%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP149^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:57 AM UTC 2026
% Result : Theorem 135.78s 45.10s
% Output : Refutation 126.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 342
% Syntax : Number of formulae : 1124 ( 582 unt; 0 typ; 4 def)
% Number of atoms : 2953 (1159 equ; 14 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 9192 ( 685 ~; 347 |; 135 &;7455 @)
% ( 0 <=>; 570 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 63 usr; 17 con; 0-5 aty)
% Number of variables : 2054 ( 233 ^;1792 !; 25 ?;2054 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bounde7994401a_real_type,type,
bounde7994401a_real: $tType ).
thf(set_set_real_type,type,
set_set_real: $tType ).
thf(set_set_a_type,type,
set_set_a: $tType ).
thf(set_real_type,type,
set_real: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(real_type,type,
real: $tType ).
thf(a_type,type,
a: $tType ).
thf(elemen1140313242l_real_decl,type,
elemen1140313242l_real: real > real > set_real ).
thf(elemen49976720ball_a_decl,type,
elemen49976720ball_a: a > real > set_a ).
thf(auto_l612940ivl0_a_decl,type,
auto_l612940ivl0_a: ( a > a ) > set_a > a > set_real ).
thf(minus_minus_real_decl,type,
minus_minus_real: real > real > real ).
thf(minus_minus_set_real_decl,type,
minus_minus_set_real: set_real > set_real > set_real ).
thf(minus_minus_set_a_decl,type,
minus_minus_set_a: set_a > set_a > set_a ).
thf(minus_minus_a_decl,type,
minus_minus_a: a > a > a ).
thf(uminus_uminus_a_a_decl,type,
uminus_uminus_a_a: ( a > a ) > a > a ).
thf(uminus_uminus_real_decl,type,
uminus_uminus_real: real > real ).
thf(uminus_uminus_set_a_decl,type,
uminus_uminus_set_a: set_a > set_a ).
thf(uminus_uminus_a_decl,type,
uminus_uminus_a: a > a ).
thf(zero_zero_real_decl,type,
zero_zero_real: real ).
thf(zero_zero_a_decl,type,
zero_zero_a: a ).
thf(initia826609931terval_decl,type,
initia826609931terval: set_real > $o ).
thf(inner_4346926r_real_decl,type,
inner_4346926r_real: real > real > real ).
thf(inner_1173012732nner_a_decl,type,
inner_1173012732nner_a: a > a > real ).
thf(auto_l630715367iant_a_decl,type,
auto_l630715367iant_a: ( a > a ) > set_a > set_a > $o ).
thf(line_c1152468841ment_a_decl,type,
line_c1152468841ment_a: a > a > set_a ).
thf(line_open_segment_a_decl,type,
line_open_segment_a: a > a > set_a ).
thf(oDE_au1996717075pped_a_decl,type,
oDE_au1996717075pped_a: ( a > a ) > set_a > a > set_a > $o ).
thf(ord_less_real_decl,type,
ord_less_real: real > real > $o ).
thf(ord_less_set_real_decl,type,
ord_less_set_real: set_real > set_real > $o ).
thf(ord_le861030508t_real_decl,type,
ord_le861030508t_real: set_set_real > set_set_real > $o ).
thf(ord_less_set_set_a_decl,type,
ord_less_set_set_a: set_set_a > set_set_a > $o ).
thf(ord_less_set_a_decl,type,
ord_less_set_a: set_a > set_a > $o ).
thf(ord_less_a_decl,type,
ord_less_a: a > a > $o ).
thf(ord_less_eq_real_decl,type,
ord_less_eq_real: real > real > $o ).
thf(ord_less_eq_set_real_decl,type,
ord_less_eq_set_real: set_real > set_real > $o ).
thf(ord_le1733505144t_real_decl,type,
ord_le1733505144t_real: set_set_real > set_set_real > $o ).
thf(ord_le318720350_set_a_decl,type,
ord_le318720350_set_a: set_set_a > set_set_a > $o ).
thf(ord_less_eq_set_a_decl,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(ord_less_eq_a_decl,type,
ord_less_eq_a: a > a > $o ).
thf(top_top_set_real_decl,type,
top_top_set_real: set_real ).
thf(top_top_set_a_decl,type,
top_top_set_a: set_a ).
thf(period720806154rbit_a_decl,type,
period720806154rbit_a: ( a > a ) > set_a > a > $o ).
thf(period1305449585riod_a_decl,type,
period1305449585riod_a: ( a > a ) > set_a > a > real ).
thf(period138238489rbit_a_decl,type,
period138238489rbit_a: ( a > a ) > set_a > a > $o ).
thf(poinca659159244_rot_a_decl,type,
poinca659159244_rot_a: a > a ).
thf(poinca522724647ment_a_decl,type,
poinca522724647ment_a: ( a > a ) > set_a > a > a > $o ).
thf(reacha1191408304tion_a_decl,type,
reacha1191408304tion_a: ( a > a ) > set_a > ( a > real ) > ( a > bounde7994401a_real ) > set_a > $o ).
thf(real_V1934908667t_real_decl,type,
real_V1934908667t_real: real > real > real ).
thf(real_V1514887919dist_a_decl,type,
real_V1514887919dist_a: a > a > real ).
thf(collect_real_decl,type,
collect_real: ( real > $o ) > set_real ).
thf(collect_a_decl,type,
collect_a: ( a > $o ) > set_a ).
thf(set_or656347191t_real_decl,type,
set_or656347191t_real: real > real > set_real ).
thf(set_or1619725421t_real_decl,type,
set_or1619725421t_real: set_real > set_real > set_set_real ).
thf(set_or2094724627_set_a_decl,type,
set_or2094724627_set_a: set_a > set_a > set_set_a ).
thf(set_or411607219Most_a_decl,type,
set_or411607219Most_a: a > a > set_a ).
thf(member_real_decl,type,
member_real: real > set_real > $o ).
thf(member_a_decl,type,
member_a: a > set_a > $o ).
thf(x_decl,type,
x: set_a ).
thf(a2_decl,type,
a2: a ).
thf(b_decl,type,
b: a ).
thf(d_decl,type,
d: real ).
thf(f_decl,type,
f: a > a ).
thf(s_decl,type,
s: a ).
thf(thesis_decl,type,
thesis: $o ).
thf(x2_decl,type,
x2: a ).
thf(z_decl,type,
z: a ).
thf(sk1_decl,type,
sk1: real > real > a ).
thf(sk2_decl,type,
sk2: set_real > set_real > real ).
thf(sk10_decl,type,
sk10: a ).
thf(sk11_decl,type,
sk11: real ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: real,B: real] :
@+[C: a] :
~ ( ( member_a @ C @ ( elemen49976720ball_a @ x2 @ B ) )
=> ( ord_less_eq_real @ A @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: set_real,B: set_real] :
@+[C: real] :
~ ( ( member_real @ C @ B )
=> ( member_real @ C @ A ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: a] :
~ ( ( member_a @ A @ ( elemen49976720ball_a @ x2 @ d ) )
=> ~ ! [B: a] :
( ( member_a @ B @ ( elemen49976720ball_a @ x2 @ d ) )
=> ( ord_less_eq_real @ ( inner_1173012732nner_a @ ( f @ A ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) @ ( inner_1173012732nner_a @ ( f @ B ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: real] :
~ ( ( ord_less_real @ zero_zero_real @ A )
=> ~ ! [B: a] :
( ( member_a @ B @ ( elemen49976720ball_a @ x2 @ A ) )
=> ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ B ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
& ( member_a @ B @ x )
& ( ( f @ B )
!= zero_zero_a ) ) ) ) ) ) ).
thf(106,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ B ) @ ( uminus_uminus_set_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_Compl__anti__mono) ).
thf(645,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ B ) @ ( uminus_uminus_set_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(162,axiom,
! [A: real,B: real,C: a] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( member_a @ C @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_rev_Ogeneral_Omem__existence__ivl__iv__defined_I2_J) ).
thf(809,plain,
! [A: real,B: real,C: a] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( member_a @ C @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(70,axiom,
( uminus_uminus_a_a
= ( ^ [A: a > a,B: a] : ( uminus_uminus_a @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_uminus__apply) ).
thf(541,plain,
( uminus_uminus_a_a
= ( ^ [A: a > a,B: a] : ( uminus_uminus_a @ ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(542,plain,
( uminus_uminus_a_a
= ( ^ [A: a > a,B: a] : ( uminus_uminus_a @ ( A @ B ) ) ) ),
inference(lifteq,[status(thm)],[541]) ).
thf(1337,plain,
! [A: a > a] :
( ( uminus_uminus_a_a @ A )
= ( ^ [B: a] : ( uminus_uminus_a @ ( A @ B ) ) ) ),
inference(func_ext,[status(esa)],[542]) ).
thf(150,axiom,
( ord_less_a
= ( ^ [A: a,B: a] : ( ord_less_a @ ( minus_minus_a @ A @ B ) @ zero_zero_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_less__iff__diff__less__0) ).
thf(779,plain,
( ord_less_a
= ( ^ [A: a,B: a] : ( ord_less_a @ ( minus_minus_a @ A @ B ) @ zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(780,plain,
( ( ^ [A: a,B: a] : ( ord_less_a @ ( minus_minus_a @ A @ B ) @ zero_zero_a ) )
= ord_less_a ),
inference(lifteq,[status(thm)],[779]) ).
thf(1411,plain,
! [A: a] :
( ( ^ [B: a] : ( ord_less_a @ ( minus_minus_a @ A @ B ) @ zero_zero_a ) )
= ( ord_less_a @ A ) ),
inference(func_ext,[status(esa)],[780]) ).
thf(143,axiom,
! [A: real,B: real,C: a] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( member_real @ B @ top_top_set_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_general_Omem__existence__ivl__iv__defined_I1_J) ).
thf(760,plain,
! [A: real,B: real,C: a] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( member_real @ B @ top_top_set_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(308,axiom,
! [A: a,B: a] :
( ( inner_1173012732nner_a @ ( uminus_uminus_a @ A ) @ B )
= ( uminus_uminus_real @ ( inner_1173012732nner_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_inner__minus__left) ).
thf(1237,plain,
! [A: a,B: a] :
( ( inner_1173012732nner_a @ ( uminus_uminus_a @ A ) @ B )
= ( uminus_uminus_real @ ( inner_1173012732nner_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(252,axiom,
member_a @ x2 @ ( line_c1152468841ment_a @ a2 @ b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12__092_060open_062x_A_092_060in_062_A_123a_N_Nb_125_092_060close_062) ).
thf(1083,plain,
member_a @ x2 @ ( line_c1152468841ment_a @ a2 @ b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(149,axiom,
! [A: a] :
( ( period138238489rbit_a @ f @ x @ A )
=> ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ f @ x @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_periodic__orbit__period_I1_J) ).
thf(777,plain,
! [A: a] :
( ( period138238489rbit_a @ f @ x @ A )
=> ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ f @ x @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(262,axiom,
( ord_less_real
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ~ ( ord_less_eq_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_eucl__less__le__not__le) ).
thf(1110,plain,
( ord_less_real
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ~ ( ord_less_eq_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(50,axiom,
( real_V1514887919dist_a
= ( ^ [A: a,B: a] : ( real_V1514887919dist_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_dist__commute) ).
thf(481,plain,
( real_V1514887919dist_a
= ( ^ [A: a,B: a] : ( real_V1514887919dist_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(9,axiom,
! [A: real,B: set_real,C: set_real] :
( ( member_real @ A @ ( minus_minus_set_real @ B @ C ) )
= ( ( member_real @ A @ B )
& ~ ( member_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_Diff__iff) ).
thf(363,plain,
! [A: real,B: set_real,C: set_real] :
( ( member_real @ A @ ( minus_minus_set_real @ B @ C ) )
= ( ( member_real @ A @ B )
& ~ ( member_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(364,plain,
! [C: set_real,B: set_real,A: real] :
( ( member_real @ A @ ( minus_minus_set_real @ B @ C ) )
= ( ( member_real @ A @ B )
& ~ ( member_real @ A @ C ) ) ),
inference(cnf,[status(esa)],[363]) ).
thf(365,plain,
! [C: set_real,B: set_real,A: real] :
( ( member_real @ A @ ( minus_minus_set_real @ B @ C ) )
= ( ( member_real @ A @ B )
& ~ ( member_real @ A @ C ) ) ),
inference(lifteq,[status(thm)],[364]) ).
thf(291,axiom,
! [A: real] :
( ( ( uminus_uminus_real @ A )
= A )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_neg__equal__zero) ).
thf(1190,plain,
! [A: real] :
( ( ( uminus_uminus_real @ A )
= A )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(49,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ B ) @ ( uminus_uminus_set_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_compl__mono) ).
thf(479,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ B ) @ ( uminus_uminus_set_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(259,axiom,
! [A: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ f @ x @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_mvar_Ointerval__axioms) ).
thf(1104,plain,
! [A: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ f @ x @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(1105,plain,
! [A: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ f @ x @ A ) ),
inference(cnf,[status(esa)],[1104]) ).
thf(194,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
= ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_minus__le__iff) ).
thf(909,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
= ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(233,axiom,
! [A: a,B: a,C: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ( ord_less_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) @ zero_zero_real )
=> ! [D: a] :
( ( member_a @ D @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ord_less_real @ ( inner_1173012732nner_a @ ( f @ D ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) @ zero_zero_real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_transversal__segment__neg) ).
thf(1031,plain,
! [A: a,B: a,C: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ( ord_less_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) @ zero_zero_real )
=> ! [D: a] :
( ( member_a @ D @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ord_less_real @ ( inner_1173012732nner_a @ ( f @ D ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) @ zero_zero_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(213,axiom,
! [A: a,B: a] :
( ( ord_less_a @ zero_zero_a @ ( minus_minus_a @ A @ B ) )
= ( ord_less_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_diff__gt__0__iff__gt) ).
thf(977,plain,
! [A: a,B: a] :
( ( ord_less_a @ zero_zero_a @ ( minus_minus_a @ A @ B ) )
= ( ord_less_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(168,axiom,
~ ! [A: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ~ ! [B: a] :
( ( member_a @ B @ ( elemen49976720ball_a @ x2 @ A ) )
=> ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ B ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
& ( member_a @ B @ x )
& ( ( f @ B )
!= zero_zero_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_O_A_092_060lbrakk_0620_A_060_Ad_059_A_092_060And_062y_O_Ay_A_092_060in_062_Acball_Ax_Ad_A_092_060Longrightarrow_062_A0_A_060_Af_Ay_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_A_092_060and_062_Ay_A_092_060in_062_AX_A_092_060and_062_Af_Ay_A_092_060noteq_062_A_I0_058_058_Ha_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(827,plain,
~ ! [A: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ~ ! [B: a] :
( ( member_a @ B @ ( elemen49976720ball_a @ x2 @ A ) )
=> ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ B ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
& ( member_a @ B @ x )
& ( ( f @ B )
!= zero_zero_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(828,plain,
~ ! [A: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ~ ! [B: a] :
( ( member_a @ B @ ( elemen49976720ball_a @ x2 @ A ) )
=> ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ B ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
& ( member_a @ B @ x )
& ( ( f @ B )
!= zero_zero_a ) ) ) ),
inference(polarity_switch,[status(thm)],[827]) ).
thf(829,plain,
! [A: a] :
( ( ord_less_real @ zero_zero_real @ sk11 )
& ( ~ ( member_a @ A @ ( elemen49976720ball_a @ x2 @ sk11 ) )
| ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ A ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) )
& ( ~ ( member_a @ A @ ( elemen49976720ball_a @ x2 @ sk11 ) )
| ( member_a @ A @ x ) )
& ( ~ ( member_a @ A @ ( elemen49976720ball_a @ x2 @ sk11 ) )
| ( ( f @ A )
!= zero_zero_a ) ) ),
inference(cnf,[status(esa)],[828]) ).
thf(830,plain,
ord_less_real @ zero_zero_real @ sk11,
inference(cnfConj,[status(thm)],[829]) ).
thf(1,conjecture,
? [A: real] :
( ( ord_less_real @ zero_zero_real @ A )
& ? [B: real] :
( ( ord_less_real @ zero_zero_real @ B )
& ! [C: a] :
( ( member_a @ C @ ( elemen49976720ball_a @ x2 @ A ) )
=> ( ord_less_eq_real @ B @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: real] :
( ( ord_less_real @ zero_zero_real @ A )
& ? [B: real] :
( ( ord_less_real @ zero_zero_real @ B )
& ! [C: a] :
( ( member_a @ C @ ( elemen49976720ball_a @ x2 @ A ) )
=> ( ord_less_eq_real @ B @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(340,plain,
~ ? [A: real] :
( ( ord_less_real @ zero_zero_real @ A )
& ? [B: real] :
( ( ord_less_real @ zero_zero_real @ B )
& ! [C: a] :
( ( member_a @ C @ ( elemen49976720ball_a @ x2 @ A ) )
=> ( ord_less_eq_real @ B @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(341,plain,
! [B: real,A: real] :
( ( ~ ( ord_less_real @ zero_zero_real @ A )
| ~ ( ord_less_real @ zero_zero_real @ B )
| ( member_a @ ( sk1 @ B @ A ) @ ( elemen49976720ball_a @ x2 @ A ) ) )
& ( ~ ( ord_less_real @ zero_zero_real @ A )
| ~ ( ord_less_real @ zero_zero_real @ B )
| ~ ( ord_less_eq_real @ B @ ( inner_1173012732nner_a @ ( f @ ( sk1 @ B @ A ) ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ) ),
inference(cnf,[status(esa)],[340]) ).
thf(342,plain,
! [B: real,A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ~ ( ord_less_real @ zero_zero_real @ B )
| ( member_a @ ( sk1 @ B @ A ) @ ( elemen49976720ball_a @ x2 @ A ) ) ),
inference(cnfConj,[status(thm)],[341]) ).
thf(1361,plain,
! [B: real,A: real] :
( ~ $true
| ~ ( ord_less_real @ zero_zero_real @ B )
| ( member_a @ ( sk1 @ B @ A ) @ ( elemen49976720ball_a @ x2 @ A ) )
| ( ( ord_less_real @ zero_zero_real @ sk11 )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[830,342]) ).
thf(1362,plain,
! [B: real,A: real] :
( ~ ( ord_less_real @ zero_zero_real @ B )
| ( member_a @ ( sk1 @ B @ A ) @ ( elemen49976720ball_a @ x2 @ A ) )
| ( ( ord_less_real @ zero_zero_real @ sk11 )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(simp,[status(thm)],[1361]) ).
thf(1363,plain,
! [A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ( member_a @ ( sk1 @ A @ sk11 ) @ ( elemen49976720ball_a @ x2 @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[1362:[bind(A,$thf( sk11 ))]]) ).
thf(1367,plain,
! [A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ( member_a @ ( sk1 @ A @ sk11 ) @ ( elemen49976720ball_a @ x2 @ sk11 ) ) ),
inference(simp,[status(thm)],[1363]) ).
thf(1404,plain,
! [A: real] :
( ~ $true
| ( member_a @ ( sk1 @ A @ sk11 ) @ ( elemen49976720ball_a @ x2 @ sk11 ) )
| ( ( ord_less_real @ zero_zero_real @ sk11 )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[830,1367]) ).
thf(1405,plain,
! [A: real] :
( ( member_a @ ( sk1 @ A @ sk11 ) @ ( elemen49976720ball_a @ x2 @ sk11 ) )
| ( ( ord_less_real @ zero_zero_real @ sk11 )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(simp,[status(thm)],[1404]) ).
thf(1406,plain,
member_a @ ( sk1 @ sk11 @ sk11 ) @ ( elemen49976720ball_a @ x2 @ sk11 ),
inference(pattern_uni,[status(thm)],[1405:[bind(A,$thf( sk11 ))]]) ).
thf(167,axiom,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
= ( ord_less_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_neg__0__less__iff__less) ).
thf(824,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
= ( ord_less_real @ A @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(825,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
= ( ord_less_real @ A @ zero_zero_real ) ),
inference(cnf,[status(esa)],[824]) ).
thf(826,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
= ( ord_less_real @ A @ zero_zero_real ) ),
inference(lifteq,[status(thm)],[825]) ).
thf(833,plain,
! [A: a] :
( ~ ( member_a @ A @ ( elemen49976720ball_a @ x2 @ sk11 ) )
| ( ( f @ A )
!= zero_zero_a ) ),
inference(cnfConj,[status(thm)],[829]) ).
thf(834,plain,
! [A: a] :
( ( ( f @ A )
!= zero_zero_a )
| ~ ( member_a @ A @ ( elemen49976720ball_a @ x2 @ sk11 ) ) ),
inference(lifteq,[status(thm)],[833]) ).
thf(1417,plain,
! [B: a,A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ( ( f @ B )
!= zero_zero_a )
| ~ $true
| ( ( member_a @ ( sk1 @ A @ sk11 ) @ ( elemen49976720ball_a @ x2 @ sk11 ) )
!= ( member_a @ B @ ( elemen49976720ball_a @ x2 @ sk11 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1367,834]) ).
thf(1418,plain,
! [B: a,A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ( ( f @ B )
!= zero_zero_a )
| ( ( member_a @ ( sk1 @ A @ sk11 ) @ ( elemen49976720ball_a @ x2 @ sk11 ) )
!= ( member_a @ B @ ( elemen49976720ball_a @ x2 @ sk11 ) ) ) ),
inference(simp,[status(thm)],[1417]) ).
thf(1419,plain,
! [A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ( ( f @ ( sk1 @ A @ sk11 ) )
!= zero_zero_a ) ),
inference(pattern_uni,[status(thm)],[1418:[bind(A,$thf( C )),bind(B,$thf( sk1 @ C @ sk11 ))]]) ).
thf(1438,plain,
! [A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ( ( f @ ( sk1 @ A @ sk11 ) )
!= zero_zero_a ) ),
inference(simp,[status(thm)],[1419]) ).
thf(4251,plain,
! [B: real,A: real] :
( ~ ( ord_less_real @ A @ zero_zero_real )
| ( ( f @ ( sk1 @ B @ sk11 ) )
!= zero_zero_a )
| ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
!= ( ord_less_real @ zero_zero_real @ B ) ) ),
inference(paramod_ordered,[status(thm)],[826,1438]) ).
thf(4252,plain,
! [A: real] :
( ~ ( ord_less_real @ A @ zero_zero_real )
| ( ( f @ ( sk1 @ ( uminus_uminus_real @ A ) @ sk11 ) )
!= zero_zero_a ) ),
inference(pattern_uni,[status(thm)],[4251:[bind(A,$thf( C )),bind(B,$thf( uminus_uminus_real @ C ))]]) ).
thf(4339,plain,
! [A: real] :
( ~ ( ord_less_real @ A @ zero_zero_real )
| ( ( f @ ( sk1 @ ( uminus_uminus_real @ A ) @ sk11 ) )
!= zero_zero_a ) ),
inference(simp,[status(thm)],[4252]) ).
thf(141,axiom,
ord_less_real @ zero_zero_real @ d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_d_I1_J) ).
thf(756,plain,
ord_less_real @ zero_zero_real @ d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(1401,plain,
! [A: real] :
( ~ $true
| ( member_a @ ( sk1 @ A @ sk11 ) @ ( elemen49976720ball_a @ x2 @ sk11 ) )
| ( ( ord_less_real @ zero_zero_real @ d )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[756,1367]) ).
thf(1402,plain,
! [A: real] :
( ( member_a @ ( sk1 @ A @ sk11 ) @ ( elemen49976720ball_a @ x2 @ sk11 ) )
| ( ( ord_less_real @ zero_zero_real @ d )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(simp,[status(thm)],[1401]) ).
thf(1403,plain,
member_a @ ( sk1 @ d @ sk11 ) @ ( elemen49976720ball_a @ x2 @ sk11 ),
inference(pattern_uni,[status(thm)],[1402:[bind(A,$thf( d ))]]) ).
thf(1441,plain,
! [A: a] :
( ( ( f @ A )
!= zero_zero_a )
| ~ $true
| ( ( member_a @ ( sk1 @ d @ sk11 ) @ ( elemen49976720ball_a @ x2 @ sk11 ) )
!= ( member_a @ A @ ( elemen49976720ball_a @ x2 @ sk11 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1403,834]) ).
thf(1442,plain,
! [A: a] :
( ( ( f @ A )
!= zero_zero_a )
| ( ( member_a @ ( sk1 @ d @ sk11 ) @ ( elemen49976720ball_a @ x2 @ sk11 ) )
!= ( member_a @ A @ ( elemen49976720ball_a @ x2 @ sk11 ) ) ) ),
inference(simp,[status(thm)],[1441]) ).
thf(1443,plain,
( ( f @ ( sk1 @ d @ sk11 ) )
!= zero_zero_a ),
inference(pattern_uni,[status(thm)],[1442:[bind(A,$thf( sk1 @ d @ sk11 ))]]) ).
thf(219,axiom,
! [A: a] :
( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ( ord_less_eq_real @ zero_zero_real @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_rev_Oclosed__orbit__period__nonneg) ).
thf(994,plain,
! [A: a] :
( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ( ord_less_eq_real @ zero_zero_real @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(296,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( ord_less_real @ A @ B )
= ( ord_less_real @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_diff__eq__diff__less) ).
thf(1205,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( ord_less_real @ A @ B )
= ( ord_less_real @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(15,axiom,
! [A: set_real,B: set_real] :
( ! [C: real] :
( ( member_real @ C @ A )
=> ( member_real @ C @ B ) )
=> ( ord_less_eq_set_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_subsetI) ).
thf(379,plain,
! [A: set_real,B: set_real] :
( ! [C: real] :
( ( member_real @ C @ A )
=> ( member_real @ C @ B ) )
=> ( ord_less_eq_set_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(36,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_subset__trans) ).
thf(440,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(297,axiom,
ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_direction_I2_J) ).
thf(1208,plain,
ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(1347,plain,
! [B: real,A: real] :
( ~ $true
| ~ ( ord_less_real @ zero_zero_real @ B )
| ( member_a @ ( sk1 @ B @ A ) @ ( elemen49976720ball_a @ x2 @ A ) )
| ( ( ord_less_real @ zero_zero_real @ d )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[756,342]) ).
thf(1348,plain,
! [B: real,A: real] :
( ~ ( ord_less_real @ zero_zero_real @ B )
| ( member_a @ ( sk1 @ B @ A ) @ ( elemen49976720ball_a @ x2 @ A ) )
| ( ( ord_less_real @ zero_zero_real @ d )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(simp,[status(thm)],[1347]) ).
thf(1349,plain,
! [A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ( member_a @ ( sk1 @ A @ d ) @ ( elemen49976720ball_a @ x2 @ d ) ) ),
inference(pattern_uni,[status(thm)],[1348:[bind(A,$thf( d ))]]) ).
thf(1353,plain,
! [A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ( member_a @ ( sk1 @ A @ d ) @ ( elemen49976720ball_a @ x2 @ d ) ) ),
inference(simp,[status(thm)],[1349]) ).
thf(1969,plain,
! [A: real] :
( ~ $true
| ( member_a @ ( sk1 @ A @ d ) @ ( elemen49976720ball_a @ x2 @ d ) )
| ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1208,1353]) ).
thf(1970,plain,
! [A: real] :
( ( member_a @ ( sk1 @ A @ d ) @ ( elemen49976720ball_a @ x2 @ d ) )
| ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(simp,[status(thm)],[1969]) ).
thf(1971,plain,
member_a @ ( sk1 @ ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) @ d ) @ ( elemen49976720ball_a @ x2 @ d ),
inference(pattern_uni,[status(thm)],[1970:[bind(A,$thf( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ))]]) ).
thf(116,axiom,
! [A: a] :
( ( member_a @ A @ ( line_c1152468841ment_a @ a2 @ b ) )
=> ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ A ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69__092_060open_062_092_060And_062z_O_Az_A_092_060in_062_A_123a_N_Nb_125_A_092_060Longrightarrow_062_A0_A_060_Af_Az_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_092_060close_062) ).
thf(677,plain,
! [A: a] :
( ( member_a @ A @ ( line_c1152468841ment_a @ a2 @ b ) )
=> ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ A ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(89,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_subset__iff__psubset__eq) ).
thf(597,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(1379,plain,
! [A: real] :
( ~ $true
| ( member_a @ ( sk1 @ A @ d ) @ ( elemen49976720ball_a @ x2 @ d ) )
| ( ( ord_less_real @ zero_zero_real @ d )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[756,1353]) ).
thf(1380,plain,
! [A: real] :
( ( member_a @ ( sk1 @ A @ d ) @ ( elemen49976720ball_a @ x2 @ d ) )
| ( ( ord_less_real @ zero_zero_real @ d )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(simp,[status(thm)],[1379]) ).
thf(1381,plain,
member_a @ ( sk1 @ d @ d ) @ ( elemen49976720ball_a @ x2 @ d ),
inference(pattern_uni,[status(thm)],[1380:[bind(A,$thf( d ))]]) ).
thf(1415,plain,
! [A: a] :
( ( ( f @ A )
!= zero_zero_a )
| ~ $true
| ( ( member_a @ ( sk1 @ d @ d ) @ ( elemen49976720ball_a @ x2 @ d ) )
!= ( member_a @ A @ ( elemen49976720ball_a @ x2 @ sk11 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1381,834]) ).
thf(1416,plain,
! [A: a] :
( ( ( f @ A )
!= zero_zero_a )
| ( ( member_a @ ( sk1 @ d @ d ) @ ( elemen49976720ball_a @ x2 @ d ) )
!= ( member_a @ A @ ( elemen49976720ball_a @ x2 @ sk11 ) ) ) ),
inference(simp,[status(thm)],[1415]) ).
thf(1432,plain,
! [A: a] :
( ( ( f @ A )
!= zero_zero_a )
| ( ( sk1 @ d @ d )
!= A )
| ( ( elemen49976720ball_a @ x2 @ sk11 )
!= ( elemen49976720ball_a @ x2 @ d ) ) ),
inference(simp,[status(thm)],[1416]) ).
thf(1437,plain,
( ( ( f @ ( sk1 @ d @ d ) )
!= zero_zero_a )
| ( ( elemen49976720ball_a @ x2 @ sk11 )
!= ( elemen49976720ball_a @ x2 @ d ) ) ),
inference(simp,[status(thm)],[1432]) ).
thf(64,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_set__eq__subset) ).
thf(522,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(523,plain,
( ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) )
= ( (=) @ set_a ) ),
inference(lifteq,[status(thm)],[522]) ).
thf(199,axiom,
! [A: a] :
( ( real_V1514887919dist_a @ A @ A )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_dist__self) ).
thf(924,plain,
! [A: a] :
( ( real_V1514887919dist_a @ A @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(925,plain,
! [A: a] :
( ( real_V1514887919dist_a @ A @ A )
= zero_zero_real ),
inference(cnf,[status(esa)],[924]) ).
thf(926,plain,
! [A: a] :
( ( real_V1514887919dist_a @ A @ A )
= zero_zero_real ),
inference(lifteq,[status(thm)],[925]) ).
thf(171,axiom,
! [A: a,B: a] :
~ ( ord_less_real @ ( real_V1514887919dist_a @ A @ B ) @ zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_dist__not__less__zero) ).
thf(841,plain,
! [A: a,B: a] :
~ ( ord_less_real @ ( real_V1514887919dist_a @ A @ B ) @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(842,plain,
~ ? [A: a,B: a] : ( ord_less_real @ ( real_V1514887919dist_a @ A @ B ) @ zero_zero_real ),
inference(miniscope,[status(thm)],[841]) ).
thf(843,plain,
! [B: a,A: a] :
~ ( ord_less_real @ ( real_V1514887919dist_a @ A @ B ) @ zero_zero_real ),
inference(cnf,[status(esa)],[842]) ).
thf(4268,plain,
! [C: a,B: a,A: real] :
( ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
| ( ( ord_less_real @ A @ zero_zero_real )
!= ( ord_less_real @ ( real_V1514887919dist_a @ B @ C ) @ zero_zero_real ) ) ),
inference(paramod_ordered,[status(thm)],[826,843]) ).
thf(4269,plain,
! [B: a,A: a] :
~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( real_V1514887919dist_a @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[4268:[bind(A,$thf( real_V1514887919dist_a @ D @ E )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(4346,plain,
! [B: a,A: a] :
~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( real_V1514887919dist_a @ A @ B ) ) ),
inference(simp,[status(thm)],[4269]) ).
thf(4354,plain,
! [C: a,B: a,A: a] :
( ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ zero_zero_real ) )
| ( ( real_V1514887919dist_a @ A @ A )
!= ( real_V1514887919dist_a @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[926,4346]) ).
thf(4355,plain,
~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ zero_zero_real ) ),
inference(pattern_uni,[status(thm)],[4354:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(278,axiom,
( ( uminus_uminus_real @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_add_Oinverse__neutral) ).
thf(1151,plain,
( ( uminus_uminus_real @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(1152,plain,
( ( uminus_uminus_real @ zero_zero_real )
= zero_zero_real ),
inference(lifteq,[status(thm)],[1151]) ).
thf(4376,plain,
~ ( ord_less_real @ zero_zero_real @ zero_zero_real ),
inference(rewrite,[status(thm)],[4355,1152]) ).
thf(250,axiom,
! [A: real] :
( ( inner_4346926r_real @ zero_zero_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_inner__zero__left) ).
thf(1078,plain,
! [A: real] :
( ( inner_4346926r_real @ zero_zero_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(17,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_psubset__subset__trans) ).
thf(385,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(315,axiom,
! [A: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
= ( ord_less_eq_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_neg__0__le__iff__le) ).
thf(1260,plain,
! [A: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
= ( ord_less_eq_real @ A @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(201,axiom,
! [A: a,B: a,C: a,D: a] :
( ( member_a @ A @ ( set_or411607219Most_a @ B @ C ) )
=> ( ( ord_less_eq_a @ zero_zero_a @ D )
=> ( ord_less_eq_real @ ( inner_1173012732nner_a @ A @ D ) @ ( inner_1173012732nner_a @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_interval__inner__leI_I2_J) ).
thf(930,plain,
! [A: a,B: a,C: a,D: a] :
( ( member_a @ A @ ( set_or411607219Most_a @ B @ C ) )
=> ( ( ord_less_eq_a @ zero_zero_a @ D )
=> ( ord_less_eq_real @ ( inner_1173012732nner_a @ A @ D ) @ ( inner_1173012732nner_a @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(164,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
= ( ( member_a @ A @ B )
& ~ ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_Diff__iff) ).
thf(814,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
= ( ( member_a @ A @ B )
& ~ ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(338,axiom,
! [A: real,B: real,C: a] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( member_a @ C @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_general_Omem__existence__ivl__iv__defined_I2_J) ).
thf(1327,plain,
! [A: real,B: real,C: a] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( member_a @ C @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(293,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ C @ D )
=> ( ord_less_real @ ( minus_minus_real @ A @ D ) @ ( minus_minus_real @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_diff__strict__mono) ).
thf(1196,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ C @ D )
=> ( ord_less_real @ ( minus_minus_real @ A @ D ) @ ( minus_minus_real @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(222,axiom,
poinca522724647ment_a @ f @ x @ a2 @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_transversal) ).
thf(1001,plain,
poinca522724647ment_a @ f @ x @ a2 @ b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(4350,plain,
! [B: a,A: a] :
( ~ $true
| ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( real_V1514887919dist_a @ A @ B ) ) )
!= ( ord_less_real @ zero_zero_real @ d ) ) ),
inference(paramod_ordered,[status(thm)],[756,4346]) ).
thf(4351,plain,
! [B: a,A: a] :
( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( real_V1514887919dist_a @ A @ B ) ) )
!= ( ord_less_real @ zero_zero_real @ d ) ),
inference(simp,[status(thm)],[4350]) ).
thf(4368,plain,
! [B: a,A: a] :
( ( zero_zero_real != zero_zero_real )
| ( ( uminus_uminus_real @ ( real_V1514887919dist_a @ A @ B ) )
!= d ) ),
inference(simp,[status(thm)],[4351]) ).
thf(4371,plain,
! [B: a,A: a] :
( ( uminus_uminus_real @ ( real_V1514887919dist_a @ A @ B ) )
!= d ),
inference(simp,[status(thm)],[4368]) ).
thf(128,axiom,
! [A: a,B: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( ( ( A != B )
=> ( ( ord_less_eq_set_a @ ( line_c1152468841ment_a @ A @ B ) @ x )
=> ~ ! [C: a] :
( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) ) ) ) )
=> ~ ( ( A != B )
=> ( ( ord_less_eq_set_a @ ( line_c1152468841ment_a @ A @ B ) @ x )
=> ~ ! [C: a] :
( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ B @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_transversal__segmentE) ).
thf(709,plain,
! [A: a,B: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( ( ( A != B )
=> ( ( ord_less_eq_set_a @ ( line_c1152468841ment_a @ A @ B ) @ x )
=> ~ ! [C: a] :
( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) ) ) ) )
=> ~ ( ( A != B )
=> ( ( ord_less_eq_set_a @ ( line_c1152468841ment_a @ A @ B ) @ x )
=> ~ ! [C: a] :
( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ B @ A ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(186,axiom,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_diff__zero) ).
thf(885,plain,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(1364,plain,
! [B: real,A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ~ $true
| ( member_a @ ( sk1 @ B @ A ) @ ( elemen49976720ball_a @ x2 @ A ) )
| ( ( ord_less_real @ zero_zero_real @ sk11 )
!= ( ord_less_real @ zero_zero_real @ B ) ) ),
inference(paramod_ordered,[status(thm)],[830,342]) ).
thf(1365,plain,
! [B: real,A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ( member_a @ ( sk1 @ B @ A ) @ ( elemen49976720ball_a @ x2 @ A ) )
| ( ( ord_less_real @ zero_zero_real @ sk11 )
!= ( ord_less_real @ zero_zero_real @ B ) ) ),
inference(simp,[status(thm)],[1364]) ).
thf(1366,plain,
! [A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ( member_a @ ( sk1 @ sk11 @ A ) @ ( elemen49976720ball_a @ x2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[1365:[bind(A,$thf( A )),bind(B,$thf( sk11 ))]]) ).
thf(317,axiom,
! [A: real] :
( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
= ( ord_less_eq_real @ zero_zero_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_neg__le__0__iff__le) ).
thf(1265,plain,
! [A: real] :
( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
= ( ord_less_eq_real @ zero_zero_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(196,axiom,
! [A: a] :
( ( minus_minus_a @ zero_zero_a @ A )
= ( uminus_uminus_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_diff__0) ).
thf(914,plain,
! [A: a] :
( ( minus_minus_a @ zero_zero_a @ A )
= ( uminus_uminus_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(915,plain,
! [A: a] :
( ( minus_minus_a @ zero_zero_a @ A )
= ( uminus_uminus_a @ A ) ),
inference(cnf,[status(esa)],[914]) ).
thf(916,plain,
! [A: a] :
( ( minus_minus_a @ zero_zero_a @ A )
= ( uminus_uminus_a @ A ) ),
inference(lifteq,[status(thm)],[915]) ).
thf(288,axiom,
! [A: a] :
( ( inner_1173012732nner_a @ A @ zero_zero_a )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_inner__zero__right) ).
thf(1183,plain,
! [A: a] :
( ( inner_1173012732nner_a @ A @ zero_zero_a )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(1184,plain,
! [A: a] :
( ( inner_1173012732nner_a @ A @ zero_zero_a )
= zero_zero_real ),
inference(cnf,[status(esa)],[1183]) ).
thf(1185,plain,
! [A: a] :
( ( inner_1173012732nner_a @ A @ zero_zero_a )
= zero_zero_real ),
inference(lifteq,[status(thm)],[1184]) ).
thf(118,axiom,
ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9__092_060open_0620_A_060_Af_Ax_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_092_060close_062) ).
thf(681,plain,
ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(255,axiom,
! [A: real] :
~ ( ord_less_real @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_verit__comp__simplify1_I1_J) ).
thf(1092,plain,
! [A: real] :
~ ( ord_less_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(1093,plain,
~ ? [A: real] : ( ord_less_real @ A @ A ),
inference(miniscope,[status(thm)],[1092]) ).
thf(1094,plain,
! [A: real] :
~ ( ord_less_real @ A @ A ),
inference(cnf,[status(esa)],[1093]) ).
thf(1885,plain,
! [A: real] :
( ~ $true
| ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
!= ( ord_less_real @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[681,1094]) ).
thf(1886,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
!= ( ord_less_real @ A @ A ) ),
inference(simp,[status(thm)],[1885]) ).
thf(1897,plain,
! [A: real] :
( ( zero_zero_real != A )
| ( ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) )
!= A ) ),
inference(simp,[status(thm)],[1886]) ).
thf(1902,plain,
( ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) )
!= zero_zero_real ),
inference(simp,[status(thm)],[1897]) ).
thf(1929,plain,
! [A: a] :
( ( zero_zero_real != zero_zero_real )
| ( ( inner_1173012732nner_a @ A @ zero_zero_a )
!= ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1185,1902]) ).
thf(1930,plain,
! [A: a] :
( ( inner_1173012732nner_a @ A @ zero_zero_a )
!= ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ),
inference(simp,[status(thm)],[1929]) ).
thf(1934,plain,
! [A: a] :
( ( A
!= ( f @ x2 ) )
| ( ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) )
!= zero_zero_a ) ),
inference(simp,[status(thm)],[1930]) ).
thf(1936,plain,
( ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) )
!= zero_zero_a ),
inference(simp,[status(thm)],[1934]) ).
thf(2742,plain,
! [A: a] :
( ( ( poinca659159244_rot_a @ ( uminus_uminus_a @ A ) )
!= zero_zero_a )
| ( ( minus_minus_a @ zero_zero_a @ A )
!= ( minus_minus_a @ a2 @ b ) ) ),
inference(paramod_ordered,[status(thm)],[916,1936]) ).
thf(2762,plain,
! [A: a] :
( ( ( poinca659159244_rot_a @ ( uminus_uminus_a @ A ) )
!= zero_zero_a )
| ( a2 != zero_zero_a )
| ( A != b ) ),
inference(simp,[status(thm)],[2742]) ).
thf(2781,plain,
( ( ( poinca659159244_rot_a @ ( uminus_uminus_a @ b ) )
!= zero_zero_a )
| ( a2 != zero_zero_a ) ),
inference(simp,[status(thm)],[2762]) ).
thf(217,axiom,
! [A: a] :
( ( poinca659159244_rot_a @ ( poinca659159244_rot_a @ A ) )
= ( uminus_uminus_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_rot__rot) ).
thf(989,plain,
! [A: a] :
( ( poinca659159244_rot_a @ ( poinca659159244_rot_a @ A ) )
= ( uminus_uminus_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(990,plain,
! [A: a] :
( ( poinca659159244_rot_a @ ( poinca659159244_rot_a @ A ) )
= ( uminus_uminus_a @ A ) ),
inference(cnf,[status(esa)],[989]) ).
thf(991,plain,
! [A: a] :
( ( poinca659159244_rot_a @ ( poinca659159244_rot_a @ A ) )
= ( uminus_uminus_a @ A ) ),
inference(lifteq,[status(thm)],[990]) ).
thf(2812,plain,
! [B: a,A: a] :
( ( ( poinca659159244_rot_a @ ( uminus_uminus_a @ A ) )
= ( uminus_uminus_a @ B ) )
| ( ( poinca659159244_rot_a @ ( poinca659159244_rot_a @ A ) )
!= ( poinca659159244_rot_a @ B ) ) ),
inference(paramod_ordered,[status(thm)],[991,991]) ).
thf(2813,plain,
! [A: a] :
( ( poinca659159244_rot_a @ ( uminus_uminus_a @ A ) )
= ( uminus_uminus_a @ ( poinca659159244_rot_a @ A ) ) ),
inference(pattern_uni,[status(thm)],[2812:[bind(A,$thf( C )),bind(B,$thf( poinca659159244_rot_a @ C ))]]) ).
thf(2840,plain,
! [A: a] :
( ( poinca659159244_rot_a @ ( uminus_uminus_a @ A ) )
= ( uminus_uminus_a @ ( poinca659159244_rot_a @ A ) ) ),
inference(simp,[status(thm)],[2813]) ).
thf(3370,plain,
( ( ( uminus_uminus_a @ ( poinca659159244_rot_a @ b ) )
!= zero_zero_a )
| ( a2 != zero_zero_a ) ),
inference(rewrite,[status(thm)],[2781,2840]) ).
thf(256,axiom,
! [A: real,B: real,C: real,D: real] :
( ( member_real @ A @ ( elemen1140313242l_real @ B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( member_real @ A @ ( elemen1140313242l_real @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_mem__cball__leI) ).
thf(1095,plain,
! [A: real,B: real,C: real,D: real] :
( ( member_real @ A @ ( elemen1140313242l_real @ B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( member_real @ A @ ( elemen1140313242l_real @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(23,axiom,
! [A: real,B: real] :
( ( A
= ( uminus_uminus_real @ B ) )
= ( B
= ( uminus_uminus_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_equation__minus__iff) ).
thf(404,plain,
! [A: real,B: real] :
( ( A
= ( uminus_uminus_real @ B ) )
= ( B
= ( uminus_uminus_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(310,axiom,
! [A: real,B: real,C: real] :
( ( member_real @ A @ ( set_or656347191t_real @ B @ C ) )
= ( ( ord_less_eq_real @ B @ A )
& ( ord_less_eq_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_atLeastAtMost__iff) ).
thf(1243,plain,
! [A: real,B: real,C: real] :
( ( member_real @ A @ ( set_or656347191t_real @ B @ C ) )
= ( ( ord_less_eq_real @ B @ A )
& ( ord_less_eq_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(269,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_subset__eq) ).
thf(1127,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(139,axiom,
( ord_less_eq_a
= ( ^ [A: a,B: a] : ( ord_less_eq_a @ ( minus_minus_a @ A @ B ) @ zero_zero_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_le__iff__diff__le__0) ).
thf(751,plain,
( ord_less_eq_a
= ( ^ [A: a,B: a] : ( ord_less_eq_a @ ( minus_minus_a @ A @ B ) @ zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(752,plain,
( ( ^ [A: a,B: a] : ( ord_less_eq_a @ ( minus_minus_a @ A @ B ) @ zero_zero_a ) )
= ord_less_eq_a ),
inference(lifteq,[status(thm)],[751]) ).
thf(1409,plain,
! [A: a] :
( ( ^ [B: a] : ( ord_less_eq_a @ ( minus_minus_a @ A @ B ) @ zero_zero_a ) )
= ( ord_less_eq_a @ A ) ),
inference(func_ext,[status(esa)],[752]) ).
thf(324,axiom,
! [A: a,B: a] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1514887919dist_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_zero__le__dist) ).
thf(1286,plain,
! [A: a,B: a] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1514887919dist_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(1287,plain,
! [B: a,A: a] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1514887919dist_a @ A @ B ) ),
inference(cnf,[status(esa)],[1286]) ).
thf(12,axiom,
( ( (=) @ set_real )
= ( ^ [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
& ( ord_less_eq_set_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_set__eq__subset) ).
thf(372,plain,
( ( (=) @ set_real )
= ( ^ [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
& ( ord_less_eq_set_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(170,axiom,
! [A: a] :
( ( period138238489rbit_a @ f @ x @ A )
= ( ( period720806154rbit_a @ f @ x @ A )
& ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ f @ x @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_periodic__orbit__def) ).
thf(838,plain,
! [A: a] :
( ( period138238489rbit_a @ f @ x @ A )
= ( ( period720806154rbit_a @ f @ x @ A )
& ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ f @ x @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(184,axiom,
! [A: a] :
( ( minus_minus_a @ A @ zero_zero_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_diff__zero) ).
thf(879,plain,
! [A: a] :
( ( minus_minus_a @ A @ zero_zero_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(880,plain,
! [A: a] :
( ( minus_minus_a @ A @ zero_zero_a )
= A ),
inference(cnf,[status(esa)],[879]) ).
thf(881,plain,
! [A: a] :
( ( minus_minus_a @ A @ zero_zero_a )
= A ),
inference(lifteq,[status(thm)],[880]) ).
thf(178,axiom,
! [A: a] :
( ( inner_1173012732nner_a @ A @ ( poinca659159244_rot_a @ A ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_dot__ortho) ).
thf(862,plain,
! [A: a] :
( ( inner_1173012732nner_a @ A @ ( poinca659159244_rot_a @ A ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(863,plain,
! [A: a] :
( ( inner_1173012732nner_a @ A @ ( poinca659159244_rot_a @ A ) )
= zero_zero_real ),
inference(cnf,[status(esa)],[862]) ).
thf(864,plain,
! [A: a] :
( ( inner_1173012732nner_a @ A @ ( poinca659159244_rot_a @ A ) )
= zero_zero_real ),
inference(lifteq,[status(thm)],[863]) ).
thf(1972,plain,
! [A: real] :
( ~ $true
| ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
!= ( ord_less_real @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1208,1094]) ).
thf(1973,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
!= ( ord_less_real @ A @ A ) ),
inference(simp,[status(thm)],[1972]) ).
thf(1982,plain,
! [A: real] :
( ( zero_zero_real != A )
| ( ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) )
!= A ) ),
inference(simp,[status(thm)],[1973]) ).
thf(1989,plain,
( ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) )
!= zero_zero_real ),
inference(simp,[status(thm)],[1982]) ).
thf(2534,plain,
! [A: a] :
( ( zero_zero_real != zero_zero_real )
| ( ( inner_1173012732nner_a @ A @ ( poinca659159244_rot_a @ A ) )
!= ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[864,1989]) ).
thf(2535,plain,
! [A: a] :
( ( inner_1173012732nner_a @ A @ ( poinca659159244_rot_a @ A ) )
!= ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ),
inference(simp,[status(thm)],[2534]) ).
thf(2551,plain,
! [A: a] :
( ( A
!= ( f @ z ) )
| ( ( poinca659159244_rot_a @ A )
!= ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ),
inference(simp,[status(thm)],[2535]) ).
thf(2565,plain,
( ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) )
!= ( poinca659159244_rot_a @ ( f @ z ) ) ),
inference(simp,[status(thm)],[2551]) ).
thf(2671,plain,
! [A: a] :
( ( ( poinca659159244_rot_a @ A )
!= ( poinca659159244_rot_a @ ( f @ z ) ) )
| ( ( minus_minus_a @ A @ zero_zero_a )
!= ( minus_minus_a @ a2 @ b ) ) ),
inference(paramod_ordered,[status(thm)],[881,2565]) ).
thf(2677,plain,
! [A: a] :
( ( ( poinca659159244_rot_a @ A )
!= ( poinca659159244_rot_a @ ( f @ z ) ) )
| ( A != a2 )
| ( b != zero_zero_a ) ),
inference(simp,[status(thm)],[2671]) ).
thf(2682,plain,
( ( ( poinca659159244_rot_a @ ( f @ z ) )
!= ( poinca659159244_rot_a @ a2 ) )
| ( b != zero_zero_a ) ),
inference(simp,[status(thm)],[2677]) ).
thf(243,axiom,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( minus_minus_real @ A @ B )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_eq__iff__diff__eq__0) ).
thf(1059,plain,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( minus_minus_real @ A @ B )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(197,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ord_less_a @ A @ B )
=> ( ( ord_less_a @ C @ D )
=> ( ord_less_a @ ( minus_minus_a @ A @ D ) @ ( minus_minus_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_diff__strict__mono) ).
thf(917,plain,
! [A: a,B: a,C: a,D: a] :
( ( ord_less_a @ A @ B )
=> ( ( ord_less_a @ C @ D )
=> ( ord_less_a @ ( minus_minus_a @ A @ D ) @ ( minus_minus_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(158,axiom,
member_a @ z @ ( line_c1152468841ment_a @ a2 @ b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_direction_I1_J) ).
thf(802,plain,
member_a @ z @ ( line_c1152468841ment_a @ a2 @ b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(3,axiom,
! [A: real,B: set_real,C: set_real] :
( ( member_real @ A @ ( minus_minus_set_real @ B @ C ) )
=> ~ ( ( member_real @ A @ B )
=> ( member_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_DiffE) ).
thf(344,plain,
! [A: real,B: set_real,C: set_real] :
( ( member_real @ A @ ( minus_minus_set_real @ B @ C ) )
=> ~ ( ( member_real @ A @ B )
=> ( member_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(208,axiom,
! [A: real,B: real,C: a] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( member_real @ A @ top_top_set_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_general_Omem__existence__ivl__subset) ).
thf(949,plain,
! [A: real,B: real,C: a] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( member_real @ A @ top_top_set_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(2537,plain,
! [A: a] :
( ( zero_zero_real != zero_zero_real )
| ( ( inner_1173012732nner_a @ A @ ( poinca659159244_rot_a @ A ) )
!= ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[864,1902]) ).
thf(2538,plain,
! [A: a] :
( ( inner_1173012732nner_a @ A @ ( poinca659159244_rot_a @ A ) )
!= ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ),
inference(simp,[status(thm)],[2537]) ).
thf(2550,plain,
! [A: a] :
( ( A
!= ( f @ x2 ) )
| ( ( poinca659159244_rot_a @ A )
!= ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ),
inference(simp,[status(thm)],[2538]) ).
thf(2564,plain,
( ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) )
!= ( poinca659159244_rot_a @ ( f @ x2 ) ) ),
inference(simp,[status(thm)],[2550]) ).
thf(2571,plain,
( ( minus_minus_a @ a2 @ b )
!= ( f @ x2 ) ),
inference(simp,[status(thm)],[2564]) ).
thf(43,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_equalityD1) ).
thf(460,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(165,axiom,
~ ! [A: a] :
( ( member_a @ A @ ( elemen49976720ball_a @ x2 @ d ) )
=> ~ ! [B: a] :
( ( member_a @ B @ ( elemen49976720ball_a @ x2 @ d ) )
=> ( ord_less_eq_real @ ( inner_1173012732nner_a @ ( f @ A ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) @ ( inner_1173012732nner_a @ ( f @ B ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062s_O_A_092_060lbrakk_062s_A_092_060in_062_Acball_Ax_Ad_059_A_092_060forall_062x_092_060in_062cball_Ax_Ad_O_Af_As_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_A_092_060le_062_Af_Ax_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(817,plain,
~ ! [A: a] :
( ( member_a @ A @ ( elemen49976720ball_a @ x2 @ d ) )
=> ~ ! [B: a] :
( ( member_a @ B @ ( elemen49976720ball_a @ x2 @ d ) )
=> ( ord_less_eq_real @ ( inner_1173012732nner_a @ ( f @ A ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) @ ( inner_1173012732nner_a @ ( f @ B ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(254,axiom,
! [A: a,B: a,C: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ( ord_less_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) @ zero_zero_real )
=> ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_transversal__segment__negD_I1_J) ).
thf(1087,plain,
! [A: a,B: a,C: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ( ord_less_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) @ zero_zero_real )
=> ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(276,axiom,
( ( poinca659159244_rot_a @ zero_zero_a )
= zero_zero_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_rot__0) ).
thf(1146,plain,
( ( poinca659159244_rot_a @ zero_zero_a )
= zero_zero_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(1147,plain,
( ( poinca659159244_rot_a @ zero_zero_a )
= zero_zero_a ),
inference(lifteq,[status(thm)],[1146]) ).
thf(1477,plain,
! [A: a] :
( ( ( f @ A )
!= zero_zero_a )
| ~ $true
| ( ( member_a @ ( sk1 @ sk11 @ sk11 ) @ ( elemen49976720ball_a @ x2 @ sk11 ) )
!= ( member_a @ A @ ( elemen49976720ball_a @ x2 @ sk11 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1406,834]) ).
thf(1478,plain,
! [A: a] :
( ( ( f @ A )
!= zero_zero_a )
| ( ( member_a @ ( sk1 @ sk11 @ sk11 ) @ ( elemen49976720ball_a @ x2 @ sk11 ) )
!= ( member_a @ A @ ( elemen49976720ball_a @ x2 @ sk11 ) ) ) ),
inference(simp,[status(thm)],[1477]) ).
thf(1479,plain,
( ( f @ ( sk1 @ sk11 @ sk11 ) )
!= zero_zero_a ),
inference(pattern_uni,[status(thm)],[1478:[bind(A,$thf( sk1 @ sk11 @ sk11 ))]]) ).
thf(93,axiom,
! [A: real,B: real] :
( ( ( uminus_uminus_real @ A )
= B )
= ( ( uminus_uminus_real @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_minus__equation__iff) ).
thf(606,plain,
! [A: real,B: real] :
( ( ( uminus_uminus_real @ A )
= B )
= ( ( uminus_uminus_real @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(227,axiom,
! [A: a] :
( ( ! [B: a] :
( ( inner_1173012732nner_a @ A @ B )
= zero_zero_real ) )
= ( A = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_all__zero__iff) ).
thf(1013,plain,
! [A: a] :
( ( ! [B: a] :
( ( inner_1173012732nner_a @ A @ B )
= zero_zero_real ) )
= ( A = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(264,axiom,
! [A: real,B: real] :
( ( member_real @ A @ ( elemen1140313242l_real @ A @ B ) )
= ( ord_less_eq_real @ zero_zero_real @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_centre__in__cball) ).
thf(1115,plain,
! [A: real,B: real] :
( ( member_real @ A @ ( elemen1140313242l_real @ A @ B ) )
= ( ord_less_eq_real @ zero_zero_real @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(39,axiom,
! [A: real,B: real > $o] :
( ( member_real @ A @ ( collect_real @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_mem__Collect__eq) ).
thf(448,plain,
! [A: real,B: real > $o] :
( ( member_real @ A @ ( collect_real @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(306,axiom,
! [A: a,B: a,C: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) )
=> ( ord_less_eq_set_a @ ( line_c1152468841ment_a @ A @ B ) @ x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_transversal__segment__posD_I2_J) ).
thf(1232,plain,
! [A: a,B: a,C: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) )
=> ( ord_less_eq_set_a @ ( line_c1152468841ment_a @ A @ B ) @ x ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(28,axiom,
! [A: a,B: a] :
( ( A
= ( uminus_uminus_a @ B ) )
= ( B
= ( uminus_uminus_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_equation__minus__iff) ).
thf(419,plain,
! [A: a,B: a] :
( ( A
= ( uminus_uminus_a @ B ) )
= ( B
= ( uminus_uminus_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(420,plain,
! [B: a,A: a] :
( ( A
= ( uminus_uminus_a @ B ) )
= ( B
= ( uminus_uminus_a @ A ) ) ),
inference(cnf,[status(esa)],[419]) ).
thf(421,plain,
! [B: a,A: a] :
( ( A
= ( uminus_uminus_a @ B ) )
= ( B
= ( uminus_uminus_a @ A ) ) ),
inference(lifteq,[status(thm)],[420]) ).
thf(180,axiom,
! [A: a] :
( ( minus_minus_a @ A @ A )
= zero_zero_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(868,plain,
! [A: a] :
( ( minus_minus_a @ A @ A )
= zero_zero_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(869,plain,
! [A: a] :
( ( minus_minus_a @ A @ A )
= zero_zero_a ),
inference(cnf,[status(esa)],[868]) ).
thf(870,plain,
! [A: a] :
( ( minus_minus_a @ A @ A )
= zero_zero_a ),
inference(lifteq,[status(thm)],[869]) ).
thf(27,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ ( uminus_uminus_a @ B ) )
= ( ord_less_eq_a @ B @ ( uminus_uminus_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_le__minus__iff) ).
thf(416,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ ( uminus_uminus_a @ B ) )
= ( ord_less_eq_a @ B @ ( uminus_uminus_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(153,axiom,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_diff__0__right) ).
thf(787,plain,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(788,plain,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
inference(cnf,[status(esa)],[787]) ).
thf(789,plain,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
inference(lifteq,[status(thm)],[788]) ).
thf(37,axiom,
! [A: a,B: a] :
( ( ord_less_a @ A @ B )
=> ( ord_less_a @ ( uminus_uminus_a @ B ) @ ( uminus_uminus_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_verit__negate__coefficient_I2_J) ).
thf(443,plain,
! [A: a,B: a] :
( ( ord_less_a @ A @ B )
=> ( ord_less_a @ ( uminus_uminus_a @ B ) @ ( uminus_uminus_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(13,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_Collect__mono__iff) ).
thf(374,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(375,plain,
! [B: a > $o,A: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(cnf,[status(esa)],[374]) ).
thf(376,plain,
! [B: a > $o,A: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(lifteq,[status(thm)],[375]) ).
thf(99,axiom,
! [A: set_real,B: set_real] :
( ( ord_less_set_real @ A @ B )
=> ~ ( ( ord_less_eq_set_real @ A @ B )
=> ( ord_less_eq_set_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_psubsetE) ).
thf(623,plain,
! [A: set_real,B: set_real] :
( ( ord_less_set_real @ A @ B )
=> ~ ( ( ord_less_eq_set_real @ A @ B )
=> ( ord_less_eq_set_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(63,axiom,
! [A: a] :
( ( uminus_uminus_a @ ( uminus_uminus_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_add_Oinverse__inverse) ).
thf(519,plain,
! [A: a] :
( ( uminus_uminus_a @ ( uminus_uminus_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(520,plain,
! [A: a] :
( ( uminus_uminus_a @ ( uminus_uminus_a @ A ) )
= A ),
inference(cnf,[status(esa)],[519]) ).
thf(521,plain,
! [A: a] :
( ( uminus_uminus_a @ ( uminus_uminus_a @ A ) )
= A ),
inference(lifteq,[status(thm)],[520]) ).
thf(2810,plain,
! [B: a,A: a] :
( ( ( inner_1173012732nner_a @ B @ ( uminus_uminus_a @ A ) )
= zero_zero_real )
| ( ( poinca659159244_rot_a @ ( poinca659159244_rot_a @ A ) )
!= ( poinca659159244_rot_a @ B ) ) ),
inference(paramod_ordered,[status(thm)],[991,864]) ).
thf(2811,plain,
! [A: a] :
( ( inner_1173012732nner_a @ ( poinca659159244_rot_a @ A ) @ ( uminus_uminus_a @ A ) )
= zero_zero_real ),
inference(pattern_uni,[status(thm)],[2810:[bind(A,$thf( C )),bind(B,$thf( poinca659159244_rot_a @ C ))]]) ).
thf(2839,plain,
! [A: a] :
( ( inner_1173012732nner_a @ ( poinca659159244_rot_a @ A ) @ ( uminus_uminus_a @ A ) )
= zero_zero_real ),
inference(simp,[status(thm)],[2811]) ).
thf(3274,plain,
! [B: a,A: a] :
( ( ( inner_1173012732nner_a @ ( poinca659159244_rot_a @ B ) @ A )
= zero_zero_real )
| ( ( uminus_uminus_a @ ( uminus_uminus_a @ A ) )
!= ( uminus_uminus_a @ B ) ) ),
inference(paramod_ordered,[status(thm)],[521,2839]) ).
thf(3275,plain,
! [A: a] :
( ( inner_1173012732nner_a @ ( poinca659159244_rot_a @ ( uminus_uminus_a @ A ) ) @ A )
= zero_zero_real ),
inference(pattern_uni,[status(thm)],[3274:[bind(A,$thf( C )),bind(B,$thf( uminus_uminus_a @ C ))]]) ).
thf(3312,plain,
! [A: a] :
( ( inner_1173012732nner_a @ ( poinca659159244_rot_a @ ( uminus_uminus_a @ A ) ) @ A )
= zero_zero_real ),
inference(simp,[status(thm)],[3275]) ).
thf(3438,plain,
! [A: a] :
( ( inner_1173012732nner_a @ ( uminus_uminus_a @ ( poinca659159244_rot_a @ A ) ) @ A )
= zero_zero_real ),
inference(rewrite,[status(thm)],[3312,2840]) ).
thf(6,axiom,
! [A: real,B: set_real,C: set_real] :
( ( member_real @ A @ B )
=> ( ~ ( member_real @ A @ C )
=> ( member_real @ A @ ( minus_minus_set_real @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_DiffI) ).
thf(353,plain,
! [A: real,B: set_real,C: set_real] :
( ( member_real @ A @ B )
=> ( ~ ( member_real @ A @ C )
=> ( member_real @ A @ ( minus_minus_set_real @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1938,plain,
( ( zero_zero_a != zero_zero_a )
| ( ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) )
!= ( poinca659159244_rot_a @ zero_zero_a ) ) ),
inference(paramod_ordered,[status(thm)],[1147,1936]) ).
thf(1939,plain,
( ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) )
!= ( poinca659159244_rot_a @ zero_zero_a ) ),
inference(simp,[status(thm)],[1938]) ).
thf(1940,plain,
( ( minus_minus_a @ a2 @ b )
!= zero_zero_a ),
inference(simp,[status(thm)],[1939]) ).
thf(2750,plain,
! [A: a] :
( ( ( uminus_uminus_a @ A )
!= zero_zero_a )
| ( ( minus_minus_a @ zero_zero_a @ A )
!= ( minus_minus_a @ a2 @ b ) ) ),
inference(paramod_ordered,[status(thm)],[916,1940]) ).
thf(2757,plain,
! [A: a] :
( ( ( uminus_uminus_a @ A )
!= zero_zero_a )
| ( a2 != zero_zero_a )
| ( A != b ) ),
inference(simp,[status(thm)],[2750]) ).
thf(2777,plain,
( ( ( uminus_uminus_a @ b )
!= zero_zero_a )
| ( a2 != zero_zero_a ) ),
inference(simp,[status(thm)],[2757]) ).
thf(204,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( member_real @ A @ top_top_set_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_local_Orev_Omem__existence__ivl__subset) ).
thf(937,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( member_real @ A @ top_top_set_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(4,axiom,
! [A: set_real,B: set_real] : ( ord_less_eq_set_real @ ( minus_minus_set_real @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_Diff__subset) ).
thf(348,plain,
! [A: set_real,B: set_real] : ( ord_less_eq_set_real @ ( minus_minus_set_real @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(81,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_psubsetE) ).
thf(574,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(323,axiom,
! [A: a,B: a,C: a] :
( ( inner_1173012732nner_a @ A @ ( minus_minus_a @ B @ C ) )
= ( minus_minus_real @ ( inner_1173012732nner_a @ A @ B ) @ ( inner_1173012732nner_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_inner__diff__right) ).
thf(1283,plain,
! [A: a,B: a,C: a] :
( ( inner_1173012732nner_a @ A @ ( minus_minus_a @ B @ C ) )
= ( minus_minus_real @ ( inner_1173012732nner_a @ A @ B ) @ ( inner_1173012732nner_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(1373,plain,
! [A: real] :
( ~ $true
| ( ( ord_less_real @ zero_zero_real @ sk11 )
!= ( ord_less_real @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[830,1094]) ).
thf(1374,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ sk11 )
!= ( ord_less_real @ A @ A ) ),
inference(simp,[status(thm)],[1373]) ).
thf(1376,plain,
! [A: real] :
( ( zero_zero_real != A )
| ( sk11 != A ) ),
inference(simp,[status(thm)],[1374]) ).
thf(1377,plain,
sk11 != zero_zero_real,
inference(simp,[status(thm)],[1376]) ).
thf(300,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_set_real @ ( elemen1140313242l_real @ C @ A ) @ ( elemen1140313242l_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_subset__cball) ).
thf(1215,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_set_real @ ( elemen1140313242l_real @ C @ A ) @ ( elemen1140313242l_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(133,axiom,
! [A: a] :
( ( ( inner_1173012732nner_a @ A @ A )
= zero_zero_real )
= ( A = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_inner__eq__zero__iff) ).
thf(734,plain,
! [A: a] :
( ( ( inner_1173012732nner_a @ A @ A )
= zero_zero_real )
= ( A = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(111,axiom,
! [A: set_real,B: set_real,C: set_real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( ord_less_set_real @ B @ C )
=> ( ord_less_set_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_subset__psubset__trans) ).
thf(660,plain,
! [A: set_real,B: set_real,C: set_real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( ord_less_set_real @ B @ C )
=> ( ord_less_set_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(1950,plain,
! [A: real] :
( ~ $true
| ( ( f @ ( sk1 @ A @ sk11 ) )
!= zero_zero_a )
| ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1208,1438]) ).
thf(1951,plain,
! [A: real] :
( ( ( f @ ( sk1 @ A @ sk11 ) )
!= zero_zero_a )
| ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(simp,[status(thm)],[1950]) ).
thf(1952,plain,
( ( f @ ( sk1 @ ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) @ sk11 ) )
!= zero_zero_a ),
inference(pattern_uni,[status(thm)],[1951:[bind(A,$thf( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ))]]) ).
thf(2185,plain,
! [A: a] :
( ( ( f @ ( sk1 @ ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ A ) ) @ sk11 ) )
!= zero_zero_a )
| ( ( minus_minus_a @ A @ zero_zero_a )
!= ( minus_minus_a @ a2 @ b ) ) ),
inference(paramod_ordered,[status(thm)],[881,1952]) ).
thf(2192,plain,
! [A: a] :
( ( ( f @ ( sk1 @ ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ A ) ) @ sk11 ) )
!= zero_zero_a )
| ( A != a2 )
| ( b != zero_zero_a ) ),
inference(simp,[status(thm)],[2185]) ).
thf(2205,plain,
( ( ( f @ ( sk1 @ ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ a2 ) ) @ sk11 ) )
!= zero_zero_a )
| ( b != zero_zero_a ) ),
inference(simp,[status(thm)],[2192]) ).
thf(2574,plain,
! [A: a] :
( ( ( poinca659159244_rot_a @ A )
!= ( poinca659159244_rot_a @ ( f @ x2 ) ) )
| ( ( minus_minus_a @ A @ zero_zero_a )
!= ( minus_minus_a @ a2 @ b ) ) ),
inference(paramod_ordered,[status(thm)],[881,2564]) ).
thf(2581,plain,
! [A: a] :
( ( A
!= ( f @ x2 ) )
| ( A != a2 )
| ( b != zero_zero_a ) ),
inference(simp,[status(thm)],[2574]) ).
thf(2586,plain,
( ( ( f @ x2 )
!= a2 )
| ( b != zero_zero_a ) ),
inference(simp,[status(thm)],[2581]) ).
thf(91,axiom,
! [A: set_real,B: set_real] :
( ( ord_less_set_real @ A @ B )
=> ( ord_less_eq_set_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_psubset__imp__subset) ).
thf(602,plain,
! [A: set_real,B: set_real] :
( ( ord_less_set_real @ A @ B )
=> ( ord_less_eq_set_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(145,axiom,
! [A: a] :
( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_rev_Operiodic__orbit__period_I1_J) ).
thf(766,plain,
! [A: a] :
( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(284,axiom,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_zero__reorient) ).
thf(1169,plain,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(20,axiom,
! [A: real,B: real,C: real] :
( ( inner_4346926r_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ ( inner_4346926r_real @ A @ C ) @ ( inner_4346926r_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_inner__diff__left) ).
thf(395,plain,
! [A: real,B: real,C: real] :
( ( inner_4346926r_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ ( inner_4346926r_real @ A @ C ) @ ( inner_4346926r_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(396,plain,
! [C: real,B: real,A: real] :
( ( inner_4346926r_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ ( inner_4346926r_real @ A @ C ) @ ( inner_4346926r_real @ B @ C ) ) ),
inference(cnf,[status(esa)],[395]) ).
thf(397,plain,
! [C: real,B: real,A: real] :
( ( inner_4346926r_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ ( inner_4346926r_real @ A @ C ) @ ( inner_4346926r_real @ B @ C ) ) ),
inference(lifteq,[status(thm)],[396]) ).
thf(248,axiom,
( ( f @ x2 )
!= zero_zero_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__092_060open_062f_Ax_A_092_060noteq_062_A_I0_058_058_Ha_J_092_060close_062) ).
thf(1072,plain,
( ( f @ x2 )
!= zero_zero_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(40,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_diff__eq__diff__eq) ).
thf(451,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(452,plain,
! [D: real,C: real,B: real,A: real] :
( ( ( minus_minus_real @ A @ B )
!= ( minus_minus_real @ C @ D ) )
| ( ( A = B )
= ( C = D ) ) ),
inference(cnf,[status(esa)],[451]) ).
thf(453,plain,
! [D: real,C: real,B: real,A: real] :
( ( ( minus_minus_real @ A @ B )
!= ( minus_minus_real @ C @ D ) )
| ( ( A = B )
= ( C = D ) ) ),
inference(lifteq,[status(thm)],[452]) ).
thf(266,axiom,
! [A: real] :
( ( minus_minus_real @ zero_zero_real @ A )
= ( uminus_uminus_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_verit__minus__simplify_I3_J) ).
thf(1119,plain,
! [A: real] :
( ( minus_minus_real @ zero_zero_real @ A )
= ( uminus_uminus_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(148,axiom,
! [A: real,B: real] :
( ( ~ ( ord_less_eq_real @ A @ B ) )
= ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_verit__comp__simplify1_I3_J) ).
thf(774,plain,
! [A: real,B: real] :
( ( ~ ( ord_less_eq_real @ A @ B ) )
= ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1073,plain,
( ( f @ x2 )
!= zero_zero_a ),
inference(polarity_switch,[status(thm)],[1072]) ).
thf(1074,plain,
( ( f @ x2 )
!= zero_zero_a ),
inference(lifteq,[status(thm)],[1073]) ).
thf(198,axiom,
! [A: a,B: a,C: a] :
( ( A != B )
=> ( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
= ( ( ( inner_1173012732nner_a @ ( minus_minus_a @ C @ A ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ B @ A ) ) )
= zero_zero_real )
& ( member_real @ ( inner_1173012732nner_a @ C @ ( minus_minus_a @ B @ A ) ) @ ( set_or656347191t_real @ ( inner_1173012732nner_a @ A @ ( minus_minus_a @ B @ A ) ) @ ( inner_1173012732nner_a @ B @ ( minus_minus_a @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_in__closed__segment__iff__rot) ).
thf(920,plain,
! [A: a,B: a,C: a] :
( ( A != B )
=> ( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
= ( ( ( inner_1173012732nner_a @ ( minus_minus_a @ C @ A ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ B @ A ) ) )
= zero_zero_real )
& ( member_real @ ( inner_1173012732nner_a @ C @ ( minus_minus_a @ B @ A ) ) @ ( set_or656347191t_real @ ( inner_1173012732nner_a @ A @ ( minus_minus_a @ B @ A ) ) @ ( inner_1173012732nner_a @ B @ ( minus_minus_a @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(35,axiom,
( ord_less_set_real
= ( ^ [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_psubset__eq) ).
thf(438,plain,
( ord_less_set_real
= ( ^ [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(439,plain,
( ord_less_set_real
= ( ^ [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
& ( A != B ) ) ) ),
inference(lifteq,[status(thm)],[438]) ).
thf(155,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ B )
=> ( ~ ( member_a @ A @ C )
=> ( member_a @ A @ ( minus_minus_set_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_DiffI) ).
thf(793,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ B )
=> ( ~ ( member_a @ A @ C )
=> ( member_a @ A @ ( minus_minus_set_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(332,axiom,
! [A: a,B: a] :
( ( minus_minus_a @ ( uminus_uminus_a @ A ) @ B )
= ( minus_minus_a @ ( uminus_uminus_a @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_minus__diff__commute) ).
thf(1306,plain,
! [A: a,B: a] :
( ( minus_minus_a @ ( uminus_uminus_a @ A ) @ B )
= ( minus_minus_a @ ( uminus_uminus_a @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(294,axiom,
! [A: set_a] :
( ( auto_l630715367iant_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= ( auto_l630715367iant_a @ f @ x @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_rev_Oinvariant__eq__rev) ).
thf(1199,plain,
! [A: set_a] :
( ( auto_l630715367iant_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= ( auto_l630715367iant_a @ f @ x @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(279,axiom,
! [A: a,B: set_a] :
( ~ ( member_a @ A @ B )
=> ( member_a @ A @ ( uminus_uminus_set_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_ComplI) ).
thf(1153,plain,
! [A: a,B: set_a] :
( ~ ( member_a @ A @ B )
=> ( member_a @ A @ ( uminus_uminus_set_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(380,plain,
! [B: set_real,A: set_real] :
( ( ( member_real @ ( sk2 @ B @ A ) @ A )
| ( ord_less_eq_set_real @ A @ B ) )
& ( ~ ( member_real @ ( sk2 @ B @ A ) @ B )
| ( ord_less_eq_set_real @ A @ B ) ) ),
inference(cnf,[status(esa)],[379]) ).
thf(381,plain,
! [B: set_real,A: set_real] :
( ( member_real @ ( sk2 @ B @ A ) @ A )
| ( ord_less_eq_set_real @ A @ B ) ),
inference(cnfConj,[status(thm)],[380]) ).
thf(10,axiom,
! [A: real,B: set_real,C: set_real] :
( ( member_real @ A @ ( minus_minus_set_real @ B @ C ) )
=> ~ ( member_real @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_DiffD2) ).
thf(366,plain,
! [A: real,B: set_real,C: set_real] :
( ( member_real @ A @ ( minus_minus_set_real @ B @ C ) )
=> ~ ( member_real @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(67,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_subset__refl) ).
thf(534,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(246,axiom,
! [A: a,B: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
= ( poinca522724647ment_a @ f @ x @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_transversal__segment__commute) ).
thf(1067,plain,
! [A: a,B: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
= ( poinca522724647ment_a @ f @ x @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(239,axiom,
! [A: a,B: a] :
( ( ord_less_real @ zero_zero_real @ ( real_V1514887919dist_a @ A @ B ) )
= ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_zero__less__dist__iff) ).
thf(1047,plain,
! [A: a,B: a] :
( ( ord_less_real @ zero_zero_real @ ( real_V1514887919dist_a @ A @ B ) )
= ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(343,plain,
! [B: real,A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ~ ( ord_less_real @ zero_zero_real @ B )
| ~ ( ord_less_eq_real @ B @ ( inner_1173012732nner_a @ ( f @ ( sk1 @ B @ A ) ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ),
inference(cnfConj,[status(thm)],[341]) ).
thf(1344,plain,
! [B: real,A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ~ $true
| ~ ( ord_less_eq_real @ B @ ( inner_1173012732nner_a @ ( f @ ( sk1 @ B @ A ) ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
| ( ( ord_less_real @ zero_zero_real @ d )
!= ( ord_less_real @ zero_zero_real @ B ) ) ),
inference(paramod_ordered,[status(thm)],[756,343]) ).
thf(1345,plain,
! [B: real,A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ~ ( ord_less_eq_real @ B @ ( inner_1173012732nner_a @ ( f @ ( sk1 @ B @ A ) ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
| ( ( ord_less_real @ zero_zero_real @ d )
!= ( ord_less_real @ zero_zero_real @ B ) ) ),
inference(simp,[status(thm)],[1344]) ).
thf(1346,plain,
! [A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ~ ( ord_less_eq_real @ d @ ( inner_1173012732nner_a @ ( f @ ( sk1 @ d @ A ) ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1345:[bind(A,$thf( A )),bind(B,$thf( d ))]]) ).
thf(1728,plain,
! [A: real] :
( ~ $true
| ~ ( ord_less_eq_real @ d @ ( inner_1173012732nner_a @ ( f @ ( sk1 @ d @ A ) ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
| ( ( ord_less_real @ zero_zero_real @ d )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[756,1346]) ).
thf(1729,plain,
! [A: real] :
( ~ ( ord_less_eq_real @ d @ ( inner_1173012732nner_a @ ( f @ ( sk1 @ d @ A ) ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
| ( ( ord_less_real @ zero_zero_real @ d )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(simp,[status(thm)],[1728]) ).
thf(1730,plain,
~ ( ord_less_eq_real @ d @ ( inner_1173012732nner_a @ ( f @ ( sk1 @ d @ d ) ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ),
inference(pattern_uni,[status(thm)],[1729:[bind(A,$thf( d ))]]) ).
thf(242,axiom,
! [A: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_rev_Omvar_Ointerval__axioms) ).
thf(1057,plain,
! [A: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(283,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ( ! [C: a,D: a] :
( ( member_a @ C @ ( line_c1152468841ment_a @ a2 @ b ) )
=> ( ( ord_less_eq_real @ ( real_V1514887919dist_a @ C @ D ) @ A )
=> ( ord_less_eq_real @ B @ ( inner_1173012732nner_a @ ( f @ D ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ) )
=> thesis ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_that) ).
thf(1163,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ( ! [C: a,D: a] :
( ( member_a @ C @ ( line_c1152468841ment_a @ a2 @ b ) )
=> ( ( ord_less_eq_real @ ( real_V1514887919dist_a @ C @ D ) @ A )
=> ( ord_less_eq_real @ B @ ( inner_1173012732nner_a @ ( f @ D ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ) )
=> thesis ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(320,axiom,
! [A: a] :
( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ A @ A ) )
= ( A != zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_inner__gt__zero__iff) ).
thf(1274,plain,
! [A: a] :
( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ A @ A ) )
= ( A != zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(189,axiom,
! [A: a] :
( ( period720806154rbit_a @ f @ x @ A )
=> ( ( ( f @ A )
!= zero_zero_a )
=> ( period138238489rbit_a @ f @ x @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_closed__orbit__periodic) ).
thf(894,plain,
! [A: a] :
( ( period720806154rbit_a @ f @ x @ A )
=> ( ( ( f @ A )
!= zero_zero_a )
=> ( period138238489rbit_a @ f @ x @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(137,axiom,
! [A: a] :
( ( member_a @ A @ ( elemen49976720ball_a @ x2 @ d ) )
=> ( ord_less_eq_real @ ( inner_1173012732nner_a @ ( f @ s ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) @ ( inner_1173012732nner_a @ ( f @ A ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062_092_060forall_062x_092_060in_062cball_Ax_Ad_O_Af_As_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_A_092_060le_062_Af_Ax_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_092_060close_062) ).
thf(746,plain,
! [A: a] :
( ( member_a @ A @ ( elemen49976720ball_a @ x2 @ d ) )
=> ( ord_less_eq_real @ ( inner_1173012732nner_a @ ( f @ s ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) @ ( inner_1173012732nner_a @ ( f @ A ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(313,axiom,
! [A: real,B: real,C: real,D: real] :
( ( member_real @ A @ ( set_or656347191t_real @ B @ C ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ D )
=> ( ord_less_eq_real @ ( inner_4346926r_real @ A @ D ) @ ( inner_4346926r_real @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_interval__inner__leI_I2_J) ).
thf(1255,plain,
! [A: real,B: real,C: real,D: real] :
( ( member_real @ A @ ( set_or656347191t_real @ B @ C ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ D )
=> ( ord_less_eq_real @ ( inner_4346926r_real @ A @ D ) @ ( inner_4346926r_real @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(161,axiom,
member_a @ s @ ( elemen49976720ball_a @ x2 @ d ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062s_A_092_060in_062_Acball_Ax_Ad_092_060close_062) ).
thf(808,plain,
member_a @ s @ ( elemen49976720ball_a @ x2 @ d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(1527,plain,
! [A: a] :
( ( ( f @ A )
!= zero_zero_a )
| ~ $true
| ( ( member_a @ s @ ( elemen49976720ball_a @ x2 @ d ) )
!= ( member_a @ A @ ( elemen49976720ball_a @ x2 @ sk11 ) ) ) ),
inference(paramod_ordered,[status(thm)],[808,834]) ).
thf(1528,plain,
! [A: a] :
( ( ( f @ A )
!= zero_zero_a )
| ( ( member_a @ s @ ( elemen49976720ball_a @ x2 @ d ) )
!= ( member_a @ A @ ( elemen49976720ball_a @ x2 @ sk11 ) ) ) ),
inference(simp,[status(thm)],[1527]) ).
thf(1529,plain,
! [A: a] :
( ( ( f @ A )
!= zero_zero_a )
| ( s != A )
| ( ( elemen49976720ball_a @ x2 @ sk11 )
!= ( elemen49976720ball_a @ x2 @ d ) ) ),
inference(simp,[status(thm)],[1528]) ).
thf(1530,plain,
( ( ( f @ s )
!= zero_zero_a )
| ( ( elemen49976720ball_a @ x2 @ sk11 )
!= ( elemen49976720ball_a @ x2 @ d ) ) ),
inference(simp,[status(thm)],[1529]) ).
thf(1569,plain,
( ( ( f @ s )
!= zero_zero_a )
| ( x2 != x2 )
| ( sk11 != d ) ),
inference(simp,[status(thm)],[1530]) ).
thf(1570,plain,
( ( ( f @ s )
!= zero_zero_a )
| ( sk11 != d ) ),
inference(simp,[status(thm)],[1569]) ).
thf(598,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( A = B ) ) ) ),
inference(lifteq,[status(thm)],[597]) ).
thf(818,plain,
~ ! [A: a] :
( ( member_a @ A @ ( elemen49976720ball_a @ x2 @ d ) )
=> ~ ! [B: a] :
( ( member_a @ B @ ( elemen49976720ball_a @ x2 @ d ) )
=> ( ord_less_eq_real @ ( inner_1173012732nner_a @ ( f @ A ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) @ ( inner_1173012732nner_a @ ( f @ B ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ) ),
inference(polarity_switch,[status(thm)],[817]) ).
thf(819,plain,
! [A: a] :
( ( member_a @ sk10 @ ( elemen49976720ball_a @ x2 @ d ) )
& ( ~ ( member_a @ A @ ( elemen49976720ball_a @ x2 @ d ) )
| ( ord_less_eq_real @ ( inner_1173012732nner_a @ ( f @ sk10 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) @ ( inner_1173012732nner_a @ ( f @ A ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ) ),
inference(cnf,[status(esa)],[818]) ).
thf(820,plain,
member_a @ sk10 @ ( elemen49976720ball_a @ x2 @ d ),
inference(cnfConj,[status(thm)],[819]) ).
thf(76,axiom,
! [A: real,B: real] :
( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
= ( minus_minus_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_minus__diff__eq) ).
thf(561,plain,
! [A: real,B: real] :
( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
= ( minus_minus_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(30,axiom,
! [A: set_real] :
( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_Collect__mem__eq) ).
thf(424,plain,
! [A: set_real] :
( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(31,axiom,
! [A: set_real,B: set_real,C: set_real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( ord_less_eq_set_real @ B @ C )
=> ( ord_less_eq_set_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_subset__trans) ).
thf(427,plain,
! [A: set_real,B: set_real,C: set_real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( ord_less_eq_set_real @ B @ C )
=> ( ord_less_eq_set_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(428,plain,
! [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
=> ! [C: set_real] :
( ( ord_less_eq_set_real @ B @ C )
=> ( ord_less_eq_set_real @ A @ C ) ) ),
inference(miniscope,[status(thm)],[427]) ).
thf(429,plain,
! [C: set_real,B: set_real,A: set_real] :
( ~ ( ord_less_eq_set_real @ A @ B )
| ~ ( ord_less_eq_set_real @ B @ C )
| ( ord_less_eq_set_real @ A @ C ) ),
inference(cnf,[status(esa)],[428]) ).
thf(237,axiom,
! [A: a] :
( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ( ( ( uminus_uminus_a_a @ f @ A )
!= zero_zero_a )
=> ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_rev_Oclosed__orbit__periodic) ).
thf(1042,plain,
! [A: a] :
( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ( ( ( uminus_uminus_a_a @ f @ A )
!= zero_zero_a )
=> ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(209,axiom,
! [A: a] :
( ( member_a @ A @ x )
=> ( ( ( f @ A )
!= zero_zero_a )
=> ~ ! [B: a,C: a] :
( ( member_a @ A @ ( line_open_segment_a @ B @ C ) )
=> ~ ( poinca522724647ment_a @ f @ x @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_transversal__segment__exists) ).
thf(952,plain,
! [A: a] :
( ( member_a @ A @ x )
=> ( ( ( f @ A )
!= zero_zero_a )
=> ~ ! [B: a,C: a] :
( ( member_a @ A @ ( line_open_segment_a @ B @ C ) )
=> ~ ( poinca522724647ment_a @ f @ x @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(349,plain,
! [B: set_real,A: set_real] : ( ord_less_eq_set_real @ ( minus_minus_set_real @ A @ B ) @ A ),
inference(cnf,[status(esa)],[348]) ).
thf(24,axiom,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ( set_or2094724627_set_a @ A @ B )
= ( set_or2094724627_set_a @ C @ D ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ~ ( ord_less_eq_set_a @ A @ B )
& ~ ( ord_less_eq_set_a @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_Icc__eq__Icc) ).
thf(407,plain,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ( set_or2094724627_set_a @ A @ B )
= ( set_or2094724627_set_a @ C @ D ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ~ ( ord_less_eq_set_a @ A @ B )
& ~ ( ord_less_eq_set_a @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(123,axiom,
! [A: real,B: real,C: real] :
( ( member_real @ A @ ( elemen1140313242l_real @ B @ C ) )
= ( ord_less_eq_real @ ( real_V1934908667t_real @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_mem__cball) ).
thf(693,plain,
! [A: real,B: real,C: real] :
( ( member_real @ A @ ( elemen1140313242l_real @ B @ C ) )
= ( ord_less_eq_real @ ( real_V1934908667t_real @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(101,axiom,
! [A: real,B: real] :
( ( ( uminus_uminus_real @ A )
= ( uminus_uminus_real @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_neg__equal__iff__equal) ).
thf(630,plain,
! [A: real,B: real] :
( ( ( uminus_uminus_real @ A )
= ( uminus_uminus_real @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(77,axiom,
! [A: a] :
( ( zero_zero_a = A )
= ( A = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_zero__reorient) ).
thf(564,plain,
! [A: a] :
( ( zero_zero_a = A )
= ( A = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(565,plain,
! [A: a] :
( ( zero_zero_a = A )
= ( A = zero_zero_a ) ),
inference(cnf,[status(esa)],[564]) ).
thf(566,plain,
! [A: a] :
( ( zero_zero_a = A )
= ( A = zero_zero_a ) ),
inference(lifteq,[status(thm)],[565]) ).
thf(34,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ ( uminus_uminus_a @ A ) @ B )
= ( ord_less_eq_a @ ( uminus_uminus_a @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_minus__le__iff) ).
thf(435,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ ( uminus_uminus_a @ A ) @ B )
= ( ord_less_eq_a @ ( uminus_uminus_a @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(425,plain,
! [A: set_real] :
( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
= A ),
inference(cnf,[status(esa)],[424]) ).
thf(426,plain,
! [A: set_real] :
( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
= A ),
inference(lifteq,[status(thm)],[425]) ).
thf(1058,plain,
! [A: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ),
inference(cnf,[status(esa)],[1057]) ).
thf(2053,plain,
! [B: a,A: set_real] :
( ( initia826609931terval
@ ( collect_real
@ ^ [C: real] : ( member_real @ C @ A ) ) )
| ( A
!= ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) ),
inference(paramod_ordered,[status(thm)],[426,1058]) ).
thf(2054,plain,
! [A: a] :
( initia826609931terval
@ ( collect_real
@ ^ [B: real] : ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[2053:[bind(A,$thf( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ E )),bind(B,$thf( E ))]]) ).
thf(2068,plain,
! [A: a] :
( initia826609931terval
@ ( collect_real
@ ^ [B: real] : ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ) ),
inference(simp,[status(thm)],[2054]) ).
thf(54,axiom,
initia826609931terval @ top_top_set_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_interval__axioms) ).
thf(493,plain,
initia826609931terval @ top_top_set_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(2180,plain,
! [A: a] :
( ( ( poinca659159244_rot_a @ A )
!= zero_zero_a )
| ( ( minus_minus_a @ A @ zero_zero_a )
!= ( minus_minus_a @ a2 @ b ) ) ),
inference(paramod_ordered,[status(thm)],[881,1936]) ).
thf(2202,plain,
! [A: a] :
( ( ( poinca659159244_rot_a @ A )
!= zero_zero_a )
| ( A != a2 )
| ( b != zero_zero_a ) ),
inference(simp,[status(thm)],[2180]) ).
thf(2213,plain,
( ( ( poinca659159244_rot_a @ a2 )
!= zero_zero_a )
| ( b != zero_zero_a ) ),
inference(simp,[status(thm)],[2202]) ).
thf(142,axiom,
! [A: a,B: set_a] :
( ( member_a @ A @ ( uminus_uminus_set_a @ B ) )
= ( ~ ( member_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_Compl__iff) ).
thf(757,plain,
! [A: a,B: set_a] :
( ( member_a @ A @ ( uminus_uminus_set_a @ B ) )
= ( ~ ( member_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(326,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
=> ~ ( member_a @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_DiffD2) ).
thf(1291,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
=> ~ ( member_a @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(212,axiom,
! [A: real] :
( ( ! [B: real] :
( ( inner_4346926r_real @ A @ B )
= zero_zero_real ) )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_all__zero__iff) ).
thf(974,plain,
! [A: real] :
( ( ! [B: real] :
( ( inner_4346926r_real @ A @ B )
= zero_zero_real ) )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(226,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_Collect__mem__eq) ).
thf(1010,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(1011,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(cnf,[status(esa)],[1010]) ).
thf(1012,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(lifteq,[status(thm)],[1011]) ).
thf(260,axiom,
! [A: a > real,B: a > bounde7994401a_real,C: set_a] :
( ( reacha1191408304tion_a @ f @ x @ A @ B @ C )
=> ( ord_less_eq_set_a @ C @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_sectionD_I5_J) ).
thf(1106,plain,
! [A: a > real,B: a > bounde7994401a_real,C: set_a] :
( ( reacha1191408304tion_a @ f @ x @ A @ B @ C )
=> ( ord_less_eq_set_a @ C @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(45,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ord_less_eq_set_a @ ( set_or411607219Most_a @ A @ B ) @ ( set_or411607219Most_a @ C @ D ) )
= ( ~ ( ord_less_eq_a @ A @ B )
| ( ( ord_less_eq_a @ C @ A )
& ( ord_less_eq_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_atLeastatMost__subset__iff) ).
thf(467,plain,
! [A: a,B: a,C: a,D: a] :
( ( ord_less_eq_set_a @ ( set_or411607219Most_a @ A @ B ) @ ( set_or411607219Most_a @ C @ D ) )
= ( ~ ( ord_less_eq_a @ A @ B )
| ( ( ord_less_eq_a @ C @ A )
& ( ord_less_eq_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(328,axiom,
member_a @ x2 @ x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__092_060open_062x_A_092_060in_062_AX_092_060close_062) ).
thf(1296,plain,
member_a @ x2 @ x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(113,axiom,
! [A: a] :
( ( member_a @ A @ x )
=> ? [B: real,C: real] :
( ( ord_less_real @ B @ zero_zero_real )
& ( ord_less_real @ zero_zero_real @ C )
& ( ord_less_eq_set_real @ ( set_or656347191t_real @ B @ C ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_rev_Oopen__existence__ivl0) ).
thf(665,plain,
! [A: a] :
( ( member_a @ A @ x )
=> ? [B: real,C: real] :
( ( ord_less_real @ B @ zero_zero_real )
& ( ord_less_real @ zero_zero_real @ C )
& ( ord_less_eq_set_real @ ( set_or656347191t_real @ B @ C ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(119,axiom,
! [A: a] :
( ( period720806154rbit_a @ f @ x @ A )
=> ( ( ( period1305449585riod_a @ f @ x @ A )
= zero_zero_real )
=> ( ( f @ A )
= zero_zero_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_closed__orbit__period__zero__fixed__point) ).
thf(682,plain,
! [A: a] :
( ( period720806154rbit_a @ f @ x @ A )
=> ( ( ( period1305449585riod_a @ f @ x @ A )
= zero_zero_real )
=> ( ( f @ A )
= zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(292,axiom,
! [A: real] :
( ( inner_4346926r_real @ A @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_inner__zero__right) ).
thf(1193,plain,
! [A: real] :
( ( inner_4346926r_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(1194,plain,
! [A: real] :
( ( inner_4346926r_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(cnf,[status(esa)],[1193]) ).
thf(1195,plain,
! [A: real] :
( ( inner_4346926r_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(lifteq,[status(thm)],[1194]) ).
thf(2179,plain,
! [A: a] :
( ~ ( ord_less_eq_real @ d @ ( inner_1173012732nner_a @ ( f @ ( sk1 @ d @ d ) ) @ ( poinca659159244_rot_a @ A ) ) )
| ( ( minus_minus_a @ A @ zero_zero_a )
!= ( minus_minus_a @ a2 @ b ) ) ),
inference(paramod_ordered,[status(thm)],[881,1730]) ).
thf(2200,plain,
! [A: a] :
( ~ ( ord_less_eq_real @ d @ ( inner_1173012732nner_a @ ( f @ ( sk1 @ d @ d ) ) @ ( poinca659159244_rot_a @ A ) ) )
| ( A != a2 )
| ( b != zero_zero_a ) ),
inference(simp,[status(thm)],[2179]) ).
thf(2211,plain,
( ~ ( ord_less_eq_real @ d @ ( inner_1173012732nner_a @ ( f @ ( sk1 @ d @ d ) ) @ ( poinca659159244_rot_a @ a2 ) ) )
| ( b != zero_zero_a ) ),
inference(simp,[status(thm)],[2200]) ).
thf(108,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_equalityD2) ).
thf(650,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(96,axiom,
! [A: set_real,B: set_real] :
( ( ord_less_set_real @ A @ B )
=> ? [C: real] : ( member_real @ C @ ( minus_minus_set_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_psubset__imp__ex__mem) ).
thf(615,plain,
! [A: set_real,B: set_real] :
( ( ord_less_set_real @ A @ B )
=> ? [C: real] : ( member_real @ C @ ( minus_minus_set_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(245,axiom,
! [A: a] :
( ( member_a @ A @ x )
=> ( ( ( uminus_uminus_a_a @ f @ A )
= zero_zero_a )
=> ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_rev_Ofixed__point__imp__closed__orbit__period__zero_I1_J) ).
thf(1064,plain,
! [A: a] :
( ( member_a @ A @ x )
=> ( ( ( uminus_uminus_a_a @ f @ A )
= zero_zero_a )
=> ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(130,axiom,
! [A: real] :
( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
= ( ord_less_eq_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_less__eq__neg__nonpos) ).
thf(725,plain,
! [A: real] :
( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
= ( ord_less_eq_real @ A @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(18,axiom,
! [A: a] :
( ( ord_less_eq_a @ ( uminus_uminus_a @ A ) @ zero_zero_a )
= ( ord_less_eq_a @ zero_zero_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_neg__le__0__iff__le) ).
thf(388,plain,
! [A: a] :
( ( ord_less_eq_a @ ( uminus_uminus_a @ A ) @ zero_zero_a )
= ( ord_less_eq_a @ zero_zero_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(121,axiom,
! [A: a] : ( ord_less_eq_real @ zero_zero_real @ ( inner_1173012732nner_a @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_inner__ge__zero) ).
thf(688,plain,
! [A: a] : ( ord_less_eq_real @ zero_zero_real @ ( inner_1173012732nner_a @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(689,plain,
! [A: a] : ( ord_less_eq_real @ zero_zero_real @ ( inner_1173012732nner_a @ A @ A ) ),
inference(cnf,[status(esa)],[688]) ).
thf(2418,plain,
! [B: a,A: a] :
( ( ord_less_eq_real @ zero_zero_real @ zero_zero_real )
| ( ( inner_1173012732nner_a @ A @ zero_zero_a )
!= ( inner_1173012732nner_a @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1185,689]) ).
thf(2419,plain,
ord_less_eq_real @ zero_zero_real @ zero_zero_real,
inference(pattern_uni,[status(thm)],[2418:[bind(A,$thf( zero_zero_a )),bind(B,$thf( zero_zero_a ))]]) ).
thf(449,plain,
! [B: real > $o,A: real] :
( ( member_real @ A @ ( collect_real @ B ) )
= ( B @ A ) ),
inference(cnf,[status(esa)],[448]) ).
thf(450,plain,
! [B: real > $o,A: real] :
( ( member_real @ A @ ( collect_real @ B ) )
= ( B @ A ) ),
inference(lifteq,[status(thm)],[449]) ).
thf(4647,plain,
! [B: real > $o,A: real] :
( ( member_real @ A @ ( collect_real @ B ) )
| ( ( ord_less_eq_real @ zero_zero_real @ zero_zero_real )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2419,450]) ).
thf(4840,plain,
( member_real @ zero_zero_real
@ ( collect_real
@ ^ [A: real] : ( ord_less_eq_real @ A @ A ) ) ),
inference(pre_uni,[status(thm)],[4647:[bind(A,$thf( zero_zero_real )),bind(B,$thf( ^ [C: real] : ( ord_less_eq_real @ C @ C ) ))]]) ).
thf(87,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ A ) @ ( uminus_uminus_set_a @ B ) )
= ( ord_less_eq_set_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_compl__le__compl__iff) ).
thf(593,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ A ) @ ( uminus_uminus_set_a @ B ) )
= ( ord_less_eq_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(265,axiom,
ord_less_eq_set_a @ ( line_c1152468841ment_a @ a2 @ b ) @ x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_seg_I2_J) ).
thf(1118,plain,
ord_less_eq_set_a @ ( line_c1152468841ment_a @ a2 @ b ) @ x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(57,axiom,
! [A: set_real,B: set_real,C: set_real,D: set_real] :
( ( ord_le861030508t_real @ ( set_or1619725421t_real @ A @ B ) @ ( set_or1619725421t_real @ C @ D ) )
= ( ( ~ ( ord_less_eq_set_real @ A @ B )
| ( ( ord_less_eq_set_real @ C @ A )
& ( ord_less_eq_set_real @ B @ D )
& ( ( ord_less_set_real @ C @ A )
| ( ord_less_set_real @ B @ D ) ) ) )
& ( ord_less_eq_set_real @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_atLeastatMost__psubset__iff) ).
thf(499,plain,
! [A: set_real,B: set_real,C: set_real,D: set_real] :
( ( ord_le861030508t_real @ ( set_or1619725421t_real @ A @ B ) @ ( set_or1619725421t_real @ C @ D ) )
= ( ( ~ ( ord_less_eq_set_real @ A @ B )
| ( ( ord_less_eq_set_real @ C @ A )
& ( ord_less_eq_set_real @ B @ D )
& ( ( ord_less_set_real @ C @ A )
| ( ord_less_set_real @ B @ D ) ) ) )
& ( ord_less_eq_set_real @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(176,axiom,
! [A: a,B: a] :
( ( ( real_V1514887919dist_a @ A @ B )
= zero_zero_real )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_dist__eq__0__iff) ).
thf(857,plain,
! [A: a,B: a] :
( ( ( real_V1514887919dist_a @ A @ B )
= zero_zero_real )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(82,axiom,
! [A: a] :
( ( zero_zero_a
= ( uminus_uminus_a @ A ) )
= ( zero_zero_a = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_neg__0__equal__iff__equal) ).
thf(578,plain,
! [A: a] :
( ( zero_zero_a
= ( uminus_uminus_a @ A ) )
= ( zero_zero_a = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(182,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_subset__iff) ).
thf(874,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(1111,plain,
( ord_less_real
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ~ ( ord_less_eq_real @ B @ A ) ) ) ),
inference(lifteq,[status(thm)],[1110]) ).
thf(304,axiom,
! [A: a] :
( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ( ( ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= zero_zero_real )
=> ( ( uminus_uminus_a_a @ f @ A )
= zero_zero_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_rev_Oclosed__orbit__period__zero__fixed__point) ).
thf(1227,plain,
! [A: a] :
( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ( ( ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= zero_zero_real )
=> ( ( uminus_uminus_a_a @ f @ A )
= zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(214,axiom,
! [A: a] :
( ( member_a @ A @ x )
=> ( ( ( uminus_uminus_a_a @ f @ A )
= zero_zero_a )
=> ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= top_top_set_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_rev_Ofixpoint__sol_I1_J) ).
thf(980,plain,
! [A: a] :
( ( member_a @ A @ x )
=> ( ( ( uminus_uminus_a_a @ f @ A )
= zero_zero_a )
=> ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= top_top_set_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(22,axiom,
! [A: a,B: a] :
( ( ord_less_a @ A @ ( uminus_uminus_a @ B ) )
= ( ord_less_a @ B @ ( uminus_uminus_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_less__minus__iff) ).
thf(401,plain,
! [A: a,B: a] :
( ( ord_less_a @ A @ ( uminus_uminus_a @ B ) )
= ( ord_less_a @ B @ ( uminus_uminus_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(402,plain,
! [B: a,A: a] :
( ( ord_less_a @ A @ ( uminus_uminus_a @ B ) )
= ( ord_less_a @ B @ ( uminus_uminus_a @ A ) ) ),
inference(cnf,[status(esa)],[401]) ).
thf(403,plain,
! [B: a,A: a] :
( ( ord_less_a @ A @ ( uminus_uminus_a @ B ) )
= ( ord_less_a @ B @ ( uminus_uminus_a @ A ) ) ),
inference(lifteq,[status(thm)],[402]) ).
thf(273,axiom,
! [A: a,B: a,C: a] :
( ( inner_1173012732nner_a @ ( minus_minus_a @ A @ B ) @ C )
= ( minus_minus_real @ ( inner_1173012732nner_a @ A @ C ) @ ( inner_1173012732nner_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_inner__diff__left) ).
thf(1138,plain,
! [A: a,B: a,C: a] :
( ( inner_1173012732nner_a @ ( minus_minus_a @ A @ B ) @ C )
= ( minus_minus_real @ ( inner_1173012732nner_a @ A @ C ) @ ( inner_1173012732nner_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(7,axiom,
! [A: set_real,B: set_real,C: set_real,D: set_real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( ord_less_eq_set_real @ C @ D )
=> ( ord_less_eq_set_real @ ( minus_minus_set_real @ A @ D ) @ ( minus_minus_set_real @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_Diff__mono) ).
thf(356,plain,
! [A: set_real,B: set_real,C: set_real,D: set_real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( ord_less_eq_set_real @ C @ D )
=> ( ord_less_eq_set_real @ ( minus_minus_set_real @ A @ D ) @ ( minus_minus_set_real @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(339,axiom,
! [A: real,B: a] :
( ( ord_less_real @ zero_zero_real @ A )
=> ? [C: a] :
( ( C != B )
& ( ord_less_real @ ( real_V1514887919dist_a @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_perfect__choose__dist) ).
thf(1329,plain,
! [A: real,B: a] :
( ( ord_less_real @ zero_zero_real @ A )
=> ? [C: a] :
( ( C != B )
& ( ord_less_real @ ( real_V1514887919dist_a @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(282,axiom,
! [A: real,B: real] :
( ( A = B )
| ~ ( ord_less_eq_real @ A @ B )
| ~ ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_verit__la__disequality) ).
thf(1160,plain,
! [A: real,B: real] :
( ( A = B )
| ~ ( ord_less_eq_real @ A @ B )
| ~ ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(232,axiom,
! [A: a] :
( ( period720806154rbit_a @ f @ x @ A )
=> ( ( auto_l612940ivl0_a @ f @ x @ A )
= top_top_set_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_closed__orbit__global__existence) ).
thf(1028,plain,
! [A: a] :
( ( period720806154rbit_a @ f @ x @ A )
=> ( ( auto_l612940ivl0_a @ f @ x @ A )
= top_top_set_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(202,axiom,
! [A: a] :
( ( period720806154rbit_a @ f @ x @ A )
=> ( ord_less_eq_real @ zero_zero_real @ ( period1305449585riod_a @ f @ x @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_closed__orbit__period__nonneg) ).
thf(933,plain,
! [A: a] :
( ( period720806154rbit_a @ f @ x @ A )
=> ( ord_less_eq_real @ zero_zero_real @ ( period1305449585riod_a @ f @ x @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(140,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( member_real @ A @ top_top_set_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_local_Omem__existence__ivl__subset) ).
thf(753,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( member_real @ A @ top_top_set_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(136,axiom,
! [A: a] :
( ( inner_1173012732nner_a @ zero_zero_a @ A )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_inner__zero__left) ).
thf(743,plain,
! [A: a] :
( ( inner_1173012732nner_a @ zero_zero_a @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(744,plain,
! [A: a] :
( ( inner_1173012732nner_a @ zero_zero_a @ A )
= zero_zero_real ),
inference(cnf,[status(esa)],[743]) ).
thf(745,plain,
! [A: a] :
( ( inner_1173012732nner_a @ zero_zero_a @ A )
= zero_zero_real ),
inference(lifteq,[status(thm)],[744]) ).
thf(1735,plain,
! [B: real,A: a] :
( ~ ( ord_less_real @ zero_zero_real @ B )
| ~ ( ord_less_eq_real @ d @ zero_zero_real )
| ( ( inner_1173012732nner_a @ zero_zero_a @ A )
!= ( inner_1173012732nner_a @ ( f @ ( sk1 @ d @ B ) ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[745,1346]) ).
thf(1736,plain,
! [B: real,A: a] :
( ~ ( ord_less_real @ zero_zero_real @ B )
| ~ ( ord_less_eq_real @ d @ zero_zero_real )
| ( ( f @ ( sk1 @ d @ B ) )
!= zero_zero_a )
| ( A
!= ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ),
inference(simp,[status(thm)],[1735]) ).
thf(1739,plain,
! [A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ~ ( ord_less_eq_real @ d @ zero_zero_real )
| ( ( f @ ( sk1 @ d @ A ) )
!= zero_zero_a ) ),
inference(simp,[status(thm)],[1736]) ).
thf(66,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_eq_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_equalityE) ).
thf(526,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_eq_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(103,axiom,
! [A: real > $o,B: real > $o] :
( ( ord_less_eq_set_real @ ( collect_real @ A ) @ ( collect_real @ B ) )
= ( ! [C: real] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_Collect__mono__iff) ).
thf(637,plain,
! [A: real > $o,B: real > $o] :
( ( ord_less_eq_set_real @ ( collect_real @ A ) @ ( collect_real @ B ) )
= ( ! [C: real] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(275,axiom,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( minus_minus_a @ A @ B )
= zero_zero_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_eq__iff__diff__eq__0) ).
thf(1144,plain,
( ( (=) @ a )
= ( ^ [A: a,B: a] :
( ( minus_minus_a @ A @ B )
= zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(1145,plain,
( ( ^ [A: a,B: a] :
( ( minus_minus_a @ A @ B )
= zero_zero_a ) )
= ( (=) @ a ) ),
inference(lifteq,[status(thm)],[1144]) ).
thf(1446,plain,
! [A: a] :
( ( ^ [B: a] :
( ( minus_minus_a @ A @ B )
= zero_zero_a ) )
= ( (=) @ a @ A ) ),
inference(func_ext,[status(esa)],[1145]) ).
thf(280,axiom,
! [A: a] :
( ( member_a @ A @ ( line_c1152468841ment_a @ a2 @ b ) )
=> ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ A ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_seg_I3_J) ).
thf(1155,plain,
! [A: a] :
( ( member_a @ A @ ( line_c1152468841ment_a @ a2 @ b ) )
=> ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ A ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(127,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ C @ D )
=> ( ord_less_eq_a @ ( minus_minus_a @ A @ D ) @ ( minus_minus_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_diff__mono) ).
thf(706,plain,
! [A: a,B: a,C: a,D: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ( ord_less_eq_a @ C @ D )
=> ( ord_less_eq_a @ ( minus_minus_a @ A @ D ) @ ( minus_minus_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(249,axiom,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
=> ( ( member_a @ A @ x )
=> ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_local_Oexistence__ivl__initial__time) ).
thf(1075,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
=> ( ( member_a @ A @ x )
=> ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(48,axiom,
! [A: real,B: real] :
( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B )
= ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_minus__diff__commute) ).
thf(476,plain,
! [A: real,B: real] :
( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B )
= ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(228,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ zero_zero_a @ ( minus_minus_a @ A @ B ) )
= ( ord_less_eq_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_diff__ge__0__iff__ge) ).
thf(1016,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ zero_zero_a @ ( minus_minus_a @ A @ B ) )
= ( ord_less_eq_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(86,axiom,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_cancel__ab__semigroup__add__class_Odiff__right__commute) ).
thf(590,plain,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(117,axiom,
( inner_1173012732nner_a
= ( ^ [A: a,B: a] : ( inner_1173012732nner_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_inner__commute) ).
thf(679,plain,
( inner_1173012732nner_a
= ( ^ [A: a,B: a] : ( inner_1173012732nner_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(236,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( minus_minus_real @ C @ B ) @ ( minus_minus_real @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_diff__left__mono) ).
thf(1039,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( minus_minus_real @ C @ B ) @ ( minus_minus_real @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(337,axiom,
! [A: a] :
( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= ( period720806154rbit_a @ f @ x @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_rev_Oclosed__orbit__eq__rev) ).
thf(1324,plain,
! [A: a] :
( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= ( period720806154rbit_a @ f @ x @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(329,axiom,
! [A: a] :
( ( minus_minus_a @ zero_zero_a @ A )
= ( uminus_uminus_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_verit__minus__simplify_I3_J) ).
thf(1297,plain,
! [A: a] :
( ( minus_minus_a @ zero_zero_a @ A )
= ( uminus_uminus_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(223,axiom,
! [A: a,B: a,C: real] :
( ( ord_less_real @ ( real_V1514887919dist_a @ A @ B ) @ C )
=> ( ord_less_real @ ( real_V1514887919dist_a @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_dist__commute__lessI) ).
thf(1002,plain,
! [A: a,B: a,C: real] :
( ( ord_less_real @ ( real_V1514887919dist_a @ A @ B ) @ C )
=> ( ord_less_real @ ( real_V1514887919dist_a @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(79,axiom,
! [A: a] :
( ( ord_less_eq_a @ zero_zero_a @ ( uminus_uminus_a @ A ) )
= ( ord_less_eq_a @ A @ zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_neg__0__le__iff__le) ).
thf(569,plain,
! [A: a] :
( ( ord_less_eq_a @ zero_zero_a @ ( uminus_uminus_a @ A ) )
= ( ord_less_eq_a @ A @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(311,axiom,
! [A: a] :
( ( member_a @ A @ x )
=> ? [B: real,C: real] :
( ( ord_less_real @ B @ zero_zero_real )
& ( ord_less_real @ zero_zero_real @ C )
& ( ord_less_eq_set_real @ ( set_or656347191t_real @ B @ C ) @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_open__existence__ivl0) ).
thf(1246,plain,
! [A: a] :
( ( member_a @ A @ x )
=> ? [B: real,C: real] :
( ( ord_less_real @ B @ zero_zero_real )
& ( ord_less_real @ zero_zero_real @ C )
& ( ord_less_eq_set_real @ ( set_or656347191t_real @ B @ C ) @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(107,axiom,
! [A: set_real,B: set_real,C: real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( member_real @ C @ A )
=> ( member_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_subsetD) ).
thf(647,plain,
! [A: set_real,B: set_real,C: real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( member_real @ C @ A )
=> ( member_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(316,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ? [C: a] : ( member_a @ C @ ( minus_minus_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_psubset__imp__ex__mem) ).
thf(1263,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ? [C: a] : ( member_a @ C @ ( minus_minus_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(271,axiom,
a2 != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_seg_I1_J) ).
thf(1131,plain,
a2 != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(109,axiom,
! [A: a] :
( ( ( uminus_uminus_a @ A )
= zero_zero_a )
= ( A = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_neg__equal__0__iff__equal) ).
thf(654,plain,
! [A: a] :
( ( ( uminus_uminus_a @ A )
= zero_zero_a )
= ( A = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(240,axiom,
! [A: set_a,B: set_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_subsetI) ).
thf(1050,plain,
! [A: set_a,B: set_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(42,axiom,
! [A: real,B: real] :
( ( inner_4346926r_real @ ( uminus_uminus_real @ A ) @ B )
= ( uminus_uminus_real @ ( inner_4346926r_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_inner__minus__left) ).
thf(457,plain,
! [A: real,B: real] :
( ( inner_4346926r_real @ ( uminus_uminus_real @ A ) @ B )
= ( uminus_uminus_real @ ( inner_4346926r_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(295,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ord_less_eq_a @ ( minus_minus_a @ A @ C ) @ ( minus_minus_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_diff__right__mono) ).
thf(1202,plain,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ord_less_eq_a @ ( minus_minus_a @ A @ C ) @ ( minus_minus_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(102,axiom,
! [A: set_real,B: set_real] :
( ( A = B )
=> ( ord_less_eq_set_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_equalityD1) ).
thf(633,plain,
! [A: set_real,B: set_real] :
( ( A = B )
=> ( ord_less_eq_set_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(160,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_diff__right__mono) ).
thf(805,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(110,axiom,
! [A: set_real,B: set_real,C: real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( member_real @ C @ A )
=> ( member_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_in__mono) ).
thf(657,plain,
! [A: set_real,B: set_real,C: real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( member_real @ C @ A )
=> ( member_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(241,axiom,
! [A: a,B: a] :
( ( uminus_uminus_a @ ( minus_minus_a @ A @ B ) )
= ( minus_minus_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_minus__diff__eq) ).
thf(1054,plain,
! [A: a,B: a] :
( ( uminus_uminus_a @ ( minus_minus_a @ A @ B ) )
= ( minus_minus_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(75,axiom,
! [A: a] :
( ( ord_less_a @ zero_zero_a @ ( uminus_uminus_a @ A ) )
= ( ord_less_a @ A @ zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_neg__0__less__iff__less) ).
thf(558,plain,
! [A: a] :
( ( ord_less_a @ zero_zero_a @ ( uminus_uminus_a @ A ) )
= ( ord_less_a @ A @ zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(1893,plain,
! [A: real] :
( ~ $true
| ( member_a @ ( sk1 @ A @ sk11 ) @ ( elemen49976720ball_a @ x2 @ sk11 ) )
| ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[681,1367]) ).
thf(1894,plain,
! [A: real] :
( ( member_a @ ( sk1 @ A @ sk11 ) @ ( elemen49976720ball_a @ x2 @ sk11 ) )
| ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(simp,[status(thm)],[1893]) ).
thf(1895,plain,
member_a @ ( sk1 @ ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) @ sk11 ) @ ( elemen49976720ball_a @ x2 @ sk11 ),
inference(pattern_uni,[status(thm)],[1894:[bind(A,$thf( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ))]]) ).
thf(187,axiom,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(888,plain,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(335,axiom,
! [A: a] :
( ( member_a @ A @ x )
=> ( ( ( uminus_uminus_a_a @ f @ A )
= zero_zero_a )
=> ( ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_rev_Ofixed__point__imp__closed__orbit__period__zero_I2_J) ).
thf(1318,plain,
! [A: a] :
( ( member_a @ A @ x )
=> ( ( ( uminus_uminus_a_a @ f @ A )
= zero_zero_a )
=> ( ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(21,axiom,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ord_less_eq_set_a @ ( minus_minus_set_a @ A @ D ) @ ( minus_minus_set_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_Diff__mono) ).
thf(398,plain,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ord_less_eq_set_a @ ( minus_minus_set_a @ A @ D ) @ ( minus_minus_set_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(4588,plain,
! [B: real > $o,A: real] :
( ~ ( member_real @ A @ ( collect_real @ B ) )
| ( ( B @ A )
!= ( ord_less_real @ zero_zero_real @ zero_zero_real ) ) ),
inference(paramod_ordered,[status(thm)],[450,4376]) ).
thf(4906,plain,
~ ( member_real @ zero_zero_real
@ ( collect_real
@ ^ [A: real] : ( ord_less_real @ A @ A ) ) ),
inference(pre_uni,[status(thm)],[4588:[bind(A,$thf( zero_zero_real )),bind(B,$thf( ^ [C: real] : ( ord_less_real @ C @ C ) ))]]) ).
thf(115,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_a @ A @ B )
=> ( ord_less_a @ ( minus_minus_a @ C @ B ) @ ( minus_minus_a @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_diff__strict__left__mono) ).
thf(674,plain,
! [A: a,B: a,C: a] :
( ( ord_less_a @ A @ B )
=> ( ord_less_a @ ( minus_minus_a @ C @ B ) @ ( minus_minus_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(193,axiom,
! [A: a] :
( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
& ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_rev_Operiodic__orbit__def) ).
thf(906,plain,
! [A: a] :
( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= ( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
& ( ord_less_real @ zero_zero_real @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(25,axiom,
! [A: a] :
( ( ord_less_a @ ( uminus_uminus_a @ A ) @ zero_zero_a )
= ( ord_less_a @ zero_zero_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_neg__less__0__iff__less) ).
thf(410,plain,
! [A: a] :
( ( ord_less_a @ ( uminus_uminus_a @ A ) @ zero_zero_a )
= ( ord_less_a @ zero_zero_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(411,plain,
! [A: a] :
( ( ord_less_a @ ( uminus_uminus_a @ A ) @ zero_zero_a )
= ( ord_less_a @ zero_zero_a @ A ) ),
inference(cnf,[status(esa)],[410]) ).
thf(412,plain,
! [A: a] :
( ( ord_less_a @ ( uminus_uminus_a @ A ) @ zero_zero_a )
= ( ord_less_a @ zero_zero_a @ A ) ),
inference(lifteq,[status(thm)],[411]) ).
thf(112,axiom,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ~ ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_subset__not__subset__eq) ).
thf(663,plain,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ~ ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(664,plain,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ~ ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(lifteq,[status(thm)],[663]) ).
thf(80,axiom,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_psubset__eq) ).
thf(572,plain,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(573,plain,
( ord_less_set_a
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( A != B ) ) ) ),
inference(lifteq,[status(thm)],[572]) ).
thf(1509,plain,
( ( ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ~ ( ord_less_eq_set_a @ B @ A ) ) )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( A != B ) ) ) )
| ( ord_less_set_a != ord_less_set_a ) ),
inference(paramod_ordered,[status(thm)],[664,573]) ).
thf(1510,plain,
( ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ~ ( ord_less_eq_set_a @ B @ A ) ) )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( A != B ) ) ) ),
inference(pattern_uni,[status(thm)],[1509:[]]) ).
thf(1759,plain,
! [A: a] :
( ~ ( ord_less_eq_real @ d @ zero_zero_real )
| ( ( inner_1173012732nner_a @ zero_zero_a @ A )
!= ( inner_1173012732nner_a @ ( f @ ( sk1 @ d @ d ) ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[745,1730]) ).
thf(1762,plain,
! [A: a] :
( ~ ( ord_less_eq_real @ d @ zero_zero_real )
| ( ( f @ ( sk1 @ d @ d ) )
!= zero_zero_a )
| ( A
!= ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ),
inference(simp,[status(thm)],[1759]) ).
thf(1764,plain,
( ~ ( ord_less_eq_real @ d @ zero_zero_real )
| ( ( f @ ( sk1 @ d @ d ) )
!= zero_zero_a ) ),
inference(simp,[status(thm)],[1762]) ).
thf(1731,plain,
! [A: real] :
( ~ $true
| ~ ( ord_less_eq_real @ d @ ( inner_1173012732nner_a @ ( f @ ( sk1 @ d @ A ) ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
| ( ( ord_less_real @ zero_zero_real @ sk11 )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[830,1346]) ).
thf(1732,plain,
! [A: real] :
( ~ ( ord_less_eq_real @ d @ ( inner_1173012732nner_a @ ( f @ ( sk1 @ d @ A ) ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
| ( ( ord_less_real @ zero_zero_real @ sk11 )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(simp,[status(thm)],[1731]) ).
thf(1733,plain,
~ ( ord_less_eq_real @ d @ ( inner_1173012732nner_a @ ( f @ ( sk1 @ d @ sk11 ) ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ),
inference(pattern_uni,[status(thm)],[1732:[bind(A,$thf( sk11 ))]]) ).
thf(2183,plain,
! [A: a] :
( ~ ( ord_less_eq_real @ d @ ( inner_1173012732nner_a @ ( f @ ( sk1 @ d @ sk11 ) ) @ ( poinca659159244_rot_a @ A ) ) )
| ( ( minus_minus_a @ A @ zero_zero_a )
!= ( minus_minus_a @ a2 @ b ) ) ),
inference(paramod_ordered,[status(thm)],[881,1733]) ).
thf(2198,plain,
! [A: a] :
( ~ ( ord_less_eq_real @ d @ ( inner_1173012732nner_a @ ( f @ ( sk1 @ d @ sk11 ) ) @ ( poinca659159244_rot_a @ A ) ) )
| ( A != a2 )
| ( b != zero_zero_a ) ),
inference(simp,[status(thm)],[2183]) ).
thf(2209,plain,
( ~ ( ord_less_eq_real @ d @ ( inner_1173012732nner_a @ ( f @ ( sk1 @ d @ sk11 ) ) @ ( poinca659159244_rot_a @ a2 ) ) )
| ( b != zero_zero_a ) ),
inference(simp,[status(thm)],[2198]) ).
thf(2533,plain,
! [A: a] :
( ~ ( ord_less_eq_real @ d @ zero_zero_real )
| ( b != zero_zero_a )
| ( ( inner_1173012732nner_a @ A @ ( poinca659159244_rot_a @ A ) )
!= ( inner_1173012732nner_a @ ( f @ ( sk1 @ d @ sk11 ) ) @ ( poinca659159244_rot_a @ a2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[864,2209]) ).
thf(2542,plain,
! [A: a] :
( ~ ( ord_less_eq_real @ d @ zero_zero_real )
| ( b != zero_zero_a )
| ( A
!= ( f @ ( sk1 @ d @ sk11 ) ) )
| ( ( poinca659159244_rot_a @ A )
!= ( poinca659159244_rot_a @ a2 ) ) ),
inference(simp,[status(thm)],[2533]) ).
thf(2556,plain,
( ~ ( ord_less_eq_real @ d @ zero_zero_real )
| ( b != zero_zero_a )
| ( ( poinca659159244_rot_a @ ( f @ ( sk1 @ d @ sk11 ) ) )
!= ( poinca659159244_rot_a @ a2 ) ) ),
inference(simp,[status(thm)],[2542]) ).
thf(2372,plain,
! [B: a,A: a > a] :
( ( initia826609931terval
@ ( auto_l612940ivl0_a
@ ^ [C: a] : ( uminus_uminus_a @ ( A @ C ) )
@ x
@ B ) )
| ( ( uminus_uminus_a_a @ A )
!= ( uminus_uminus_a_a @ f ) ) ),
inference(paramod_ordered,[status(thm)],[1337,1058]) ).
thf(2373,plain,
! [A: a] :
( initia826609931terval
@ ( auto_l612940ivl0_a
@ ^ [B: a] : ( uminus_uminus_a @ ( f @ B ) )
@ x
@ A ) ),
inference(pattern_uni,[status(thm)],[2372:[bind(A,$thf( f )),bind(B,$thf( B ))]]) ).
thf(2374,plain,
! [A: a] :
( initia826609931terval
@ ( auto_l612940ivl0_a
@ ^ [B: a] : ( uminus_uminus_a @ ( f @ B ) )
@ x
@ A ) ),
inference(simp,[status(thm)],[2373]) ).
thf(2377,plain,
! [B: a,A: set_real] :
( ( initia826609931terval
@ ( collect_real
@ ^ [C: real] : ( member_real @ C @ A ) ) )
| ( A
!= ( auto_l612940ivl0_a
@ ^ [C: a] : ( uminus_uminus_a @ ( f @ C ) )
@ x
@ B ) ) ),
inference(paramod_ordered,[status(thm)],[426,2374]) ).
thf(2378,plain,
! [A: a] :
( initia826609931terval
@ ( collect_real
@ ^ [B: real] :
( member_real @ B
@ ( auto_l612940ivl0_a
@ ^ [C: a] : ( uminus_uminus_a @ ( f @ C ) )
@ x
@ A ) ) ) ),
inference(pattern_uni,[status(thm)],[2377:[bind(A,$thf( auto_l612940ivl0_a @ ^ [D: a] : ( uminus_uminus_a @ ( f @ D ) ) @ x @ E )),bind(B,$thf( E ))]]) ).
thf(2379,plain,
! [A: a] :
( initia826609931terval
@ ( collect_real
@ ^ [B: real] :
( member_real @ B
@ ( auto_l612940ivl0_a
@ ^ [C: a] : ( uminus_uminus_a @ ( f @ C ) )
@ x
@ A ) ) ) ),
inference(simp,[status(thm)],[2378]) ).
thf(2597,plain,
! [B: a,A: set_real] :
( ( initia826609931terval
@ ( collect_real
@ ^ [C: real] : ( member_real @ C @ A ) ) )
| ( A
!= ( collect_real
@ ^ [C: real] :
( member_real @ C
@ ( auto_l612940ivl0_a
@ ^ [D: a] : ( uminus_uminus_a @ ( f @ D ) )
@ x
@ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[426,2379]) ).
thf(2598,plain,
! [A: a] :
( initia826609931terval
@ ( collect_real
@ ^ [B: real] :
( member_real @ B
@ ( collect_real
@ ^ [C: real] :
( member_real @ C
@ ( auto_l612940ivl0_a
@ ^ [D: a] : ( uminus_uminus_a @ ( f @ D ) )
@ x
@ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2597:[bind(A,$thf( collect_real @ ^ [C: real] : ( member_real @ C @ ( auto_l612940ivl0_a @ ^ [D: a] : ( uminus_uminus_a @ ( f @ D ) ) @ x @ B ) ) )),bind(B,$thf( B ))]]) ).
thf(2602,plain,
! [A: a] :
( initia826609931terval
@ ( collect_real
@ ^ [B: real] :
( member_real @ B
@ ( collect_real
@ ^ [C: real] :
( member_real @ C
@ ( auto_l612940ivl0_a
@ ^ [D: a] : ( uminus_uminus_a @ ( f @ D ) )
@ x
@ A ) ) ) ) ) ),
inference(simp,[status(thm)],[2598]) ).
thf(444,plain,
! [B: a,A: a] :
( ~ ( ord_less_a @ A @ B )
| ( ord_less_a @ ( uminus_uminus_a @ B ) @ ( uminus_uminus_a @ A ) ) ),
inference(cnf,[status(esa)],[443]) ).
thf(132,axiom,
! [A: real] :
( ( minus_minus_real @ zero_zero_real @ A )
= ( uminus_uminus_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_diff__0) ).
thf(731,plain,
! [A: real] :
( ( minus_minus_real @ zero_zero_real @ A )
= ( uminus_uminus_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(732,plain,
! [A: real] :
( ( minus_minus_real @ zero_zero_real @ A )
= ( uminus_uminus_real @ A ) ),
inference(cnf,[status(esa)],[731]) ).
thf(733,plain,
! [A: real] :
( ( minus_minus_real @ zero_zero_real @ A )
= ( uminus_uminus_real @ A ) ),
inference(lifteq,[status(thm)],[732]) ).
thf(61,axiom,
! [A: a,B: a] :
( ( ord_less_a @ ( uminus_uminus_a @ A ) @ ( uminus_uminus_a @ B ) )
= ( ord_less_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_neg__less__iff__less) ).
thf(513,plain,
! [A: a,B: a] :
( ( ord_less_a @ ( uminus_uminus_a @ A ) @ ( uminus_uminus_a @ B ) )
= ( ord_less_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(32,axiom,
( ord_less_set_real
= ( ^ [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
& ~ ( ord_less_eq_set_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_subset__not__subset__eq) ).
thf(430,plain,
( ord_less_set_real
= ( ^ [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
& ~ ( ord_less_eq_set_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(84,axiom,
! [A: a,B: a] :
( ( A = B )
=> ( ( uminus_uminus_a @ A )
= ( uminus_uminus_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_verit__negate__coefficient_I3_J) ).
thf(584,plain,
! [A: a,B: a] :
( ( A = B )
=> ( ( uminus_uminus_a @ A )
= ( uminus_uminus_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(4041,plain,
( ~ ( ord_less_eq_real @ d @ zero_zero_real )
| ( b != zero_zero_a )
| ( ( f @ ( sk1 @ d @ sk11 ) )
!= a2 ) ),
inference(simp,[status(thm)],[2556]) ).
thf(29,axiom,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ ( minus_minus_set_a @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_Diff__subset) ).
thf(422,plain,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ ( minus_minus_set_a @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(423,plain,
! [B: set_a,A: set_a] : ( ord_less_eq_set_a @ ( minus_minus_set_a @ A @ B ) @ A ),
inference(cnf,[status(esa)],[422]) ).
thf(225,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ord_less_eq_real @ ( minus_minus_real @ A @ D ) @ ( minus_minus_real @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_diff__mono) ).
thf(1007,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ord_less_eq_real @ ( minus_minus_real @ A @ D ) @ ( minus_minus_real @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(1882,plain,
! [A: real] :
( ~ $true
| ( member_a @ ( sk1 @ A @ d ) @ ( elemen49976720ball_a @ x2 @ d ) )
| ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[681,1353]) ).
thf(1883,plain,
! [A: real] :
( ( member_a @ ( sk1 @ A @ d ) @ ( elemen49976720ball_a @ x2 @ d ) )
| ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(simp,[status(thm)],[1882]) ).
thf(1884,plain,
member_a @ ( sk1 @ ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) @ d ) @ ( elemen49976720ball_a @ x2 @ d ),
inference(pattern_uni,[status(thm)],[1883:[bind(A,$thf( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ))]]) ).
thf(72,axiom,
! [A: a,B: a] :
( ( ( uminus_uminus_a @ A )
= ( uminus_uminus_a @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_neg__equal__iff__equal) ).
thf(545,plain,
! [A: a,B: a] :
( ( ( uminus_uminus_a @ A )
= ( uminus_uminus_a @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(26,axiom,
! [A: real] :
( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_verit__minus__simplify_I4_J) ).
thf(413,plain,
! [A: real] :
( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(268,axiom,
! [A: a] :
( ( period720806154rbit_a @ f @ x @ A )
=> ( member_a @ A @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_closed__orbit__in__domain) ).
thf(1125,plain,
! [A: a] :
( ( period720806154rbit_a @ f @ x @ A )
=> ( member_a @ A @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(210,axiom,
! [A: real,B: real,C: real > real > $o] :
( ( ord_less_eq_real @ A @ B )
=> ( ! [D: real,E: real,F: real] :
( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( ( ord_less_eq_real @ D @ E )
=> ( ( ord_less_eq_real @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( ! [D: real] :
( ( ord_less_eq_real @ A @ D )
=> ( ( ord_less_eq_real @ D @ B )
=> ? [E: real] :
( ( ord_less_real @ zero_zero_real @ E )
& ! [F: real,G: real] :
( ( ( ord_less_eq_real @ F @ D )
& ( ord_less_eq_real @ D @ G )
& ( ord_less_real @ ( minus_minus_real @ G @ F ) @ E ) )
=> ( C @ F @ G ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_Bolzano) ).
thf(958,plain,
! [A: real,B: real,C: real > real > $o] :
( ( ord_less_eq_real @ A @ B )
=> ( ! [D: real,E: real,F: real] :
( ( C @ D @ E )
=> ( ( C @ E @ F )
=> ( ( ord_less_eq_real @ D @ E )
=> ( ( ord_less_eq_real @ E @ F )
=> ( C @ D @ F ) ) ) ) )
=> ( ! [D: real] :
( ( ord_less_eq_real @ A @ D )
=> ( ( ord_less_eq_real @ D @ B )
=> ? [E: real] :
( ( ord_less_real @ zero_zero_real @ E )
& ! [F: real,G: real] :
( ( ( ord_less_eq_real @ F @ D )
& ( ord_less_eq_real @ D @ G )
& ( ord_less_real @ ( minus_minus_real @ G @ F ) @ E ) )
=> ( C @ F @ G ) ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(19,axiom,
! [A: set_real,B: set_real] :
( ( A = B )
=> ( ord_less_eq_set_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_equalityD2) ).
thf(391,plain,
! [A: set_real,B: set_real] :
( ( A = B )
=> ( ord_less_eq_set_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(38,axiom,
! [A: a,B: a] :
( ( ord_less_a @ ( uminus_uminus_a @ A ) @ B )
= ( ord_less_a @ ( uminus_uminus_a @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_minus__less__iff) ).
thf(445,plain,
! [A: a,B: a] :
( ( ord_less_a @ ( uminus_uminus_a @ A ) @ B )
= ( ord_less_a @ ( uminus_uminus_a @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(382,plain,
! [B: set_real,A: set_real] :
( ~ ( member_real @ ( sk2 @ B @ A ) @ B )
| ( ord_less_eq_set_real @ A @ B ) ),
inference(cnfConj,[status(thm)],[380]) ).
thf(319,axiom,
! [A: a,B: a] :
( ( A != B )
=> ( ord_less_real @ zero_zero_real @ ( real_V1514887919dist_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_dist__pos__lt) ).
thf(1271,plain,
! [A: a,B: a] :
( ( A != B )
=> ( ord_less_real @ zero_zero_real @ ( real_V1514887919dist_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(334,axiom,
! [A: a] :
( ( member_a @ A @ ( elemen49976720ball_a @ x2 @ d ) )
=> ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ A ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
& ( member_a @ A @ x )
& ( ( f @ A )
!= zero_zero_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_d_I2_J) ).
thf(1312,plain,
! [A: a] :
( ( member_a @ A @ ( elemen49976720ball_a @ x2 @ d ) )
=> ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ A ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
& ( member_a @ A @ x )
& ( ( f @ A )
!= zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(1863,plain,
! [A: real] :
( ~ $true
| ( ( f @ ( sk1 @ A @ sk11 ) )
!= zero_zero_a )
| ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[681,1438]) ).
thf(1864,plain,
! [A: real] :
( ( ( f @ ( sk1 @ A @ sk11 ) )
!= zero_zero_a )
| ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(simp,[status(thm)],[1863]) ).
thf(1865,plain,
( ( f @ ( sk1 @ ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) @ sk11 ) )
!= zero_zero_a ),
inference(pattern_uni,[status(thm)],[1864:[bind(A,$thf( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ))]]) ).
thf(314,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( ord_less_eq_set_real @ ( set_or656347191t_real @ A @ zero_zero_real ) @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_local_Oivl__subset__existence__ivl_H) ).
thf(1258,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( ord_less_eq_set_real @ ( set_or656347191t_real @ A @ zero_zero_real ) @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(431,plain,
( ord_less_set_real
= ( ^ [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
& ~ ( ord_less_eq_set_real @ B @ A ) ) ) ),
inference(lifteq,[status(thm)],[430]) ).
thf(1463,plain,
( ( ( ^ [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
& ~ ( ord_less_eq_set_real @ B @ A ) ) )
= ( ^ [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
& ( A != B ) ) ) )
| ( ord_less_set_real != ord_less_set_real ) ),
inference(paramod_ordered,[status(thm)],[439,431]) ).
thf(1464,plain,
( ( ^ [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
& ~ ( ord_less_eq_set_real @ B @ A ) ) )
= ( ^ [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
& ( A != B ) ) ) ),
inference(pattern_uni,[status(thm)],[1463:[]]) ).
thf(303,axiom,
! [A: a,B: a,C: a] :
( ( inner_1173012732nner_a @ A @ ( poinca659159244_rot_a @ ( minus_minus_a @ B @ C ) ) )
= ( inner_1173012732nner_a @ ( uminus_uminus_a @ A ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_nrm__reverse) ).
thf(1224,plain,
! [A: a,B: a,C: a] :
( ( inner_1173012732nner_a @ A @ ( poinca659159244_rot_a @ ( minus_minus_a @ B @ C ) ) )
= ( inner_1173012732nner_a @ ( uminus_uminus_a @ A ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(5,axiom,
! [A: real,B: set_real,C: set_real] :
( ( member_real @ A @ ( minus_minus_set_real @ B @ C ) )
=> ( member_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_DiffD1) ).
thf(350,plain,
! [A: real,B: set_real,C: set_real] :
( ( member_real @ A @ ( minus_minus_set_real @ B @ C ) )
=> ( member_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(69,axiom,
( ord_less_eq_set_real
= ( ^ [A: set_real,B: set_real] :
( ( ord_less_set_real @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_subset__iff__psubset__eq) ).
thf(539,plain,
( ord_less_eq_set_real
= ( ^ [A: set_real,B: set_real] :
( ( ord_less_set_real @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(540,plain,
( ord_less_eq_set_real
= ( ^ [A: set_real,B: set_real] :
( ( ord_less_set_real @ A @ B )
| ( A = B ) ) ) ),
inference(lifteq,[status(thm)],[539]) ).
thf(2190,plain,
! [A: a] :
( ( ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ A ) )
!= zero_zero_real )
| ( ( minus_minus_a @ A @ zero_zero_a )
!= ( minus_minus_a @ a2 @ b ) ) ),
inference(paramod_ordered,[status(thm)],[881,1902]) ).
thf(2193,plain,
! [A: a] :
( ( ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ A ) )
!= zero_zero_real )
| ( A != a2 )
| ( b != zero_zero_a ) ),
inference(simp,[status(thm)],[2190]) ).
thf(2206,plain,
( ( ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ a2 ) )
!= zero_zero_real )
| ( b != zero_zero_a ) ),
inference(simp,[status(thm)],[2193]) ).
thf(2539,plain,
! [A: a] :
( ( zero_zero_real != zero_zero_real )
| ( b != zero_zero_a )
| ( ( inner_1173012732nner_a @ A @ ( poinca659159244_rot_a @ A ) )
!= ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ a2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[864,2206]) ).
thf(2540,plain,
! [A: a] :
( ( b != zero_zero_a )
| ( ( inner_1173012732nner_a @ A @ ( poinca659159244_rot_a @ A ) )
!= ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ a2 ) ) ) ),
inference(simp,[status(thm)],[2539]) ).
thf(2543,plain,
! [A: a] :
( ( b != zero_zero_a )
| ( A
!= ( f @ x2 ) )
| ( ( poinca659159244_rot_a @ A )
!= ( poinca659159244_rot_a @ a2 ) ) ),
inference(simp,[status(thm)],[2540]) ).
thf(2557,plain,
( ( b != zero_zero_a )
| ( ( poinca659159244_rot_a @ ( f @ x2 ) )
!= ( poinca659159244_rot_a @ a2 ) ) ),
inference(simp,[status(thm)],[2543]) ).
thf(3478,plain,
! [A: a] :
( ( zero_zero_real != zero_zero_real )
| ( ( inner_1173012732nner_a @ ( uminus_uminus_a @ ( poinca659159244_rot_a @ A ) ) @ A )
!= ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3438,1989]) ).
thf(3479,plain,
! [A: a] :
( ( inner_1173012732nner_a @ ( uminus_uminus_a @ ( poinca659159244_rot_a @ A ) ) @ A )
!= ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ),
inference(simp,[status(thm)],[3478]) ).
thf(3501,plain,
! [A: a] :
( ( ( uminus_uminus_a @ ( poinca659159244_rot_a @ A ) )
!= ( f @ z ) )
| ( A
!= ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ),
inference(simp,[status(thm)],[3479]) ).
thf(3522,plain,
( ( uminus_uminus_a @ ( poinca659159244_rot_a @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
!= ( f @ z ) ),
inference(simp,[status(thm)],[3501]) ).
thf(3641,plain,
( ( uminus_uminus_a @ ( uminus_uminus_a @ ( minus_minus_a @ a2 @ b ) ) )
!= ( f @ z ) ),
inference(rewrite,[status(thm)],[3522,991]) ).
thf(92,axiom,
( uminus_uminus_a_a
= ( ^ [A: a > a,B: a] : ( uminus_uminus_a @ ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_fun__Compl__def) ).
thf(604,plain,
( uminus_uminus_a_a
= ( ^ [A: a > a,B: a] : ( uminus_uminus_a @ ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(298,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ord_less_eq_a @ ( minus_minus_a @ C @ B ) @ ( minus_minus_a @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_diff__left__mono) ).
thf(1209,plain,
! [A: a,B: a,C: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ord_less_eq_a @ ( minus_minus_a @ C @ B ) @ ( minus_minus_a @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(2182,plain,
! [A: a] :
( ( ( f @ ( sk1 @ ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ A ) ) @ sk11 ) )
!= zero_zero_a )
| ( ( minus_minus_a @ A @ zero_zero_a )
!= ( minus_minus_a @ a2 @ b ) ) ),
inference(paramod_ordered,[status(thm)],[881,1865]) ).
thf(2203,plain,
! [A: a] :
( ( ( f @ ( sk1 @ ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ A ) ) @ sk11 ) )
!= zero_zero_a )
| ( A != a2 )
| ( b != zero_zero_a ) ),
inference(simp,[status(thm)],[2182]) ).
thf(2214,plain,
( ( ( f @ ( sk1 @ ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ a2 ) ) @ sk11 ) )
!= zero_zero_a )
| ( b != zero_zero_a ) ),
inference(simp,[status(thm)],[2203]) ).
thf(152,axiom,
! [A: set_a] :
( ( auto_l630715367iant_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= ( auto_l630715367iant_a @ ( uminus_uminus_a_a @ f ) @ x @ ( minus_minus_set_a @ x @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_rev_Oinvariant__iff__compl__invariant) ).
thf(784,plain,
! [A: set_a] :
( ( auto_l630715367iant_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= ( auto_l630715367iant_a @ ( uminus_uminus_a_a @ f ) @ x @ ( minus_minus_set_a @ x @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(134,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_diff__strict__right__mono) ).
thf(737,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(267,axiom,
! [A: a,B: real,C: a,D: real] :
( ( ( elemen49976720ball_a @ A @ B )
= ( elemen49976720ball_a @ C @ D ) )
= ( ( ( ord_less_real @ B @ zero_zero_real )
& ( ord_less_real @ D @ zero_zero_real ) )
| ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_cball__eq__cball__iff) ).
thf(1122,plain,
! [A: a,B: real,C: a,D: real] :
( ( ( elemen49976720ball_a @ A @ B )
= ( elemen49976720ball_a @ C @ D ) )
= ( ( ( ord_less_real @ B @ zero_zero_real )
& ( ord_less_real @ D @ zero_zero_real ) )
| ( ( A = C )
& ( B = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(2187,plain,
! [A: a] :
( ( A != zero_zero_a )
| ( ( minus_minus_a @ A @ zero_zero_a )
!= ( minus_minus_a @ a2 @ b ) ) ),
inference(paramod_ordered,[status(thm)],[881,1940]) ).
thf(2197,plain,
( ( a2 != zero_zero_a )
| ( b != zero_zero_a ) ),
inference(simp,[status(thm)],[2187]) ).
thf(286,axiom,
! [A: a,B: a,C: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) )
=> ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_transversal__segment__posD_I1_J) ).
thf(1175,plain,
! [A: a,B: a,C: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) )
=> ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(191,axiom,
! [A: real,B: real,C: a] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_set_a @ ( elemen49976720ball_a @ C @ A ) @ ( elemen49976720ball_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_subset__cball) ).
thf(900,plain,
! [A: real,B: real,C: a] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_set_a @ ( elemen49976720ball_a @ C @ A ) @ ( elemen49976720ball_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(405,plain,
! [B: real,A: real] :
( ( A
= ( uminus_uminus_real @ B ) )
= ( B
= ( uminus_uminus_real @ A ) ) ),
inference(cnf,[status(esa)],[404]) ).
thf(406,plain,
! [B: real,A: real] :
( ( A
= ( uminus_uminus_real @ B ) )
= ( B
= ( uminus_uminus_real @ A ) ) ),
inference(lifteq,[status(thm)],[405]) ).
thf(14,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ A ) @ B )
=> ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_compl__le__swap2) ).
thf(377,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ A ) @ B )
=> ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(220,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_subsetD) ).
thf(996,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(8,axiom,
! [A: set_real,B: set_real,C: set_real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( ord_less_eq_set_real @ B @ C )
=> ( ( minus_minus_set_real @ B @ ( minus_minus_set_real @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_double__diff) ).
thf(359,plain,
! [A: set_real,B: set_real,C: set_real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( ord_less_eq_set_real @ B @ C )
=> ( ( minus_minus_set_real @ B @ ( minus_minus_set_real @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(360,plain,
! [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
=> ! [C: set_real] :
( ( ord_less_eq_set_real @ B @ C )
=> ( ( minus_minus_set_real @ B @ ( minus_minus_set_real @ C @ A ) )
= A ) ) ),
inference(miniscope,[status(thm)],[359]) ).
thf(361,plain,
! [C: set_real,B: set_real,A: set_real] :
( ~ ( ord_less_eq_set_real @ A @ B )
| ~ ( ord_less_eq_set_real @ B @ C )
| ( ( minus_minus_set_real @ B @ ( minus_minus_set_real @ C @ A ) )
= A ) ),
inference(cnf,[status(esa)],[360]) ).
thf(362,plain,
! [C: set_real,B: set_real,A: set_real] :
( ( ( minus_minus_set_real @ B @ ( minus_minus_set_real @ C @ A ) )
= A )
| ~ ( ord_less_eq_set_real @ A @ B )
| ~ ( ord_less_eq_set_real @ B @ C ) ),
inference(lifteq,[status(thm)],[361]) ).
thf(78,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_psubset__imp__subset) ).
thf(567,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(2048,plain,
! [B: a,A: set_real] :
( ( initia826609931terval
@ ( collect_real
@ ^ [C: real] : ( member_real @ C @ A ) ) )
| ( A
!= ( auto_l612940ivl0_a @ f @ x @ B ) ) ),
inference(paramod_ordered,[status(thm)],[426,1105]) ).
thf(2049,plain,
! [A: a] :
( initia826609931terval
@ ( collect_real
@ ^ [B: real] : ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[2048:[bind(A,$thf( auto_l612940ivl0_a @ f @ x @ E )),bind(B,$thf( E ))]]) ).
thf(2066,plain,
! [A: a] :
( initia826609931terval
@ ( collect_real
@ ^ [B: real] : ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ),
inference(simp,[status(thm)],[2049]) ).
thf(2112,plain,
! [B: a,A: set_real] :
( ( initia826609931terval
@ ( collect_real
@ ^ [C: real] : ( member_real @ C @ A ) ) )
| ( A
!= ( collect_real
@ ^ [C: real] : ( member_real @ C @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[426,2066]) ).
thf(2113,plain,
! [A: a] :
( initia826609931terval
@ ( collect_real
@ ^ [B: real] :
( member_real @ B
@ ( collect_real
@ ^ [C: real] : ( member_real @ C @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2112:[bind(A,$thf( collect_real @ ^ [C: real] : ( member_real @ C @ ( auto_l612940ivl0_a @ f @ x @ B ) ) )),bind(B,$thf( B ))]]) ).
thf(2116,plain,
! [A: a] :
( initia826609931terval
@ ( collect_real
@ ^ [B: real] :
( member_real @ B
@ ( collect_real
@ ^ [C: real] : ( member_real @ C @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[2113]) ).
thf(60,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_Collect__mono) ).
thf(509,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(33,axiom,
! [A: real,B: real,C: real] :
( ( inner_4346926r_real @ A @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( inner_4346926r_real @ A @ B ) @ ( inner_4346926r_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_inner__diff__right) ).
thf(432,plain,
! [A: real,B: real,C: real] :
( ( inner_4346926r_real @ A @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( inner_4346926r_real @ A @ B ) @ ( inner_4346926r_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(433,plain,
! [C: real,B: real,A: real] :
( ( inner_4346926r_real @ A @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( inner_4346926r_real @ A @ B ) @ ( inner_4346926r_real @ A @ C ) ) ),
inference(cnf,[status(esa)],[432]) ).
thf(434,plain,
! [C: real,B: real,A: real] :
( ( inner_4346926r_real @ A @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( inner_4346926r_real @ A @ B ) @ ( inner_4346926r_real @ A @ C ) ) ),
inference(lifteq,[status(thm)],[433]) ).
thf(90,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ A ) @ ( uminus_uminus_set_a @ B ) )
= ( ord_less_eq_set_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_Compl__subset__Compl__iff) ).
thf(599,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ A ) @ ( uminus_uminus_set_a @ B ) )
= ( ord_less_eq_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(1060,plain,
( ( ^ [A: real,B: real] :
( ( minus_minus_real @ A @ B )
= zero_zero_real ) )
= ( (=) @ real ) ),
inference(lifteq,[status(thm)],[1059]) ).
thf(1439,plain,
! [A: real] :
( ( ^ [B: real] :
( ( minus_minus_real @ A @ B )
= zero_zero_real ) )
= ( (=) @ real @ A ) ),
inference(func_ext,[status(esa)],[1060]) ).
thf(889,plain,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
inference(cnf,[status(esa)],[888]) ).
thf(890,plain,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
inference(lifteq,[status(thm)],[889]) ).
thf(680,plain,
( inner_1173012732nner_a
= ( ^ [A: a,B: a] : ( inner_1173012732nner_a @ B @ A ) ) ),
inference(lifteq,[status(thm)],[679]) ).
thf(1339,plain,
! [A: a] :
( ( inner_1173012732nner_a @ A )
= ( ^ [B: a] : ( inner_1173012732nner_a @ B @ A ) ) ),
inference(func_ext,[status(esa)],[680]) ).
thf(94,axiom,
! [A: a] :
( ( uminus_uminus_a @ ( uminus_uminus_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_verit__minus__simplify_I4_J) ).
thf(609,plain,
! [A: a] :
( ( uminus_uminus_a @ ( uminus_uminus_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(5421,plain,
( ~ $true
| ( ( member_real @ zero_zero_real
@ ( collect_real
@ ^ [A: real] : ( ord_less_eq_real @ A @ A ) ) )
!= ( member_real @ zero_zero_real
@ ( collect_real
@ ^ [A: real] : ( ord_less_real @ A @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4840,4906]) ).
thf(5422,plain,
( ( member_real @ zero_zero_real
@ ( collect_real
@ ^ [A: real] : ( ord_less_eq_real @ A @ A ) ) )
!= ( member_real @ zero_zero_real
@ ( collect_real
@ ^ [A: real] : ( ord_less_real @ A @ A ) ) ) ),
inference(simp,[status(thm)],[5421]) ).
thf(5431,plain,
( ( zero_zero_real != zero_zero_real )
| ( ( collect_real
@ ^ [A: real] : ( ord_less_eq_real @ A @ A ) )
!= ( collect_real
@ ^ [A: real] : ( ord_less_real @ A @ A ) ) ) ),
inference(simp,[status(thm)],[5422]) ).
thf(5439,plain,
( ( collect_real
@ ^ [A: real] : ( ord_less_eq_real @ A @ A ) )
!= ( collect_real
@ ^ [A: real] : ( ord_less_real @ A @ A ) ) ),
inference(simp,[status(thm)],[5431]) ).
thf(157,axiom,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( set_or411607219Most_a @ B @ C ) )
= ( ( ord_less_eq_a @ B @ A )
& ( ord_less_eq_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_atLeastAtMost__iff) ).
thf(799,plain,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( set_or411607219Most_a @ B @ C ) )
= ( ( ord_less_eq_a @ B @ A )
& ( ord_less_eq_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(51,axiom,
! [A: set_real,B: set_real,C: set_real] :
( ( ord_less_set_real @ A @ B )
=> ( ( ord_less_eq_set_real @ B @ C )
=> ( ord_less_set_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_psubset__subset__trans) ).
thf(483,plain,
! [A: set_real,B: set_real,C: set_real] :
( ( ord_less_set_real @ A @ B )
=> ( ( ord_less_eq_set_real @ B @ C )
=> ( ord_less_set_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(173,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
= ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_neg__le__iff__le) ).
thf(848,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
= ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(461,plain,
! [B: set_a,A: set_a] :
( ( A != B )
| ( ord_less_eq_set_a @ A @ B ) ),
inference(cnf,[status(esa)],[460]) ).
thf(462,plain,
! [B: set_a,A: set_a] :
( ( A != B )
| ( ord_less_eq_set_a @ A @ B ) ),
inference(lifteq,[status(thm)],[461]) ).
thf(463,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(simp,[status(thm)],[462]) ).
thf(378,plain,
! [B: set_a,A: set_a] :
( ~ ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ A ) @ B )
| ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ B ) @ A ) ),
inference(cnf,[status(esa)],[377]) ).
thf(1821,plain,
! [C: set_a,B: set_a,A: set_a] :
( ~ $true
| ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ C ) @ B )
| ( ( ord_less_eq_set_a @ A @ A )
!= ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[463,378]) ).
thf(1822,plain,
! [C: set_a,B: set_a,A: set_a] :
( ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ C ) @ B )
| ( ( ord_less_eq_set_a @ A @ A )
!= ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ B ) @ C ) ) ),
inference(simp,[status(thm)],[1821]) ).
thf(1823,plain,
! [A: set_a] : ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ ( uminus_uminus_set_a @ A ) ) @ A ),
inference(pattern_uni,[status(thm)],[1822:[bind(A,$thf( uminus_uminus_set_a @ E )),bind(B,$thf( E )),bind(C,$thf( uminus_uminus_set_a @ E ))]]) ).
thf(1838,plain,
! [A: set_a] : ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ ( uminus_uminus_set_a @ A ) ) @ A ),
inference(simp,[status(thm)],[1823]) ).
thf(2731,plain,
! [A: a] :
( ( ( uminus_uminus_a @ A )
!= ( f @ x2 ) )
| ( ( minus_minus_a @ zero_zero_a @ A )
!= ( minus_minus_a @ a2 @ b ) ) ),
inference(paramod_ordered,[status(thm)],[916,2571]) ).
thf(2766,plain,
! [A: a] :
( ( ( uminus_uminus_a @ A )
!= ( f @ x2 ) )
| ( a2 != zero_zero_a )
| ( A != b ) ),
inference(simp,[status(thm)],[2731]) ).
thf(2785,plain,
( ( ( f @ x2 )
!= ( uminus_uminus_a @ b ) )
| ( a2 != zero_zero_a ) ),
inference(simp,[status(thm)],[2766]) ).
thf(1382,plain,
! [A: real] :
( ~ $true
| ( member_a @ ( sk1 @ A @ d ) @ ( elemen49976720ball_a @ x2 @ d ) )
| ( ( ord_less_real @ zero_zero_real @ sk11 )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[830,1353]) ).
thf(1383,plain,
! [A: real] :
( ( member_a @ ( sk1 @ A @ d ) @ ( elemen49976720ball_a @ x2 @ d ) )
| ( ( ord_less_real @ zero_zero_real @ sk11 )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(simp,[status(thm)],[1382]) ).
thf(1384,plain,
member_a @ ( sk1 @ sk11 @ d ) @ ( elemen49976720ball_a @ x2 @ d ),
inference(pattern_uni,[status(thm)],[1383:[bind(A,$thf( sk11 ))]]) ).
thf(1427,plain,
! [A: a] :
( ( ( f @ A )
!= zero_zero_a )
| ~ $true
| ( ( member_a @ ( sk1 @ sk11 @ d ) @ ( elemen49976720ball_a @ x2 @ d ) )
!= ( member_a @ A @ ( elemen49976720ball_a @ x2 @ sk11 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1384,834]) ).
thf(1428,plain,
! [A: a] :
( ( ( f @ A )
!= zero_zero_a )
| ( ( member_a @ ( sk1 @ sk11 @ d ) @ ( elemen49976720ball_a @ x2 @ d ) )
!= ( member_a @ A @ ( elemen49976720ball_a @ x2 @ sk11 ) ) ) ),
inference(simp,[status(thm)],[1427]) ).
thf(1430,plain,
! [A: a] :
( ( ( f @ A )
!= zero_zero_a )
| ( ( sk1 @ sk11 @ d )
!= A )
| ( ( elemen49976720ball_a @ x2 @ sk11 )
!= ( elemen49976720ball_a @ x2 @ d ) ) ),
inference(simp,[status(thm)],[1428]) ).
thf(1435,plain,
( ( ( f @ ( sk1 @ sk11 @ d ) )
!= zero_zero_a )
| ( ( elemen49976720ball_a @ x2 @ sk11 )
!= ( elemen49976720ball_a @ x2 @ d ) ) ),
inference(simp,[status(thm)],[1430]) ).
thf(1459,plain,
( ( ( f @ ( sk1 @ sk11 @ d ) )
!= zero_zero_a )
| ( x2 != x2 )
| ( sk11 != d ) ),
inference(simp,[status(thm)],[1435]) ).
thf(1460,plain,
( ( ( f @ ( sk1 @ sk11 @ d ) )
!= zero_zero_a )
| ( sk11 != d ) ),
inference(simp,[status(thm)],[1459]) ).
thf(230,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_in__mono) ).
thf(1022,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(327,axiom,
! [A: real] :
( ( ( inner_4346926r_real @ A @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_inner__eq__zero__iff) ).
thf(1293,plain,
! [A: real] :
( ( ( inner_4346926r_real @ A @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(263,axiom,
! [A: real] :
( ( ( uminus_uminus_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_neg__equal__0__iff__equal) ).
thf(1112,plain,
! [A: real] :
( ( ( uminus_uminus_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(163,axiom,
! [A: a] :
( ( ( poinca659159244_rot_a @ A )
= zero_zero_a )
= ( A = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_rot__eq__0__iff) ).
thf(811,plain,
! [A: a] :
( ( ( poinca659159244_rot_a @ A )
= zero_zero_a )
= ( A = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(386,plain,
! [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
=> ! [C: set_a] :
( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
inference(miniscope,[status(thm)],[385]) ).
thf(387,plain,
! [C: set_a,B: set_a,A: set_a] :
( ~ ( ord_less_set_a @ A @ B )
| ~ ( ord_less_eq_set_a @ B @ C )
| ( ord_less_set_a @ A @ C ) ),
inference(cnf,[status(esa)],[386]) ).
thf(55,axiom,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_less_set_set_a @ ( set_or2094724627_set_a @ A @ B ) @ ( set_or2094724627_set_a @ C @ D ) )
= ( ( ~ ( ord_less_eq_set_a @ A @ B )
| ( ( ord_less_eq_set_a @ C @ A )
& ( ord_less_eq_set_a @ B @ D )
& ( ( ord_less_set_a @ C @ A )
| ( ord_less_set_a @ B @ D ) ) ) )
& ( ord_less_eq_set_a @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_atLeastatMost__psubset__iff) ).
thf(494,plain,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_less_set_set_a @ ( set_or2094724627_set_a @ A @ B ) @ ( set_or2094724627_set_a @ C @ D ) )
= ( ( ~ ( ord_less_eq_set_a @ A @ B )
| ( ( ord_less_eq_set_a @ C @ A )
& ( ord_less_eq_set_a @ B @ D )
& ( ( ord_less_set_a @ C @ A )
| ( ord_less_set_a @ B @ D ) ) ) )
& ( ord_less_eq_set_a @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(1079,plain,
! [A: real] :
( ( inner_4346926r_real @ zero_zero_real @ A )
= zero_zero_real ),
inference(cnf,[status(esa)],[1078]) ).
thf(1080,plain,
! [A: real] :
( ( inner_4346926r_real @ zero_zero_real @ A )
= zero_zero_real ),
inference(lifteq,[status(thm)],[1079]) ).
thf(244,axiom,
! [A: a,B: a,C: a,D: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) )
=> ( ( member_a @ D @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ D ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_transversal__segment__posD_I3_J) ).
thf(1061,plain,
! [A: a,B: a,C: a,D: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) )
=> ( ( member_a @ D @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ D ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(4352,plain,
! [B: a,A: a] :
( ~ $true
| ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( real_V1514887919dist_a @ A @ B ) ) )
!= ( ord_less_real @ zero_zero_real @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[830,4346]) ).
thf(4353,plain,
! [B: a,A: a] :
( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( real_V1514887919dist_a @ A @ B ) ) )
!= ( ord_less_real @ zero_zero_real @ sk11 ) ),
inference(simp,[status(thm)],[4352]) ).
thf(4364,plain,
! [B: a,A: a] :
( ( zero_zero_real != zero_zero_real )
| ( ( uminus_uminus_real @ ( real_V1514887919dist_a @ A @ B ) )
!= sk11 ) ),
inference(simp,[status(thm)],[4353]) ).
thf(4373,plain,
! [B: a,A: a] :
( ( uminus_uminus_real @ ( real_V1514887919dist_a @ A @ B ) )
!= sk11 ),
inference(simp,[status(thm)],[4364]) ).
thf(174,axiom,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( inner_4346926r_real @ A @ A ) )
= ( A != zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_inner__gt__zero__iff) ).
thf(851,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( inner_4346926r_real @ A @ A ) )
= ( A != zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(875,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(lifteq,[status(thm)],[874]) ).
thf(1562,plain,
( ( ^ [A: set_a,B: set_a] :
( ( ord_less_set_a @ A @ B )
| ( A = B ) ) )
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(rewrite,[status(thm)],[875,598]) ).
thf(195,axiom,
! [A: a,B: set_a] :
( ( member_a @ A @ ( uminus_uminus_set_a @ B ) )
=> ~ ( member_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_ComplD) ).
thf(912,plain,
! [A: a,B: set_a] :
( ( member_a @ A @ ( uminus_uminus_set_a @ B ) )
=> ~ ( member_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(120,axiom,
! [A: a,B: a,C: real] :
( ( member_a @ A @ ( elemen49976720ball_a @ B @ C ) )
= ( ord_less_eq_real @ ( real_V1514887919dist_a @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_mem__cball) ).
thf(685,plain,
! [A: a,B: a,C: real] :
( ( member_a @ A @ ( elemen49976720ball_a @ B @ C ) )
= ( ord_less_eq_real @ ( real_V1514887919dist_a @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(1170,plain,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
inference(cnf,[status(esa)],[1169]) ).
thf(1171,plain,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
inference(lifteq,[status(thm)],[1170]) ).
thf(105,axiom,
( ( uminus_uminus_a @ zero_zero_a )
= zero_zero_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_add_Oinverse__neutral) ).
thf(643,plain,
( ( uminus_uminus_a @ zero_zero_a )
= zero_zero_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(644,plain,
( ( uminus_uminus_a @ zero_zero_a )
= zero_zero_a ),
inference(lifteq,[status(thm)],[643]) ).
thf(3535,plain,
( ( zero_zero_a != zero_zero_a )
| ( a2 != zero_zero_a )
| ( ( uminus_uminus_a @ ( poinca659159244_rot_a @ b ) )
!= ( uminus_uminus_a @ zero_zero_a ) ) ),
inference(paramod_ordered,[status(thm)],[644,3370]) ).
thf(3536,plain,
( ( a2 != zero_zero_a )
| ( ( uminus_uminus_a @ ( poinca659159244_rot_a @ b ) )
!= ( uminus_uminus_a @ zero_zero_a ) ) ),
inference(simp,[status(thm)],[3535]) ).
thf(3539,plain,
( ( a2 != zero_zero_a )
| ( ( poinca659159244_rot_a @ b )
!= zero_zero_a ) ),
inference(simp,[status(thm)],[3536]) ).
thf(215,axiom,
! [A: a] :
( ( minus_minus_a @ A @ zero_zero_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_diff__0__right) ).
thf(983,plain,
! [A: a] :
( ( minus_minus_a @ A @ zero_zero_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(146,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
= ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_less__minus__iff) ).
thf(768,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
= ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(392,plain,
! [B: set_real,A: set_real] :
( ( A != B )
| ( ord_less_eq_set_real @ B @ A ) ),
inference(cnf,[status(esa)],[391]) ).
thf(393,plain,
! [B: set_real,A: set_real] :
( ( A != B )
| ( ord_less_eq_set_real @ B @ A ) ),
inference(lifteq,[status(thm)],[392]) ).
thf(394,plain,
! [A: set_real] : ( ord_less_eq_set_real @ A @ A ),
inference(simp,[status(thm)],[393]) ).
thf(216,axiom,
! [A: a,B: a,C: real,D: real] :
( ( member_a @ A @ ( elemen49976720ball_a @ B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( member_a @ A @ ( elemen49976720ball_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_mem__cball__leI) ).
thf(986,plain,
! [A: a,B: a,C: real,D: real] :
( ( member_a @ A @ ( elemen49976720ball_a @ B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( member_a @ A @ ( elemen49976720ball_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(129,axiom,
! [A: real,B: real] :
( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
= ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_minus__less__iff) ).
thf(722,plain,
! [A: real,B: real] :
( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
= ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(234,axiom,
! [A: real,B: a] :
( ( member_real @ A @ top_top_set_real )
=> ( ( member_a @ B @ x )
=> ( member_real @ ( minus_minus_real @ A @ A ) @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_general_Oexistence__ivl__initial__time) ).
thf(1034,plain,
! [A: real,B: a] :
( ( member_real @ A @ top_top_set_real )
=> ( ( member_a @ B @ x )
=> ( member_real @ ( minus_minus_real @ A @ A ) @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(53,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ ( uminus_uminus_a @ A ) @ ( uminus_uminus_a @ B ) )
= ( ord_less_eq_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_neg__le__iff__le) ).
thf(490,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ ( uminus_uminus_a @ A ) @ ( uminus_uminus_a @ B ) )
= ( ord_less_eq_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(206,axiom,
! [A: a] :
( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ( member_a @ A @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_rev_Oclosed__orbit__in__domain) ).
thf(944,plain,
! [A: a] :
( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ( member_a @ A @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(321,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_set_real @ ( set_or656347191t_real @ A @ B ) @ ( set_or656347191t_real @ C @ D ) )
= ( ~ ( ord_less_eq_real @ A @ B )
| ( ( ord_less_eq_real @ C @ A )
& ( ord_less_eq_real @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_atLeastatMost__subset__iff) ).
thf(1277,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_set_real @ ( set_or656347191t_real @ A @ B ) @ ( set_or656347191t_real @ C @ D ) )
= ( ~ ( ord_less_eq_real @ A @ B )
| ( ( ord_less_eq_real @ C @ A )
& ( ord_less_eq_real @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(272,axiom,
! [A: a] :
( ( member_a @ A @ x )
=> ~ ! [B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ~ ( ord_less_eq_set_real @ ( set_or656347191t_real @ ( uminus_uminus_real @ B ) @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_rev_Oopen__existence__ivl_H) ).
thf(1134,plain,
! [A: a] :
( ( member_a @ A @ x )
=> ~ ! [B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ~ ( ord_less_eq_set_real @ ( set_or656347191t_real @ ( uminus_uminus_real @ B ) @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(251,axiom,
! [A: a,B: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( ( ord_less_real @ ( inner_1173012732nner_a @ ( f @ A ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) @ zero_zero_real )
=> ! [C: a] :
( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ord_less_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) @ zero_zero_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_transversal__segment__sign__less) ).
thf(1081,plain,
! [A: a,B: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( ( ord_less_real @ ( inner_1173012732nner_a @ ( f @ A ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) @ zero_zero_real )
=> ! [C: a] :
( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ord_less_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) @ zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(159,axiom,
( ord_less_real
= ( ^ [A: real,B: real] : ( ord_less_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_less__iff__diff__less__0) ).
thf(803,plain,
( ord_less_real
= ( ^ [A: real,B: real] : ( ord_less_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(804,plain,
( ( ^ [A: real,B: real] : ( ord_less_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) )
= ord_less_real ),
inference(lifteq,[status(thm)],[803]) ).
thf(1413,plain,
! [A: real] :
( ( ^ [B: real] : ( ord_less_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) )
= ( ord_less_real @ A ) ),
inference(func_ext,[status(esa)],[804]) ).
thf(47,axiom,
! [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( ord_less_eq_set_real @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_subset__antisym) ).
thf(473,plain,
! [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( ord_less_eq_set_real @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(73,axiom,
! [A: set_real,B: set_real] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_real @ A @ B )
=> ~ ( ord_less_eq_set_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_equalityE) ).
thf(548,plain,
! [A: set_real,B: set_real] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_real @ A @ B )
=> ~ ( ord_less_eq_set_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(200,axiom,
! [A: a] :
( ( member_a @ A @ x )
=> ( ( ( f @ A )
= zero_zero_a )
=> ( ( period1305449585riod_a @ f @ x @ A )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_fixed__point__imp__closed__orbit__period__zero_I2_J) ).
thf(927,plain,
! [A: a] :
( ( member_a @ A @ x )
=> ( ( ( f @ A )
= zero_zero_a )
=> ( ( period1305449585riod_a @ f @ x @ A )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(2031,plain,
! [A: a] :
( ( zero_zero_real != zero_zero_real )
| ( ( inner_1173012732nner_a @ zero_zero_a @ A )
!= ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[745,1989]) ).
thf(2032,plain,
! [A: a] :
( ( inner_1173012732nner_a @ zero_zero_a @ A )
!= ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ),
inference(simp,[status(thm)],[2031]) ).
thf(2035,plain,
! [A: a] :
( ( ( f @ z )
!= zero_zero_a )
| ( A
!= ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ),
inference(simp,[status(thm)],[2032]) ).
thf(2037,plain,
( ( f @ z )
!= zero_zero_a ),
inference(simp,[status(thm)],[2035]) ).
thf(97,axiom,
! [A: real] :
( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_add_Oinverse__inverse) ).
thf(617,plain,
! [A: real] :
( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(62,axiom,
! [A: set_real,B: set_real,C: set_real,D: set_real] :
( ( ( set_or1619725421t_real @ A @ B )
= ( set_or1619725421t_real @ C @ D ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ~ ( ord_less_eq_set_real @ A @ B )
& ~ ( ord_less_eq_set_real @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_Icc__eq__Icc) ).
thf(516,plain,
! [A: set_real,B: set_real,C: set_real,D: set_real] :
( ( ( set_or1619725421t_real @ A @ B )
= ( set_or1619725421t_real @ C @ D ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ~ ( ord_less_eq_set_real @ A @ B )
& ~ ( ord_less_eq_set_real @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(65,axiom,
! [A: real] : ( member_real @ A @ top_top_set_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_UNIV__I) ).
thf(524,plain,
! [A: real] : ( member_real @ A @ top_top_set_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(525,plain,
! [A: real] : ( member_real @ A @ top_top_set_real ),
inference(cnf,[status(esa)],[524]) ).
thf(579,plain,
! [A: a] :
( ( zero_zero_a
= ( uminus_uminus_a @ A ) )
= ( zero_zero_a = A ) ),
inference(cnf,[status(esa)],[578]) ).
thf(580,plain,
! [A: a] :
( ( zero_zero_a
= ( uminus_uminus_a @ A ) )
= ( zero_zero_a = A ) ),
inference(lifteq,[status(thm)],[579]) ).
thf(122,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( minus_minus_a @ A @ B )
= ( minus_minus_a @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_diff__eq__diff__eq) ).
thf(690,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( minus_minus_a @ A @ B )
= ( minus_minus_a @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(104,axiom,
! [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( A != B )
=> ( ord_less_set_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_psubsetI) ).
thf(640,plain,
! [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
=> ( ( A != B )
=> ( ord_less_set_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(231,axiom,
! [A: a,B: a] :
( ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) )
= ( uminus_uminus_a @ ( poinca659159244_rot_a @ ( minus_minus_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_rot__diff__commute) ).
thf(1025,plain,
! [A: a,B: a] :
( ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) )
= ( uminus_uminus_a @ ( poinca659159244_rot_a @ ( minus_minus_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(247,axiom,
! [A: a,B: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( poinca522724647ment_a @ f @ x @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_transversal__segment__reverse) ).
thf(1070,plain,
! [A: a,B: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( poinca522724647ment_a @ f @ x @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(2006,plain,
! [C: set_real,B: set_real,A: real] :
( ~ $true
| ( ord_less_eq_set_real @ B @ C )
| ( ( member_real @ A @ top_top_set_real )
!= ( member_real @ ( sk2 @ C @ B ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[525,382]) ).
thf(2007,plain,
! [C: set_real,B: set_real,A: real] :
( ( ord_less_eq_set_real @ B @ C )
| ( ( member_real @ A @ top_top_set_real )
!= ( member_real @ ( sk2 @ C @ B ) @ C ) ) ),
inference(simp,[status(thm)],[2006]) ).
thf(2008,plain,
! [A: set_real] : ( ord_less_eq_set_real @ A @ top_top_set_real ),
inference(pattern_uni,[status(thm)],[2007:[bind(A,$thf( sk2 @ top_top_set_real @ E )),bind(B,$thf( E )),bind(C,$thf( top_top_set_real ))]]) ).
thf(2012,plain,
! [A: set_real] : ( ord_less_eq_set_real @ A @ top_top_set_real ),
inference(simp,[status(thm)],[2008]) ).
thf(307,axiom,
! [A: a] : ( member_a @ A @ top_top_set_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_UNIV__I) ).
thf(1235,plain,
! [A: a] : ( member_a @ A @ top_top_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(1236,plain,
! [A: a] : ( member_a @ A @ top_top_set_a ),
inference(cnf,[status(esa)],[1235]) ).
thf(1644,plain,
! [B: a,A: a] :
( ( ( f @ B )
!= zero_zero_a )
| ~ $true
| ( ( member_a @ A @ top_top_set_a )
!= ( member_a @ B @ ( elemen49976720ball_a @ x2 @ sk11 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1236,834]) ).
thf(1645,plain,
! [B: a,A: a] :
( ( ( f @ B )
!= zero_zero_a )
| ( ( member_a @ A @ top_top_set_a )
!= ( member_a @ B @ ( elemen49976720ball_a @ x2 @ sk11 ) ) ) ),
inference(simp,[status(thm)],[1644]) ).
thf(1646,plain,
! [B: a,A: a] :
( ( ( f @ B )
!= zero_zero_a )
| ( A != B )
| ( ( elemen49976720ball_a @ x2 @ sk11 )
!= top_top_set_a ) ),
inference(simp,[status(thm)],[1645]) ).
thf(1647,plain,
! [A: a] :
( ( ( f @ A )
!= zero_zero_a )
| ( ( elemen49976720ball_a @ x2 @ sk11 )
!= top_top_set_a ) ),
inference(simp,[status(thm)],[1646]) ).
thf(3389,plain,
! [B: a,A: a] :
( ( ( poinca659159244_rot_a @ A )
= ( uminus_uminus_a @ ( poinca659159244_rot_a @ B ) ) )
| ( ( uminus_uminus_a @ ( uminus_uminus_a @ A ) )
!= ( uminus_uminus_a @ B ) ) ),
inference(paramod_ordered,[status(thm)],[521,2840]) ).
thf(3390,plain,
! [A: a] :
( ( poinca659159244_rot_a @ A )
= ( uminus_uminus_a @ ( poinca659159244_rot_a @ ( uminus_uminus_a @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[3389:[bind(A,$thf( C )),bind(B,$thf( uminus_uminus_a @ C ))]]) ).
thf(3436,plain,
! [A: a] :
( ( poinca659159244_rot_a @ A )
= ( uminus_uminus_a @ ( poinca659159244_rot_a @ ( uminus_uminus_a @ A ) ) ) ),
inference(simp,[status(thm)],[3390]) ).
thf(3659,plain,
! [A: a] :
( ( uminus_uminus_a @ ( uminus_uminus_a @ ( poinca659159244_rot_a @ A ) ) )
= ( poinca659159244_rot_a @ A ) ),
inference(rewrite,[status(thm)],[3436,2840]) ).
thf(312,axiom,
! [A: a,B: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
= ( ( A != B )
& ( ord_less_eq_set_a @ ( line_c1152468841ment_a @ A @ B ) @ x )
& ! [C: a] :
( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) )
!= zero_zero_real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_transversal__segment__def) ).
thf(1252,plain,
! [A: a,B: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
= ( ( A != B )
& ( ord_less_eq_set_a @ ( line_c1152468841ment_a @ A @ B ) @ x )
& ! [C: a] :
( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) )
!= zero_zero_real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(257,axiom,
! [A: a] :
( ( member_a @ A @ x )
=> ( ( ( f @ A )
= zero_zero_a )
=> ( period720806154rbit_a @ f @ x @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_fixed__point__imp__closed__orbit__period__zero_I1_J) ).
thf(1098,plain,
! [A: a] :
( ( member_a @ A @ x )
=> ( ( ( f @ A )
= zero_zero_a )
=> ( period720806154rbit_a @ f @ x @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(408,plain,
! [D: set_a,C: set_a,B: set_a,A: set_a] :
( ( ( set_or2094724627_set_a @ A @ B )
= ( set_or2094724627_set_a @ C @ D ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ~ ( ord_less_eq_set_a @ A @ B )
& ~ ( ord_less_eq_set_a @ C @ D ) ) ) ),
inference(cnf,[status(esa)],[407]) ).
thf(409,plain,
! [D: set_a,C: set_a,B: set_a,A: set_a] :
( ( ( set_or2094724627_set_a @ A @ B )
= ( set_or2094724627_set_a @ C @ D ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ~ ( ord_less_eq_set_a @ A @ B )
& ~ ( ord_less_eq_set_a @ C @ D ) ) ) ),
inference(lifteq,[status(thm)],[408]) ).
thf(305,axiom,
! [A: a] :
( ( member_a @ A @ x )
=> ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_existence__ivl__zero) ).
thf(1230,plain,
! [A: a] :
( ( member_a @ A @ x )
=> ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(330,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
= ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_diff__gt__0__iff__gt) ).
thf(1300,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
= ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(58,axiom,
! [A: real > $o,B: real > $o] :
( ! [C: real] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_real @ ( collect_real @ A ) @ ( collect_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_Collect__mono) ).
thf(502,plain,
! [A: real > $o,B: real > $o] :
( ! [C: real] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_real @ ( collect_real @ A ) @ ( collect_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(46,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( A != B )
=> ( ord_less_set_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_psubsetI) ).
thf(470,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( A != B )
=> ( ord_less_set_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(3482,plain,
! [A: a] :
( ( zero_zero_real != zero_zero_real )
| ( ( inner_1173012732nner_a @ ( uminus_uminus_a @ ( poinca659159244_rot_a @ A ) ) @ A )
!= ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3438,1902]) ).
thf(3483,plain,
! [A: a] :
( ( inner_1173012732nner_a @ ( uminus_uminus_a @ ( poinca659159244_rot_a @ A ) ) @ A )
!= ( inner_1173012732nner_a @ ( f @ x2 ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ),
inference(simp,[status(thm)],[3482]) ).
thf(3495,plain,
! [A: a] :
( ( ( uminus_uminus_a @ ( poinca659159244_rot_a @ A ) )
!= ( f @ x2 ) )
| ( A
!= ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) ),
inference(simp,[status(thm)],[3483]) ).
thf(3517,plain,
( ( uminus_uminus_a @ ( poinca659159244_rot_a @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
!= ( f @ x2 ) ),
inference(simp,[status(thm)],[3495]) ).
thf(3623,plain,
( ( uminus_uminus_a @ ( uminus_uminus_a @ ( minus_minus_a @ a2 @ b ) ) )
!= ( f @ x2 ) ),
inference(rewrite,[status(thm)],[3517,991]) ).
thf(290,axiom,
! [A: a] :
( ( member_a @ A @ x )
=> ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_rev_Oexistence__ivl__zero) ).
thf(1188,plain,
! [A: a] :
( ( member_a @ A @ x )
=> ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(289,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( member_a @ B @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_local_Orev_Omem__existence__ivl__iv__defined_I2_J) ).
thf(1186,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( member_a @ B @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(1537,plain,
( ( ( f @ ( sk1 @ d @ d ) )
!= zero_zero_a )
| ( x2 != x2 )
| ( sk11 != d ) ),
inference(simp,[status(thm)],[1437]) ).
thf(1538,plain,
( ( ( f @ ( sk1 @ d @ d ) )
!= zero_zero_a )
| ( sk11 != d ) ),
inference(simp,[status(thm)],[1537]) ).
thf(301,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_psubsetD) ).
thf(1218,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(5426,plain,
! [A: real] :
( ~ $true
| ( ( member_real @ A @ top_top_set_real )
!= ( member_real @ zero_zero_real
@ ( collect_real
@ ^ [B: real] : ( ord_less_real @ B @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[525,4906]) ).
thf(5427,plain,
! [A: real] :
( ( member_real @ A @ top_top_set_real )
!= ( member_real @ zero_zero_real
@ ( collect_real
@ ^ [B: real] : ( ord_less_real @ B @ B ) ) ) ),
inference(simp,[status(thm)],[5426]) ).
thf(5433,plain,
! [A: real] :
( ( A != zero_zero_real )
| ( ( collect_real
@ ^ [B: real] : ( ord_less_real @ B @ B ) )
!= top_top_set_real ) ),
inference(simp,[status(thm)],[5427]) ).
thf(5440,plain,
( ( collect_real
@ ^ [A: real] : ( ord_less_real @ A @ A ) )
!= top_top_set_real ),
inference(simp,[status(thm)],[5433]) ).
thf(5445,plain,
! [A: set_real] :
( ( A != top_top_set_real )
| ( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
!= ( collect_real
@ ^ [B: real] : ( ord_less_real @ B @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[426,5440]) ).
thf(5449,plain,
( ( ^ [A: real] : ( member_real @ A @ top_top_set_real ) )
!= ( ^ [A: real] : ( ord_less_real @ A @ A ) ) ),
inference(simp,[status(thm)],[5445]) ).
thf(5450,plain,
( ( ^ [A: real] : ( ord_less_real @ A @ A ) )
!= ( ^ [A: real] : $true ) ),
inference(rewrite,[status(thm)],[5449,525]) ).
thf(126,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( inner_4346926r_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_inner__nonneg__nonneg) ).
thf(703,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( inner_4346926r_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(274,axiom,
! [A: a,B: a,C: a] :
( ( minus_minus_a @ ( minus_minus_a @ A @ B ) @ C )
= ( minus_minus_a @ ( minus_minus_a @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_cancel__ab__semigroup__add__class_Odiff__right__commute) ).
thf(1141,plain,
! [A: a,B: a,C: a] :
( ( minus_minus_a @ ( minus_minus_a @ A @ B ) @ C )
= ( minus_minus_a @ ( minus_minus_a @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(655,plain,
! [A: a] :
( ( ( uminus_uminus_a @ A )
= zero_zero_a )
= ( A = zero_zero_a ) ),
inference(cnf,[status(esa)],[654]) ).
thf(656,plain,
! [A: a] :
( ( ( uminus_uminus_a @ A )
= zero_zero_a )
= ( A = zero_zero_a ) ),
inference(lifteq,[status(thm)],[655]) ).
thf(302,axiom,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( line_c1152468841ment_a @ B @ C ) )
=> ( ( inner_1173012732nner_a @ ( minus_minus_a @ A @ B ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ C @ B ) ) )
= zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_in__segment__inner__rot) ).
thf(1221,plain,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( line_c1152468841ment_a @ B @ C ) )
=> ( ( inner_1173012732nner_a @ ( minus_minus_a @ A @ B ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ C @ B ) ) )
= zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(570,plain,
! [A: a] :
( ( ord_less_eq_a @ zero_zero_a @ ( uminus_uminus_a @ A ) )
= ( ord_less_eq_a @ A @ zero_zero_a ) ),
inference(cnf,[status(esa)],[569]) ).
thf(571,plain,
! [A: a] :
( ( ord_less_eq_a @ zero_zero_a @ ( uminus_uminus_a @ A ) )
= ( ord_less_eq_a @ A @ zero_zero_a ) ),
inference(lifteq,[status(thm)],[570]) ).
thf(95,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_subset__psubset__trans) ).
thf(612,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_set_a @ B @ C )
=> ( ord_less_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(56,axiom,
( ord_less_eq_set_real
= ( ^ [A: set_real,B: set_real] :
! [C: real] :
( ( member_real @ C @ A )
=> ( member_real @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_subset__iff) ).
thf(497,plain,
( ord_less_eq_set_real
= ( ^ [A: set_real,B: set_real] :
! [C: real] :
( ( member_real @ C @ A )
=> ( member_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(183,axiom,
! [A: a] :
( ( minus_minus_a @ A @ A )
= zero_zero_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_diff__self) ).
thf(876,plain,
! [A: a] :
( ( minus_minus_a @ A @ A )
= zero_zero_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(309,axiom,
! [A: a] :
( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= top_top_set_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_rev_Oclosed__orbit__global__existence) ).
thf(1240,plain,
! [A: a] :
( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= top_top_set_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(100,axiom,
! [A: a,B: a] :
( ( ( uminus_uminus_a @ A )
= B )
= ( ( uminus_uminus_a @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_minus__equation__iff) ).
thf(627,plain,
! [A: a,B: a] :
( ( ( uminus_uminus_a @ A )
= B )
= ( ( uminus_uminus_a @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(2473,plain,
! [B: a,A: set_real] :
( ( initia826609931terval
@ ( collect_real
@ ^ [C: real] : ( member_real @ C @ A ) ) )
| ( A
!= ( collect_real
@ ^ [C: real] : ( member_real @ C @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[426,2068]) ).
thf(2474,plain,
! [A: a] :
( initia826609931terval
@ ( collect_real
@ ^ [B: real] :
( member_real @ B
@ ( collect_real
@ ^ [C: real] : ( member_real @ C @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2473:[bind(A,$thf( collect_real @ ^ [C: real] : ( member_real @ C @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) )),bind(B,$thf( B ))]]) ).
thf(2479,plain,
! [A: a] :
( initia826609931terval
@ ( collect_real
@ ^ [B: real] :
( member_real @ B
@ ( collect_real
@ ^ [C: real] : ( member_real @ C @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[2474]) ).
thf(287,axiom,
! [A: real,B: real,C: real,D: real] :
( ( member_real @ A @ ( set_or656347191t_real @ B @ C ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ D )
=> ( ord_less_eq_real @ ( inner_4346926r_real @ B @ D ) @ ( inner_4346926r_real @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_interval__inner__leI_I1_J) ).
thf(1180,plain,
! [A: real,B: real,C: real,D: real] :
( ( member_real @ A @ ( set_or656347191t_real @ B @ C ) )
=> ( ( ord_less_eq_real @ zero_zero_real @ D )
=> ( ord_less_eq_real @ ( inner_4346926r_real @ B @ D ) @ ( inner_4346926r_real @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(482,plain,
( real_V1514887919dist_a
= ( ^ [A: a,B: a] : ( real_V1514887919dist_a @ B @ A ) ) ),
inference(lifteq,[status(thm)],[481]) ).
thf(114,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_mem__Collect__eq) ).
thf(671,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(16,axiom,
( ord_less_eq_set_real
= ( ^ [A: set_real,B: set_real] :
! [C: real] :
( ( member_real @ C @ A )
=> ( member_real @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_subset__eq) ).
thf(383,plain,
( ord_less_eq_set_real
= ( ^ [A: set_real,B: set_real] :
! [C: real] :
( ( member_real @ C @ A )
=> ( member_real @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(384,plain,
( ord_less_eq_set_real
= ( ^ [A: set_real,B: set_real] :
! [C: real] :
( ( member_real @ C @ A )
=> ( member_real @ C @ B ) ) ) ),
inference(lifteq,[status(thm)],[383]) ).
thf(1448,plain,
( ( ^ [A: set_real,B: set_real] :
( ( ord_less_set_real @ A @ B )
| ( A = B ) ) )
= ( ^ [A: set_real,B: set_real] :
! [C: real] :
( ( member_real @ C @ A )
=> ( member_real @ C @ B ) ) ) ),
inference(rewrite,[status(thm)],[384,540]) ).
thf(147,axiom,
! [A: a,B: a] :
( ( inner_1173012732nner_a @ A @ ( uminus_uminus_a @ B ) )
= ( uminus_uminus_real @ ( inner_1173012732nner_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_inner__minus__right) ).
thf(771,plain,
! [A: a,B: a] :
( ( inner_1173012732nner_a @ A @ ( uminus_uminus_a @ B ) )
= ( uminus_uminus_real @ ( inner_1173012732nner_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(261,axiom,
( ord_less_eq_real
= ( ^ [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_le__iff__diff__le__0) ).
thf(1108,plain,
( ord_less_eq_real
= ( ^ [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(1558,plain,
! [A: a] :
( ( ( f @ A )
!= zero_zero_a )
| ~ $true
| ( ( member_a @ sk10 @ ( elemen49976720ball_a @ x2 @ d ) )
!= ( member_a @ A @ ( elemen49976720ball_a @ x2 @ sk11 ) ) ) ),
inference(paramod_ordered,[status(thm)],[820,834]) ).
thf(1559,plain,
! [A: a] :
( ( ( f @ A )
!= zero_zero_a )
| ( ( member_a @ sk10 @ ( elemen49976720ball_a @ x2 @ d ) )
!= ( member_a @ A @ ( elemen49976720ball_a @ x2 @ sk11 ) ) ) ),
inference(simp,[status(thm)],[1558]) ).
thf(1560,plain,
! [A: a] :
( ( ( f @ A )
!= zero_zero_a )
| ( sk10 != A )
| ( ( elemen49976720ball_a @ x2 @ sk11 )
!= ( elemen49976720ball_a @ x2 @ d ) ) ),
inference(simp,[status(thm)],[1559]) ).
thf(1561,plain,
( ( ( f @ sk10 )
!= zero_zero_a )
| ( ( elemen49976720ball_a @ x2 @ sk11 )
!= ( elemen49976720ball_a @ x2 @ d ) ) ),
inference(simp,[status(thm)],[1560]) ).
thf(1648,plain,
( ( ( f @ sk10 )
!= zero_zero_a )
| ( x2 != x2 )
| ( sk11 != d ) ),
inference(simp,[status(thm)],[1561]) ).
thf(1649,plain,
( ( ( f @ sk10 )
!= zero_zero_a )
| ( sk11 != d ) ),
inference(simp,[status(thm)],[1648]) ).
thf(253,axiom,
! [A: set_a] :
( ( auto_l630715367iant_a @ f @ x @ A )
= ( ! [B: a] :
( ( member_a @ B @ A )
=> ( oDE_au1996717075pped_a @ f @ x @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_invariant__def) ).
thf(1084,plain,
! [A: set_a] :
( ( auto_l630715367iant_a @ f @ x @ A )
= ( ! [B: a] :
( ( member_a @ B @ A )
=> ( oDE_au1996717075pped_a @ f @ x @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(74,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ ( uminus_uminus_set_a @ B ) )
=> ( ord_less_eq_set_a @ B @ ( uminus_uminus_set_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_compl__le__swap1) ).
thf(556,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ ( uminus_uminus_set_a @ B ) )
=> ( ord_less_eq_set_a @ B @ ( uminus_uminus_set_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(281,axiom,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_diff__self) ).
thf(1157,plain,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(336,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
= ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_le__minus__iff) ).
thf(1321,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
= ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(192,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( ord_less_eq_real @ A @ B )
= ( ord_less_eq_real @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_diff__eq__diff__less__eq) ).
thf(903,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( ord_less_eq_real @ A @ B )
= ( ord_less_eq_real @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(83,axiom,
! [A: set_real,B: set_real,C: real] :
( ( ord_less_set_real @ A @ B )
=> ( ( member_real @ C @ A )
=> ( member_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_psubsetD) ).
thf(581,plain,
! [A: set_real,B: set_real,C: real] :
( ( ord_less_set_real @ A @ B )
=> ( ( member_real @ C @ A )
=> ( member_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(188,axiom,
! [A: a,B: a,C: a,D: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ( ord_less_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) @ zero_zero_real )
=> ( ( member_a @ D @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ord_less_real @ ( inner_1173012732nner_a @ ( f @ D ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) @ zero_zero_real ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_transversal__segment__negD_I3_J) ).
thf(891,plain,
! [A: a,B: a,C: a,D: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ( ord_less_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) @ zero_zero_real )
=> ( ( member_a @ D @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ord_less_real @ ( inner_1173012732nner_a @ ( f @ D ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) @ zero_zero_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(11,axiom,
! [A: real,B: real] :
( ( A = B )
=> ( ( uminus_uminus_real @ A )
= ( uminus_uminus_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_verit__negate__coefficient_I3_J) ).
thf(368,plain,
! [A: real,B: real] :
( ( A = B )
=> ( ( uminus_uminus_real @ A )
= ( uminus_uminus_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(172,axiom,
! [A: a,B: a,C: a,D: a] :
( ( member_a @ A @ ( line_c1152468841ment_a @ B @ C ) )
=> ( ( member_a @ D @ ( line_c1152468841ment_a @ B @ C ) )
=> ( ( inner_1173012732nner_a @ ( minus_minus_a @ A @ D ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ B @ C ) ) )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_in__segment__inner__rot2) ).
thf(844,plain,
! [A: a,B: a,C: a,D: a] :
( ( member_a @ A @ ( line_c1152468841ment_a @ B @ C ) )
=> ( ( member_a @ D @ ( line_c1152468841ment_a @ B @ C ) )
=> ( ( inner_1173012732nner_a @ ( minus_minus_a @ A @ D ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ B @ C ) ) )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(812,plain,
! [A: a] :
( ( ( poinca659159244_rot_a @ A )
= zero_zero_a )
= ( A = zero_zero_a ) ),
inference(cnf,[status(esa)],[811]) ).
thf(813,plain,
! [A: a] :
( ( ( poinca659159244_rot_a @ A )
= zero_zero_a )
= ( A = zero_zero_a ) ),
inference(lifteq,[status(thm)],[812]) ).
thf(138,axiom,
! [A: real] :
( ( A
= ( uminus_uminus_real @ A ) )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_equal__neg__zero) ).
thf(748,plain,
! [A: real] :
( ( A
= ( uminus_uminus_real @ A ) )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(389,plain,
! [A: a] :
( ( ord_less_eq_a @ ( uminus_uminus_a @ A ) @ zero_zero_a )
= ( ord_less_eq_a @ zero_zero_a @ A ) ),
inference(cnf,[status(esa)],[388]) ).
thf(390,plain,
! [A: a] :
( ( ord_less_eq_a @ ( uminus_uminus_a @ A ) @ zero_zero_a )
= ( ord_less_eq_a @ zero_zero_a @ A ) ),
inference(lifteq,[status(thm)],[389]) ).
thf(151,axiom,
! [A: a,B: a,C: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) )
=> ! [D: a] :
( ( member_a @ D @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ D ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_transversal__segment__pos) ).
thf(781,plain,
! [A: a,B: a,C: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) )
=> ! [D: a] :
( ( member_a @ D @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ D ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(85,axiom,
! [A: set_real] : ( ord_less_eq_set_real @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_subset__refl) ).
thf(588,plain,
! [A: set_real] : ( ord_less_eq_set_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(125,axiom,
! [A: a] :
( ( member_a @ A @ x )
=> ~ ! [B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ~ ( ord_less_eq_set_real @ ( set_or656347191t_real @ ( uminus_uminus_real @ B ) @ B ) @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_open__existence__ivl_H) ).
thf(699,plain,
! [A: a] :
( ( member_a @ A @ x )
=> ~ ! [B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ~ ( ord_less_eq_set_real @ ( set_or656347191t_real @ ( uminus_uminus_real @ B ) @ B ) @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(207,axiom,
! [A: a] :
( ( member_a @ A @ x )
=> ( ( ( f @ A )
= zero_zero_a )
=> ( ( auto_l612940ivl0_a @ f @ x @ A )
= top_top_set_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_fixpoint__sol_I1_J) ).
thf(946,plain,
! [A: a] :
( ( member_a @ A @ x )
=> ( ( ( f @ A )
= zero_zero_a )
=> ( ( auto_l612940ivl0_a @ f @ x @ A )
= top_top_set_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(258,axiom,
! [A: real] :
( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
= ( ord_less_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_less__neg__neg) ).
thf(1101,plain,
! [A: real] :
( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
= ( ord_less_real @ A @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(417,plain,
! [B: a,A: a] :
( ( ord_less_eq_a @ A @ ( uminus_uminus_a @ B ) )
= ( ord_less_eq_a @ B @ ( uminus_uminus_a @ A ) ) ),
inference(cnf,[status(esa)],[416]) ).
thf(418,plain,
! [B: a,A: a] :
( ( ord_less_eq_a @ A @ ( uminus_uminus_a @ B ) )
= ( ord_less_eq_a @ B @ ( uminus_uminus_a @ A ) ) ),
inference(lifteq,[status(thm)],[417]) ).
thf(299,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ zero_zero_a @ A )
=> ( ( ord_less_eq_a @ zero_zero_a @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( inner_1173012732nner_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_inner__nonneg__nonneg) ).
thf(1212,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ zero_zero_a @ A )
=> ( ( ord_less_eq_a @ zero_zero_a @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( inner_1173012732nner_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(144,axiom,
! [A: real] :
( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
= ( ord_less_real @ zero_zero_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_neg__less__pos) ).
thf(763,plain,
! [A: real] :
( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
= ( ord_less_real @ zero_zero_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(333,axiom,
! [A: a,B: a,C: a] :
( ( ord_less_a @ A @ B )
=> ( ord_less_a @ ( minus_minus_a @ A @ C ) @ ( minus_minus_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_diff__strict__right__mono) ).
thf(1309,plain,
! [A: a,B: a,C: a] :
( ( ord_less_a @ A @ B )
=> ( ord_less_a @ ( minus_minus_a @ A @ C ) @ ( minus_minus_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(1109,plain,
( ( ^ [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) )
= ord_less_eq_real ),
inference(lifteq,[status(thm)],[1108]) ).
thf(1444,plain,
! [A: real] :
( ( ^ [B: real] : ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) )
= ( ord_less_eq_real @ A ) ),
inference(func_ext,[status(esa)],[1109]) ).
thf(238,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( ord_less_eq_set_real @ ( set_or656347191t_real @ A @ zero_zero_real ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_local_Orev_Oivl__subset__existence__ivl_H) ).
thf(1045,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( ord_less_eq_set_real @ ( set_or656347191t_real @ A @ zero_zero_real ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(2741,plain,
! [A: a] :
( ( ( poinca659159244_rot_a @ ( uminus_uminus_a @ A ) )
!= ( poinca659159244_rot_a @ ( f @ z ) ) )
| ( ( minus_minus_a @ zero_zero_a @ A )
!= ( minus_minus_a @ a2 @ b ) ) ),
inference(paramod_ordered,[status(thm)],[916,2565]) ).
thf(2760,plain,
! [A: a] :
( ( ( uminus_uminus_a @ A )
!= ( f @ z ) )
| ( a2 != zero_zero_a )
| ( A != b ) ),
inference(simp,[status(thm)],[2741]) ).
thf(2779,plain,
( ( ( f @ z )
!= ( uminus_uminus_a @ b ) )
| ( a2 != zero_zero_a ) ),
inference(simp,[status(thm)],[2760]) ).
thf(68,axiom,
! [A: real,B: real] :
( ( inner_4346926r_real @ A @ ( uminus_uminus_real @ B ) )
= ( uminus_uminus_real @ ( inner_4346926r_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_inner__minus__right) ).
thf(536,plain,
! [A: real,B: real] :
( ( inner_4346926r_real @ A @ ( uminus_uminus_real @ B ) )
= ( uminus_uminus_real @ ( inner_4346926r_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(1132,plain,
a2 != b,
inference(polarity_switch,[status(thm)],[1131]) ).
thf(1133,plain,
b != a2,
inference(lifteq,[status(thm)],[1132]) ).
thf(322,axiom,
! [A: real] :
( ( zero_zero_real
= ( uminus_uminus_real @ A ) )
= ( zero_zero_real = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_neg__0__equal__iff__equal) ).
thf(1280,plain,
! [A: real] :
( ( zero_zero_real
= ( uminus_uminus_real @ A ) )
= ( zero_zero_real = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(169,axiom,
! [A: a,B: a,C: a,D: a] :
( ( member_a @ A @ ( set_or411607219Most_a @ B @ C ) )
=> ( ( ord_less_eq_a @ zero_zero_a @ D )
=> ( ord_less_eq_real @ ( inner_1173012732nner_a @ B @ D ) @ ( inner_1173012732nner_a @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_interval__inner__leI_I1_J) ).
thf(835,plain,
! [A: a,B: a,C: a,D: a] :
( ( member_a @ A @ ( set_or411607219Most_a @ B @ C ) )
=> ( ( ord_less_eq_a @ zero_zero_a @ D )
=> ( ord_less_eq_real @ ( inner_1173012732nner_a @ B @ D ) @ ( inner_1173012732nner_a @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(277,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
= ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_diff__ge__0__iff__ge) ).
thf(1148,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
= ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(179,axiom,
! [A: real] :
( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
= ( ord_less_real @ zero_zero_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_neg__less__0__iff__less) ).
thf(865,plain,
! [A: real] :
( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
= ( ord_less_real @ zero_zero_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(373,plain,
( ( ^ [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
& ( ord_less_eq_set_real @ B @ A ) ) )
= ( (=) @ set_real ) ),
inference(lifteq,[status(thm)],[372]) ).
thf(221,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( member_a @ B @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_local_Omem__existence__ivl__iv__defined_I2_J) ).
thf(999,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( member_a @ B @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(98,axiom,
! [A: set_a,B: set_a] :
( ( minus_minus_set_a @ ( minus_minus_set_a @ A @ B ) @ B )
= ( minus_minus_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_Diff__idemp) ).
thf(620,plain,
! [A: set_a,B: set_a] :
( ( minus_minus_set_a @ ( minus_minus_set_a @ A @ B ) @ B )
= ( minus_minus_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(2678,plain,
! [A: a] :
( ( A
!= ( f @ z ) )
| ( A != a2 )
| ( b != zero_zero_a ) ),
inference(simp,[status(thm)],[2671]) ).
thf(2683,plain,
( ( ( f @ z )
!= a2 )
| ( b != zero_zero_a ) ),
inference(simp,[status(thm)],[2678]) ).
thf(446,plain,
! [B: a,A: a] :
( ( ord_less_a @ ( uminus_uminus_a @ A ) @ B )
= ( ord_less_a @ ( uminus_uminus_a @ B ) @ A ) ),
inference(cnf,[status(esa)],[445]) ).
thf(447,plain,
! [B: a,A: a] :
( ( ord_less_a @ ( uminus_uminus_a @ A ) @ B )
= ( ord_less_a @ ( uminus_uminus_a @ B ) @ A ) ),
inference(lifteq,[status(thm)],[446]) ).
thf(175,axiom,
! [A: a,B: real] :
( ( member_a @ A @ ( elemen49976720ball_a @ A @ B ) )
= ( ord_less_eq_real @ zero_zero_real @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_centre__in__cball) ).
thf(854,plain,
! [A: a,B: real] :
( ( member_a @ A @ ( elemen49976720ball_a @ A @ B ) )
= ( ord_less_eq_real @ zero_zero_real @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(331,axiom,
! [A: set_a] :
( ( auto_l630715367iant_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= ( ! [B: a] :
( ( member_a @ B @ A )
=> ( oDE_au1996717075pped_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_rev_Oinvariant__def) ).
thf(1303,plain,
! [A: set_a] :
( ( auto_l630715367iant_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= ( ! [B: a] :
( ( member_a @ B @ A )
=> ( oDE_au1996717075pped_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(154,axiom,
! [A: real] :
( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
= ( ord_less_eq_real @ zero_zero_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_neg__less__eq__nonneg) ).
thf(790,plain,
! [A: real] :
( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
= ( ord_less_eq_real @ zero_zero_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(59,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_subset__antisym) ).
thf(506,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(357,plain,
! [A: set_real,B: set_real] :
( ( ord_less_eq_set_real @ A @ B )
=> ! [C: set_real,D: set_real] :
( ( ord_less_eq_set_real @ C @ D )
=> ( ord_less_eq_set_real @ ( minus_minus_set_real @ A @ D ) @ ( minus_minus_set_real @ B @ C ) ) ) ),
inference(miniscope,[status(thm)],[356]) ).
thf(358,plain,
! [D: set_real,C: set_real,B: set_real,A: set_real] :
( ~ ( ord_less_eq_set_real @ A @ B )
| ~ ( ord_less_eq_set_real @ C @ D )
| ( ord_less_eq_set_real @ ( minus_minus_set_real @ A @ D ) @ ( minus_minus_set_real @ B @ C ) ) ),
inference(cnf,[status(esa)],[357]) ).
thf(124,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( minus_minus_real @ C @ B ) @ ( minus_minus_real @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_diff__strict__left__mono) ).
thf(696,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( minus_minus_real @ C @ B ) @ ( minus_minus_real @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(2668,plain,
( ( minus_minus_a @ a2 @ b )
!= ( f @ z ) ),
inference(simp,[status(thm)],[2565]) ).
thf(156,axiom,
! [A: real,B: real] :
( ( ord_less_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
= ( ord_less_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_neg__less__iff__less) ).
thf(796,plain,
! [A: real,B: real] :
( ( ord_less_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
= ( ord_less_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(414,plain,
! [A: real] :
( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
= A ),
inference(cnf,[status(esa)],[413]) ).
thf(415,plain,
! [A: real] :
( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
= A ),
inference(lifteq,[status(thm)],[414]) ).
thf(436,plain,
! [B: a,A: a] :
( ( ord_less_eq_a @ ( uminus_uminus_a @ A ) @ B )
= ( ord_less_eq_a @ ( uminus_uminus_a @ B ) @ A ) ),
inference(cnf,[status(esa)],[435]) ).
thf(437,plain,
! [B: a,A: a] :
( ( ord_less_eq_a @ ( uminus_uminus_a @ A ) @ B )
= ( ord_less_eq_a @ ( uminus_uminus_a @ B ) @ A ) ),
inference(lifteq,[status(thm)],[436]) ).
thf(1335,plain,
! [A: a] :
( ( real_V1514887919dist_a @ A )
= ( ^ [B: a] : ( real_V1514887919dist_a @ B @ A ) ) ),
inference(func_ext,[status(esa)],[482]) ).
thf(285,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( set_or656347191t_real @ A @ B )
= ( set_or656347191t_real @ C @ D ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ~ ( ord_less_eq_real @ A @ B )
& ~ ( ord_less_eq_real @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_Icc__eq__Icc) ).
thf(1172,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( set_or656347191t_real @ A @ B )
= ( set_or656347191t_real @ C @ D ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ~ ( ord_less_eq_real @ A @ B )
& ~ ( ord_less_eq_real @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(190,axiom,
! [A: set_a] :
( ( auto_l630715367iant_a @ f @ x @ A )
= ( auto_l630715367iant_a @ f @ x @ ( minus_minus_set_a @ x @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_invariant__iff__compl__invariant) ).
thf(897,plain,
! [A: set_a] :
( ( auto_l630715367iant_a @ f @ x @ A )
= ( auto_l630715367iant_a @ f @ x @ ( minus_minus_set_a @ x @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(325,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
=> ( member_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_DiffD1) ).
thf(1288,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
=> ( member_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(399,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ! [C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ C @ D )
=> ( ord_less_eq_set_a @ ( minus_minus_set_a @ A @ D ) @ ( minus_minus_set_a @ B @ C ) ) ) ),
inference(miniscope,[status(thm)],[398]) ).
thf(400,plain,
! [D: set_a,C: set_a,B: set_a,A: set_a] :
( ~ ( ord_less_eq_set_a @ A @ B )
| ~ ( ord_less_eq_set_a @ C @ D )
| ( ord_less_eq_set_a @ ( minus_minus_set_a @ A @ D ) @ ( minus_minus_set_a @ B @ C ) ) ),
inference(cnf,[status(esa)],[399]) ).
thf(270,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_le__imp__neg__le) ).
thf(1129,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(318,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( minus_minus_a @ A @ B )
= ( minus_minus_a @ C @ D ) )
=> ( ( ord_less_a @ A @ B )
= ( ord_less_a @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_diff__eq__diff__less) ).
thf(1268,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( minus_minus_a @ A @ B )
= ( minus_minus_a @ C @ D ) )
=> ( ( ord_less_a @ A @ B )
= ( ord_less_a @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(177,axiom,
! [A: a] : ( ord_less_eq_set_real @ ( auto_l612940ivl0_a @ f @ x @ A ) @ top_top_set_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_local_Oexistence__ivl__subset) ).
thf(860,plain,
! [A: a] : ( ord_less_eq_set_real @ ( auto_l612940ivl0_a @ f @ x @ A ) @ top_top_set_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(229,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_set_real @ ( set_or656347191t_real @ A @ B ) @ ( set_or656347191t_real @ C @ D ) )
= ( ( ~ ( ord_less_eq_real @ A @ B )
| ( ( ord_less_eq_real @ C @ A )
& ( ord_less_eq_real @ B @ D )
& ( ( ord_less_real @ C @ A )
| ( ord_less_real @ B @ D ) ) ) )
& ( ord_less_eq_real @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_atLeastatMost__psubset__iff) ).
thf(1019,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_set_real @ ( set_or656347191t_real @ A @ B ) @ ( set_or656347191t_real @ C @ D ) )
= ( ( ~ ( ord_less_eq_real @ A @ B )
| ( ( ord_less_eq_real @ C @ A )
& ( ord_less_eq_real @ B @ D )
& ( ( ord_less_real @ C @ A )
| ( ord_less_real @ B @ D ) ) ) )
& ( ord_less_eq_real @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(218,axiom,
! [A: a > real,B: a > bounde7994401a_real,C: set_a] :
( ( reacha1191408304tion_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B @ C )
=> ( ord_less_eq_set_a @ C @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_rev_OsectionD_I5_J) ).
thf(992,plain,
! [A: a > real,B: a > bounde7994401a_real,C: set_a] :
( ( reacha1191408304tion_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B @ C )
=> ( ord_less_eq_set_a @ C @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(166,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( ord_less_eq_set_real @ ( set_or656347191t_real @ zero_zero_real @ A ) @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_local_Oivl__subset__existence__ivl) ).
thf(822,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( ord_less_eq_set_real @ ( set_or656347191t_real @ zero_zero_real @ A ) @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(224,axiom,
! [A: a,B: a] :
( ( ord_less_eq_real @ ( real_V1514887919dist_a @ A @ B ) @ zero_zero_real )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_dist__le__zero__iff) ).
thf(1004,plain,
! [A: a,B: a] :
( ( ord_less_eq_real @ ( real_V1514887919dist_a @ A @ B ) @ zero_zero_real )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(441,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ! [C: set_a] :
( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(miniscope,[status(thm)],[440]) ).
thf(442,plain,
! [C: set_a,B: set_a,A: set_a] :
( ~ ( ord_less_eq_set_a @ A @ B )
| ~ ( ord_less_eq_set_a @ B @ C )
| ( ord_less_eq_set_a @ A @ C ) ),
inference(cnf,[status(esa)],[441]) ).
thf(181,axiom,
! [A: a,B: a,C: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ( ord_less_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) @ zero_zero_real )
=> ( ord_less_eq_set_a @ ( line_c1152468841ment_a @ A @ B ) @ x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_transversal__segment__negD_I2_J) ).
thf(871,plain,
! [A: a,B: a,C: a] :
( ( poinca522724647ment_a @ f @ x @ A @ B )
=> ( ( member_a @ C @ ( line_c1152468841ment_a @ A @ B ) )
=> ( ( ord_less_real @ ( inner_1173012732nner_a @ ( f @ C ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) ) @ zero_zero_real )
=> ( ord_less_eq_set_a @ ( line_c1152468841ment_a @ A @ B ) @ x ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(131,axiom,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
=> ( ( member_a @ A @ x )
=> ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_local_Orev_Oexistence__ivl__initial__time) ).
thf(728,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
=> ( ( member_a @ A @ x )
=> ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(135,axiom,
! [A: a,B: a,C: a,D: a] :
( ( ( minus_minus_a @ A @ B )
= ( minus_minus_a @ C @ D ) )
=> ( ( ord_less_eq_a @ A @ B )
= ( ord_less_eq_a @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_diff__eq__diff__less__eq) ).
thf(740,plain,
! [A: a,B: a,C: a,D: a] :
( ( ( minus_minus_a @ A @ B )
= ( minus_minus_a @ C @ D ) )
=> ( ( ord_less_eq_a @ A @ B )
= ( ord_less_eq_a @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(1350,plain,
! [B: real,A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ~ $true
| ( member_a @ ( sk1 @ B @ A ) @ ( elemen49976720ball_a @ x2 @ A ) )
| ( ( ord_less_real @ zero_zero_real @ d )
!= ( ord_less_real @ zero_zero_real @ B ) ) ),
inference(paramod_ordered,[status(thm)],[756,342]) ).
thf(1351,plain,
! [B: real,A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ( member_a @ ( sk1 @ B @ A ) @ ( elemen49976720ball_a @ x2 @ A ) )
| ( ( ord_less_real @ zero_zero_real @ d )
!= ( ord_less_real @ zero_zero_real @ B ) ) ),
inference(simp,[status(thm)],[1350]) ).
thf(1352,plain,
! [A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ( member_a @ ( sk1 @ d @ A ) @ ( elemen49976720ball_a @ x2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[1351:[bind(A,$thf( A )),bind(B,$thf( d ))]]) ).
thf(44,axiom,
! [A: set_real,B: set_real,C: set_real,D: set_real] :
( ( ord_le1733505144t_real @ ( set_or1619725421t_real @ A @ B ) @ ( set_or1619725421t_real @ C @ D ) )
= ( ~ ( ord_less_eq_set_real @ A @ B )
| ( ( ord_less_eq_set_real @ C @ A )
& ( ord_less_eq_set_real @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_atLeastatMost__subset__iff) ).
thf(464,plain,
! [A: set_real,B: set_real,C: set_real,D: set_real] :
( ( ord_le1733505144t_real @ ( set_or1619725421t_real @ A @ B ) @ ( set_or1619725421t_real @ C @ D ) )
= ( ~ ( ord_less_eq_set_real @ A @ B )
| ( ( ord_less_eq_set_real @ C @ A )
& ( ord_less_eq_set_real @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(88,axiom,
poinca522724647ment_a = poinca522724647ment_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_c1__on__open__R2_Otransversal__segment_Ocong) ).
thf(596,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(1371,plain,
! [A: real] :
( ~ $true
| ( ( ord_less_real @ zero_zero_real @ d )
!= ( ord_less_real @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[756,1094]) ).
thf(1372,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ d )
!= ( ord_less_real @ A @ A ) ),
inference(simp,[status(thm)],[1371]) ).
thf(1375,plain,
! [A: real] :
( ( zero_zero_real != A )
| ( d != A ) ),
inference(simp,[status(thm)],[1372]) ).
thf(1378,plain,
d != zero_zero_real,
inference(simp,[status(thm)],[1375]) ).
thf(52,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ( minus_minus_set_a @ B @ ( minus_minus_set_a @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_double__diff) ).
thf(486,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ( minus_minus_set_a @ B @ ( minus_minus_set_a @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(71,axiom,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ord_less_eq_a @ ( uminus_uminus_a @ B ) @ ( uminus_uminus_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_le__imp__neg__le) ).
thf(543,plain,
! [A: a,B: a] :
( ( ord_less_eq_a @ A @ B )
=> ( ord_less_eq_a @ ( uminus_uminus_a @ B ) @ ( uminus_uminus_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(41,axiom,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_le318720350_set_a @ ( set_or2094724627_set_a @ A @ B ) @ ( set_or2094724627_set_a @ C @ D ) )
= ( ~ ( ord_less_eq_set_a @ A @ B )
| ( ( ord_less_eq_set_a @ C @ A )
& ( ord_less_eq_set_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_atLeastatMost__subset__iff) ).
thf(454,plain,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_le318720350_set_a @ ( set_or2094724627_set_a @ A @ B ) @ ( set_or2094724627_set_a @ C @ D ) )
= ( ~ ( ord_less_eq_set_a @ A @ B )
| ( ( ord_less_eq_set_a @ C @ A )
& ( ord_less_eq_set_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(185,axiom,
! [A: a,B: a] :
( ( inner_1173012732nner_a @ ( minus_minus_a @ A @ B ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_nrm__dot) ).
thf(882,plain,
! [A: a,B: a] :
( ( inner_1173012732nner_a @ ( minus_minus_a @ A @ B ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ A @ B ) ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(211,axiom,
! [A: real,B: real,C: a] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( ( member_a @ C @ x )
=> ( ! [D: real,E: real,F: a] :
( ( member_a @ F @ x )
=> ( ( f @ F )
= ( f @ F ) ) )
=> ( ( top_top_set_real = top_top_set_real )
=> ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_mem__existence__ivl__shift__autonomous2) ).
thf(972,plain,
! [A: real,B: real,C: a] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( ( member_a @ C @ x )
=> ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(205,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
=> ~ ( ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_DiffE) ).
thf(940,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( minus_minus_set_a @ B @ C ) )
=> ~ ( ( member_a @ A @ B )
=> ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(203,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( ord_less_eq_set_real @ ( set_or656347191t_real @ zero_zero_real @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_local_Orev_Oivl__subset__existence__ivl) ).
thf(935,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( ord_less_eq_set_real @ ( set_or656347191t_real @ zero_zero_real @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(1943,plain,
! [A: real] :
( ~ $true
| ( member_a @ ( sk1 @ A @ sk11 ) @ ( elemen49976720ball_a @ x2 @ sk11 ) )
| ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1208,1367]) ).
thf(1944,plain,
! [A: real] :
( ( member_a @ ( sk1 @ A @ sk11 ) @ ( elemen49976720ball_a @ x2 @ sk11 ) )
| ( ( ord_less_real @ zero_zero_real @ ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(simp,[status(thm)],[1943]) ).
thf(1945,plain,
member_a @ ( sk1 @ ( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ) @ sk11 ) @ ( elemen49976720ball_a @ x2 @ sk11 ),
inference(pattern_uni,[status(thm)],[1944:[bind(A,$thf( inner_1173012732nner_a @ ( f @ z ) @ ( poinca659159244_rot_a @ ( minus_minus_a @ a2 @ b ) ) ))]]) ).
thf(235,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_verit__negate__coefficient_I2_J) ).
thf(1037,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(559,plain,
! [A: a] :
( ( ord_less_a @ zero_zero_a @ ( uminus_uminus_a @ A ) )
= ( ord_less_a @ A @ zero_zero_a ) ),
inference(cnf,[status(esa)],[558]) ).
thf(560,plain,
! [A: a] :
( ( ord_less_a @ zero_zero_a @ ( uminus_uminus_a @ A ) )
= ( ord_less_a @ A @ zero_zero_a ) ),
inference(lifteq,[status(thm)],[559]) ).
thf(18180,plain,
$false,
inference(e,[status(thm)],[645,809,1337,1411,760,1237,1083,777,1110,481,365,1190,479,1105,909,1031,977,1406,4339,1443,994,1205,379,440,1971,677,597,1437,523,4376,1078,385,1260,340,930,814,1327,1196,1001,4371,709,841,885,1366,1265,3370,1095,404,1243,1127,1409,1287,372,838,2682,1059,917,751,802,344,949,2571,542,460,817,1087,1147,1479,606,1013,1115,448,1232,421,870,881,416,924,756,789,443,376,623,834,3438,353,2777,1151,937,348,574,1183,1283,1377,1215,734,660,1104,2205,2586,602,766,1169,397,1072,453,1119,774,1074,920,439,1438,793,1306,1199,1153,381,366,534,1067,1047,1730,1057,1163,1274,894,746,1255,1570,598,820,561,424,429,1042,952,862,349,407,693,630,566,435,2068,493,2213,757,1291,974,1012,1106,916,467,2565,879,1296,665,522,830,682,1195,2211,1936,650,615,1064,725,388,4840,593,1118,499,989,857,519,578,874,2840,1111,1227,980,403,1138,356,1329,1160,1028,933,753,1739,526,637,1446,1155,706,2419,1075,476,1016,590,679,1039,1324,1297,1530,1002,569,1246,779,647,1263,1131,654,1050,457,1202,633,805,541,657,1054,558,1895,1185,888,926,343,1318,1286,398,4906,674,906,412,1510,1764,2556,824,745,2602,573,689,444,733,513,1146,430,584,4041,423,1007,1884,743,826,545,413,843,1125,958,1403,391,445,382,572,1271,1312,787,1865,1733,1058,1092,1258,1464,1224,350,540,2557,3641,604,1209,681,2214,784,419,1144,737,1122,2197,1175,900,406,377,996,362,451,567,2116,2839,509,434,599,1439,890,1339,609,5439,799,483,848,1838,2785,1460,1022,1293,1381,1112,811,387,494,1080,1061,1952,868,4373,1435,851,438,1562,912,685,521,1171,3539,983,768,827,394,986,722,1034,490,426,1208,944,680,1277,1134,1081,342,2564,1413,473,663,548,927,2037,374,617,516,525,580,690,640,1025,1070,2012,1647,3659,1252,1098,409,1230,4346,1300,502,1235,463,470,3623,359,643,1188,1186,1538,808,1218,5450,703,1141,656,2379,1221,1353,864,1094,571,612,497,876,1240,991,1940,627,2479,1180,539,482,671,1448,1010,771,1108,1649,450,1084,363,556,1157,1321,688,903,524,581,891,2209,368,844,813,748,390,401,781,588,699,946,1101,731,418,2066,1193,1212,763,383,1309,1444,1045,914,378,2779,536,1133,2374,1280,432,410,835,1148,865,373,999,620,2683,447,854,1303,422,790,564,1989,506,358,1561,696,2668,1346,5440,796,415,437,1335,1172,897,1288,400,395,1236,1129,1268,860,1384,1019,644,992,822,1004,1902,442,871,728,740,1352,464,1152,427,596,1378,486,803,2206,543,454,882,972,1367,940,935,1945,1037,560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP149^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.22 % Computer : n020.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 20:01:54 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.89/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.49/1.23 % [INFO] Parsing done (448ms).
% 2.49/1.25 % [INFO] Running in sequential loop mode.
% 3.69/1.64 % [INFO] eprover registered as external prover.
% 3.69/1.65 % [INFO] Scanning for conjecture ...
% 4.12/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 352 axioms. Running axiom selection ...
% 4.46/1.92 % [INFO] Axiom selection finished. Selected 337 axioms (removed 15 axioms).
% 5.09/2.11 % [INFO] Problem is higher-order (TPTP THF).
% 5.09/2.13 % [INFO] Type checking passed.
% 5.09/2.13 % [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 ...
% 135.78/45.09 % External prover 'e' found a proof!
% 135.78/45.09 % [INFO] Killing All external provers ...
% 135.78/45.09 % Time passed: 44735ms (effective reasoning time: 43836ms)
% 135.78/45.09 % 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)>
% 135.78/45.10 % Axioms used in derivation (337): fact_195_less__eq__neg__nonpos, fact_204_diff__0, fact_201_neg__less__0__iff__less, fact_17_centre__in__cball, fact_192_neg__0__le__iff__le, fact_122_interval__inner__leI_I1_J, fact_10_dot__ortho, fact_213_less__minus__iff, fact_241_Diff__iff, fact_216_minus__diff__commute, fact_305_psubset__subset__trans, fact_23_inner__zero__right, fact_307_psubset__imp__subset, fact_97_inner__diff__right, fact_53_transversal__segment__negD_I2_J, fact_105_less__iff__diff__less__0, fact_150_rev_Operiodic__orbit__period_I1_J, fact_154_closed__orbit__period__nonneg, fact_287_compl__mono, fact_169_rev_Oclosed__orbit__periodic, fact_244_DiffI, fact_237_subset__antisym, fact_74_cancel__ab__semigroup__add__class_Odiff__right__commute, fact_87_diff__mono, fact_256_Collect__mono, fact_337_rev_Ofixpoint__sol_I1_J, fact_16_inner__gt__zero__iff, fact_26_inner__eq__zero__iff, fact_70_c1__on__open__R2_Otransversal__segment_Ocong, fact_261_subset__iff, fact_176_equal__neg__zero, fact_86_diff__mono, fact_302_subset__not__subset__eq, fact_254_subset__trans, fact_281_psubsetD, fact_223_psubsetI, fact_247_verit__comp__simplify1_I1_J, fact_273_in__mono, fact_153_closed__orbit__period__zero__fixed__point, fact_239_subsetI, fact_231_verit__minus__simplify_I4_J, fact_229_nrm__reverse, fact_36_transversal__segment__commute, fact_2_seg_I1_J, fact_12__092_060open_062x_A_092_060in_062_A_123a_N_Nb_125_092_060close_062, fact_84_diff__left__mono, fact_11__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062s_O_A_092_060lbrakk_062s_A_092_060in_062_Acball_Ax_Ad_059_A_092_060forall_062x_092_060in_062cball_Ax_Ad_O_Af_As_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_A_092_060le_062_Af_Ax_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_268_equalityE, fact_270_subsetD, fact_274_DiffD2, fact_257_Collect__mono, fact_271_subsetD, fact_131_atLeastatMost__subset__iff, fact_253_set__eq__subset, fact_15_inner__gt__zero__iff, fact_285_compl__le__swap1, fact_265_equalityD1, fact_99_inner__diff__left, fact_243_DiffI, fact_151_periodic__orbit__def, fact_194_neg__le__0__iff__le, fact_130_atLeastatMost__subset__iff, fact_5__092_060open_062_092_060forall_062x_092_060in_062cball_Ax_Ad_O_Af_As_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_A_092_060le_062_Af_Ax_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_092_060close_062, fact_221_verit__minus__simplify_I3_J, fact_349_fixpoint__sol_I1_J, fact_303_subset__not__subset__eq, fact_79_eq__iff__diff__eq__0, fact_62_transversal__segment__sign__less, fact_172_neg__0__equal__iff__equal, fact_24_inner__zero__right, fact_187_inner__minus__right, fact_88_diff__strict__right__mono, fact_20_all__zero__iff, fact_175_neg__equal__0__iff__equal, fact_34_direction_I1_J, fact_107_fixed__point__imp__closed__orbit__period__zero_I2_J, fact_134_atLeastAtMost__iff, fact_162_rev_Oinvariant__eq__rev, fact_218_equation__minus__iff, fact_143_dist__commute__lessI, fact_312_psubset__imp__ex__mem, fact_326_local_Oivl__subset__existence__ivl_H, fact_341_local_Omem__existence__ivl__subset, fact_28_diff__gt__0__iff__gt, fact_63_transversal__segment__pos, fact_33_seg_I3_J, fact_140_Icc__eq__Icc, fact_64_transversal__segment__neg, fact_275_DiffD2, fact_347_general_Omem__existence__ivl__subset, fact_32_rot__eq__0__iff, fact_167_closed__orbit__periodic, fact_111_in__closed__segment__iff__rot, fact_160_rev_Oclosed__orbit__eq__rev, fact_113_transversal__segment__exists, fact_197_less__neg__neg, fact_199_neg__0__less__iff__less, fact_29_diff__ge__0__iff__ge, fact_346_mem__existence__ivl__shift__autonomous2, fact_39_seg_I2_J, fact_293_double__diff, fact_168_rev_Oinvariant__def, fact_251_Collect__mono__iff, fact_137_atLeastAtMost__iff, fact_315_open__existence__ivl_H, fact_96_inner__diff__right, fact_246_verit__la__disequality, fact_61_Collect__mem__eq, fact_184_inner__minus__left, fact_25_inner__eq__zero__iff, fact_71_zero__reorient, fact_60_Collect__mem__eq, fact_166_rev_Oinvariant__iff__compl__invariant, fact_279_DiffE, fact_161_rev_Oclosed__orbit__in__domain, fact_171_add_Oinverse__neutral, fact_108_that, fact_98_inner__diff__left, fact_138_Icc__eq__Icc, fact_290_verit__negate__coefficient_I2_J, fact_73_cancel__ab__semigroup__add__class_Odiff__right__commute, fact_196_neg__less__eq__nonneg, fact_181_neg__less__iff__less, fact_212_minus__less__iff, fact_259_subset__refl, fact_85_diff__left__mono, fact_255_subset__trans, fact_230_verit__minus__simplify_I4_J, fact_45_diff__0__right, fact_310_psubsetE, fact_65_transversal__segment__posD_I1_J, fact_141_dist__eq__0__iff, fact_202_neg__less__0__iff__less, fact_101_mem__cball__leI, fact_156_add_Oinverse__inverse, fact_318_general_Omem__existence__ivl__iv__defined_I2_J, fact_266_subset__eq, fact_249_verit__negate__coefficient_I3_J, fact_102_le__iff__diff__le__0, fact_56_mem__Collect__eq, fact_103_le__iff__diff__le__0, fact_95_diff__strict__mono, fact_157_add_Oinverse__inverse, fact_222_verit__minus__simplify_I3_J, fact_129_atLeastatMost__subset__iff, fact_38_in__segment__inner__rot, fact_313_psubset__imp__ex__mem, fact_316_rev_Oopen__existence__ivl0, fact_164_rev_Ofixed__point__imp__closed__orbit__period__zero_I1_J, fact_269_equalityE, fact_282_verit__comp__simplify1_I3_J, fact_43_diff__zero, fact_57_mem__Collect__eq, fact_240_Diff__idemp, fact_219_minus__equation__iff, fact_321_ComplI, fact_115_cball__eq__cball__iff, fact_314_rev_Oopen__existence__ivl_H, fact_89_diff__strict__right__mono, fact_300_subset__psubset__trans, fact_142_dist__commute, fact_127_zero__less__dist__iff, fact_350_closed__orbit__global__existence, fact_228_rot__diff__commute, fact_170_add_Oinverse__neutral, fact_31_rot__0, fact_329_local_Orev_Oivl__subset__existence__ivl_H, fact_51_transversal__segmentE, fact_158_neg__equal__iff__equal, fact_121_interval__inner__leI_I2_J, fact_298_subset__iff__psubset__eq, fact_250_Collect__mono__iff, fact_112_sectionD_I5_J, fact_280_psubsetD, fact_342_local_Oexistence__ivl__initial__time, fact_52_transversal__segment__posD_I2_J, fact_120_interval__inner__leI_I2_J, fact_283_compl__le__swap2, fact_210_le__minus__iff, fact_324_rev_Ogeneral_Omem__existence__ivl__iv__defined_I2_J, fact_165_rev_OsectionD_I5_J, fact_35_transversal__segment__reverse, fact_182_minus__diff__eq, fact_6__092_060open_062f_Ax_A_092_060noteq_062_A_I0_058_058_Ha_J_092_060close_062, fact_0_d_I1_J, fact_18_centre__in__cball, fact_66_transversal__segment__posD_I3_J, fact_343_local_Orev_Omem__existence__ivl__subset, fact_152_rev_Ofixed__point__imp__closed__orbit__period__zero_I2_J, fact_13__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_O_A_092_060lbrakk_0620_A_060_Ad_059_A_092_060And_062y_O_Ay_A_092_060in_062_Acball_Ax_Ad_A_092_060Longrightarrow_062_A0_A_060_Af_Ay_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_A_092_060and_062_Ay_A_092_060in_062_AX_A_092_060and_062_Af_Ay_A_092_060noteq_062_A_I0_058_058_Ha_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_47_diff__self, fact_276_DiffD1, fact_67_transversal__segment__negD_I1_J, fact_41_cancel__comm__monoid__add__class_Odiff__cancel, fact_278_DiffE, fact_177_neg__equal__zero, fact_232_Compl__subset__Compl__iff, fact_331_local_Orev_Omem__existence__ivl__iv__defined_I2_J, fact_75_diff__eq__diff__eq, fact_311_psubsetE, fact_82_diff__right__mono, fact_110_inner__nonneg__nonneg, fact_245_rot__rot, fact_340_UNIV__I, fact_178_neg__le__iff__le, fact_207_minus__le__iff, fact_69__092_060open_062_092_060And_062z_O_Az_A_092_060in_062_A_123a_N_Nb_125_A_092_060Longrightarrow_062_A0_A_060_Af_Az_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_092_060close_062, fact_93_diff__eq__diff__less, fact_248_verit__negate__coefficient_I3_J, fact_128_dist__le__zero__iff, fact_123_interval__inner__leI_I1_J, fact_117_mem__cball, fact_132_atLeastatMost__subset__iff, fact_272_in__mono, fact_114_invariant__iff__compl__invariant, fact_46_diff__self, fact_291_fun__Compl__def, fact_133_dist__self, fact_264_equalityD1, fact_345_general_Oexistence__ivl__initial__time, fact_214_less__minus__iff, fact_191_neg__0__le__iff__le, fact_339_UNIV__I, fact_173_neg__0__equal__iff__equal, fact_299_subset__iff__psubset__eq, fact_188_rev_Oclosed__orbit__period__nonneg, fact_206_le__imp__neg__le, fact_205_le__imp__neg__le, fact_179_neg__le__iff__le, fact_8_d_I2_J, fact_306_psubset__imp__subset, fact_118_mem__cball, fact_40_cancel__comm__monoid__add__class_Odiff__cancel, fact_234_Compl__anti__mono, fact_9__092_060open_0620_A_060_Af_Ax_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_092_060close_062, fact_186_inner__minus__right, fact_146_atLeastatMost__psubset__iff, fact_336_rev_Oclosed__orbit__global__existence, fact_180_neg__less__iff__less, fact_30_diff__ge__0__iff__ge, fact_200_neg__0__less__iff__less, fact_252_set__eq__subset, fact_203_diff__0, fact_209_le__minus__iff, fact_338_interval__axioms, fact_242_Diff__iff, fact_348_local_Oexistence__ivl__subset, fact_14_transversal, fact_139_Icc__eq__Icc, fact_208_minus__le__iff, fact_263_equalityD2, fact_42_diff__zero, fact_193_neg__le__0__iff__le, fact_81_diff__eq__diff__less__eq, fact_145_atLeastatMost__psubset__iff, fact_190_rev_Operiodic__orbit__def, fact_148_dist__not__less__zero, fact_1__092_060open_062s_A_092_060in_062_Acball_Ax_Ad_092_060close_062, fact_215_minus__diff__commute, fact_83_diff__right__mono, fact_72_zero__reorient, fact_344_general_Omem__existence__ivl__iv__defined_I1_J, fact_226_compl__le__compl__iff, fact_267_subset__eq, fact_289_verit__negate__coefficient_I2_J, fact_198_neg__less__pos, fact_19_all__zero__iff, fact_106_inner__ge__zero, fact_185_inner__minus__left, fact_217_equation__minus__iff, fact_27_diff__gt__0__iff__gt, fact_334_rev_Omvar_Ointerval__axioms, fact_68_transversal__segment__negD_I3_J, fact_332_ComplD, fact_21_inner__zero__left, fact_308_psubset__eq, fact_90_diff__strict__left__mono, fact_211_minus__less__iff, fact_225_uminus__apply, fact_124_eucl__less__le__not__le, fact_104_less__iff__diff__less__0, fact_100_mem__cball__leI, fact_76_diff__eq__diff__eq, fact_335_mvar_Ointerval__axioms, fact_77_inner__commute, fact_224_psubsetI, fact_22_inner__zero__left, fact_7_direction_I2_J, fact_144_atLeastatMost__psubset__iff, fact_220_minus__equation__iff, fact_49_subset__cball, fact_4__092_060open_062x_A_092_060in_062_AX_092_060close_062, fact_125_invariant__def, fact_295_Diff__subset, fact_159_neg__equal__iff__equal, fact_37_in__segment__inner__rot2, fact_325_local_Oivl__subset__existence__ivl, fact_44_diff__0__right, fact_80_diff__eq__diff__less__eq, fact_317_existence__ivl__zero, fact_328_local_Orev_Oivl__subset__existence__ivl, fact_294_Diff__subset, fact_94_diff__strict__mono, fact_304_psubset__subset__trans, fact_78_eq__iff__diff__eq__0, fact_3_nrm__dot, fact_163_fixed__point__imp__closed__orbit__period__zero_I1_J, fact_236_subset__antisym, fact_92_diff__eq__diff__less, fact_260_subset__iff, fact_262_equalityD2, fact_174_neg__equal__0__iff__equal, fact_50_transversal__segment__def, fact_109_inner__nonneg__nonneg, fact_301_subset__psubset__trans, fact_189_rev_Oclosed__orbit__period__zero__fixed__point, fact_147_zero__le__dist, fact_155_closed__orbit__in__domain, fact_351_local_Orev_Oexistence__ivl__initial__time, fact_116_Bolzano, fact_297_Diff__mono, fact_323_rev_Oexistence__ivl__zero, fact_48_subset__cball, fact_277_DiffD1, fact_258_subset__refl, fact_292_double__diff, fact_309_psubset__eq, fact_330_local_Omem__existence__ivl__iv__defined_I2_J, fact_119_perfect__choose__dist, fact_296_Diff__mono, fact_327_open__existence__ivl0, fact_91_diff__strict__left__mono, fact_238_subsetI, fact_149_dist__pos__lt, fact_126_periodic__orbit__period_I1_J, fact_183_minus__diff__eq, fact_319_Compl__iff
% 135.78/45.10 % No. of inferences in proof: 1120
% 135.78/45.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 44735 ms resp. 43836 ms w/o parsing
% 126.81/45.40 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 126.81/45.41 % [INFO] Killing All external provers ...
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