_nat @ E @ A )
& ( C @ E @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(106,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_eq__iff) ).
thf(728,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(264,axiom,
! [A: set_nat,B: nat > set_Product_prod_a_a] :
( ( finite_finite_nat @ A )
=> ( ! [C: nat] :
( ( member_nat @ C @ A )
=> ( finite179568208od_a_a @ ( B @ C ) ) )
=> ( finite1297454819od_a_a @ ( produc1182842125od_a_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_finite__SigmaI) ).
thf(1261,plain,
! [A: set_nat,B: nat > set_Product_prod_a_a] :
( ( finite_finite_nat @ A )
=> ( ! [C: nat] :
( ( member_nat @ C @ A )
=> ( finite179568208od_a_a @ ( B @ C ) ) )
=> ( finite1297454819od_a_a @ ( produc1182842125od_a_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(31,axiom,
! [A: set_nat,B: set_nat] :
( ( A = B )
=> ( ord_less_eq_set_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_eq__refl) ).
thf(427,plain,
! [A: set_nat,B: set_nat] :
( ( A = B )
=> ( ord_less_eq_set_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(155,axiom,
! [A: pair_p1765063010t_unit] :
( ( pair_p374947051od_a_a @ A )
=> ( pair_p504738056od_a_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_pair__fin__digraph_Oaxioms_I2_J) ).
thf(908,plain,
! [A: pair_p1765063010t_unit] :
( ( pair_p374947051od_a_a @ A )
=> ( pair_p504738056od_a_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(181,axiom,
( pair_p1802376898raph_a
= ( ^ [A: pair_p125712459t_unit] :
( ( pair_p68905728raph_a @ A )
& ( pair_p1864019935ioms_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_pair__fin__digraph__def) ).
thf(982,plain,
( pair_p1802376898raph_a
= ( ^ [A: pair_p125712459t_unit] :
( ( pair_p68905728raph_a @ A )
& ( pair_p1864019935ioms_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(277,axiom,
! [A: set_Product_prod_a_a,B: set_a] :
( ~ ( finite179568208od_a_a @ A )
=> ( ~ ( finite_finite_a @ B )
=> ~ ( finite1919032935_a_a_a
@ ( produc1282482655_a_a_a @ A
@ ^ [C: product_prod_a_a] : B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_infinite__cartesian__product) ).
thf(1299,plain,
! [A: set_Product_prod_a_a,B: set_a] :
( ~ ( finite179568208od_a_a @ A )
=> ( ~ ( finite_finite_a @ B )
=> ~ ( finite1919032935_a_a_a
@ ( produc1282482655_a_a_a @ A
@ ^ [C: product_prod_a_a] : B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(100,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_ord__le__eq__subst) ).
thf(691,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(221,axiom,
! [A: produc1572603623od_a_a > $o,B: produc1572603623od_a_a > $o] :
( ( finite1664988688od_a_a
@ ( collec1635618130od_a_a
@ ^ [C: produc1572603623od_a_a] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite1664988688od_a_a @ ( collec1635618130od_a_a @ A ) )
& ( finite1664988688od_a_a @ ( collec1635618130od_a_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_finite__Collect__disjI) ).
thf(1120,plain,
! [A: produc1572603623od_a_a > $o,B: produc1572603623od_a_a > $o] :
( ( finite1664988688od_a_a
@ ( collec1635618130od_a_a
@ ^ [C: produc1572603623od_a_a] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite1664988688od_a_a @ ( collec1635618130od_a_a @ A ) )
& ( finite1664988688od_a_a @ ( collec1635618130od_a_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(49,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_dual__order_Otrans) ).
thf(501,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(215,axiom,
! [A: set_nat,B: nat] :
( ( finite_finite_nat @ A )
=> ( ( member_nat @ B @ A )
=> ? [C: nat] :
( ( member_nat @ C @ A )
& ( ord_less_eq_nat @ C @ B )
& ! [D: nat] :
( ( member_nat @ D @ A )
=> ( ( ord_less_eq_nat @ D @ C )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_finite__has__minimal2) ).
thf(1093,plain,
! [A: set_nat,B: nat] :
( ( finite_finite_nat @ A )
=> ( ( member_nat @ B @ A )
=> ? [C: nat] :
( ( member_nat @ C @ A )
& ( ord_less_eq_nat @ C @ B )
& ! [D: nat] :
( ( member_nat @ D @ A )
=> ( ( ord_less_eq_nat @ D @ C )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(83,axiom,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_ord__le__eq__subst) ).
thf(624,plain,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(135,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ C @ A )
=> ( ord_le1824328871od_a_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_dual__order_Otrans) ).
thf(839,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_le1824328871od_a_a @ C @ A )
=> ( ord_le1824328871od_a_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(266,axiom,
( pair_p504738056od_a_a
= ( ^ [A: pair_p1765063010t_unit] :
( ( finite179568208od_a_a @ ( pair_p447552203t_unit @ A ) )
& ( finite1664988688od_a_a @ ( pair_p1783210148t_unit @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_pair__fin__digraph__axioms__def) ).
thf(1268,plain,
( pair_p504738056od_a_a
= ( ^ [A: pair_p1765063010t_unit] :
( ( finite179568208od_a_a @ ( pair_p447552203t_unit @ A ) )
& ( finite1664988688od_a_a @ ( pair_p1783210148t_unit @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(70,axiom,
! [A: set_a,B: set_a,C: set_a > nat,D: nat] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_order__subst2) ).
thf(575,plain,
! [A: set_a,B: set_a,C: set_a > nat,D: nat] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(45,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_order__class_Oorder_Oeq__iff) ).
thf(486,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(9,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_eq_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_equalityE) ).
thf(337,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_eq_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
! [A: set_nat,B: set_nat > set_nat,C: set_nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_ord__eq__le__subst) ).
thf(354,plain,
! [A: set_nat,B: set_nat > set_nat,C: set_nat,D: set_nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_nat @ C @ D )
=> ( ! [E: set_nat,F: set_nat] :
( ( ord_less_eq_set_nat @ E @ F )
=> ( ord_less_eq_set_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(112,axiom,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a > nat,D: nat] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: set_Product_prod_a_a,F: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_order__subst2) ).
thf(755,plain,
! [A: set_Product_prod_a_a,B: set_Product_prod_a_a,C: set_Product_prod_a_a > nat,D: nat] :
( ( ord_le1824328871od_a_a @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: set_Product_prod_a_a,F: set_Product_prod_a_a] :
( ( ord_le1824328871od_a_a @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(74,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_subsetD) ).
thf(592,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(178,axiom,
! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
( ( ord_le456379495od_a_a @ A @ B )
=> ( ( finite1664988688od_a_a @ B )
=> ( finite1664988688od_a_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_finite__subset) ).
thf(972,plain,
! [A: set_Pr1948701895od_a_a,B: set_Pr1948701895od_a_a] :
( ( ord_le456379495od_a_a @ A @ B )
=> ( ( finite1664988688od_a_a @ B )
=> ( finite1664988688od_a_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(298,axiom,
! [A: product_prod_a_a > $o,B: product_prod_a_a > $o] :
( ( ( finite179568208od_a_a @ ( collec645855634od_a_a @ A ) )
| ( finite179568208od_a_a @ ( collec645855634od_a_a @ B ) ) )
=> ( finite179568208od_a_a
@ ( collec645855634od_a_a
@ ^ [C: product_prod_a_a] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_finite__Collect__conjI) ).
thf(1367,plain,
! [A: product_prod_a_a > $o,B: product_prod_a_a > $o] :
( ( ( finite179568208od_a_a @ ( collec645855634od_a_a @ A ) )
| ( finite179568208od_a_a @ ( collec645855634od_a_a @ B ) ) )
=> ( finite179568208od_a_a
@ ( collec645855634od_a_a
@ ^ [C: product_prod_a_a] :
( ( A @ C )
& ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(167,axiom,
! [A: set_nat,B: nat > $o] :
( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( member_nat @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_Collect__restrict) ).
thf(940,plain,
! [A: set_nat,B: nat > $o] :
( ord_less_eq_set_nat
@ ( collect_nat
@ ^ [C: nat] :
( ( member_nat @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(47,axiom,
! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_empty__subsetI) ).
thf(496,plain,
! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(38,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_eq__refl) ).
thf(454,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1547,plain,
$false,
inference(cvc4,[status(thm)],[892,1024,365,479,347,962,481,333,1031,1200,1211,1068,449,655,677,1041,1173,523,1158,582,762,730,1290,1305,597,1078,1310,1164,1327,913,1222,829,1127,709,1359,1265,1228,651,785,372,504,1330,1313,1191,949,542,802,344,817,559,853,1379,1087,1147,1247,1013,325,1319,870,969,1347,924,1302,1373,1151,806,1383,1020,1051,821,1377,1215,877,396,1351,411,1242,527,380,661,810,1338,942,439,1274,910,746,778,952,1123,561,1370,1238,957,894,435,1178,1296,682,551,842,974,1350,1270,1017,980,1138,874,1143,488,1361,1182,669,637,1155,554,753,686,1075,476,622,1099,738,1131,984,569,605,393,1114,647,997,1333,1202,938,508,921,1054,1170,1071,1026,530,398,1035,906,618,425,513,824,856,573,965,750,1007,402,1125,772,579,545,584,1154,936,382,1271,787,498,1058,335,1090,764,1194,1282,1117,377,318,1307,863,362,451,880,649,520,1325,1029,1149,915,1344,1293,1381,932,1061,1198,959,1245,883,306,1000,1250,1102,431,658,473,1208,795,1277,458,836,1049,927,374,776,1003,640,872,707,993,409,1230,791,1038,717,1235,1218,1220,1188,1186,1336,643,1257,613,1284,314,595,859,991,1353,600,845,465,1084,539,759,1010,368,1108,688,903,813,517,1341,946,351,390,632,781,1253,699,510,929,549,536,1045,1161,800,1133,447,1280,833,405,865,603,305,918,897,1056,635,1065,720,955,886,728,1261,427,908,982,1299,691,1120,501,1093,624,839,1268,575,486,337,354,755,592,972,1367,940,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP093^1 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n015.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 14:34:09 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.88/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.61/1.03 % [INFO] Parsing done (257ms).
% 1.61/1.04 % [INFO] Running in sequential loop mode.
% 2.62/1.27 % [INFO] eprover registered as external prover.
% 2.62/1.27 % [INFO] cvc4 registered as external prover.
% 2.62/1.28 % [INFO] Scanning for conjecture ...
% 2.87/1.37 % [INFO] Found a conjecture and 354 axioms. Running axiom selection ...
% 3.21/1.48 % [INFO] Axiom selection finished. Selected 302 axioms (removed 52 axioms).
% 3.75/1.67 % [INFO] Problem is higher-order (TPTP THF).
% 3.90/1.69 % [INFO] Type checking passed.
% 3.90/1.69 % [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 ...
% 16.27/4.71 % External prover 'cvc4' found a proof!
% 16.27/4.71 % [INFO] Killing All external provers ...
% 16.27/4.71 % Time passed: 4231ms (effective reasoning time: 3662ms)
% 16.27/4.71 % 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)>
% 16.27/4.71 % Axioms used in derivation (302): fact_184_order__class_Oorder_Oeq__iff, fact_22_infinite__super, fact_64_not__finite__existsD, fact_302_Collect__restrict, fact_72_pigeonhole__infinite__rel, fact_11_pair__fin__digraph__axioms_Ointro, fact_233_order__subst2, fact_120_Sigma__mono, fact_174_mem__Collect__eq, fact_148_dual__order_Oeq__iff, fact_350_finite__nat__set__iff__bounded__le, fact_62_not__finite__existsD, fact_160_dual__order_Orefl, fact_52_finite__SigmaI, fact_254_set__eq__subset, fact_113_Times__subset__cancel2, fact_227_ord__eq__le__subst, fact_158_dual__order_Orefl, fact_300_Collect__restrict, fact_196_le__cases, fact_330_finite__cartesian__product__iff, fact_139_Collect__subset, fact_292_member__product, fact_71_pigeonhole__infinite__rel, fact_13_pair__fin__digraph_Opair__finite__arcs, fact_198_eq__refl, fact_156_linorder__wlog, fact_30_finite__has__maximal2, fact_213_ord__le__eq__subst, fact_276_subset__eq, fact_173_mem__Collect__eq, fact_190_antisym__conv, fact_119_Sigma__mono, fact_253_set__eq__subset, fact_342_empty__Collect__eq, fact_311_pair__pre__digraph_Oselect__convs_I2_J, fact_162_order__trans, fact_264_subset__refl, fact_217_ord__le__eq__subst, fact_164_order__trans, fact_285_in__mono, fact_166_order__class_Oorder_Oantisym, fact_218_ord__le__eq__subst, fact_102_infinite__cartesian__product, fact_54_finite__SigmaI, fact_117_Sigma__mono, fact_226_ord__eq__le__subst, fact_349_finite__Collect__le__nat, fact_297_subset__CollectI, fact_242_order__subst1, fact_329_finite__cartesian__product__iff, fact_175_Collect__mem__eq, fact_70_pigeonhole__infinite__rel, fact_126_subset__antisym, fact_53_finite__SigmaI, fact_252_Collect__mono__iff, fact_108_Times__subset__cancel2, fact_29_rev__finite__subset, fact_336_empty__iff, fact_322_pair__fin__digraph__def, fact_262_subset__refl, fact_79_finite__cartesian__product, fact_245_order__subst1, fact_136_Sigma__cong, fact_67_pigeonhole__infinite__rel, fact_345_empty__subsetI, fact_176_Collect__mem__eq, fact_145_dual__order_Oantisym, fact_225_ord__eq__le__subst, fact_43_finite__Collect__disjI, fact_278_equalityE, fact_55_finite__SigmaI, fact_203_antisym, fact_144_dual__order_Oantisym, fact_16_finite__subset, fact_215_ord__le__eq__subst, fact_251_Collect__mono__iff, fact_68_pigeonhole__infinite__rel, fact_69_pigeonhole__infinite__rel, fact_294_subset__Collect__iff, fact_157_dual__order_Orefl, fact_293_Product__Type_Oproduct__def, fact_337_empty__iff, fact_182_ord__eq__le__trans, fact_219_ord__le__eq__subst, fact_141_less__eq__set__def, fact_179_ord__eq__le__trans, fact_63_not__finite__existsD, fact_130_order__refl, fact_177_Collect__cong, fact_1__092_060open_062parcs_AG_A_092_060subseteq_062_Apverts_AG_A_092_060times_062_Apverts_AG_092_060close_062, fact_338_all__not__in__conv, fact_257_subset__trans, fact_50_finite__SigmaI, fact_163_order__trans, fact_92_pair__fin__digraph_Opair__finite__verts, fact_332_finite__cartesian__product__iff, fact_272_equalityD1, fact_326_finite__cartesian__product__iff, fact_77_pair__fin__digraph_Opair__fin__digraph, fact_133_pair__pre__digraph_Oequality, fact_224_ord__eq__le__subst, fact_147_dual__order_Oantisym, fact_38_finite__Collect__conjI, fact_40_finite__Collect__disjI, fact_205_antisym, fact_340_Collect__empty__eq, fact_82_finite__cartesian__product, fact_170_ord__le__eq__trans, fact_247_order__subst1, fact_49_finite__SigmaI, fact_306_conj__subset__def, fact_275_subset__eq, fact_344_empty__subsetI, fact_90_pair__fin__digraph_Opair__finite__verts, fact_84_finite__cartesian__product, fact_307_conj__subset__def, fact_284_in__mono, fact_353_finite__less__ub, fact_206_eq__iff, fact_135_pair__pre__digraph_Oequality, fact_260_Collect__mono, fact_114_Sigma__mono, fact_17_finite__subset, fact_347_subset__empty, fact_201_linear, fact_76_pigeonhole__infinite__rel, fact_343_empty__Collect__eq, fact_270_equalityD2, fact_89_pair__fin__digraph_Opair__finite__verts, fact_27_rev__finite__subset, fact_188_antisym__conv, fact_94_finite__has__minimal2, fact_325_pair__fin__digraph_Ointro, fact_23_infinite__super, fact_204_antisym, fact_232_order__subst2, fact_211_ord__le__eq__subst, fact_115_Sigma__mono, fact_250_Collect__mono__iff, fact_255_set__eq__subset, fact_283_in__mono, fact_155_dual__order_Otrans, fact_74_pigeonhole__infinite__rel, fact_199_eq__refl, fact_221_ord__eq__le__subst, fact_214_ord__le__eq__subst, fact_258_subset__trans, fact_200_eq__refl, fact_186_order__class_Oorder_Oeq__iff, fact_178_Collect__cong, fact_132_order__refl, fact_351_infinite__nat__iff__unbounded__le, fact_189_antisym__conv, fact_149_dual__order_Oeq__iff, fact_93_finite__has__minimal2, fact_181_ord__eq__le__trans, fact_267_subset__iff, fact_101_infinite__cartesian__product, fact_229_ord__eq__le__subst, fact_301_Collect__restrict, fact_246_order__subst1, fact_274_subset__eq, fact_81_finite__cartesian__product, fact_286_pred__subset__eq, fact_235_order__subst2, fact_123_subsetI, fact_36_finite__Collect__conjI, fact_0__092_060open_062finite_A_Ipverts_AG_A_092_060times_062_Apverts_AG_J_092_060close_062, fact_256_subset__trans, fact_124_subsetI, fact_39_finite__Collect__disjI, fact_116_Sigma__mono, fact_83_finite__cartesian__product, fact_271_equalityD1, fact_202_antisym, fact_150_dual__order_Oeq__iff, fact_138_Collect__subset, fact_34_finite__Collect__conjI, fact_187_antisym__conv, fact_128_subset__antisym, fact_312_pair__pre__digraph_Oselect__convs_I1_J, fact_137_Times__eq__cancel2, fact_111_Times__subset__cancel2, fact_320_pair__fin__digraph__def, fact_59_pair__fin__digraph_Oaxioms_I2_J, fact_299_subset__CollectI, fact_238_order__subst2, fact_303_prop__restrict, fact_125_subsetI, fact_86_finite__cartesian__product, fact_26_rev__finite__subset, fact_339_all__not__in__conv, fact_97_infinite__cartesian__product, fact_298_subset__CollectI, fact_241_order__subst1, fact_183_order__class_Oorder_Oeq__iff, fact_268_equalityD2, fact_280_subsetD, fact_222_ord__eq__le__subst, fact_159_dual__order_Orefl, fact_109_Times__subset__cancel2, fact_295_subset__Collect__iff, fact_169_ord__le__eq__trans, fact_165_order__class_Oorder_Oantisym, fact_265_subset__iff, fact_209_eq__iff, fact_18_finite__subset, fact_289_pair__pre__digraph_Osurjective, fact_28_rev__finite__subset, fact_346_empty__subsetI, fact_192_order_Otrans, fact_98_infinite__cartesian__product, fact_9_pair__fin__digraph__axioms_Ointro, fact_24_infinite__super, fact_78_finite__cartesian__product, fact_151_dual__order_Oeq__iff, fact_31_finite__has__maximal2, fact_334_finite__cartesian__product__iff, fact_57_finite__SigmaI, fact_172_ord__le__eq__trans, fact_122_Sigma__mono, fact_121_Sigma__mono, fact_208_eq__iff, fact_154_dual__order_Otrans, fact_66_not__finite__existsD, fact_327_finite__cartesian__product__iff, fact_167_order__class_Oorder_Oantisym, fact_230_order__subst2, fact_309_pair__pre__digraph_Oselect__convs_I2_J, fact_249_order__subst1, fact_41_finite__Collect__disjI, fact_296_subset__Collect__iff, fact_352_bounded__Max__nat, fact_129_order__refl, fact_193_order_Otrans, fact_273_equalityD1, fact_112_Times__subset__cancel2, fact_35_finite__Collect__conjI, fact_168_order__class_Oorder_Oantisym, fact_194_order_Otrans, fact_180_ord__eq__le__trans, fact_259_Collect__mono, fact_244_order__subst1, fact_240_order__subst1, fact_105_infinite__cartesian__product, fact_261_Collect__mono, fact_236_order__subst2, fact_314_pair__pre__digraph_Oselect__convs_I1_J, fact_210_ord__le__eq__subst, fact_131_order__refl, fact_223_ord__eq__le__subst, fact_269_equalityD2, fact_21_infinite__super, fact_152_dual__order_Otrans, fact_231_order__subst2, fact_195_order_Otrans, fact_19_finite__subset, fact_277_equalityE, fact_348_calculation, fact_61_pair__fin__digraph_Oaxioms_I2_J, fact_304_prop__restrict, fact_234_order__subst2, fact_263_subset__refl, fact_75_pigeonhole__infinite__rel, fact_207_eq__iff, fact_146_dual__order_Oantisym, fact_308_conj__subset__def, fact_279_equalityE, fact_185_order__class_Oorder_Oeq__iff, fact_317_Fpow__def, fact_305_prop__restrict, fact_216_ord__le__eq__subst, fact_281_subsetD, fact_191_le__cases3, fact_4_pair__fin__digraph__axioms__def, fact_212_ord__le__eq__subst, fact_243_order__subst1, fact_14_pair__fin__digraph_Opair__finite__arcs, fact_239_order__subst2, fact_161_order__trans, fact_140_Collect__subset, fact_291_pair__pre__digraph_Osurjective, fact_46_finite__Collect__subsets, fact_237_order__subst2, fact_220_ord__eq__le__subst, fact_107_Times__subset__cancel2, fact_197_eq__refl, fact_73_pigeonhole__infinite__rel, fact_228_ord__eq__le__subst, fact_171_ord__le__eq__trans, fact_127_subset__antisym, fact_282_subsetD, fact_248_order__subst1, fact_103_infinite__cartesian__product, fact_331_finite__cartesian__product__iff, fact_153_dual__order_Otrans, fact_341_Collect__empty__eq, fact_6_pair__fin__digraph__axioms__def, fact_323_pair__fin__digraph_Ointro, fact_100_infinite__cartesian__product, fact_266_subset__iff
% 16.27/4.71 % No. of inferences in proof: 608
% 16.27/4.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4231 ms resp. 3662 ms w/o parsing
% 17.04/4.87 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.04/4.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------