%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP115^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n007.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 08:06:49 AM UTC 2026
% Result : Theorem 9.87s 3.44s
% Output : Refutation 10.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 138
% Syntax : Number of formulae : 278 ( 152 unt; 0 typ; 0 def)
% Number of atoms : 728 ( 316 equ; 6 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 2214 ( 128 ~; 6 |; 94 &;1740 @)
% ( 0 <=>; 246 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 6 con; 0-2 aty)
% Number of variables : 692 ( 36 ^; 624 !; 32 ?; 692 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_b_type,type,
set_b: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(minus_minus_set_b_decl,type,
minus_minus_set_b: set_b > set_b > set_b ).
thf(inf_inf_set_b_decl,type,
inf_inf_set_b: set_b > set_b > set_b ).
thf(lower_464587817at_a_b_decl,type,
lower_464587817at_a_b: a > ( a > b ) > $o ).
thf(bot_bot_b_o_decl,type,
bot_bot_b_o: b > $o ).
thf(bot_bot_set_b_decl,type,
bot_bot_set_b: set_b ).
thf(ord_less_eq_b_decl,type,
ord_less_eq_b: b > b > $o ).
thf(insert_b_decl,type,
insert_b: b > set_b > set_b ).
thf(is_empty_b_decl,type,
is_empty_b: set_b > $o ).
thf(is_singleton_b_decl,type,
is_singleton_b: set_b > $o ).
thf(the_elem_b_decl,type,
the_elem_b: set_b > b ).
thf(topolo1276428101open_a_decl,type,
topolo1276428101open_a: set_a > $o ).
thf(topolo1276428102open_b_decl,type,
topolo1276428102open_b: set_b > $o ).
thf(member_a_decl,type,
member_a: a > set_a > $o ).
thf(member_b_decl,type,
member_b: b > set_b > $o ).
thf(a2_decl,type,
a2: b ).
thf(f_decl,type,
f: a > b ).
thf(thesis_decl,type,
thesis: $o ).
thf(x0_decl,type,
x0: a ).
thf(56,axiom,
! [A: b,B: b,C: b] :
( ( ord_less_eq_b @ A @ B )
=> ( ( ord_less_eq_b @ B @ C )
=> ( ord_less_eq_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_order_Otrans) ).
thf(336,plain,
! [A: b,B: b,C: b] :
( ( ord_less_eq_b @ A @ B )
=> ( ( ord_less_eq_b @ B @ C )
=> ( ord_less_eq_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(78,axiom,
! [A: set_b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ C )
= ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_inf__assoc) ).
thf(422,plain,
! [A: set_b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ C )
= ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(102,axiom,
! [A: set_b] :
( ( ! [B: b] :
~ ( member_b @ B @ A ) )
= ( A = bot_bot_set_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_all__not__in__conv) ).
thf(518,plain,
! [A: set_b] :
( ( ! [B: b] :
~ ( member_b @ B @ A ) )
= ( A = bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(55,axiom,
! [A: set_b,B: b,C: set_b] :
( ( minus_minus_set_b @ A @ ( insert_b @ B @ C ) )
= ( minus_minus_set_b @ ( minus_minus_set_b @ A @ C ) @ ( insert_b @ B @ bot_bot_set_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_Diff__insert) ).
thf(333,plain,
! [A: set_b,B: b,C: set_b] :
( ( minus_minus_set_b @ A @ ( insert_b @ B @ C ) )
= ( minus_minus_set_b @ ( minus_minus_set_b @ A @ C ) @ ( insert_b @ B @ bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(32,axiom,
! [A: set_b,B: b] :
( ( topolo1276428102open_b @ A )
=> ( topolo1276428102open_b @ ( minus_minus_set_b @ A @ ( insert_b @ B @ bot_bot_set_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_open__delete) ).
thf(249,plain,
! [A: set_b,B: b] :
( ( topolo1276428102open_b @ A )
=> ( topolo1276428102open_b @ ( minus_minus_set_b @ A @ ( insert_b @ B @ bot_bot_set_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(93,axiom,
! [A: set_b,B: set_b] :
( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ B )
= ( inf_inf_set_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_inf__right__idem) ).
thf(481,plain,
! [A: set_b,B: set_b] :
( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ B )
= ( inf_inf_set_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(61,axiom,
! [A: b,B: b,C: set_b] :
( ( member_b @ A @ ( insert_b @ B @ C ) )
=> ( ( A != B )
=> ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_insertE) ).
thf(352,plain,
! [A: b,B: b,C: set_b] :
( ( member_b @ A @ ( insert_b @ B @ C ) )
=> ( ( A != B )
=> ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(104,axiom,
! [A: set_b] :
( ( inf_inf_set_b @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_inf__idem) ).
thf(523,plain,
! [A: set_b] :
( ( inf_inf_set_b @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(22,axiom,
! [A: b] : ( is_singleton_b @ ( insert_b @ A @ bot_bot_set_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_is__singletonI) ).
thf(217,plain,
! [A: b] : ( is_singleton_b @ ( insert_b @ A @ bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(129,axiom,
! [A: b,B: set_b,C: set_b] :
( ~ ( member_b @ A @ B )
=> ( ( inf_inf_set_b @ ( insert_b @ A @ C ) @ B )
= ( inf_inf_set_b @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_Int__insert__left__if0) ).
thf(614,plain,
! [A: b,B: set_b,C: set_b] :
( ~ ( member_b @ A @ B )
=> ( ( inf_inf_set_b @ ( insert_b @ A @ C ) @ B )
= ( inf_inf_set_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(113,axiom,
! [A: set_b,B: set_b] :
( ( ( inf_inf_set_b @ A @ B )
= bot_bot_set_b )
= ( ! [C: b] :
( ( member_b @ C @ A )
=> ~ ( member_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_disjoint__iff) ).
thf(550,plain,
! [A: set_b,B: set_b] :
( ( ( inf_inf_set_b @ A @ B )
= bot_bot_set_b )
= ( ! [C: b] :
( ( member_b @ C @ A )
=> ~ ( member_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(96,axiom,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( inf_inf_set_b @ B @ C ) )
=> ( member_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_IntD1) ).
thf(500,plain,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( inf_inf_set_b @ B @ C ) )
=> ( member_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(74,axiom,
! [A: b,B: b] :
( ( A != B )
= ( ? [C: set_b] :
( ( topolo1276428102open_b @ C )
& ( member_b @ A @ C )
& ~ ( member_b @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_separation__t1) ).
thf(404,plain,
! [A: b,B: b] :
( ( A != B )
= ( ? [C: set_b] :
( ( topolo1276428102open_b @ C )
& ( member_b @ A @ C )
& ~ ( member_b @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(83,axiom,
! [A: b,B: b] :
( ( member_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_singletonD) ).
thf(436,plain,
! [A: b,B: b] :
( ( member_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(69,axiom,
! [A: set_b,B: b,C: set_b] :
( ( ( inf_inf_set_b @ A @ ( insert_b @ B @ C ) )
= bot_bot_set_b )
= ( ~ ( member_b @ B @ A )
& ( ( inf_inf_set_b @ A @ C )
= bot_bot_set_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_disjoint__insert_I1_J) ).
thf(389,plain,
! [A: set_b,B: b,C: set_b] :
( ( ( inf_inf_set_b @ A @ ( insert_b @ B @ C ) )
= bot_bot_set_b )
= ( ~ ( member_b @ B @ A )
& ( ( inf_inf_set_b @ A @ C )
= bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(66,axiom,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ~ ! [C: set_b] :
( ( B
= ( insert_b @ A @ C ) )
=> ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_Set_Oset__insert) ).
thf(372,plain,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ~ ! [C: set_b] :
( ( B
= ( insert_b @ A @ C ) )
=> ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(110,axiom,
( a2
!= ( f @ x0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062) ).
thf(542,plain,
( a2
!= ( f @ x0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(116,axiom,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( inf_inf_set_b @ B @ C ) )
= ( ( member_b @ A @ B )
& ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Int__iff) ).
thf(559,plain,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( inf_inf_set_b @ B @ C ) )
= ( ( member_b @ A @ B )
& ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(13,axiom,
! [A: set_b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ ( minus_minus_set_b @ A @ B ) @ C )
= ( minus_minus_set_b @ ( inf_inf_set_b @ A @ C ) @ ( inf_inf_set_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_Diff__Int__distrib2) ).
thf(189,plain,
! [A: set_b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ ( minus_minus_set_b @ A @ B ) @ C )
= ( minus_minus_set_b @ ( inf_inf_set_b @ A @ C ) @ ( inf_inf_set_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(45,axiom,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
=> ~ ( ( member_b @ A @ B )
=> ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_DiffE) ).
thf(289,plain,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
=> ~ ( ( member_b @ A @ B )
=> ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(86,axiom,
! [A: b,B: b] :
( ( A != B )
=> ? [C: set_b,D: set_b] :
( ( topolo1276428102open_b @ C )
& ( topolo1276428102open_b @ D )
& ( member_b @ A @ C )
& ( member_b @ B @ D )
& ( ( inf_inf_set_b @ C @ D )
= bot_bot_set_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_hausdorff) ).
thf(448,plain,
! [A: b,B: b] :
( ( A != B )
=> ? [C: set_b,D: set_b] :
( ( topolo1276428102open_b @ C )
& ( topolo1276428102open_b @ D )
& ( member_b @ A @ C )
& ( member_b @ B @ D )
& ( ( inf_inf_set_b @ C @ D )
= bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(51,axiom,
! [A: b,B: b,C: b,D: b] :
( ( ( insert_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
= ( insert_b @ C @ ( insert_b @ D @ bot_bot_set_b ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_doubleton__eq__iff) ).
thf(316,plain,
! [A: b,B: b,C: b,D: b] :
( ( ( insert_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
= ( insert_b @ C @ ( insert_b @ D @ bot_bot_set_b ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(7,axiom,
! [A: b > b > $o,B: b,C: b] :
( ! [D: b,E: b] :
( ( ord_less_eq_b @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: b,E: b] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_linorder__wlog) ).
thf(164,plain,
! [A: b > b > $o,B: b,C: b] :
( ! [D: b,E: b] :
( ( ord_less_eq_b @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: b,E: b] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(124,axiom,
! [A: set_b,B: set_b,C: set_b,D: set_b] :
( ( A
= ( inf_inf_set_b @ B @ C ) )
=> ( ( inf_inf_set_b @ D @ A )
= ( inf_inf_set_b @ B @ ( inf_inf_set_b @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_boolean__algebra__cancel_Oinf2) ).
thf(591,plain,
! [A: set_b,B: set_b,C: set_b,D: set_b] :
( ( A
= ( inf_inf_set_b @ B @ C ) )
=> ( ( inf_inf_set_b @ D @ A )
= ( inf_inf_set_b @ B @ ( inf_inf_set_b @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(85,axiom,
! [A: set_b] :
( ( ( topolo1276428102open_b @ A )
& ( member_b @ ( f @ x0 ) @ A ) )
=> ? [B: set_a] :
( ( topolo1276428101open_a @ B )
& ( member_a @ x0 @ B )
& ! [C: a] :
( ( member_a @ C @ B )
=> ( ( ord_less_eq_b @ ( f @ C ) @ ( f @ x0 ) )
=> ( member_b @ ( f @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36__092_060open_062_092_060forall_062S_O_Aopen_AS_A_092_060and_062_Af_Ax0_A_092_060in_062_AS_A_092_060longrightarrow_062_A_I_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062x_H_092_060in_062T_O_Af_Ax_H_A_092_060le_062_Af_Ax0_A_092_060longrightarrow_062_Af_Ax_H_A_092_060in_062_AS_J_J_092_060close_062) ).
thf(443,plain,
! [A: set_b] :
( ( ( topolo1276428102open_b @ A )
& ( member_b @ ( f @ x0 ) @ A ) )
=> ? [B: set_a] :
( ( topolo1276428101open_a @ B )
& ( member_a @ x0 @ B )
& ! [C: a] :
( ( member_a @ C @ B )
=> ( ( ord_less_eq_b @ ( f @ C ) @ ( f @ x0 ) )
=> ( member_b @ ( f @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(139,axiom,
! [A: set_b,B: set_b] :
( ( ( topolo1276428102open_b @ A )
& ( topolo1276428102open_b @ B )
& ( member_b @ ( f @ x0 ) @ A )
& ( member_b @ a2 @ B )
& ( ( inf_inf_set_b @ A @ B )
= bot_bot_set_b ) )
=> thesis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(646,plain,
! [A: set_b,B: set_b] :
( ( ( topolo1276428102open_b @ A )
& ( topolo1276428102open_b @ B )
& ( member_b @ ( f @ x0 ) @ A )
& ( member_b @ a2 @ B )
& ( ( inf_inf_set_b @ A @ B )
= bot_bot_set_b ) )
=> thesis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(72,axiom,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( inf_inf_set_b @ B @ C ) )
=> ~ ( ( member_b @ A @ B )
=> ~ ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_IntE) ).
thf(397,plain,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( inf_inf_set_b @ B @ C ) )
=> ~ ( ( member_b @ A @ B )
=> ~ ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(42,axiom,
! [A: b,B: b] :
( ( ( insert_b @ A @ bot_bot_set_b )
= ( insert_b @ B @ bot_bot_set_b ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_singleton__inject) ).
thf(280,plain,
! [A: b,B: b] :
( ( ( insert_b @ A @ bot_bot_set_b )
= ( insert_b @ B @ bot_bot_set_b ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(46,axiom,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ( ( insert_b @ A @ ( minus_minus_set_b @ B @ ( insert_b @ A @ bot_bot_set_b ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_insert__Diff) ).
thf(293,plain,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ( ( insert_b @ A @ ( minus_minus_set_b @ B @ ( insert_b @ A @ bot_bot_set_b ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(30,axiom,
! [A: set_b,B: b,C: set_b] :
( ( minus_minus_set_b @ A @ ( insert_b @ B @ C ) )
= ( minus_minus_set_b @ ( minus_minus_set_b @ A @ ( insert_b @ B @ bot_bot_set_b ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_Diff__insert2) ).
thf(243,plain,
! [A: set_b,B: b,C: set_b] :
( ( minus_minus_set_b @ A @ ( insert_b @ B @ C ) )
= ( minus_minus_set_b @ ( minus_minus_set_b @ A @ ( insert_b @ B @ bot_bot_set_b ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(80,axiom,
( inf_inf_set_b
= ( ^ [A: set_b,B: set_b] : ( inf_inf_set_b @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_inf_Ocommute) ).
thf(428,plain,
( inf_inf_set_b
= ( ^ [A: set_b,B: set_b] : ( inf_inf_set_b @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(38,axiom,
! [A: b,B: b,C: b] :
( ( A = B )
=> ( ( ord_less_eq_b @ B @ C )
=> ( ord_less_eq_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_ord__eq__le__trans) ).
thf(265,plain,
! [A: b,B: b,C: b] :
( ( A = B )
=> ( ( ord_less_eq_b @ B @ C )
=> ( ord_less_eq_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(49,axiom,
! [A: b,B: set_b,C: b,D: set_b] :
( ~ ( member_b @ A @ B )
=> ( ~ ( member_b @ C @ D )
=> ( ( ( insert_b @ A @ B )
= ( insert_b @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_b] :
( ( B
= ( insert_b @ C @ E ) )
& ~ ( member_b @ C @ E )
& ( D
= ( insert_b @ A @ E ) )
& ~ ( member_b @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_insert__eq__iff) ).
thf(307,plain,
! [A: b,B: set_b,C: b,D: set_b] :
( ~ ( member_b @ A @ B )
=> ( ~ ( member_b @ C @ D )
=> ( ( ( insert_b @ A @ B )
= ( insert_b @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_b] :
( ( B
= ( insert_b @ C @ E ) )
& ~ ( member_b @ C @ E )
& ( D
= ( insert_b @ A @ E ) )
& ~ ( member_b @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(68,axiom,
! [A: set_b] :
( ( A != bot_bot_set_b )
=> ( ! [B: b,C: b] :
( ( member_b @ B @ A )
=> ( ( member_b @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton_b @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_is__singletonI_H) ).
thf(380,plain,
! [A: set_b] :
( ( A != bot_bot_set_b )
=> ( ! [B: b,C: b] :
( ( member_b @ B @ A )
=> ( ( member_b @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(108,axiom,
! [A: set_b,B: b,C: set_b] :
( ( bot_bot_set_b
= ( inf_inf_set_b @ A @ ( insert_b @ B @ C ) ) )
= ( ~ ( member_b @ B @ A )
& ( bot_bot_set_b
= ( inf_inf_set_b @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_disjoint__insert_I2_J) ).
thf(534,plain,
! [A: set_b,B: b,C: set_b] :
( ( bot_bot_set_b
= ( inf_inf_set_b @ A @ ( insert_b @ B @ C ) ) )
= ( ~ ( member_b @ B @ A )
& ( bot_bot_set_b
= ( inf_inf_set_b @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(100,axiom,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ B )
=> ( ( inf_inf_set_b @ ( insert_b @ A @ C ) @ B )
= ( insert_b @ A @ ( inf_inf_set_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_Int__insert__left__if1) ).
thf(512,plain,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ B )
=> ( ( inf_inf_set_b @ ( insert_b @ A @ C ) @ B )
= ( insert_b @ A @ ( inf_inf_set_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(84,axiom,
! [A: b,B: set_b,C: set_b] :
( ~ ( member_b @ A @ B )
=> ( ( inf_inf_set_b @ B @ ( insert_b @ A @ C ) )
= ( inf_inf_set_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_Int__insert__right__if0) ).
thf(439,plain,
! [A: b,B: set_b,C: set_b] :
( ~ ( member_b @ A @ B )
=> ( ( inf_inf_set_b @ B @ ( insert_b @ A @ C ) )
= ( inf_inf_set_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(39,axiom,
( ( (=) @ b )
= ( ^ [A: b,B: b] :
( ( ord_less_eq_b @ A @ B )
& ( ord_less_eq_b @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_eq__iff) ).
thf(270,plain,
( ( (=) @ b )
= ( ^ [A: b,B: b] :
( ( ord_less_eq_b @ A @ B )
& ( ord_less_eq_b @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(106,axiom,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ B )
=> ( ( member_b @ A @ C )
=> ( member_b @ A @ ( inf_inf_set_b @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_IntI) ).
thf(529,plain,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ B )
=> ( ( member_b @ A @ C )
=> ( member_b @ A @ ( inf_inf_set_b @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(70,axiom,
( inf_inf_set_b
= ( ^ [A: set_b,B: set_b] : ( inf_inf_set_b @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_Int__commute) ).
thf(392,plain,
( inf_inf_set_b
= ( ^ [A: set_b,B: set_b] : ( inf_inf_set_b @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(41,axiom,
! [A: b,B: b > b,C: b,D: b] :
( ( ord_less_eq_b @ A @ ( B @ C ) )
=> ( ( ord_less_eq_b @ C @ D )
=> ( ! [E: b,F: b] :
( ( ord_less_eq_b @ E @ F )
=> ( ord_less_eq_b @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_b @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_order__subst1) ).
thf(275,plain,
! [A: b,B: b > b,C: b,D: b] :
( ( ord_less_eq_b @ A @ ( B @ C ) )
=> ( ( ord_less_eq_b @ C @ D )
=> ( ! [E: b,F: b] :
( ( ord_less_eq_b @ E @ F )
=> ( ord_less_eq_b @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_b @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(36,axiom,
! [A: b,B: b] :
( ( ord_less_eq_b @ A @ B )
=> ( ( ord_less_eq_b @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_order__class_Oorder_Oantisym) ).
thf(260,plain,
! [A: b,B: b] :
( ( ord_less_eq_b @ A @ B )
=> ( ( ord_less_eq_b @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(60,axiom,
! [A: set_b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ A @ ( minus_minus_set_b @ B @ C ) )
= ( minus_minus_set_b @ ( inf_inf_set_b @ A @ B ) @ ( inf_inf_set_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_Diff__Int__distrib) ).
thf(349,plain,
! [A: set_b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ A @ ( minus_minus_set_b @ B @ C ) )
= ( minus_minus_set_b @ ( inf_inf_set_b @ A @ B ) @ ( inf_inf_set_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(14,axiom,
! [A: set_b] :
( ( minus_minus_set_b @ A @ bot_bot_set_b )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_Diff__empty) ).
thf(192,plain,
! [A: set_b] :
( ( minus_minus_set_b @ A @ bot_bot_set_b )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(75,axiom,
! [A: set_b,B: set_b] :
( ! [C: b] :
( ( member_b @ C @ A )
=> ~ ( member_b @ C @ B ) )
=> ( ( inf_inf_set_b @ A @ B )
= bot_bot_set_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Int__emptyI) ).
thf(407,plain,
! [A: set_b,B: set_b] :
( ! [C: b] :
( ( member_b @ C @ A )
=> ~ ( member_b @ C @ B ) )
=> ( ( inf_inf_set_b @ A @ B )
= bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(134,axiom,
! [A: set_b,B: set_b] :
( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ A @ B ) )
= ( inf_inf_set_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_inf_Oleft__idem) ).
thf(630,plain,
! [A: set_b,B: set_b] :
( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ A @ B ) )
= ( inf_inf_set_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(89,axiom,
! [A: b,B: b] :
( ( member_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_singleton__iff) ).
thf(467,plain,
! [A: b,B: b] :
( ( member_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(94,axiom,
! [A: set_b,B: set_b] :
( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ A @ B ) )
= ( inf_inf_set_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_inf__left__idem) ).
thf(484,plain,
! [A: set_b,B: set_b] :
( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ A @ B ) )
= ( inf_inf_set_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(33,axiom,
! [A: set_b] :
( ( minus_minus_set_b @ bot_bot_set_b @ A )
= bot_bot_set_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_empty__Diff) ).
thf(252,plain,
! [A: set_b] :
( ( minus_minus_set_b @ bot_bot_set_b @ A )
= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(64,axiom,
! [A: b,B: b,C: b > b,D: b] :
( ( ord_less_eq_b @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: b,F: b] :
( ( ord_less_eq_b @ E @ F )
=> ( ord_less_eq_b @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_b @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_ord__le__eq__subst) ).
thf(361,plain,
! [A: b,B: b,C: b > b,D: b] :
( ( ord_less_eq_b @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: b,F: b] :
( ( ord_less_eq_b @ E @ F )
=> ( ord_less_eq_b @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_b @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(123,axiom,
! [A: b,B: set_b,C: set_b] :
( ( ( member_b @ A @ B )
=> ( ( inf_inf_set_b @ B @ ( insert_b @ A @ C ) )
= ( insert_b @ A @ ( inf_inf_set_b @ B @ C ) ) ) )
& ( ~ ( member_b @ A @ B )
=> ( ( inf_inf_set_b @ B @ ( insert_b @ A @ C ) )
= ( inf_inf_set_b @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_Int__insert__right) ).
thf(583,plain,
! [A: b,B: set_b,C: set_b] :
( ( ( member_b @ A @ B )
=> ( ( inf_inf_set_b @ B @ ( insert_b @ A @ C ) )
= ( insert_b @ A @ ( inf_inf_set_b @ B @ C ) ) ) )
& ( ~ ( member_b @ A @ B )
=> ( ( inf_inf_set_b @ B @ ( insert_b @ A @ C ) )
= ( inf_inf_set_b @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(87,axiom,
! [A: b,B: set_b,C: set_b] :
( ( bot_bot_set_b
= ( inf_inf_set_b @ ( insert_b @ A @ B ) @ C ) )
= ( ~ ( member_b @ A @ C )
& ( bot_bot_set_b
= ( inf_inf_set_b @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_insert__disjoint_I2_J) ).
thf(461,plain,
! [A: b,B: set_b,C: set_b] :
( ( bot_bot_set_b
= ( inf_inf_set_b @ ( insert_b @ A @ B ) @ C ) )
= ( ~ ( member_b @ A @ C )
& ( bot_bot_set_b
= ( inf_inf_set_b @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(121,axiom,
! [A: set_b,B: set_b] :
( ( ( inf_inf_set_b @ A @ B )
= bot_bot_set_b )
= ( ! [C: b] :
( ( member_b @ C @ A )
=> ! [D: b] :
( ( member_b @ D @ B )
=> ( C != D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_disjoint__iff__not__equal) ).
thf(578,plain,
! [A: set_b,B: set_b] :
( ( ( inf_inf_set_b @ A @ B )
= bot_bot_set_b )
= ( ! [C: b] :
( ( member_b @ C @ A )
=> ! [D: b] :
( ( member_b @ D @ B )
=> ( C != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(3,axiom,
! [A: b] :
( ( the_elem_b @ ( insert_b @ A @ bot_bot_set_b ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_the__elem__eq) ).
thf(141,plain,
! [A: b] :
( ( the_elem_b @ ( insert_b @ A @ bot_bot_set_b ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(53,axiom,
! [A: b] : ( ord_less_eq_b @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_dual__order_Orefl) ).
thf(328,plain,
! [A: b] : ( ord_less_eq_b @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(57,axiom,
! [A: set_b] :
( ( is_singleton_b @ A )
=> ~ ! [B: b] :
( A
!= ( insert_b @ B @ bot_bot_set_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_is__singletonE) ).
thf(339,plain,
! [A: set_b] :
( ( is_singleton_b @ A )
=> ~ ! [B: b] :
( A
!= ( insert_b @ B @ bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(109,axiom,
! [A: set_b,B: b] :
( ( A = bot_bot_set_b )
=> ~ ( member_b @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_equals0D) ).
thf(537,plain,
! [A: set_b,B: b] :
( ( A = bot_bot_set_b )
=> ~ ( member_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(92,axiom,
! [A: set_b,B: set_b,C: set_b,D: set_b] :
( ( A
= ( inf_inf_set_b @ B @ C ) )
=> ( ( inf_inf_set_b @ A @ D )
= ( inf_inf_set_b @ B @ ( inf_inf_set_b @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_boolean__algebra__cancel_Oinf1) ).
thf(476,plain,
! [A: set_b,B: set_b,C: set_b,D: set_b] :
( ( A
= ( inf_inf_set_b @ B @ C ) )
=> ( ( inf_inf_set_b @ A @ D )
= ( inf_inf_set_b @ B @ ( inf_inf_set_b @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(105,axiom,
! [A: b] :
~ ( member_b @ A @ bot_bot_set_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_empty__iff) ).
thf(526,plain,
! [A: b] :
~ ( member_b @ A @ bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(136,axiom,
! [A: set_b,B: set_b] :
( ( topolo1276428102open_b @ A )
=> ( ( topolo1276428102open_b @ B )
=> ( topolo1276428102open_b @ ( inf_inf_set_b @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_open__Int) ).
thf(637,plain,
! [A: set_b,B: set_b] :
( ( topolo1276428102open_b @ A )
=> ( ( topolo1276428102open_b @ B )
=> ( topolo1276428102open_b @ ( inf_inf_set_b @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(9,axiom,
! [A: b,B: b,C: b > b,D: b] :
( ( ord_less_eq_b @ A @ B )
=> ( ( ord_less_eq_b @ ( C @ B ) @ D )
=> ( ! [E: b,F: b] :
( ( ord_less_eq_b @ E @ F )
=> ( ord_less_eq_b @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_b @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_order__subst2) ).
thf(173,plain,
! [A: b,B: b,C: b > b,D: b] :
( ( ord_less_eq_b @ A @ B )
=> ( ( ord_less_eq_b @ ( C @ B ) @ D )
=> ( ! [E: b,F: b] :
( ( ord_less_eq_b @ E @ F )
=> ( ord_less_eq_b @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_b @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(97,axiom,
! [A: set_b,B: set_b] :
( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ A @ B ) )
= ( inf_inf_set_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Int__left__absorb) ).
thf(503,plain,
! [A: set_b,B: set_b] :
( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ A @ B ) )
= ( inf_inf_set_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(58,axiom,
! [A: set_b] :
( ( minus_minus_set_b @ A @ A )
= bot_bot_set_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_Diff__cancel) ).
thf(343,plain,
! [A: set_b] :
( ( minus_minus_set_b @ A @ A )
= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(135,axiom,
! [A: set_b] :
( ! [B: b] :
~ ( member_b @ B @ A )
=> ( A = bot_bot_set_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_equals0I) ).
thf(633,plain,
! [A: set_b] :
( ! [B: b] :
~ ( member_b @ B @ A )
=> ( A = bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(50,axiom,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ? [C: set_b] :
( ( B
= ( insert_b @ A @ C ) )
& ~ ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_mk__disjoint__insert) ).
thf(311,plain,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ? [C: set_b] :
( ( B
= ( insert_b @ A @ C ) )
& ~ ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(130,axiom,
! [A: set_b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) )
= ( inf_inf_set_b @ B @ ( inf_inf_set_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Int__left__commute) ).
thf(618,plain,
! [A: set_b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) )
= ( inf_inf_set_b @ B @ ( inf_inf_set_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(79,axiom,
! [A: set_b] :
( ( inf_inf_set_b @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Int__absorb) ).
thf(425,plain,
! [A: set_b] :
( ( inf_inf_set_b @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(81,axiom,
! [A: b,B: b] :
( ( A != B )
= ( ? [C: set_b,D: set_b] :
( ( topolo1276428102open_b @ C )
& ( topolo1276428102open_b @ D )
& ( member_b @ A @ C )
& ( member_b @ B @ D )
& ( ( inf_inf_set_b @ C @ D )
= bot_bot_set_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_separation__t2) ).
thf(430,plain,
! [A: b,B: b] :
( ( A != B )
= ( ? [C: set_b,D: set_b] :
( ( topolo1276428102open_b @ C )
& ( topolo1276428102open_b @ D )
& ( member_b @ A @ C )
& ( member_b @ B @ D )
& ( ( inf_inf_set_b @ C @ D )
= bot_bot_set_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(47,axiom,
! [A: b,B: set_b,C: set_b] :
( ( ( member_b @ A @ B )
=> ( ( minus_minus_set_b @ ( insert_b @ A @ C ) @ B )
= ( minus_minus_set_b @ C @ B ) ) )
& ( ~ ( member_b @ A @ B )
=> ( ( minus_minus_set_b @ ( insert_b @ A @ C ) @ B )
= ( insert_b @ A @ ( minus_minus_set_b @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_insert__Diff__if) ).
thf(296,plain,
! [A: b,B: set_b,C: set_b] :
( ( ( member_b @ A @ B )
=> ( ( minus_minus_set_b @ ( insert_b @ A @ C ) @ B )
= ( minus_minus_set_b @ C @ B ) ) )
& ( ~ ( member_b @ A @ B )
=> ( ( minus_minus_set_b @ ( insert_b @ A @ C ) @ B )
= ( insert_b @ A @ ( minus_minus_set_b @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(117,axiom,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( inf_inf_set_b @ B @ C ) )
=> ( member_b @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_IntD2) ).
thf(562,plain,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( inf_inf_set_b @ B @ C ) )
=> ( member_b @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(44,axiom,
! [A: b,B: b] :
( ( ord_less_eq_b @ A @ B )
=> ( ( ord_less_eq_b @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_antisym) ).
thf(286,plain,
! [A: b,B: b] :
( ( ord_less_eq_b @ A @ B )
=> ( ( ord_less_eq_b @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(18,axiom,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ( ( insert_b @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_insert__absorb) ).
thf(204,plain,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ( ( insert_b @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(111,axiom,
! [A: set_b,B: set_b] :
( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ ( minus_minus_set_b @ A @ B ) )
= bot_bot_set_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_Int__Diff__disjoint) ).
thf(545,plain,
! [A: set_b,B: set_b] :
( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ ( minus_minus_set_b @ A @ B ) )
= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(76,axiom,
! [A: b,B: b] :
( ( A != B )
=> ? [C: set_b] :
( ( topolo1276428102open_b @ C )
& ( ( member_b @ A @ C )
!= ( member_b @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_t0__space) ).
thf(413,plain,
! [A: b,B: b] :
( ( A != B )
=> ? [C: set_b] :
( ( topolo1276428102open_b @ C )
& ( ( member_b @ A @ C )
!= ( member_b @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(138,axiom,
( ~ ! [A: set_b] :
( ( ( topolo1276428102open_b @ A )
& ( member_b @ ( f @ x0 ) @ A ) )
=> ? [B: set_a] :
( ( topolo1276428101open_a @ B )
& ( member_a @ x0 @ B )
& ! [C: a] :
( ( member_a @ C @ B )
=> ( ( ord_less_eq_b @ ( f @ C ) @ ( f @ x0 ) )
=> ( member_b @ ( f @ C ) @ A ) ) ) ) )
=> ~ ( lower_464587817at_a_b @ x0 @ f ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_calculation) ).
thf(641,plain,
( ~ ! [A: set_b] :
( ( ( topolo1276428102open_b @ A )
& ( member_b @ ( f @ x0 ) @ A ) )
=> ? [B: set_a] :
( ( topolo1276428101open_a @ B )
& ( member_a @ x0 @ B )
& ! [C: a] :
( ( member_a @ C @ B )
=> ( ( ord_less_eq_b @ ( f @ C ) @ ( f @ x0 ) )
=> ( member_b @ ( f @ C ) @ A ) ) ) ) )
=> ~ ( lower_464587817at_a_b @ x0 @ f ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(119,axiom,
! [A: set_b,B: set_b] :
( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ B )
= ( inf_inf_set_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_inf_Oright__idem) ).
thf(572,plain,
! [A: set_b,B: set_b] :
( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ B )
= ( inf_inf_set_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(128,axiom,
! [A: set_b] :
( ( inf_inf_set_b @ A @ bot_bot_set_b )
= bot_bot_set_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_Int__empty__right) ).
thf(611,plain,
! [A: set_b] :
( ( inf_inf_set_b @ A @ bot_bot_set_b )
= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(4,axiom,
! [A: b,B: b,C: b] :
( ( ( ord_less_eq_b @ A @ B )
=> ~ ( ord_less_eq_b @ B @ C ) )
=> ( ( ( ord_less_eq_b @ B @ A )
=> ~ ( ord_less_eq_b @ A @ C ) )
=> ( ( ( ord_less_eq_b @ A @ C )
=> ~ ( ord_less_eq_b @ C @ B ) )
=> ( ( ( ord_less_eq_b @ C @ B )
=> ~ ( ord_less_eq_b @ B @ A ) )
=> ( ( ( ord_less_eq_b @ B @ C )
=> ~ ( ord_less_eq_b @ C @ A ) )
=> ~ ( ( ord_less_eq_b @ C @ A )
=> ~ ( ord_less_eq_b @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_le__cases3) ).
thf(144,plain,
! [A: b,B: b,C: b] :
( ( ( ord_less_eq_b @ A @ B )
=> ~ ( ord_less_eq_b @ B @ C ) )
=> ( ( ( ord_less_eq_b @ B @ A )
=> ~ ( ord_less_eq_b @ A @ C ) )
=> ( ( ( ord_less_eq_b @ A @ C )
=> ~ ( ord_less_eq_b @ C @ B ) )
=> ( ( ( ord_less_eq_b @ C @ B )
=> ~ ( ord_less_eq_b @ B @ A ) )
=> ( ( ( ord_less_eq_b @ B @ C )
=> ~ ( ord_less_eq_b @ C @ A ) )
=> ~ ( ( ord_less_eq_b @ C @ A )
=> ~ ( ord_less_eq_b @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(27,axiom,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
= ( ( member_b @ A @ B )
& ~ ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_Diff__iff) ).
thf(236,plain,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
= ( ( member_b @ A @ B )
& ~ ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(11,axiom,
! [A: b,B: set_b,C: b] :
( ( ~ ( member_b @ A @ B )
=> ( A = C ) )
=> ( member_b @ A @ ( insert_b @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_insertCI) ).
thf(181,plain,
! [A: b,B: set_b,C: b] :
( ( ~ ( member_b @ A @ B )
=> ( A = C ) )
=> ( member_b @ A @ ( insert_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
=> ( member_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_DiffD1) ).
thf(159,plain,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
=> ( member_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
=> ~ ( member_b @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_DiffD2) ).
thf(187,plain,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
=> ~ ( member_b @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(23,axiom,
! [A: b,B: b] :
( ( A = B )
=> ( ord_less_eq_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_eq__refl) ).
thf(219,plain,
! [A: b,B: b] :
( ( A = B )
=> ( ord_less_eq_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(77,axiom,
! [A: set_b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) )
= ( inf_inf_set_b @ B @ ( inf_inf_set_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_inf__left__commute) ).
thf(419,plain,
! [A: set_b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) )
= ( inf_inf_set_b @ B @ ( inf_inf_set_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(67,axiom,
! [A: set_b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ C )
= ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_inf__sup__aci_I2_J) ).
thf(377,plain,
! [A: set_b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ C )
= ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(99,axiom,
! [A: set_b] :
( ( ? [B: b] : ( member_b @ B @ A ) )
= ( A != bot_bot_set_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_ex__in__conv) ).
thf(509,plain,
! [A: set_b] :
( ( ? [B: b] : ( member_b @ B @ A ) )
= ( A != bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(126,axiom,
! [A: b,B: set_b,C: set_b] :
( ( ( member_b @ A @ B )
=> ( ( inf_inf_set_b @ ( insert_b @ A @ C ) @ B )
= ( insert_b @ A @ ( inf_inf_set_b @ C @ B ) ) ) )
& ( ~ ( member_b @ A @ B )
=> ( ( inf_inf_set_b @ ( insert_b @ A @ C ) @ B )
= ( inf_inf_set_b @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_Int__insert__left) ).
thf(599,plain,
! [A: b,B: set_b,C: set_b] :
( ( ( member_b @ A @ B )
=> ( ( inf_inf_set_b @ ( insert_b @ A @ C ) @ B )
= ( insert_b @ A @ ( inf_inf_set_b @ C @ B ) ) ) )
& ( ~ ( member_b @ A @ B )
=> ( ( inf_inf_set_b @ ( insert_b @ A @ C ) @ B )
= ( inf_inf_set_b @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(1,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ thesis,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(140,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(131,axiom,
! [A: set_b] :
( ( inf_inf_set_b @ A @ bot_bot_set_b )
= bot_bot_set_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_inf__bot__right) ).
thf(621,plain,
! [A: set_b] :
( ( inf_inf_set_b @ A @ bot_bot_set_b )
= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(16,axiom,
( is_singleton_b
= ( ^ [A: set_b] :
( A
= ( insert_b @ ( the_elem_b @ A ) @ bot_bot_set_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_is__singleton__the__elem) ).
thf(198,plain,
( is_singleton_b
= ( ^ [A: set_b] :
( A
= ( insert_b @ ( the_elem_b @ A ) @ bot_bot_set_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(54,axiom,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ B )
=> ( ~ ( member_b @ A @ C )
=> ( member_b @ A @ ( minus_minus_set_b @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_DiffI) ).
thf(330,plain,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ B )
=> ( ~ ( member_b @ A @ C )
=> ( member_b @ A @ ( minus_minus_set_b @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(103,axiom,
( inf_inf_set_b
= ( ^ [A: set_b,B: set_b] : ( inf_inf_set_b @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_inf__commute) ).
thf(521,plain,
( inf_inf_set_b
= ( ^ [A: set_b,B: set_b] : ( inf_inf_set_b @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(24,axiom,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ B )
=> ( ( minus_minus_set_b @ ( insert_b @ A @ C ) @ B )
= ( minus_minus_set_b @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_insert__Diff1) ).
thf(223,plain,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ B )
=> ( ( minus_minus_set_b @ ( insert_b @ A @ C ) @ B )
= ( minus_minus_set_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(71,axiom,
! [A: set_b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) )
= ( inf_inf_set_b @ B @ ( inf_inf_set_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_inf_Oleft__commute) ).
thf(394,plain,
! [A: set_b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) )
= ( inf_inf_set_b @ B @ ( inf_inf_set_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(29,axiom,
( ( (=) @ b )
= ( ^ [A: b,B: b] :
( ( ord_less_eq_b @ A @ B )
& ( ord_less_eq_b @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_order__class_Oorder_Oeq__iff) ).
thf(241,plain,
( ( (=) @ b )
= ( ^ [A: b,B: b] :
( ( ord_less_eq_b @ A @ B )
& ( ord_less_eq_b @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(91,axiom,
! [A: set_b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) )
= ( inf_inf_set_b @ B @ ( inf_inf_set_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_inf__sup__aci_I3_J) ).
thf(473,plain,
! [A: set_b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) )
= ( inf_inf_set_b @ B @ ( inf_inf_set_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(6,axiom,
( is_singleton_b
= ( ^ [A: set_b] :
? [B: b] :
( A
= ( insert_b @ B @ bot_bot_set_b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_is__singleton__def) ).
thf(162,plain,
( is_singleton_b
= ( ^ [A: set_b] :
? [B: b] :
( A
= ( insert_b @ B @ bot_bot_set_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(112,axiom,
( is_empty_b
= ( ^ [A: set_b] : ( A = bot_bot_set_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_Set_Ois__empty__def) ).
thf(548,plain,
( is_empty_b
= ( ^ [A: set_b] : ( A = bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(34,axiom,
! [A: b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ ( insert_b @ A @ B ) @ ( insert_b @ A @ C ) )
= ( insert_b @ A @ ( inf_inf_set_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_insert__inter__insert) ).
thf(255,plain,
! [A: b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ ( insert_b @ A @ B ) @ ( insert_b @ A @ C ) )
= ( insert_b @ A @ ( inf_inf_set_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(95,axiom,
( ( ( f @ x0 )
!= a2 )
=> ? [A: set_b,B: set_b] :
( ( topolo1276428102open_b @ A )
& ( topolo1276428102open_b @ B )
& ( member_b @ ( f @ x0 ) @ A )
& ( member_b @ a2 @ B )
& ( ( inf_inf_set_b @ A @ B )
= bot_bot_set_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062f_Ax0_A_092_060noteq_062_AA_A_092_060Longrightarrow_062_A_092_060exists_062U_AV_O_Aopen_AU_A_092_060and_062_Aopen_AV_A_092_060and_062_Af_Ax0_A_092_060in_062_AU_A_092_060and_062_AA_A_092_060in_062_AV_A_092_060and_062_AU_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062) ).
thf(487,plain,
( ( ( f @ x0 )
!= a2 )
=> ? [A: set_b,B: set_b] :
( ( topolo1276428102open_b @ A )
& ( topolo1276428102open_b @ B )
& ( member_b @ ( f @ x0 ) @ A )
& ( member_b @ a2 @ B )
& ( ( inf_inf_set_b @ A @ B )
= bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(101,axiom,
( bot_bot_b_o
= ( ^ [A: b] : ( member_b @ A @ bot_bot_set_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_bot__empty__eq) ).
thf(516,plain,
( bot_bot_b_o
= ( ^ [A: b] : ( member_b @ A @ bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(62,axiom,
! [A: b,B: b,C: set_b] :
( ( member_b @ A @ ( insert_b @ B @ C ) )
= ( ( A = B )
| ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_insert__iff) ).
thf(355,plain,
! [A: b,B: b,C: set_b] :
( ( member_b @ A @ ( insert_b @ B @ C ) )
= ( ( A = B )
| ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(114,axiom,
! [A: set_b,B: set_b] :
( ( ( inf_inf_set_b @ A @ B )
= bot_bot_set_b )
=> ( ( minus_minus_set_b @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_Diff__triv) ).
thf(553,plain,
! [A: set_b,B: set_b] :
( ( ( inf_inf_set_b @ A @ B )
= bot_bot_set_b )
=> ( ( minus_minus_set_b @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(137,axiom,
topolo1276428102open_b @ bot_bot_set_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_open__empty) ).
thf(640,plain,
topolo1276428102open_b @ bot_bot_set_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(37,axiom,
! [A: b,B: set_b] : ( member_b @ A @ ( insert_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_insertI1) ).
thf(263,plain,
! [A: b,B: set_b] : ( member_b @ A @ ( insert_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(65,axiom,
( ( (=) @ b )
= ( ^ [A: b,B: b] :
( ( ord_less_eq_b @ B @ A )
& ( ord_less_eq_b @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_dual__order_Oeq__iff) ).
thf(370,plain,
( ( (=) @ b )
= ( ^ [A: b,B: b] :
( ( ord_less_eq_b @ B @ A )
& ( ord_less_eq_b @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(90,axiom,
! [A: set_b] :
( ( inf_inf_set_b @ bot_bot_set_b @ A )
= bot_bot_set_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_inf__bot__left) ).
thf(470,plain,
! [A: set_b] :
( ( inf_inf_set_b @ bot_bot_set_b @ A )
= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(133,axiom,
! [A: set_b,B: set_b] :
( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ A @ B ) )
= ( inf_inf_set_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_inf__sup__aci_I4_J) ).
thf(627,plain,
! [A: set_b,B: set_b] :
( ( inf_inf_set_b @ A @ ( inf_inf_set_b @ A @ B ) )
= ( inf_inf_set_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(115,axiom,
! [A: set_b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ C )
= ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Int__assoc) ).
thf(556,plain,
! [A: set_b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ C )
= ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(122,axiom,
( inf_inf_set_b
= ( ^ [A: set_b,B: set_b] : ( inf_inf_set_b @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_inf__sup__aci_I1_J) ).
thf(581,plain,
( inf_inf_set_b
= ( ^ [A: set_b,B: set_b] : ( inf_inf_set_b @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(52,axiom,
! [A: b,B: b > b,C: b,D: b] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_b @ C @ D )
=> ( ! [E: b,F: b] :
( ( ord_less_eq_b @ E @ F )
=> ( ord_less_eq_b @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_b @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_ord__eq__le__subst) ).
thf(319,plain,
! [A: b,B: b > b,C: b,D: b] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_b @ C @ D )
=> ( ! [E: b,F: b] :
( ( ord_less_eq_b @ E @ F )
=> ( ord_less_eq_b @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_b @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(48,axiom,
! [A: b,B: b,C: b] :
( ( ord_less_eq_b @ A @ B )
=> ( ( ord_less_eq_b @ B @ C )
=> ( ord_less_eq_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_order__trans) ).
thf(304,plain,
! [A: b,B: b,C: b] :
( ( ord_less_eq_b @ A @ B )
=> ( ( ord_less_eq_b @ B @ C )
=> ( ord_less_eq_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(35,axiom,
! [A: b,B: b] :
( ( ord_less_eq_b @ A @ B )
| ( ord_less_eq_b @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_linear) ).
thf(258,plain,
! [A: b,B: b] :
( ( ord_less_eq_b @ A @ B )
| ( ord_less_eq_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(73,axiom,
! [A: set_b,B: set_b] :
( ( inf_inf_set_b @ A @ ( minus_minus_set_b @ B @ A ) )
= bot_bot_set_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_Diff__disjoint) ).
thf(401,plain,
! [A: set_b,B: set_b] :
( ( inf_inf_set_b @ A @ ( minus_minus_set_b @ B @ A ) )
= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(8,axiom,
! [A: b] : ( ord_less_eq_b @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_order__refl) ).
thf(171,plain,
! [A: b] : ( ord_less_eq_b @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(31,axiom,
! [A: set_b,B: set_b,C: set_b] :
( ( minus_minus_set_b @ ( inf_inf_set_b @ A @ B ) @ ( inf_inf_set_b @ C @ B ) )
= ( minus_minus_set_b @ ( inf_inf_set_b @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_Diff__Int2) ).
thf(246,plain,
! [A: set_b,B: set_b,C: set_b] :
( ( minus_minus_set_b @ ( inf_inf_set_b @ A @ B ) @ ( inf_inf_set_b @ C @ B ) )
= ( minus_minus_set_b @ ( inf_inf_set_b @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(82,axiom,
! [A: b] :
~ ( member_b @ A @ bot_bot_set_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_emptyE) ).
thf(433,plain,
! [A: b] :
~ ( member_b @ A @ bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(19,axiom,
! [A: set_b,B: set_b,C: set_b] :
( ( minus_minus_set_b @ ( inf_inf_set_b @ A @ B ) @ C )
= ( inf_inf_set_b @ A @ ( minus_minus_set_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_Int__Diff) ).
thf(207,plain,
! [A: set_b,B: set_b,C: set_b] :
( ( minus_minus_set_b @ ( inf_inf_set_b @ A @ B ) @ C )
= ( inf_inf_set_b @ A @ ( minus_minus_set_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(40,axiom,
! [A: b,B: b] :
( ( ord_less_eq_b @ A @ B )
=> ( ( ord_less_eq_b @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_antisym__conv) ).
thf(272,plain,
! [A: b,B: b] :
( ( ord_less_eq_b @ A @ B )
=> ( ( ord_less_eq_b @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(59,axiom,
! [A: b,B: b] :
( ( ord_less_eq_b @ A @ B )
=> ( ( ord_less_eq_b @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_dual__order_Oantisym) ).
thf(346,plain,
! [A: b,B: b] :
( ( ord_less_eq_b @ A @ B )
=> ( ( ord_less_eq_b @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(21,axiom,
! [A: b,B: b,C: b] :
( ( ord_less_eq_b @ A @ B )
=> ( ( ord_less_eq_b @ C @ A )
=> ( ord_less_eq_b @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_dual__order_Otrans) ).
thf(214,plain,
! [A: b,B: b,C: b] :
( ( ord_less_eq_b @ A @ B )
=> ( ( ord_less_eq_b @ C @ A )
=> ( ord_less_eq_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(118,axiom,
! [A: b,B: b] :
( ( A != B )
=> ? [C: set_b] :
( ( topolo1276428102open_b @ C )
& ( member_b @ A @ C )
& ~ ( member_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_t1__space) ).
thf(564,plain,
! [A: b,B: b] :
( ( A != B )
=> ? [C: set_b] :
( ( topolo1276428102open_b @ C )
& ( member_b @ A @ C )
& ~ ( member_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(20,axiom,
! [A: b,B: set_b,C: set_b] :
( ~ ( member_b @ A @ B )
=> ( ( minus_minus_set_b @ B @ ( insert_b @ A @ C ) )
= ( minus_minus_set_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_Diff__insert0) ).
thf(210,plain,
! [A: b,B: set_b,C: set_b] :
( ~ ( member_b @ A @ B )
=> ( ( minus_minus_set_b @ B @ ( insert_b @ A @ C ) )
= ( minus_minus_set_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(28,axiom,
! [A: b,B: b] :
( ~ ( ord_less_eq_b @ A @ B )
=> ( ord_less_eq_b @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_le__cases) ).
thf(239,plain,
! [A: b,B: b] :
( ~ ( ord_less_eq_b @ A @ B )
=> ( ord_less_eq_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(98,axiom,
! [A: set_b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ C )
= ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_inf_Oassoc) ).
thf(506,plain,
! [A: set_b,B: set_b,C: set_b] :
( ( inf_inf_set_b @ ( inf_inf_set_b @ A @ B ) @ C )
= ( inf_inf_set_b @ A @ ( inf_inf_set_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(63,axiom,
! [A: b,B: set_b] :
( ( insert_b @ A @ ( minus_minus_set_b @ B @ ( insert_b @ A @ bot_bot_set_b ) ) )
= ( insert_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_insert__Diff__single) ).
thf(358,plain,
! [A: b,B: set_b] :
( ( insert_b @ A @ ( minus_minus_set_b @ B @ ( insert_b @ A @ bot_bot_set_b ) ) )
= ( insert_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(15,axiom,
! [A: b,B: set_b,C: b] :
( ( member_b @ A @ B )
=> ( member_b @ A @ ( insert_b @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_insertI2) ).
thf(195,plain,
! [A: b,B: set_b,C: b] :
( ( member_b @ A @ B )
=> ( member_b @ A @ ( insert_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(107,axiom,
! [A: b] : ( member_b @ A @ ( insert_b @ A @ bot_bot_set_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_singletonI) ).
thf(532,plain,
! [A: b] : ( member_b @ A @ ( insert_b @ A @ bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(43,axiom,
! [A: b,B: set_b] :
( ~ ( member_b @ A @ B )
=> ( ( minus_minus_set_b @ ( insert_b @ A @ B ) @ ( insert_b @ A @ bot_bot_set_b ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_Diff__insert__absorb) ).
thf(283,plain,
! [A: b,B: set_b] :
( ~ ( member_b @ A @ B )
=> ( ( minus_minus_set_b @ ( insert_b @ A @ B ) @ ( insert_b @ A @ bot_bot_set_b ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(132,axiom,
! [A: set_b] :
( ( inf_inf_set_b @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_inf_Oidem) ).
thf(624,plain,
! [A: set_b] :
( ( inf_inf_set_b @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(88,axiom,
! [A: b,B: set_b,C: set_b] :
( ( ( inf_inf_set_b @ ( insert_b @ A @ B ) @ C )
= bot_bot_set_b )
= ( ~ ( member_b @ A @ C )
& ( ( inf_inf_set_b @ B @ C )
= bot_bot_set_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_insert__disjoint_I1_J) ).
thf(464,plain,
! [A: b,B: set_b,C: set_b] :
( ( ( inf_inf_set_b @ ( insert_b @ A @ B ) @ C )
= bot_bot_set_b )
= ( ~ ( member_b @ A @ C )
& ( ( inf_inf_set_b @ B @ C )
= bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(120,axiom,
! [A: b,B: b] :
( ( A != B )
= ( ? [C: set_b] :
( ( topolo1276428102open_b @ C )
& ( ( member_b @ A @ C )
!= ( member_b @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_separation__t0) ).
thf(575,plain,
! [A: b,B: b] :
( ( A != B )
= ( ? [C: set_b] :
( ( topolo1276428102open_b @ C )
& ( ( member_b @ A @ C )
!= ( member_b @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(125,axiom,
! [A: set_b] :
( ( inf_inf_set_b @ bot_bot_set_b @ A )
= bot_bot_set_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_Int__empty__left) ).
thf(596,plain,
! [A: set_b] :
( ( inf_inf_set_b @ bot_bot_set_b @ A )
= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(17,axiom,
! [A: b,B: set_b,C: set_b] :
( ~ ( member_b @ A @ B )
=> ( ~ ( member_b @ A @ C )
=> ( ( ( insert_b @ A @ B )
= ( insert_b @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_insert__ident) ).
thf(200,plain,
! [A: b,B: set_b,C: set_b] :
( ~ ( member_b @ A @ B )
=> ( ~ ( member_b @ A @ C )
=> ( ( ( insert_b @ A @ B )
= ( insert_b @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(10,axiom,
! [A: set_b,B: set_b] :
( ( minus_minus_set_b @ A @ ( minus_minus_set_b @ A @ B ) )
= ( inf_inf_set_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_Diff__Diff__Int) ).
thf(178,plain,
! [A: set_b,B: set_b] :
( ( minus_minus_set_b @ A @ ( minus_minus_set_b @ A @ B ) )
= ( inf_inf_set_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(127,axiom,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ B )
=> ( ( inf_inf_set_b @ B @ ( insert_b @ A @ C ) )
= ( insert_b @ A @ ( inf_inf_set_b @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_Int__insert__right__if1) ).
thf(607,plain,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ B )
=> ( ( inf_inf_set_b @ B @ ( insert_b @ A @ C ) )
= ( insert_b @ A @ ( inf_inf_set_b @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(25,axiom,
! [A: b,B: b,C: b] :
( ( ord_less_eq_b @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_b @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_ord__le__eq__trans) ).
thf(227,plain,
! [A: b,B: b,C: b] :
( ( ord_less_eq_b @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(26,axiom,
! [A: b,B: set_b] :
( ( insert_b @ A @ B )
!= bot_bot_set_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_insert__not__empty) ).
thf(232,plain,
! [A: b,B: set_b] :
( ( insert_b @ A @ B )
!= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(670,plain,
$false,
inference(e,[status(thm)],[336,422,518,333,249,481,352,523,217,614,550,500,404,436,389,372,542,559,189,289,448,316,164,591,443,646,397,280,293,243,428,265,307,380,534,512,439,270,529,392,275,260,349,192,407,630,467,484,252,361,583,461,578,141,328,339,537,476,526,637,173,503,343,633,311,618,425,430,296,562,286,204,545,413,641,572,611,144,236,181,159,187,219,419,377,509,599,140,621,198,330,521,223,394,241,473,162,548,255,487,516,355,553,640,263,370,470,627,556,581,319,304,258,401,171,246,433,207,272,346,214,564,210,239,506,358,195,532,283,624,464,575,596,200,178,607,227,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP115^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n007.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 19:53:41 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.85/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.04/1.17 % [INFO] Parsing done (394ms).
% 2.04/1.18 % [INFO] Running in sequential loop mode.
% 3.12/1.56 % [INFO] eprover registered as external prover.
% 3.12/1.57 % [INFO] Scanning for conjecture ...
% 3.55/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 356 axioms. Running axiom selection ...
% 3.78/1.82 % [INFO] Axiom selection finished. Selected 137 axioms (removed 219 axioms).
% 4.13/2.01 % [INFO] Problem is higher-order (TPTP THF).
% 4.46/2.04 % [INFO] Type checking passed.
% 4.46/2.04 % [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 ...
% 9.87/3.43 % External prover 'e' found a proof!
% 9.87/3.43 % [INFO] Killing All external provers ...
% 9.87/3.43 % Time passed: 3084ms (effective reasoning time: 2241ms)
% 9.87/3.43 % 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)>
% 9.87/3.43 % Axioms used in derivation (137): fact_101_disjoint__iff, fact_59_boolean__algebra__cancel_Oinf2, fact_20_inf_Oleft__idem, fact_342_is__singleton__the__elem, fact_61_boolean__algebra__cancel_Oinf1, fact_189_dual__order_Oantisym, fact_248_Diff__Int2, fact_116_insert__disjoint_I1_J, fact_236_doubleton__eq__iff, fact_32_inf_Oright__idem, fact_135_singletonI, fact_71_Int__left__commute, fact_340_Int__Diff__disjoint, fact_51_inf__commute, fact_337_Diff__triv, fact_151_Diff__cancel, fact_97_Int__empty__right, fact_9_inf__bot__right, fact_195_order__class_Oorder_Oantisym, fact_106_Set_Ois__empty__def, fact_149_empty__Diff, fact_232_singletonD, fact_196_ord__le__eq__trans, fact_202_le__cases, fact_28_empty__iff, fact_211_Diff__insert__absorb, fact_118_insert__disjoint_I2_J, fact_57_inf_Oassoc, fact_34_inf__left__idem, fact_123_insert__iff, fact_183_insert__eq__iff, fact_65_inf__sup__aci_I2_J, fact_145_Int__insert__right__if1, fact_92_separation__t0, fact_208_ord__eq__le__subst, fact_194_order__trans, fact_163_is__singletonI, fact_199_antisym__conv, fact_120_order__refl, fact_137_Int__insert__left__if0, fact_157_disjoint__insert_I2_J, fact_13_IntI, fact_95_disjoint__iff__not__equal, fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062, fact_161_insert__Diff__single, fact_173_insertI1, fact_4_open__empty, fact_39_ex__in__conv, fact_242_Int__insert__left, fact_85_IntD2, fact_75_Int__commute, fact_197_ord__eq__le__trans, fact_165_DiffE, fact_36__092_060open_062_092_060forall_062S_O_Aopen_AS_A_092_060and_062_Af_Ax0_A_092_060in_062_AS_A_092_060longrightarrow_062_A_I_092_060exists_062T_O_Aopen_AT_A_092_060and_062_Ax0_A_092_060in_062_AT_A_092_060and_062_A_I_092_060forall_062x_H_092_060in_062T_O_Af_Ax_H_A_092_060le_062_Af_Ax0_A_092_060longrightarrow_062_Af_Ax_H_A_092_060in_062_AS_J_J_092_060close_062, fact_45_emptyE, fact_63_inf__sup__aci_I1_J, fact_185_insert__Diff__if, fact_205_antisym, fact_192_linorder__wlog, fact_26_all__not__in__conv, fact_125_DiffI, fact_2_open__Int, fact_167_DiffD1, fact_147_Diff__empty, fact_206_eq__iff, fact_203_eq__refl, fact_215_insert__Diff, fact_103_Int__emptyI, fact_55_inf__assoc, fact_230_is__singletonE, fact_112_is__singletonI_H, fact_10_hausdorff, fact_18_inf__idem, fact_193_dual__order_Orefl, fact_190_dual__order_Oeq__iff, fact_204_linear, fact_171_insertE, fact_153_Diff__insert0, fact_139_Int__insert__left__if1, fact_228_is__singleton__def, fact_7_inf__bot__left, fact_175_insertI2, fact_41_equals0I, fact_155_insert__Diff1, fact_47_inf__left__commute, fact_69_inf__sup__aci_I4_J, fact_177_Set_Oset__insert, fact_43_equals0D, fact_209_order__subst2, fact_234_singleton__iff, fact_344_the__elem__eq, fact_210_order__subst1, fact_252_Diff__Int__distrib, fact_91_separation__t1, fact_217_Diff__insert, fact_246_Int__Diff, fact_11_separation__t2, fact_207_ord__le__eq__subst, fact_250_Diff__Diff__Int, fact_121_insertCI, fact_1__092_060open_062f_Ax0_A_092_060noteq_062_AA_A_092_060Longrightarrow_062_A_092_060exists_062U_AV_O_Aopen_AU_A_092_060and_062_Aopen_AV_A_092_060and_062_Af_Ax0_A_092_060in_062_AU_A_092_060and_062_AA_A_092_060in_062_AV_A_092_060and_062_AU_A_092_060inter_062_AV_A_061_A_123_125_092_060close_062, fact_16_inf_Oidem, fact_105_calculation, fact_141_insert__inter__insert, fact_73_Int__left__absorb, fact_159_disjoint__insert_I1_J, fact_77_Int__absorb, fact_67_inf__sup__aci_I3_J, fact_15_Int__iff, fact_87_IntD1, fact_254_Diff__Int__distrib2, fact_187_mk__disjoint__insert, fact_179_insert__ident, fact_201_order_Otrans, fact_200_le__cases3, fact_114_Diff__disjoint, fact_198_order__class_Oorder_Oeq__iff, fact_169_DiffD2, fact_79_Int__assoc, fact_53_inf_Ocommute, fact_238_insert__not__empty, fact_339_open__delete, conj_0, fact_49_inf_Oleft__commute, fact_240_singleton__inject, fact_94_t0__space, fact_127_Diff__iff, fact_244_Int__insert__right, fact_143_Int__insert__right__if0, fact_89_IntE, fact_191_dual__order_Otrans, fact_213_Diff__insert2, fact_99_Int__empty__left, fact_93_t1__space, fact_30_inf__right__idem, fact_110_bot__empty__eq, fact_181_insert__absorb
% 9.87/3.44 % No. of inferences in proof: 278
% 9.87/3.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3084 ms resp. 2241 ms w/o parsing
% 10.47/3.58 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.47/3.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------