%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP042^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:31 AM UTC 2026
% Result : Theorem 12.78s 4.40s
% Output : Refutation 13.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 208
% Syntax : Number of formulae : 418 ( 252 unt; 0 typ; 0 def)
% Number of atoms : 1057 ( 347 equ; 8 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 2734 ( 22 ~; 11 |; 67 &;2360 @)
% ( 0 <=>; 274 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 29 ( 28 usr)
% Number of type conns : 108 ( 108 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 45 usr; 13 con; 0-3 aty)
% Number of variables : 1023 ( 181 ^; 813 !; 29 ?;1023 :)
% Comments :
%------------------------------------------------------------------------------
thf(produc1149990247eal_sz_type,type,
produc1149990247eal_sz: $tType ).
thf(produc133005365real_b_type,type,
produc133005365real_b: $tType ).
thf(bounde472938360z_real_type,type,
bounde472938360z_real: $tType ).
thf(set_De208295462t_unit_type,type,
set_De208295462t_unit: $tType ).
thf(set_De153000604t_unit_type,type,
set_De153000604t_unit: $tType ).
thf(denota610675952t_unit_type,type,
denota610675952t_unit: $tType ).
thf(denota723907260t_unit_type,type,
denota723907260t_unit: $tType ).
thf(set_Su111624115um_c_b_type,type,
set_Su111624115um_c_b: $tType ).
thf(set_Fi291318197eal_sz_type,type,
set_Fi291318197eal_sz: $tType ).
thf(set_Fi268318752real_b_type,type,
set_Fi268318752real_b: $tType ).
thf(freche2095075217_sc_sz_type,type,
freche2095075217_sc_sz: $tType ).
thf(freche1734198479_a_c_b_type,type,
freche1734198479_a_c_b: $tType ).
thf(sum_su1965225555um_c_b_type,type,
sum_su1965225555um_c_b: $tType ).
thf(finite824932053eal_sz_type,type,
finite824932053eal_sz: $tType ).
thf(finite1390225514real_b_type,type,
finite1390225514real_b: $tType ).
thf(frechet_strm_sf_sz_type,type,
frechet_strm_sf_sz: $tType ).
thf(set_Sum_sum_sz_sz_type,type,
set_Sum_sum_sz_sz: $tType ).
thf(frechet_strm_a_b_type,type,
frechet_strm_a_b: $tType ).
thf(set_Sum_sum_b_b_type,type,
set_Sum_sum_b_b: $tType ).
thf(set_trm_sf_sz_type,type,
set_trm_sf_sz: $tType ).
thf(set_trm_a_b_type,type,
set_trm_a_b: $tType ).
thf(sum_sum_b_b_type,type,
sum_sum_b_b: $tType ).
thf(trm_sf_sz_type,type,
trm_sf_sz: $tType ).
thf(trm_a_b_type,type,
trm_a_b: $tType ).
thf(set_sf_type,type,
set_sf: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(real_type,type,
real: $tType ).
thf(a_type,type,
a: $tType ).
thf(denota896875430_a_c_b_decl,type,
denota896875430_a_c_b: denota723907260t_unit > denota723907260t_unit > set_Su111624115um_c_b > $o ).
thf(denota1997846517gree_b_decl,type,
denota1997846517gree_b: produc133005365real_b > produc133005365real_b > set_Sum_sum_b_b > $o ).
thf(denota102976244t_unit_decl,type,
denota102976244t_unit: denota723907260t_unit > a > finite1390225514real_b > real ).
thf(denota1086158987_a_c_b_decl,type,
denota1086158987_a_c_b: denota723907260t_unit > $o ).
thf(denota722380397_a_c_b_decl,type,
denota722380397_a_c_b: denota723907260t_unit > trm_a_b > finite1390225514real_b > real ).
thf(frechet_cr_strm_a_b_decl,type,
frechet_cr_strm_a_b: trm_a_b > frechet_strm_a_b > $o ).
thf(if_Bou1785791806z_real_decl,type,
if_Bou1785791806z_real: $o > bounde472938360z_real > bounde472938360z_real > bounde472938360z_real ).
thf(sup_su1211201046_c_b_o_decl,type,
sup_su1211201046_c_b_o: ( sum_su1965225555um_c_b > $o ) > ( sum_su1965225555um_c_b > $o ) > sum_su1965225555um_c_b > $o ).
thf(sup_sup_a_o_decl,type,
sup_sup_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
thf(sup_sup_o_decl,type,
sup_sup_o: $o > $o > $o ).
thf(sup_su2133361046real_b_decl,type,
sup_su2133361046real_b: finite1390225514real_b > finite1390225514real_b > finite1390225514real_b ).
thf(sup_su1581595657real_b_decl,type,
sup_su1581595657real_b: produc133005365real_b > produc133005365real_b > produc133005365real_b ).
thf(sup_su296826759um_c_b_decl,type,
sup_su296826759um_c_b: set_Su111624115um_c_b > set_Su111624115um_c_b > set_Su111624115um_c_b ).
thf(sup_su2137030215um_b_b_decl,type,
sup_su2137030215um_b_b: set_Sum_sum_b_b > set_Sum_sum_b_b > set_Sum_sum_b_b ).
thf(sup_sup_set_a_decl,type,
sup_sup_set_a: set_a > set_a > set_a ).
thf(ord_le1534094666_c_b_o_decl,type,
ord_le1534094666_c_b_o: ( sum_su1965225555um_c_b > $o ) > ( sum_su1965225555um_c_b > $o ) > $o ).
thf(ord_less_eq_a_o_decl,type,
ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(ord_le767445194real_b_decl,type,
ord_le767445194real_b: finite1390225514real_b > finite1390225514real_b > $o ).
thf(ord_le793200597real_b_decl,type,
ord_le793200597real_b: produc133005365real_b > produc133005365real_b > $o ).
thf(ord_le1404954451um_c_b_decl,type,
ord_le1404954451um_c_b: set_Su111624115um_c_b > set_Su111624115um_c_b > $o ).
thf(ord_less_eq_set_a_decl,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(top_to1849113498_c_b_o_decl,type,
top_to1849113498_c_b_o: sum_su1965225555um_c_b > $o ).
thf(top_top_a_o_decl,type,
top_top_a_o: a > $o ).
thf(top_to502572752real_b_decl,type,
top_to502572752real_b: set_Fi268318752real_b ).
thf(top_to999478531um_c_b_decl,type,
top_to999478531um_c_b: set_Su111624115um_c_b ).
thf(top_to301096907um_b_b_decl,type,
top_to301096907um_b_b: set_Sum_sum_b_b ).
thf(top_top_set_a_decl,type,
top_top_set_a: set_a ).
thf(produc936751193real_b_decl,type,
produc936751193real_b: produc133005365real_b > finite1390225514real_b ).
thf(domain134596861rm_a_b_decl,type,
domain134596861rm_a_b: ( trm_a_b > frechet_strm_a_b > $o ) > trm_a_b > $o ).
thf(collec1166375742um_c_b_decl,type,
collec1166375742um_c_b: ( sum_su1965225555um_c_b > $o ) > set_Su111624115um_c_b ).
thf(collect_a_decl,type,
collect_a: ( a > $o ) > set_a ).
thf(static_FVT_a_b_decl,type,
static_FVT_a_b: trm_a_b > set_Sum_sum_b_b ).
thf(static_SIGT_a_b_decl,type,
static_SIGT_a_b: trm_a_b > set_a ).
thf(sum_In811702836um_c_b_decl,type,
sum_In811702836um_c_b: a > sum_su1965225555um_c_b ).
thf(dfree_a_b_decl,type,
dfree_a_b: trm_a_b > $o ).
thf(times_a_b_decl,type,
times_a_b: trm_a_b > trm_a_b > trm_a_b ).
thf(topolo238266006b_real_decl,type,
topolo238266006b_real: set_Fi268318752real_b > ( finite1390225514real_b > real ) > $o ).
thf(member973578748um_c_b_decl,type,
member973578748um_c_b: sum_su1965225555um_c_b > set_Su111624115um_c_b > $o ).
thf(member_a_decl,type,
member_a: a > set_a > $o ).
thf(i_decl,type,
i: denota723907260t_unit ).
thf(j_decl,type,
j: denota723907260t_unit ).
thf(nu_decl,type,
nu: produc133005365real_b ).
thf(nu2_decl,type,
nu2: produc133005365real_b ).
thf(theta_1_decl,type,
theta_1: trm_a_b ).
thf(theta_2_decl,type,
theta_2: trm_a_b ).
thf(48,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_sup_Obounded__iff) ).
thf(347,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(16,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( sup_su296826759um_c_b @ A @ ( sup_su296826759um_c_b @ A @ B ) )
= ( sup_su296826759um_c_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_sup_Oleft__idem) ).
thf(249,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( sup_su296826759um_c_b @ A @ ( sup_su296826759um_c_b @ A @ B ) )
= ( sup_su296826759um_c_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(44,axiom,
! [A: sum_su1965225555um_c_b > $o,B: sum_su1965225555um_c_b > $o] :
( ( sup_su1211201046_c_b_o @ A @ ( sup_su1211201046_c_b_o @ A @ B ) )
= ( sup_su1211201046_c_b_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_sup__left__idem) ).
thf(333,plain,
! [A: sum_su1965225555um_c_b > $o,B: sum_su1965225555um_c_b > $o] :
( ( sup_su1211201046_c_b_o @ A @ ( sup_su1211201046_c_b_o @ A @ B ) )
= ( sup_su1211201046_c_b_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(139,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ ( sup_sup_a_o @ A @ B ) @ C )
= ( ( ord_less_eq_a_o @ A @ C )
& ( ord_less_eq_a_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_sup_Obounded__iff) ).
thf(628,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ ( sup_sup_a_o @ A @ B ) @ C )
= ( ( ord_less_eq_a_o @ A @ C )
& ( ord_less_eq_a_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(66,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( sup_su296826759um_c_b @ ( sup_su296826759um_c_b @ A @ B ) @ B )
= ( sup_su296826759um_c_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_sup_Oright__idem) ).
thf(408,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( sup_su296826759um_c_b @ ( sup_su296826759um_c_b @ A @ B ) @ B )
= ( sup_su296826759um_c_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(105,axiom,
! [A: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ top_to999478531um_c_b @ A )
= ( A = top_to999478531um_c_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_top_Oextremum__unique) ).
thf(523,plain,
! [A: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ top_to999478531um_c_b @ A )
= ( A = top_to999478531um_c_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(5,axiom,
! [A: bounde472938360z_real,B: bounde472938360z_real] :
( ( if_Bou1785791806z_real @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T) ).
thf(217,plain,
! [A: bounde472938360z_real,B: bounde472938360z_real] :
( ( if_Bou1785791806z_real @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(81,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_Un__upper2) ).
thf(449,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(136,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( A = B )
=> ~ ( ( ord_le1404954451um_c_b @ A @ B )
=> ~ ( ord_le1404954451um_c_b @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_equalityE) ).
thf(614,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( A = B )
=> ~ ( ( ord_le1404954451um_c_b @ A @ B )
=> ~ ( ord_le1404954451um_c_b @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(78,axiom,
! [A: a > $o] :
( ( sup_sup_a_o @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_sup__idem) ).
thf(440,plain,
! [A: a > $o] :
( ( sup_sup_a_o @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(101,axiom,
! [A: set_Su111624115um_c_b] :
( ( sup_su296826759um_c_b @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_sup_Oidem) ).
thf(511,plain,
! [A: set_Su111624115um_c_b] :
( ( sup_su296826759um_c_b @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(60,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b > set_Su111624115um_c_b,D: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_Su111624115um_c_b,F: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ E @ F )
=> ( ord_le1404954451um_c_b @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1404954451um_c_b @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_ord__le__eq__subst) ).
thf(384,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b > set_Su111624115um_c_b,D: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_Su111624115um_c_b,F: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ E @ F )
=> ( ord_le1404954451um_c_b @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1404954451um_c_b @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(171,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_Collect__mem__eq) ).
thf(715,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(165,axiom,
! [A: denota723907260t_unit,B: denota723907260t_unit] :
( ( denota896875430_a_c_b @ A @ B
@ ( collec1166375742um_c_b
@ ^ [C: sum_su1965225555um_c_b] :
? [D: a] :
( ( C
= ( sum_In811702836um_c_b @ D ) )
& ( member_a @ D @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) )
=> ( denota896875430_a_c_b @ A @ B
@ ( collec1166375742um_c_b
@ ^ [C: sum_su1965225555um_c_b] :
? [D: a] :
( ( C
= ( sum_In811702836um_c_b @ D ) )
& ( member_a @ D @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0621_125_092_060close_062) ).
thf(698,plain,
! [A: denota723907260t_unit,B: denota723907260t_unit] :
( ( denota896875430_a_c_b @ A @ B
@ ( collec1166375742um_c_b
@ ^ [C: sum_su1965225555um_c_b] :
? [D: a] :
( ( C
= ( sum_In811702836um_c_b @ D ) )
& ( member_a @ D @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) )
=> ( denota896875430_a_c_b @ A @ B
@ ( collec1166375742um_c_b
@ ^ [C: sum_su1965225555um_c_b] :
? [D: a] :
( ( C
= ( sum_In811702836um_c_b @ D ) )
& ( member_a @ D @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(169,axiom,
! [A: set_a] :
( ! [B: a] : ( member_a @ B @ A )
=> ( top_top_set_a = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_UNIV__eq__I) ).
thf(709,plain,
! [A: set_a] :
( ! [B: a] : ( member_a @ B @ A )
=> ( top_top_set_a = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(69,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_order__class_Oorder_Oantisym) ).
thf(417,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(39,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ C @ B )
=> ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_sup__least) ).
thf(320,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ C @ B )
=> ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(173,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_168_subsetD) ).
thf(719,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)],[173]) ).
thf(56,axiom,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ A @ B ) )
= ( sup_su2137030215um_b_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_sup_Oleft__idem) ).
thf(372,plain,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ A @ B ) )
= ( sup_su2137030215um_b_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(99,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( sup_su296826759um_c_b @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_sup__absorb1) ).
thf(504,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( sup_su296826759um_c_b @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(126,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( A = B )
=> ( ord_le1404954451um_c_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_eq__refl) ).
thf(587,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( A = B )
=> ( ord_le1404954451um_c_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(47,axiom,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ B )
= ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_sup_Oright__idem) ).
thf(344,plain,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ ( sup_sup_set_a @ A @ B ) @ B )
= ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(51,axiom,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ B @ C ) )
= ( sup_su2137030215um_b_b @ B @ ( sup_su2137030215um_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_sup_Oleft__commute) ).
thf(357,plain,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ B @ C ) )
= ( sup_su2137030215um_b_b @ B @ ( sup_su2137030215um_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(167,axiom,
( sup_su296826759um_c_b
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( collec1166375742um_c_b
@ ^ [C: sum_su1965225555um_c_b] :
( ( member973578748um_c_b @ C @ A )
| ( member973578748um_c_b @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_Un__def) ).
thf(702,plain,
( sup_su296826759um_c_b
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( collec1166375742um_c_b
@ ^ [C: sum_su1965225555um_c_b] :
( ( member973578748um_c_b @ C @ A )
| ( member973578748um_c_b @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(187,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( sup_sup_set_a @ B @ C ) )
=> ( ~ ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_UnE) ).
thf(751,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( sup_sup_set_a @ B @ C ) )
=> ( ~ ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(143,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ C @ A )
=> ( ord_le1404954451um_c_b @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_dual__order_Otrans) ).
thf(638,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ C @ A )
=> ( ord_le1404954451um_c_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(9,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( A = B )
=> ( ord_le1404954451um_c_b @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_equalityD2) ).
thf(228,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( A = B )
=> ( ord_le1404954451um_c_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(28,axiom,
! [A: sum_su1965225555um_c_b > $o,B: sum_su1965225555um_c_b > $o] :
( ( sup_su1211201046_c_b_o @ ( sup_su1211201046_c_b_o @ A @ B ) @ B )
= ( sup_su1211201046_c_b_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_sup_Oright__idem) ).
thf(289,plain,
! [A: sum_su1965225555um_c_b > $o,B: sum_su1965225555um_c_b > $o] :
( ( sup_su1211201046_c_b_o @ ( sup_su1211201046_c_b_o @ A @ B ) @ B )
= ( sup_su1211201046_c_b_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(18,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ B ) @ C )
=> ~ ( ( ord_le1404954451um_c_b @ A @ C )
=> ~ ( ord_le1404954451um_c_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_sup_OboundedE) ).
thf(261,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ B ) @ C )
=> ~ ( ( ord_le1404954451um_c_b @ A @ C )
=> ~ ( ord_le1404954451um_c_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(90,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ B ) @ C )
= ( ( ord_le1404954451um_c_b @ A @ C )
& ( ord_le1404954451um_c_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_le__sup__iff) ).
thf(475,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ B ) @ C )
= ( ( ord_le1404954451um_c_b @ A @ C )
& ( ord_le1404954451um_c_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(190,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_166_in__mono) ).
thf(756,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)],[190]) ).
thf(203,axiom,
! [A: a,B: set_a,C: set_a] :
( ( ~ ( member_a @ A @ B )
=> ( member_a @ A @ C ) )
=> ( member_a @ A @ ( sup_sup_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_UnCI) ).
thf(789,plain,
! [A: a,B: set_a,C: set_a] :
( ( ~ ( member_a @ A @ B )
=> ( member_a @ A @ C ) )
=> ( member_a @ A @ ( sup_sup_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(127,axiom,
( ord_le1404954451um_c_b
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( sup_su296826759um_c_b @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_sup_Oabsorb__iff1) ).
thf(591,plain,
( ord_le1404954451um_c_b
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( sup_su296826759um_c_b @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(79,axiom,
! [A: trm_a_b,B: trm_a_b] :
( ( dfree_a_b @ A )
=> ( ( dfree_a_b @ B )
=> ( dfree_a_b @ ( times_a_b @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_dfree_Odfree__Times) ).
thf(443,plain,
! [A: trm_a_b,B: trm_a_b] :
( ( dfree_a_b @ A )
=> ( ( dfree_a_b @ B )
=> ( dfree_a_b @ ( times_a_b @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(93,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( sup_su296826759um_c_b @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_sup_Oabsorb2) ).
thf(485,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( sup_su296826759um_c_b @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(12,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ B ) @ C )
= ( ( ord_le1404954451um_c_b @ A @ C )
& ( ord_le1404954451um_c_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Un__subset__iff) ).
thf(238,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ B ) @ C )
= ( ( ord_le1404954451um_c_b @ A @ C )
& ( ord_le1404954451um_c_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(102,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ C @ B )
=> ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_sup_OboundedI) ).
thf(514,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ C @ B )
=> ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(3,axiom,
! [A: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ top_to301096907um_b_b @ A )
= top_to301096907um_b_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_sup__top__left) ).
thf(211,plain,
! [A: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ top_to301096907um_b_b @ A )
= top_to301096907um_b_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(146,axiom,
( ( (=) @ set_Su111624115um_c_b )
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ B @ A )
& ( ord_le1404954451um_c_b @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_dual__order_Oeq__iff) ).
thf(646,plain,
( ( (=) @ set_Su111624115um_c_b )
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ B @ A )
& ( ord_le1404954451um_c_b @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(132,axiom,
! [A: set_Su111624115um_c_b] :
( ( sup_su296826759um_c_b @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_sup__idem) ).
thf(602,plain,
! [A: set_Su111624115um_c_b] :
( ( sup_su296826759um_c_b @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(25,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Collect__cong) ).
thf(280,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(63,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_sup_Oidem) ).
thf(396,plain,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(67,axiom,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ ( sup_su2137030215um_b_b @ A @ B ) @ B )
= ( sup_su2137030215um_b_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_sup_Oright__idem) ).
thf(411,plain,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ ( sup_su2137030215um_b_b @ A @ B ) @ B )
= ( sup_su2137030215um_b_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(14,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b,D: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ C @ D )
=> ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ C ) @ ( sup_su296826759um_c_b @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_sup_Omono) ).
thf(243,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b,D: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ C @ D )
=> ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ C ) @ ( sup_su296826759um_c_b @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(73,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_inf__sup__ord_I3_J) ).
thf(428,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(19,axiom,
( sup_su2137030215um_b_b
= ( ^ [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b] : ( sup_su2137030215um_b_b @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_Un__commute) ).
thf(265,plain,
( sup_su2137030215um_b_b
= ( ^ [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b] : ( sup_su2137030215um_b_b @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(100,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ B ) @ C )
=> ~ ( ( ord_le1404954451um_c_b @ A @ C )
=> ~ ( ord_le1404954451um_c_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_le__supE) ).
thf(507,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ B ) @ C )
=> ~ ( ( ord_le1404954451um_c_b @ A @ C )
=> ~ ( ord_le1404954451um_c_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(36,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_dual__order_Oantisym) ).
thf(312,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(34,axiom,
! [A: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_dual__order_Orefl) ).
thf(307,plain,
! [A: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(29,axiom,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ ( sup_su2137030215um_b_b @ A @ B ) @ C )
= ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_sup_Oassoc) ).
thf(292,plain,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ ( sup_su2137030215um_b_b @ A @ B ) @ C )
= ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(157,axiom,
( ord_le1404954451um_c_b
@ ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] :
? [B: a] :
( ( A
= ( sum_In811702836um_c_b @ B ) )
& ( member_a @ B @ ( static_SIGT_a_b @ theta_2 ) ) ) )
@ ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] :
? [B: a] :
( ( A
= ( sum_In811702836um_c_b @ B ) )
& ( member_a @ B @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_Isubs_I2_J) ).
thf(678,plain,
( ord_le1404954451um_c_b
@ ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] :
? [B: a] :
( ( A
= ( sum_In811702836um_c_b @ B ) )
& ( member_a @ B @ ( static_SIGT_a_b @ theta_2 ) ) ) )
@ ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] :
? [B: a] :
( ( A
= ( sum_In811702836um_c_b @ B ) )
& ( member_a @ B @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(21,axiom,
( ord_le1404954451um_c_b
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
! [C: sum_su1965225555um_c_b] :
( ( member973578748um_c_b @ C @ A )
=> ( member973578748um_c_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_subset__iff) ).
thf(270,plain,
( ord_le1404954451um_c_b
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
! [C: sum_su1965225555um_c_b] :
( ( member973578748um_c_b @ C @ A )
=> ( member973578748um_c_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(192,axiom,
! [A: denota723907260t_unit,B: denota723907260t_unit,C: set_Su111624115um_c_b] :
( ( denota896875430_a_c_b @ A @ B @ C )
=> ( denota896875430_a_c_b @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Iagree__comm) ).
thf(761,plain,
! [A: denota723907260t_unit,B: denota723907260t_unit,C: set_Su111624115um_c_b] :
( ( denota896875430_a_c_b @ A @ B @ C )
=> ( denota896875430_a_c_b @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(59,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_122_subset__antisym) ).
thf(381,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)],[59]) ).
thf(6,axiom,
! [A: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ top_to301096907um_b_b )
= top_to301096907um_b_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_sup__top__right) ).
thf(220,plain,
! [A: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ top_to301096907um_b_b )
= top_to301096907um_b_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(109,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_le__supI1) ).
thf(534,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(206,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_175_subset__iff) ).
thf(798,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)],[206]) ).
thf(113,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_sup_OcoboundedI2) ).
thf(546,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(204,axiom,
( ( denota1997846517gree_b @ nu @ nu2 @ ( static_FVT_a_b @ theta_2 ) )
=> ( ( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] :
? [B: a] :
( ( A
= ( sum_In811702836um_c_b @ B ) )
& ( member_a @ B @ ( static_SIGT_a_b @ theta_2 ) ) ) ) )
=> ( ( denota722380397_a_c_b @ i @ theta_2 @ ( produc936751193real_b @ nu ) )
= ( denota722380397_a_c_b @ j @ theta_2 @ ( produc936751193real_b @ nu2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_IH2) ).
thf(793,plain,
( ( denota1997846517gree_b @ nu @ nu2 @ ( static_FVT_a_b @ theta_2 ) )
=> ( ( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] :
? [B: a] :
( ( A
= ( sum_In811702836um_c_b @ B ) )
& ( member_a @ B @ ( static_SIGT_a_b @ theta_2 ) ) ) ) )
=> ( ( denota722380397_a_c_b @ i @ theta_2 @ ( produc936751193real_b @ nu ) )
= ( denota722380397_a_c_b @ j @ theta_2 @ ( produc936751193real_b @ nu2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(130,axiom,
! [A: produc133005365real_b,B: produc133005365real_b,C: set_Sum_sum_b_b] :
( ( denota1997846517gree_b @ A @ B @ C )
=> ( denota1997846517gree_b @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_agree__comm) ).
thf(598,plain,
! [A: produc133005365real_b,B: produc133005365real_b,C: set_Sum_sum_b_b] :
( ( denota1997846517gree_b @ A @ B @ C )
=> ( denota1997846517gree_b @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(23,axiom,
( ( (=) @ set_Su111624115um_c_b )
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
& ( ord_le1404954451um_c_b @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_set__eq__subset) ).
thf(275,plain,
( ( (=) @ set_Su111624115um_c_b )
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
& ( ord_le1404954451um_c_b @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(177,axiom,
( top_to999478531um_c_b
= ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_UNIV__def) ).
thf(729,plain,
( top_to999478531um_c_b
= ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(88,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( sup_su296826759um_c_b @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_Un__absorb1) ).
thf(467,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( sup_su296826759um_c_b @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(17,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b > set_Su111624115um_c_b,C: set_Su111624115um_c_b,D: set_Su111624115um_c_b] :
( ( A
= ( B @ C ) )
=> ( ( ord_le1404954451um_c_b @ C @ D )
=> ( ! [E: set_Su111624115um_c_b,F: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ E @ F )
=> ( ord_le1404954451um_c_b @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1404954451um_c_b @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_ord__eq__le__subst) ).
thf(252,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b > set_Su111624115um_c_b,C: set_Su111624115um_c_b,D: set_Su111624115um_c_b] :
( ( A
= ( B @ C ) )
=> ( ( ord_le1404954451um_c_b @ C @ D )
=> ( ! [E: set_Su111624115um_c_b,F: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ E @ F )
=> ( ord_le1404954451um_c_b @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1404954451um_c_b @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(138,axiom,
! [A: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ top_to999478531um_c_b @ A )
=> ( A = top_to999478531um_c_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_top_Oextremum__uniqueI) ).
thf(625,plain,
! [A: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ top_to999478531um_c_b @ A )
=> ( A = top_to999478531um_c_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(76,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ B @ C )
=> ( ord_le1404954451um_c_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_order_Otrans) ).
thf(435,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ B @ C )
=> ( ord_le1404954451um_c_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(153,axiom,
! [A: sum_su1965225555um_c_b > $o,B: sum_su1965225555um_c_b > $o,C: sum_su1965225555um_c_b > $o] :
( ( ord_le1534094666_c_b_o @ ( sup_su1211201046_c_b_o @ A @ B ) @ C )
= ( ( ord_le1534094666_c_b_o @ A @ C )
& ( ord_le1534094666_c_b_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_sup_Obounded__iff) ).
thf(665,plain,
! [A: sum_su1965225555um_c_b > $o,B: sum_su1965225555um_c_b > $o,C: sum_su1965225555um_c_b > $o] :
( ( ord_le1534094666_c_b_o @ ( sup_su1211201046_c_b_o @ A @ B ) @ C )
= ( ( ord_le1534094666_c_b_o @ A @ C )
& ( ord_le1534094666_c_b_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(86,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_le__sup__iff) ).
thf(461,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(96,axiom,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b,D: set_Sum_sum_b_b] :
( ( A
= ( sup_su2137030215um_b_b @ B @ C ) )
=> ( ( sup_su2137030215um_b_b @ D @ A )
= ( sup_su2137030215um_b_b @ B @ ( sup_su2137030215um_b_b @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_boolean__algebra__cancel_Osup2) ).
thf(493,plain,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b,D: set_Sum_sum_b_b] :
( ( A
= ( sup_su2137030215um_b_b @ B @ C ) )
=> ( ( sup_su2137030215um_b_b @ D @ A )
= ( sup_su2137030215um_b_b @ B @ ( sup_su2137030215um_b_b @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(159,axiom,
! [A: a,B: a] :
( ( ( sum_In811702836um_c_b @ A )
= ( sum_In811702836um_c_b @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_sum_Oinject_I1_J) ).
thf(682,plain,
! [A: a,B: a] :
( ( ( sum_In811702836um_c_b @ A )
= ( sum_In811702836um_c_b @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(84,axiom,
! [A: produc133005365real_b,B: produc133005365real_b] :
( ( ord_le793200597real_b @ A @ B )
=> ( ord_le767445194real_b @ ( produc936751193real_b @ A ) @ ( produc936751193real_b @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_fst__mono) ).
thf(456,plain,
! [A: produc133005365real_b,B: produc133005365real_b] :
( ( ord_le793200597real_b @ A @ B )
=> ( ord_le767445194real_b @ ( produc936751193real_b @ A ) @ ( produc936751193real_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(41,axiom,
( sup_sup_a_o
= ( ^ [A: a > $o,B: a > $o,C: a] : ( sup_sup_o @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_sup__apply) ).
thf(324,plain,
( sup_sup_a_o
= ( ^ [A: a > $o,B: a > $o,C: a] : ( sup_sup_o @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(38,axiom,
! [A: sum_su1965225555um_c_b > $o,B: sum_su1965225555um_c_b > $o,C: sum_su1965225555um_c_b > $o] :
( ( ord_le1534094666_c_b_o @ ( sup_su1211201046_c_b_o @ A @ B ) @ C )
= ( ( ord_le1534094666_c_b_o @ A @ C )
& ( ord_le1534094666_c_b_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_le__sup__iff) ).
thf(317,plain,
! [A: sum_su1965225555um_c_b > $o,B: sum_su1965225555um_c_b > $o,C: sum_su1965225555um_c_b > $o] :
( ( ord_le1534094666_c_b_o @ ( sup_su1211201046_c_b_o @ A @ B ) @ C )
= ( ( ord_le1534094666_c_b_o @ A @ C )
& ( ord_le1534094666_c_b_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(148,axiom,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ B @ C ) )
= ( sup_su2137030215um_b_b @ B @ ( sup_su2137030215um_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_Un__left__commute) ).
thf(650,plain,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ B @ C ) )
= ( sup_su2137030215um_b_b @ B @ ( sup_su2137030215um_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(175,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_less__eq__set__def) ).
thf(725,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(128,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( A
= ( sup_su296826759um_c_b @ A @ B ) )
=> ( ord_le1404954451um_c_b @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_sup_OorderI) ).
thf(593,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( A
= ( sup_su296826759um_c_b @ A @ B ) )
=> ( ord_le1404954451um_c_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(135,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( A = B )
=> ( ord_le1404954451um_c_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_equalityD1) ).
thf(610,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( A = B )
=> ( ord_le1404954451um_c_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(70,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_antisym) ).
thf(420,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(183,axiom,
! [A: set_Su111624115um_c_b,B: sum_su1965225555um_c_b > $o,C: sum_su1965225555um_c_b > $o] :
( ( ord_le1404954451um_c_b @ A
@ ( collec1166375742um_c_b
@ ^ [D: sum_su1965225555um_c_b] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_le1404954451um_c_b @ A @ ( collec1166375742um_c_b @ B ) )
& ( ord_le1404954451um_c_b @ A @ ( collec1166375742um_c_b @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_conj__subset__def) ).
thf(742,plain,
! [A: set_Su111624115um_c_b,B: sum_su1965225555um_c_b > $o,C: sum_su1965225555um_c_b > $o] :
( ( ord_le1404954451um_c_b @ A
@ ( collec1166375742um_c_b
@ ^ [D: sum_su1965225555um_c_b] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_le1404954451um_c_b @ A @ ( collec1166375742um_c_b @ B ) )
& ( ord_le1404954451um_c_b @ A @ ( collec1166375742um_c_b @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(123,axiom,
! [A: sum_su1965225555um_c_b > $o,B: sum_su1965225555um_c_b > $o] :
( ( sup_su1211201046_c_b_o @ A @ ( sup_su1211201046_c_b_o @ A @ B ) )
= ( sup_su1211201046_c_b_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_sup_Oleft__idem) ).
thf(578,plain,
! [A: sum_su1965225555um_c_b > $o,B: sum_su1965225555um_c_b > $o] :
( ( sup_su1211201046_c_b_o @ A @ ( sup_su1211201046_c_b_o @ A @ B ) )
= ( sup_su1211201046_c_b_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(94,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ B @ C )
=> ( ord_le1404954451um_c_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_order__trans) ).
thf(488,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ B @ C )
=> ( ord_le1404954451um_c_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(110,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ C @ B )
=> ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_Un__least) ).
thf(537,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ C @ B )
=> ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(161,axiom,
! [A: a] : ( member_a @ A @ top_top_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_iso__tuple__UNIV__I) ).
thf(686,plain,
! [A: a] : ( member_a @ A @ top_top_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(106,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_inf__sup__ord_I4_J) ).
thf(526,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(158,axiom,
! [A: sum_su1965225555um_c_b > $o,B: sum_su1965225555um_c_b > $o] :
( ( ord_le1404954451um_c_b @ ( collec1166375742um_c_b @ A ) @ ( collec1166375742um_c_b @ B ) )
= ( ! [C: sum_su1965225555um_c_b] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_Collect__mono__iff) ).
thf(679,plain,
! [A: sum_su1965225555um_c_b > $o,B: sum_su1965225555um_c_b > $o] :
( ( ord_le1404954451um_c_b @ ( collec1166375742um_c_b @ A ) @ ( collec1166375742um_c_b @ B ) )
= ( ! [C: sum_su1965225555um_c_b] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(116,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( sup_su296826759um_c_b @ A @ ( sup_su296826759um_c_b @ A @ B ) )
= ( sup_su296826759um_c_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_sup__left__idem) ).
thf(554,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( sup_su296826759um_c_b @ A @ ( sup_su296826759um_c_b @ A @ B ) )
= ( sup_su296826759um_c_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(188,axiom,
( top_top_a_o
= ( ^ [A: a] : ( member_a @ A @ top_top_set_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_top__empty__eq) ).
thf(753,plain,
( top_top_a_o
= ( ^ [A: a] : ( member_a @ A @ top_top_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(137,axiom,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ B @ C ) )
= ( sup_su2137030215um_b_b @ B @ ( sup_su2137030215um_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_sup__left__commute) ).
thf(622,plain,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ B @ C ) )
= ( sup_su2137030215um_b_b @ B @ ( sup_su2137030215um_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(61,axiom,
denota1997846517gree_b @ nu @ nu2 @ ( static_FVT_a_b @ theta_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_VAs_I2_J) ).
thf(393,plain,
denota1997846517gree_b @ nu @ nu2 @ ( static_FVT_a_b @ theta_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(199,axiom,
! [A: denota723907260t_unit,B: set_Su111624115um_c_b] : ( denota896875430_a_c_b @ A @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_Iagree__refl) ).
thf(779,plain,
! [A: denota723907260t_unit,B: set_Su111624115um_c_b] : ( denota896875430_a_c_b @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(133,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: sum_su1965225555um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( member973578748um_c_b @ C @ A )
=> ( member973578748um_c_b @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_in__mono) ).
thf(605,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: sum_su1965225555um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( member973578748um_c_b @ C @ A )
=> ( member973578748um_c_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(194,axiom,
! [A: sum_su1965225555um_c_b > $o,B: sum_su1965225555um_c_b > $o] :
( ( collec1166375742um_c_b
@ ^ [C: sum_su1965225555um_c_b] :
( ( A @ C )
| ( B @ C ) ) )
= ( sup_su296826759um_c_b @ ( collec1166375742um_c_b @ A ) @ ( collec1166375742um_c_b @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_Collect__disj__eq) ).
thf(765,plain,
! [A: sum_su1965225555um_c_b > $o,B: sum_su1965225555um_c_b > $o] :
( ( collec1166375742um_c_b
@ ^ [C: sum_su1965225555um_c_b] :
( ( A @ C )
| ( B @ C ) ) )
= ( sup_su296826759um_c_b @ ( collec1166375742um_c_b @ A ) @ ( collec1166375742um_c_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(197,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ B )
=> ( member_a @ A @ ( sup_sup_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_UnI2) ).
thf(773,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ B )
=> ( member_a @ A @ ( sup_sup_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(141,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_sup_Ocobounded1) ).
thf(633,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(52,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_sup__ge2) ).
thf(360,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(152,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_antisym__conv) ).
thf(662,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(172,axiom,
( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] :
? [B: a] :
( ( A
= ( sum_In811702836um_c_b @ B ) )
& ( ( member_a @ B @ ( static_SIGT_a_b @ theta_1 ) )
| ( member_a @ B @ ( static_SIGT_a_b @ theta_2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_IA) ).
thf(718,plain,
( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] :
? [B: a] :
( ( A
= ( sum_In811702836um_c_b @ B ) )
& ( ( member_a @ B @ ( static_SIGT_a_b @ theta_1 ) )
| ( member_a @ B @ ( static_SIGT_a_b @ theta_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(72,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1534094666_c_b_o
@ ^ [C: sum_su1965225555um_c_b] : ( member973578748um_c_b @ C @ A )
@ ^ [C: sum_su1965225555um_c_b] : ( member973578748um_c_b @ C @ B ) )
= ( ord_le1404954451um_c_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_pred__subset__eq) ).
thf(425,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1534094666_c_b_o
@ ^ [C: sum_su1965225555um_c_b] : ( member973578748um_c_b @ C @ A )
@ ^ [C: sum_su1965225555um_c_b] : ( member973578748um_c_b @ C @ B ) )
= ( ord_le1404954451um_c_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(74,axiom,
! [A: sum_su1965225555um_c_b > $o] :
( ( sup_su1211201046_c_b_o @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_sup_Oidem) ).
thf(430,plain,
! [A: sum_su1965225555um_c_b > $o] :
( ( sup_su1211201046_c_b_o @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(184,axiom,
! [A: sum_su1965225555um_c_b > $o,B: sum_su1965225555um_c_b > $o] :
( ! [C: sum_su1965225555um_c_b] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec1166375742um_c_b @ A )
= ( collec1166375742um_c_b @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_Collect__cong) ).
thf(745,plain,
! [A: sum_su1965225555um_c_b > $o,B: sum_su1965225555um_c_b > $o] :
( ! [C: sum_su1965225555um_c_b] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collec1166375742um_c_b @ A )
= ( collec1166375742um_c_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(57,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ ( sup_sup_a_o @ A @ B ) @ C )
= ( ( ord_less_eq_a_o @ A @ C )
& ( ord_less_eq_a_o @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_le__sup__iff) ).
thf(375,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ ( sup_sup_a_o @ A @ B ) @ C )
= ( ( ord_less_eq_a_o @ A @ C )
& ( ord_less_eq_a_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(180,axiom,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] :
( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
| ( member_a @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_Un__def) ).
thf(733,plain,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] :
( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
| ( member_a @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(125,axiom,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_sup__idem) ).
thf(584,plain,
! [A: set_a] :
( ( sup_sup_set_a @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(119,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T) ).
thf(562,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(71,axiom,
! [A: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ top_to999478531um_c_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_subset__UNIV) ).
thf(423,plain,
! [A: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ top_to999478531um_c_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(164,axiom,
! [A: sum_su1965225555um_c_b > $o,B: sum_su1965225555um_c_b > $o] :
( ! [C: sum_su1965225555um_c_b] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le1404954451um_c_b @ ( collec1166375742um_c_b @ A ) @ ( collec1166375742um_c_b @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_Collect__mono) ).
thf(694,plain,
! [A: sum_su1965225555um_c_b > $o,B: sum_su1965225555um_c_b > $o] :
( ! [C: sum_su1965225555um_c_b] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le1404954451um_c_b @ ( collec1166375742um_c_b @ A ) @ ( collec1166375742um_c_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(65,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ B @ C ) )
=> ~ ! [D: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ D @ B )
=> ! [E: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ E @ C )
=> ( A
!= ( sup_su296826759um_c_b @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_subset__UnE) ).
thf(402,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ B @ C ) )
=> ~ ! [D: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ D @ B )
=> ! [E: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ E @ C )
=> ( A
!= ( sup_su296826759um_c_b @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(179,axiom,
( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] :
? [B: a] :
( ( A
= ( sum_In811702836um_c_b @ B ) )
& ( member_a @ B @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_dfree__Times_Oprems_I2_J) ).
thf(732,plain,
( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] :
? [B: a] :
( ( A
= ( sum_In811702836um_c_b @ B ) )
& ( member_a @ B @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(27,axiom,
! [A: trm_a_b,B: trm_a_b,C: trm_a_b,D: trm_a_b] :
( ( ( times_a_b @ A @ B )
= ( times_a_b @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_trm_Oinject_I5_J) ).
thf(286,plain,
! [A: trm_a_b,B: trm_a_b,C: trm_a_b,D: trm_a_b] :
( ( ( times_a_b @ A @ B )
= ( times_a_b @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(144,axiom,
! [A: produc133005365real_b,B: set_Sum_sum_b_b] : ( denota1997846517gree_b @ A @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_agree__refl) ).
thf(641,plain,
! [A: produc133005365real_b,B: set_Sum_sum_b_b] : ( denota1997846517gree_b @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(121,axiom,
! [A: a > $o] :
( ( sup_sup_a_o @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_sup_Oidem) ).
thf(572,plain,
! [A: a > $o] :
( ( sup_sup_a_o @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(202,axiom,
! [A: a] : ( member_a @ A @ top_top_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_UNIV__I) ).
thf(787,plain,
! [A: a] : ( member_a @ A @ top_top_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(97,axiom,
! [A: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_sup__idem) ).
thf(498,plain,
! [A: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(168,axiom,
! [A: a,B: a] :
( ( ( sum_In811702836um_c_b @ A )
= ( sum_In811702836um_c_b @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Inl__inject) ).
thf(704,plain,
! [A: a,B: a] :
( ( ( sum_In811702836um_c_b @ A )
= ( sum_In811702836um_c_b @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(49,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b > set_Su111624115um_c_b,D: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ ( C @ B ) @ D )
=> ( ! [E: set_Su111624115um_c_b,F: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ E @ F )
=> ( ord_le1404954451um_c_b @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1404954451um_c_b @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_order__subst2) ).
thf(350,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b > set_Su111624115um_c_b,D: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ ( C @ B ) @ D )
=> ( ! [E: set_Su111624115um_c_b,F: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ E @ F )
=> ( ord_le1404954451um_c_b @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le1404954451um_c_b @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(111,axiom,
! [A: sum_su1965225555um_c_b > $o] :
( ( sup_su1211201046_c_b_o @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_sup__idem) ).
thf(540,plain,
! [A: sum_su1965225555um_c_b > $o] :
( ( sup_su1211201046_c_b_o @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(201,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_mem__Collect__eq) ).
thf(784,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(32,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_sup_Ocobounded2) ).
thf(303,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(53,axiom,
( sup_su2137030215um_b_b
= ( ^ [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b] : ( sup_su2137030215um_b_b @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_sup_Ocommute) ).
thf(362,plain,
( sup_su2137030215um_b_b
= ( ^ [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b] : ( sup_su2137030215um_b_b @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(82,axiom,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ ( sup_su2137030215um_b_b @ A @ B ) @ C )
= ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_inf__sup__aci_I6_J) ).
thf(451,plain,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ ( sup_su2137030215um_b_b @ A @ B ) @ C )
= ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(140,axiom,
( ord_le1404954451um_c_b
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
! [C: sum_su1965225555um_c_b] :
( ( member973578748um_c_b @ C @ A )
=> ( member973578748um_c_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_subset__eq) ).
thf(631,plain,
( ord_le1404954451um_c_b
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
! [C: sum_su1965225555um_c_b] :
( ( member973578748um_c_b @ C @ A )
=> ( member973578748um_c_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(115,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_Un__upper1) ).
thf(552,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(40,axiom,
dfree_a_b @ theta_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_dfree__Times_Ohyps_I2_J) ).
thf(323,plain,
dfree_a_b @ theta_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(154,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b,D: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ C @ D )
=> ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ C ) @ ( sup_su296826759um_c_b @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_Un__mono) ).
thf(668,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b,D: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ C @ D )
=> ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ C ) @ ( sup_su296826759um_c_b @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(43,axiom,
! [A: a > $o,B: a > $o] :
( ( sup_sup_a_o @ A @ ( sup_sup_a_o @ A @ B ) )
= ( sup_sup_a_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_sup__left__idem) ).
thf(330,plain,
! [A: a > $o,B: a > $o] :
( ( sup_sup_a_o @ A @ ( sup_sup_a_o @ A @ B ) )
= ( sup_sup_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(166,axiom,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] :
( collect_a
@ ( sup_sup_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_sup__set__def) ).
thf(700,plain,
( sup_sup_set_a
= ( ^ [A: set_a,B: set_a] :
( collect_a
@ ( sup_sup_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(104,axiom,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ B @ C ) )
= ( sup_su2137030215um_b_b @ B @ ( sup_su2137030215um_b_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_inf__sup__aci_I7_J) ).
thf(520,plain,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ B @ C ) )
= ( sup_su2137030215um_b_b @ B @ ( sup_su2137030215um_b_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(160,axiom,
( ord_le1404954451um_c_b
@ ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] :
? [B: a] :
( ( A
= ( sum_In811702836um_c_b @ B ) )
& ( member_a @ B @ ( static_SIGT_a_b @ theta_1 ) ) ) )
@ ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] :
? [B: a] :
( ( A
= ( sum_In811702836um_c_b @ B ) )
& ( member_a @ B @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_Isubs_I1_J) ).
thf(685,plain,
( ord_le1404954451um_c_b
@ ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] :
? [B: a] :
( ( A
= ( sum_In811702836um_c_b @ B ) )
& ( member_a @ B @ ( static_SIGT_a_b @ theta_1 ) ) ) )
@ ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] :
? [B: a] :
( ( A
= ( sum_In811702836um_c_b @ B ) )
& ( member_a @ B @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(64,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ C @ B )
=> ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_le__supI) ).
thf(399,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ C @ B )
=> ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(195,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: denota723907260t_unit,D: denota723907260t_unit] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( denota896875430_a_c_b @ C @ D @ B )
=> ( denota896875430_a_c_b @ C @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_Iagree__sub) ).
thf(768,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: denota723907260t_unit,D: denota723907260t_unit] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( denota896875430_a_c_b @ C @ D @ B )
=> ( denota896875430_a_c_b @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(62,axiom,
! [A: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_order__refl) ).
thf(394,plain,
! [A: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(120,axiom,
! [A: set_Su111624115um_c_b > set_Su111624115um_c_b > set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ! [D: set_Su111624115um_c_b,E: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ D @ ( A @ D @ E ) )
=> ( ! [D: set_Su111624115um_c_b,E: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ E @ ( A @ D @ E ) )
=> ( ! [D: set_Su111624115um_c_b,E: set_Su111624115um_c_b,F: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ E @ D )
=> ( ( ord_le1404954451um_c_b @ F @ D )
=> ( ord_le1404954451um_c_b @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup_su296826759um_c_b @ B @ C )
= ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_sup__unique) ).
thf(563,plain,
! [A: set_Su111624115um_c_b > set_Su111624115um_c_b > set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ! [D: set_Su111624115um_c_b,E: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ D @ ( A @ D @ E ) )
=> ( ! [D: set_Su111624115um_c_b,E: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ E @ ( A @ D @ E ) )
=> ( ! [D: set_Su111624115um_c_b,E: set_Su111624115um_c_b,F: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ E @ D )
=> ( ( ord_le1404954451um_c_b @ F @ D )
=> ( ord_le1404954451um_c_b @ ( A @ E @ F ) @ D ) ) )
=> ( ( sup_su296826759um_c_b @ B @ C )
= ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(8,axiom,
( ord_le1404954451um_c_b
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ord_le1534094666_c_b_o
@ ^ [C: sum_su1965225555um_c_b] : ( member973578748um_c_b @ C @ A )
@ ^ [C: sum_su1965225555um_c_b] : ( member973578748um_c_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_less__eq__set__def) ).
thf(226,plain,
( ord_le1404954451um_c_b
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ord_le1534094666_c_b_o
@ ^ [C: sum_su1965225555um_c_b] : ( member973578748um_c_b @ C @ A )
@ ^ [C: sum_su1965225555um_c_b] : ( member973578748um_c_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(20,axiom,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ A @ B ) )
= ( sup_su2137030215um_b_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_Un__left__absorb) ).
thf(267,plain,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ A @ B ) )
= ( sup_su2137030215um_b_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(77,axiom,
( ord_le1404954451um_c_b
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( sup_su296826759um_c_b @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_le__iff__sup) ).
thf(438,plain,
( ord_le1404954451um_c_b
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( sup_su296826759um_c_b @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(7,axiom,
! [A: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ top_to301096907um_b_b )
= top_to301096907um_b_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_Un__UNIV__right) ).
thf(223,plain,
! [A: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ top_to301096907um_b_b )
= top_to301096907um_b_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(134,axiom,
( sup_su2137030215um_b_b
= ( ^ [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b] : ( sup_su2137030215um_b_b @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_sup__commute) ).
thf(608,plain,
( sup_su2137030215um_b_b
= ( ^ [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b] : ( sup_su2137030215um_b_b @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(13,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_sup__ge1) ).
thf(241,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(149,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ B ) @ C )
= ( ( ord_le1404954451um_c_b @ A @ C )
& ( ord_le1404954451um_c_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_sup_Obounded__iff) ).
thf(653,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ B ) @ C )
= ( ( ord_le1404954451um_c_b @ A @ C )
& ( ord_le1404954451um_c_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(174,axiom,
( ( denota1997846517gree_b @ nu @ nu2 @ ( static_FVT_a_b @ theta_1 ) )
=> ( ( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] :
? [B: a] :
( ( A
= ( sum_In811702836um_c_b @ B ) )
& ( member_a @ B @ ( static_SIGT_a_b @ theta_1 ) ) ) ) )
=> ( ( denota722380397_a_c_b @ i @ theta_1 @ ( produc936751193real_b @ nu ) )
= ( denota722380397_a_c_b @ j @ theta_1 @ ( produc936751193real_b @ nu2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_IH1) ).
thf(722,plain,
( ( denota1997846517gree_b @ nu @ nu2 @ ( static_FVT_a_b @ theta_1 ) )
=> ( ( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] :
? [B: a] :
( ( A
= ( sum_In811702836um_c_b @ B ) )
& ( member_a @ B @ ( static_SIGT_a_b @ theta_1 ) ) ) ) )
=> ( ( denota722380397_a_c_b @ i @ theta_1 @ ( produc936751193real_b @ nu ) )
= ( denota722380397_a_c_b @ j @ theta_1 @ ( produc936751193real_b @ nu2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(156,axiom,
! [A: a,B: a] :
( ( ( sum_In811702836um_c_b @ A )
= ( sum_In811702836um_c_b @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_old_Osum_Oinject_I1_J) ).
thf(675,plain,
! [A: a,B: a] :
( ( ( sum_In811702836um_c_b @ A )
= ( sum_In811702836um_c_b @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(108,axiom,
! [A: trm_a_b,B: trm_a_b] :
( ( dfree_a_b @ ( times_a_b @ A @ B ) )
= ( ( dfree_a_b @ A )
& ( dfree_a_b @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_dfree__Times__simps) ).
thf(531,plain,
! [A: trm_a_b,B: trm_a_b] :
( ( dfree_a_b @ ( times_a_b @ A @ B ) )
= ( ( dfree_a_b @ A )
& ( dfree_a_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(147,axiom,
( sup_su2137030215um_b_b
= ( ^ [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b] : ( sup_su2137030215um_b_b @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_inf__sup__aci_I5_J) ).
thf(648,plain,
( sup_su2137030215um_b_b
= ( ^ [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b] : ( sup_su2137030215um_b_b @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(186,axiom,
! [A: denota723907260t_unit,B: denota723907260t_unit] :
( ( denota896875430_a_c_b @ A @ B
@ ( collec1166375742um_c_b
@ ^ [C: sum_su1965225555um_c_b] :
? [D: a] :
( ( C
= ( sum_In811702836um_c_b @ D ) )
& ( member_a @ D @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) )
=> ( denota896875430_a_c_b @ A @ B
@ ( collec1166375742um_c_b
@ ^ [C: sum_su1965225555um_c_b] :
? [D: a] :
( ( C
= ( sum_In811702836um_c_b @ D ) )
& ( member_a @ D @ ( static_SIGT_a_b @ theta_2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0622_125_092_060close_062) ).
thf(749,plain,
! [A: denota723907260t_unit,B: denota723907260t_unit] :
( ( denota896875430_a_c_b @ A @ B
@ ( collec1166375742um_c_b
@ ^ [C: sum_su1965225555um_c_b] :
? [D: a] :
( ( C
= ( sum_In811702836um_c_b @ D ) )
& ( member_a @ D @ ( static_SIGT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ) ) ) ) )
=> ( denota896875430_a_c_b @ A @ B
@ ( collec1166375742um_c_b
@ ^ [C: sum_su1965225555um_c_b] :
? [D: a] :
( ( C
= ( sum_In811702836um_c_b @ D ) )
& ( member_a @ D @ ( static_SIGT_a_b @ theta_2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(50,axiom,
( ( domain134596861rm_a_b @ frechet_cr_strm_a_b )
= dfree_a_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_strm_Odomain) ).
thf(355,plain,
( ( domain134596861rm_a_b @ frechet_cr_strm_a_b )
= dfree_a_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(85,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Un__subset__iff) ).
thf(458,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A @ B ) @ C )
= ( ( ord_less_eq_set_a @ A @ C )
& ( ord_less_eq_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(198,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_pred__subset__eq) ).
thf(776,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(30,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b > set_Su111624115um_c_b,C: set_Su111624115um_c_b,D: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ ( B @ C ) )
=> ( ( ord_le1404954451um_c_b @ C @ D )
=> ( ! [E: set_Su111624115um_c_b,F: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ E @ F )
=> ( ord_le1404954451um_c_b @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1404954451um_c_b @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_order__subst1) ).
thf(295,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b > set_Su111624115um_c_b,C: set_Su111624115um_c_b,D: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ ( B @ C ) )
=> ( ( ord_le1404954451um_c_b @ C @ D )
=> ( ! [E: set_Su111624115um_c_b,F: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ E @ F )
=> ( ord_le1404954451um_c_b @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le1404954451um_c_b @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(68,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ B @ C )
=> ( ord_le1404954451um_c_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_subset__trans) ).
thf(414,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ B @ C )
=> ( ord_le1404954451um_c_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(182,axiom,
! [A: set_Su111624115um_c_b] :
( ( collec1166375742um_c_b
@ ^ [B: sum_su1965225555um_c_b] : ( member973578748um_c_b @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_Collect__mem__eq) ).
thf(739,plain,
! [A: set_Su111624115um_c_b] :
( ( collec1166375742um_c_b
@ ^ [B: sum_su1965225555um_c_b] : ( member973578748um_c_b @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(170,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( sup_sup_set_a @ B @ C ) )
= ( ( member_a @ A @ B )
| ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_Un__iff) ).
thf(712,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( sup_sup_set_a @ B @ C ) )
= ( ( member_a @ A @ B )
| ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(117,axiom,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ A @ B ) )
= ( sup_su2137030215um_b_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_sup__left__idem) ).
thf(557,plain,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ A @ B ) )
= ( sup_su2137030215um_b_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(89,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( A = B )
=> ( ( ord_le1404954451um_c_b @ B @ C )
=> ( ord_le1404954451um_c_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_ord__eq__le__trans) ).
thf(470,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( A = B )
=> ( ( ord_le1404954451um_c_b @ B @ C )
=> ( ord_le1404954451um_c_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(145,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_le__supI2) ).
thf(643,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(45,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( B = C )
=> ( ord_le1404954451um_c_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_ord__le__eq__trans) ).
thf(336,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( B = C )
=> ( ord_le1404954451um_c_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(150,axiom,
! [A: a > $o,B: a > $o] :
( ( sup_sup_a_o @ ( sup_sup_a_o @ A @ B ) @ B )
= ( sup_sup_a_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_sup_Oright__idem) ).
thf(656,plain,
! [A: a > $o,B: a > $o] :
( ( sup_sup_a_o @ ( sup_sup_a_o @ A @ B ) @ B )
= ( sup_sup_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(131,axiom,
( ord_le1404954451um_c_b
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( B
= ( sup_su296826759um_c_b @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_sup_Oorder__iff) ).
thf(600,plain,
( ord_le1404954451um_c_b
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( B
= ( sup_su296826759um_c_b @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(176,axiom,
? [A: a] : ( member_a @ A @ top_top_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_UNIV__witness) ).
thf(727,plain,
? [A: a] : ( member_a @ A @ top_top_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(80,axiom,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_sup__left__idem) ).
thf(446,plain,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(92,axiom,
! [A: produc133005365real_b,B: produc133005365real_b] :
( ( produc936751193real_b @ ( sup_su1581595657real_b @ A @ B ) )
= ( sup_su2133361046real_b @ ( produc936751193real_b @ A ) @ ( produc936751193real_b @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_fst__sup) ).
thf(482,plain,
! [A: produc133005365real_b,B: produc133005365real_b] :
( ( produc936751193real_b @ ( sup_su1581595657real_b @ A @ B ) )
= ( sup_su2133361046real_b @ ( produc936751193real_b @ A ) @ ( produc936751193real_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(155,axiom,
! [A: denota723907260t_unit,B: denota723907260t_unit,C: set_Su111624115um_c_b,D: a] :
( ( denota896875430_a_c_b @ A @ B @ C )
=> ( ( member973578748um_c_b @ ( sum_In811702836um_c_b @ D ) @ C )
=> ( ( denota102976244t_unit @ A @ D )
= ( denota102976244t_unit @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Iagree__Func) ).
thf(671,plain,
! [A: denota723907260t_unit,B: denota723907260t_unit,C: set_Su111624115um_c_b,D: a] :
( ( denota896875430_a_c_b @ A @ B @ C )
=> ( ( member973578748um_c_b @ ( sum_In811702836um_c_b @ D ) @ C )
=> ( ( denota102976244t_unit @ A @ D )
= ( denota102976244t_unit @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(162,axiom,
! [A: trm_a_b,B: trm_a_b] :
( ( static_SIGT_a_b @ ( times_a_b @ A @ B ) )
= ( sup_sup_set_a @ ( static_SIGT_a_b @ A ) @ ( static_SIGT_a_b @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_SIGT_Osimps_I5_J) ).
thf(688,plain,
! [A: trm_a_b,B: trm_a_b] :
( ( static_SIGT_a_b @ ( times_a_b @ A @ B ) )
= ( sup_sup_set_a @ ( static_SIGT_a_b @ A ) @ ( static_SIGT_a_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(124,axiom,
! [A: produc133005365real_b,B: produc133005365real_b] :
( ( denota1997846517gree_b @ A @ B @ top_to301096907um_b_b )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_agree__UNIV__eq) ).
thf(581,plain,
! [A: produc133005365real_b,B: produc133005365real_b] :
( ( denota1997846517gree_b @ A @ B @ top_to301096907um_b_b )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(191,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_171_subset__eq) ).
thf(759,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)],[191]) ).
thf(196,axiom,
! [A: set_Su111624115um_c_b,B: sum_su1965225555um_c_b > $o] :
( ord_le1404954451um_c_b
@ ( collec1166375742um_c_b
@ ^ [C: sum_su1965225555um_c_b] :
( ( member973578748um_c_b @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_Collect__subset) ).
thf(771,plain,
! [A: set_Su111624115um_c_b,B: sum_su1965225555um_c_b > $o] :
( ord_le1404954451um_c_b
@ ( collec1166375742um_c_b
@ ^ [C: sum_su1965225555um_c_b] :
( ( member973578748um_c_b @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(103,axiom,
! [A: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_Un__absorb) ).
thf(517,plain,
! [A: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(185,axiom,
denota1997846517gree_b @ nu @ nu2 @ ( static_FVT_a_b @ theta_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_VAs_I1_J) ).
thf(748,plain,
denota1997846517gree_b @ nu @ nu2 @ ( static_FVT_a_b @ theta_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(178,axiom,
denota1997846517gree_b @ nu @ nu2 @ ( static_FVT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_dfree__Times_Oprems_I1_J) ).
thf(731,plain,
denota1997846517gree_b @ nu @ nu2 @ ( static_FVT_a_b @ ( times_a_b @ theta_1 @ theta_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(200,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ B )
=> ( member_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_UnI1) ).
thf(781,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ B )
=> ( member_a @ A @ ( sup_sup_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(58,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( sup_su296826759um_c_b @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_Un__absorb2) ).
thf(378,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( sup_su296826759um_c_b @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(75,axiom,
( ( (=) @ set_Su111624115um_c_b )
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
& ( ord_le1404954451um_c_b @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_eq__iff) ).
thf(433,plain,
( ( (=) @ set_Su111624115um_c_b )
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
& ( ord_le1404954451um_c_b @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(91,axiom,
! [A: produc133005365real_b,B: produc133005365real_b,C: trm_a_b,D: denota723907260t_unit] :
( ( denota1997846517gree_b @ A @ B @ ( static_FVT_a_b @ C ) )
=> ( ( denota722380397_a_c_b @ D @ C @ ( produc936751193real_b @ A ) )
= ( denota722380397_a_c_b @ D @ C @ ( produc936751193real_b @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_coincidence__sterm) ).
thf(478,plain,
! [A: produc133005365real_b,B: produc133005365real_b,C: trm_a_b,D: denota723907260t_unit] :
( ( denota1997846517gree_b @ A @ B @ ( static_FVT_a_b @ C ) )
=> ( ( denota722380397_a_c_b @ D @ C @ ( produc936751193real_b @ A ) )
= ( denota722380397_a_c_b @ D @ C @ ( produc936751193real_b @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(114,axiom,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_sup_Oleft__idem) ).
thf(549,plain,
! [A: set_a,B: set_a] :
( ( sup_sup_set_a @ A @ ( sup_sup_set_a @ A @ B ) )
= ( sup_sup_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(11,axiom,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ ( sup_su2137030215um_b_b @ A @ B ) @ C )
= ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_Un__assoc) ).
thf(235,plain,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ ( sup_su2137030215um_b_b @ A @ B ) @ C )
= ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,axiom,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ A @ B ) )
= ( sup_su2137030215um_b_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_inf__sup__aci_I8_J) ).
thf(246,plain,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ A @ B ) )
= ( sup_su2137030215um_b_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(193,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_207_Collect__subset) ).
thf(763,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)],[193]) ).
thf(22,axiom,
! [A: denota723907260t_unit,B: trm_a_b,C: set_Fi268318752real_b] :
( ( denota1086158987_a_c_b @ A )
=> ( ( dfree_a_b @ B )
=> ( topolo238266006b_real @ C @ ( denota722380397_a_c_b @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_sterm__continuous_H) ).
thf(272,plain,
! [A: denota723907260t_unit,B: trm_a_b,C: set_Fi268318752real_b] :
( ( denota1086158987_a_c_b @ A )
=> ( ( dfree_a_b @ B )
=> ( topolo238266006b_real @ C @ ( denota722380397_a_c_b @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(4,axiom,
! [A: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ top_to301096907um_b_b @ A )
= top_to301096907um_b_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_Un__UNIV__left) ).
thf(214,plain,
! [A: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ top_to301096907um_b_b @ A )
= top_to301096907um_b_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(207,axiom,
dfree_a_b @ theta_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_dfree__Times_Ohyps_I1_J) ).
thf(800,plain,
dfree_a_b @ theta_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(31,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_subset__antisym) ).
thf(300,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(37,axiom,
( sup_su1211201046_c_b_o
= ( ^ [A: sum_su1965225555um_c_b > $o,B: sum_su1965225555um_c_b > $o,C: sum_su1965225555um_c_b] : ( sup_sup_o @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_sup__apply) ).
thf(315,plain,
( sup_su1211201046_c_b_o
= ( ^ [A: sum_su1965225555um_c_b > $o,B: sum_su1965225555um_c_b > $o,C: sum_su1965225555um_c_b] : ( sup_sup_o @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(181,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_118_subsetI) ).
thf(735,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)],[181]) ).
thf(33,axiom,
! [A: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ top_to999478531um_c_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_top__greatest) ).
thf(305,plain,
! [A: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ top_to999478531um_c_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1,conjecture,
( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] :
? [B: a] :
( ( A
= ( sum_In811702836um_c_b @ B ) )
& ( member_a @ B @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] :
? [B: a] :
( ( A
= ( sum_In811702836um_c_b @ B ) )
& ( member_a @ B @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(210,plain,
~ ( denota896875430_a_c_b @ i @ j
@ ( collec1166375742um_c_b
@ ^ [A: sum_su1965225555um_c_b] :
? [B: a] :
( ( A
= ( sum_In811702836um_c_b @ B ) )
& ( member_a @ B @ ( static_SIGT_a_b @ theta_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(42,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ! [C: sum_su1965225555um_c_b] :
( ( member973578748um_c_b @ C @ A )
=> ( member973578748um_c_b @ C @ B ) )
=> ( ord_le1404954451um_c_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_subsetI) ).
thf(326,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ! [C: sum_su1965225555um_c_b] :
( ( member973578748um_c_b @ C @ A )
=> ( member973578748um_c_b @ C @ B ) )
=> ( ord_le1404954451um_c_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(208,axiom,
( top_to999478531um_c_b
= ( collec1166375742um_c_b @ top_to1849113498_c_b_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_top__set__def) ).
thf(801,plain,
( top_to999478531um_c_b
= ( collec1166375742um_c_b @ top_to1849113498_c_b_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(46,axiom,
! [A: bounde472938360z_real,B: bounde472938360z_real] :
( ( if_Bou1785791806z_real @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T) ).
thf(341,plain,
! [A: bounde472938360z_real,B: bounde472938360z_real] :
( ( if_Bou1785791806z_real @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(142,axiom,
! [A: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_sup_Oidem) ).
thf(635,plain,
! [A: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(205,axiom,
( sup_su296826759um_c_b
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( collec1166375742um_c_b
@ ( sup_su1211201046_c_b_o
@ ^ [C: sum_su1965225555um_c_b] : ( member973578748um_c_b @ C @ A )
@ ^ [C: sum_su1965225555um_c_b] : ( member973578748um_c_b @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_sup__set__def) ).
thf(796,plain,
( sup_su296826759um_c_b
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( collec1166375742um_c_b
@ ( sup_su1211201046_c_b_o
@ ^ [C: sum_su1965225555um_c_b] : ( member973578748um_c_b @ C @ A )
@ ^ [C: sum_su1965225555um_c_b] : ( member973578748um_c_b @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(26,axiom,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ ( sup_su2137030215um_b_b @ A @ B ) @ C )
= ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_sup__assoc) ).
thf(283,plain,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b] :
( ( sup_su2137030215um_b_b @ ( sup_su2137030215um_b_b @ A @ B ) @ C )
= ( sup_su2137030215um_b_b @ A @ ( sup_su2137030215um_b_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(87,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b,D: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ C @ D )
=> ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ C ) @ ( sup_su296826759um_c_b @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_sup__mono) ).
thf(464,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b,D: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( ord_le1404954451um_c_b @ C @ D )
=> ( ord_le1404954451um_c_b @ ( sup_su296826759um_c_b @ A @ C ) @ ( sup_su296826759um_c_b @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(122,axiom,
! [A: a > $o,B: a > $o] :
( ( sup_sup_a_o @ A @ ( sup_sup_a_o @ A @ B ) )
= ( sup_sup_a_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_sup_Oleft__idem) ).
thf(575,plain,
! [A: a > $o,B: a > $o] :
( ( sup_sup_a_o @ A @ ( sup_sup_a_o @ A @ B ) )
= ( sup_sup_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(129,axiom,
( ( (=) @ set_Su111624115um_c_b )
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
& ( ord_le1404954451um_c_b @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_order__class_Oorder_Oeq__iff) ).
thf(596,plain,
( ( (=) @ set_Su111624115um_c_b )
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
& ( ord_le1404954451um_c_b @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(107,axiom,
! [A: denota723907260t_unit,B: trm_a_b] :
( ( denota1086158987_a_c_b @ A )
=> ( ( dfree_a_b @ B )
=> ( topolo238266006b_real @ top_to502572752real_b @ ( denota722380397_a_c_b @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_sterm__continuous) ).
thf(528,plain,
! [A: denota723907260t_unit,B: trm_a_b] :
( ( denota1086158987_a_c_b @ A )
=> ( ( dfree_a_b @ B )
=> ( topolo238266006b_real @ top_to502572752real_b @ ( denota722380397_a_c_b @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(98,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( B
= ( sup_su296826759um_c_b @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_sup_OorderE) ).
thf(501,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( B
= ( sup_su296826759um_c_b @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(55,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: sum_su1965225555um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( member973578748um_c_b @ C @ A )
=> ( member973578748um_c_b @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_subsetD) ).
thf(369,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: sum_su1965225555um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( member973578748um_c_b @ C @ A )
=> ( member973578748um_c_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(24,axiom,
! [A: trm_a_b,B: trm_a_b] :
( ( static_FVT_a_b @ ( times_a_b @ A @ B ) )
= ( sup_su2137030215um_b_b @ ( static_FVT_a_b @ A ) @ ( static_FVT_a_b @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_FVT_Osimps_I5_J) ).
thf(277,plain,
! [A: trm_a_b,B: trm_a_b] :
( ( static_FVT_a_b @ ( times_a_b @ A @ B ) )
= ( sup_su2137030215um_b_b @ ( static_FVT_a_b @ A ) @ ( static_FVT_a_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(163,axiom,
! [A: sum_su1965225555um_c_b,B: sum_su1965225555um_c_b > $o] :
( ( member973578748um_c_b @ A @ ( collec1166375742um_c_b @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_mem__Collect__eq) ).
thf(691,plain,
! [A: sum_su1965225555um_c_b,B: sum_su1965225555um_c_b > $o] :
( ( member973578748um_c_b @ A @ ( collec1166375742um_c_b @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(209,axiom,
! [A: set_a,B: set_a] :
( ( sup_sup_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) )
= ( ^ [C: a] : ( member_a @ C @ ( sup_sup_set_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_sup__Un__eq) ).
thf(803,plain,
! [A: set_a,B: set_a] :
( ( sup_sup_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) )
= ( ^ [C: a] : ( member_a @ C @ ( sup_sup_set_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(112,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( sup_su296826759um_c_b @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_sup__absorb2) ).
thf(543,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( sup_su296826759um_c_b @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(118,axiom,
( ord_le1404954451um_c_b
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( sup_su296826759um_c_b @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_sup_Oabsorb__iff2) ).
thf(560,plain,
( ord_le1404954451um_c_b
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( sup_su296826759um_c_b @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(189,axiom,
denota1997846517gree_b @ nu @ nu2 @ ( sup_su2137030215um_b_b @ ( static_FVT_a_b @ theta_1 ) @ ( static_FVT_a_b @ theta_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_VA) ).
thf(755,plain,
denota1997846517gree_b @ nu @ nu2 @ ( sup_su2137030215um_b_b @ ( static_FVT_a_b @ theta_1 ) @ ( static_FVT_a_b @ theta_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(95,axiom,
! [A: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_subset__refl) ).
thf(491,plain,
! [A: set_Su111624115um_c_b] : ( ord_le1404954451um_c_b @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(83,axiom,
( ord_le1404954451um_c_b
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( sup_su296826759um_c_b @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_subset__Un__eq) ).
thf(454,plain,
( ord_le1404954451um_c_b
= ( ^ [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( sup_su296826759um_c_b @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(54,axiom,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b,D: set_Sum_sum_b_b] :
( ( A
= ( sup_su2137030215um_b_b @ B @ C ) )
=> ( ( sup_su2137030215um_b_b @ A @ D )
= ( sup_su2137030215um_b_b @ B @ ( sup_su2137030215um_b_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_boolean__algebra__cancel_Osup1) ).
thf(364,plain,
! [A: set_Sum_sum_b_b,B: set_Sum_sum_b_b,C: set_Sum_sum_b_b,D: set_Sum_sum_b_b] :
( ( A
= ( sup_su2137030215um_b_b @ B @ C ) )
=> ( ( sup_su2137030215um_b_b @ A @ D )
= ( sup_su2137030215um_b_b @ B @ ( sup_su2137030215um_b_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(10,axiom,
! [A: produc133005365real_b,B: produc133005365real_b,C: set_Sum_sum_b_b,D: set_Sum_sum_b_b] :
( ( denota1997846517gree_b @ A @ B @ C )
=> ( ( denota1997846517gree_b @ A @ B @ D )
=> ( denota1997846517gree_b @ A @ B @ ( sup_su2137030215um_b_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_agree__union) ).
thf(232,plain,
! [A: produc133005365real_b,B: produc133005365real_b,C: set_Sum_sum_b_b,D: set_Sum_sum_b_b] :
( ( denota1997846517gree_b @ A @ B @ C )
=> ( ( denota1997846517gree_b @ A @ B @ D )
=> ( denota1997846517gree_b @ A @ B @ ( sup_su2137030215um_b_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(35,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( sup_su296826759um_c_b @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_sup_Oabsorb1) ).
thf(309,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ( sup_su296826759um_c_b @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(151,axiom,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_sup_OcoboundedI1) ).
thf(659,plain,
! [A: set_Su111624115um_c_b,B: set_Su111624115um_c_b,C: set_Su111624115um_c_b] :
( ( ord_le1404954451um_c_b @ A @ B )
=> ( ord_le1404954451um_c_b @ A @ ( sup_su296826759um_c_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(820,plain,
$false,
inference(e,[status(thm)],[347,249,333,628,408,523,217,449,614,440,511,384,715,698,709,417,320,719,372,504,587,344,357,702,751,638,228,289,261,475,756,789,591,443,485,238,514,211,646,602,280,396,411,243,428,265,507,312,307,292,678,270,761,381,220,534,798,546,793,598,275,729,467,252,625,435,665,461,493,682,456,324,317,650,725,593,610,420,742,578,488,537,686,526,679,554,753,622,393,779,605,765,773,633,360,662,718,425,430,745,375,733,584,562,423,694,402,732,286,641,572,787,498,704,350,540,784,303,362,451,631,552,323,668,330,700,520,685,399,768,394,563,226,267,438,223,608,241,653,722,675,531,648,749,355,458,776,295,414,739,712,557,470,643,336,656,600,727,446,482,671,688,581,759,771,517,748,731,781,378,433,478,549,235,246,763,272,214,800,300,315,735,305,210,326,801,341,635,796,283,464,575,596,528,501,369,277,691,803,543,560,755,491,454,364,232,309,659]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP042^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.09/0.20 % Computer : n020.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 19:41:34 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.88/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.12/1.18 % [INFO] Parsing done (397ms).
% 2.12/1.19 % [INFO] Running in sequential loop mode.
% 2.94/1.57 % [INFO] eprover registered as external prover.
% 2.94/1.58 % [INFO] Scanning for conjecture ...
% 3.32/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 358 axioms. Running axiom selection ...
% 3.49/1.87 % [INFO] Axiom selection finished. Selected 207 axioms (removed 151 axioms).
% 4.13/2.05 % [INFO] Problem is higher-order (TPTP THF).
% 4.13/2.07 % [INFO] Type checking passed.
% 4.13/2.08 % [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 ...
% 12.17/4.39 % External prover 'e' found a proof!
% 12.17/4.39 % [INFO] Killing All external provers ...
% 12.17/4.39 % Time passed: 4042ms (effective reasoning time: 3190ms)
% 12.17/4.39 % 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)>
% 12.17/4.40 % Axioms used in derivation (207): fact_29_dfree__Times__simps, fact_295_dual__order_Oeq__iff, fact_4_dfree__Times_Ohyps_I1_J, fact_188_sup_Oassoc, fact_325_top_Oextremum__uniqueI, fact_332_Un__UNIV__left, fact_52_Iagree__sub, fact_196_UnI1, fact_278_Un__upper2, fact_181_Collect__mono__iff, fact_178_Collect__mono, fact_83_sup_Obounded__iff, fact_183_inf__sup__aci_I7_J, fact_157_UnCI, fact_280_Un__absorb1, fact_97_SIGT_Osimps_I5_J, fact_297_dual__order_Orefl, fact_349_iso__tuple__UNIV__I, fact_255_sup_OboundedI, fact_179_subset__trans, fact_156_sup_Oright__idem, fact_169_subsetD, fact_296_dual__order_Otrans, fact_303_antisym__conv, fact_193_sup__left__commute, fact_177_subset__refl, fact_229_le__supI2, fact_305_eq__refl, fact_9_Iagree__comm, fact_182_inf__sup__aci_I8_J, help_If_1_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T, fact_318_UNIV__I, fact_185_inf__sup__aci_I5_J, fact_130_sup_Oidem, fact_77_Un__subset__iff, fact_329_top__greatest, fact_202_Un__assoc, fact_57_fst__sup, fact_235_sup__least, fact_1__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0622_125_092_060close_062, fact_322_sup__top__left, fact_294_dual__order_Oantisym, fact_172_subset__eq, fact_314_sup__Un__eq, fact_198_UnI2, fact_127_sup_Oidem, fact_7_Isubs_I2_J, fact_134_sup__idem, fact_12_IH1, fact_74_Collect__cong, fact_334_Un__UNIV__right, fact_168_subsetD, fact_233_sup__mono, fact_338_UNIV__eq__I, fact_276_Un__upper1, fact_152_sup_Oright__idem, fact_265_sup_Oabsorb__iff2, fact_69_Collect__mem__eq, fact_272_Un__mono, fact_311_order__subst1, fact_44_trm_Oinject_I5_J, fact_243_sup__unique, fact_189_sup__assoc, fact_263_sup_Oabsorb__iff1, fact_257_sup_Oorder__iff, fact_126_sup__apply, fact_208_Collect__subset, fact_227_le__supI1, fact_133_sup__idem, fact_118_subsetI, fact_313_sterm__continuous, fact_247_sup_Oabsorb2, fact_340_UNIV__def, help_If_2_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T, fact_221_le__supI, fact_223_sup__ge1, fact_162_sup__set__def, fact_144_sup_Oleft__idem, fact_142_sup_Oleft__idem, fact_90_le__sup__iff, fact_54_dfree_Odfree__Times, fact_151_sup_Oright__idem, fact_316_pred__subset__eq, fact_346_top__set__def, fact_288_order__refl, fact_241_sup_OorderI, fact_91_le__sup__iff, fact_5_sum_Oinject_I1_J, fact_336_UNIV__witness, fact_301_ord__eq__le__trans, fact_6_old_Osum_Oinject_I1_J, fact_180_set__eq__subset, fact_331_subset__UNIV, help_If_3_1_If_001t__Bounded____Linear____Function__Oblinfun_It__Finite____Cartesian____Product__Ovec_It__Real__Oreal_Mtf__sz_J_Mt__Real__Oreal_J_T, fact_298_order__trans, fact_14_Iagree__Func, fact_89_le__sup__iff, fact_207_Collect__subset, fact_125_sup__apply, fact_308_ord__le__eq__subst, fact_84_sup_Obounded__iff, fact_309_ord__eq__le__subst, fact_327_top_Oextremum__unique, fact_149_sup__left__idem, fact_320_sup__top__right, fact_261_sup_Ocobounded2, fact_215_inf__sup__ord_I4_J, fact_205_Un__left__absorb, fact_269_sup_OcoboundedI2, fact_128_sup_Oidem, fact_25_agree__refl, fact_154_sup_Oright__idem, fact_3_dfree__Times_Oprems_I2_J, fact_93_le__sup__iff, fact_217_inf__sup__ord_I3_J, fact_18_coincidence__sterm, fact_145_sup__left__idem, fact_132_sup_Oidem, fact_354_conj__subset__def, fact_317_pred__subset__eq, fact_2_IA, fact_184_inf__sup__aci_I6_J, fact_251_sup__absorb2, fact_284_subset__UnE, fact_299_order__class_Oorder_Oantisym, fact_307_eq__iff, fact_286_subset__Un__eq, fact_11_Inl__inject, fact_237_le__iff__sup, fact_62_mem__Collect__eq, fact_24_agree__comm, fact_21_VAs_I1_J, fact_148_sup__left__idem, fact_155_sup_Oright__idem, fact_300_ord__le__eq__trans, fact_159_Un__iff, fact_140_sup_Oleft__idem, fact_16_dfree__Times_Ohyps_I2_J, fact_166_in__mono, fact_68_Collect__mem__eq, fact_304_order_Otrans, fact_86_sup_Obounded__iff, fact_0__092_060open_062_092_060And_062J_AI_O_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_ITimes_A_092_060theta_062_092_060_094sub_0621_A_092_060theta_062_092_060_094sub_0622_J_125_A_092_060Longrightarrow_062_AIagree_AI_AJ_A_123Inl_Ax_A_124x_O_Ax_A_092_060in_062_ASIGT_A_092_060theta_062_092_060_094sub_0621_125_092_060close_062, fact_282_Un__absorb2, fact_206_Un__left__commute, fact_292_strm_Odomain, fact_190_sup_Ocommute, fact_212_Collect__disj__eq, fact_267_sup_OcoboundedI1, fact_249_sup__absorb1, fact_245_sup_Oabsorb1, fact_164_less__eq__set__def, fact_344_top__empty__eq, fact_302_order__class_Oorder_Oeq__iff, fact_13_IH2, fact_95_FVT_Osimps_I5_J, fact_270_fst__mono, fact_210_Un__def, fact_187_boolean__algebra__cancel_Osup2, fact_290_sterm__continuous_H, fact_209_Un__def, fact_171_subset__eq, fact_253_sup_OboundedE, fact_75_Collect__cong, fact_191_sup__commute, fact_122_subset__antisym, fact_167_in__mono, fact_343_agree__UNIV__eq, fact_19_dfree__Times_Oprems_I1_J, fact_131_sup_Oidem, fact_20_VAs_I2_J, fact_146_sup__left__idem, fact_119_subsetI, fact_138_sup__idem, fact_136_sup__idem, fact_176_subset__iff, fact_161_sup__set__def, fact_22_VA, fact_203_Un__absorb, fact_143_sup_Oleft__idem, fact_173_equalityD1, fact_170_equalityE, fact_239_sup_OorderE, fact_82_sup_Obounded__iff, fact_225_sup__ge2, fact_219_le__supE, fact_51_agree__union, fact_10_Iagree__refl, fact_139_sup_Oleft__idem, fact_310_order__subst2, fact_174_equalityD2, fact_79_Un__subset__iff, fact_165_less__eq__set__def, fact_150_sup__left__idem, fact_175_subset__iff, fact_194_UnE, fact_137_sup__idem, fact_186_boolean__algebra__cancel_Osup1, fact_274_Un__least, fact_8_Isubs_I1_J, fact_204_Un__commute, fact_192_sup_Oleft__commute, fact_306_antisym, fact_259_sup_Ocobounded1, fact_63_mem__Collect__eq, fact_231_sup_Omono, fact_123_subset__antisym
% 12.17/4.40 % No. of inferences in proof: 418
% 12.78/4.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4042 ms resp. 3190 ms w/o parsing
% 13.25/4.58 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.25/4.58 % [INFO] Killing All external provers ...
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