%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP146^1 : 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 : n018.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 08:06:56 AM UTC 2026
% Result : Theorem 77.85s 20.33s
% Output : Refutation 76.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 248
% Syntax : Number of formulae : 905 ( 411 unt; 0 typ; 3 def)
% Number of atoms : 2379 (1183 equ; 4 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 8208 ( 601 ~; 373 |; 62 &;6753 @)
% ( 0 <=>; 419 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 35 usr; 19 con; 0-4 aty)
% Number of variables : 1609 ( 161 ^;1439 !; 6 ?;1609 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
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(auto_l612940ivl0_a_decl,type,
auto_l612940ivl0_a: ( a > a ) > set_a > a > set_real ).
thf(auto_ll_on_flow0_a_decl,type,
auto_ll_on_flow0_a: ( a > a ) > set_a > a > real > a ).
thf(minus_minus_real_decl,type,
minus_minus_real: real > real > real ).
thf(plus_plus_real_decl,type,
plus_plus_real: real > real > real ).
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(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(bot_bot_set_real_decl,type,
bot_bot_set_real: set_real ).
thf(ord_less_real_decl,type,
ord_less_real: real > real > $o ).
thf(top_top_set_real_decl,type,
top_top_set_real: set_real ).
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(collect_real_decl,type,
collect_real: ( real > $o ) > set_real ).
thf(collect_a_decl,type,
collect_a: ( a > $o ) > 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(d_decl,type,
d: real ).
thf(f_decl,type,
f: a > a ).
thf(i1_decl,type,
i1: real ).
thf(i2_decl,type,
i2: real ).
thf(ss_decl,type,
ss: real ).
thf(t_decl,type,
t: real ).
thf(tt_decl,type,
tt: real ).
thf(x2_decl,type,
x2: a ).
thf(xx_decl,type,
xx: a ).
thf(sk1_decl,type,
sk1: ( a > $o ) > ( a > $o ) > a ).
thf(sk2_decl,type,
sk2: ( real > $o ) > ( real > $o ) > real ).
thf(sk3_decl,type,
sk3: real > real > real ).
thf(sk7_decl,type,
sk7: a ).
thf(sk9_decl,type,
sk9: a ).
thf(sk11_decl,type,
sk11: a ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: a > $o,B: a > $o] :
@+[C: a] :
( ( B @ C )
!= ( A @ C ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: real > $o,B: real > $o] :
@+[C: real] :
( ( B @ C )
!= ( A @ C ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: real > real > real] :
! [B: real,C: real] :
( ( A @ B @ ( plus_plus_real @ B @ C ) )
= C ) ) ) ).
thf(133,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_71_general_Omem__existence__ivl__subset) ).
thf(645,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)],[133]) ).
thf(130,axiom,
! [A: real,B: a] :
( ( ( ( member_real @ A @ top_top_set_real )
& ( member_a @ B @ x ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ ( minus_minus_real @ A @ A ) )
= B ) )
& ( ~ ( ( member_real @ A @ top_top_set_real )
& ( member_a @ B @ x ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ ( minus_minus_real @ A @ A ) )
= zero_zero_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_rev_Ogeneral_Oflow__initial__time__if) ).
thf(629,plain,
! [A: real,B: a] :
( ( ( ( member_real @ A @ top_top_set_real )
& ( member_a @ B @ x ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ ( minus_minus_real @ A @ A ) )
= B ) )
& ( ~ ( ( member_real @ A @ top_top_set_real )
& ( member_a @ B @ x ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ ( minus_minus_real @ A @ A ) )
= zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(43,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_add__right__cancel) ).
thf(363,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(364,plain,
! [C: real,B: real,A: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
= ( A = C ) ),
inference(cnf,[status(esa)],[363]) ).
thf(365,plain,
! [C: real,B: real,A: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
= ( A = C ) ),
inference(lifteq,[status(thm)],[364]) ).
thf(167,axiom,
! [A: real,B: real,C: a] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) @ ( minus_minus_real @ B @ A ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_rev_Ogeneral_Oflows__reverse) ).
thf(760,plain,
! [A: real,B: real,C: a] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) @ ( minus_minus_real @ B @ A ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(37,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
= ( ord_less_real @ zero_zero_real @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_less__add__same__cancel1) ).
thf(345,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
= ( ord_less_real @ zero_zero_real @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(346,plain,
! [B: real,A: real] :
( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
= ( ord_less_real @ zero_zero_real @ B ) ),
inference(cnf,[status(esa)],[345]) ).
thf(347,plain,
! [B: real,A: real] :
( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
= ( ord_less_real @ zero_zero_real @ B ) ),
inference(lifteq,[status(thm)],[346]) ).
thf(33,axiom,
! [A: set_real] :
( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_Collect__mem__eq) ).
thf(333,plain,
! [A: set_real] :
( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(334,plain,
! [A: set_real] :
( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
= A ),
inference(cnf,[status(esa)],[333]) ).
thf(335,plain,
! [A: set_real] :
( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
= A ),
inference(lifteq,[status(thm)],[334]) ).
thf(107,axiom,
! [A: a] :
( ~ ( member_real @ zero_zero_real @ top_top_set_real )
=> ( ( auto_l612940ivl0_a @ f @ x @ A )
= bot_bot_set_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_local_Oexistence__ivl__empty1) ).
thf(557,plain,
! [A: a] :
( ~ ( member_real @ zero_zero_real @ top_top_set_real )
=> ( ( auto_l612940ivl0_a @ f @ x @ A )
= bot_bot_set_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(558,plain,
( ~ ( member_real @ zero_zero_real @ top_top_set_real )
=> ! [A: a] :
( ( auto_l612940ivl0_a @ f @ x @ A )
= bot_bot_set_real ) ),
inference(miniscope,[status(thm)],[557]) ).
thf(559,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( ( auto_l612940ivl0_a @ f @ x @ A )
= bot_bot_set_real ) ),
inference(cnf,[status(esa)],[558]) ).
thf(560,plain,
! [A: a] :
( ( ( auto_l612940ivl0_a @ f @ x @ A )
= bot_bot_set_real )
| ( member_real @ zero_zero_real @ top_top_set_real ) ),
inference(lifteq,[status(thm)],[559]) ).
thf(1286,plain,
! [B: a,A: set_real] :
( ( ( collect_real
@ ^ [C: real] : ( member_real @ C @ A ) )
= bot_bot_set_real )
| ( member_real @ zero_zero_real @ top_top_set_real )
| ( A
!= ( auto_l612940ivl0_a @ f @ x @ B ) ) ),
inference(paramod_ordered,[status(thm)],[335,560]) ).
thf(1287,plain,
! [A: a] :
( ( ( collect_real
@ ^ [B: real] : ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ A ) ) )
= bot_bot_set_real )
| ( member_real @ zero_zero_real @ top_top_set_real ) ),
inference(pattern_uni,[status(thm)],[1286:[bind(A,$thf( auto_l612940ivl0_a @ f @ x @ E )),bind(B,$thf( E ))]]) ).
thf(1315,plain,
! [A: a] :
( ( ( collect_real
@ ^ [B: real] : ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ A ) ) )
= bot_bot_set_real )
| ( member_real @ zero_zero_real @ top_top_set_real ) ),
inference(simp,[status(thm)],[1287]) ).
thf(237,axiom,
! [A: a] :
( ( period720806154rbit_a @ f @ x @ A )
=> ~ ! [B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ~ ! [C: real] :
( ( auto_ll_on_flow0_a @ f @ x @ A @ ( plus_plus_real @ C @ B ) )
= ( auto_ll_on_flow0_a @ f @ x @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_closed__orbitE) ).
thf(962,plain,
! [A: a] :
( ( period720806154rbit_a @ f @ x @ A )
=> ~ ! [B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ~ ! [C: real] :
( ( auto_ll_on_flow0_a @ f @ x @ A @ ( plus_plus_real @ C @ B ) )
= ( auto_ll_on_flow0_a @ f @ x @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(137,axiom,
! [A: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ f @ x @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_mvar_Ointerval__axioms) ).
thf(665,plain,
! [A: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ f @ x @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(666,plain,
! [A: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ f @ x @ A ) ),
inference(cnf,[status(esa)],[665]) ).
thf(243,axiom,
! [A: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_rev_Omvar_Ointerval__axioms) ).
thf(980,plain,
! [A: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(981,plain,
! [A: a] : ( initia826609931terval @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ),
inference(cnf,[status(esa)],[980]) ).
thf(1088,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)],[335,981]) ).
thf(1089,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)],[1088:[bind(A,$thf( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ E )),bind(B,$thf( E ))]]) ).
thf(1110,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)],[1089]) ).
thf(81,axiom,
! [A: real,B: real,C: real,D: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ( ( plus_plus_real @ D @ A )
= ( plus_plus_real @ B @ ( plus_plus_real @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_group__cancel_Oadd2) ).
thf(481,plain,
! [A: real,B: real,C: real,D: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ( ( plus_plus_real @ D @ A )
= ( plus_plus_real @ B @ ( plus_plus_real @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(3,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Collect__cong) ).
thf(249,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(204,axiom,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_diff__0__right) ).
thf(862,plain,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(863,plain,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
inference(cnf,[status(esa)],[862]) ).
thf(864,plain,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
inference(lifteq,[status(thm)],[863]) ).
thf(214,axiom,
! [A: a] :
( ( ( ( member_real @ zero_zero_real @ top_top_set_real )
& ( member_a @ A @ x ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
= A ) )
& ( ~ ( ( member_real @ zero_zero_real @ top_top_set_real )
& ( member_a @ A @ x ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
= zero_zero_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_local_Oflow__initial__time__if) ).
thf(889,plain,
! [A: a] :
( ( ( ( member_real @ zero_zero_real @ top_top_set_real )
& ( member_a @ A @ x ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
= A ) )
& ( ~ ( ( member_real @ zero_zero_real @ top_top_set_real )
& ( member_a @ A @ x ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
= zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(890,plain,
( ! [A: a] :
( ( ( member_real @ zero_zero_real @ top_top_set_real )
& ( member_a @ A @ x ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
= A ) )
& ! [A: a] :
( ~ ( ( member_real @ zero_zero_real @ top_top_set_real )
& ( member_a @ A @ x ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
= zero_zero_a ) ) ),
inference(miniscope,[status(thm)],[889]) ).
thf(891,plain,
! [B: a,A: a] :
( ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
| ~ ( member_a @ A @ x )
| ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
= A ) )
& ( ( member_real @ zero_zero_real @ top_top_set_real )
| ( ( auto_ll_on_flow0_a @ f @ x @ B @ zero_zero_real )
= zero_zero_a ) )
& ( ( member_a @ B @ x )
| ( ( auto_ll_on_flow0_a @ f @ x @ B @ zero_zero_real )
= zero_zero_a ) ) ),
inference(cnf,[status(esa)],[890]) ).
thf(893,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
= zero_zero_a ) ),
inference(cnfConj,[status(thm)],[891]) ).
thf(896,plain,
! [A: a] :
( ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
= zero_zero_a )
| ( member_real @ zero_zero_real @ top_top_set_real ) ),
inference(lifteq,[status(thm)],[893]) ).
thf(897,plain,
! [A: a] :
( ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
= zero_zero_a )
| ( member_real @ zero_zero_real @ top_top_set_real ) ),
inference(simp,[status(thm)],[896]) ).
thf(1,conjecture,
( xx
= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( minus_minus_real @ ss @ tt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( xx
!= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( minus_minus_real @ ss @ tt ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(247,plain,
( xx
!= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( minus_minus_real @ ss @ tt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(248,plain,
( ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( minus_minus_real @ ss @ tt ) )
!= xx ),
inference(lifteq,[status(thm)],[247]) ).
thf(2559,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( xx != zero_zero_a )
| ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
!= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( minus_minus_real @ ss @ tt ) ) ) ),
inference(paramod_ordered,[status(thm)],[897,248]) ).
thf(2572,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( xx != zero_zero_a )
| ( f != f )
| ( x != x )
| ( A != x2 )
| ( ( minus_minus_real @ ss @ tt )
!= zero_zero_real ) ),
inference(simp,[status(thm)],[2559]) ).
thf(2583,plain,
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( xx != zero_zero_a )
| ( ( minus_minus_real @ ss @ tt )
!= zero_zero_real ) ),
inference(simp,[status(thm)],[2572]) ).
thf(187,axiom,
member_a @ xx @ x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062xx_A_092_060in_062_AX_092_060close_062) ).
thf(813,plain,
member_a @ xx @ x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(194,axiom,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
=> ( ( member_a @ A @ x )
=> ( ( auto_l612940ivl0_a @ f @ x @ A )
!= bot_bot_set_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_local_Oexistence__ivl__notempty) ).
thf(828,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
=> ( ( member_a @ A @ x )
=> ( ( auto_l612940ivl0_a @ f @ x @ A )
!= bot_bot_set_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(829,plain,
( ( member_real @ zero_zero_real @ top_top_set_real )
=> ! [A: a] :
( ( member_a @ A @ x )
=> ( ( auto_l612940ivl0_a @ f @ x @ A )
!= bot_bot_set_real ) ) ),
inference(miniscope,[status(thm)],[828]) ).
thf(830,plain,
! [A: a] :
( ~ ( member_real @ zero_zero_real @ top_top_set_real )
| ~ ( member_a @ A @ x )
| ( ( auto_l612940ivl0_a @ f @ x @ A )
!= bot_bot_set_real ) ),
inference(cnf,[status(esa)],[829]) ).
thf(831,plain,
! [A: a] :
( ( ( auto_l612940ivl0_a @ f @ x @ A )
!= bot_bot_set_real )
| ~ ( member_real @ zero_zero_real @ top_top_set_real )
| ~ ( member_a @ A @ x ) ),
inference(lifteq,[status(thm)],[830]) ).
thf(1011,plain,
! [A: a] :
( ( ( auto_l612940ivl0_a @ f @ x @ A )
!= bot_bot_set_real )
| ~ ( member_real @ zero_zero_real @ top_top_set_real )
| ~ $true
| ( ( member_a @ xx @ x )
!= ( member_a @ A @ x ) ) ),
inference(paramod_ordered,[status(thm)],[813,831]) ).
thf(1012,plain,
! [A: a] :
( ( ( auto_l612940ivl0_a @ f @ x @ A )
!= bot_bot_set_real )
| ~ ( member_real @ zero_zero_real @ top_top_set_real )
| ( ( member_a @ xx @ x )
!= ( member_a @ A @ x ) ) ),
inference(simp,[status(thm)],[1011]) ).
thf(1013,plain,
( ( ( auto_l612940ivl0_a @ f @ x @ xx )
!= bot_bot_set_real )
| ~ ( member_real @ zero_zero_real @ top_top_set_real ) ),
inference(pattern_uni,[status(thm)],[1012:[bind(A,$thf( xx ))]]) ).
thf(2594,plain,
( ( xx != zero_zero_a )
| ( ( minus_minus_real @ ss @ tt )
!= zero_zero_real )
| ( ( auto_l612940ivl0_a @ f @ x @ xx )
!= bot_bot_set_real )
| ~ $true
| ( ( member_real @ zero_zero_real @ top_top_set_real )
!= ( member_real @ zero_zero_real @ top_top_set_real ) ) ),
inference(paramod_ordered,[status(thm)],[2583,1013]) ).
thf(2595,plain,
( ( xx != zero_zero_a )
| ( ( minus_minus_real @ ss @ tt )
!= zero_zero_real )
| ( ( auto_l612940ivl0_a @ f @ x @ xx )
!= bot_bot_set_real )
| ( ( member_real @ zero_zero_real @ top_top_set_real )
!= ( member_real @ zero_zero_real @ top_top_set_real ) ) ),
inference(simp,[status(thm)],[2594]) ).
thf(2596,plain,
( ( xx != zero_zero_a )
| ( ( minus_minus_real @ ss @ tt )
!= zero_zero_real )
| ( ( auto_l612940ivl0_a @ f @ x @ xx )
!= bot_bot_set_real ) ),
inference(pattern_uni,[status(thm)],[2595:[]]) ).
thf(2792,plain,
! [A: real] :
( ( xx != zero_zero_a )
| ( A != zero_zero_real )
| ( ( auto_l612940ivl0_a @ f @ x @ xx )
!= bot_bot_set_real )
| ( ( minus_minus_real @ A @ zero_zero_real )
!= ( minus_minus_real @ ss @ tt ) ) ),
inference(paramod_ordered,[status(thm)],[864,2596]) ).
thf(2805,plain,
( ( xx != zero_zero_a )
| ( ( auto_l612940ivl0_a @ f @ x @ xx )
!= bot_bot_set_real )
| ( ( minus_minus_real @ ss @ tt )
!= ( minus_minus_real @ zero_zero_real @ zero_zero_real ) ) ),
inference(simp,[status(thm)],[2792]) ).
thf(138,axiom,
! [A: real] :
( ( minus_minus_real @ zero_zero_real @ A )
= ( uminus_uminus_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_verit__minus__simplify_I3_J) ).
thf(667,plain,
! [A: real] :
( ( minus_minus_real @ zero_zero_real @ A )
= ( uminus_uminus_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(668,plain,
! [A: real] :
( ( minus_minus_real @ zero_zero_real @ A )
= ( uminus_uminus_real @ A ) ),
inference(cnf,[status(esa)],[667]) ).
thf(669,plain,
! [A: real] :
( ( minus_minus_real @ zero_zero_real @ A )
= ( uminus_uminus_real @ A ) ),
inference(lifteq,[status(thm)],[668]) ).
thf(3509,plain,
( ( xx != zero_zero_a )
| ( ( auto_l612940ivl0_a @ f @ x @ xx )
!= bot_bot_set_real )
| ( ( minus_minus_real @ ss @ tt )
!= ( uminus_uminus_real @ zero_zero_real ) ) ),
inference(rewrite,[status(thm)],[2805,669]) ).
thf(71,axiom,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_add_Oleft__neutral) ).
thf(449,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(48,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
= ( ord_less_real @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_add__less__cancel__left) ).
thf(379,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
= ( ord_less_real @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(68,axiom,
! [A: real] :
( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_add_Oinverse__inverse) ).
thf(440,plain,
! [A: real] :
( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(125,axiom,
member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ x2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_ss__ex) ).
thf(614,plain,
member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ x2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(120,axiom,
! [A: real,B: real,C: a] :
( ( A != B )
=> ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( ( ( auto_ll_on_flow0_a @ f @ x @ C @ A )
= ( auto_ll_on_flow0_a @ f @ x @ C @ B ) )
=> ( ( ( f @ C )
!= zero_zero_a )
=> ( period138238489rbit_a @ f @ x @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_periodic__orbitI) ).
thf(597,plain,
! [A: real,B: real,C: a] :
( ( A != B )
=> ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( ( ( auto_ll_on_flow0_a @ f @ x @ C @ A )
= ( auto_ll_on_flow0_a @ f @ x @ C @ B ) )
=> ( ( ( f @ C )
!= zero_zero_a )
=> ( period138238489rbit_a @ f @ x @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(13,axiom,
( ( uminus_uminus_real @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_add_Oinverse__neutral) ).
thf(276,plain,
( ( uminus_uminus_real @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(46,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_mem__Collect__eq) ).
thf(373,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(374,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(cnf,[status(esa)],[373]) ).
thf(375,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(lifteq,[status(thm)],[374]) ).
thf(6451,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( B @ A )
!= ( member_a @ xx @ x ) ) ),
inference(paramod_ordered,[status(thm)],[375,813]) ).
thf(6528,plain,
( member_a @ xx
@ ( collect_a
@ ^ [A: a] : ( member_a @ A @ x ) ) ),
inference(pre_uni,[status(thm)],[6451:[bind(A,$thf( xx )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ x ) ))]]) ).
thf(6785,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( B @ A )
!= ( member_a @ xx
@ ( collect_a
@ ^ [C: a] : ( member_a @ C @ x ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[375,6528]) ).
thf(6800,plain,
( member_a @ xx
@ ( collect_a
@ ^ [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ x ) ) ) ) ),
inference(pre_uni,[status(thm)],[6785:[bind(A,$thf( xx )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ ( collect_a @ ^ [D: a] : ( member_a @ D @ x ) ) ) ))]]) ).
thf(47,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_219_neg__0__less__iff__less) ).
thf(376,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)],[47]) ).
thf(377,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
= ( ord_less_real @ A @ zero_zero_real ) ),
inference(cnf,[status(esa)],[376]) ).
thf(378,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
= ( ord_less_real @ A @ zero_zero_real ) ),
inference(lifteq,[status(thm)],[377]) ).
thf(7,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_217_neg__less__pos) ).
thf(261,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)],[7]) ).
thf(262,plain,
! [A: real] :
( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
= ( ord_less_real @ zero_zero_real @ A ) ),
inference(cnf,[status(esa)],[261]) ).
thf(263,plain,
! [A: real] :
( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
= ( ord_less_real @ zero_zero_real @ A ) ),
inference(lifteq,[status(thm)],[262]) ).
thf(2094,plain,
! [B: real,A: real] :
( ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
= ( ord_less_real @ zero_zero_real @ B ) )
| ( ( ord_less_real @ A @ zero_zero_real )
!= ( ord_less_real @ ( uminus_uminus_real @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[378,263]) ).
thf(2095,plain,
( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( uminus_uminus_real @ zero_zero_real ) ) )
= ( ord_less_real @ zero_zero_real @ zero_zero_real ) ),
inference(pattern_uni,[status(thm)],[2094:[bind(A,$thf( uminus_uminus_real @ zero_zero_real )),bind(B,$thf( zero_zero_real ))]]) ).
thf(39,axiom,
! [A: real] :
( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_verit__minus__simplify_I4_J) ).
thf(351,plain,
! [A: real] :
( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(352,plain,
! [A: real] :
( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
= A ),
inference(cnf,[status(esa)],[351]) ).
thf(353,plain,
! [A: real] :
( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
= A ),
inference(lifteq,[status(thm)],[352]) ).
thf(20,axiom,
! [A: real] :
~ ( ord_less_real @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_verit__comp__simplify1_I1_J) ).
thf(293,plain,
! [A: real] :
~ ( ord_less_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(294,plain,
~ ? [A: real] : ( ord_less_real @ A @ A ),
inference(miniscope,[status(thm)],[293]) ).
thf(295,plain,
! [A: real] :
~ ( ord_less_real @ A @ A ),
inference(cnf,[status(esa)],[294]) ).
thf(2186,plain,
~ ( ord_less_real @ zero_zero_real @ zero_zero_real ),
inference(rewrite,[status(thm)],[2095,353,295]) ).
thf(6477,plain,
! [B: a > $o,A: a] :
( ~ ( member_a @ A @ ( collect_a @ B ) )
| ( ( B @ A )
!= ( ord_less_real @ zero_zero_real @ zero_zero_real ) ) ),
inference(paramod_ordered,[status(thm)],[375,2186]) ).
thf(6560,plain,
! [A: a] :
~ ( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( ord_less_real @ zero_zero_real @ zero_zero_real ) ) ),
inference(pre_uni,[status(thm)],[6477:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ( ord_less_real @ zero_zero_real @ zero_zero_real ) ))]]) ).
thf(6841,plain,
! [A: a] :
~ ( member_a @ A
@ ( collect_a
@ ^ [B: a] : $false ) ),
inference(rewrite,[status(thm)],[6560,2186]) ).
thf(6848,plain,
! [A: a] :
( ~ $true
| ( ( member_a @ xx
@ ( collect_a
@ ^ [B: a] :
( member_a @ B
@ ( collect_a
@ ^ [C: a] : ( member_a @ C @ x ) ) ) ) )
!= ( member_a @ A
@ ( collect_a
@ ^ [B: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[6800,6841]) ).
thf(6849,plain,
! [A: a] :
( ( member_a @ xx
@ ( collect_a
@ ^ [B: a] :
( member_a @ B
@ ( collect_a
@ ^ [C: a] : ( member_a @ C @ x ) ) ) ) )
!= ( member_a @ A
@ ( collect_a
@ ^ [B: a] : $false ) ) ),
inference(simp,[status(thm)],[6848]) ).
thf(6861,plain,
! [A: a] :
( ( xx != A )
| ( ( collect_a
@ ^ [B: a] :
( member_a @ B
@ ( collect_a
@ ^ [C: a] : ( member_a @ C @ x ) ) ) )
!= ( collect_a
@ ^ [B: a] : $false ) ) ),
inference(simp,[status(thm)],[6849]) ).
thf(6868,plain,
( ( collect_a
@ ^ [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ x ) ) ) )
!= ( collect_a
@ ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[6861]) ).
thf(6332,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( B @ A )
!= ( member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ x2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[375,614]) ).
thf(6518,plain,
( member_a @ x2
@ ( collect_a
@ ^ [A: a] : ( member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ),
inference(pre_uni,[status(thm)],[6332:[bind(A,$thf( x2 )),bind(B,$thf( ^ [C: a] : ( member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ C ) ) ))]]) ).
thf(8708,plain,
! [A: a] :
( ~ $true
| ( ( member_a @ x2
@ ( collect_a
@ ^ [B: a] : ( member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ) )
!= ( member_a @ A
@ ( collect_a
@ ^ [B: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[6518,6841]) ).
thf(8709,plain,
! [A: a] :
( ( member_a @ x2
@ ( collect_a
@ ^ [B: a] : ( member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ) )
!= ( member_a @ A
@ ( collect_a
@ ^ [B: a] : $false ) ) ),
inference(simp,[status(thm)],[8708]) ).
thf(8729,plain,
! [A: a] :
( ( x2 != A )
| ( ( collect_a
@ ^ [B: a] : ( member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ B ) ) )
!= ( collect_a
@ ^ [B: a] : $false ) ) ),
inference(simp,[status(thm)],[8709]) ).
thf(8733,plain,
( ( collect_a
@ ^ [A: a] : ( member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ A ) ) )
!= ( collect_a
@ ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[8729]) ).
thf(50,axiom,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_add_Ogroup__left__neutral) ).
thf(385,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(49,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_309_less__minus__iff) ).
thf(382,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)],[49]) ).
thf(383,plain,
! [B: real,A: real] :
( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
= ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ),
inference(cnf,[status(esa)],[382]) ).
thf(384,plain,
! [B: real,A: real] :
( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
= ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ),
inference(lifteq,[status(thm)],[383]) ).
thf(181,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_79_fixpoint__sol_I1_J) ).
thf(797,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)],[181]) ).
thf(153,axiom,
! [A: real,B: a,C: real] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( ( member_real @ C @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ ( plus_plus_real @ A @ C ) )
= ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_local_Orev_Oflow__trans) ).
thf(715,plain,
! [A: real,B: a,C: real] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( ( member_real @ C @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ ( plus_plus_real @ A @ C ) )
= ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(188,axiom,
! [A: a] :
( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= ( ? [B: real] :
( ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) )
& ( B != zero_zero_real )
& ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_rev_Oclosed__orbit__def) ).
thf(814,plain,
! [A: a] :
( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= ( ? [B: real] :
( ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) )
& ( B != zero_zero_real )
& ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(6,axiom,
! [A: real,B: real] :
( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
= ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_minus__add__distrib) ).
thf(258,plain,
! [A: real,B: real] :
( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
= ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(259,plain,
! [B: real,A: real] :
( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
= ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ),
inference(cnf,[status(esa)],[258]) ).
thf(260,plain,
! [B: real,A: real] :
( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
= ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) ) ),
inference(lifteq,[status(thm)],[259]) ).
thf(84,axiom,
! [A: real] :
( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_add_Oleft__inverse) ).
thf(492,plain,
! [A: real] :
( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(493,plain,
! [A: real] :
( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
= zero_zero_real ),
inference(cnf,[status(esa)],[492]) ).
thf(494,plain,
! [A: real] :
( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
= zero_zero_real ),
inference(lifteq,[status(thm)],[493]) ).
thf(1432,plain,
! [C: real,B: real,A: real] :
( ( ( uminus_uminus_real @ ( plus_plus_real @ B @ C ) )
= zero_zero_real )
| ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
!= ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[494,260]) ).
thf(1433,plain,
! [A: real] :
( ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) )
= zero_zero_real ),
inference(pattern_uni,[status(thm)],[1432:[bind(A,$thf( uminus_uminus_real @ D )),bind(B,$thf( uminus_uminus_real @ D )),bind(C,$thf( D ))]]) ).
thf(1450,plain,
! [A: real] :
( ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) )
= zero_zero_real ),
inference(simp,[status(thm)],[1433]) ).
thf(52,axiom,
ord_less_real @ zero_zero_real @ d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_d) ).
thf(392,plain,
ord_less_real @ zero_zero_real @ d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(23,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_221_neg__less__0__iff__less) ).
thf(304,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)],[23]) ).
thf(305,plain,
! [A: real] :
( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
= ( ord_less_real @ zero_zero_real @ A ) ),
inference(cnf,[status(esa)],[304]) ).
thf(306,plain,
! [A: real] :
( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
= ( ord_less_real @ zero_zero_real @ A ) ),
inference(lifteq,[status(thm)],[305]) ).
thf(2014,plain,
! [B: real,A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
!= ( ord_less_real @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[306,295]) ).
thf(2024,plain,
! [B: real,A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ( ( uminus_uminus_real @ A )
!= B )
| ( zero_zero_real != B ) ),
inference(simp,[status(thm)],[2014]) ).
thf(2045,plain,
! [A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ( ( uminus_uminus_real @ A )
!= zero_zero_real ) ),
inference(simp,[status(thm)],[2024]) ).
thf(2263,plain,
! [A: real] :
( ~ $true
| ( ( uminus_uminus_real @ A )
!= zero_zero_real )
| ( ( ord_less_real @ zero_zero_real @ d )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[392,2045]) ).
thf(2264,plain,
! [A: real] :
( ( ( uminus_uminus_real @ A )
!= zero_zero_real )
| ( ( ord_less_real @ zero_zero_real @ d )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(simp,[status(thm)],[2263]) ).
thf(2265,plain,
( ( uminus_uminus_real @ d )
!= zero_zero_real ),
inference(pattern_uni,[status(thm)],[2264:[bind(A,$thf( d ))]]) ).
thf(2426,plain,
! [A: real] :
( ( zero_zero_real != zero_zero_real )
| ( ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) )
!= ( uminus_uminus_real @ d ) ) ),
inference(paramod_ordered,[status(thm)],[1450,2265]) ).
thf(2427,plain,
! [A: real] :
( ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) )
!= ( uminus_uminus_real @ d ) ),
inference(simp,[status(thm)],[2426]) ).
thf(2431,plain,
! [A: real] :
( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
!= d ),
inference(simp,[status(thm)],[2427]) ).
thf(2772,plain,
! [C: real,B: real,A: real] :
( ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
!= d )
| ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
!= ( plus_plus_real @ ( uminus_uminus_real @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[260,2431]) ).
thf(2773,plain,
! [A: real] :
( ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) )
!= d ),
inference(pattern_uni,[status(thm)],[2772:[bind(A,$thf( uminus_uminus_real @ D )),bind(B,$thf( D )),bind(C,$thf( uminus_uminus_real @ D ))]]) ).
thf(2786,plain,
! [A: real] :
( ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) )
!= d ),
inference(simp,[status(thm)],[2773]) ).
thf(3391,plain,
! [B: real,A: real] :
( ( A != d )
| ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
!= ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ B ) @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[353,2786]) ).
thf(3407,plain,
! [A: real] :
( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
!= ( uminus_uminus_real @ d ) ),
inference(simp,[status(thm)],[3391]) ).
thf(3414,plain,
! [A: real] :
( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
!= ( uminus_uminus_real @ d ) ),
inference(simp,[status(thm)],[3407]) ).
thf(231,axiom,
! [A: real,B: real,C: a] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_general_Oflow__in__domain) ).
thf(945,plain,
! [A: real,B: real,C: a] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(139,axiom,
member_real @ t @ ( auto_l612940ivl0_a @ f @ x @ x2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_assms_I8_J) ).
thf(670,plain,
member_real @ t @ ( auto_l612940ivl0_a @ f @ x @ x2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(87,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_diff__add__eq) ).
thf(500,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(2091,plain,
! [B: real,A: real] :
( ~ ( ord_less_real @ A @ zero_zero_real )
| ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
!= ( ord_less_real @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[378,295]) ).
thf(2148,plain,
! [B: real,A: real] :
( ~ ( ord_less_real @ A @ zero_zero_real )
| ( zero_zero_real != B )
| ( ( uminus_uminus_real @ A )
!= B ) ),
inference(simp,[status(thm)],[2091]) ).
thf(2184,plain,
! [A: real] :
( ~ ( ord_less_real @ A @ zero_zero_real )
| ( ( uminus_uminus_real @ A )
!= zero_zero_real ) ),
inference(simp,[status(thm)],[2148]) ).
thf(56,axiom,
! [A: real] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_linordered__ab__group__add__class_Odouble__zero) ).
thf(404,plain,
! [A: real] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(198,axiom,
! [A: a,B: real] :
( ( period720806154rbit_a @ f @ x @ A )
=> ( period720806154rbit_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_closed__orbit__flow0) ).
thf(841,plain,
! [A: a,B: real] :
( ( period720806154rbit_a @ f @ x @ A )
=> ( period720806154rbit_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(240,axiom,
! [A: real,B: real,C: a] :
( ~ ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) )
= zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_rev_Ogeneral_Oflow__undefined0) ).
thf(973,plain,
! [A: real,B: real,C: a] :
( ~ ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) )
= zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(17,axiom,
! [A: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
= ( ord_less_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_double__add__less__zero__iff__single__add__less__zero) ).
thf(288,plain,
! [A: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
= ( ord_less_real @ A @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(22,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_add__left__imp__eq) ).
thf(299,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(300,plain,
! [C: real,B: real,A: real] :
( ( ( plus_plus_real @ A @ B )
!= ( plus_plus_real @ A @ C ) )
| ( B = C ) ),
inference(cnf,[status(esa)],[299]) ).
thf(301,plain,
! [C: real,B: real,A: real] :
( ( ( plus_plus_real @ A @ B )
!= ( plus_plus_real @ A @ C ) )
| ( B = C ) ),
inference(lifteq,[status(thm)],[300]) ).
thf(32,axiom,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_comm__monoid__add__class_Oadd__0) ).
thf(330,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(331,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(cnf,[status(esa)],[330]) ).
thf(332,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(lifteq,[status(thm)],[331]) ).
thf(19,axiom,
ord_less_real @ zero_zero_real @ i1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_i2_I2_J) ).
thf(292,plain,
ord_less_real @ zero_zero_real @ i1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(2257,plain,
! [A: real] :
( ~ $true
| ( ( uminus_uminus_real @ A )
!= zero_zero_real )
| ( ( ord_less_real @ zero_zero_real @ i1 )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[292,2045]) ).
thf(2258,plain,
! [A: real] :
( ( ( uminus_uminus_real @ A )
!= zero_zero_real )
| ( ( ord_less_real @ zero_zero_real @ i1 )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(simp,[status(thm)],[2257]) ).
thf(2259,plain,
( ( uminus_uminus_real @ i1 )
!= zero_zero_real ),
inference(pattern_uni,[status(thm)],[2258:[bind(A,$thf( i1 ))]]) ).
thf(2408,plain,
! [A: real] :
( ( zero_zero_real != zero_zero_real )
| ( ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) )
!= ( uminus_uminus_real @ i1 ) ) ),
inference(paramod_ordered,[status(thm)],[1450,2259]) ).
thf(2409,plain,
! [A: real] :
( ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) )
!= ( uminus_uminus_real @ i1 ) ),
inference(simp,[status(thm)],[2408]) ).
thf(2413,plain,
! [A: real] :
( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
!= i1 ),
inference(simp,[status(thm)],[2409]) ).
thf(2648,plain,
! [C: real,B: real,A: real] :
( ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
!= i1 )
| ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
!= ( plus_plus_real @ ( uminus_uminus_real @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[260,2413]) ).
thf(2649,plain,
! [A: real] :
( ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) )
!= i1 ),
inference(pattern_uni,[status(thm)],[2648:[bind(A,$thf( uminus_uminus_real @ D )),bind(B,$thf( D )),bind(C,$thf( uminus_uminus_real @ D ))]]) ).
thf(2665,plain,
! [A: real] :
( ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) )
!= i1 ),
inference(simp,[status(thm)],[2649]) ).
thf(3129,plain,
! [B: real,A: real] :
( ( ( uminus_uminus_real @ A )
!= i1 )
| ( ( plus_plus_real @ zero_zero_real @ A )
!= ( plus_plus_real @ ( uminus_uminus_real @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[332,2665]) ).
thf(3136,plain,
! [B: real,A: real] :
( ( ( uminus_uminus_real @ A )
!= i1 )
| ( ( uminus_uminus_real @ B )
!= zero_zero_real )
| ( A != B ) ),
inference(simp,[status(thm)],[3129]) ).
thf(3140,plain,
! [A: real] :
( ( ( uminus_uminus_real @ A )
!= i1 )
| ( ( uminus_uminus_real @ A )
!= zero_zero_real ) ),
inference(simp,[status(thm)],[3136]) ).
thf(1082,plain,
! [B: a,A: set_real] :
( ( initia826609931terval
@ ( collect_real
@ ^ [C: real] : ( member_real @ C @ A ) ) )
| ( A
!= ( auto_l612940ivl0_a @ f @ x @ B ) ) ),
inference(paramod_ordered,[status(thm)],[335,666]) ).
thf(1083,plain,
! [A: a] :
( initia826609931terval
@ ( collect_real
@ ^ [B: real] : ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[1082:[bind(A,$thf( auto_l612940ivl0_a @ f @ x @ E )),bind(B,$thf( E ))]]) ).
thf(1114,plain,
! [A: a] :
( initia826609931terval
@ ( collect_real
@ ^ [B: real] : ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ),
inference(simp,[status(thm)],[1083]) ).
thf(1199,plain,
! [B: a,A: set_real] :
( ( initia826609931terval
@ ( collect_real
@ ^ [C: real] :
( member_real @ C
@ ( collect_real
@ ^ [D: real] : ( member_real @ D @ A ) ) ) ) )
| ( A
!= ( auto_l612940ivl0_a @ f @ x @ B ) ) ),
inference(paramod_ordered,[status(thm)],[335,1114]) ).
thf(1200,plain,
! [A: a] :
( initia826609931terval
@ ( collect_real
@ ^ [B: real] :
( member_real @ B
@ ( collect_real
@ ^ [C: real] : ( member_real @ C @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1199:[bind(A,$thf( auto_l612940ivl0_a @ f @ x @ E )),bind(B,$thf( E ))]]) ).
thf(1206,plain,
! [A: a] :
( initia826609931terval
@ ( collect_real
@ ^ [B: real] :
( member_real @ B
@ ( collect_real
@ ^ [C: real] : ( member_real @ C @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[1200]) ).
thf(1887,plain,
! [B: a,A: set_real] :
( ( initia826609931terval
@ ( collect_real
@ ^ [C: real] :
( member_real @ C
@ ( collect_real
@ ^ [D: real] :
( member_real @ D
@ ( collect_real
@ ^ [E: real] : ( member_real @ E @ A ) ) ) ) ) ) )
| ( A
!= ( auto_l612940ivl0_a @ f @ x @ B ) ) ),
inference(paramod_ordered,[status(thm)],[335,1206]) ).
thf(1888,plain,
! [A: a] :
( initia826609931terval
@ ( collect_real
@ ^ [B: real] :
( member_real @ B
@ ( collect_real
@ ^ [C: real] :
( member_real @ C
@ ( collect_real
@ ^ [D: real] : ( member_real @ D @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1887:[bind(A,$thf( auto_l612940ivl0_a @ f @ x @ E )),bind(B,$thf( E ))]]) ).
thf(1904,plain,
! [A: a] :
( initia826609931terval
@ ( collect_real
@ ^ [B: real] :
( member_real @ B
@ ( collect_real
@ ^ [C: real] :
( member_real @ C
@ ( collect_real
@ ^ [D: real] : ( member_real @ D @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[1888]) ).
thf(135,axiom,
! [A: a] :
( ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ A ) )
= ( ( member_real @ zero_zero_real @ top_top_set_real )
& ( member_a @ A @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_local_Oexistence__ivl__initial__time__iff) ).
thf(651,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ f @ x @ A ) )
= ( ( member_real @ zero_zero_real @ top_top_set_real )
& ( member_a @ A @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(5,axiom,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_zero__reorient) ).
thf(255,plain,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(256,plain,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
inference(cnf,[status(esa)],[255]) ).
thf(257,plain,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
inference(lifteq,[status(thm)],[256]) ).
thf(155,axiom,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_diff__self) ).
thf(722,plain,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(723,plain,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
inference(cnf,[status(esa)],[722]) ).
thf(724,plain,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
inference(lifteq,[status(thm)],[723]) ).
thf(154,axiom,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
= ( minus_minus_real @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_add__diff__cancel__right) ).
thf(719,plain,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
= ( minus_minus_real @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(4414,plain,
! [B: real,A: real] :
( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
| ( ( ord_less_real @ zero_zero_real @ B )
!= ( ord_less_real @ zero_zero_real @ i1 ) ) ),
inference(paramod_ordered,[status(thm)],[347,292]) ).
thf(4415,plain,
! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ i1 ) ),
inference(pattern_uni,[status(thm)],[4414:[bind(A,$thf( A )),bind(B,$thf( i1 ))]]) ).
thf(117,axiom,
! [A: real,B: real,C: a,D: real] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( ( member_real @ D @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ ( plus_plus_real @ A @ D ) @ B ) )
= ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_rev_Ogeneral_Oflow__trans) ).
thf(587,plain,
! [A: real,B: real,C: a,D: real] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( ( member_real @ D @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ ( plus_plus_real @ A @ D ) @ B ) )
= ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(1278,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( member_real @ ss @ bot_bot_set_real )
| ( ( auto_l612940ivl0_a @ f @ x @ A )
!= ( auto_l612940ivl0_a @ f @ x @ x2 ) ) ),
inference(paramod_ordered,[status(thm)],[560,614]) ).
thf(1279,plain,
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( member_real @ ss @ bot_bot_set_real ) ),
inference(pattern_uni,[status(thm)],[1278:[bind(A,$thf( x2 ))]]) ).
thf(127,axiom,
! [A: a] :
( ~ ( member_real @ zero_zero_real @ top_top_set_real )
=> ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= bot_bot_set_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_local_Orev_Oexistence__ivl__empty1) ).
thf(618,plain,
! [A: a] :
( ~ ( member_real @ zero_zero_real @ top_top_set_real )
=> ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= bot_bot_set_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(619,plain,
( ~ ( member_real @ zero_zero_real @ top_top_set_real )
=> ! [A: a] :
( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= bot_bot_set_real ) ),
inference(miniscope,[status(thm)],[618]) ).
thf(620,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= bot_bot_set_real ) ),
inference(cnf,[status(esa)],[619]) ).
thf(621,plain,
! [A: a] :
( ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= bot_bot_set_real )
| ( member_real @ zero_zero_real @ top_top_set_real ) ),
inference(lifteq,[status(thm)],[620]) ).
thf(2453,plain,
! [B: a,A: set_real] :
( ( ( collect_real
@ ^ [C: real] : ( member_real @ C @ A ) )
= bot_bot_set_real )
| ( member_real @ zero_zero_real @ top_top_set_real )
| ( A
!= ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) ),
inference(paramod_ordered,[status(thm)],[335,621]) ).
thf(2454,plain,
! [A: a] :
( ( ( collect_real
@ ^ [B: real] : ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) )
= bot_bot_set_real )
| ( member_real @ zero_zero_real @ top_top_set_real ) ),
inference(pattern_uni,[status(thm)],[2453:[bind(A,$thf( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ E )),bind(B,$thf( E ))]]) ).
thf(2488,plain,
! [A: a] :
( ( ( collect_real
@ ^ [B: real] : ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) ) )
= bot_bot_set_real )
| ( member_real @ zero_zero_real @ top_top_set_real ) ),
inference(simp,[status(thm)],[2454]) ).
thf(41,axiom,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
= ( ord_less_real @ zero_zero_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_linordered__ab__group__add__class_Ozero__less__double__add__iff__zero__less__single__add) ).
thf(357,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
= ( ord_less_real @ zero_zero_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(302,plain,
? [A: real > real > real] :
! [B: real,C: real] :
( ( A @ B @ ( plus_plus_real @ B @ C ) )
= C ),
inference(detectInverse,[status(thm)],[301]) ).
thf(303,plain,
! [B: real,A: real] :
( ( sk3 @ A @ ( plus_plus_real @ A @ B ) )
= B ),
inference(cnf,[status(esa)],[302]) ).
thf(2737,plain,
! [B: real,A: real] :
( ( sk3 @ A @ ( plus_plus_real @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[303]) ).
thf(2744,plain,
! [C: real,B: real,A: real] :
( ( ( sk3 @ B @ A )
= C )
| ( ( plus_plus_real @ zero_zero_real @ A )
!= ( plus_plus_real @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[332,2737]) ).
thf(2745,plain,
! [A: real] :
( ( sk3 @ zero_zero_real @ A )
= A ),
inference(pattern_uni,[status(thm)],[2744:[bind(A,$thf( A )),bind(B,$thf( zero_zero_real )),bind(C,$thf( A ))]]) ).
thf(102,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_81_rev_Oclosed__orbit__global__existence) ).
thf(542,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)],[102]) ).
thf(221,axiom,
! [A: real,B: a] :
( ( member_real @ ( minus_minus_real @ A @ A ) @ ( auto_l612940ivl0_a @ f @ x @ B ) )
= ( ( member_real @ A @ top_top_set_real )
& ( member_a @ B @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_general_Oexistence__ivl__initial__time__iff) ).
thf(917,plain,
! [A: real,B: a] :
( ( member_real @ ( minus_minus_real @ A @ A ) @ ( auto_l612940ivl0_a @ f @ x @ B ) )
= ( ( member_real @ A @ top_top_set_real )
& ( member_a @ B @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(164,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_55_local_Omem__existence__ivl__subset) ).
thf(751,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)],[164]) ).
thf(183,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_85_rev_Oclosed__orbit__periodic) ).
thf(802,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)],[183]) ).
thf(36,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
= ( ord_less_real @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_add__less__cancel__right) ).
thf(342,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
= ( ord_less_real @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(343,plain,
! [C: real,B: real,A: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
= ( ord_less_real @ A @ C ) ),
inference(cnf,[status(esa)],[342]) ).
thf(344,plain,
! [C: real,B: real,A: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
= ( ord_less_real @ A @ C ) ),
inference(lifteq,[status(thm)],[343]) ).
thf(189,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( member_real @ zero_zero_real @ top_top_set_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_local_Omem__existence__ivl__iv__defined_I1_J) ).
thf(817,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( member_real @ zero_zero_real @ top_top_set_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(60,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_216_less__neg__neg) ).
thf(416,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)],[60]) ).
thf(30,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Collect__mem__eq) ).
thf(325,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(27,axiom,
! [A: real,B: real] :
( ( ( uminus_uminus_real @ A )
= ( uminus_uminus_real @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_neg__equal__iff__equal) ).
thf(316,plain,
! [A: real,B: real] :
( ( ( uminus_uminus_real @ A )
= ( uminus_uminus_real @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(7226,plain,
( ( ^ [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ x ) ) ) )
!= ( ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[6868]) ).
thf(16,axiom,
! [A: real,B: real,C: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ( ( uminus_uminus_real @ A )
= ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_group__cancel_Oneg1) ).
thf(284,plain,
! [A: real,B: real,C: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ( ( uminus_uminus_real @ A )
= ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(79,axiom,
! [A: real,B: real] :
( ( ( uminus_uminus_real @ A )
= B )
= ( ( uminus_uminus_real @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_minus__equation__iff) ).
thf(475,plain,
! [A: real,B: real] :
( ( ( uminus_uminus_real @ A )
= B )
= ( ( uminus_uminus_real @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(118,axiom,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_diff__add__eq__diff__diff__swap) ).
thf(591,plain,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(69,axiom,
! [A: real,B: real] :
( ( A
= ( uminus_uminus_real @ B ) )
= ( B
= ( uminus_uminus_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_equation__minus__iff) ).
thf(443,plain,
! [A: real,B: real] :
( ( A
= ( uminus_uminus_real @ B ) )
= ( B
= ( uminus_uminus_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(28,axiom,
! [A: real] :
( ( A
= ( uminus_uminus_real @ A ) )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_equal__neg__zero) ).
thf(319,plain,
! [A: real] :
( ( A
= ( uminus_uminus_real @ A ) )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(320,plain,
! [A: real] :
( ( A
= ( uminus_uminus_real @ A ) )
= ( A = zero_zero_real ) ),
inference(cnf,[status(esa)],[319]) ).
thf(321,plain,
! [A: real] :
( ( A
= ( uminus_uminus_real @ A ) )
= ( A = zero_zero_real ) ),
inference(lifteq,[status(thm)],[320]) ).
thf(196,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_113_minus__diff__eq) ).
thf(834,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)],[196]) ).
thf(191,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_52_existence__ivl__zero) ).
thf(821,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)],[191]) ).
thf(38,axiom,
! [A: real] :
( ( ( uminus_uminus_real @ A )
= A )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_neg__equal__zero) ).
thf(348,plain,
! [A: real] :
( ( ( uminus_uminus_real @ A )
= A )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(4682,plain,
! [B: real,A: real] :
( ~ $true
| ( ( ord_less_real @ A @ ( plus_plus_real @ A @ i1 ) )
!= ( ord_less_real @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4415,295]) ).
thf(4683,plain,
! [B: real,A: real] :
( ( ord_less_real @ A @ ( plus_plus_real @ A @ i1 ) )
!= ( ord_less_real @ B @ B ) ),
inference(simp,[status(thm)],[4682]) ).
thf(4724,plain,
! [B: real,A: real] :
( ( A != B )
| ( ( plus_plus_real @ A @ i1 )
!= B ) ),
inference(simp,[status(thm)],[4683]) ).
thf(4751,plain,
! [A: real] :
( ( plus_plus_real @ A @ i1 )
!= A ),
inference(simp,[status(thm)],[4724]) ).
thf(14,axiom,
! [A: real] :
( ( ( uminus_uminus_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_neg__equal__0__iff__equal) ).
thf(278,plain,
! [A: real] :
( ( ( uminus_uminus_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(279,plain,
! [A: real] :
( ( ( uminus_uminus_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(cnf,[status(esa)],[278]) ).
thf(280,plain,
! [A: real] :
( ( ( uminus_uminus_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(lifteq,[status(thm)],[279]) ).
thf(6336,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( member_real @ t @ ( auto_l612940ivl0_a @ f @ x @ x2 ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[670,375]) ).
thf(6507,plain,
( member_a @ x2
@ ( collect_a
@ ^ [A: a] : ( member_real @ t @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ),
inference(pre_uni,[status(thm)],[6336:[bind(A,$thf( x2 )),bind(B,$thf( ^ [C: a] : ( member_real @ t @ ( auto_l612940ivl0_a @ f @ x @ C ) ) ))]]) ).
thf(8474,plain,
! [A: a] :
( ~ $true
| ( ( member_a @ x2
@ ( collect_a
@ ^ [B: a] : ( member_real @ t @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ) )
!= ( member_a @ A
@ ( collect_a
@ ^ [B: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[6507,6841]) ).
thf(8475,plain,
! [A: a] :
( ( member_a @ x2
@ ( collect_a
@ ^ [B: a] : ( member_real @ t @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ) )
!= ( member_a @ A
@ ( collect_a
@ ^ [B: a] : $false ) ) ),
inference(simp,[status(thm)],[8474]) ).
thf(8493,plain,
! [A: a] :
( ( x2 != A )
| ( ( collect_a
@ ^ [B: a] : ( member_real @ t @ ( auto_l612940ivl0_a @ f @ x @ B ) ) )
!= ( collect_a
@ ^ [B: a] : $false ) ) ),
inference(simp,[status(thm)],[8475]) ).
thf(8499,plain,
( ( collect_a
@ ^ [A: a] : ( member_real @ t @ ( auto_l612940ivl0_a @ f @ x @ A ) ) )
!= ( collect_a
@ ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[8493]) ).
thf(8763,plain,
( ( ^ [A: a] : ( member_real @ t @ ( auto_l612940ivl0_a @ f @ x @ A ) ) )
!= ( ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[8499]) ).
thf(8774,plain,
member_real @ t @ ( auto_l612940ivl0_a @ f @ x @ sk11 ),
inference(func_ext,[status(esa)],[8763]) ).
thf(246,axiom,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( minus_minus_real @ A @ B )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_eq__iff__diff__eq__0) ).
thf(988,plain,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( minus_minus_real @ A @ B )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(169,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_add__diff__eq) ).
thf(766,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(209,axiom,
! [A: a] :
( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ( member_a @ A @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_rev_Oclosed__orbit__in__domain) ).
thf(877,plain,
! [A: a] :
( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ( member_a @ A @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(147,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( member_real @ zero_zero_real @ top_top_set_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_local_Orev_Omem__existence__ivl__iv__defined_I1_J) ).
thf(692,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( member_real @ zero_zero_real @ top_top_set_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(54,axiom,
! [A: real,B: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
= ( ord_less_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_add__less__same__cancel2) ).
thf(396,plain,
! [A: real,B: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
= ( ord_less_real @ A @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(1522,plain,
! [A: real] :
( ( ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( uminus_uminus_real @ A ) )
!= xx )
| ( ( minus_minus_real @ zero_zero_real @ A )
!= ( minus_minus_real @ ss @ tt ) ) ),
inference(paramod_ordered,[status(thm)],[669,248]) ).
thf(1524,plain,
! [A: real] :
( ( ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( uminus_uminus_real @ A ) )
!= xx )
| ( ss != zero_zero_real )
| ( A != tt ) ),
inference(simp,[status(thm)],[1522]) ).
thf(1526,plain,
( ( ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( uminus_uminus_real @ tt ) )
!= xx )
| ( ss != zero_zero_real ) ),
inference(simp,[status(thm)],[1524]) ).
thf(97,axiom,
! [A: a] :
( ( ( auto_l612940ivl0_a @ f @ x @ A )
= bot_bot_set_real )
= ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
| ~ ( member_a @ A @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_local_Oexistence__ivl__empty__iff) ).
thf(527,plain,
! [A: a] :
( ( ( auto_l612940ivl0_a @ f @ x @ A )
= bot_bot_set_real )
= ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
| ~ ( member_a @ A @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(25,axiom,
! [A: real,B: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ A )
= ( ord_less_real @ B @ zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_add__less__same__cancel1) ).
thf(310,plain,
! [A: real,B: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ A )
= ( ord_less_real @ B @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(311,plain,
! [B: real,A: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ A )
= ( ord_less_real @ B @ zero_zero_real ) ),
inference(cnf,[status(esa)],[310]) ).
thf(312,plain,
! [B: real,A: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ A )
= ( ord_less_real @ B @ zero_zero_real ) ),
inference(lifteq,[status(thm)],[311]) ).
thf(24,axiom,
! [A: real,B: real] :
( ( ( plus_plus_real @ A @ B )
= B )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_add__cancel__left__left) ).
thf(307,plain,
! [A: real,B: real] :
( ( ( plus_plus_real @ A @ B )
= B )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(190,axiom,
ord_less_real @ zero_zero_real @ tt,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_tt_I1_J) ).
thf(820,plain,
ord_less_real @ zero_zero_real @ tt,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(4424,plain,
! [B: real,A: real] :
( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
| ( ( ord_less_real @ zero_zero_real @ B )
!= ( ord_less_real @ zero_zero_real @ tt ) ) ),
inference(paramod_ordered,[status(thm)],[347,820]) ).
thf(4425,plain,
! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ tt ) ),
inference(pattern_uni,[status(thm)],[4424:[bind(A,$thf( A )),bind(B,$thf( tt ))]]) ).
thf(4899,plain,
! [B: real,A: real] :
( ~ $true
| ( ( ord_less_real @ A @ ( plus_plus_real @ A @ tt ) )
!= ( ord_less_real @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4425,295]) ).
thf(4900,plain,
! [B: real,A: real] :
( ( ord_less_real @ A @ ( plus_plus_real @ A @ tt ) )
!= ( ord_less_real @ B @ B ) ),
inference(simp,[status(thm)],[4899]) ).
thf(4942,plain,
! [B: real,A: real] :
( ( A != B )
| ( ( plus_plus_real @ A @ tt )
!= B ) ),
inference(simp,[status(thm)],[4900]) ).
thf(4962,plain,
! [A: real] :
( ( plus_plus_real @ A @ tt )
!= A ),
inference(simp,[status(thm)],[4942]) ).
thf(11,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ B @ C )
=> ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_pos__add__strict) ).
thf(270,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ B @ C )
=> ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(179,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( member_real @ ( minus_minus_real @ zero_zero_real @ A ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_local_Oexistence__ivl__reverse) ).
thf(793,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( member_real @ ( minus_minus_real @ zero_zero_real @ A ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(9,axiom,
initia826609931terval @ top_top_set_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_interval__axioms) ).
thf(267,plain,
initia826609931terval @ top_top_set_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6425,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( initia826609931terval @ top_top_set_real )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[267,375]) ).
thf(6645,plain,
! [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( initia826609931terval @ top_top_set_real ) ) ),
inference(pre_uni,[status(thm)],[6425:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ( initia826609931terval @ top_top_set_real ) ))]]) ).
thf(8382,plain,
! [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : $true ) ),
inference(rewrite,[status(thm)],[6645,267]) ).
thf(186,axiom,
! [A: real,B: real,C: real] :
( ( ( minus_minus_real @ A @ B )
= C )
= ( A
= ( plus_plus_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_diff__eq__eq) ).
thf(810,plain,
! [A: real,B: real,C: real] :
( ( ( minus_minus_real @ A @ B )
= C )
= ( A
= ( plus_plus_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(380,plain,
! [C: real,B: real,A: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
= ( ord_less_real @ B @ C ) ),
inference(cnf,[status(esa)],[379]) ).
thf(381,plain,
! [C: real,B: real,A: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
= ( ord_less_real @ B @ C ) ),
inference(lifteq,[status(thm)],[380]) ).
thf(99,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_68_general_Omem__existence__ivl__iv__defined_I1_J) ).
thf(534,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)],[99]) ).
thf(152,axiom,
member_real @ ( uminus_uminus_real @ tt ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ xx @ tt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_neg__tt__ex) ).
thf(714,plain,
member_real @ ( uminus_uminus_real @ tt ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ xx @ tt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(72,axiom,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_add_Ocomm__neutral) ).
thf(452,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(222,axiom,
( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ xx @ tt ) @ ( uminus_uminus_real @ tt ) )
= ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) @ ( uminus_uminus_real @ tt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062flow0_A_Iflow0_Axx_Att_J_A_I_N_Att_J_A_061_Aflow0_A_Iflow0_Ax_Ass_J_A_I_N_Att_J_092_060close_062) ).
thf(920,plain,
( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ xx @ tt ) @ ( uminus_uminus_real @ tt ) )
= ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) @ ( uminus_uminus_real @ tt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(91,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_149_fixed__point__imp__closed__orbit__period__zero_I2_J) ).
thf(512,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)],[91]) ).
thf(230,axiom,
! [A: a,B: real] :
( ( auto_ll_on_flow0_a @ f @ x @ A @ B )
= ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ ( uminus_uminus_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_rev_Orev__eq__flow) ).
thf(942,plain,
! [A: a,B: real] :
( ( auto_ll_on_flow0_a @ f @ x @ A @ B )
= ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ ( uminus_uminus_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(67,axiom,
! [A: real] :
( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_add_Oright__inverse) ).
thf(437,plain,
! [A: real] :
( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(438,plain,
! [A: real] :
( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
= zero_zero_real ),
inference(cnf,[status(esa)],[437]) ).
thf(439,plain,
! [A: real] :
( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
= zero_zero_real ),
inference(lifteq,[status(thm)],[438]) ).
thf(2260,plain,
! [A: real] :
( ~ $true
| ( ( uminus_uminus_real @ A )
!= zero_zero_real )
| ( ( ord_less_real @ zero_zero_real @ tt )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[820,2045]) ).
thf(2261,plain,
! [A: real] :
( ( ( uminus_uminus_real @ A )
!= zero_zero_real )
| ( ( ord_less_real @ zero_zero_real @ tt )
!= ( ord_less_real @ zero_zero_real @ A ) ) ),
inference(simp,[status(thm)],[2260]) ).
thf(2262,plain,
( ( uminus_uminus_real @ tt )
!= zero_zero_real ),
inference(pattern_uni,[status(thm)],[2261:[bind(A,$thf( tt ))]]) ).
thf(2417,plain,
! [A: real] :
( ( zero_zero_real != zero_zero_real )
| ( ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) )
!= ( uminus_uminus_real @ tt ) ) ),
inference(paramod_ordered,[status(thm)],[1450,2262]) ).
thf(2418,plain,
! [A: real] :
( ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) )
!= ( uminus_uminus_real @ tt ) ),
inference(simp,[status(thm)],[2417]) ).
thf(2422,plain,
! [A: real] :
( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
!= tt ),
inference(simp,[status(thm)],[2418]) ).
thf(2673,plain,
! [C: real,B: real,A: real] :
( ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
!= tt )
| ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
!= ( plus_plus_real @ ( uminus_uminus_real @ C ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[260,2422]) ).
thf(2674,plain,
! [A: real] :
( ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) )
!= tt ),
inference(pattern_uni,[status(thm)],[2673:[bind(A,$thf( uminus_uminus_real @ D )),bind(B,$thf( D )),bind(C,$thf( uminus_uminus_real @ D ))]]) ).
thf(2685,plain,
! [A: real] :
( ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) )
!= tt ),
inference(simp,[status(thm)],[2674]) ).
thf(3246,plain,
! [B: real,A: real] :
( ( A != tt )
| ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
!= ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ B ) @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[353,2685]) ).
thf(3264,plain,
! [A: real] :
( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
!= ( uminus_uminus_real @ tt ) ),
inference(simp,[status(thm)],[3246]) ).
thf(3265,plain,
! [A: real] :
( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
!= ( uminus_uminus_real @ tt ) ),
inference(simp,[status(thm)],[3264]) ).
thf(224,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_62_local_Orev_Oexistence__ivl__initial__time) ).
thf(925,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)],[224]) ).
thf(44,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_add_Oright__cancel) ).
thf(366,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(1213,plain,
! [A: real] :
( ( ( auto_ll_on_flow0_a @ f @ x @ x2 @ zero_zero_real )
!= xx )
| ( ( minus_minus_real @ A @ A )
!= ( minus_minus_real @ ss @ tt ) ) ),
inference(paramod_ordered,[status(thm)],[724,248]) ).
thf(1215,plain,
! [A: real] :
( ( ( auto_ll_on_flow0_a @ f @ x @ x2 @ zero_zero_real )
!= xx )
| ( A != ss )
| ( A != tt ) ),
inference(simp,[status(thm)],[1213]) ).
thf(1218,plain,
( ( ( auto_ll_on_flow0_a @ f @ x @ x2 @ zero_zero_real )
!= xx )
| ( tt != ss ) ),
inference(simp,[status(thm)],[1215]) ).
thf(2567,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( xx != zero_zero_a )
| ( tt != ss )
| ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
!= ( auto_ll_on_flow0_a @ f @ x @ x2 @ zero_zero_real ) ) ),
inference(paramod_ordered,[status(thm)],[897,1218]) ).
thf(2568,plain,
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( xx != zero_zero_a )
| ( tt != ss ) ),
inference(pattern_uni,[status(thm)],[2567:[bind(A,$thf( x2 ))]]) ).
thf(2587,plain,
( ( xx != zero_zero_a )
| ( tt != ss )
| ( ( auto_l612940ivl0_a @ f @ x @ xx )
!= bot_bot_set_real )
| ~ $true
| ( ( member_real @ zero_zero_real @ top_top_set_real )
!= ( member_real @ zero_zero_real @ top_top_set_real ) ) ),
inference(paramod_ordered,[status(thm)],[2568,1013]) ).
thf(2588,plain,
( ( xx != zero_zero_a )
| ( tt != ss )
| ( ( auto_l612940ivl0_a @ f @ x @ xx )
!= bot_bot_set_real )
| ( ( member_real @ zero_zero_real @ top_top_set_real )
!= ( member_real @ zero_zero_real @ top_top_set_real ) ) ),
inference(simp,[status(thm)],[2587]) ).
thf(2589,plain,
( ( xx != zero_zero_a )
| ( tt != ss )
| ( ( auto_l612940ivl0_a @ f @ x @ xx )
!= bot_bot_set_real ) ),
inference(pattern_uni,[status(thm)],[2588:[]]) ).
thf(219,axiom,
! [A: real,B: a] :
( ( member_real @ A @ top_top_set_real )
=> ( ( member_a @ B @ x )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ ( minus_minus_real @ A @ A ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_rev_Ogeneral_Oflow__initial__time) ).
thf(910,plain,
! [A: real,B: a] :
( ( member_real @ A @ top_top_set_real )
=> ( ( member_a @ B @ x )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ ( minus_minus_real @ A @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(235,axiom,
! [A: real,B: real,C: real,D: a] :
( ( member_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) @ ( auto_l612940ivl0_a @ f @ x @ D ) )
=> ( ( member_real @ ( minus_minus_real @ A @ C ) @ ( auto_l612940ivl0_a @ f @ x @ D ) )
=> ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ D @ ( minus_minus_real @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_general_Oexistence__ivl__trans_H) ).
thf(957,plain,
! [A: real,B: real,C: real,D: a] :
( ( member_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) @ ( auto_l612940ivl0_a @ f @ x @ D ) )
=> ( ( member_real @ ( minus_minus_real @ A @ C ) @ ( auto_l612940ivl0_a @ f @ x @ D ) )
=> ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ D @ ( minus_minus_real @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(193,axiom,
! [A: real,B: a,C: real] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( ( member_real @ C @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) ) )
=> ( member_real @ ( plus_plus_real @ A @ C ) @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_local_Oexistence__ivl__trans) ).
thf(825,plain,
! [A: real,B: a,C: real] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( ( member_real @ C @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) ) )
=> ( member_real @ ( plus_plus_real @ A @ C ) @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(233,axiom,
! [A: a] :
( ( period720806154rbit_a @ f @ x @ A )
=> ( member_a @ A @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_closed__orbit__in__domain) ).
thf(952,plain,
! [A: a] :
( ( period720806154rbit_a @ f @ x @ A )
=> ( member_a @ A @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(108,axiom,
! [A: real,B: a,C: real] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( ( member_real @ C @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( member_real @ ( minus_minus_real @ C @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_rev_Odiff__existence__ivl__trans) ).
thf(561,plain,
! [A: real,B: a,C: real] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( ( member_real @ C @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( member_real @ ( minus_minus_real @ C @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(64,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( ord_less_real @ A @ B )
& ( ord_less_real @ C @ D ) )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_add__mono__thms__linordered__field_I5_J) ).
thf(429,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( ord_less_real @ A @ B )
& ( ord_less_real @ C @ D ) )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(157,axiom,
! [A: a,B: real] :
( ( period138238489rbit_a @ f @ x @ A )
=> ( ( f @ ( auto_ll_on_flow0_a @ f @ x @ A @ B ) )
!= zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_periodic__orbit__imp__flow0__regular) ).
thf(729,plain,
! [A: a,B: real] :
( ( period138238489rbit_a @ f @ x @ A )
=> ( ( f @ ( auto_ll_on_flow0_a @ f @ x @ A @ B ) )
!= zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(277,plain,
( ( uminus_uminus_real @ zero_zero_real )
= zero_zero_real ),
inference(lifteq,[status(thm)],[276]) ).
thf(3131,plain,
! [A: real] :
( ( ( uminus_uminus_real @ ( plus_plus_real @ zero_zero_real @ A ) )
!= i1 )
| ( ( uminus_uminus_real @ zero_zero_real )
!= ( uminus_uminus_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[277,2665]) ).
thf(3132,plain,
( ( uminus_uminus_real @ ( plus_plus_real @ zero_zero_real @ zero_zero_real ) )
!= i1 ),
inference(pattern_uni,[status(thm)],[3131:[bind(A,$thf( zero_zero_real ))]]) ).
thf(3233,plain,
( ( uminus_uminus_real @ zero_zero_real )
!= i1 ),
inference(rewrite,[status(thm)],[3132,332]) ).
thf(57,axiom,
! [A: real,B: real] :
( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
= ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_add_Oinverse__distrib__swap) ).
thf(407,plain,
! [A: real,B: real] :
( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
= ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(12,axiom,
! [A: real] :
( ( zero_zero_real
= ( plus_plus_real @ A @ A ) )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_double__zero__sym) ).
thf(273,plain,
! [A: real] :
( ( zero_zero_real
= ( plus_plus_real @ A @ A ) )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(274,plain,
! [A: real] :
( ( zero_zero_real
= ( plus_plus_real @ A @ A ) )
= ( A = zero_zero_real ) ),
inference(cnf,[status(esa)],[273]) ).
thf(275,plain,
! [A: real] :
( ( zero_zero_real
= ( plus_plus_real @ A @ A ) )
= ( A = zero_zero_real ) ),
inference(lifteq,[status(thm)],[274]) ).
thf(177,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_137_diff__eq__diff__eq) ).
thf(788,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)],[177]) ).
thf(200,axiom,
! [A: real,B: real,C: a] :
( ( A != B )
=> ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( ( ( auto_ll_on_flow0_a @ f @ x @ C @ A )
= ( auto_ll_on_flow0_a @ f @ x @ C @ B ) )
=> ( period720806154rbit_a @ f @ x @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_closed__orbitI) ).
thf(847,plain,
! [A: real,B: real,C: a] :
( ( A != B )
=> ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( ( ( auto_ll_on_flow0_a @ f @ x @ C @ A )
= ( auto_ll_on_flow0_a @ f @ x @ C @ B ) )
=> ( period720806154rbit_a @ f @ x @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(4,axiom,
! [A: real > $o,B: real > $o] :
( ! [C: real] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_real @ A )
= ( collect_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_Collect__cong) ).
thf(252,plain,
! [A: real > $o,B: real > $o] :
( ! [C: real] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_real @ A )
= ( collect_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(210,axiom,
! [A: real] :
( ( minus_minus_real @ zero_zero_real @ A )
= ( uminus_uminus_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_diff__0) ).
thf(879,plain,
! [A: real] :
( ( minus_minus_real @ zero_zero_real @ A )
= ( uminus_uminus_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(166,axiom,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_diff__diff__add) ).
thf(757,plain,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(144,axiom,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_diff__diff__eq2) ).
thf(682,plain,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(105,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_69_general_Oexistence__ivl__initial__time) ).
thf(551,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)],[105]) ).
thf(1280,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( member_real @ t @ bot_bot_set_real )
| ( ( auto_l612940ivl0_a @ f @ x @ A )
!= ( auto_l612940ivl0_a @ f @ x @ x2 ) ) ),
inference(paramod_ordered,[status(thm)],[560,670]) ).
thf(1281,plain,
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( member_real @ t @ bot_bot_set_real ) ),
inference(pattern_uni,[status(thm)],[1280:[bind(A,$thf( x2 ))]]) ).
thf(29,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_311_minus__less__iff) ).
thf(322,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)],[29]) ).
thf(323,plain,
! [B: real,A: real] :
( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
= ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ),
inference(cnf,[status(esa)],[322]) ).
thf(324,plain,
! [B: real,A: real] :
( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
= ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ),
inference(lifteq,[status(thm)],[323]) ).
thf(76,axiom,
! [A: real,B: real > $o] :
( ( member_real @ A @ ( collect_real @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_mem__Collect__eq) ).
thf(467,plain,
! [A: real,B: real > $o] :
( ( member_real @ A @ ( collect_real @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(7663,plain,
( member_a @ sk9
@ ( collect_a
@ ^ [A: a] : ( member_a @ A @ x ) ) ),
inference(func_ext,[status(esa)],[7226]) ).
thf(1295,plain,
! [B: a,A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( initia826609931terval
@ ( collect_real
@ ^ [C: real] : ( member_real @ C @ bot_bot_set_real ) ) )
| ( ( auto_l612940ivl0_a @ f @ x @ A )
!= ( auto_l612940ivl0_a @ f @ x @ B ) ) ),
inference(paramod_ordered,[status(thm)],[560,1114]) ).
thf(1296,plain,
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( initia826609931terval
@ ( collect_real
@ ^ [A: real] : ( member_real @ A @ bot_bot_set_real ) ) ) ),
inference(pattern_uni,[status(thm)],[1295:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(116,axiom,
! [A: real,B: a,C: real] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( ( member_real @ C @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ B @ ( plus_plus_real @ A @ C ) )
= ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_local_Oflow__trans) ).
thf(583,plain,
! [A: real,B: a,C: real] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( ( member_real @ C @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ B @ ( plus_plus_real @ A @ C ) )
= ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(95,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_212_periodic__orbit__def) ).
thf(522,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)],[95]) ).
thf(149,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_15_fixed__point__imp__closed__orbit__period__zero_I1_J) ).
thf(697,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)],[149]) ).
thf(208,axiom,
! [A: real,B: a] :
( ~ ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ B @ A )
= zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_local_Oflow__undefined0) ).
thf(874,plain,
! [A: real,B: a] :
( ~ ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ B @ A )
= zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(126,axiom,
! [A: a] :
( ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) )
= ( ( member_real @ zero_zero_real @ top_top_set_real )
& ( member_a @ A @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_local_Orev_Oexistence__ivl__initial__time__iff) ).
thf(615,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) )
= ( ( member_real @ zero_zero_real @ top_top_set_real )
& ( member_a @ A @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(96,axiom,
( ( auto_ll_on_flow0_a @ f @ x @ xx @ tt )
= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_eq) ).
thf(525,plain,
( ( auto_ll_on_flow0_a @ f @ x @ xx @ tt )
= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(526,plain,
( ( auto_ll_on_flow0_a @ f @ x @ xx @ tt )
= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) ),
inference(lifteq,[status(thm)],[525]) ).
thf(1121,plain,
member_real @ ( uminus_uminus_real @ tt ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) ),
inference(rewrite,[status(thm)],[714,526]) ).
thf(156,axiom,
! [A: real,B: real,C: a] :
( ( A != B )
=> ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ A )
= ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ B ) )
=> ( ( ( uminus_uminus_a_a @ f @ C )
!= zero_zero_a )
=> ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_rev_Operiodic__orbitI) ).
thf(725,plain,
! [A: real,B: real,C: a] :
( ( A != B )
=> ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ A )
= ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ B ) )
=> ( ( ( uminus_uminus_a_a @ f @ C )
!= zero_zero_a )
=> ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(1003,plain,
! [A: real] :
( ~ $true
| ( ( ord_less_real @ zero_zero_real @ d )
!= ( ord_less_real @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[392,295]) ).
thf(1004,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ d )
!= ( ord_less_real @ A @ A ) ),
inference(simp,[status(thm)],[1003]) ).
thf(1005,plain,
! [A: real] :
( ( zero_zero_real != A )
| ( d != A ) ),
inference(simp,[status(thm)],[1004]) ).
thf(1006,plain,
d != zero_zero_real,
inference(simp,[status(thm)],[1005]) ).
thf(51,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus_real @ A @ C )
= ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_add__mono__thms__linordered__semiring_I4_J) ).
thf(388,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus_real @ A @ C )
= ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(40,axiom,
! [A: real,B: real] :
( ( ( plus_plus_real @ A @ B )
= A )
= ( B = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_add__cancel__left__right) ).
thf(354,plain,
! [A: real,B: real] :
( ( ( plus_plus_real @ A @ B )
= A )
= ( B = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(355,plain,
! [B: real,A: real] :
( ( ( plus_plus_real @ A @ B )
= A )
= ( B = zero_zero_real ) ),
inference(cnf,[status(esa)],[354]) ).
thf(356,plain,
! [B: real,A: real] :
( ( ( plus_plus_real @ A @ B )
= A )
= ( B = zero_zero_real ) ),
inference(lifteq,[status(thm)],[355]) ).
thf(326,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(cnf,[status(esa)],[325]) ).
thf(327,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(lifteq,[status(thm)],[326]) ).
thf(6856,plain,
! [A: a] :
( ~ $true
| ( ( member_a @ xx @ x )
!= ( member_a @ A
@ ( collect_a
@ ^ [B: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[813,6841]) ).
thf(6857,plain,
! [A: a] :
( ( member_a @ xx @ x )
!= ( member_a @ A
@ ( collect_a
@ ^ [B: a] : $false ) ) ),
inference(simp,[status(thm)],[6856]) ).
thf(6860,plain,
! [A: a] :
( ( xx != A )
| ( ( collect_a
@ ^ [B: a] : $false )
!= x ) ),
inference(simp,[status(thm)],[6857]) ).
thf(6867,plain,
( ( collect_a
@ ^ [A: a] : $false )
!= x ),
inference(simp,[status(thm)],[6860]) ).
thf(7185,plain,
! [A: set_a] :
( ( A != x )
| ( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
!= ( collect_a
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[327,6867]) ).
thf(7189,plain,
( ( ^ [A: a] : ( member_a @ A @ x ) )
!= ( ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[7185]) ).
thf(7191,plain,
member_a @ sk7 @ x,
inference(func_ext,[status(esa)],[7189]) ).
thf(2591,plain,
! [A: a] :
( ( xx != zero_zero_a )
| ( tt != ss )
| ( ( auto_l612940ivl0_a @ f @ x @ A )
!= bot_bot_set_real )
| ~ $true
| ~ ( member_a @ A @ x )
| ( ( member_real @ zero_zero_real @ top_top_set_real )
!= ( member_real @ zero_zero_real @ top_top_set_real ) ) ),
inference(paramod_ordered,[status(thm)],[2568,831]) ).
thf(2592,plain,
! [A: a] :
( ( xx != zero_zero_a )
| ( tt != ss )
| ( ( auto_l612940ivl0_a @ f @ x @ A )
!= bot_bot_set_real )
| ~ ( member_a @ A @ x )
| ( ( member_real @ zero_zero_real @ top_top_set_real )
!= ( member_real @ zero_zero_real @ top_top_set_real ) ) ),
inference(simp,[status(thm)],[2591]) ).
thf(2593,plain,
! [A: a] :
( ( xx != zero_zero_a )
| ( tt != ss )
| ( ( auto_l612940ivl0_a @ f @ x @ A )
!= bot_bot_set_real )
| ~ ( member_a @ A @ x ) ),
inference(pattern_uni,[status(thm)],[2592:[]]) ).
thf(7202,plain,
! [A: a] :
( ( xx != zero_zero_a )
| ( tt != ss )
| ( ( auto_l612940ivl0_a @ f @ x @ A )
!= bot_bot_set_real )
| ~ $true
| ( ( member_a @ sk7 @ x )
!= ( member_a @ A @ x ) ) ),
inference(paramod_ordered,[status(thm)],[7191,2593]) ).
thf(7203,plain,
! [A: a] :
( ( xx != zero_zero_a )
| ( tt != ss )
| ( ( auto_l612940ivl0_a @ f @ x @ A )
!= bot_bot_set_real )
| ( ( member_a @ sk7 @ x )
!= ( member_a @ A @ x ) ) ),
inference(simp,[status(thm)],[7202]) ).
thf(7204,plain,
( ( xx != zero_zero_a )
| ( tt != ss )
| ( ( auto_l612940ivl0_a @ f @ x @ sk7 )
!= bot_bot_set_real ) ),
inference(pattern_uni,[status(thm)],[7203:[bind(A,$thf( sk7 ))]]) ).
thf(124,axiom,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
=> ( ( member_a @ A @ x )
=> ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_local_Oflow__initial__time) ).
thf(610,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
=> ( ( member_a @ A @ x )
=> ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(175,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_61_rev_Ofixed__point__imp__closed__orbit__period__zero_I1_J) ).
thf(783,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)],[175]) ).
thf(94,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_148_rev_Ofixed__point__imp__closed__orbit__period__zero_I2_J) ).
thf(519,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)],[94]) ).
thf(161,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_144_rev_Oclosed__orbit__period__zero__fixed__point) ).
thf(742,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)],[161]) ).
thf(114,axiom,
! [A: real,B: real,C: a] :
( ~ ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) )
= zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_general_Oflow__undefined0) ).
thf(578,plain,
! [A: real,B: real,C: a] :
( ~ ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) )
= zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(216,axiom,
ord_less_real @ tt @ d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_tt_I2_J) ).
thf(903,plain,
ord_less_real @ tt @ d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(1014,plain,
! [A: real] :
( ~ $true
| ( ( ord_less_real @ tt @ d )
!= ( ord_less_real @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[903,295]) ).
thf(1015,plain,
! [A: real] :
( ( ord_less_real @ tt @ d )
!= ( ord_less_real @ A @ A ) ),
inference(simp,[status(thm)],[1014]) ).
thf(1016,plain,
! [A: real] :
( ( tt != A )
| ( d != A ) ),
inference(simp,[status(thm)],[1015]) ).
thf(1017,plain,
tt != d,
inference(simp,[status(thm)],[1016]) ).
thf(55,axiom,
! [A: real,B: real,C: real,D: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ( ( plus_plus_real @ A @ D )
= ( plus_plus_real @ B @ ( plus_plus_real @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_group__cancel_Oadd1) ).
thf(399,plain,
! [A: real,B: real,C: real,D: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ( ( plus_plus_real @ A @ D )
= ( plus_plus_real @ B @ ( plus_plus_real @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(400,plain,
! [A: real,B: real,C: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ! [D: real] :
( ( plus_plus_real @ A @ D )
= ( plus_plus_real @ B @ ( plus_plus_real @ C @ D ) ) ) ),
inference(miniscope,[status(thm)],[399]) ).
thf(401,plain,
! [D: real,C: real,B: real,A: real] :
( ( A
!= ( plus_plus_real @ B @ C ) )
| ( ( plus_plus_real @ A @ D )
= ( plus_plus_real @ B @ ( plus_plus_real @ C @ D ) ) ) ),
inference(cnf,[status(esa)],[400]) ).
thf(402,plain,
! [D: real,C: real,B: real,A: real] :
( ( A
!= ( plus_plus_real @ B @ C ) )
| ( ( plus_plus_real @ A @ D )
= ( plus_plus_real @ B @ ( plus_plus_real @ C @ D ) ) ) ),
inference(lifteq,[status(thm)],[401]) ).
thf(403,plain,
! [C: real,B: real,A: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
inference(simp,[status(thm)],[402]) ).
thf(31,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
=> ( ord_less_real @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_add__less__imp__less__left) ).
thf(328,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
=> ( ord_less_real @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(212,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_local_Oflow__in__domain) ).
thf(884,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(35,axiom,
! [A: a] :
( ( zero_zero_a = A )
= ( A = zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_zero__reorient) ).
thf(339,plain,
! [A: a] :
( ( zero_zero_a = A )
= ( A = zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(227,axiom,
! [A: a,B: real] :
( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_rev_Oclosed__orbit__flow0) ).
thf(933,plain,
! [A: a,B: real] :
( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(106,axiom,
! [A: real,B: real,C: a] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) @ ( minus_minus_real @ B @ A ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_general_Oflows__reverse) ).
thf(554,plain,
! [A: real,B: real,C: a] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) @ ( minus_minus_real @ B @ A ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(6400,plain,
! [B: a > $o,A: a] :
( ( xx != zero_zero_a )
| ( tt != ss )
| ( member_a @ A @ ( collect_a @ B ) )
| ( ( member_real @ zero_zero_real @ top_top_set_real )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2568,375]) ).
thf(6581,plain,
! [A: a] :
( ( xx != zero_zero_a )
| ( tt != ss )
| ( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( member_real @ zero_zero_real @ top_top_set_real ) ) ) ),
inference(pre_uni,[status(thm)],[6400:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ( member_real @ zero_zero_real @ top_top_set_real ) ))]]) ).
thf(6879,plain,
! [B: a,A: a] :
( ( xx != zero_zero_a )
| ( tt != ss )
| ~ $true
| ( ( member_a @ A
@ ( collect_a
@ ^ [C: a] : ( member_real @ zero_zero_real @ top_top_set_real ) ) )
!= ( member_a @ B
@ ( collect_a
@ ^ [C: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[6581,6841]) ).
thf(6880,plain,
! [B: a,A: a] :
( ( xx != zero_zero_a )
| ( tt != ss )
| ( ( member_a @ A
@ ( collect_a
@ ^ [C: a] : ( member_real @ zero_zero_real @ top_top_set_real ) ) )
!= ( member_a @ B
@ ( collect_a
@ ^ [C: a] : $false ) ) ) ),
inference(simp,[status(thm)],[6879]) ).
thf(6937,plain,
! [B: a,A: a] :
( ( xx != zero_zero_a )
| ( tt != ss )
| ( A != B )
| ( ( collect_a
@ ^ [C: a] : ( member_real @ zero_zero_real @ top_top_set_real ) )
!= ( collect_a
@ ^ [C: a] : $false ) ) ),
inference(simp,[status(thm)],[6880]) ).
thf(6946,plain,
( ( xx != zero_zero_a )
| ( tt != ss )
| ( ( collect_a
@ ^ [A: a] : ( member_real @ zero_zero_real @ top_top_set_real ) )
!= ( collect_a
@ ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[6937]) ).
thf(3121,plain,
! [B: real,A: real] :
( ( A != i1 )
| ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
!= ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ B ) @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[353,2665]) ).
thf(3139,plain,
! [A: real] :
( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
!= ( uminus_uminus_real @ i1 ) ),
inference(simp,[status(thm)],[3121]) ).
thf(3143,plain,
! [A: real] :
( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
!= ( uminus_uminus_real @ i1 ) ),
inference(simp,[status(thm)],[3139]) ).
thf(100,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_53_rev_Ogeneral_Omem__existence__ivl__iv__defined_I2_J) ).
thf(537,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)],[100]) ).
thf(83,axiom,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_add__pos__pos) ).
thf(489,plain,
! [A: real,B: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ( ( ord_less_real @ zero_zero_real @ B )
=> ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(143,axiom,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_add__diff__cancel__right_H) ).
thf(679,plain,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(1034,plain,
( ( ( auto_l612940ivl0_a @ f @ x @ xx )
!= bot_bot_set_real )
| ~ $true
| ( ( member_real @ t @ ( auto_l612940ivl0_a @ f @ x @ x2 ) )
!= ( member_real @ zero_zero_real @ top_top_set_real ) ) ),
inference(paramod_ordered,[status(thm)],[670,1013]) ).
thf(1035,plain,
( ( ( auto_l612940ivl0_a @ f @ x @ xx )
!= bot_bot_set_real )
| ( ( member_real @ t @ ( auto_l612940ivl0_a @ f @ x @ x2 ) )
!= ( member_real @ zero_zero_real @ top_top_set_real ) ) ),
inference(simp,[status(thm)],[1034]) ).
thf(1039,plain,
( ( ( auto_l612940ivl0_a @ f @ x @ xx )
!= bot_bot_set_real )
| ( t != zero_zero_real )
| ( ( auto_l612940ivl0_a @ f @ x @ x2 )
!= top_top_set_real ) ),
inference(simp,[status(thm)],[1035]) ).
thf(239,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_26_closed__orbit__periodic) ).
thf(970,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)],[239]) ).
thf(245,axiom,
! [A: a] :
( ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= bot_bot_set_real )
= ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
| ~ ( member_a @ A @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_local_Orev_Oexistence__ivl__empty__iff) ).
thf(985,plain,
! [A: a] :
( ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= bot_bot_set_real )
= ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
| ~ ( member_a @ A @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(92,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_169_periodic__orbit__period_I1_J) ).
thf(515,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)],[92]) ).
thf(136,axiom,
! [A: real,B: a] :
( ( ( ( member_real @ A @ top_top_set_real )
& ( member_a @ B @ x ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ B @ ( minus_minus_real @ A @ A ) )
= B ) )
& ( ~ ( ( member_real @ A @ top_top_set_real )
& ( member_a @ B @ x ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ B @ ( minus_minus_real @ A @ A ) )
= zero_zero_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_general_Oflow__initial__time__if) ).
thf(654,plain,
! [A: real,B: a] :
( ( ( ( member_real @ A @ top_top_set_real )
& ( member_a @ B @ x ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ B @ ( minus_minus_real @ A @ A ) )
= B ) )
& ( ~ ( ( member_real @ A @ top_top_set_real )
& ( member_a @ B @ x ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ B @ ( minus_minus_real @ A @ A ) )
= zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(8384,plain,
! [B: a,A: a] :
( ~ $true
| ( ( member_a @ A
@ ( collect_a
@ ^ [C: a] : $true ) )
!= ( member_a @ B
@ ( collect_a
@ ^ [C: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[8382,6841]) ).
thf(8385,plain,
! [B: a,A: a] :
( ( member_a @ A
@ ( collect_a
@ ^ [C: a] : $true ) )
!= ( member_a @ B
@ ( collect_a
@ ^ [C: a] : $false ) ) ),
inference(simp,[status(thm)],[8384]) ).
thf(8403,plain,
! [B: a,A: a] :
( ( A != B )
| ( ( collect_a
@ ^ [C: a] : $false )
!= ( collect_a
@ ^ [C: a] : $true ) ) ),
inference(simp,[status(thm)],[8385]) ).
thf(8410,plain,
( ( collect_a
@ ^ [A: a] : $false )
!= ( collect_a
@ ^ [A: a] : $true ) ),
inference(simp,[status(thm)],[8403]) ).
thf(1041,plain,
( ( ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss )
!= xx )
| ( ( auto_ll_on_flow0_a @ f @ x @ xx @ tt )
!= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ( minus_minus_real @ ss @ tt ) ) ) ),
inference(paramod_ordered,[status(thm)],[526,248]) ).
thf(1042,plain,
( ( ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss )
!= xx )
| ( f != f )
| ( x != x )
| ( xx != x2 )
| ( ( minus_minus_real @ ss @ tt )
!= tt ) ),
inference(simp,[status(thm)],[1041]) ).
thf(1043,plain,
( ( ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss )
!= xx )
| ( xx != x2 )
| ( ( minus_minus_real @ ss @ tt )
!= tt ) ),
inference(simp,[status(thm)],[1042]) ).
thf(1523,plain,
! [A: real] :
( ( ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss )
!= xx )
| ( xx != x2 )
| ( ( uminus_uminus_real @ A )
!= tt )
| ( ( minus_minus_real @ zero_zero_real @ A )
!= ( minus_minus_real @ ss @ tt ) ) ),
inference(paramod_ordered,[status(thm)],[669,1043]) ).
thf(1525,plain,
! [A: real] :
( ( ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss )
!= xx )
| ( xx != x2 )
| ( ( uminus_uminus_real @ A )
!= tt )
| ( ss != zero_zero_real )
| ( A != tt ) ),
inference(simp,[status(thm)],[1523]) ).
thf(1527,plain,
( ( ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss )
!= xx )
| ( xx != x2 )
| ( ( uminus_uminus_real @ tt )
!= tt )
| ( ss != zero_zero_real ) ),
inference(simp,[status(thm)],[1525]) ).
thf(2571,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( xx != zero_zero_a )
| ( xx != x2 )
| ( ( uminus_uminus_real @ tt )
!= tt )
| ( ss != zero_zero_real )
| ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
!= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) ) ),
inference(paramod_ordered,[status(thm)],[897,1527]) ).
thf(2578,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( xx != zero_zero_a )
| ( xx != x2 )
| ( ( uminus_uminus_real @ tt )
!= tt )
| ( ss != zero_zero_real )
| ( f != f )
| ( x != x )
| ( A != x2 )
| ( ss != zero_zero_real ) ),
inference(simp,[status(thm)],[2571]) ).
thf(2581,plain,
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( xx != zero_zero_a )
| ( xx != x2 )
| ( ( uminus_uminus_real @ tt )
!= tt )
| ( ss != zero_zero_real ) ),
inference(simp,[status(thm)],[2578]) ).
thf(111,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 @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_rev_Ogeneral_Oexistence__ivl__initial__time) ).
thf(569,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 @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(173,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( member_a @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_rev_Oflow0__defined) ).
thf(779,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( member_a @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(88,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_diff__add__cancel) ).
thf(503,plain,
! [A: real,B: real] :
( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(128,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= C )
=> ( A
= ( minus_minus_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_add__implies__diff) ).
thf(622,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= C )
=> ( A
= ( minus_minus_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(197,axiom,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
=> ( ( member_a @ A @ x )
=> ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
!= bot_bot_set_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_local_Orev_Oexistence__ivl__notempty) ).
thf(837,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
=> ( ( member_a @ A @ x )
=> ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
!= bot_bot_set_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(53,axiom,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ A @ B ) )
= ( B = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_add__cancel__right__right) ).
thf(393,plain,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ A @ B ) )
= ( B = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(8,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ C @ D )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_add__strict__mono) ).
thf(264,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_real @ A @ B )
=> ( ( ord_less_real @ C @ D )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(265,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ B )
=> ! [C: real,D: real] :
( ( ord_less_real @ C @ D )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ),
inference(miniscope,[status(thm)],[264]) ).
thf(266,plain,
! [D: real,C: real,B: real,A: real] :
( ~ ( ord_less_real @ A @ B )
| ~ ( ord_less_real @ C @ D )
| ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
inference(cnf,[status(esa)],[265]) ).
thf(42,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_add_Oleft__commute) ).
thf(360,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(184,axiom,
! [A: real,B: real,C: a] :
( ( member_real @ ( plus_plus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_local_Oexistence__ivl__trans_H) ).
thf(805,plain,
! [A: real,B: real,C: a] :
( ( member_real @ ( plus_plus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(2738,plain,
! [C: real,B: real,A: real] :
( ( ( sk3 @ B @ zero_zero_real )
= C )
| ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
!= ( plus_plus_real @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[439,2737]) ).
thf(2739,plain,
! [A: real] :
( ( sk3 @ A @ zero_zero_real )
= ( uminus_uminus_real @ A ) ),
inference(pattern_uni,[status(thm)],[2738:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( uminus_uminus_real @ D ))]]) ).
thf(2748,plain,
! [A: real] :
( ( sk3 @ A @ zero_zero_real )
= ( uminus_uminus_real @ A ) ),
inference(simp,[status(thm)],[2739]) ).
thf(397,plain,
! [B: real,A: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
= ( ord_less_real @ A @ zero_zero_real ) ),
inference(cnf,[status(esa)],[396]) ).
thf(398,plain,
! [B: real,A: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
= ( ord_less_real @ A @ zero_zero_real ) ),
inference(lifteq,[status(thm)],[397]) ).
thf(141,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_45_rev_Oexistence__ivl__zero) ).
thf(674,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)],[141]) ).
thf(98,axiom,
! [A: a,B: real] :
( ( member_a @ A @ x )
=> ( ( ( f @ A )
= zero_zero_a )
=> ( ( auto_ll_on_flow0_a @ f @ x @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_fixpoint__sol_I2_J) ).
thf(530,plain,
! [A: a,B: real] :
( ( member_a @ A @ x )
=> ( ( ( f @ A )
= zero_zero_a )
=> ( ( auto_ll_on_flow0_a @ f @ x @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(21,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_add__left__cancel) ).
thf(296,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(297,plain,
! [C: real,B: real,A: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
= ( B = C ) ),
inference(cnf,[status(esa)],[296]) ).
thf(298,plain,
! [C: real,B: real,A: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
= ( B = C ) ),
inference(lifteq,[status(thm)],[297]) ).
thf(202,axiom,
! [A: a] :
( ~ ( member_a @ A @ x )
=> ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= bot_bot_set_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_local_Orev_Oexistence__ivl__undefined) ).
thf(856,plain,
! [A: a] :
( ~ ( member_a @ A @ x )
=> ( ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
= bot_bot_set_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(162,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A )
= B )
=> ( member_real @ ( uminus_uminus_real @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_rev_Orecurrence__time__flip__sign_I1_J) ).
thf(745,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A )
= B )
=> ( member_real @ ( uminus_uminus_real @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(121,axiom,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
= ( minus_minus_real @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_add__diff__cancel__left) ).
thf(601,plain,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
= ( minus_minus_real @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(3256,plain,
! [A: real] :
( ( ( uminus_uminus_real @ ( plus_plus_real @ zero_zero_real @ A ) )
!= tt )
| ( ( uminus_uminus_real @ zero_zero_real )
!= ( uminus_uminus_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[277,2685]) ).
thf(3257,plain,
( ( uminus_uminus_real @ ( plus_plus_real @ zero_zero_real @ zero_zero_real ) )
!= tt ),
inference(pattern_uni,[status(thm)],[3256:[bind(A,$thf( zero_zero_real ))]]) ).
thf(3274,plain,
( ( uminus_uminus_real @ zero_zero_real )
!= tt ),
inference(rewrite,[status(thm)],[3257,332]) ).
thf(158,axiom,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_add__diff__cancel__left_H) ).
thf(733,plain,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(217,axiom,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_add__diff__cancel) ).
thf(904,plain,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(62,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_add_Oassoc) ).
thf(423,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(6842,plain,
! [A: a] :
( ~ $true
| ( ( member_a @ xx
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ x ) ) )
!= ( member_a @ A
@ ( collect_a
@ ^ [B: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[6528,6841]) ).
thf(6843,plain,
! [A: a] :
( ( member_a @ xx
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ x ) ) )
!= ( member_a @ A
@ ( collect_a
@ ^ [B: a] : $false ) ) ),
inference(simp,[status(thm)],[6842]) ).
thf(6863,plain,
! [A: a] :
( ( xx != A )
| ( ( collect_a
@ ^ [B: a] : ( member_a @ B @ x ) )
!= ( collect_a
@ ^ [B: a] : $false ) ) ),
inference(simp,[status(thm)],[6843]) ).
thf(6870,plain,
( ( collect_a
@ ^ [A: a] : ( member_a @ A @ x ) )
!= ( collect_a
@ ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[6863]) ).
thf(171,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_37_rev_Oclosed__orbit__eq__rev) ).
thf(772,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)],[171]) ).
thf(151,axiom,
! [A: a] :
( ( ( ( member_real @ zero_zero_real @ top_top_set_real )
& ( member_a @ A @ x ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ zero_zero_real )
= A ) )
& ( ~ ( ( member_real @ zero_zero_real @ top_top_set_real )
& ( member_a @ A @ x ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ zero_zero_real )
= zero_zero_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_local_Orev_Oflow__initial__time__if) ).
thf(703,plain,
! [A: a] :
( ( ( ( member_real @ zero_zero_real @ top_top_set_real )
& ( member_a @ A @ x ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ zero_zero_real )
= A ) )
& ( ~ ( ( member_real @ zero_zero_real @ top_top_set_real )
& ( member_a @ A @ x ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ zero_zero_real )
= zero_zero_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(704,plain,
( ! [A: a] :
( ( ( member_real @ zero_zero_real @ top_top_set_real )
& ( member_a @ A @ x ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ zero_zero_real )
= A ) )
& ! [A: a] :
( ~ ( ( member_real @ zero_zero_real @ top_top_set_real )
& ( member_a @ A @ x ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ zero_zero_real )
= zero_zero_a ) ) ),
inference(miniscope,[status(thm)],[703]) ).
thf(705,plain,
! [B: a,A: a] :
( ( ~ ( member_real @ zero_zero_real @ top_top_set_real )
| ~ ( member_a @ A @ x )
| ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ zero_zero_real )
= A ) )
& ( ( member_real @ zero_zero_real @ top_top_set_real )
| ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ zero_zero_real )
= zero_zero_a ) )
& ( ( member_a @ B @ x )
| ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ zero_zero_real )
= zero_zero_a ) ) ),
inference(cnf,[status(esa)],[704]) ).
thf(707,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ zero_zero_real )
= zero_zero_a ) ),
inference(cnfConj,[status(thm)],[705]) ).
thf(710,plain,
! [A: a] :
( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ zero_zero_real )
= zero_zero_a )
| ( member_real @ zero_zero_real @ top_top_set_real ) ),
inference(lifteq,[status(thm)],[707]) ).
thf(711,plain,
! [A: a] :
( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ zero_zero_real )
= zero_zero_a )
| ( member_real @ zero_zero_real @ top_top_set_real ) ),
inference(simp,[status(thm)],[710]) ).
thf(18,axiom,
ord_less_real @ i1 @ i2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_i2_I3_J) ).
thf(291,plain,
ord_less_real @ i1 @ i2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
! [A: real] :
( ( zero_zero_real
= ( uminus_uminus_real @ A ) )
= ( zero_zero_real = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_neg__0__equal__iff__equal) ).
thf(281,plain,
! [A: real] :
( ( zero_zero_real
= ( uminus_uminus_real @ A ) )
= ( zero_zero_real = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(103,axiom,
! [A: real,B: real] :
( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
= ( plus_plus_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_diff__minus__eq__add) ).
thf(545,plain,
! [A: real,B: real] :
( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
= ( plus_plus_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(59,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
= ( ord_less_real @ zero_zero_real @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_less__add__same__cancel2) ).
thf(413,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
= ( ord_less_real @ zero_zero_real @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(228,axiom,
! [A: a,B: real] :
( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ( ( uminus_uminus_a_a @ f @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B ) )
!= zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_rev_Operiodic__orbit__imp__flow0__regular) ).
thf(936,plain,
! [A: a,B: real] :
( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ( ( uminus_uminus_a_a @ f @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B ) )
!= zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(26,axiom,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ B @ A ) )
= ( B = zero_zero_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_add__cancel__right__left) ).
thf(313,plain,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ B @ A ) )
= ( B = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(132,axiom,
member_real @ tt @ ( auto_l612940ivl0_a @ f @ x @ xx ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_tt__ex) ).
thf(644,plain,
member_real @ tt @ ( auto_l612940ivl0_a @ f @ x @ xx ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1311,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( member_real @ tt @ bot_bot_set_real )
| ( ( auto_l612940ivl0_a @ f @ x @ A )
!= ( auto_l612940ivl0_a @ f @ x @ xx ) ) ),
inference(paramod_ordered,[status(thm)],[560,644]) ).
thf(1312,plain,
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( member_real @ tt @ bot_bot_set_real ) ),
inference(pattern_uni,[status(thm)],[1311:[bind(A,$thf( xx ))]]) ).
thf(232,axiom,
! [A: a] :
( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ~ ! [B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ~ ! [C: real] :
( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ ( plus_plus_real @ C @ B ) )
= ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_rev_Oclosed__orbitE) ).
thf(947,plain,
! [A: a] :
( ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ~ ! [B: real] :
( ( ord_less_real @ zero_zero_real @ B )
=> ~ ! [C: real] :
( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ ( plus_plus_real @ C @ B ) )
= ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(349,plain,
! [A: real] :
( ( ( uminus_uminus_real @ A )
= A )
= ( A = zero_zero_real ) ),
inference(cnf,[status(esa)],[348]) ).
thf(350,plain,
! [A: real] :
( ( ( uminus_uminus_real @ A )
= A )
= ( A = zero_zero_real ) ),
inference(lifteq,[status(thm)],[349]) ).
thf(7199,plain,
! [A: a] :
( ( ( auto_l612940ivl0_a @ f @ x @ A )
!= bot_bot_set_real )
| ~ ( member_real @ zero_zero_real @ top_top_set_real )
| ~ $true
| ( ( member_a @ sk7 @ x )
!= ( member_a @ A @ x ) ) ),
inference(paramod_ordered,[status(thm)],[7191,831]) ).
thf(7200,plain,
! [A: a] :
( ( ( auto_l612940ivl0_a @ f @ x @ A )
!= bot_bot_set_real )
| ~ ( member_real @ zero_zero_real @ top_top_set_real )
| ( ( member_a @ sk7 @ x )
!= ( member_a @ A @ x ) ) ),
inference(simp,[status(thm)],[7199]) ).
thf(7201,plain,
( ( ( auto_l612940ivl0_a @ f @ x @ sk7 )
!= bot_bot_set_real )
| ~ ( member_real @ zero_zero_real @ top_top_set_real ) ),
inference(pattern_uni,[status(thm)],[7200:[bind(A,$thf( sk7 ))]]) ).
thf(112,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_real @ A @ top_top_set_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_rev_Ogeneral_Omem__existence__ivl__subset) ).
thf(572,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_real @ A @ top_top_set_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(61,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( ord_less_real @ A @ B )
& ( C = D ) )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_add__mono__thms__linordered__field_I1_J) ).
thf(419,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( ord_less_real @ A @ B )
& ( C = D ) )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(78,axiom,
( plus_plus_real
= ( ^ [A: real,B: real] : ( plus_plus_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_add_Ocommute) ).
thf(473,plain,
( plus_plus_real
= ( ^ [A: real,B: real] : ( plus_plus_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(474,plain,
( plus_plus_real
= ( ^ [A: real,B: real] : ( plus_plus_real @ B @ A ) ) ),
inference(lifteq,[status(thm)],[473]) ).
thf(990,plain,
! [A: real] :
( ( plus_plus_real @ A )
= ( ^ [B: real] : ( plus_plus_real @ B @ A ) ) ),
inference(func_ext,[status(esa)],[474]) ).
thf(361,plain,
! [C: real,B: real,A: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) ) ),
inference(cnf,[status(esa)],[360]) ).
thf(362,plain,
! [C: real,B: real,A: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) ) ),
inference(lifteq,[status(thm)],[361]) ).
thf(317,plain,
! [B: real,A: real] :
( ( ( uminus_uminus_real @ A )
= ( uminus_uminus_real @ B ) )
= ( A = B ) ),
inference(cnf,[status(esa)],[316]) ).
thf(318,plain,
! [B: real,A: real] :
( ( ( uminus_uminus_real @ A )
= ( uminus_uminus_real @ B ) )
= ( A = B ) ),
inference(lifteq,[status(thm)],[317]) ).
thf(242,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 )
=> ( ! [D: real,E: real,F: a] :
( ( member_a @ F @ x )
=> ( ( uminus_uminus_a_a @ f @ F )
= ( uminus_uminus_a_a @ f @ F ) ) )
=> ( ( top_top_set_real = top_top_set_real )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) )
= ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_rev_Oflow__shift__autonomous2) ).
thf(979,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(122,axiom,
! [A: real,B: a,C: real] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( ( member_real @ C @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( member_real @ ( minus_minus_real @ C @ A ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_diff__existence__ivl__trans) ).
thf(604,plain,
! [A: real,B: a,C: real] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( ( member_real @ C @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( member_real @ ( minus_minus_real @ C @ A ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(215,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ ( minus_minus_real @ B @ C ) )
= ( ord_less_real @ ( plus_plus_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_less__diff__eq) ).
thf(900,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ ( minus_minus_real @ B @ C ) )
= ( ord_less_real @ ( plus_plus_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(405,plain,
! [A: real] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(cnf,[status(esa)],[404]) ).
thf(406,plain,
! [A: real] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(lifteq,[status(thm)],[405]) ).
thf(3401,plain,
! [A: real] :
( ( ( uminus_uminus_real @ ( plus_plus_real @ zero_zero_real @ A ) )
!= d )
| ( ( uminus_uminus_real @ zero_zero_real )
!= ( uminus_uminus_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[277,2786]) ).
thf(3402,plain,
( ( uminus_uminus_real @ ( plus_plus_real @ zero_zero_real @ zero_zero_real ) )
!= d ),
inference(pattern_uni,[status(thm)],[3401:[bind(A,$thf( zero_zero_real ))]]) ).
thf(453,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(cnf,[status(esa)],[452]) ).
thf(454,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(lifteq,[status(thm)],[453]) ).
thf(3419,plain,
( ( uminus_uminus_real @ zero_zero_real )
!= d ),
inference(rewrite,[status(thm)],[3402,454]) ).
thf(159,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_313_diff__strict__right__mono) ).
thf(736,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)],[159]) ).
thf(66,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_187_neg__less__iff__less) ).
thf(434,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)],[66]) ).
thf(119,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
= ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_diff__less__eq) ).
thf(594,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
= ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(3931,plain,
! [B: a,A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( initia826609931terval
@ ( collect_real
@ ^ [C: real] :
( member_real @ C
@ ( collect_real
@ ^ [D: real] :
( member_real @ D
@ ( collect_real
@ ^ [E: real] : ( member_real @ E @ bot_bot_set_real ) ) ) ) ) ) )
| ( ( auto_l612940ivl0_a @ f @ x @ A )
!= ( auto_l612940ivl0_a @ f @ x @ B ) ) ),
inference(paramod_ordered,[status(thm)],[560,1904]) ).
thf(3932,plain,
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( initia826609931terval
@ ( collect_real
@ ^ [A: real] :
( member_real @ A
@ ( collect_real
@ ^ [B: real] :
( member_real @ B
@ ( collect_real
@ ^ [C: real] : ( member_real @ C @ bot_bot_set_real ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3931:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(150,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_63_local_Oexistence__ivl__initial__time) ).
thf(700,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)],[150]) ).
thf(250,plain,
! [B: a > $o,A: a > $o] :
( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
inference(cnf,[status(esa)],[249]) ).
thf(251,plain,
! [B: a > $o,A: a > $o] :
( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
inference(lifteq,[status(thm)],[250]) ).
thf(129,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_real @ B @ top_top_set_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_rev_Ogeneral_Omem__existence__ivl__iv__defined_I1_J) ).
thf(626,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_real @ B @ top_top_set_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(170,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_215_rev_Operiodic__orbit__def) ).
thf(769,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)],[170]) ).
thf(145,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_54_local_Orev_Omem__existence__ivl__subset) ).
thf(685,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)],[145]) ).
thf(236,axiom,
! [A: a] :
( ( period138238489rbit_a @ f @ x @ A )
=> ( ( auto_ll_on_flow0_a @ f @ x @ A @ ( period1305449585riod_a @ f @ x @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_periodic__orbit__period_I2_J) ).
thf(959,plain,
! [A: a] :
( ( period138238489rbit_a @ f @ x @ A )
=> ( ( auto_ll_on_flow0_a @ f @ x @ A @ ( period1305449585riod_a @ f @ x @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(148,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_115_local_Orev_Omem__existence__ivl__iv__defined_I2_J) ).
thf(695,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)],[148]) ).
thf(73,axiom,
! [A: real,B: real] :
( ( A = B )
=> ( ( uminus_uminus_real @ A )
= ( uminus_uminus_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_verit__negate__coefficient_I3_J) ).
thf(455,plain,
! [A: real,B: real] :
( ( A = B )
=> ( ( uminus_uminus_real @ A )
= ( uminus_uminus_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(65,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_add_Oleft__cancel) ).
thf(431,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(206,axiom,
! [A: real,B: a] :
( ~ ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A )
= zero_zero_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_local_Orev_Oflow__undefined0) ).
thf(868,plain,
! [A: real,B: a] :
( ~ ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A )
= zero_zero_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(201,axiom,
! [A: real,B: real,C: real,D: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ( ( minus_minus_real @ A @ D )
= ( plus_plus_real @ B @ ( minus_minus_real @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_group__cancel_Osub1) ).
thf(851,plain,
! [A: real,B: real,C: real,D: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ( ( minus_minus_real @ A @ D )
= ( plus_plus_real @ B @ ( minus_minus_real @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(8922,plain,
( ( ^ [A: a] : ( member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ A ) ) )
!= ( ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[8733]) ).
thf(223,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_233_diff__gt__0__iff__gt) ).
thf(922,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)],[223]) ).
thf(63,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_minus__add__cancel) ).
thf(426,plain,
! [A: real,B: real] :
( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(180,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_real @ ( minus_minus_real @ B @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_rev_Ogeneral_Oexistence__ivl__reverse) ).
thf(795,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_real @ ( minus_minus_real @ B @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(104,axiom,
! [A: a] :
( ( period720806154rbit_a @ f @ x @ A )
= ( ? [B: real] :
( ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ A ) )
& ( B != zero_zero_real )
& ( ( auto_ll_on_flow0_a @ f @ x @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_closed__orbit__def) ).
thf(548,plain,
! [A: a] :
( ( period720806154rbit_a @ f @ x @ A )
= ( ? [B: real] :
( ( member_real @ B @ ( auto_l612940ivl0_a @ f @ x @ A ) )
& ( B != zero_zero_real )
& ( ( auto_ll_on_flow0_a @ f @ x @ A @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(1276,plain,
! [B: a,A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( initia826609931terval @ bot_bot_set_real )
| ( ( auto_l612940ivl0_a @ f @ x @ A )
!= ( auto_l612940ivl0_a @ f @ x @ B ) ) ),
inference(paramod_ordered,[status(thm)],[560,666]) ).
thf(1277,plain,
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( initia826609931terval @ bot_bot_set_real ) ),
inference(pattern_uni,[status(thm)],[1276:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(134,axiom,
! [A: real,B: real,C: a,D: real] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( ( member_real @ D @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) ) )
=> ( member_real @ ( minus_minus_real @ ( plus_plus_real @ A @ D ) @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_general_Oexistence__ivl__trans) ).
thf(648,plain,
! [A: real,B: real,C: a,D: real] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( ( member_real @ D @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) ) )
=> ( member_real @ ( minus_minus_real @ ( plus_plus_real @ A @ D ) @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(989,plain,
( ( ^ [A: real,B: real] :
( ( minus_minus_real @ A @ B )
= zero_zero_real ) )
= ( (=) @ real ) ),
inference(lifteq,[status(thm)],[988]) ).
thf(1018,plain,
! [A: real] :
( ( ^ [B: real] :
( ( minus_minus_real @ A @ B )
= zero_zero_real ) )
= ( (=) @ real @ A ) ),
inference(func_ext,[status(esa)],[989]) ).
thf(165,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_317_diff__eq__diff__less) ).
thf(754,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)],[165]) ).
thf(192,axiom,
! [A: real,B: real,C: a] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( member_real @ ( minus_minus_real @ B @ A ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_general_Oexistence__ivl__reverse) ).
thf(823,plain,
! [A: real,B: real,C: a] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( member_real @ ( minus_minus_real @ B @ A ) @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(1752,plain,
! [A: real] :
( ( ( auto_ll_on_flow0_a @ f @ x @ x2 @ zero_zero_real )
!= xx )
| ( ss != zero_zero_real )
| ( ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) )
!= ( uminus_uminus_real @ tt ) ) ),
inference(paramod_ordered,[status(thm)],[1450,1526]) ).
thf(1785,plain,
! [A: real] :
( ( ( auto_ll_on_flow0_a @ f @ x @ x2 @ zero_zero_real )
!= xx )
| ( ss != zero_zero_real )
| ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
!= tt ) ),
inference(simp,[status(thm)],[1752]) ).
thf(2565,plain,
! [B: real,A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( xx != zero_zero_a )
| ( ss != zero_zero_real )
| ( ( plus_plus_real @ ( uminus_uminus_real @ B ) @ B )
!= tt )
| ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
!= ( auto_ll_on_flow0_a @ f @ x @ x2 @ zero_zero_real ) ) ),
inference(paramod_ordered,[status(thm)],[897,1785]) ).
thf(2566,plain,
! [A: real] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( xx != zero_zero_a )
| ( ss != zero_zero_real )
| ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
!= tt ) ),
inference(pattern_uni,[status(thm)],[2565:[bind(A,$thf( x2 ))]]) ).
thf(2582,plain,
! [A: real] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( xx != zero_zero_a )
| ( ss != zero_zero_real )
| ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
!= tt ) ),
inference(simp,[status(thm)],[2566]) ).
thf(1532,plain,
! [B: a,A: set_real] :
( ( initia826609931terval
@ ( collect_real
@ ^ [C: real] :
( member_real @ C
@ ( collect_real
@ ^ [D: real] : ( member_real @ D @ A ) ) ) ) )
| ( A
!= ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) ),
inference(paramod_ordered,[status(thm)],[335,1110]) ).
thf(1533,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)],[1532:[bind(A,$thf( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ E )),bind(B,$thf( E ))]]) ).
thf(1547,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)],[1533]) ).
thf(131,axiom,
! [A: real,B: real,C: a] :
( ( A != B )
=> ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ A )
= ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ B ) )
=> ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_rev_Oclosed__orbitI) ).
thf(640,plain,
! [A: real,B: real,C: a] :
( ( A != B )
=> ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ A )
= ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ B ) )
=> ( period720806154rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(234,axiom,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(954,plain,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(160,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_82_closed__orbit__global__existence) ).
thf(739,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)],[160]) ).
thf(2746,plain,
! [C: real,B: real,A: real] :
( ( ( sk3 @ B @ A )
= C )
| ( ( plus_plus_real @ A @ zero_zero_real )
!= ( plus_plus_real @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[454,2737]) ).
thf(2747,plain,
! [A: real] :
( ( sk3 @ A @ A )
= zero_zero_real ),
inference(pattern_uni,[status(thm)],[2746:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( zero_zero_real ))]]) ).
thf(178,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_flow0__defined) ).
thf(791,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( member_a @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(1032,plain,
( ( ( auto_l612940ivl0_a @ f @ x @ xx )
!= bot_bot_set_real )
| ~ $true
| ( ( member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ x2 ) )
!= ( member_real @ zero_zero_real @ top_top_set_real ) ) ),
inference(paramod_ordered,[status(thm)],[614,1013]) ).
thf(1033,plain,
( ( ( auto_l612940ivl0_a @ f @ x @ xx )
!= bot_bot_set_real )
| ( ( member_real @ ss @ ( auto_l612940ivl0_a @ f @ x @ x2 ) )
!= ( member_real @ zero_zero_real @ top_top_set_real ) ) ),
inference(simp,[status(thm)],[1032]) ).
thf(1038,plain,
( ( ( auto_l612940ivl0_a @ f @ x @ xx )
!= bot_bot_set_real )
| ( ss != zero_zero_real )
| ( ( auto_l612940ivl0_a @ f @ x @ x2 )
!= top_top_set_real ) ),
inference(simp,[status(thm)],[1033]) ).
thf(77,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_add__minus__cancel) ).
thf(470,plain,
! [A: real,B: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(358,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
= ( ord_less_real @ zero_zero_real @ A ) ),
inference(cnf,[status(esa)],[357]) ).
thf(359,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
= ( ord_less_real @ zero_zero_real @ A ) ),
inference(lifteq,[status(thm)],[358]) ).
thf(218,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_315_diff__strict__left__mono) ).
thf(907,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)],[218]) ).
thf(34,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_add__strict__right__mono) ).
thf(336,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(7198,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( B @ A )
!= ( member_a @ sk7 @ x ) ) ),
inference(paramod_ordered,[status(thm)],[375,7191]) ).
thf(7207,plain,
( member_a @ sk7
@ ( collect_a
@ ^ [A: a] : ( member_a @ A @ x ) ) ),
inference(pre_uni,[status(thm)],[7198:[bind(A,$thf( sk7 )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ x ) ))]]) ).
thf(4430,plain,
! [B: real,A: real] :
( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
| ( ( ord_less_real @ zero_zero_real @ B )
!= ( ord_less_real @ zero_zero_real @ d ) ) ),
inference(paramod_ordered,[status(thm)],[347,392]) ).
thf(4431,plain,
! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ d ) ),
inference(pattern_uni,[status(thm)],[4430:[bind(A,$thf( A )),bind(B,$thf( d ))]]) ).
thf(70,axiom,
! [A: real,B: real] :
( ( ord_less_real @ A @ zero_zero_real )
=> ( ( ord_less_real @ B @ zero_zero_real )
=> ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_add__neg__neg) ).
thf(446,plain,
! [A: real,B: real] :
( ( ord_less_real @ A @ zero_zero_real )
=> ( ( ord_less_real @ B @ zero_zero_real )
=> ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(86,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( ( ( auto_ll_on_flow0_a @ f @ x @ B @ A )
= B )
=> ( ( auto_ll_on_flow0_a @ f @ x @ B @ ( uminus_uminus_real @ A ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_recurrence__time__flip__sign_I2_J) ).
thf(497,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( ( ( auto_ll_on_flow0_a @ f @ x @ B @ A )
= B )
=> ( ( auto_ll_on_flow0_a @ f @ x @ B @ ( uminus_uminus_real @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(203,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_78_rev_Ofixpoint__sol_I1_J) ).
thf(859,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)],[203]) ).
thf(2563,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( xx != zero_zero_a )
| ( xx != x2 )
| ( ( minus_minus_real @ ss @ tt )
!= tt )
| ( ( auto_ll_on_flow0_a @ f @ x @ A @ zero_zero_real )
!= ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) ) ),
inference(paramod_ordered,[status(thm)],[897,1043]) ).
thf(2576,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( xx != zero_zero_a )
| ( xx != x2 )
| ( ( minus_minus_real @ ss @ tt )
!= tt )
| ( f != f )
| ( x != x )
| ( A != x2 )
| ( ss != zero_zero_real ) ),
inference(simp,[status(thm)],[2563]) ).
thf(2579,plain,
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( xx != zero_zero_a )
| ( xx != x2 )
| ( ( minus_minus_real @ ss @ tt )
!= tt )
| ( ss != zero_zero_real ) ),
inference(simp,[status(thm)],[2576]) ).
thf(7675,plain,
! [B: a > $o,A: a] :
( ( B @ A )
| ( ( member_a @ sk9
@ ( collect_a
@ ^ [C: a] : ( member_a @ C @ x ) ) )
!= ( member_a @ A @ ( collect_a @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[7663,375]) ).
thf(7676,plain,
member_a @ sk9 @ x,
inference(pattern_uni,[status(thm)],[7675:[bind(A,$thf( sk9 )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ x ) ))]]) ).
thf(1549,plain,
! [A: real] :
( ( ( auto_ll_on_flow0_a @ f @ x @ x2 @ A )
!= xx )
| ( ss != zero_zero_real )
| ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
!= ( uminus_uminus_real @ tt ) ) ),
inference(paramod_ordered,[status(thm)],[353,1526]) ).
thf(1553,plain,
! [A: real] :
( ( ( auto_ll_on_flow0_a @ f @ x @ x2 @ A )
!= xx )
| ( ss != zero_zero_real )
| ( ( uminus_uminus_real @ A )
!= tt ) ),
inference(simp,[status(thm)],[1549]) ).
thf(140,axiom,
! [A: real,B: a,C: real] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( ( member_real @ C @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) ) )
=> ( member_real @ ( plus_plus_real @ A @ C ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_local_Orev_Oexistence__ivl__trans) ).
thf(671,plain,
! [A: real,B: a,C: real] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( ( member_real @ C @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) ) )
=> ( member_real @ ( plus_plus_real @ A @ C ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(115,axiom,
! [A: real,B: real,C: a] :
( ( member_real @ ( plus_plus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_local_Orev_Oexistence__ivl__trans_H) ).
thf(581,plain,
! [A: real,B: real,C: a] :
( ( member_real @ ( plus_plus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(85,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_307_verit__negate__coefficient_I2_J) ).
thf(495,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)],[85]) ).
thf(1007,plain,
! [A: real] :
( ~ $true
| ( ( ord_less_real @ zero_zero_real @ tt )
!= ( ord_less_real @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[820,295]) ).
thf(1008,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ tt )
!= ( ord_less_real @ A @ A ) ),
inference(simp,[status(thm)],[1007]) ).
thf(1009,plain,
! [A: real] :
( ( zero_zero_real != A )
| ( tt != A ) ),
inference(simp,[status(thm)],[1008]) ).
thf(1010,plain,
tt != zero_zero_real,
inference(simp,[status(thm)],[1009]) ).
thf(226,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 @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_rev_Ogeneral_Oflow__in__domain) ).
thf(931,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 @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(101,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_143_minus__diff__commute) ).
thf(539,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)],[101]) ).
thf(241,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_319_diff__strict__mono) ).
thf(976,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)],[241]) ).
thf(146,axiom,
! [A: real,B: a] :
( ( member_real @ A @ top_top_set_real )
=> ( ( member_a @ B @ x )
=> ( ( auto_ll_on_flow0_a @ f @ x @ B @ ( minus_minus_real @ A @ A ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_general_Oflow__initial__time) ).
thf(688,plain,
! [A: real,B: a] :
( ( member_real @ A @ top_top_set_real )
=> ( ( member_a @ B @ x )
=> ( ( auto_ll_on_flow0_a @ f @ x @ B @ ( minus_minus_real @ A @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(1288,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( member_real @ ( uminus_uminus_real @ tt ) @ bot_bot_set_real )
| ( ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ) )
!= ( auto_l612940ivl0_a @ f @ x @ A ) ) ),
inference(paramod_ordered,[status(thm)],[560,1121]) ).
thf(1289,plain,
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( member_real @ ( uminus_uminus_real @ tt ) @ bot_bot_set_real ) ),
inference(pattern_uni,[status(thm)],[1288:[bind(A,$thf( auto_ll_on_flow0_a @ f @ x @ x2 @ ss ))]]) ).
thf(199,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_139_cancel__ab__semigroup__add__class_Odiff__right__commute) ).
thf(844,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)],[199]) ).
thf(93,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_12_general_Omem__existence__ivl__iv__defined_I2_J) ).
thf(517,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)],[93]) ).
thf(163,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) @ ( minus_minus_real @ zero_zero_real @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_local_Orev_Oflows__reverse) ).
thf(748,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) @ ( minus_minus_real @ zero_zero_real @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(2252,plain,
! [B: real,A: real] :
( ~ ( ord_less_real @ zero_zero_real @ B )
| ( zero_zero_real != zero_zero_real )
| ( ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) )
!= ( uminus_uminus_real @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1450,2045]) ).
thf(2253,plain,
! [B: real,A: real] :
( ~ ( ord_less_real @ zero_zero_real @ B )
| ( ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) )
!= ( uminus_uminus_real @ B ) ) ),
inference(simp,[status(thm)],[2252]) ).
thf(2254,plain,
! [A: real] :
~ ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[2253:[bind(A,$thf( D )),bind(B,$thf( plus_plus_real @ ( uminus_uminus_real @ D ) @ D ))]]) ).
thf(2290,plain,
! [A: real] :
~ ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) ),
inference(simp,[status(thm)],[2254]) ).
thf(1902,plain,
! [B: a,A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( initia826609931terval
@ ( collect_real
@ ^ [C: real] :
( member_real @ C
@ ( collect_real
@ ^ [D: real] : ( member_real @ D @ bot_bot_set_real ) ) ) ) )
| ( ( auto_l612940ivl0_a @ f @ x @ A )
!= ( auto_l612940ivl0_a @ f @ x @ B ) ) ),
inference(paramod_ordered,[status(thm)],[560,1206]) ).
thf(1903,plain,
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( initia826609931terval
@ ( collect_real
@ ^ [A: real] :
( member_real @ A
@ ( collect_real
@ ^ [B: real] : ( member_real @ B @ bot_bot_set_real ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1902:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(176,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_21_local_Omem__existence__ivl__iv__defined_I2_J) ).
thf(786,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)],[176]) ).
thf(174,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_70_mem__existence__ivl__shift__autonomous2) ).
thf(781,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)],[174]) ).
thf(992,plain,
! [A: real] :
( ~ $true
| ( ( ord_less_real @ i1 @ i2 )
!= ( ord_less_real @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[291,295]) ).
thf(993,plain,
! [A: real] :
( ( ord_less_real @ i1 @ i2 )
!= ( ord_less_real @ A @ A ) ),
inference(simp,[status(thm)],[992]) ).
thf(994,plain,
! [A: real] :
( ( i1 != A )
| ( i2 != A ) ),
inference(simp,[status(thm)],[993]) ).
thf(995,plain,
i2 != i1,
inference(simp,[status(thm)],[994]) ).
thf(110,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 )
=> ( ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) )
= ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_flow__shift__autonomous2) ).
thf(568,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(7251,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( B @ A )
!= ( member_a @ sk7
@ ( collect_a
@ ^ [C: a] : ( member_a @ C @ x ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[375,7207]) ).
thf(7266,plain,
( member_a @ sk7
@ ( collect_a
@ ^ [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ x ) ) ) ) ),
inference(pre_uni,[status(thm)],[7251:[bind(A,$thf( sk7 )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ ( collect_a @ ^ [D: a] : ( member_a @ D @ x ) ) ) ))]]) ).
thf(90,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( member_real @ ( minus_minus_real @ zero_zero_real @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_local_Orev_Oexistence__ivl__reverse) ).
thf(510,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( member_real @ ( minus_minus_real @ zero_zero_real @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(7713,plain,
! [A: a] :
( ( xx != zero_zero_a )
| ( tt != ss )
| ( ( auto_l612940ivl0_a @ f @ x @ A )
!= bot_bot_set_real )
| ~ $true
| ( ( member_a @ sk9 @ x )
!= ( member_a @ A @ x ) ) ),
inference(paramod_ordered,[status(thm)],[7676,2593]) ).
thf(7714,plain,
! [A: a] :
( ( xx != zero_zero_a )
| ( tt != ss )
| ( ( auto_l612940ivl0_a @ f @ x @ A )
!= bot_bot_set_real )
| ( ( member_a @ sk9 @ x )
!= ( member_a @ A @ x ) ) ),
inference(simp,[status(thm)],[7713]) ).
thf(7715,plain,
( ( xx != zero_zero_a )
| ( tt != ss )
| ( ( auto_l612940ivl0_a @ f @ x @ sk9 )
!= bot_bot_set_real ) ),
inference(pattern_uni,[status(thm)],[7714:[bind(A,$thf( sk9 ))]]) ).
thf(2597,plain,
! [A: real] :
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( xx != zero_zero_a )
| ( A != zero_zero_real )
| ( ( minus_minus_real @ A @ zero_zero_real )
!= ( minus_minus_real @ ss @ tt ) ) ),
inference(paramod_ordered,[status(thm)],[864,2583]) ).
thf(2605,plain,
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( xx != zero_zero_a )
| ( ( minus_minus_real @ ss @ tt )
!= ( minus_minus_real @ zero_zero_real @ zero_zero_real ) ) ),
inference(simp,[status(thm)],[2597]) ).
thf(3149,plain,
( ( member_real @ zero_zero_real @ top_top_set_real )
| ( xx != zero_zero_a )
| ( ( minus_minus_real @ ss @ tt )
!= ( uminus_uminus_real @ zero_zero_real ) ) ),
inference(rewrite,[status(thm)],[2605,669]) ).
thf(80,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(478,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(195,axiom,
! [A: real,B: real,C: real,D: a] :
( ( member_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ D ) )
=> ( ( member_real @ ( minus_minus_real @ A @ C ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ D ) )
=> ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ D @ ( minus_minus_real @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_rev_Ogeneral_Oexistence__ivl__trans_H) ).
thf(832,plain,
! [A: real,B: real,C: real,D: a] :
( ( member_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ D ) )
=> ( ( member_real @ ( minus_minus_real @ A @ C ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ D ) )
=> ( member_real @ B @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ D @ ( minus_minus_real @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(182,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 )
=> ( ! [D: real,E: real,F: a] :
( ( member_a @ F @ x )
=> ( ( uminus_uminus_a_a @ f @ F )
= ( uminus_uminus_a_a @ f @ F ) ) )
=> ( ( top_top_set_real = top_top_set_real )
=> ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_rev_Omem__existence__ivl__shift__autonomous2) ).
thf(800,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 )
=> ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(289,plain,
! [A: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
= ( ord_less_real @ A @ zero_zero_real ) ),
inference(cnf,[status(esa)],[288]) ).
thf(290,plain,
! [A: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
= ( ord_less_real @ A @ zero_zero_real ) ),
inference(lifteq,[status(thm)],[289]) ).
thf(220,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_145_closed__orbit__period__zero__fixed__point) ).
thf(914,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)],[220]) ).
thf(8102,plain,
( ( xx != zero_zero_a )
| ( tt != ss )
| ( ( ^ [A: a] : ( member_real @ zero_zero_real @ top_top_set_real ) )
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[6946]) ).
thf(168,axiom,
! [A: real,B: a] :
( ( member_real @ ( minus_minus_real @ A @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
= ( ( member_real @ A @ top_top_set_real )
& ( member_a @ B @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_rev_Ogeneral_Oexistence__ivl__initial__time__iff) ).
thf(763,plain,
! [A: real,B: a] :
( ( member_real @ ( minus_minus_real @ A @ A ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
= ( ( member_real @ A @ top_top_set_real )
& ( member_a @ B @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(271,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ A )
=> ! [B: real,C: real] :
( ( ord_less_real @ B @ C )
=> ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ),
inference(miniscope,[status(thm)],[270]) ).
thf(272,plain,
! [C: real,B: real,A: real] :
( ~ ( ord_less_real @ zero_zero_real @ A )
| ~ ( ord_less_real @ B @ C )
| ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ),
inference(cnf,[status(esa)],[271]) ).
thf(314,plain,
! [B: real,A: real] :
( ( A
= ( plus_plus_real @ B @ A ) )
= ( B = zero_zero_real ) ),
inference(cnf,[status(esa)],[313]) ).
thf(315,plain,
! [B: real,A: real] :
( ( A
= ( plus_plus_real @ B @ A ) )
= ( B = zero_zero_real ) ),
inference(lifteq,[status(thm)],[314]) ).
thf(3783,plain,
( ( xx != zero_zero_a )
| ( xx != x2 )
| ( ( uminus_uminus_real @ tt )
!= tt )
| ( ss != zero_zero_real )
| ( ( auto_l612940ivl0_a @ f @ x @ xx )
!= bot_bot_set_real )
| ~ $true
| ( ( member_real @ zero_zero_real @ top_top_set_real )
!= ( member_real @ zero_zero_real @ top_top_set_real ) ) ),
inference(paramod_ordered,[status(thm)],[2581,1013]) ).
thf(3784,plain,
( ( xx != zero_zero_a )
| ( xx != x2 )
| ( ( uminus_uminus_real @ tt )
!= tt )
| ( ss != zero_zero_real )
| ( ( auto_l612940ivl0_a @ f @ x @ xx )
!= bot_bot_set_real )
| ( ( member_real @ zero_zero_real @ top_top_set_real )
!= ( member_real @ zero_zero_real @ top_top_set_real ) ) ),
inference(simp,[status(thm)],[3783]) ).
thf(3785,plain,
( ( xx != zero_zero_a )
| ( xx != x2 )
| ( ( uminus_uminus_real @ tt )
!= tt )
| ( ss != zero_zero_real )
| ( ( auto_l612940ivl0_a @ f @ x @ xx )
!= bot_bot_set_real ) ),
inference(pattern_uni,[status(thm)],[3784:[]]) ).
thf(7710,plain,
! [A: a] :
( ( ( auto_l612940ivl0_a @ f @ x @ A )
!= bot_bot_set_real )
| ~ ( member_real @ zero_zero_real @ top_top_set_real )
| ~ $true
| ( ( member_a @ sk9 @ x )
!= ( member_a @ A @ x ) ) ),
inference(paramod_ordered,[status(thm)],[7676,831]) ).
thf(7711,plain,
! [A: a] :
( ( ( auto_l612940ivl0_a @ f @ x @ A )
!= bot_bot_set_real )
| ~ ( member_real @ zero_zero_real @ top_top_set_real )
| ( ( member_a @ sk9 @ x )
!= ( member_a @ A @ x ) ) ),
inference(simp,[status(thm)],[7710]) ).
thf(7712,plain,
( ( ( auto_l612940ivl0_a @ f @ x @ sk9 )
!= bot_bot_set_real )
| ~ ( member_real @ zero_zero_real @ top_top_set_real ) ),
inference(pattern_uni,[status(thm)],[7711:[bind(A,$thf( sk9 ))]]) ).
thf(205,axiom,
! [A: a] :
( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_rev_Operiodic__orbit__period_I2_J) ).
thf(865,plain,
! [A: a] :
( ( period138238489rbit_a @ ( uminus_uminus_a_a @ f ) @ x @ A )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ ( period1305449585riod_a @ ( uminus_uminus_a_a @ f ) @ x @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(996,plain,
! [A: real] :
( ~ $true
| ( ( ord_less_real @ zero_zero_real @ i1 )
!= ( ord_less_real @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[292,295]) ).
thf(997,plain,
! [A: real] :
( ( ord_less_real @ zero_zero_real @ i1 )
!= ( ord_less_real @ A @ A ) ),
inference(simp,[status(thm)],[996]) ).
thf(998,plain,
! [A: real] :
( ( zero_zero_real != A )
| ( i1 != A ) ),
inference(simp,[status(thm)],[997]) ).
thf(999,plain,
i1 != zero_zero_real,
inference(simp,[status(thm)],[998]) ).
thf(5298,plain,
! [B: real,A: real] :
( ~ $true
| ( ( ord_less_real @ A @ ( plus_plus_real @ A @ d ) )
!= ( ord_less_real @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4431,295]) ).
thf(5299,plain,
! [B: real,A: real] :
( ( ord_less_real @ A @ ( plus_plus_real @ A @ d ) )
!= ( ord_less_real @ B @ B ) ),
inference(simp,[status(thm)],[5298]) ).
thf(5333,plain,
! [B: real,A: real] :
( ( A != B )
| ( ( plus_plus_real @ A @ d )
!= B ) ),
inference(simp,[status(thm)],[5299]) ).
thf(5357,plain,
! [A: real] :
( ( plus_plus_real @ A @ d )
!= A ),
inference(simp,[status(thm)],[5333]) ).
thf(58,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_add__strict__left__mono) ).
thf(410,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ A @ B )
=> ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(238,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) @ ( minus_minus_real @ zero_zero_real @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_local_Oflows__reverse) ).
thf(967,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ B @ A ) @ ( minus_minus_real @ zero_zero_real @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(109,axiom,
! [A: real,B: real,C: a,D: real] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( ( member_real @ D @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ ( plus_plus_real @ A @ D ) @ B ) )
= ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_general_Oflow__trans) ).
thf(564,plain,
! [A: real,B: real,C: a,D: real] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ f @ x @ C ) )
=> ( ( member_real @ D @ ( auto_l612940ivl0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) ) )
=> ( ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ ( plus_plus_real @ A @ D ) @ B ) )
= ( auto_ll_on_flow0_a @ f @ x @ ( auto_ll_on_flow0_a @ f @ x @ C @ ( minus_minus_real @ A @ B ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(340,plain,
! [A: a] :
( ( zero_zero_a = A )
= ( A = zero_zero_a ) ),
inference(cnf,[status(esa)],[339]) ).
thf(341,plain,
! [A: a] :
( ( zero_zero_a = A )
= ( A = zero_zero_a ) ),
inference(lifteq,[status(thm)],[340]) ).
thf(185,axiom,
! [A: a] :
( ~ ( member_a @ A @ x )
=> ( ( auto_l612940ivl0_a @ f @ x @ A )
= bot_bot_set_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_local_Oexistence__ivl__undefined) ).
thf(807,plain,
! [A: a] :
( ~ ( member_a @ A @ x )
=> ( ( auto_l612940ivl0_a @ f @ x @ A )
= bot_bot_set_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(89,axiom,
! [A: a,B: real] :
( ( member_a @ A @ x )
=> ( ( ( uminus_uminus_a_a @ f @ A )
= zero_zero_a )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_rev_Ofixpoint__sol_I2_J) ).
thf(506,plain,
! [A: a,B: real] :
( ( member_a @ A @ x )
=> ( ( ( uminus_uminus_a_a @ f @ A )
= zero_zero_a )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(10,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
=> ( ord_less_real @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_add__less__imp__less__right) ).
thf(268,plain,
! [A: real,B: real,C: real] :
( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
=> ( ord_less_real @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6482,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( member_real @ tt @ ( auto_l612940ivl0_a @ f @ x @ xx ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[644,375]) ).
thf(6537,plain,
( member_a @ xx
@ ( collect_a
@ ^ [A: a] : ( member_real @ tt @ ( auto_l612940ivl0_a @ f @ x @ A ) ) ) ),
inference(pre_uni,[status(thm)],[6482:[bind(A,$thf( xx )),bind(B,$thf( ^ [C: a] : ( member_real @ tt @ ( auto_l612940ivl0_a @ f @ x @ C ) ) ))]]) ).
thf(282,plain,
! [A: real] :
( ( zero_zero_real
= ( uminus_uminus_real @ A ) )
= ( zero_zero_real = A ) ),
inference(cnf,[status(esa)],[281]) ).
thf(283,plain,
! [A: real] :
( ( zero_zero_real
= ( uminus_uminus_real @ A ) )
= ( zero_zero_real = A ) ),
inference(lifteq,[status(thm)],[282]) ).
thf(213,axiom,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_diff__zero) ).
thf(886,plain,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(225,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A )
= B )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ ( uminus_uminus_real @ A ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_rev_Orecurrence__time__flip__sign_I2_J) ).
thf(928,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A )
= B )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ ( uminus_uminus_real @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(394,plain,
! [B: real,A: real] :
( ( A
= ( plus_plus_real @ A @ B ) )
= ( B = zero_zero_real ) ),
inference(cnf,[status(esa)],[393]) ).
thf(395,plain,
! [B: real,A: real] :
( ( A
= ( plus_plus_real @ A @ B ) )
= ( B = zero_zero_real ) ),
inference(lifteq,[status(thm)],[394]) ).
thf(75,axiom,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_verit__sum__simplify) ).
thf(464,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(113,axiom,
! [A: a,B: real] :
( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B )
= ( auto_ll_on_flow0_a @ f @ x @ A @ ( uminus_uminus_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_rev__eq__flow) ).
thf(575,plain,
! [A: a,B: real] :
( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ B )
= ( auto_ll_on_flow0_a @ f @ x @ A @ ( uminus_uminus_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(4334,plain,
! [B: real,A: real] :
( ~ ( ord_less_real @ B @ zero_zero_real )
| ( zero_zero_real != zero_zero_real )
| ( ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) )
!= ( uminus_uminus_real @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1450,2184]) ).
thf(4335,plain,
! [B: real,A: real] :
( ~ ( ord_less_real @ B @ zero_zero_real )
| ( ( uminus_uminus_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) )
!= ( uminus_uminus_real @ B ) ) ),
inference(simp,[status(thm)],[4334]) ).
thf(4336,plain,
! [A: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) @ zero_zero_real ),
inference(pattern_uni,[status(thm)],[4335:[bind(A,$thf( D )),bind(B,$thf( plus_plus_real @ ( uminus_uminus_real @ D ) @ D ))]]) ).
thf(4382,plain,
! [A: real] :
~ ( ord_less_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A ) @ zero_zero_real ),
inference(simp,[status(thm)],[4336]) ).
thf(244,axiom,
! [A: real,B: real,C: real] :
( ( A
= ( minus_minus_real @ B @ C ) )
= ( ( plus_plus_real @ A @ C )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_eq__diff__eq) ).
thf(982,plain,
! [A: real,B: real,C: real] :
( ( A
= ( minus_minus_real @ B @ C ) )
= ( ( plus_plus_real @ A @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(7677,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( member_a @ sk9
@ ( collect_a
@ ^ [C: a] : ( member_a @ C @ x ) ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7663,375]) ).
thf(7694,plain,
( member_a @ sk9
@ ( collect_a
@ ^ [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ x ) ) ) ) ),
inference(pre_uni,[status(thm)],[7677:[bind(A,$thf( sk9 )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ ( collect_a @ ^ [D: a] : ( member_a @ D @ x ) ) ) ))]]) ).
thf(207,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
= ( minus_minus_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_uminus__add__conv__diff) ).
thf(871,plain,
! [A: real,B: real] :
( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
= ( minus_minus_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(74,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_add__right__imp__eq) ).
thf(459,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(45,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( A = B )
& ( ord_less_real @ C @ D ) )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_add__mono__thms__linordered__field_I2_J) ).
thf(369,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( A = B )
& ( ord_less_real @ C @ D ) )
=> ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(123,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( ( ( auto_ll_on_flow0_a @ f @ x @ B @ A )
= B )
=> ( member_real @ ( uminus_uminus_real @ A ) @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_recurrence__time__flip__sign_I1_J) ).
thf(607,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ f @ x @ B ) )
=> ( ( ( auto_ll_on_flow0_a @ f @ x @ B @ A )
= B )
=> ( member_real @ ( uminus_uminus_real @ A ) @ ( auto_l612940ivl0_a @ f @ x @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(253,plain,
! [B: real > $o,A: real > $o] :
( ( ( A @ ( sk2 @ B @ A ) )
!= ( B @ ( sk2 @ B @ A ) ) )
| ( ( collect_real @ A )
= ( collect_real @ B ) ) ),
inference(cnf,[status(esa)],[252]) ).
thf(254,plain,
! [B: real > $o,A: real > $o] :
( ( ( A @ ( sk2 @ B @ A ) )
!= ( B @ ( sk2 @ B @ A ) ) )
| ( ( collect_real @ A )
= ( collect_real @ B ) ) ),
inference(lifteq,[status(thm)],[253]) ).
thf(82,axiom,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_add_Oright__neutral) ).
thf(486,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(229,axiom,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( member_a @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_local_Orev_Oflow__in__domain) ).
thf(940,plain,
! [A: real,B: a] :
( ( member_real @ A @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ B ) )
=> ( member_a @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ B @ A ) @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(308,plain,
! [B: real,A: real] :
( ( ( plus_plus_real @ A @ B )
= B )
= ( A = zero_zero_real ) ),
inference(cnf,[status(esa)],[307]) ).
thf(309,plain,
! [B: real,A: real] :
( ( ( plus_plus_real @ A @ B )
= B )
= ( A = zero_zero_real ) ),
inference(lifteq,[status(thm)],[308]) ).
thf(142,axiom,
! [A: real,B: real,C: a,D: real] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( ( member_real @ D @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) ) )
=> ( member_real @ ( minus_minus_real @ ( plus_plus_real @ A @ D ) @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_rev_Ogeneral_Oexistence__ivl__trans) ).
thf(676,plain,
! [A: real,B: real,C: a,D: real] :
( ( member_real @ ( minus_minus_real @ A @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) )
=> ( ( member_real @ D @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ C @ ( minus_minus_real @ A @ B ) ) ) )
=> ( member_real @ ( minus_minus_real @ ( plus_plus_real @ A @ D ) @ B ) @ ( auto_l612940ivl0_a @ ( uminus_uminus_a_a @ f ) @ x @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(211,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_211_rev_Operiodic__orbit__period_I1_J) ).
thf(882,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)],[211]) ).
thf(172,axiom,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
=> ( ( member_a @ A @ x )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ zero_zero_real )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_local_Orev_Oflow__initial__time) ).
thf(775,plain,
! [A: a] :
( ( member_real @ zero_zero_real @ top_top_set_real )
=> ( ( member_a @ A @ x )
=> ( ( auto_ll_on_flow0_a @ ( uminus_uminus_a_a @ f ) @ x @ A @ zero_zero_real )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(9854,plain,
$false,
inference(e,[status(thm)],[645,629,365,760,347,1315,962,666,1110,481,333,249,3509,449,247,379,440,614,597,276,6868,8733,385,384,797,715,814,3414,945,670,500,2184,404,841,973,288,301,3140,1904,651,257,724,719,4415,587,1279,2488,357,2745,542,917,751,802,344,817,416,325,316,261,7226,1013,284,475,492,1450,591,443,321,834,353,821,376,2259,6841,348,4751,280,8774,293,988,981,766,877,692,396,1526,527,312,307,292,4962,270,793,8382,810,381,534,714,1206,452,920,248,512,942,439,3265,925,2737,366,2589,910,957,825,952,2596,820,561,392,429,729,260,862,6528,3233,407,275,788,847,252,879,889,757,682,551,1281,324,467,7663,1296,665,583,522,697,874,615,1121,725,1006,388,356,7204,610,783,519,742,578,1017,2685,980,403,328,884,7189,339,933,554,669,526,6946,3143,6518,537,4425,489,8499,679,1039,970,985,515,654,8410,2581,569,779,503,622,837,393,1114,266,360,805,2748,398,674,530,298,6507,264,856,745,601,618,2413,296,3274,375,733,904,423,6870,772,6581,2568,711,291,281,545,413,936,313,1312,335,947,350,382,7201,572,7191,831,2422,419,990,362,318,979,604,900,406,3419,736,1043,434,494,345,6800,594,3932,621,700,251,2593,626,769,330,685,399,959,695,455,306,299,431,8763,278,868,267,851,8922,922,473,722,426,2665,795,548,255,1277,648,342,1018,754,823,2582,1547,525,557,640,295,327,954,739,263,310,2747,791,1038,1785,470,359,1218,907,336,703,7207,4431,446,497,859,2579,864,7676,2045,363,1553,671,581,495,6867,1010,931,539,976,688,903,1289,844,813,517,319,748,2290,1903,304,258,351,2431,786,781,995,2262,2786,568,7266,510,7715,667,3149,478,832,800,290,914,378,8102,763,272,315,3785,7712,1527,273,865,373,999,5357,410,967,564,341,2186,807,437,828,506,268,897,474,6537,283,886,928,395,464,332,575,4382,2265,644,982,7694,277,871,459,2583,369,607,254,322,486,940,354,309,676,454,882,775,560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP146^1 : 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
% 0.10/0.22 % Computer : n018.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 20:02:56 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 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
% 1.02/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.32/1.22 % [INFO] Parsing done (392ms).
% 2.32/1.23 % [INFO] Running in sequential loop mode.
% 3.79/1.63 % [INFO] eprover registered as external prover.
% 3.79/1.63 % [INFO] Scanning for conjecture ...
% 4.03/1.79 % [INFO] Found a conjecture (or negated_conjecture) and 342 axioms. Running axiom selection ...
% 4.63/1.94 % [INFO] Axiom selection finished. Selected 244 axioms (removed 98 axioms).
% 5.46/2.18 % [INFO] Problem is higher-order (TPTP THF).
% 5.71/2.20 % [INFO] Type checking passed.
% 5.71/2.20 % [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 ...
% 77.85/20.32 % External prover 'e' found a proof!
% 77.85/20.32 % [INFO] Killing All external provers ...
% 77.85/20.32 % Time passed: 19949ms (effective reasoning time: 19084ms)
% 77.85/20.33 % 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)>
% 77.85/20.33 % Axioms used in derivation (244): fact_307_verit__negate__coefficient_I2_J, fact_263_add__strict__mono, fact_76_rev_Orecurrence__time__flip__sign_I2_J, fact_185_add__cancel__right__right, fact_81_rev_Oclosed__orbit__global__existence, fact_200_add__diff__cancel__right_H, fact_48_Collect__mem__eq, fact_175_add_Oright__neutral, fact_78_rev_Ofixpoint__sol_I1_J, fact_196_minus__add__cancel, fact_77_rev_Orecurrence__time__flip__sign_I1_J, fact_335_add__diff__eq, fact_157_add__left__cancel, fact_187_neg__less__iff__less, fact_73_rev_Ogeneral_Oexistence__ivl__reverse, fact_249_add__neg__neg, fact_303_add_Ocomm__neutral, fact_273_add_Oleft__commute, fact_57_rev__eq__flow, fact_71_general_Omem__existence__ivl__subset, fact_251_add__pos__pos, fact_213_tt_I2_J, fact_67_rev_Ogeneral_Omem__existence__ivl__subset, fact_119_local_Orev_Oexistence__ivl__initial__time__iff, fact_113_minus__diff__eq, fact_283_group__cancel_Oadd2, fact_313_diff__strict__right__mono, fact_22_local_Oflow__in__domain, fact_122_local_Orev_Oflow__initial__time, fact_10_general_Oflow__in__domain, fact_237_add_Oright__inverse, fact_120_local_Omem__existence__ivl__iv__defined_I1_J, fact_34_local_Oexistence__ivl__reverse, fact_291_add__mono__thms__linordered__field_I2_J, fact_147_periodic__orbit__period_I2_J, fact_8_diff__existence__ivl__trans, fact_225_add__less__same__cancel2, fact_325_add__implies__diff, fact_54_local_Orev_Omem__existence__ivl__subset, fact_7_neg__tt__ex, fact_192_add__less__cancel__left, fact_230_double__add__less__zero__iff__single__add__less__zero, fact_107_diff__0__right, fact_223_add__less__same__cancel1, fact_1__092_060open_062flow0_A_Iflow0_Axx_Att_J_A_I_N_Att_J_A_061_Aflow0_A_Iflow0_Ax_Ass_J_A_I_N_Att_J_092_060close_062, fact_53_rev_Ogeneral_Omem__existence__ivl__iv__defined_I2_J, fact_75_rev_Ogeneral_Oflows__reverse, fact_194_add__minus__cancel, fact_89_flow__shift__autonomous2, fact_115_local_Orev_Omem__existence__ivl__iv__defined_I2_J, fact_241_diff__minus__eq__add, fact_244_local_Oexistence__ivl__empty__iff, fact_70_mem__existence__ivl__shift__autonomous2, fact_58_rev_Ofixpoint__sol_I2_J, fact_148_rev_Ofixed__point__imp__closed__orbit__period__zero_I2_J, fact_214_rev_Oclosed__orbitE, fact_231_linordered__ab__group__add__class_Ozero__less__double__add__iff__zero__less__single__add, fact_26_closed__orbit__periodic, fact_33_local_Oflows__reverse, fact_257_add__less__imp__less__left, fact_15_fixed__point__imp__closed__orbit__period__zero_I1_J, fact_66_rev_Omem__existence__ivl__shift__autonomous2, fact_160_local_Oexistence__ivl__trans_H, fact_72_rev_Odiff__existence__ivl__trans, fact_135_verit__negate__coefficient_I3_J, fact_91_local_Oflow__initial__time__if, fact_0__092_060open_062xx_A_092_060in_062_AX_092_060close_062, fact_3_assms_I8_J, fact_50_Collect__cong, fact_285_group__cancel_Oadd1, fact_183_add__cancel__right__left, fact_211_rev_Operiodic__orbit__period_I1_J, fact_287_add__mono__thms__linordered__semiring_I4_J, fact_227_less__add__same__cancel1, fact_20_general_Oflow__undefined0, fact_275_add_Ocommute, fact_329_diff__add__eq__diff__diff__swap, fact_161_local_Oexistence__ivl__trans, fact_188_closed__orbitE, fact_212_periodic__orbit__def, fact_327_diff__diff__add, fact_94_rev_Ogeneral_Oflow__initial__time__if, fact_149_fixed__point__imp__closed__orbit__period__zero_I2_J, fact_317_diff__eq__diff__less, fact_60_rev_Omvar_Ointerval__axioms, fact_166_general_Oflow__trans, fact_242_local_Oexistence__ivl__undefined, fact_96_neg__equal__zero, fact_337_eq__diff__eq, fact_277_add_Oright__cancel, fact_105_diff__self, fact_17_recurrence__time__flip__sign_I2_J, fact_297_verit__comp__simplify1_I1_J, fact_144_rev_Oclosed__orbit__period__zero__fixed__point, fact_56_rev_Orev__eq__flow, fact_92_rev_Oclosed__orbit__def, fact_19_closed__orbitI, fact_295_ab__semigroup__add__class_Oadd__ac_I1_J, fact_126_rev_Ogeneral_Oflow__initial__time, fact_16_recurrence__time__flip__sign_I1_J, fact_176_linordered__ab__group__add__class_Odouble__zero, fact_158_d, fact_24_mvar_Ointerval__axioms, fact_155_add__right__cancel, fact_341_group__cancel_Osub1, fact_281_add_Oassoc, fact_255_add__less__imp__less__right, fact_167_general_Oexistence__ivl__trans_H, fact_85_rev_Oclosed__orbit__periodic, fact_37_rev_Oclosed__orbit__eq__rev, fact_101_neg__0__equal__iff__equal, fact_46_mem__Collect__eq, fact_32_closed__orbit__def, fact_177_double__zero__sym, fact_141_eq__iff__diff__eq__0, fact_9_general_Oexistence__ivl__reverse, fact_29_diff__0, fact_145_closed__orbit__period__zero__fixed__point, fact_173_add_Oleft__neutral, fact_31_verit__minus__simplify_I3_J, fact_62_local_Orev_Oexistence__ivl__initial__time, fact_25_periodic__orbitI, fact_168_general_Oexistence__ivl__trans, fact_179_add__cancel__left__left, fact_139_cancel__ab__semigroup__add__class_Odiff__right__commute, fact_18_local_Oflow__undefined0, fact_114_tt_I1_J, fact_27_periodic__orbit__imp__flow0__regular, fact_4_tt__ex, fact_90_local_Orev_Oflow__initial__time__if, fact_279_add_Oleft__cancel, fact_5_ss__ex, fact_259_add__strict__right__mono, fact_215_rev_Operiodic__orbit__def, fact_153_i2_I2_J, fact_125_general_Oexistence__ivl__initial__time__iff, fact_165_local_Orev_Oexistence__ivl__trans, fact_309_less__minus__iff, fact_82_closed__orbit__global__existence, fact_79_fixpoint__sol_I1_J, fact_63_local_Oexistence__ivl__initial__time, fact_261_add__strict__left__mono, fact_11_general_Oflows__reverse, fact_221_neg__less__0__iff__less, fact_339_diff__eq__eq, fact_65_rev_Ogeneral_Oexistence__ivl__initial__time, fact_116_rev_Oflow0__defined, fact_80_local_Orev_Oflow__undefined0, fact_323_add_Oinverse__distrib__swap, fact_206_add__diff__cancel__left, fact_127_general_Oflow__initial__time, fact_235_add_Oleft__inverse, fact_204_add__diff__cancel__left_H, fact_333_diff__diff__eq2, fact_88_rev_Oflow__shift__autonomous2, fact_305_add_Ogroup__left__neutral, fact_124_rev_Ogeneral_Oexistence__ivl__initial__time__iff, fact_143_minus__diff__commute, fact_45_rev_Oexistence__ivl__zero, fact_121_local_Oexistence__ivl__initial__time__iff, fact_61_rev_Ofixed__point__imp__closed__orbit__period__zero_I1_J, fact_129_zero__reorient, fact_21_local_Omem__existence__ivl__iv__defined_I2_J, fact_51_Collect__cong, fact_202_add__diff__cancel__right, fact_163_local_Orev_Oflow__trans, fact_271_diff__less__eq, fact_111_cancel__comm__monoid__add__class_Odiff__cancel, fact_216_less__neg__neg, fact_181_add__cancel__left__right, fact_84_rev_Operiodic__orbit__imp__flow0__regular, fact_162_i2_I3_J, fact_169_periodic__orbit__period_I1_J, fact_59_rev_Oclosed__orbit__flow0, fact_118_local_Orev_Omem__existence__ivl__iv__defined_I1_J, fact_265_add__right__imp__eq, fact_42_add_Oinverse__inverse, fact_269_less__diff__eq, fact_74_rev_Ogeneral_Oflow__in__domain, fact_49_Collect__mem__eq, fact_164_local_Orev_Oexistence__ivl__trans_H, fact_64_rev_Ogeneral_Omem__existence__ivl__iv__defined_I1_J, fact_2_eq, fact_99_neg__equal__0__iff__equal, fact_117_local_Orev_Oflow__in__domain, fact_152_rev_Ogeneral_Oexistence__ivl__trans, fact_86_local_Orev_Oexistence__ivl__reverse, fact_6_fixpoint__sol_I2_J, fact_243_local_Orev_Oexistence__ivl__undefined, fact_55_local_Omem__existence__ivl__subset, fact_87_local_Orev_Oflows__reverse, fact_52_existence__ivl__zero, fact_245_local_Oexistence__ivl__empty1, fact_150_local_Orev_Oexistence__ivl__notempty, fact_35_general_Oflow__initial__time__if, fact_315_diff__strict__left__mono, fact_253_pos__add__strict, fact_36_interval__axioms, fact_109_diff__zero, fact_13_closed__orbit__flow0, fact_171_rev_Ogeneral_Oexistence__ivl__trans_H, fact_128_zero__reorient, fact_311_minus__less__iff, fact_198_minus__add__distrib, fact_299_verit__sum__simplify, fact_151_local_Oexistence__ivl__notempty, fact_83_rev_Oclosed__orbitI, fact_319_diff__strict__mono, fact_133_equation__minus__iff, fact_69_general_Oexistence__ivl__initial__time, fact_14_closed__orbit__in__domain, fact_23_flow0__defined, fact_38_rev_Oclosed__orbit__in__domain, fact_47_mem__Collect__eq, fact_219_neg__0__less__iff__less, fact_137_diff__eq__diff__eq, fact_95_rev_Operiodic__orbitI, fact_97_equal__neg__zero, fact_246_local_Orev_Oexistence__ivl__empty__iff, fact_12_general_Omem__existence__ivl__iv__defined_I2_J, fact_293_add__mono__thms__linordered__field_I5_J, fact_170_rev_Ogeneral_Oflow__trans, fact_229_less__add__same__cancel2, fact_93_rev_Ogeneral_Oflow__undefined0, fact_68_general_Omem__existence__ivl__iv__defined_I1_J, fact_301_comm__monoid__add__class_Oadd__0, fact_267_add__left__imp__eq, fact_103_add_Oinverse__neutral, fact_239_uminus__add__conv__diff, fact_146_rev_Operiodic__orbit__period_I2_J, fact_217_neg__less__pos, fact_233_diff__gt__0__iff__gt, fact_159_local_Oflow__trans, fact_44_verit__minus__simplify_I4_J, fact_40_neg__equal__iff__equal, fact_289_add__mono__thms__linordered__field_I1_J, fact_208_diff__add__cancel, fact_247_local_Orev_Oexistence__ivl__empty1, fact_190_add__less__cancel__right, fact_210_add__diff__cancel, fact_123_local_Oflow__initial__time, fact_321_group__cancel_Oneg1, fact_331_diff__add__eq, fact_131_minus__equation__iff
% 77.85/20.33 % No. of inferences in proof: 902
% 77.85/20.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 19949 ms resp. 19084 ms w/o parsing
% 76.64/20.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 76.64/20.63 % [INFO] Killing All external provers ...
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