%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP117^2 : 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 : n015.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 08:06:50 AM UTC 2026
% Result : Theorem 66.27s 25.16s
% Output : Refutation 52.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 381
% Syntax : Number of formulae : 791 ( 335 unt; 0 typ; 0 def)
% Number of atoms : 2679 ( 569 equ; 2 cnn)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 9301 ( 98 ~; 23 |; 136 &;8474 @)
% ( 0 <=>; 570 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 253 ( 253 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 62 usr; 9 con; 0-4 aty)
% Number of variables : 2191 ( 180 ^;1967 !; 44 ?;2191 :)
% Comments :
%------------------------------------------------------------------------------
thf(extend1814228343nnreal_type,type,
extend1814228343nnreal: $tType ).
thf(real_type,type,
real: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(n_type,type,
n: $tType ).
thf(ring_1_decl,type,
ring_1:
!>[TA: $tType] : $o ).
thf(ordere890947078_space_decl,type,
ordere890947078_space:
!>[TA: $tType] : $o ).
thf(type_decl,type,
type:
!>[TA: $tType] : $o ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(neg_numeral_decl,type,
neg_numeral:
!>[TA: $tType] : $o ).
thf(group_add_decl,type,
group_add:
!>[TA: $tType] : $o ).
thf(finite_finite_decl,type,
finite_finite:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(countable_decl,type,
countable:
!>[TA: $tType] : $o ).
thf(ab_group_add_decl,type,
ab_group_add:
!>[TA: $tType] : $o ).
thf(semigroup_add_decl,type,
semigroup_add:
!>[TA: $tType] : $o ).
thf(complete_Sup_decl,type,
complete_Sup:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_decl,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(comm_monoid_diff_decl,type,
comm_monoid_diff:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_decl,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(cancel1352612707id_add_decl,type,
cancel1352612707id_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(ordere779506340up_add_decl,type,
ordere779506340up_add:
!>[TA: $tType] : $o ).
thf(linord1659791738miring_decl,type,
linord1659791738miring:
!>[TA: $tType] : $o ).
thf(comple187826305attice_decl,type,
comple187826305attice:
!>[TA: $tType] : $o ).
thf(comple1035589618norder_decl,type,
comple1035589618norder:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_decl,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_decl,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(ordere223160158up_add_decl,type,
ordere223160158up_add:
!>[TA: $tType] : $o ).
thf(strict2144017051up_add_decl,type,
strict2144017051up_add:
!>[TA: $tType] : $o ).
thf(ordere516151231imp_le_decl,type,
ordere516151231imp_le:
!>[TA: $tType] : $o ).
thf(complete_Sup_Sup_decl,type,
complete_Sup_Sup:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(complete_completion_decl,type,
complete_completion:
!>[TA: $tType] : ( ( sigma_measure @ TA ) > ( sigma_measure @ TA ) ) ).
thf(counta609264050t_into_decl,type,
counta609264050t_into:
!>[TA: $tType] : ( ( set @ TA ) > nat > TA ) ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(inf_inf_decl,type,
inf_inf:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(lebesgue_lborel_decl,type,
lebesgue_lborel:
!>[TA: $tType] : ( sigma_measure @ TA ) ).
thf(measure_null_sets_decl,type,
measure_null_sets:
!>[TA: $tType] : ( ( sigma_measure @ TA ) > ( set @ ( set @ TA ) ) ) ).
thf(minkow1937162798nt_vec_decl,type,
minkow1937162798nt_vec:
!>[TA: $tType,TB: $tType] : ( ( finite_Cartesian_vec @ int @ TB ) > ( finite_Cartesian_vec @ TA @ TB ) ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(top_top_decl,type,
top_top:
!>[TA: $tType] : TA ).
thf(sums_decl,type,
sums:
!>[TA: $tType] : ( ( nat > TA ) > TA > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(image_decl,type,
image:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TB ) > ( set @ TA ) ) ).
thf(vimage_decl,type,
vimage:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TA ) > ( set @ TB ) ) ).
thf(sigma_emeasure_decl,type,
sigma_emeasure:
!>[TA: $tType] : ( ( sigma_measure @ TA ) > ( set @ TA ) > extend1814228343nnreal ) ).
thf(sigma_sets_decl,type,
sigma_sets:
!>[TA: $tType] : ( ( sigma_measure @ TA ) > ( set @ ( set @ TA ) ) ) ).
thf(sigma_space_decl,type,
sigma_space:
!>[TA: $tType] : ( ( sigma_measure @ TA ) > ( set @ TA ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(r_decl,type,
r: ( finite_Cartesian_vec @ int @ n ) > ( set @ ( finite_Cartesian_vec @ real @ n ) ) ).
thf(s_decl,type,
s: set @ ( finite_Cartesian_vec @ real @ n ) ).
thf(t_decl,type,
t: ( finite_Cartesian_vec @ int @ n ) > ( set @ ( finite_Cartesian_vec @ real @ n ) ) ).
thf(t2_decl,type,
t2: ( finite_Cartesian_vec @ int @ n ) > ( set @ ( finite_Cartesian_vec @ real @ n ) ) ).
thf(f_decl,type,
f: nat > ( finite_Cartesian_vec @ int @ n ) ).
thf(sk27_decl,type,
sk27: nat ).
thf(sk28_decl,type,
sk28: nat ).
thf(103,axiom,
! [TA: $tType,A: ( set @ TA ) > TA,B: set @ TA] :
( ( A
@ ( image @ TA @ TA
@ ^ [C: TA] : C
@ B ) )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_Sup_OSUP__identity__eq) ).
thf(645,plain,
! [TA: $tType,A: ( set @ TA ) > TA,B: set @ TA] :
( ( A
@ ( image @ TA @ TA
@ ^ [C: TA] : C
@ B ) )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(306,axiom,
ordered_ab_group_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__group__add) ).
thf(1168,plain,
ordered_ab_group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(280,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_diff__eq__diff__eq) ).
thf(1105,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(198,axiom,
! [TA: $tType,A: sigma_measure @ TA,B: TA > $o,C: TA > $o] :
( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( B @ D ) ) )
@ ( measure_null_sets @ TA @ A ) )
=> ( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( C @ D ) ) )
@ ( measure_null_sets @ TA @ A ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( ( C @ D )
| ( B @ D ) ) ) )
@ ( measure_null_sets @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_null__sets_Osets__Collect__disj) ).
thf(893,plain,
! [TA: $tType,A: sigma_measure @ TA,B: TA > $o,C: TA > $o] :
( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( B @ D ) ) )
@ ( measure_null_sets @ TA @ A ) )
=> ( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( C @ D ) ) )
@ ( measure_null_sets @ TA @ A ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( ( C @ D )
| ( B @ D ) ) ) )
@ ( measure_null_sets @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(218,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_diff__strict__mono) ).
thf(941,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(42,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_one__reorient) ).
thf(481,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(340,axiom,
( sums @ extend1814228343nnreal
@ ^ [A: nat] : ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( t2 @ ( f @ A ) ) )
@ ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) )
@ ( complete_Sup_Sup @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
@ ( image @ nat @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
@ ^ [A: nat] : ( t2 @ ( f @ A ) )
@ ( top_top @ ( set @ nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9__092_060open_062_I_092_060lambda_062n_O_Aemeasure_Alebesgue_A_IT_A_If_An_J_J_J_Asums_Aemeasure_Alebesgue_A_I_092_060Union_062n_O_AT_A_If_An_J_J_092_060close_062) ).
thf(1237,plain,
( sums @ extend1814228343nnreal
@ ^ [A: nat] : ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( t2 @ ( f @ A ) ) )
@ ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) )
@ ( complete_Sup_Sup @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
@ ( image @ nat @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
@ ^ [A: nat] : ( t2 @ ( f @ A ) )
@ ( top_top @ ( set @ nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(182,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_add__diff__cancel__right_H) ).
thf(846,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(226,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ? [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_bex__imageD) ).
thf(962,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ? [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) )
=> ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(37,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ( one @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Oone_32) ).
thf(468,plain,
! [TA: $tType] :
( ( one @ TA )
=> ( one @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TA )
& ( ring_char_0 @ TB ) )
=> ! [A: finite_Cartesian_vec @ int @ TA,B: finite_Cartesian_vec @ int @ TA] :
( ( ( minkow1937162798nt_vec @ TA @ TB @ A )
= ( minkow1937162798nt_vec @ TA @ TB @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_of__int__vec__eq__iff) ).
thf(666,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TA )
& ( ring_char_0 @ TB ) )
=> ! [A: finite_Cartesian_vec @ int @ TA,B: finite_Cartesian_vec @ int @ TA] :
( ( ( minkow1937162798nt_vec @ TA @ TB @ A )
= ( minkow1937162798nt_vec @ TA @ TB @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(376,axiom,
! [A: finite_Cartesian_vec @ int @ n] :
( ( t @ A )
= ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
@ ^ [B: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
@ ( t2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_T_H__altdef) ).
thf(1295,plain,
! [A: finite_Cartesian_vec @ int @ n] :
( ( t @ A )
= ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
@ ^ [B: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
@ ( t2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(322,axiom,
! [TA: $tType,A: nat > ( set @ TA ),B: sigma_measure @ TA] :
( ! [C: nat] : ( member @ ( set @ TA ) @ ( A @ C ) @ ( sigma_sets @ TA @ B ) )
=> ( ! [C: nat,D: nat] :
( ( C != D )
=> ( ( sigma_emeasure @ TA @ B @ ( inf_inf @ ( set @ TA ) @ ( A @ C ) @ ( A @ D ) ) )
= ( zero_zero @ extend1814228343nnreal ) ) )
=> ( sums @ extend1814228343nnreal
@ ^ [C: nat] : ( sigma_emeasure @ TA @ B @ ( A @ C ) )
@ ( sigma_emeasure @ TA @ B @ ( complete_Sup_Sup @ ( set @ TA ) @ ( image @ nat @ ( set @ TA ) @ A @ ( top_top @ ( set @ nat ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_sums__emeasure_H) ).
thf(1200,plain,
! [TA: $tType,A: nat > ( set @ TA ),B: sigma_measure @ TA] :
( ! [C: nat] : ( member @ ( set @ TA ) @ ( A @ C ) @ ( sigma_sets @ TA @ B ) )
=> ( ! [C: nat,D: nat] :
( ( C != D )
=> ( ( sigma_emeasure @ TA @ B @ ( inf_inf @ ( set @ TA ) @ ( A @ C ) @ ( A @ D ) ) )
= ( zero_zero @ extend1814228343nnreal ) ) )
=> ( sums @ extend1814228343nnreal
@ ^ [C: nat] : ( sigma_emeasure @ TA @ B @ ( A @ C ) )
@ ( sigma_emeasure @ TA @ B @ ( complete_Sup_Sup @ ( set @ TA ) @ ( image @ nat @ ( set @ TA ) @ A @ ( top_top @ ( set @ nat ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(228,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_add__strict__left__mono) ).
thf(977,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(325,axiom,
! [A: finite_Cartesian_vec @ int @ n] :
( ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( t @ A ) )
= ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( t2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_emeasure__T_H) ).
thf(1211,plain,
! [A: finite_Cartesian_vec @ int @ n] :
( ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( t @ A ) )
= ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( t2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(78,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_add__less__same__cancel1) ).
thf(582,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(372,axiom,
neg_numeral @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Num_Oneg__numeral_55) ).
thf(1290,plain,
neg_numeral @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(235,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_double__zero__sym) ).
thf(994,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(265,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( measure_null_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ C @ ( measure_null_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( measure_null_sets @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_null__sets_OInt) ).
thf(1073,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( measure_null_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ C @ ( measure_null_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( measure_null_sets @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) )
= ( image @ TA @ TC
@ ^ [D: TA] : ( A @ ( B @ D ) )
@ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_image__image) ).
thf(597,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: set @ TA] :
( ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ C ) )
= ( image @ TA @ TC
@ ^ [D: TA] : ( A @ ( B @ D ) )
@ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(251,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ ( sigma_space @ TA @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_sets_OInt__space__eq1) ).
thf(1041,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ ( sigma_space @ TA @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(296,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
=> ~ ! [C: TA] :
( A
!= ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_rangeE) ).
thf(1142,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) )
=> ~ ! [C: TA] :
( A
!= ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(360,axiom,
cancel1352612707id_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_45) ).
thf(1269,plain,
cancel1352612707id_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(192,axiom,
ring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Oring__1_3) ).
thf(878,plain,
ring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(25,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_add__strict__right__mono) ).
thf(440,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(106,axiom,
ab_group_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oab__group__add) ).
thf(655,plain,
ab_group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(3,axiom,
! [TA: $tType] : ( comple187826305attice @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_23) ).
thf(385,plain,
! [TA: $tType] : ( comple187826305attice @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
( ( ^ [A: nat] : ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( t2 @ ( f @ A ) ) ) )
= ( ^ [A: nat] : ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( t @ ( f @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( ^ [A: nat] : ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( t2 @ ( f @ A ) ) ) )
!= ( ^ [A: nat] : ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( t @ ( f @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(383,plain,
( ( ^ [A: nat] : ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( t2 @ ( f @ A ) ) ) )
!= ( ^ [A: nat] : ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( t @ ( f @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(384,plain,
( ( ^ [A: nat] : ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( t2 @ ( f @ A ) ) ) )
!= ( ^ [A: nat] : ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( t @ ( f @ A ) ) ) ) ),
inference(lifteq,[status(thm)],[383]) ).
thf(293,axiom,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: TB > TA,B: set @ TB,C: TA,D: TB] :
( ( ord_less @ TA @ ( complete_Sup_Sup @ TA @ ( image @ TB @ TA @ A @ B ) ) @ C )
=> ( ( member @ TB @ D @ B )
=> ( ord_less @ TA @ ( A @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_SUP__lessD) ).
thf(1137,plain,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ! [A: TB > TA,B: set @ TB,C: TA,D: TB] :
( ( ord_less @ TA @ ( complete_Sup_Sup @ TA @ ( image @ TB @ TA @ A @ B ) ) @ C )
=> ( ( member @ TB @ D @ B )
=> ( ord_less @ TA @ ( A @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(1310,plain,
( ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( t2 @ ( f @ sk27 ) ) )
!= ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( t @ ( f @ sk27 ) ) ) ),
inference(func_ext,[status(esa)],[384]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comple187826305attice @ TC )
=> ! [A: TB > TA > TC,B: set @ TA,C: set @ TB] :
( ( complete_Sup_Sup @ TC
@ ( image @ TB @ TC
@ ^ [D: TB] : ( complete_Sup_Sup @ TC @ ( image @ TA @ TC @ ( A @ D ) @ B ) )
@ C ) )
= ( complete_Sup_Sup @ TC
@ ( image @ TA @ TC
@ ^ [D: TA] :
( complete_Sup_Sup @ TC
@ ( image @ TB @ TC
@ ^ [E: TB] : ( A @ E @ D )
@ C ) )
@ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_SUP__commute) ).
thf(500,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comple187826305attice @ TC )
=> ! [A: TB > TA > TC,B: set @ TA,C: set @ TB] :
( ( complete_Sup_Sup @ TC
@ ( image @ TB @ TC
@ ^ [D: TB] : ( complete_Sup_Sup @ TC @ ( image @ TA @ TC @ ( A @ D ) @ B ) )
@ C ) )
= ( complete_Sup_Sup @ TC
@ ( image @ TA @ TC
@ ^ [D: TA] :
( complete_Sup_Sup @ TC
@ ( image @ TB @ TC
@ ^ [E: TB] : ( A @ E @ D )
@ C ) )
@ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(338,axiom,
( t
= ( ^ [A: finite_Cartesian_vec @ int @ n] :
( image @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
@ ^ [B: finite_Cartesian_vec @ real @ n] : ( minus_minus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
@ ( t2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_T_H__def) ).
thf(1233,plain,
( t
= ( ^ [A: finite_Cartesian_vec @ int @ n] :
( image @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
@ ^ [B: finite_Cartesian_vec @ real @ n] : ( minus_minus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
@ ( t2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(170,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_zero__less__iff__neq__zero) ).
thf(814,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(262,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( finite_finite @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Finite__Set_Ofinite_30) ).
thf(1063,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( finite_finite @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(144,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_Int__UNIV__left) ).
thf(747,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( top_top @ ( set @ TA ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(207,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( measure_null_sets @ TA @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ ( sigma_space @ TA @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_null__sets_OInt__space__eq1) ).
thf(913,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( measure_null_sets @ TA @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ ( sigma_space @ TA @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(330,axiom,
linord219039673up_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Olinordered__ab__group__add_43) ).
thf(1222,plain,
linord219039673up_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(214,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_top__set__def) ).
thf(930,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA @ ( top_top @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(320,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordere516151231imp_le @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__monoid__add__imp__le_61) ).
thf(1196,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordere516151231imp_le @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(200,axiom,
semigroup_add @ extend1814228343nnreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nonnegative__Real_Oennreal___Groups_Osemigroup__add_91) ).
thf(898,plain,
semigroup_add @ extend1814228343nnreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(156,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ B @ A ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_add__cancel__right__left) ).
thf(782,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ B @ A ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(358,axiom,
! [TA: $tType] :
( ( measure_null_sets @ TA )
= ( ^ [A: sigma_measure @ TA] :
( collect @ ( set @ TA )
@ ^ [B: set @ TA] :
( ( member @ ( set @ TA ) @ B @ ( sigma_sets @ TA @ A ) )
& ( ( sigma_emeasure @ TA @ A @ B )
= ( zero_zero @ extend1814228343nnreal ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_null__sets__def) ).
thf(1265,plain,
! [TA: $tType] :
( ( measure_null_sets @ TA )
= ( ^ [A: sigma_measure @ TA] :
( collect @ ( set @ TA )
@ ^ [B: set @ TA] :
( ( member @ ( set @ TA ) @ B @ ( sigma_sets @ TA @ A ) )
& ( ( sigma_emeasure @ TA @ A @ B )
= ( zero_zero @ extend1814228343nnreal ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(334,axiom,
ab_group_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oab__group__add_52) ).
thf(1228,plain,
ab_group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ( comple187826305attice @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Complete__Lattices_Ocomplete__lattice) ).
thf(389,plain,
! [TA: $tType,TB: $tType] :
( ( comple187826305attice @ TA )
=> ( comple187826305attice @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(371,axiom,
! [A: finite_Cartesian_vec @ int @ n,B: finite_Cartesian_vec @ int @ n] :
( ( A != B )
=> ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( inf_inf @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t2 @ A ) @ ( t2 @ B ) ) @ ( measure_null_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_T__Int) ).
thf(1287,plain,
! [A: finite_Cartesian_vec @ int @ n,B: finite_Cartesian_vec @ int @ n] :
( ( A != B )
=> ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( inf_inf @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t2 @ A ) @ ( t2 @ B ) ) @ ( measure_null_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(377,axiom,
ordere236663937imp_le @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_40) ).
thf(1298,plain,
ordere236663937imp_le @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(157,axiom,
cancel1352612707id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_13) ).
thf(785,plain,
cancel1352612707id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TB] :
( ( image @ TA @ TB @ A @ ( vimage @ TA @ TB @ A @ B ) )
= ( inf_inf @ ( set @ TB ) @ B @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_image__vimage__eq) ).
thf(504,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TB] :
( ( image @ TA @ TB @ A @ ( vimage @ TA @ TB @ A @ B ) )
= ( inf_inf @ ( set @ TB ) @ B @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(5,axiom,
canoni770627133id_add @ extend1814228343nnreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nonnegative__Real_Oennreal___Groups_Ocanonically__ordered__monoid__add_84) ).
thf(388,plain,
canoni770627133id_add @ extend1814228343nnreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(165,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_not__less__zero) ).
thf(802,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(803,plain,
! [TA: $tType,A: TA] :
( ~ ( canoni770627133id_add @ TA )
| ~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(cnf,[status(esa)],[802]) ).
thf(1328,plain,
! [TA: $tType,A: TA] :
( ~ $true
| ~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
| ( ( canoni770627133id_add @ extend1814228343nnreal )
!= ( canoni770627133id_add @ TA ) ) ),
inference(paramod_ordered,[status(thm)],[388,803]) ).
thf(1329,plain,
! [TA: $tType,A: TA] :
( ~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
| ( ( canoni770627133id_add @ extend1814228343nnreal )
!= ( canoni770627133id_add @ TA ) ) ),
inference(simp,[status(thm)],[1328]) ).
thf(1330,plain,
! [A: extend1814228343nnreal] :
~ ( ord_less @ extend1814228343nnreal @ A @ ( zero_zero @ extend1814228343nnreal ) ),
inference(pattern_uni,[status(thm)],[1329:[bind_type(TA,$thf( extend1814228343nnreal ))]]) ).
thf(80,axiom,
ordere779506340up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_11) ).
thf(587,plain,
ordere779506340up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(123,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_add_Oright__cancel) ).
thf(702,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(368,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( measure_null_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ B ) )
=> ( ( sigma_emeasure @ TA @ B @ ( minus_minus @ ( set @ TA ) @ C @ A ) )
= ( sigma_emeasure @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_emeasure__Diff__null__set) ).
thf(1279,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( measure_null_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ B ) )
=> ( ( sigma_emeasure @ TA @ B @ ( minus_minus @ ( set @ TA ) @ C @ A ) )
= ( sigma_emeasure @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(317,axiom,
monoid_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Omonoid__add_53) ).
thf(1191,plain,
monoid_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
=> ( member @ TA @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_vimageE) ).
thf(460,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
=> ( member @ TA @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(271,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ( monoid_add @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Omonoid__add_29) ).
thf(1087,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ( monoid_add @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(346,axiom,
comm_monoid_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ocomm__monoid__add_49) ).
thf(1247,plain,
comm_monoid_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(227,axiom,
! [TA: $tType,TB: $tType] :
( ( complete_Sup @ TB )
=> ! [A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ C @ A ) )
= ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_SUP__cong) ).
thf(969,plain,
! [TA: $tType,TB: $tType] :
( ( complete_Sup @ TB )
=> ! [A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ C @ A ) )
= ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(337,axiom,
ab_semigroup_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oab__semigroup__add_48) ).
thf(1232,plain,
ab_semigroup_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(171,axiom,
! [TA: $tType,A: set @ ( sigma_measure @ TA )] :
( ( sigma_space @ TA @ ( complete_Sup_Sup @ ( sigma_measure @ TA ) @ A ) )
= ( complete_Sup_Sup @ ( set @ TA ) @ ( image @ ( sigma_measure @ TA ) @ ( set @ TA ) @ ( sigma_space @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_space__Sup__eq__UN) ).
thf(817,plain,
! [TA: $tType,A: set @ ( sigma_measure @ TA )] :
( ( sigma_space @ TA @ ( complete_Sup_Sup @ ( sigma_measure @ TA ) @ A ) )
= ( complete_Sup_Sup @ ( set @ TA ) @ ( image @ ( sigma_measure @ TA ) @ ( set @ TA ) @ ( sigma_space @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(203,axiom,
! [TA: $tType] :
( ( comple1035589618norder @ TA )
=> ! [A: TA,B: set @ TA] :
( ( ord_less @ TA @ A @ ( complete_Sup_Sup @ TA @ B ) )
= ( ? [C: TA] :
( ( member @ TA @ C @ B )
& ( ord_less @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_less__Sup__iff) ).
thf(902,plain,
! [TA: $tType] :
( ( comple1035589618norder @ TA )
=> ! [A: TA,B: set @ TA] :
( ( ord_less @ TA @ A @ ( complete_Sup_Sup @ TA @ B ) )
= ( ? [C: TA] :
( ( member @ TA @ C @ B )
& ( ord_less @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(211,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_add_Ocommute) ).
thf(924,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(379,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ab_semigroup_add @ TB )
& ( finite_finite @ TA ) )
=> ( ab_semigroup_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oab__semigroup__add_70) ).
thf(1302,plain,
! [TA: $tType,TB: $tType] :
( ( ( ab_semigroup_add @ TB )
& ( finite_finite @ TA ) )
=> ( ab_semigroup_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(82,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ A @ ( minus_minus @ TA @ B @ C ) )
= ( minus_minus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_diff__diff__eq2) ).
thf(591,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ A @ ( minus_minus @ TA @ B @ C ) )
= ( minus_minus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(27,axiom,
comm_monoid_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__add_16) ).
thf(443,plain,
comm_monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(250,axiom,
comm_monoid_add @ extend1814228343nnreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nonnegative__Real_Oennreal___Groups_Ocomm__monoid__add_89) ).
thf(1040,plain,
comm_monoid_add @ extend1814228343nnreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(216,axiom,
countable @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Countable_Ocountable_19) ).
thf(937,plain,
countable @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(312,axiom,
ordere516151231imp_le @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le_37) ).
thf(1183,plain,
ordere516151231imp_le @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(204,axiom,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: TB > $o] :
( ( ? [D: TB] :
( ( member @ TB @ D @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ B )
& ? [E: TB] :
( ( member @ TB @ E @ ( A @ D ) )
& ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_bex__UN) ).
thf(905,plain,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: TB > $o] :
( ( ? [D: TB] :
( ( member @ TB @ D @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ B )
& ? [E: TB] :
( ( member @ TB @ E @ ( A @ D ) )
& ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(292,axiom,
linord1659791738miring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__nonzero__semiring) ).
thf(1136,plain,
linord1659791738miring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(178,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ C @ B ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_Diff__Int2) ).
thf(834,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ C @ B ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(245,axiom,
! [TA: $tType,TB: $tType] :
( ( complete_Sup @ TB )
=> ( ( complete_Sup_Sup @ ( TA > TB ) )
= ( ^ [A: set @ ( TA > TB ),B: TA] :
( complete_Sup_Sup @ TB
@ ( image @ ( TA > TB ) @ TB
@ ^ [C: TA > TB] : ( C @ B )
@ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_Sup__apply) ).
thf(1020,plain,
! [TA: $tType,TB: $tType] :
( ( complete_Sup @ TB )
=> ( ( complete_Sup_Sup @ ( TA > TB ) )
= ( ^ [A: set @ ( TA > TB ),B: TA] :
( complete_Sup_Sup @ TB
@ ( image @ ( TA > TB ) @ TB
@ ^ [C: TA > TB] : ( C @ B )
@ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(75,axiom,
! [TA: $tType] :
( ( semigroup_add @ TA )
=> ( semigroup_add @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Osemigroup__add_27) ).
thf(574,plain,
! [TA: $tType] :
( ( semigroup_add @ TA )
=> ( semigroup_add @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(256,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_IntD2) ).
thf(1051,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(173,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_less__add__same__cancel1) ).
thf(821,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(99,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_add__less__same__cancel2) ).
thf(634,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(136,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_IntI) ).
thf(734,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(224,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_add__less__cancel__right) ).
thf(956,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(285,axiom,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_Int__def) ).
thf(1119,plain,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(11,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(396,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(108,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_Int__left__absorb) ).
thf(660,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(52,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( measure_null_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( measure_null_sets @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_null__set__Int2) ).
thf(507,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( measure_null_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( measure_null_sets @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(60,axiom,
comm_monoid_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocomm__monoid__add) ).
thf(527,plain,
comm_monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(307,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ( ( minus_minus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_diff__numeral__special_I9_J) ).
thf(1169,plain,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ( ( minus_minus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(118,axiom,
( ( complete_Sup_Sup @ $o )
= ( member @ $o @ $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_Sup__bool__def) ).
thf(687,plain,
( ( complete_Sup_Sup @ $o )
= ( member @ $o @ $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(191,axiom,
one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone_22) ).
thf(877,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( set @ TB ),C: set @ TA] :
( ( member @ TB @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) )
=> ~ ! [D: TA] :
( ( member @ TA @ D @ C )
=> ~ ( member @ TB @ A @ ( B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_UN__E) ).
thf(692,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( set @ TB ),C: set @ TA] :
( ( member @ TB @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) )
=> ~ ! [D: TA] :
( ( member @ TA @ D @ C )
=> ~ ( member @ TB @ A @ ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(15,axiom,
! [TA: $tType,A: TA,B: set @ ( set @ TA )] :
( ( member @ TA @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) )
=> ~ ! [C: set @ TA] :
( ( member @ TA @ A @ C )
=> ~ ( member @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_UnionE) ).
thf(411,plain,
! [TA: $tType,A: TA,B: set @ ( set @ TA )] :
( ( member @ TA @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) )
=> ~ ! [C: set @ TA] :
( ( member @ TA @ A @ C )
=> ~ ( member @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(232,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > ( set @ TB )] :
( ( member @ TA @ A @ B )
=> ( ( member @ TB @ C @ ( D @ A ) )
=> ( member @ TB @ C @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_UN__I) ).
thf(988,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > ( set @ TB )] :
( ( member @ TA @ A @ B )
=> ( ( member @ TB @ C @ ( D @ A ) )
=> ( member @ TB @ C @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(343,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ring_1 @ TB )
& ( finite_finite @ TA ) )
=> ( ring_1 @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Rings_Oring__1) ).
thf(1242,plain,
! [TA: $tType,TB: $tType] :
( ( ( ring_1 @ TB )
& ( finite_finite @ TA ) )
=> ( ring_1 @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(183,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(849,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(54,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_diff__self) ).
thf(512,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(381,axiom,
! [TA: $tType,TB: $tType] :
( ( ( countable @ TB )
& ( finite_finite @ TA ) )
=> ( countable @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Countable_Ocountable_75) ).
thf(1306,plain,
! [TA: $tType,TB: $tType] :
( ( ( countable @ TB )
& ( finite_finite @ TA ) )
=> ( countable @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(168,axiom,
group_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ogroup__add) ).
thf(810,plain,
group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(129,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( set @ TB ),C: set @ TA] :
( ( member @ TB @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( member @ TB @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_UN__iff) ).
thf(714,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( set @ TB ),C: set @ TA] :
( ( member @ TB @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( member @ TB @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(323,axiom,
! [TA: $tType,A: sigma_measure @ TA,B: set @ TA] :
( ( ( sigma_emeasure @ TA @ A @ B )
= ( zero_zero @ extend1814228343nnreal ) )
=> ( ( member @ ( set @ TA ) @ B @ ( sigma_sets @ TA @ A ) )
=> ( member @ ( set @ TA ) @ B @ ( measure_null_sets @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_null__setsI) ).
thf(1206,plain,
! [TA: $tType,A: sigma_measure @ TA,B: set @ TA] :
( ( ( sigma_emeasure @ TA @ A @ B )
= ( zero_zero @ extend1814228343nnreal ) )
=> ( ( member @ ( set @ TA ) @ B @ ( sigma_sets @ TA @ A ) )
=> ( member @ ( set @ TA ) @ B @ ( measure_null_sets @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(31,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_diff__diff__add) ).
thf(452,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(300,axiom,
! [TA: $tType,A: ( set @ TA ) > TA,B: set @ TA] :
( ( A
@ ( image @ TA @ TA
@ ^ [C: TA] : C
@ B ) )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_Inf_OINF__identity__eq) ).
thf(1153,plain,
! [TA: $tType,A: ( set @ TA ) > TA,B: set @ TA] :
( ( A
@ ( image @ TA @ TA
@ ^ [C: TA] : C
@ B ) )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(149,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_less__numeral__extra_I1_J) ).
thf(761,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(1309,plain,
( ( ( ^ [A: nat] : ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) )
!= ( ^ [A: nat] : ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) )
| ( ( ^ [A: nat] : ( t2 @ ( f @ A ) ) )
!= ( ^ [A: nat] : ( t @ ( f @ A ) ) ) ) ),
inference(simp,[status(thm)],[384]) ).
thf(1311,plain,
( ( ^ [A: nat] : ( t2 @ ( f @ A ) ) )
!= ( ^ [A: nat] : ( t @ ( f @ A ) ) ) ),
inference(simp,[status(thm)],[1309]) ).
thf(63,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_translation__diff) ).
thf(534,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(253,axiom,
ordere516151231imp_le @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__monoid__add__imp__le) ).
thf(1047,plain,
ordere516151231imp_le @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(259,axiom,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: TB > $o] :
( ( ? [D: TB] :
( ( member @ TB @ D @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ B )
& ? [E: TB] :
( ( member @ TB @ E @ ( A @ D ) )
& ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_UN__ball__bex__simps_I4_J) ).
thf(1057,plain,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: TB > $o] :
( ( ? [D: TB] :
( ( member @ TB @ D @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ B )
& ? [E: TB] :
( ( member @ TB @ E @ ( A @ D ) )
& ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(304,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_is__num__normalize_I1_J) ).
thf(1163,plain,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(365,axiom,
! [A: finite_Cartesian_vec @ int @ n] :
( ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t2 @ A ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) )
=> ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
@ ( inf_inf @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
@ ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
@ ^ [B: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
@ ( t2 @ A ) )
@ ( sigma_space @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) )
@ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_A_092_060Longrightarrow_062_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_N_096_AT_Aa_A_092_060inter_062_Aspace_Alebesgue_A_092_060in_062_Asets_Alebesgue_092_060close_062) ).
thf(1274,plain,
! [A: finite_Cartesian_vec @ int @ n] :
( ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t2 @ A ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) )
=> ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
@ ( inf_inf @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
@ ( vimage @ ( finite_Cartesian_vec @ real @ n ) @ ( finite_Cartesian_vec @ real @ n )
@ ^ [B: finite_Cartesian_vec @ real @ n] : ( plus_plus @ ( finite_Cartesian_vec @ real @ n ) @ B @ ( minkow1937162798nt_vec @ n @ real @ A ) )
@ ( t2 @ A ) )
@ ( sigma_space @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) )
@ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(206,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( measure_null_sets @ TA @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ A @ ( sigma_space @ TA @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_null__sets_OInt__space__eq2) ).
thf(910,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( measure_null_sets @ TA @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ A @ ( sigma_space @ TA @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(331,axiom,
zero @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ozero_57) ).
thf(1223,plain,
zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(397,plain,
! [TA: $tType,A: TA] :
( ~ ( cancel1352612707id_add @ TA )
| ( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(cnf,[status(esa)],[396]) ).
thf(398,plain,
! [TA: $tType,A: TA] :
( ( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) )
| ~ ( cancel1352612707id_add @ TA ) ),
inference(lifteq,[status(thm)],[397]) ).
thf(255,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_less__numeral__extra_I3_J) ).
thf(1049,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(1050,plain,
! [TA: $tType] :
( ~ ( linord1659791738miring @ TA )
| ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(cnf,[status(esa)],[1049]) ).
thf(1338,plain,
! [TB: $tType,A: TB] :
( ~ ( cancel1352612707id_add @ TB )
| ~ ( linord1659791738miring @ TB )
| ~ ( ord_less @ TB @ ( minus_minus @ TB @ A @ A ) @ ( zero_zero @ TB ) )
| ( ( zero_zero @ TB )
!= ( zero_zero @ TB ) ) ),
inference(paramod_ordered,[status(thm)],[398,1050]) ).
thf(1339,plain,
! [TB: $tType,A: TB] :
( ~ ( cancel1352612707id_add @ TB )
| ~ ( linord1659791738miring @ TB )
| ~ ( ord_less @ TB @ ( minus_minus @ TB @ A @ A ) @ ( zero_zero @ TB ) ) ),
inference(pattern_uni,[status(thm)],[1338:[]]) ).
thf(1343,plain,
! [TA: $tType,A: TA] :
( ~ ( cancel1352612707id_add @ TA )
| ~ ( linord1659791738miring @ TA )
| ~ ( ord_less @ TA @ ( minus_minus @ TA @ A @ A ) @ ( zero_zero @ TA ) ) ),
inference(simp,[status(thm)],[1339]) ).
thf(154,axiom,
! [TA: $tType,TB: $tType] :
( ( comple1035589618norder @ TB )
=> ! [A: TB,B: TA > TB,C: set @ TA] :
( ( ord_less @ TB @ A @ ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ B @ C ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_less__SUP__iff) ).
thf(778,plain,
! [TA: $tType,TB: $tType] :
( ( comple1035589618norder @ TB )
=> ! [A: TB,B: TA > TB,C: set @ TA] :
( ( ord_less @ TB @ A @ ( complete_Sup_Sup @ TB @ ( image @ TA @ TB @ B @ C ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(351,axiom,
ord_less @ extend1814228343nnreal @ ( one_one @ extend1814228343nnreal ) @ ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ s ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_assms_I2_J) ).
thf(1255,plain,
ord_less @ extend1814228343nnreal @ ( one_one @ extend1814228343nnreal ) @ ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ s ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(287,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
=> ( ord_less @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_add__less__imp__less__left) ).
thf(1123,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
=> ( ord_less @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(172,axiom,
countable @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Countable_Ocountable_5) ).
thf(820,plain,
countable @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(8,axiom,
! [TA: $tType] : ( comple187826305attice @ ( sigma_measure @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Sigma__Algebra_Omeasure___Complete__Lattices_Ocomplete__lattice_59) ).
thf(392,plain,
! [TA: $tType] : ( comple187826305attice @ ( sigma_measure @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(98,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ A @ D )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_group__cancel_Oadd1) ).
thf(630,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ A @ D )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(159,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( set @ TA )] :
( ( inf_inf @ ( set @ TA ) @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) )
= ( complete_Sup_Sup @ ( set @ TA ) @ ( image @ ( set @ TA ) @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Int__Union) ).
thf(788,plain,
! [TA: $tType,A: set @ TA,B: set @ ( set @ TA )] :
( ( inf_inf @ ( set @ TA ) @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) )
= ( complete_Sup_Sup @ ( set @ TA ) @ ( image @ ( set @ TA ) @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(341,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_77) ).
thf(1238,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(143,axiom,
strict2144017051up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ostrict__ordered__ab__semigroup__add) ).
thf(746,plain,
strict2144017051up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(274,axiom,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ( ( complete_Sup_Sup @ TA @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_Sup__UNIV) ).
thf(1091,plain,
! [TA: $tType] :
( ( comple187826305attice @ TA )
=> ( ( complete_Sup_Sup @ TA @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(208,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_gr__zeroI) ).
thf(916,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(43,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_DiffE) ).
thf(484,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(96,axiom,
! [TA: $tType,A: sigma_measure @ TA] : ( member @ ( set @ TA ) @ ( sigma_space @ TA @ A ) @ ( sigma_sets @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_sets_Otop) ).
thf(625,plain,
! [TA: $tType,A: sigma_measure @ TA] : ( member @ ( set @ TA ) @ ( sigma_space @ TA @ A ) @ ( sigma_sets @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(193,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_comm__monoid__add__class_Oadd__0) ).
thf(879,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(310,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_Int__left__commute) ).
thf(1178,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(302,axiom,
linord1659791738miring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_10) ).
thf(1159,plain,
linord1659791738miring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(46,axiom,
ab_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add_15) ).
thf(493,plain,
ab_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(268,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_Diff__idemp) ).
thf(1079,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(116,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( zero @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ozero_31) ).
thf(682,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( zero @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(289,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA] :
( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_surj__plus) ).
thf(1128,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA] :
( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(243,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_IntE) ).
thf(1012,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(184,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Int__Diff) ).
thf(852,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(23,axiom,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_UNIV__def) ).
thf(435,plain,
! [TA: $tType] :
( ( top_top @ ( set @ TA ) )
= ( collect @ TA
@ ^ [A: TA] : $true ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(58,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ B ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_zero__eq__add__iff__both__eq__0) ).
thf(522,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ B ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(176,axiom,
comple1035589618norder @ extend1814228343nnreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nonnegative__Real_Oennreal___Complete__Lattices_Ocomplete__linorder) ).
thf(830,plain,
comple1035589618norder @ extend1814228343nnreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(373,axiom,
( sums @ extend1814228343nnreal
@ ^ [A: nat] : ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( t2 @ ( f @ A ) ) )
@ ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_calculation) ).
thf(1291,plain,
( sums @ extend1814228343nnreal
@ ^ [A: nat] : ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( t2 @ ( f @ A ) ) )
@ ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(127,axiom,
! [TA: $tType,A: set @ ( set @ TA ),B: TA > $o] :
( ( ! [C: TA] :
( ( member @ TA @ C @ ( complete_Sup_Sup @ ( set @ TA ) @ A ) )
=> ( B @ C ) ) )
= ( ! [C: set @ TA] :
( ( member @ ( set @ TA ) @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ C )
=> ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_UN__ball__bex__simps_I1_J) ).
thf(710,plain,
! [TA: $tType,A: set @ ( set @ TA ),B: TA > $o] :
( ( ! [C: TA] :
( ( member @ TA @ C @ ( complete_Sup_Sup @ ( set @ TA ) @ A ) )
=> ( B @ C ) ) )
= ( ! [C: set @ TA] :
( ( member @ ( set @ TA ) @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ C )
=> ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(140,axiom,
ordere516151231imp_le @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le_6) ).
thf(742,plain,
ordere516151231imp_le @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(272,axiom,
linord1659791738miring @ extend1814228343nnreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nonnegative__Real_Oennreal___Rings_Olinordered__nonzero__semiring_86) ).
thf(1089,plain,
linord1659791738miring @ extend1814228343nnreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(190,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_add__less__cancel__left) ).
thf(874,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(92,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( top_top @ ( set @ TA ) ) )
= ( ( A
= ( top_top @ ( set @ TA ) ) )
& ( B
= ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Int__UNIV) ).
thf(615,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( top_top @ ( set @ TA ) ) )
= ( ( A
= ( top_top @ ( set @ TA ) ) )
& ( B
= ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(282,axiom,
ordere223160158up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(1111,plain,
ordere223160158up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
( ( A = B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image @ TA @ TB @ C @ A ) )
= ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Sup_OSUP__cong) ).
thf(403,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
( ( A = B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image @ TA @ TB @ C @ A ) )
= ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(239,axiom,
zero @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ozero) ).
thf(1006,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(188,axiom,
! [TA: $tType] :
( ( semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_add_Oassoc) ).
thf(869,plain,
! [TA: $tType] :
( ( semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(90,axiom,
! [TA: $tType] : ( complete_Sup @ ( sigma_measure @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Sigma__Algebra_Omeasure___Complete__Lattices_OSup_60) ).
thf(610,plain,
! [TA: $tType] : ( complete_Sup @ ( sigma_measure @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(361,axiom,
cancel_semigroup_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ocancel__semigroup__add_47) ).
thf(1270,plain,
cancel_semigroup_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(354,axiom,
! [TA: $tType,TB: $tType] :
( ( ( monoid_add @ TB )
& ( finite_finite @ TA ) )
=> ( monoid_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Omonoid__add_76) ).
thf(1259,plain,
! [TA: $tType,TB: $tType] :
( ( ( monoid_add @ TB )
& ( finite_finite @ TA ) )
=> ( monoid_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(195,axiom,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_zero__diff) ).
thf(884,plain,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(303,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > ( set @ TC ),B: set @ TA,C: TB > ( set @ TC ),D: set @ TB] :
( ( inf_inf @ ( set @ TC ) @ ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TA @ ( set @ TC ) @ A @ B ) ) @ ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ C @ D ) ) )
= ( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TA @ ( set @ TC )
@ ^ [E: TA] :
( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TB @ ( set @ TC )
@ ^ [F: TB] : ( inf_inf @ ( set @ TC ) @ ( A @ E ) @ ( C @ F ) )
@ D ) )
@ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_Int__UN__distrib2) ).
thf(1160,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA > ( set @ TC ),B: set @ TA,C: TB > ( set @ TC ),D: set @ TB] :
( ( inf_inf @ ( set @ TC ) @ ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TA @ ( set @ TC ) @ A @ B ) ) @ ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ C @ D ) ) )
= ( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TA @ ( set @ TC )
@ ^ [E: TA] :
( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TB @ ( set @ TC )
@ ^ [F: TB] : ( inf_inf @ ( set @ TC ) @ ( A @ E ) @ ( C @ F ) )
@ D ) )
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(269,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
=> ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_add__less__imp__less__right) ).
thf(1082,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
=> ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(44,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_diff__strict__right__mono) ).
thf(488,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(64,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_zero__less__double__add__iff__zero__less__single__add) ).
thf(537,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(111,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus @ TA @ A @ C )
= ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_add__mono__thms__linordered__semiring_I4_J) ).
thf(669,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus @ TA @ A @ C )
= ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > $o] :
( ( vimage @ TA @ TB @ A @ ( collect @ TB @ B ) )
= ( collect @ TA
@ ^ [C: TA] : ( B @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_vimage__Collect__eq) ).
thf(642,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > $o] :
( ( vimage @ TA @ TB @ A @ ( collect @ TB @ B ) )
= ( collect @ TA
@ ^ [C: TA] : ( B @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(100,axiom,
! [TA: $tType,A: TA,B: set @ ( set @ TA )] :
( ( member @ TA @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) )
= ( ? [C: set @ TA] :
( ( member @ ( set @ TA ) @ C @ B )
& ( member @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_Union__iff) ).
thf(637,plain,
! [TA: $tType,A: TA,B: set @ ( set @ TA )] :
( ( member @ TA @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) )
= ( ? [C: set @ TA] :
( ( member @ ( set @ TA ) @ C @ B )
& ( member @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(326,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordere779506340up_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__add_65) ).
thf(1214,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordere779506340up_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(244,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_add__mono__thms__linordered__field_I2_J) ).
thf(1016,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(115,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less @ TA @ A @ B )
= ( ord_less @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_diff__eq__diff__less) ).
thf(679,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less @ TA @ A @ B )
= ( ord_less @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(374,axiom,
one @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oone_58) ).
thf(1292,plain,
one @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(215,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ D @ A )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_group__cancel_Oadd2) ).
thf(933,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ D @ A )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(69,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ ( sigma_space @ TA @ B ) @ A ) @ ( sigma_sets @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_sets_Ocompl__sets) ).
thf(554,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ ( sigma_space @ TA @ B ) @ A ) @ ( sigma_sets @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(146,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( measure_null_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( measure_null_sets @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_null__set__Diff) ).
thf(753,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( measure_null_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( measure_null_sets @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(266,axiom,
cancel1352612707id_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__comm__monoid__add) ).
thf(1075,plain,
cancel1352612707id_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(40,axiom,
! [TA: $tType] :
( ( strict2144017051up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_add__strict__mono) ).
thf(476,plain,
! [TA: $tType] :
( ( strict2144017051up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(393,plain,
! [TA: $tType] : ( comple187826305attice @ ( sigma_measure @ TA ) ),
inference(cnf,[status(esa)],[392]) ).
thf(336,axiom,
finite_finite @ n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
thf(1231,plain,
finite_finite @ n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(290,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( measure_null_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ C @ ( measure_null_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( measure_null_sets @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_null__sets_ODiff) ).
thf(1131,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( measure_null_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ C @ ( measure_null_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( measure_null_sets @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(318,axiom,
ordere223160158up_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__cancel__ab__semigroup__add_39) ).
thf(1192,plain,
ordere223160158up_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(345,axiom,
semigroup_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Osemigroup__add_51) ).
thf(1246,plain,
semigroup_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(50,axiom,
ab_semigroup_add @ extend1814228343nnreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nonnegative__Real_Oennreal___Groups_Oab__semigroup__add_88) ).
thf(503,plain,
ab_semigroup_add @ extend1814228343nnreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(95,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_add_Ocomm__neutral) ).
thf(622,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(179,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= B )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_add__cancel__left__left) ).
thf(837,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= B )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(357,axiom,
! [TA: $tType,TB: $tType] :
( ( ( cancel_semigroup_add @ TB )
& ( finite_finite @ TA ) )
=> ( cancel_semigroup_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__semigroup__add_69) ).
thf(1263,plain,
! [TA: $tType,TB: $tType] :
( ( ( cancel_semigroup_add @ TB )
& ( finite_finite @ TA ) )
=> ( cancel_semigroup_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(236,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_UNIV__eq__I) ).
thf(997,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] : ( member @ TA @ B @ A )
=> ( ( top_top @ ( set @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(277,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Diff__Diff__Int) ).
thf(1099,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(231,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
= ( member @ TA @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_vimage__eq) ).
thf(985,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
= ( member @ TA @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(55,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( measure_null_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_null__setsD2) ).
thf(515,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( measure_null_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(348,axiom,
! [A: finite_Cartesian_vec @ int @ n] : ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t2 @ A ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062) ).
thf(1249,plain,
! [A: finite_Cartesian_vec @ int @ n] : ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t2 @ A ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(260,axiom,
semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Osemigroup__add) ).
thf(1060,plain,
semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(33,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_eq__iff__diff__eq__0) ).
thf(457,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(4,axiom,
canoni770627133id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(387,plain,
canoni770627133id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1331,plain,
! [TA: $tType,A: TA] :
( ~ $true
| ~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
| ( ( canoni770627133id_add @ nat )
!= ( canoni770627133id_add @ TA ) ) ),
inference(paramod_ordered,[status(thm)],[387,803]) ).
thf(1332,plain,
! [TA: $tType,A: TA] :
( ~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
| ( ( canoni770627133id_add @ nat )
!= ( canoni770627133id_add @ TA ) ) ),
inference(simp,[status(thm)],[1331]) ).
thf(1333,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(pattern_uni,[status(thm)],[1332:[bind_type(TA,$thf( nat ))]]) ).
thf(217,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_add__diff__cancel__left_H) ).
thf(938,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType] :
( ( countable @ TB )
=> ! [A: TB > ( set @ TA ),B: sigma_measure @ TA] :
( ! [C: TB] : ( member @ ( set @ TA ) @ ( A @ C ) @ ( measure_null_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( complete_Sup_Sup @ ( set @ TA ) @ ( image @ TB @ ( set @ TA ) @ A @ ( top_top @ ( set @ TB ) ) ) ) @ ( measure_null_sets @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_null__sets__UN) ).
thf(674,plain,
! [TA: $tType,TB: $tType] :
( ( countable @ TB )
=> ! [A: TB > ( set @ TA ),B: sigma_measure @ TA] :
( ! [C: TB] : ( member @ ( set @ TA ) @ ( A @ C ) @ ( measure_null_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( complete_Sup_Sup @ ( set @ TA ) @ ( image @ TB @ ( set @ TA ) @ A @ ( top_top @ ( set @ TB ) ) ) ) @ ( measure_null_sets @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(247,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image @ TA @ TB @ C @ A )
= ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_image__cong) ).
thf(1026,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB] :
( ( A = B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image @ TA @ TB @ C @ A )
= ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(223,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comple187826305attice @ TC )
=> ! [A: TB > TC,B: TA > ( set @ TB ),C: set @ TA] :
( ( complete_Sup_Sup @ TC @ ( image @ TB @ TC @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) ) )
= ( complete_Sup_Sup @ TC
@ ( image @ TA @ TC
@ ^ [D: TA] : ( complete_Sup_Sup @ TC @ ( image @ TB @ TC @ A @ ( B @ D ) ) )
@ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_SUP__UNION) ).
thf(953,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( comple187826305attice @ TC )
=> ! [A: TB > TC,B: TA > ( set @ TB ),C: set @ TA] :
( ( complete_Sup_Sup @ TC @ ( image @ TB @ TC @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) ) )
= ( complete_Sup_Sup @ TC
@ ( image @ TA @ TC
@ ^ [D: TA] : ( complete_Sup_Sup @ TC @ ( image @ TB @ TC @ A @ ( B @ D ) ) )
@ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(161,axiom,
ordere223160158up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add_8) ).
thf(794,plain,
ordere223160158up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(367,axiom,
ring_char_0 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Nat_Oring__char__0_56) ).
thf(1278,plain,
ring_char_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(145,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ ( set @ TA )] :
( ( vimage @ TB @ TA @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) )
= ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ ( set @ TA ) @ ( set @ TB ) @ ( vimage @ TB @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_vimage__Union) ).
thf(750,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ ( set @ TA )] :
( ( vimage @ TB @ TA @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) )
= ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ ( set @ TA ) @ ( set @ TB ) @ ( vimage @ TB @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: TA] :
( ( A
= ( B @ D ) )
=> ~ ( member @ TA @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_imageE) ).
thf(425,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
=> ~ ! [D: TA] :
( ( A
= ( B @ D ) )
=> ~ ( member @ TA @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(279,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_diff__strict__left__mono) ).
thf(1103,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(174,axiom,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: set @ TB] :
( ( inf_inf @ ( set @ TB ) @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) @ C )
= ( complete_Sup_Sup @ ( set @ TB )
@ ( image @ TA @ ( set @ TB )
@ ^ [D: TA] : ( inf_inf @ ( set @ TB ) @ ( A @ D ) @ C )
@ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_UN__extend__simps_I4_J) ).
thf(824,plain,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: set @ TB] :
( ( inf_inf @ ( set @ TB ) @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) @ C )
= ( complete_Sup_Sup @ ( set @ TB )
@ ( image @ TA @ ( set @ TB )
@ ^ [D: TA] : ( inf_inf @ ( set @ TB ) @ ( A @ D ) @ C )
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(364,axiom,
linord1659791738miring @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_41) ).
thf(1273,plain,
linord1659791738miring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(119,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_zero__reorient) ).
thf(689,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: TB > $o] :
( ( ! [D: TB] :
( ( member @ TB @ D @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ! [E: TB] :
( ( member @ TB @ E @ ( A @ D ) )
=> ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_UN__ball__bex__simps_I2_J) ).
thf(444,plain,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: TB > $o] :
( ( ! [D: TB] :
( ( member @ TB @ D @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ! [E: TB] :
( ( member @ TB @ E @ ( A @ D ) )
=> ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(87,axiom,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_diff__add__zero) ).
thf(601,plain,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(349,axiom,
! [A: finite_Cartesian_vec @ int @ n] : ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t @ A ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062_092_060And_062a_O_AT_H_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062) ).
thf(1251,plain,
! [A: finite_Cartesian_vec @ int @ n] : ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t @ A ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(93,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_add__left__imp__eq) ).
thf(618,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(298,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB] :
( ! [C: TA] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_surjI) ).
thf(1146,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > TB] :
( ! [C: TA] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > ( set @ TC ),B: TA > ( set @ TB ),C: set @ TA] :
( ( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TA @ ( set @ TC )
@ ^ [D: TA] : ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ A @ ( B @ D ) ) )
@ C ) )
= ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_UN__extend__simps_I9_J) ).
thf(430,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > ( set @ TC ),B: TA > ( set @ TB ),C: set @ TA] :
( ( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TA @ ( set @ TC )
@ ^ [D: TA] : ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ A @ ( B @ D ) ) )
@ C ) )
= ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(240,axiom,
! [TA: $tType,A: sigma_measure @ TA,B: TA > $o,C: TA > $o] :
( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( B @ D ) ) )
@ ( measure_null_sets @ TA @ A ) )
=> ( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( C @ D ) ) )
@ ( measure_null_sets @ TA @ A ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( C @ D )
& ( B @ D ) ) )
@ ( measure_null_sets @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_null__sets_Osets__Collect__conj) ).
thf(1007,plain,
! [TA: $tType,A: sigma_measure @ TA,B: TA > $o,C: TA > $o] :
( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( B @ D ) ) )
@ ( measure_null_sets @ TA @ A ) )
=> ( ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( C @ D ) ) )
@ ( measure_null_sets @ TA @ A ) )
=> ( member @ ( set @ TA )
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ ( sigma_space @ TA @ A ) )
& ( C @ D )
& ( B @ D ) ) )
@ ( measure_null_sets @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( vimage @ TA @ TB @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_vimage__UNIV) ).
thf(400,plain,
! [TA: $tType,TB: $tType,A: TA > TB] :
( ( vimage @ TA @ TB @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(401,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( vimage @ TB @ TA @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) ),
inference(cnf,[status(esa)],[400]) ).
thf(402,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( vimage @ TB @ TA @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) ),
inference(lifteq,[status(thm)],[401]) ).
thf(153,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_ball__imageD) ).
thf(772,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ! [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
=> ( C @ D ) )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(141,axiom,
cancel146912293up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(743,plain,
cancel146912293up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType] :
( ( vimage @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TB] :
( collect @ TA
@ ^ [C: TA] : ( member @ TB @ ( A @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_vimage__def) ).
thf(579,plain,
! [TA: $tType,TB: $tType] :
( ( vimage @ TA @ TB )
= ( ^ [A: TA > TB,B: set @ TB] :
( collect @ TA
@ ^ [C: TA] : ( member @ TB @ ( A @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(181,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_Int__absorb) ).
thf(843,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(288,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( complete_Sup @ TC )
=> ! [A: TA > TB > TC,B: set @ TA,C: TB] :
( ( complete_Sup_Sup @ ( TB > TC ) @ ( image @ TA @ ( TB > TC ) @ A @ B ) @ C )
= ( complete_Sup_Sup @ TC
@ ( image @ TA @ TC
@ ^ [D: TA] : ( A @ D @ C )
@ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_SUP__apply) ).
thf(1125,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( complete_Sup @ TC )
=> ! [A: TA > TB > TC,B: set @ TA,C: TB] :
( ( complete_Sup_Sup @ ( TB > TC ) @ ( image @ TA @ ( TB > TC ) @ A @ B ) @ C )
= ( complete_Sup_Sup @ TC
@ ( image @ TA @ TC
@ ^ [D: TA] : ( A @ D @ C )
@ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(352,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordere890947078_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Ordered__Euclidean__Space_Oordered__euclidean__space) ).
thf(1256,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordere890947078_space @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(333,axiom,
( f
= ( counta609264050t_into @ ( finite_Cartesian_vec @ int @ n ) @ ( top_top @ ( set @ ( finite_Cartesian_vec @ int @ n ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_f__def) ).
thf(1226,plain,
( f
= ( counta609264050t_into @ ( finite_Cartesian_vec @ int @ n ) @ ( top_top @ ( set @ ( finite_Cartesian_vec @ int @ n ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(67,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA] :
( ( image @ TA @ TA
@ ^ [B: TA] : ( minus_minus @ TA @ B @ A )
@ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_surj__diff__right) ).
thf(545,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA] :
( ( image @ TA @ TA
@ ^ [B: TA] : ( minus_minus @ TA @ B @ A )
@ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(362,axiom,
group_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ogroup__add_54) ).
thf(1271,plain,
group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(1312,plain,
( ( t2 @ ( f @ sk28 ) )
!= ( t @ ( f @ sk28 ) ) ),
inference(func_ext,[status(esa)],[1311]) ).
thf(611,plain,
! [TA: $tType] : ( complete_Sup @ ( sigma_measure @ TA ) ),
inference(cnf,[status(esa)],[610]) ).
thf(128,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(713,plain,
linord219039673up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(273,axiom,
zero @ extend1814228343nnreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nonnegative__Real_Oennreal___Groups_Ozero_93) ).
thf(1090,plain,
zero @ extend1814228343nnreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(353,axiom,
ring_1 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Oring__1_2) ).
thf(1258,plain,
ring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(221,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_translation__Int) ).
thf(947,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ B ) @ ( image @ TA @ TA @ ( plus_plus @ TA @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(332,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( strict2144017051up_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ostrict__ordered__ab__semigroup__add_62) ).
thf(1224,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( strict2144017051up_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(65,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( minus_minus @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_add__diff__cancel__right) ).
thf(540,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( minus_minus @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(7,axiom,
finite_finite @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Finite__Set_Ofinite_36) ).
thf(391,plain,
finite_finite @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(294,axiom,
ordere779506340up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__add) ).
thf(1139,plain,
ordere779506340up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(209,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_Int__assoc) ).
thf(919,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(166,axiom,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA] :
? [C: TB] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_surj__def) ).
thf(804,plain,
! [TA: $tType,TB: $tType,A: TB > TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
= ( ! [B: TA] :
? [C: TB] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(324,axiom,
( t2
= ( ^ [A: finite_Cartesian_vec @ int @ n] : ( inf_inf @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ s @ ( r @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_T__def) ).
thf(1209,plain,
( t2
= ( ^ [A: finite_Cartesian_vec @ int @ n] : ( inf_inf @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ s @ ( r @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(202,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_DiffD1) ).
thf(900,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(177,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( minus_minus @ TA @ B @ C ) )
= ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_add__diff__eq) ).
thf(831,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( minus_minus @ TA @ B @ C ) )
= ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(369,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( complete_Sup @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Complete__Lattices_OSup_72) ).
thf(1282,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( complete_Sup @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(18,axiom,
! [TA: $tType,A: set @ TA] :
( ( image @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_image__ident) ).
thf(419,plain,
! [TA: $tType,A: set @ TA] :
( ( image @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(233,axiom,
ordere236663937imp_le @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le_9) ).
thf(990,plain,
ordere236663937imp_le @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(72,axiom,
neg_numeral @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Num_Oneg__numeral) ).
thf(567,plain,
neg_numeral @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(53,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_add__cancel__right__right) ).
thf(509,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(286,axiom,
countable @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Countable_Ocountable_35) ).
thf(1122,plain,
countable @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(229,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > ( set @ TC ),B: TA > TB,C: set @ TA] :
( ( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TA @ ( set @ TC )
@ ^ [D: TA] : ( A @ ( B @ D ) )
@ C ) )
= ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ A @ ( image @ TA @ TB @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_UN__extend__simps_I10_J) ).
thf(979,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > ( set @ TC ),B: TA > TB,C: set @ TA] :
( ( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TA @ ( set @ TC )
@ ^ [D: TA] : ( A @ ( B @ D ) )
@ C ) )
= ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ A @ ( image @ TA @ TB @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(88,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_diff__add__eq__diff__diff__swap) ).
thf(604,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(254,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add_12) ).
thf(1048,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(137,axiom,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: set @ TB] :
( ( minus_minus @ ( set @ TB ) @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) @ C )
= ( complete_Sup_Sup @ ( set @ TB )
@ ( image @ TA @ ( set @ TB )
@ ^ [D: TA] : ( minus_minus @ ( set @ TB ) @ ( A @ D ) @ C )
@ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_UN__extend__simps_I6_J) ).
thf(736,plain,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: set @ TB] :
( ( minus_minus @ ( set @ TB ) @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) @ C )
= ( complete_Sup_Sup @ ( set @ TB )
@ ( image @ TA @ ( set @ TB )
@ ^ [D: TA] : ( minus_minus @ ( set @ TB ) @ ( A @ D ) @ C )
@ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(187,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TB,D: set @ TB] :
( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( inf_inf @ ( set @ TA ) @ ( vimage @ TA @ TB @ B @ D ) @ A )
= ( inf_inf @ ( set @ TA ) @ ( vimage @ TA @ TB @ C @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_vimage__inter__cong) ).
thf(863,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > TB,C: TA > TB,D: set @ TB] :
( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( inf_inf @ ( set @ TA ) @ ( vimage @ TA @ TB @ B @ D ) @ A )
= ( inf_inf @ ( set @ TA ) @ ( vimage @ TA @ TB @ C @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(309,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(1175,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(197,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_Diff__Int__distrib) ).
thf(890,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(47,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > ( set @ TB ),C: set @ TA] :
( ( vimage @ TC @ TB @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) )
= ( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TA @ ( set @ TC )
@ ^ [D: TA] : ( vimage @ TC @ TB @ A @ ( B @ D ) )
@ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_vimage__UN) ).
thf(494,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TB,B: TA > ( set @ TB ),C: set @ TA] :
( ( vimage @ TC @ TB @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) )
= ( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TA @ ( set @ TC )
@ ^ [D: TA] : ( vimage @ TC @ TB @ A @ ( B @ D ) )
@ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(148,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_add__right__cancel) ).
thf(758,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: set @ TA] :
( ( member @ TA @ ( A @ B ) @ C )
=> ( member @ TB @ B @ ( vimage @ TB @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_vimageI2) ).
thf(594,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: set @ TA] :
( ( member @ TA @ ( A @ B ) @ C )
=> ( member @ TB @ B @ ( vimage @ TB @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(94,axiom,
strict2144017051up_add @ extend1814228343nnreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nonnegative__Real_Oennreal___Groups_Ostrict__ordered__ab__semigroup__add_83) ).
thf(621,plain,
strict2144017051up_add @ extend1814228343nnreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(199,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA,C: set @ TA] :
( ( vimage @ TB @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TB ) @ ( vimage @ TB @ TA @ A @ B ) @ ( vimage @ TB @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_vimage__Diff) ).
thf(895,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA,C: set @ TA] :
( ( vimage @ TB @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TB ) @ ( vimage @ TB @ TA @ A @ B ) @ ( vimage @ TB @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(299,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_rev__image__eqI) ).
thf(1149,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TB,D: TA > TB] :
( ( member @ TA @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member @ TB @ C @ ( image @ TA @ TB @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(152,axiom,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: TB > $o] :
( ( ! [D: TB] :
( ( member @ TB @ D @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ! [E: TB] :
( ( member @ TB @ E @ ( A @ D ) )
=> ( C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_ball__UN) ).
thf(769,plain,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ TA,C: TB > $o] :
( ( ! [D: TB] :
( ( member @ TB @ D @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ B ) ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ B )
=> ! [E: TB] :
( ( member @ TB @ E @ ( A @ D ) )
=> ( C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(219,axiom,
complete_Sup @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Complete__Lattices_OSup_4) ).
thf(943,plain,
complete_Sup @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(375,axiom,
! [TA: $tType,TB: $tType] :
( ( ( zero @ TB )
& ( finite_finite @ TA ) )
=> ( zero @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ozero_81) ).
thf(1293,plain,
! [TA: $tType,TB: $tType] :
( ( ( zero @ TB )
& ( finite_finite @ TA ) )
=> ( zero @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(283,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( minus_minus @ TA @ A @ D )
= ( plus_plus @ TA @ B @ ( minus_minus @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_group__cancel_Osub1) ).
thf(1112,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( minus_minus @ TA @ A @ D )
= ( plus_plus @ TA @ B @ ( minus_minus @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(169,axiom,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Int__commute) ).
thf(811,plain,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(164,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_double__zero) ).
thf(799,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(133,axiom,
! [TA: $tType,A: set @ TA,B: set @ ( set @ TA ),C: TA] :
( ( member @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_UnionI) ).
thf(726,plain,
! [TA: $tType,A: set @ TA,B: set @ ( set @ TA ),C: TA] :
( ( member @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ( collect @ TB
@ ^ [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) ) )
= ( image @ TA @ TB @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_Compr__image__eq) ).
thf(462,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ TA,C: TB > $o] :
( ( collect @ TB
@ ^ [D: TB] :
( ( member @ TB @ D @ ( image @ TA @ TB @ A @ B ) )
& ( C @ D ) ) )
= ( image @ TA @ TB @ A
@ ( collect @ TA
@ ^ [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(261,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( type @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Finite__Set_Ofinite___HOL_Otype) ).
thf(1061,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( type @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(57,axiom,
complete_Sup @ extend1814228343nnreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nonnegative__Real_Oennreal___Complete__Lattices_OSup_90) ).
thf(521,plain,
complete_Sup @ extend1814228343nnreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(321,axiom,
( ( complete_Sup_Sup @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( image @ ( finite_Cartesian_vec @ int @ n ) @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ t2 @ ( top_top @ ( set @ ( finite_Cartesian_vec @ int @ n ) ) ) ) )
= ( complete_Sup_Sup @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
@ ( image @ nat @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
@ ^ [A: nat] : ( t2 @ ( f @ A ) )
@ ( top_top @ ( set @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23__092_060open_062_092_060Union_062_A_Irange_AT_J_A_061_A_I_092_060Union_062n_O_AT_A_If_An_J_J_092_060close_062) ).
thf(1198,plain,
( ( complete_Sup_Sup @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( image @ ( finite_Cartesian_vec @ int @ n ) @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ t2 @ ( top_top @ ( set @ ( finite_Cartesian_vec @ int @ n ) ) ) ) )
= ( complete_Sup_Sup @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
@ ( image @ nat @ ( set @ ( finite_Cartesian_vec @ real @ n ) )
@ ^ [A: nat] : ( t2 @ ( f @ A ) )
@ ( top_top @ ( set @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(12,axiom,
one @ extend1814228343nnreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nonnegative__Real_Oennreal___Groups_Oone_94) ).
thf(399,plain,
one @ extend1814228343nnreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(225,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > TB,C: TA > $o] :
( ! [D: TA] :
( ( A @ ( B @ D ) )
= ( C @ D ) )
=> ( ( vimage @ TA @ TB @ B @ ( collect @ TB @ A ) )
= ( collect @ TA @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_vimage__Collect) ).
thf(959,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TA > TB,C: TA > $o] :
( ! [D: TA] :
( ( A @ ( B @ D ) )
= ( C @ D ) )
=> ( ( vimage @ TA @ TB @ B @ ( collect @ TB @ A ) )
= ( collect @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(252,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_add_Ogroup__left__neutral) ).
thf(1044,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType] :
( ( complete_Sup @ TA )
=> ( complete_Sup @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Complete__Lattices_OSup) ).
thf(455,plain,
! [TA: $tType,TB: $tType] :
( ( complete_Sup @ TA )
=> ( complete_Sup @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(9,axiom,
comple187826305attice @ extend1814228343nnreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nonnegative__Real_Oennreal___Complete__Lattices_Ocomplete__lattice_85) ).
thf(394,plain,
comple187826305attice @ extend1814228343nnreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(237,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ C )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_Diff__Int__distrib2) ).
thf(1000,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ C )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(278,axiom,
ordere236663937imp_le @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(1102,plain,
ordere236663937imp_le @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(24,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( measure_null_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ C @ A ) @ ( measure_null_sets @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_null__set__Int1) ).
thf(438,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( measure_null_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ C @ A ) @ ( measure_null_sets @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(210,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ( ab_semigroup_add @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Oab__semigroup__add_24) ).
thf(922,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ( ab_semigroup_add @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(151,axiom,
strict2144017051up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add_7) ).
thf(768,plain,
strict2144017051up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(175,axiom,
! [TA: $tType,TB: $tType] :
( ( complete_Sup @ TB )
=> ( ( complete_Sup_Sup @ ( TA > TB ) )
= ( ^ [A: set @ ( TA > TB ),B: TA] :
( complete_Sup_Sup @ TB
@ ( image @ ( TA > TB ) @ TB
@ ^ [C: TA > TB] : ( C @ B )
@ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_Sup__fun__def) ).
thf(827,plain,
! [TA: $tType,TB: $tType] :
( ( complete_Sup @ TB )
=> ( ( complete_Sup_Sup @ ( TA > TB ) )
= ( ^ [A: set @ ( TA > TB ),B: TA] :
( complete_Sup_Sup @ TB
@ ( image @ ( TA > TB ) @ TB
@ ^ [C: TA > TB] : ( C @ B )
@ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(248,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_Int__iff) ).
thf(1034,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(45,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ ( minus_minus @ TA @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_diff__add__cancel) ).
thf(490,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ ( minus_minus @ TA @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(380,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordered_ab_group_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__group__add_68) ).
thf(1304,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordered_ab_group_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(305,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( countable @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Finite__Set_Ofinite___Countable_Ocountable) ).
thf(1166,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( countable @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(162,axiom,
ab_semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oab__semigroup__add) ).
thf(795,plain,
ab_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(212,axiom,
cancel_semigroup_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(927,plain,
cancel_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(104,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_add__mono__thms__linordered__field_I1_J) ).
thf(648,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(297,axiom,
ordere779506340up_add @ extend1814228343nnreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nonnegative__Real_Oennreal___Groups_Oordered__ab__semigroup__add_87) ).
thf(1145,plain,
ordere779506340up_add @ extend1814228343nnreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(311,axiom,
! [TA: $tType,TB: $tType] :
( ( ( semigroup_add @ TB )
& ( finite_finite @ TA ) )
=> ( semigroup_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Osemigroup__add_73) ).
thf(1181,plain,
! [TA: $tType,TB: $tType] :
( ( ( semigroup_add @ TB )
& ( finite_finite @ TA ) )
=> ( semigroup_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(39,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_add__right__imp__eq) ).
thf(473,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(267,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ ( set @ TA )] :
( ( image @ TA @ TB @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) )
= ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ ( set @ TA ) @ ( set @ TB ) @ ( image @ TA @ TB @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_image__Union) ).
thf(1076,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: set @ ( set @ TA )] :
( ( image @ TA @ TB @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) )
= ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ ( set @ TA ) @ ( set @ TB ) @ ( image @ TA @ TB @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(62,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_add_Oright__neutral) ).
thf(531,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(220,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
& ( B @ C ) ) )
= ( inf_inf @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_Collect__conj__eq) ).
thf(944,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( collect @ TA
@ ^ [C: TA] :
( ( A @ C )
& ( B @ C ) ) )
= ( inf_inf @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(109,axiom,
! [TA: $tType] :
( ( comple1035589618norder @ TA )
=> ! [A: set @ TA] :
( ( ( complete_Sup_Sup @ TA @ A )
= ( top_top @ TA ) )
= ( ! [B: TA] :
( ( ord_less @ TA @ B @ ( top_top @ TA ) )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less @ TA @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_Sup__eq__top__iff) ).
thf(663,plain,
! [TA: $tType] :
( ( comple1035589618norder @ TA )
=> ! [A: set @ TA] :
( ( ( complete_Sup_Sup @ TA @ A )
= ( top_top @ TA ) )
= ( ! [B: TA] :
( ( ord_less @ TA @ B @ ( top_top @ TA ) )
=> ? [C: TA] :
( ( member @ TA @ C @ A )
& ( ord_less @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > ( sigma_measure @ TB ),C: TA > ( sigma_measure @ TB )] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( sigma_sets @ TB @ ( B @ D ) )
= ( sigma_sets @ TB @ ( C @ D ) ) ) )
=> ( ( sigma_sets @ TB @ ( complete_Sup_Sup @ ( sigma_measure @ TB ) @ ( image @ TA @ ( sigma_measure @ TB ) @ B @ A ) ) )
= ( sigma_sets @ TB @ ( complete_Sup_Sup @ ( sigma_measure @ TB ) @ ( image @ TA @ ( sigma_measure @ TB ) @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_sets__SUP__cong) ).
thf(548,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: TA > ( sigma_measure @ TB ),C: TA > ( sigma_measure @ TB )] :
( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( ( sigma_sets @ TB @ ( B @ D ) )
= ( sigma_sets @ TB @ ( C @ D ) ) ) )
=> ( ( sigma_sets @ TB @ ( complete_Sup_Sup @ ( sigma_measure @ TB ) @ ( image @ TA @ ( sigma_measure @ TB ) @ B @ A ) ) )
= ( sigma_sets @ TB @ ( complete_Sup_Sup @ ( sigma_measure @ TB ) @ ( image @ TA @ ( sigma_measure @ TB ) @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( countable @ TA ) )
=> ( countable @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Countable_Ocountable) ).
thf(525,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( countable @ TA ) )
=> ( countable @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(238,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( minus_minus @ TA @ A @ B )
= C )
= ( A
= ( plus_plus @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_diff__eq__eq) ).
thf(1003,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( minus_minus @ TA @ A @ B )
= C )
= ( A
= ( plus_plus @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(185,axiom,
! [TA: $tType,A: set @ ( sigma_measure @ TA ),B: set @ TA,C: sigma_measure @ TA,D: set @ TA] :
( ! [E: sigma_measure @ TA] :
( ( member @ ( sigma_measure @ TA ) @ E @ A )
=> ( ( sigma_space @ TA @ E )
= B ) )
=> ( ( member @ ( sigma_measure @ TA ) @ C @ A )
=> ( ( member @ ( set @ TA ) @ D @ ( sigma_sets @ TA @ C ) )
=> ( member @ ( set @ TA ) @ D @ ( sigma_sets @ TA @ ( complete_Sup_Sup @ ( sigma_measure @ TA ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_in__sets__Sup) ).
thf(855,plain,
! [TA: $tType,A: set @ ( sigma_measure @ TA ),B: set @ TA,C: sigma_measure @ TA,D: set @ TA] :
( ! [E: sigma_measure @ TA] :
( ( member @ ( sigma_measure @ TA ) @ E @ A )
=> ( ( sigma_space @ TA @ E )
= B ) )
=> ( ( member @ ( sigma_measure @ TA ) @ C @ A )
=> ( ( member @ ( set @ TA ) @ D @ ( sigma_sets @ TA @ C ) )
=> ( member @ ( set @ TA ) @ D @ ( sigma_sets @ TA @ ( complete_Sup_Sup @ ( sigma_measure @ TA ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(101,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_add__mono__thms__linordered__field_I5_J) ).
thf(640,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(189,axiom,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_UNIV__witness) ).
thf(872,plain,
! [TA: $tType] :
? [A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(125,axiom,
complete_Sup @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Complete__Lattices_OSup_17) ).
thf(707,plain,
complete_Sup @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(196,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_diff__add__eq) ).
thf(887,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(138,axiom,
semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add_18) ).
thf(739,plain,
semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(124,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_DiffD2) ).
thf(705,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(301,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA > $o] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ ( collect @ TA @ C ) ) )
= ( ( member @ TA @ A @ B )
& ( C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_Int__Collect) ).
thf(1156,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA > $o] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ ( collect @ TA @ C ) ) )
= ( ( member @ TA @ A @ B )
& ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(257,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_add_Oleft__cancel) ).
thf(1053,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(112,axiom,
complete_Sup @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Complete__Lattices_OSup_34) ).
thf(673,plain,
complete_Sup @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(160,axiom,
! [TA: $tType,A: set @ TA] :
( ( vimage @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_vimage__ident) ).
thf(791,plain,
! [TA: $tType,A: set @ TA] :
( ( vimage @ TA @ TA
@ ^ [B: TA] : B
@ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(79,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] : ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_rangeI) ).
thf(585,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TA] : ( member @ TB @ ( A @ B ) @ ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ A @ ( vimage @ TB @ TA @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_surj__image__vimage__eq) ).
thf(717,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA] :
( ( ( image @ TB @ TA @ A @ ( top_top @ ( set @ TB ) ) )
= ( top_top @ ( set @ TA ) ) )
=> ( ( image @ TB @ TA @ A @ ( vimage @ TB @ TA @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(180,axiom,
! [TA: $tType] :
( ( minus_minus @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ( minus_minus @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_minus__set__def) ).
thf(840,plain,
! [TA: $tType] :
( ( minus_minus @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ( minus_minus @ ( TA > $o )
@ ^ [C: TA] : ( member @ TA @ C @ A )
@ ^ [C: TA] : ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(328,axiom,
! [TA: $tType,TB: $tType] :
( ( ( comm_monoid_add @ TB )
& ( finite_finite @ TA ) )
=> ( comm_monoid_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ocomm__monoid__add_71) ).
thf(1218,plain,
! [TA: $tType,TB: $tType] :
( ( ( comm_monoid_add @ TB )
& ( finite_finite @ TA ) )
=> ( comm_monoid_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(329,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordere223160158up_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__cancel__ab__semigroup__add_63) ).
thf(1220,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordere223160158up_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(315,axiom,
member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ s @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_assms_I1_J) ).
thf(1188,plain,
member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ s @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(314,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordere236663937imp_le @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__add__imp__le_64) ).
thf(1186,plain,
! [TA: $tType,TB: $tType] :
( ( ( ordere890947078_space @ TB )
& ( finite_finite @ TA ) )
=> ( ordere236663937imp_le @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(356,axiom,
ordere890947078_space @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Ordered__Euclidean__Space_Oordered__euclidean__space_1) ).
thf(1262,plain,
ordere890947078_space @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(339,axiom,
! [TA: $tType,TB: $tType] :
( ( ( cancel1352612707id_add @ TB )
& ( finite_finite @ TA ) )
=> ( cancel1352612707id_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__comm__monoid__add_67) ).
thf(1235,plain,
! [TA: $tType,TB: $tType] :
( ( ( cancel1352612707id_add @ TB )
& ( finite_finite @ TA ) )
=> ( cancel1352612707id_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(38,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_less__add__same__cancel2) ).
thf(470,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > ( set @ TB ),C: set @ TA] :
( ( image @ TB @ TC @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) )
= ( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TA @ ( set @ TC )
@ ^ [D: TA] : ( image @ TB @ TC @ A @ ( B @ D ) )
@ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_image__UN) ).
thf(576,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > ( set @ TB ),C: set @ TA] :
( ( image @ TB @ TC @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) )
= ( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TA @ ( set @ TC )
@ ^ [D: TA] : ( image @ TB @ TC @ A @ ( B @ D ) )
@ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(142,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_imageI) ).
thf(744,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > TB] :
( ( member @ TA @ A @ B )
=> ( member @ TB @ ( C @ A ) @ ( image @ TA @ TB @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(295,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_less__numeral__extra_I4_J) ).
thf(1140,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(1141,plain,
! [TA: $tType] :
( ~ ( linord1659791738miring @ TA )
| ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(cnf,[status(esa)],[1140]) ).
thf(370,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( measure_null_sets @ TA @ B ) )
=> ( ( sigma_emeasure @ TA @ B @ A )
= ( zero_zero @ extend1814228343nnreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_null__setsD1) ).
thf(1284,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( measure_null_sets @ TA @ B ) )
=> ( ( sigma_emeasure @ TA @ B @ A )
= ( zero_zero @ extend1814228343nnreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(86,axiom,
monoid_add @ extend1814228343nnreal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nonnegative__Real_Oennreal___Groups_Omonoid__add_92) ).
thf(600,plain,
monoid_add @ extend1814228343nnreal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(74,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_diff__right__commute) ).
thf(571,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(48,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ B )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_translation__subtract__diff) ).
thf(497,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ B )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_image__eqI) ).
thf(656,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA,D: set @ TA] :
( ( A
= ( B @ C ) )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(246,axiom,
! [TA: $tType] :
( ( complete_Sup_Sup @ ( set @ TA ) @ ( top_top @ ( set @ ( set @ TA ) ) ) )
= ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_Union__UNIV) ).
thf(1023,plain,
! [TA: $tType] :
( ( complete_Sup_Sup @ ( set @ TA ) @ ( top_top @ ( set @ ( set @ TA ) ) ) )
= ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(386,plain,
! [TA: $tType] : ( comple187826305attice @ ( set @ TA ) ),
inference(cnf,[status(esa)],[385]) ).
thf(275,axiom,
! [TA: $tType,TB: $tType] :
( ( comple1035589618norder @ TA )
=> ! [A: TB > TA,B: set @ TB] :
( ( ( complete_Sup_Sup @ TA @ ( image @ TB @ TA @ A @ B ) )
= ( top_top @ TA ) )
= ( ! [C: TA] :
( ( ord_less @ TA @ C @ ( top_top @ TA ) )
=> ? [D: TB] :
( ( member @ TB @ D @ B )
& ( ord_less @ TA @ C @ ( A @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_SUP__eq__top__iff) ).
thf(1094,plain,
! [TA: $tType,TB: $tType] :
( ( comple1035589618norder @ TA )
=> ! [A: TB > TA,B: set @ TB] :
( ( ( complete_Sup_Sup @ TA @ ( image @ TB @ TA @ A @ B ) )
= ( top_top @ TA ) )
= ( ! [C: TA] :
( ( ord_less @ TA @ C @ ( top_top @ TA ) )
=> ? [D: TB] :
( ( member @ TB @ D @ B )
& ( ord_less @ TA @ C @ ( A @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(363,axiom,
strict2144017051up_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ostrict__ordered__ab__semigroup__add_38) ).
thf(1272,plain,
strict2144017051up_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(91,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
= ( minus_minus @ TA @ B @ C ) )
= ( ( plus_plus @ TA @ A @ C )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_eq__diff__eq) ).
thf(612,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
= ( minus_minus @ TA @ B @ C ) )
= ( ( plus_plus @ TA @ A @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(342,axiom,
! [A: finite_Cartesian_vec @ int @ n] : ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( r @ A ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__092_060open_062_092_060And_062a_O_AR_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062) ).
thf(1240,plain,
! [A: finite_Cartesian_vec @ int @ n] : ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( r @ A ) @ ( sigma_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(234,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: set @ TA] :
( ( image @ TA @ TA @ ( plus_plus @ TA @ ( zero_zero @ TA ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_image__add__0) ).
thf(991,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: set @ TA] :
( ( image @ TA @ TA @ ( plus_plus @ TA @ ( zero_zero @ TA ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(36,axiom,
! [TA: $tType] :
( ( complete_Sup @ TA )
=> ! [A: set @ TA] :
( ( complete_Sup_Sup @ TA
@ ( image @ TA @ TA
@ ^ [B: TA] : B
@ A ) )
= ( complete_Sup_Sup @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_SUP__identity__eq) ).
thf(465,plain,
! [TA: $tType] :
( ( complete_Sup @ TA )
=> ! [A: set @ TA] :
( ( complete_Sup_Sup @ TA
@ ( image @ TA @ TA
@ ^ [B: TA] : B
@ A ) )
= ( complete_Sup_Sup @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(97,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(627,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
( ( A = B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image @ TA @ TB @ C @ A ) )
= ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_Inf_OINF__cong) ).
thf(556,plain,
! [TA: $tType,TB: $tType,A: set @ TA,B: set @ TA,C: TA > TB,D: TA > TB,E: ( set @ TB ) > TB] :
( ( A = B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image @ TA @ TB @ C @ A ) )
= ( E @ ( image @ TA @ TB @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(327,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ring_char_0 @ TB )
& ( finite_finite @ TA ) )
=> ( ring_char_0 @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Nat_Oring__char__0_80) ).
thf(1216,plain,
! [TA: $tType,TB: $tType] :
( ( ( ring_char_0 @ TB )
& ( finite_finite @ TA ) )
=> ( ring_char_0 @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(316,axiom,
( s
= ( complete_Sup_Sup @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( image @ ( finite_Cartesian_vec @ int @ n ) @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ t2 @ ( top_top @ ( set @ ( finite_Cartesian_vec @ int @ n ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_S__decompose) ).
thf(1189,plain,
( s
= ( complete_Sup_Sup @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( image @ ( finite_Cartesian_vec @ int @ n ) @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ t2 @ ( top_top @ ( set @ ( finite_Cartesian_vec @ int @ n ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(242,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_UNIV__I) ).
thf(1010,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(281,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_double__add__less__zero__iff__single__add__less__zero) ).
thf(1108,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(30,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_DiffI) ).
thf(450,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(270,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ~ ! [C: TA] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_surjE) ).
thf(1084,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ~ ! [C: TA] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(366,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ring_1 @ TB )
& ( finite_finite @ TA ) )
=> ( neg_numeral @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Num_Oneg__numeral_79) ).
thf(1276,plain,
! [TA: $tType,TB: $tType] :
( ( ( ring_1 @ TB )
& ( finite_finite @ TA ) )
=> ( neg_numeral @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA] :
( ( A
= ( B @ C ) )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_range__eqI) ).
thf(517,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: TA] :
( ( A
= ( B @ C ) )
=> ( member @ TB @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA,C: set @ TA] :
( ( vimage @ TB @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TB ) @ ( vimage @ TB @ TA @ A @ B ) @ ( vimage @ TB @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_vimage__Int) ).
thf(652,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: set @ TA,C: set @ TA] :
( ( vimage @ TB @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TB ) @ ( vimage @ TB @ TA @ A @ B ) @ ( vimage @ TB @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(390,plain,
! [TA: $tType,TB: $tType] :
( ~ ( comple187826305attice @ TB )
| ( comple187826305attice @ ( TA > TB ) ) ),
inference(cnf,[status(esa)],[389]) ).
thf(344,axiom,
! [TA: $tType,TB: $tType] :
( ( ( one @ TB )
& ( finite_finite @ TA ) )
=> ( one @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oone_82) ).
thf(1244,plain,
! [TA: $tType,TB: $tType] :
( ( ( one @ TB )
& ( finite_finite @ TA ) )
=> ( one @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(155,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add_14) ).
thf(781,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(81,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( minus_minus @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_add__diff__cancel__left) ).
thf(588,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( minus_minus @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(350,axiom,
! [TA: $tType,TB: $tType] :
( ( ( group_add @ TB )
& ( finite_finite @ TA ) )
=> ( group_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ogroup__add_78) ).
thf(1253,plain,
! [TA: $tType,TB: $tType] :
( ( ( group_add @ TB )
& ( finite_finite @ TA ) )
=> ( group_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(122,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_image__iff) ).
thf(699,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > TB,C: set @ TA] :
( ( member @ TB @ A @ ( image @ TA @ TB @ B @ C ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(135,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_add__eq__0__iff__both__eq__0) ).
thf(731,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(17,axiom,
one @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oone) ).
thf(418,plain,
one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(158,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_IntD1) ).
thf(786,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(73,axiom,
! [TA: $tType] :
( ( minus_minus @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ~ ( member @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_set__diff__eq) ).
thf(568,plain,
! [TA: $tType] :
( ( minus_minus @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( collect @ TA
@ ^ [C: TA] :
( ( member @ TA @ C @ A )
& ~ ( member @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(22,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ? [C: TA] : ( member @ TA @ C @ ( minus_minus @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_psubset__imp__ex__mem) ).
thf(433,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less @ ( set @ TA ) @ A @ B )
=> ? [C: TA] : ( member @ TA @ C @ ( minus_minus @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(382,axiom,
ordered_ab_group_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__group__add_46) ).
thf(1308,plain,
ordered_ab_group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(319,axiom,
! [A: finite_Cartesian_vec @ int @ n,B: finite_Cartesian_vec @ int @ n] :
( ( A != B )
=> ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( inf_inf @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( r @ A ) @ ( r @ B ) ) @ ( measure_null_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_R__Int) ).
thf(1193,plain,
! [A: finite_Cartesian_vec @ int @ n,B: finite_Cartesian_vec @ int @ n] :
( ( A != B )
=> ( member @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( inf_inf @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( r @ A ) @ ( r @ B ) ) @ ( measure_null_sets @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ ( set @ TA )] :
( ( complete_Sup_Sup @ ( set @ TB )
@ ( image @ ( set @ TA ) @ ( set @ TB )
@ ^ [C: set @ TA] : ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ C ) )
@ B ) )
= ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_UN__extend__simps_I8_J) ).
thf(478,plain,
! [TA: $tType,TB: $tType,A: TA > ( set @ TB ),B: set @ ( set @ TA )] :
( ( complete_Sup_Sup @ ( set @ TB )
@ ( image @ ( set @ TA ) @ ( set @ TB )
@ ^ [C: set @ TA] : ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ C ) )
@ B ) )
= ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ A @ ( complete_Sup_Sup @ ( set @ TA ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(150,axiom,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > ( sigma_measure @ TB ),D: set @ TB,E: set @ TB] :
( ( member @ TA @ A @ B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( sigma_space @ TB @ ( C @ F ) )
= D ) )
=> ( ( member @ ( set @ TB ) @ E @ ( sigma_sets @ TB @ ( C @ A ) ) )
=> ( member @ ( set @ TB ) @ E @ ( sigma_sets @ TB @ ( complete_Sup_Sup @ ( sigma_measure @ TB ) @ ( image @ TA @ ( sigma_measure @ TB ) @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_in__sets__SUP) ).
thf(763,plain,
! [TA: $tType,TB: $tType,A: TA,B: set @ TA,C: TA > ( sigma_measure @ TB ),D: set @ TB,E: set @ TB] :
( ( member @ TA @ A @ B )
=> ( ! [F: TA] :
( ( member @ TA @ F @ B )
=> ( ( sigma_space @ TB @ ( C @ F ) )
= D ) )
=> ( ( member @ ( set @ TB ) @ E @ ( sigma_sets @ TB @ ( C @ A ) ) )
=> ( member @ ( set @ TB ) @ E @ ( sigma_sets @ TB @ ( complete_Sup_Sup @ ( sigma_measure @ TB ) @ ( image @ TA @ ( sigma_measure @ TB ) @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(201,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero_21) ).
thf(899,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(117,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_diff__0__right) ).
thf(684,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(284,axiom,
! [TA: $tType,A: set @ ( set @ TA ),B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( complete_Sup_Sup @ ( set @ TA ) @ A ) @ B )
= ( complete_Sup_Sup @ ( set @ TA )
@ ( image @ ( set @ TA ) @ ( set @ TA )
@ ^ [C: set @ TA] : ( inf_inf @ ( set @ TA ) @ C @ B )
@ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Int__Union2) ).
thf(1116,plain,
! [TA: $tType,A: set @ ( set @ TA ),B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( complete_Sup_Sup @ ( set @ TA ) @ A ) @ B )
= ( complete_Sup_Sup @ ( set @ TA )
@ ( image @ ( set @ TA ) @ ( set @ TA )
@ ^ [C: set @ TA] : ( inf_inf @ ( set @ TA ) @ C @ B )
@ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(291,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_diff__gt__0__iff__gt) ).
thf(1133,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(29,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_Diff__iff) ).
thf(447,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(335,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ab_group_add @ TB )
& ( finite_finite @ TA ) )
=> ( ab_group_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Oab__group__add_74) ).
thf(1229,plain,
! [TA: $tType,TB: $tType] :
( ( ( ab_group_add @ TB )
& ( finite_finite @ TA ) )
=> ( ab_group_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(222,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_add__diff__cancel) ).
thf(950,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(276,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
=> ( member @ TA @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_vimageD) ).
thf(1097,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
=> ( member @ TA @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(19,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ B )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_translation__subtract__Int) ).
thf(422,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA] :
( ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ B )
@ ( image @ TA @ TA
@ ^ [D: TA] : ( minus_minus @ TA @ D @ A )
@ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(347,axiom,
cancel146912293up_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_44) ).
thf(1248,plain,
cancel146912293up_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(71,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_not__gr__zero) ).
thf(564,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(167,axiom,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ? [C: TA] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_surjD) ).
thf(807,plain,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB] :
( ( ( image @ TA @ TB @ A @ ( top_top @ ( set @ TA ) ) )
= ( top_top @ ( set @ TB ) ) )
=> ? [C: TA] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1334,plain,
( ( ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) )
!= ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) )
| ( ( t2 @ ( f @ sk27 ) )
!= ( t @ ( f @ sk27 ) ) ) ),
inference(simp,[status(thm)],[1310]) ).
thf(1335,plain,
( ( t2 @ ( f @ sk27 ) )
!= ( t @ ( f @ sk27 ) ) ),
inference(simp,[status(thm)],[1334]) ).
thf(308,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_add_Oleft__commute) ).
thf(1172,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(258,axiom,
monoid_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__add_20) ).
thf(1056,plain,
monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(263,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TA,D: set @ TA] :
( ( ( A @ B )
= C )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ B @ ( vimage @ TB @ TA @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_vimageI) ).
thf(1065,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TB,C: TA,D: set @ TA] :
( ( ( A @ B )
= C )
=> ( ( member @ TA @ C @ D )
=> ( member @ TB @ B @ ( vimage @ TB @ TA @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(121,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_Int__UNIV__right) ).
thf(696,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( top_top @ ( set @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(131,axiom,
! [TA: $tType,A: set @ ( set @ TA ),B: TA > $o] :
( ( ? [C: TA] :
( ( member @ TA @ C @ ( complete_Sup_Sup @ ( set @ TA ) @ A ) )
& ( B @ C ) ) )
= ( ? [C: set @ TA] :
( ( member @ ( set @ TA ) @ C @ A )
& ? [D: TA] :
( ( member @ TA @ D @ C )
& ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_UN__ball__bex__simps_I3_J) ).
thf(720,plain,
! [TA: $tType,A: set @ ( set @ TA ),B: TA > $o] :
( ( ? [C: TA] :
( ( member @ TA @ C @ ( complete_Sup_Sup @ ( set @ TA ) @ A ) )
& ( B @ C ) ) )
= ( ? [C: set @ TA] :
( ( member @ ( set @ TA ) @ C @ A )
& ? [D: TA] :
( ( member @ TA @ D @ C )
& ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(163,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ A @ ( sigma_space @ TA @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_sets_OInt__space__eq2) ).
thf(796,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ A @ ( sigma_space @ TA @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(213,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( countable @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Countable_Ocountable_28) ).
thf(928,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ( countable @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(16,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(415,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(10,axiom,
comple187826305attice @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_33) ).
thf(395,plain,
comple187826305attice @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(355,axiom,
ordere779506340up_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_42) ).
thf(1261,plain,
ordere779506340up_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(359,axiom,
complete_Sup @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Complete__Lattices_OSup_50) ).
thf(1268,plain,
complete_Sup @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(186,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_add_Oleft__neutral) ).
thf(860,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(84,axiom,
monoid_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Omonoid__add) ).
thf(596,plain,
monoid_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
( ( image @ TA @ TC
@ ^ [C: TA] : ( A @ ( B @ C ) )
@ ( top_top @ ( set @ TA ) ) )
= ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_range__composition) ).
thf(528,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB] :
( ( image @ TA @ TC
@ ^ [C: TA] : ( A @ ( B @ C ) )
@ ( top_top @ ( set @ TA ) ) )
= ( image @ TB @ TC @ A @ ( image @ TA @ TB @ B @ ( top_top @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(205,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( sigma_sets @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_sets_ODiff) ).
thf(908,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( sigma_sets @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(132,axiom,
! [TA: $tType] :
( ( complete_Sup_Sup @ ( set @ TA ) )
= ( ^ [A: set @ ( set @ TA )] :
( collect @ TA
@ ^ [B: TA] : ( complete_Sup_Sup @ $o @ ( image @ ( set @ TA ) @ $o @ ( member @ TA @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_Sup__set__def) ).
thf(723,plain,
! [TA: $tType] :
( ( complete_Sup_Sup @ ( set @ TA ) )
= ( ^ [A: set @ ( set @ TA )] :
( collect @ TA
@ ^ [B: TA] : ( complete_Sup_Sup @ $o @ ( image @ ( set @ TA ) @ $o @ ( member @ TA @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(230,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > ( set @ TC ),B: TA > ( set @ TB ),C: set @ TA] :
( ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) ) )
= ( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TA @ ( set @ TC )
@ ^ [D: TA] : ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ A @ ( B @ D ) ) )
@ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_UN__UN__flatten) ).
thf(982,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > ( set @ TC ),B: TA > ( set @ TB ),C: set @ TA] :
( ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) ) )
= ( complete_Sup_Sup @ ( set @ TC )
@ ( image @ TA @ ( set @ TC )
@ ^ [D: TA] : ( complete_Sup_Sup @ ( set @ TC ) @ ( image @ TB @ ( set @ TC ) @ A @ ( B @ D ) ) )
@ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(378,axiom,
! [A: finite_Cartesian_vec @ int @ n,B: finite_Cartesian_vec @ int @ n] :
( ( A != B )
=> ( ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( inf_inf @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t2 @ A ) @ ( t2 @ B ) ) )
= ( zero_zero @ extend1814228343nnreal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_emeasure__T__Int) ).
thf(1299,plain,
! [A: finite_Cartesian_vec @ int @ n,B: finite_Cartesian_vec @ int @ n] :
( ( A != B )
=> ( ( sigma_emeasure @ ( finite_Cartesian_vec @ real @ n ) @ ( complete_completion @ ( finite_Cartesian_vec @ real @ n ) @ ( lebesgue_lborel @ ( finite_Cartesian_vec @ real @ n ) ) ) @ ( inf_inf @ ( set @ ( finite_Cartesian_vec @ real @ n ) ) @ ( t2 @ A ) @ ( t2 @ B ) ) )
= ( zero_zero @ extend1814228343nnreal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(26,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Nat_Oring__char__0) ).
thf(442,plain,
ring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(89,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_add__left__cancel) ).
thf(607,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(134,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_diff__zero) ).
thf(728,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(139,axiom,
! [TA: $tType] : ( complete_Sup @ ( set @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Complete__Lattices_OSup_26) ).
thf(740,plain,
! [TA: $tType] : ( complete_Sup @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(241,axiom,
comm_monoid_diff @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__diff) ).
thf(1009,plain,
comm_monoid_diff @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(313,axiom,
! [TA: $tType,TB: $tType] :
( ( ( cancel146912293up_add @ TB )
& ( finite_finite @ TA ) )
=> ( cancel146912293up_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__ab__semigroup__add_66) ).
thf(1184,plain,
! [TA: $tType,TB: $tType] :
( ( ( cancel146912293up_add @ TB )
& ( finite_finite @ TA ) )
=> ( cancel146912293up_add @ ( finite_Cartesian_vec @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(66,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ( comm_monoid_add @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Groups_Ocomm__monoid__add_25) ).
thf(543,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ( comm_monoid_add @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(249,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > ( set @ TB ),C: set @ TA] :
( ( inf_inf @ ( set @ TB ) @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) )
= ( complete_Sup_Sup @ ( set @ TB )
@ ( image @ TA @ ( set @ TB )
@ ^ [D: TA] : ( inf_inf @ ( set @ TB ) @ A @ ( B @ D ) )
@ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_UN__extend__simps_I5_J) ).
thf(1037,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > ( set @ TB ),C: set @ TA] :
( ( inf_inf @ ( set @ TB ) @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) )
= ( complete_Sup_Sup @ ( set @ TB )
@ ( image @ TA @ ( set @ TB )
@ ^ [D: TA] : ( inf_inf @ ( set @ TB ) @ A @ ( B @ D ) )
@ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(264,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_gr__implies__not__zero) ).
thf(1069,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(126,axiom,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( sigma_sets @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_sets_OInt) ).
thf(708,plain,
! [TA: $tType,A: set @ TA,B: sigma_measure @ TA,C: set @ TA] :
( ( member @ ( set @ TA ) @ A @ ( sigma_sets @ TA @ B ) )
=> ( ( member @ ( set @ TA ) @ C @ ( sigma_sets @ TA @ B ) )
=> ( member @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( sigma_sets @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(194,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Finite__Set_Ofinite) ).
thf(882,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TB )
& ( finite_finite @ TA ) )
=> ( finite_finite @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(147,axiom,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > ( set @ TB ),C: set @ TA] :
( ( inf_inf @ ( set @ TB ) @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) )
= ( complete_Sup_Sup @ ( set @ TB )
@ ( image @ TA @ ( set @ TB )
@ ^ [D: TA] : ( inf_inf @ ( set @ TB ) @ A @ ( B @ D ) )
@ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_Int__UN__distrib) ).
thf(755,plain,
! [TA: $tType,TB: $tType,A: set @ TB,B: TA > ( set @ TB ),C: set @ TA] :
( ( inf_inf @ ( set @ TB ) @ A @ ( complete_Sup_Sup @ ( set @ TB ) @ ( image @ TA @ ( set @ TB ) @ B @ C ) ) )
= ( complete_Sup_Sup @ ( set @ TB )
@ ( image @ TA @ ( set @ TB )
@ ^ [D: TA] : ( inf_inf @ ( set @ TB ) @ A @ ( B @ D ) )
@ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(114,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= A )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_add__cancel__left__right) ).
thf(676,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= A )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(3028,plain,
$false,
inference(e,[status(thm)],[645,1168,1105,893,941,481,1237,846,962,468,666,1295,1200,977,1211,582,1290,994,1073,597,1041,1142,1269,878,440,655,385,384,1137,1310,500,1233,814,1063,747,913,1222,930,1196,898,782,1265,1228,389,1287,1298,785,504,1330,587,702,802,1279,1191,460,1087,1247,969,1232,817,902,924,1302,591,443,1040,937,1183,905,1136,834,1020,574,1051,821,634,734,956,1119,396,660,507,527,1169,687,877,692,411,988,1242,849,512,1306,810,714,1206,452,1153,761,1311,534,1047,1057,1163,1274,910,1223,1343,778,1255,1123,820,392,630,788,1238,746,1091,916,484,625,879,1178,1159,493,1079,682,1128,1012,852,435,522,830,1291,710,742,1089,874,615,1111,403,1006,388,869,610,1270,1259,884,1160,1082,488,537,669,642,637,1214,1016,679,1292,933,554,753,1075,476,393,1231,1131,1192,1246,503,622,837,1263,997,1099,985,515,1249,1060,1050,457,1333,938,398,674,1026,953,794,1278,750,425,1103,824,1273,689,444,601,1251,618,1146,430,1007,402,772,743,579,843,1125,1256,1226,545,1271,1312,611,713,1090,1258,947,1224,540,391,1139,919,804,1209,900,831,1282,419,990,567,509,1122,979,604,1048,736,863,1175,890,494,758,594,621,895,1149,769,943,1293,1112,811,387,799,726,462,1061,521,1198,399,959,1044,455,394,1000,1102,438,922,768,827,1034,490,1304,1166,795,927,648,1145,1181,1049,473,1076,531,944,663,548,525,1003,855,640,872,707,887,739,705,1156,1053,673,791,585,717,840,1218,1220,1188,1186,1262,1235,470,576,744,1141,1284,600,571,497,656,1023,386,1094,1140,1272,612,1240,991,465,627,556,1216,1189,1010,1108,450,1084,1276,517,652,390,1244,781,588,1253,699,731,418,786,568,433,1308,1193,478,763,383,899,684,1116,1133,447,1229,950,1097,422,1248,564,807,1335,1172,1056,400,1065,696,720,796,928,415,395,1261,1268,860,596,528,908,723,982,1299,442,607,728,740,803,1009,1184,543,1037,1069,708,882,755,676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP117^2 : 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
% 0.09/0.21 % Computer : n015.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 19:59:33 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 1.04/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.84/1.12 % [INFO] Parsing done (311ms).
% 1.84/1.13 % [INFO] Running in sequential loop mode.
% 3.02/1.34 % [INFO] eprover registered as external prover.
% 3.02/1.35 % [INFO] Scanning for conjecture ...
% 3.40/1.45 % [INFO] Found a conjecture (or negated_conjecture) and 381 axioms. Running axiom selection ...
% 4.21/1.62 % [INFO] Axiom selection finished. Selected 380 axioms (removed 1 axioms).
% 5.26/1.98 % [INFO] Problem is higher-order (TPTP THF).
% 5.26/2.01 % [INFO] Type checking passed.
% 5.26/2.02 % [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 ...
% 66.27/25.15 % External prover 'e' found a proof!
% 66.27/25.15 % [INFO] Killing All external provers ...
% 66.27/25.15 % Time passed: 24800ms (effective reasoning time: 24023ms)
% 66.27/25.15 % 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)>
% 66.27/25.16 % Axioms used in derivation (380): fact_167_less__add__same__cancel2, fact_58_UN__I, fact_216_add_Oassoc, fact_185_zero__eq__add__iff__both__eq__0, fact_240_add__less__imp__less__left, fact_4_assms_I1_J, tcon_Finite__Cartesian__Product_Ovec___Groups_Ocomm__monoid__add_71, fact_101_IntD2, fact_197_add__diff__cancel__right, fact_191_add__less__cancel__left, fact_195_add__diff__cancel__left, fact_33_UnionI, tcon_Nat_Onat___Groups_Oab__semigroup__add_15, tcon_Real_Oreal___Complete__Lattices_OSup_50, fact_88_ball__imageD, fact_173_Diff__iff, tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_42, tcon_HOL_Obool___Complete__Lattices_OSup_34, tfree_0, fact_120_less__numeral__extra_I4_J, fact_182_add__cancel__right__left, fact_139_UN__UN__flatten, fact_242_diff__strict__mono, fact_183_add__cancel__right__right, fact_1__092_060open_062_092_060And_062a_O_AT_H_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062, fact_206_DiffD2, tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__comm__monoid__add_67, tcon_Extended__Nonnegative__Real_Oennreal___Complete__Lattices_Ocomplete__lattice_85, fact_132_null__setsD2, tcon_Real_Oreal___Groups_Omonoid__add_53, tcon_Nat_Onat___Groups_Ocomm__monoid__diff, fact_0_emeasure__T_H, fact_121_range__eqI, fact_133_vimage__inter__cong, fact_19_null__setsI, fact_62_null__sets_OInt__space__eq1, tcon_fun___Finite__Set_Ofinite, fact_76_null__sets_Osets__Collect__disj, fact_78_translation__diff, fact_112_image__image, fact_103_IntE, tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__add__imp__le_64, tcon_Int_Oint___Groups_Ozero, fact_234_add__mono__thms__linordered__field_I5_J, fact_241_add__less__imp__less__right, fact_179_double__zero__sym, tcon_Int_Oint___Groups_Ostrict__ordered__ab__semigroup__add, fact_123_rangeI, tcon_Real_Oreal___Groups_Olinordered__ab__group__add_43, fact_208_minus__set__def, fact_143_less__numeral__extra_I1_J, tcon_Nat_Onat___Groups_Ozero_21, fact_165_zero__less__double__add__iff__zero__less__single__add, fact_67_space__Sup__eq__UN, fact_225_one__reorient, tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add_7, tcon_Int_Oint___Nat_Oring__char__0, fact_235_add__mono__thms__linordered__field_I2_J, fact_113_imageE, fact_171_add__right__cancel, fact_174_Diff__idemp, fact_6_T__Int, fact_156_UN__extend__simps_I4_J, fact_85_Sup_OSUP__cong, fact_142_UN__extend__simps_I9_J, fact_249_add__diff__eq, fact_222_add__right__imp__eq, fact_196_add__diff__cancel__left_H, fact_15_R__Int, tcon_Int_Oint___Groups_Oab__group__add, fact_134_translation__subtract__diff, fact_163_diff__add__zero, tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_41, fact_201_sets_ODiff, tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_23, tcon_Int_Oint___Groups_Oordered__ab__group__add, tcon_Finite__Cartesian__Product_Ovec___Groups_Omonoid__add_76, fact_108_vimageD, fact_39_image__ident, fact_199_sets_OInt, fact_95_UNIV__eq__I, fact_50_UN__ball__bex__simps_I2_J, fact_111_Compr__image__eq, fact_145_surj__image__vimage__eq, fact_116_Int__Collect, tcon_Real_Oreal___Groups_Ocancel__semigroup__add_47, fact_219_add_Ocommute, tcon_Extended__Nonnegative__Real_Oennreal___Groups_Osemigroup__add_91, fact_90_bex__imageD, tcon_Finite__Cartesian__Product_Ovec___Groups_Oab__semigroup__add_70, tcon_Real_Oreal___Num_Oneg__numeral_55, fact_232_add_Ogroup__left__neutral, fact_137_SUP__commute, tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__monoid__add__imp__le_61, fact_11_f__def, tcon_Sigma__Algebra_Omeasure___Complete__Lattices_Ocomplete__lattice_59, tcon_Set_Oset___Groups_Oone_32, fact_169_add__less__same__cancel2, fact_202_add__less__same__cancel1, fact_160_null__sets__def, tcon_Extended__Nonnegative__Real_Oennreal___Groups_Oone_94, fact_92_imageI, tcon_Real_Oreal___Groups_Oordered__ab__group__add_46, fact_96_Int__left__commute, tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__semigroup__add_65, fact_147_null__set__Int1, tcon_Int_Oint___Groups_Ocancel__semigroup__add, fact_35_UN__ball__bex__simps_I3_J, tcon_Set_Oset___Groups_Osemigroup__add_27, tcon_Finite__Cartesian__Product_Ovec___Groups_Oab__group__add_74, fact_72_Diff__Int2, tcon_Int_Oint___Groups_Omonoid__add, fact_74_vimage__Diff, fact_227_not__less__zero, fact_207_set__diff__eq, fact_46_Collect__mem__eq, tcon_Real_Oreal___Ordered__Euclidean__Space_Oordered__euclidean__space_1, tcon_Int_Oint___Groups_Oab__semigroup__add, fact_141_UN__extend__simps_I8_J, fact_63_in__sets__SUP, tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add_12, fact_28_image__eqI, fact_91_image__iff, fact_252_diff__add__eq__diff__diff__swap, fact_158_vimage__UN, fact_29_UNIV__I, fact_237_add__strict__mono, fact_218_add_Oright__cancel, tcon_Int_Oint___Groups_Osemigroup__add, fact_61_null__sets_OInt__space__eq2, tcon_Nat_Onat___Complete__Lattices_OSup_17, fact_22_surj__diff__right, fact_253_diff__diff__add, fact_124_surjI, subcl_Finite__Set_Ofinite___Countable_Ocountable, fact_86_Inf_OINF__cong, fact_157_UN__extend__simps_I5_J, tcon_Extended__Nonnegative__Real_Oennreal___Groups_Omonoid__add_92, fact_250_diff__diff__eq2, fact_114_UNIV__def, tcon_Real_Oreal___Groups_Oab__semigroup__add_48, fact_54_vimage__Int, tcon_fun___Countable_Ocountable, fact_243_diff__eq__diff__less, tcon_Real_Oreal___Groups_Osemigroup__add_51, fact_102_IntD1, fact_209_psubset__imp__ex__mem, fact_146_null__set__Int2, fact_203_sets_Ocompl__sets, fact_161_sets_OInt__space__eq2, fact_226_gr__zeroI, fact_184_add__eq__0__iff__both__eq__0, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le_6, fact_57_UN__iff, fact_119_less__numeral__extra_I3_J, tcon_Int_Oint___Groups_Oordered__ab__semigroup__monoid__add__imp__le, fact_164_diff__gt__0__iff__gt, fact_42_vimage__ident, fact_223_diff__eq__diff__eq, tcon_Int_Oint___Groups_Ocancel__comm__monoid__add, tcon_Nat_Onat___Groups_Ocomm__monoid__add_16, fact_40_Sup__apply, fact_245_diff__strict__right__mono, fact_64_in__sets__Sup, fact_73_Int__Diff, fact_31_IntI, fact_144_translation__Int, fact_83_UN__extend__simps_I6_J, fact_27_diff__numeral__special_I9_J, fact_126_surjD, fact_25_Sup__eq__top__iff, tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__semigroup__add_69, fact_13_of__int__vec__eq__iff, fact_244_diff__strict__left__mono, tcon_Set_Oset___Groups_Ozero_31, fact_51_UN__ball__bex__simps_I4_J, tcon_Finite__Cartesian__Product_Ovec___Groups_Ozero_81, fact_130_Int__UNIV__left, fact_131_Union__UNIV, fact_180_add__cancel__left__left, tcon_Real_Oreal___Groups_Ostrict__ordered__ab__semigroup__add_38, fact_153_UN__extend__simps_I10_J, fact_188_zero__diff, fact_204_DiffE, fact_9__092_060open_062_I_092_060lambda_062n_O_Aemeasure_Alebesgue_A_IT_A_If_An_J_J_J_Asums_Aemeasure_Alebesgue_A_I_092_060Union_062n_O_AT_A_If_An_J_J_092_060close_062, fact_152_image__UN, fact_37_vimage__eq, tcon_Extended__Nonnegative__Real_Oennreal___Complete__Lattices_OSup_90, fact_159_SUP__UNION, fact_45_mem__Collect__eq, fact_24_Sup__UNIV, fact_230_comm__monoid__add__class_Oadd__0, tcon_Real_Oreal___Groups_Ocomm__monoid__add_49, fact_5_emeasure__T__Int, fact_87_rev__image__eqI, tcon_Real_Oreal___Groups_Oordered__cancel__ab__semigroup__add_39, fact_231_add_Ocomm__neutral, tcon_Set_Oset___Countable_Ocountable_28, fact_211_zero__reorient, fact_104_UnionE, fact_177_add_Oright__neutral, fact_68_top__set__def, tcon_Int_Oint___Groups_Oordered__ab__semigroup__add, fact_77_null__sets_Osets__Collect__conj, fact_125_surjE, tcon_Extended__Nonnegative__Real_Oennreal___Rings_Olinordered__nonzero__semiring_86, fact_21__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_A_092_060Longrightarrow_062_A_I_092_060lambda_062x_O_Ax_A_L_Aof__int__vec_Aa_J_A_N_096_AT_Aa_A_092_060inter_062_Aspace_Alebesgue_A_092_060in_062_Asets_Alebesgue_092_060close_062, fact_8__092_060open_062_092_060And_062a_O_AR_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062, tcon_Int_Oint___Countable_Ocountable_5, tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_44, tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__cancel__ab__semigroup__add_63, tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_40, tcon_Nat_Onat___Groups_Oone_22, fact_148_null__setsD1, tcon_Int_Oint___Groups_Ocomm__monoid__add, tcon_fun___Complete__Lattices_OSup, fact_59_S__decompose, tcon_Extended__Nonnegative__Real_Oennreal___Groups_Oab__semigroup__add_88, fact_194_diff__add__cancel, fact_98_Int__commute, fact_84_emeasure__Diff__null__set, tcon_Extended__Nonnegative__Real_Oennreal___Groups_Oordered__ab__semigroup__add_87, tcon_Int_Oint___Groups_Ocancel__ab__semigroup__add, fact_238_add__strict__left__mono, fact_170_add__left__cancel, tcon_Real_Oreal___Groups_Ogroup__add_54, tcon_Nat_Onat___Countable_Ocountable_19, tcon_Finite__Cartesian__Product_Ovec___Groups_Osemigroup__add_73, fact_178_double__zero, fact_18_SUP__eq__top__iff, tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_45, tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_33, fact_65_sets__SUP__cong, fact_136_rangeE, fact_49_bex__UN, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le_9, tcon_Int_Oint___Groups_Ogroup__add, fact_20_image__vimage__eq, fact_155_Int__UN__distrib, fact_47_Collect__cong, tcon_Finite__Cartesian__Product_Ovec___Ordered__Euclidean__Space_Oordered__euclidean__space, tcon_Sigma__Algebra_Omeasure___Complete__Lattices_OSup_60, fact_150_SUP__lessD, fact_200_sets_Otop, fact_175_not__gr__zero, fact_248_eq__diff__eq, fact_10_T_H__def, tcon_Finite__Cartesian__Product_Ovec___Finite__Set_Ofinite_77, tcon_Real_Oreal___Groups_Ozero_57, fact_30_Int__iff, tcon_Int_Oint___Num_Oneg__numeral, tcon_Extended__Nonnegative__Real_Oennreal___Groups_Ozero_93, fact_247_diff__eq__eq, fact_190_cancel__comm__monoid__add__class_Odiff__cancel, tcon_Extended__Nonnegative__Real_Oennreal___Complete__Lattices_Ocomplete__linorder, fact_81_Int__Union, tcon_Finite__Cartesian__Product_Ovec___Groups_Ogroup__add_78, fact_186_diff__self, fact_93_is__num__normalize_I1_J, fact_110_Inf_OINF__identity__eq, fact_107_vimageE, fact_172_DiffI, tcon_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le, fact_189_diff__zero, tcon_Int_Oint___Groups_Olinordered__ab__group__add, fact_3_calculation, fact_106_vimageI2, fact_217_add_Oleft__cancel, tcon_Int_Oint___Rings_Oring__1_3, tcon_Finite__Cartesian__Product_Ovec___Num_Oneg__numeral_79, fact_193_add__diff__cancel, fact_181_add__cancel__left__right, tcon_HOL_Obool___Countable_Ocountable_35, fact_221_add__left__imp__eq, fact_168_less__add__same__cancel1, fact_118_vimage__def, fact_205_DiffD1, fact_70_Diff__Int__distrib, fact_32_Union__iff, fact_80_Int__Union2, fact_66_Sup__set__def, fact_115_Collect__conj__eq, fact_43_Int__UNIV, fact_34_UN__ball__bex__simps_I1_J, tcon_Finite__Cartesian__Product_Ovec___Complete__Lattices_OSup_72, tcon_Nat_Onat___Groups_Ocancel__semigroup__add_14, tcon_Int_Oint___Complete__Lattices_OSup_4, fact_41_vimage__Collect__eq, tcon_Real_Oreal___Nat_Oring__char__0_56, fact_229_zero__less__iff__neq__zero, tcon_Extended__Nonnegative__Real_Oennreal___Groups_Ostrict__ordered__ab__semigroup__add_83, tcon_Nat_Onat___Groups_Osemigroup__add_18, tcon_fun___Complete__Lattices_Ocomplete__lattice, fact_36_null__sets_ODiff, fact_99_Int__absorb, fact_236_add__mono__thms__linordered__field_I1_J, tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add_8, subcl_Finite__Set_Ofinite___HOL_Otype, fact_135_range__composition, tcon_Finite__Cartesian__Product_Ovec___Groups_Oone_82, fact_198_add__diff__cancel__right_H, fact_187_diff__0__right, fact_12_T_H__altdef, fact_176_add_Oleft__neutral, fact_56_SUP__apply, fact_251_diff__add__eq, fact_97_Int__left__absorb, fact_220_add_Oleft__commute, fact_71_Diff__Diff__Int, fact_109_Sup_OSUP__identity__eq, fact_140_UN__E, fact_129_Int__UNIV__right, tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_13, tcon_Real_Oreal___Groups_Oab__group__add_52, fact_214_group__cancel_Oadd1, fact_215_group__cancel_Oadd2, fact_127_less__Sup__iff, fact_2__092_060open_062_092_060And_062a_O_AT_Aa_A_092_060in_062_Asets_Alebesgue_092_060close_062, fact_138_image__Union, fact_151_translation__subtract__Int, fact_122_surj__def, fact_154_Int__UN__distrib2, fact_100_Int__assoc, fact_128_SUP__cong, fact_162_sets_OInt__space__eq1, fact_228_gr__implies__not__zero, fact_149_less__SUP__iff, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_11, fact_17_null__sets__UN, tcon_Real_Oreal___Rings_Oring__1_2, fact_75_Sup__fun__def, tcon_Set_Oset___Complete__Lattices_OSup_26, fact_233_eq__iff__diff__eq__0, tcon_Finite__Cartesian__Product_Ovec___Groups_Ostrict__ordered__ab__semigroup__add_62, tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le_37, fact_60_image__add__0, tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_10, fact_55_SUP__identity__eq, fact_44_ball__UN, fact_53_null__sets_OInt, fact_89_image__cong, tcon_Real_Oreal___Groups_Oone_58, tcon_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, tcon_Set_Oset___Groups_Ocomm__monoid__add_25, fact_82_vimage__Union, fact_213_add__mono__thms__linordered__semiring_I4_J, tcon_Nat_Onat___Groups_Omonoid__add_20, fact_16_sums__emeasure_H, fact_14_T__def, tcon_Finite__Cartesian__Product_Ovec___Groups_Oordered__ab__group__add_68, fact_38_vimageI, tcon_Extended__Nonnegative__Real_Oennreal___Groups_Ocanonically__ordered__monoid__add_84, tcon_Extended__Nonnegative__Real_Oennreal___Groups_Ocomm__monoid__add_89, tcon_Finite__Cartesian__Product_Ovec___Countable_Ocountable_75, fact_105_vimage__Collect, tcon_Set_Oset___Groups_Oab__semigroup__add_24, fact_117_Int__def, tcon_Finite__Cartesian__Product_Ovec___Groups_Ocancel__ab__semigroup__add_66, fact_52_vimage__UNIV, fact_94_UNIV__witness, fact_246_group__cancel_Osub1, tcon_Int_Oint___Groups_Oone, fact_7_assms_I2_J, fact_23__092_060open_062_092_060Union_062_A_Irange_AT_J_A_061_A_I_092_060Union_062n_O_AT_A_If_An_J_J_092_060close_062, fact_239_add__strict__right__mono, fact_212_ab__semigroup__add__class_Oadd__ac_I1_J, tcon_Int_Oint___Rings_Olinordered__nonzero__semiring, fact_79_null__set__Diff, fact_166_double__add__less__zero__iff__single__add__less__zero, fact_210_Sup__bool__def, tcon_Set_Oset___Finite__Set_Ofinite_30, tcon_HOL_Obool___Finite__Set_Ofinite_36, tcon_Finite__Cartesian__Product_Ovec___Nat_Oring__char__0_80, fact_192_add__less__cancel__right, tcon_Finite__Cartesian__Product_Ovec___Rings_Oring__1, fact_224_diff__right__commute, tcon_Set_Oset___Groups_Omonoid__add_29, fact_69_Diff__Int__distrib2, fact_26_surj__plus
% 66.27/25.16 % No. of inferences in proof: 791
% 66.27/25.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 24800 ms resp. 24023 ms w/o parsing
% 52.48/25.43 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 52.48/25.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------