TSTP Solution File: ITP115^2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP115^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:23:03 EDT 2024
% Result : Theorem 26.99s 13.00s
% Output : Refutation 27.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 217
% Syntax : Number of formulae : 402 ( 156 unt; 34 typ; 0 def)
% Number of atoms : 1572 ( 360 equ; 2 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 4997 ( 132 ~; 8 |; 120 &;4423 @)
% ( 0 <=>; 314 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 33 usr; 7 con; 0-4 aty)
% Number of variables : 1160 ( 36 ^1056 !; 40 ?;1160 :)
% ( 28 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(topolo2117631714pology_type,type,
topolo2117631714pology:
!>[TA: $tType] : $o ).
thf(comple1035589618norder_type,type,
comple1035589618norder:
!>[TA: $tType] : $o ).
thf(topological_t0_space_type,type,
topological_t0_space:
!>[TA: $tType] : $o ).
thf(topological_t1_space_type,type,
topological_t1_space:
!>[TA: $tType] : $o ).
thf(topological_t2_space_type,type,
topological_t2_space:
!>[TA: $tType] : $o ).
thf(bounded_lattice_bot_type,type,
bounded_lattice_bot:
!>[TA: $tType] : $o ).
thf(topolo890362671_space_type,type,
topolo890362671_space:
!>[TA: $tType] : $o ).
thf(topolo47006728_space_type,type,
topolo47006728_space:
!>[TA: $tType] : $o ).
thf(topolo2133971006pology_type,type,
topolo2133971006pology:
!>[TA: $tType] : $o ).
thf(topolo503727757_space_type,type,
topolo503727757_space:
!>[TA: $tType] : $o ).
thf(topolo2135403230pology_type,type,
topolo2135403230pology:
!>[TA: $tType] : $o ).
thf(minus_minus_type,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(inf_inf_type,type,
inf_inf:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(lower_582600101lsc_at_type,type,
lower_582600101lsc_at:
!>[TA: $tType,TB: $tType] : ( TB > ( TB > TA ) > $o ) ).
thf(bot_bot_type,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(top_top_type,type,
top_top:
!>[TA: $tType] : TA ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(is_empty_type,type,
is_empty:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(is_singleton_type,type,
is_singleton:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(remove_type,type,
remove:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(the_elem_type,type,
the_elem:
!>[TA: $tType] : ( ( set @ TA ) > TA ) ).
thf(topolo1751647064n_open_type,type,
topolo1751647064n_open:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(topolo507301023within_type,type,
topolo507301023within:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( filter @ TA ) ) ).
thf(topolo406746546ounded_type,type,
topolo406746546ounded:
!>[TA: $tType] : ( ( set @ TA ) > $o ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(a2_type,type,
a2: b ).
thf(f_type,type,
f: a > b ).
thf(thesis_type,type,
thesis: $o ).
thf(x0_type,type,
x0: a ).
thf(184,axiom,
! [A: set @ b,B: set @ b] :
( ( ( topolo1751647064n_open @ b @ A )
& ( topolo1751647064n_open @ 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/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(715,plain,
! [A: set @ b,B: set @ b] :
( ( ( topolo1751647064n_open @ b @ A )
& ( topolo1751647064n_open @ 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)],[184]) ).
thf(112,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_Diff__insert__absorb) ).
thf(479,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(108,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_empty__Diff) ).
thf(468,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(21,axiom,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_is__singleton__def) ).
thf(234,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
? [B: TA] :
( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(67,axiom,
topological_t2_space @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Ot2__space_32) ).
thf(352,plain,
topological_t2_space @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(145,axiom,
! [TA: $tType] :
( ( topological_t0_space @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
= ( ? [C: set @ TA] :
( ( topolo1751647064n_open @ TA @ C )
& ( ( member @ TA @ A @ C )
!= ( member @ TA @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_separation__t0) ).
thf(582,plain,
! [TA: $tType] :
( ( topological_t0_space @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
= ( ? [C: set @ TA] :
( ( topolo1751647064n_open @ TA @ C )
& ( ( member @ TA @ A @ C )
!= ( member @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(38,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( minus_minus @ ( set @ TA ) @ C @ B ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_insert__Diff__if) ).
thf(276,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( minus_minus @ ( set @ TA ) @ C @ B ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(51,axiom,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_is__singleton__the__elem) ).
thf(308,plain,
! [TA: $tType] :
( ( is_singleton @ TA )
= ( ^ [A: set @ TA] :
( A
= ( insert @ TA @ ( the_elem @ TA @ A ) @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(101,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ C )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_Diff__Int__distrib2) ).
thf(449,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ C )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(155,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_singleton__inject) ).
thf(614,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(173,axiom,
! [TA: $tType] :
( ( topological_t1_space @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ? [C: set @ TA] :
( ( topolo1751647064n_open @ TA @ C )
& ( member @ TA @ A @ C )
& ~ ( member @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_t1__space) ).
thf(677,plain,
! [TA: $tType] :
( ( topological_t1_space @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ? [C: set @ TA] :
( ( topolo1751647064n_open @ TA @ C )
& ( member @ TA @ A @ C )
& ~ ( member @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(9,axiom,
! [TA: $tType] :
( ( topolo2117631714pology @ TA )
=> ( topolo503727757_space @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Topological__Spaces_Olinorder__topology___Topological__Spaces_Otopological__space) ).
thf(202,plain,
! [TA: $tType] :
( ( topolo2117631714pology @ TA )
=> ( topolo503727757_space @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(150,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_Diff__cancel) ).
thf(597,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(1,conjecture,
thesis,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ thesis,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(185,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(89,axiom,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_the__elem__eq) ).
thf(417,plain,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(48,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( minus_minus @ ( set @ TA ) @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_double__diff) ).
thf(301,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( minus_minus @ ( set @ TA ) @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(31,axiom,
! [TA: $tType] :
( ( topological_t1_space @ TA )
=> ! [A: set @ TA,B: TA] :
( ( topolo1751647064n_open @ TA @ A )
=> ( topolo1751647064n_open @ TA @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_open__delete) ).
thf(257,plain,
! [TA: $tType] :
( ( topological_t1_space @ TA )
=> ! [A: set @ TA,B: TA] :
( ( topolo1751647064n_open @ TA @ A )
=> ( topolo1751647064n_open @ TA @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(147,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) @ ( inf_inf @ ( set @ TA ) @ B @ ( collect @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_Int__Collect__mono) ).
thf(587,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o,D: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ! [E: TA] :
( ( member @ TA @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ ( collect @ TA @ C ) ) @ ( inf_inf @ ( set @ TA ) @ B @ ( collect @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(179,axiom,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_bot__empty__eq) ).
thf(702,plain,
! [TA: $tType] :
( ( bot_bot @ ( TA > $o ) )
= ( ^ [A: TA] : ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(64,axiom,
! [TA: $tType] :
( ( topolo47006728_space @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( topolo406746546ounded @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( topolo406746546ounded @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_totally__bounded__subset) ).
thf(344,plain,
! [TA: $tType] :
( ( topolo47006728_space @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( topolo406746546ounded @ TA @ A )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( topolo406746546ounded @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(7,axiom,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: TA] :
( ( ( topolo507301023within @ TA @ A @ ( top_top @ ( set @ TA ) ) )
= ( bot_bot @ ( filter @ TA ) ) )
= ( topolo1751647064n_open @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_at__eq__bot__iff) ).
thf(196,plain,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: TA] :
( ( ( topolo507301023within @ TA @ A @ ( top_top @ ( set @ TA ) ) )
= ( bot_bot @ ( filter @ TA ) ) )
= ( topolo1751647064n_open @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(133,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_Int__absorb1) ).
thf(542,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(105,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_Diff__Int__distrib) ).
thf(460,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(163,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ C @ B ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_Diff__Int2) ).
thf(638,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( inf_inf @ ( set @ TA ) @ C @ B ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(153,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_Int__absorb2) ).
thf(606,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(33,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_Collect__empty__eq__bot) ).
thf(261,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(15,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_subset__trans) ).
thf(216,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(148,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( bot_bot @ ( set @ TA ) ) )
= ( ~ ( member @ TA @ B @ A )
& ( ( inf_inf @ ( set @ TA ) @ A @ C )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_disjoint__insert_I1_J) ).
thf(591,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( bot_bot @ ( set @ TA ) ) )
= ( ~ ( member @ TA @ B @ A )
& ( ( inf_inf @ ( set @ TA ) @ A @ C )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(54,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Diff__insert0) ).
thf(321,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(158,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
=> ( ( minus_minus @ ( set @ TA ) @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_Diff__triv) ).
thf(623,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
=> ( ( minus_minus @ ( set @ TA ) @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(114,axiom,
! [TA: $tType] :
( ( topological_t2_space @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
= ( ? [C: set @ TA,D: set @ TA] :
( ( topolo1751647064n_open @ TA @ C )
& ( topolo1751647064n_open @ TA @ D )
& ( member @ TA @ A @ C )
& ( member @ TA @ B @ D )
& ( ( inf_inf @ ( set @ TA ) @ C @ D )
= ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_separation__t2) ).
thf(485,plain,
! [TA: $tType] :
( ( topological_t2_space @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
= ( ? [C: set @ TA,D: set @ TA] :
( ( topolo1751647064n_open @ TA @ C )
& ( topolo1751647064n_open @ TA @ D )
& ( member @ TA @ A @ C )
& ( member @ TA @ B @ D )
& ( ( inf_inf @ ( set @ TA ) @ C @ D )
= ( bot_bot @ ( set @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(142,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( bot_bot @ ( set @ TA ) ) )
= ( ~ ( member @ TA @ A @ C )
& ( ( inf_inf @ ( set @ TA ) @ B @ C )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_insert__disjoint_I1_J) ).
thf(574,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( bot_bot @ ( set @ TA ) ) )
= ( ~ ( member @ TA @ A @ C )
& ( ( inf_inf @ ( set @ TA ) @ B @ C )
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(68,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_insert__iff) ).
thf(353,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(82,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_in__mono) ).
thf(397,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(17,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( minus_minus @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_Diff__eq__empty__iff) ).
thf(221,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( minus_minus @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(44,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_subset__refl) ).
thf(293,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(168,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_empty__iff) ).
thf(660,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(11,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_subset__antisym) ).
thf(206,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(102,axiom,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( topolo1751647064n_open @ TA @ A )
=> ( ( topolo1751647064n_open @ TA @ B )
=> ( topolo1751647064n_open @ TA @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_open__Int) ).
thf(452,plain,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: set @ TA,B: set @ TA] :
( ( topolo1751647064n_open @ TA @ A )
=> ( ( topolo1751647064n_open @ TA @ B )
=> ( topolo1751647064n_open @ TA @ ( inf_inf @ ( set @ TA ) @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(28,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( insert @ TA @ A @ B ) )
=> ( C @ D ) ) )
= ( ( C @ A )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_ball__insert) ).
thf(248,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( insert @ TA @ A @ B ) )
=> ( C @ D ) ) )
= ( ( C @ A )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(76,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_singleton__insert__inj__eq) ).
thf(380,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( insert @ TA @ B @ C ) )
= ( ( B = A )
& ( ord_less_eq @ ( set @ TA ) @ C @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(123,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ ( insert @ TA @ A @ C ) )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_insert__inter__insert) ).
thf(512,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ ( insert @ TA @ A @ C ) )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(36,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_set__eq__subset) ).
thf(270,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(130,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Diff__iff) ).
thf(534,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(60,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_Set_Oset__insert) ).
thf(334,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ~ ! [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(66,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(349,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(137,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_IntE) ).
thf(561,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(46,axiom,
topological_t1_space @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Ot1__space_33) ).
thf(297,plain,
topological_t1_space @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(176,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_equals0I) ).
thf(693,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(96,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_Int__subset__iff) ).
thf(435,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(126,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Int__absorb) ).
thf(522,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(117,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ A ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_Diff__disjoint) ).
thf(493,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ A ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(182,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_Int__mono) ).
thf(710,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ C ) @ ( inf_inf @ ( set @ TA ) @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(55,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A = C )
& ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_singleton__insert__inj__eq_H) ).
thf(324,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A = C )
& ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(41,axiom,
! [TA: $tType] :
( ( comple1035589618norder @ TA )
=> ( bounded_lattice_bot @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Complete__Lattices_Ocomplete__linorder___Lattices_Obounded__lattice__bot) ).
thf(285,plain,
! [TA: $tType] :
( ( comple1035589618norder @ TA )
=> ( bounded_lattice_bot @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(18,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_insert__absorb) ).
thf(224,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(125,axiom,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_Set_Ois__empty__def) ).
thf(519,plain,
! [TA: $tType] :
( ( is_empty @ TA )
= ( ^ [A: set @ TA] :
( A
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(85,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_Int__assoc) ).
thf(403,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(4,axiom,
! [TA: $tType] :
( ( topolo2133971006pology @ TA )
=> ( ( topolo507301023within @ TA )
= ( ^ [A: TA,B: set @ TA] : ( bot_bot @ ( filter @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_at__discrete) ).
thf(188,plain,
! [TA: $tType] :
( ( topolo2133971006pology @ TA )
=> ( ( topolo507301023within @ TA )
= ( ^ [A: TA,B: set @ TA] : ( bot_bot @ ( filter @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(79,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_insert__eq__iff) ).
thf(388,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA,D: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ C @ D )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set @ TA] :
( ( B
= ( insert @ TA @ C @ E ) )
& ~ ( member @ TA @ C @ E )
& ( D
= ( insert @ TA @ A @ E ) )
& ~ ( member @ TA @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(69,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(356,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(90,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_subset__eq) ).
thf(420,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(109,axiom,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_ex__in__conv) ).
thf(471,plain,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(115,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_Int__Diff) ).
thf(488,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ C )
= ( inf_inf @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(62,axiom,
! [TA: $tType] :
( ( topolo2117631714pology @ TA )
=> ( topological_t0_space @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Topological__Spaces_Olinorder__topology___Topological__Spaces_Ot0__space) ).
thf(339,plain,
! [TA: $tType] :
( ( topolo2117631714pology @ TA )
=> ( topological_t0_space @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(131,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_insert__Diff) ).
thf(537,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(111,axiom,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: set @ TA] :
( ! [B: TA] :
( ( member @ TA @ B @ A )
=> ? [C: set @ TA] :
( ( topolo1751647064n_open @ TA @ C )
& ( member @ TA @ B @ C )
& ( ord_less_eq @ ( set @ TA ) @ C @ A ) ) )
=> ( topolo1751647064n_open @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_topological__space__class_OopenI) ).
thf(476,plain,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: set @ TA] :
( ! [B: TA] :
( ( member @ TA @ B @ A )
=> ? [C: set @ TA] :
( ( topolo1751647064n_open @ TA @ C )
& ( member @ TA @ B @ C )
& ( ord_less_eq @ ( set @ TA ) @ C @ A ) ) )
=> ( topolo1751647064n_open @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(13,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_insert__mono) ).
thf(212,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ C @ A ) @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(124,axiom,
! [A: set @ b] :
( ( ( topolo1751647064n_open @ b @ A )
& ( member @ b @ ( f @ x0 ) @ A ) )
=> ? [B: set @ a] :
( ( topolo1751647064n_open @ 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/sandbox2/benchmark/theBenchmark.p',fact_21__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(515,plain,
! [A: set @ b] :
( ( ( topolo1751647064n_open @ b @ A )
& ( member @ b @ ( f @ x0 ) @ A ) )
=> ? [B: set @ a] :
( ( topolo1751647064n_open @ 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)],[124]) ).
thf(104,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_empty__Collect__eq) ).
thf(457,plain,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(22,axiom,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_is__singletonI) ).
thf(237,plain,
! [TA: $tType,A: TA] : ( is_singleton @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(26,axiom,
! [TA: $tType] :
( ( topolo2117631714pology @ TA )
=> ( topological_t2_space @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Topological__Spaces_Olinorder__topology___Topological__Spaces_Ot2__space) ).
thf(244,plain,
! [TA: $tType] :
( ( topolo2117631714pology @ TA )
=> ( topological_t2_space @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(52,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Diff__idemp) ).
thf(311,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(136,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_singletonD) ).
thf(558,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(172,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_singleton__iff) ).
thf(674,plain,
! [TA: $tType,A: TA,B: TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(169,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_singletonI) ).
thf(662,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(47,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( ( ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C ) )
& ( ~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_subset__insert__iff) ).
thf(298,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( ( ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C ) )
& ( ~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(88,axiom,
! [TA: $tType] :
( ( topolo2135403230pology @ TA )
=> ! [A: TA] :
? [B: nat > ( set @ TA )] :
( ! [C: nat] :
( ( member @ TA @ A @ ( B @ C ) )
& ( topolo1751647064n_open @ TA @ ( B @ C ) ) )
& ! [C: set @ TA] :
( ( ( topolo1751647064n_open @ TA @ C )
& ( member @ TA @ A @ C ) )
=> ? [D: nat] : ( ord_less_eq @ ( set @ TA ) @ ( B @ D ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_first__countable__basis) ).
thf(412,plain,
! [TA: $tType] :
( ( topolo2135403230pology @ TA )
=> ! [A: TA] :
? [B: nat > ( set @ TA )] :
( ! [C: nat] :
( ( member @ TA @ A @ ( B @ C ) )
& ( topolo1751647064n_open @ TA @ ( B @ C ) ) )
& ! [C: set @ TA] :
( ( ( topolo1751647064n_open @ TA @ C )
& ( member @ TA @ A @ C ) )
=> ? [D: nat] : ( ord_less_eq @ ( set @ TA ) @ ( B @ D ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(92,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_Int__greatest) ).
thf(425,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(94,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( bot_bot @ ( set @ TA ) )
= ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C ) )
= ( ~ ( member @ TA @ A @ C )
& ( ( bot_bot @ ( set @ TA ) )
= ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_insert__disjoint_I2_J) ).
thf(430,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( bot_bot @ ( set @ TA ) )
= ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C ) )
= ( ~ ( member @ TA @ A @ C )
& ( ( bot_bot @ ( set @ TA ) )
= ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(34,axiom,
! [TA: $tType,A: set @ TA] :
( ( is_singleton @ TA @ A )
=> ~ ! [B: TA] :
( A
!= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_is__singletonE) ).
thf(264,plain,
! [TA: $tType,A: set @ TA] :
( ( is_singleton @ TA @ A )
=> ~ ! [B: TA] :
( A
!= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(99,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ~ ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_disjoint__iff) ).
thf(444,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ~ ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(91,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_DiffD1) ).
thf(423,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(5,axiom,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: TA] :
( ( topolo507301023within @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( filter @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_at__within__empty) ).
thf(191,plain,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: TA] :
( ( topolo507301023within @ TA @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( filter @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(143,axiom,
! [TA: $tType] :
( ( topolo2133971006pology @ TA )
=> ! [A: set @ TA] : ( topolo1751647064n_open @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_open__discrete) ).
thf(577,plain,
! [TA: $tType] :
( ( topolo2133971006pology @ TA )
=> ! [A: set @ TA] : ( topolo1751647064n_open @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(144,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C != D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_disjoint__iff__not__equal) ).
thf(579,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(134,axiom,
! [TA: $tType] :
( ( topological_t2_space @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ? [C: set @ TA,D: set @ TA] :
( ( topolo1751647064n_open @ TA @ C )
& ( topolo1751647064n_open @ TA @ D )
& ( member @ TA @ A @ C )
& ( member @ TA @ B @ D )
& ( ( inf_inf @ ( set @ TA ) @ C @ D )
= ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_hausdorff) ).
thf(545,plain,
! [TA: $tType] :
( ( topological_t2_space @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ? [C: set @ TA,D: set @ TA] :
( ( topolo1751647064n_open @ TA @ C )
& ( topolo1751647064n_open @ TA @ D )
& ( member @ TA @ A @ C )
& ( member @ TA @ B @ D )
& ( ( inf_inf @ ( set @ TA ) @ C @ D )
= ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType] :
( ( topolo503727757_space @ TA )
=> ( topolo503727757_space @ ( TB > TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Topological__Spaces_Otopological__space) ).
thf(259,plain,
! [TA: $tType,TB: $tType] :
( ( topolo503727757_space @ TA )
=> ( topolo503727757_space @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(39,axiom,
topological_t0_space @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Ot0__space_34) ).
thf(281,plain,
topological_t0_space @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(10,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_subset__insertI2) ).
thf(204,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(164,axiom,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ ( bot_bot @ TA ) @ A )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_inf__bot__left) ).
thf(641,plain,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ ( bot_bot @ TA ) @ A )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(80,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_insert__subset) ).
thf(391,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(119,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_Int__empty__right) ).
thf(498,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(107,axiom,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ( topolo1751647064n_open @ TA @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_open__empty) ).
thf(466,plain,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ( topolo1751647064n_open @ TA @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(132,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_UNIV__I) ).
thf(540,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( top_top @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(86,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( inf_inf @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_Int__insert__left__if0) ).
thf(406,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( inf_inf @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(20,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_mk__disjoint__insert) ).
thf(230,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ B )
=> ? [C: set @ TA] :
( ( B
= ( insert @ TA @ A @ C ) )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(139,axiom,
comple1035589618norder @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
thf(567,plain,
comple1035589618norder @ b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(122,axiom,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ ( bot_bot @ TA ) )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_inf__bot__right) ).
thf(509,plain,
! [TA: $tType] :
( ( bounded_lattice_bot @ TA )
=> ! [A: TA] :
( ( inf_inf @ TA @ A @ ( bot_bot @ TA ) )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(160,axiom,
topolo2117631714pology @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_1) ).
thf(631,plain,
topolo2117631714pology @ b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(72,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Diff__insert) ).
thf(367,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(154,axiom,
! [TA: $tType] :
( ( topological_t0_space @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ? [C: set @ TA] :
( ( topolo1751647064n_open @ TA @ C )
& ( ( member @ TA @ A @ C )
!= ( member @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_t0__space) ).
thf(609,plain,
! [TA: $tType] :
( ( topological_t0_space @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ? [C: set @ TA] :
( ( topolo1751647064n_open @ TA @ C )
& ( ( member @ TA @ A @ C )
!= ( member @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(149,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_subsetI) ).
thf(594,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(159,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_Int__insert__right) ).
thf(626,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(57,axiom,
topolo503727757_space @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Otopological__space_29) ).
thf(330,plain,
topolo503727757_space @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(24,axiom,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_subset__insertI) ).
thf(240,plain,
! [TA: $tType,A: set @ TA,B: TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(29,axiom,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_bot__set__def) ).
thf(251,plain,
! [TA: $tType] :
( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ ( bot_bot @ ( TA > $o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(83,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_Int__lower2) ).
thf(399,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(35,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_Diff__insert2) ).
thf(267,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(97,axiom,
( ~ ! [A: set @ b] :
( ( ( topolo1751647064n_open @ b @ A )
& ( member @ b @ ( f @ x0 ) @ A ) )
=> ? [B: set @ a] :
( ( topolo1751647064n_open @ 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_582600101lsc_at @ a @ b @ x0 @ f ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_calculation) ).
thf(438,plain,
( ~ ! [A: set @ b] :
( ( ( topolo1751647064n_open @ b @ A )
& ( member @ b @ ( f @ x0 ) @ A ) )
=> ? [B: set @ a] :
( ( topolo1751647064n_open @ 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_582600101lsc_at @ a @ b @ x0 @ f ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(167,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_DiffD2) ).
thf(658,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(81,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_Collect__mono) ).
thf(394,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(50,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ D ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_Diff__mono) ).
thf(306,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ D ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(129,axiom,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_all__not__in__conv) ).
thf(531,plain,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(12,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_insert__ident) ).
thf(209,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(156,axiom,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_Int__empty__left) ).
thf(617,plain,
! [TA: $tType,A: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(6,axiom,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( filter @ TA ) @ ( topolo507301023within @ TA @ C @ A ) @ ( topolo507301023within @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_at__le) ).
thf(194,plain,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( filter @ TA ) @ ( topolo507301023within @ TA @ C @ A ) @ ( topolo507301023within @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(127,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Collect__empty__eq) ).
thf(525,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(183,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( remove @ TA @ B @ C ) )
= ( ( member @ TA @ A @ C )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_member__remove) ).
thf(712,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( remove @ TA @ B @ C ) )
= ( ( member @ TA @ A @ C )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(45,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_Diff__single__insert) ).
thf(295,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(181,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_doubleton__eq__iff) ).
thf(707,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( insert @ TA @ C @ ( insert @ TA @ D @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(56,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ C @ D ) ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ D ) )
& ~ ( member @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_subset__Diff__insert) ).
thf(327,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ C @ D ) ) )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ D ) )
& ~ ( member @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(87,axiom,
! [TA: $tType] :
( ( topological_t1_space @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
= ( ? [C: set @ TA] :
( ( topolo1751647064n_open @ TA @ C )
& ( member @ TA @ A @ C )
& ~ ( member @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_separation__t1) ).
thf(409,plain,
! [TA: $tType] :
( ( topological_t1_space @ TA )
=> ! [A: TA,B: TA] :
( ( A != B )
= ( ? [C: set @ TA] :
( ( topolo1751647064n_open @ TA @ C )
& ( member @ TA @ A @ C )
& ~ ( member @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(180,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_subsetD) ).
thf(705,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(40,axiom,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( topolo1751647064n_open @ TA @ B )
=> ( ( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ C @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ D @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
=> ( ( topolo507301023within @ TA @ A @ C )
= ( topolo507301023within @ TA @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_at__within__nhd) ).
thf(282,plain,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( topolo1751647064n_open @ TA @ B )
=> ( ( ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ C @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) )
= ( minus_minus @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ D @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
=> ( ( topolo507301023within @ TA @ A @ C )
= ( topolo507301023within @ TA @ A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(8,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_subset__singletonD) ).
thf(199,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
=> ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(58,axiom,
bounded_lattice_bot @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Obounded__lattice__bot_31) ).
thf(331,plain,
bounded_lattice_bot @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(106,axiom,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ( ( topolo1751647064n_open @ TA )
= ( ^ [A: set @ TA] :
! [B: TA] :
( ( member @ TA @ B @ A )
=> ? [C: set @ TA] :
( ( topolo1751647064n_open @ TA @ C )
& ( member @ TA @ B @ C )
& ( ord_less_eq @ ( set @ TA ) @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_open__subopen) ).
thf(463,plain,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ( ( topolo1751647064n_open @ TA )
= ( ^ [A: set @ TA] :
! [B: TA] :
( ( member @ TA @ B @ A )
=> ? [C: set @ TA] :
( ( topolo1751647064n_open @ TA @ C )
& ( member @ TA @ B @ C )
& ( ord_less_eq @ ( set @ TA ) @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(61,axiom,
topolo2133971006pology @ $o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Odiscrete__topology_30) ).
thf(338,plain,
topolo2133971006pology @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(70,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_equalityD2) ).
thf(359,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(146,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_IntD2) ).
thf(585,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(73,axiom,
! [TA: $tType] :
( ( remove @ TA )
= ( ^ [A: TA,B: set @ TA] : ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_remove__def) ).
thf(370,plain,
! [TA: $tType] :
( ( remove @ TA )
= ( ^ [A: TA,B: set @ TA] : ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(166,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_DiffI) ).
thf(656,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(151,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Int__iff) ).
thf(600,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(78,axiom,
! [TA: $tType] :
( ( topolo2135403230pology @ TA )
=> ( topolo503727757_space @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Topological__Spaces_Ofirst__countable__topology___Topological__Spaces_Otopological__space) ).
thf(386,plain,
! [TA: $tType] :
( ( topolo2135403230pology @ TA )
=> ( topolo503727757_space @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(53,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_equalityE) ).
thf(314,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(141,axiom,
( a2
!= ( f @ x0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062) ).
thf(571,plain,
( a2
!= ( f @ x0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(113,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_Int__insert__left__if1) ).
thf(482,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(171,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_Diff__empty) ).
thf(671,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(175,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ~ ( member @ TA @ C @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_Int__emptyI) ).
thf(688,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ~ ( member @ TA @ C @ B ) )
=> ( ( inf_inf @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(16,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_subset__singleton__iff) ).
thf(218,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
| ( A
= ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(71,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_equalityD1) ).
thf(363,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(135,axiom,
! [TA: $tType] :
( ( topolo47006728_space @ TA )
=> ( topolo406746546ounded @ TA @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_totally__bounded__empty) ).
thf(556,plain,
! [TA: $tType] :
( ( topolo47006728_space @ TA )
=> ( topolo406746546ounded @ TA @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(178,axiom,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_Int__commute) ).
thf(699,plain,
! [TA: $tType] :
( ( inf_inf @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( inf_inf @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(49,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_insert__subsetI) ).
thf(304,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(3,axiom,
! [TA: $tType] : ( bounded_lattice_bot @ ( filter @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Filter_Ofilter___Lattices_Obounded__lattice__bot_45) ).
thf(186,plain,
! [TA: $tType] : ( bounded_lattice_bot @ ( filter @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(161,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_Int__insert__right__if1) ).
thf(632,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(84,axiom,
! [TA: $tType] :
( ( topolo890362671_space @ TA )
=> ! [A: TA] :
~ ( topolo1751647064n_open @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_not__open__singleton) ).
thf(401,plain,
! [TA: $tType] :
( ( topolo890362671_space @ TA )
=> ! [A: TA] :
~ ( topolo1751647064n_open @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(140,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_Int__left__absorb) ).
thf(568,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(27,axiom,
! [TA: $tType] : ( bounded_lattice_bot @ ( set @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Lattices_Obounded__lattice__bot_19) ).
thf(246,plain,
! [TA: $tType] : ( bounded_lattice_bot @ ( set @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(95,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_subset__emptyI) ).
thf(433,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(77,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_Collect__mono__iff) ).
thf(383,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(174,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_equals0D) ).
thf(684,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(65,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(346,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(43,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( minus_minus @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_insert__Diff1) ).
thf(290,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( minus_minus @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(75,axiom,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_insertI1) ).
thf(378,plain,
! [TA: $tType,A: TA,B: set @ TA] : ( member @ TA @ A @ ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(14,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_insertI2) ).
thf(214,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(42,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_subset__insert) ).
thf(287,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(157,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_Int__insert__right__if0) ).
thf(620,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(100,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_IntI) ).
thf(447,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(37,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_insert__Diff__single) ).
thf(273,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(74,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_insertCI) ).
thf(373,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(152,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_insert__not__empty) ).
thf(603,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ B )
!= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(138,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_Int__Diff__disjoint) ).
thf(564,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(63,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_insertE) ).
thf(341,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
=> ( ( A != B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(121,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_DiffE) ).
thf(506,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(110,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_emptyE) ).
thf(474,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(170,axiom,
! [TA: $tType,A: set @ TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [B: TA,C: TA] :
( ( member @ TA @ B @ A )
=> ( ( member @ TA @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_is__singletonI_H) ).
thf(664,plain,
! [TA: $tType,A: set @ TA] :
( ( A
!= ( bot_bot @ ( set @ TA ) ) )
=> ( ! [B: TA,C: TA] :
( ( member @ TA @ B @ A )
=> ( ( member @ TA @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(162,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( ( bot_bot @ ( set @ TA ) )
= ( inf_inf @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) ) )
= ( ~ ( member @ TA @ B @ A )
& ( ( bot_bot @ ( set @ TA ) )
= ( inf_inf @ ( set @ TA ) @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_disjoint__insert_I2_J) ).
thf(635,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( ( bot_bot @ ( set @ TA ) )
= ( inf_inf @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) ) )
= ( ~ ( member @ TA @ B @ A )
& ( ( bot_bot @ ( set @ TA ) )
= ( inf_inf @ ( set @ TA ) @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(177,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_Int__left__commute) ).
thf(696,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( inf_inf @ ( set @ TA ) @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
= ( inf_inf @ ( set @ TA ) @ B @ ( inf_inf @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(23,axiom,
topolo2135403230pology @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_2) ).
thf(239,plain,
topolo2135403230pology @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(25,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_Diff__subset) ).
thf(242,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(59,axiom,
! [TA: $tType] :
( ( topolo2117631714pology @ TA )
=> ( topological_t1_space @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subcl_Topological__Spaces_Olinorder__topology___Topological__Spaces_Ot1__space) ).
thf(332,plain,
! [TA: $tType] :
( ( topolo2117631714pology @ TA )
=> ( topological_t1_space @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(93,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_subset__iff) ).
thf(427,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(128,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_Diff__Diff__Int) ).
thf(528,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
= ( inf_inf @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(165,axiom,
( ( ( f @ x0 )
!= a2 )
=> ? [A: set @ b,B: set @ b] :
( ( topolo1751647064n_open @ b @ A )
& ( topolo1751647064n_open @ b @ B )
& ( member @ b @ ( f @ x0 ) @ A )
& ( member @ b @ a2 @ B )
& ( ( inf_inf @ ( set @ b ) @ A @ B )
= ( bot_bot @ ( set @ b ) ) ) ) ),
file('/export/starexec/sandbox2/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(644,plain,
( ( ( f @ x0 )
!= a2 )
=> ? [A: set @ b,B: set @ b] :
( ( topolo1751647064n_open @ b @ A )
& ( topolo1751647064n_open @ 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)],[165]) ).
thf(98,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_empty__subsetI) ).
thf(442,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(120,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ C @ B ) ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( inf_inf @ ( set @ TA ) @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_Int__insert__left) ).
thf(501,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( insert @ TA @ A @ ( inf_inf @ ( set @ TA ) @ C @ B ) ) ) )
& ( ~ ( member @ TA @ A @ B )
=> ( ( inf_inf @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( inf_inf @ ( set @ TA ) @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(116,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_IntD1) ).
thf(491,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( inf_inf @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(30,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_insert__absorb2) ).
thf(254,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(19,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_insert__commute) ).
thf(227,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(118,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_Int__lower1) ).
thf(496,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( inf_inf @ ( set @ TA ) @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(103,axiom,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_subset__empty) ).
thf(454,plain,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(719,plain,
$false,
inference(e,[status(thm)],[715,479,468,234,352,582,276,308,449,614,677,202,597,185,417,301,257,587,702,344,196,542,460,638,606,261,216,591,321,623,485,574,353,397,221,293,660,206,452,248,380,512,270,534,334,349,561,297,693,435,522,493,710,324,285,224,519,403,188,388,356,420,471,488,339,537,476,212,515,457,237,244,311,558,674,662,298,412,425,430,264,444,423,191,577,579,545,259,281,204,641,391,498,466,540,406,230,567,509,631,367,609,594,626,330,240,251,399,267,438,658,394,306,531,209,617,194,525,712,295,707,327,409,705,282,199,331,463,338,359,585,370,656,600,386,314,571,482,671,688,218,363,556,699,304,186,632,401,568,246,433,383,684,346,290,378,214,287,620,447,273,373,603,564,341,506,474,664,635,696,239,242,332,427,528,644,442,501,491,254,227,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP115^2 : TPTP v8.2.0. Released v7.5.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat May 18 17:00:24 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.98/1.01 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.13/1.41 % [INFO] Parsing done (394ms).
% 2.13/1.42 % [INFO] Running in sequential loop mode.
% 3.41/1.80 % [INFO] eprover registered as external prover.
% 3.41/1.80 % [INFO] cvc4 registered as external prover.
% 3.41/1.81 % [INFO] Scanning for conjecture ...
% 3.66/1.95 % [INFO] Found a conjecture (or negated_conjecture) and 357 axioms. Running axiom selection ...
% 4.27/2.09 % [INFO] Axiom selection finished. Selected 182 axioms (removed 175 axioms).
% 4.95/2.36 % [INFO] Problem is higher-order (TPTP THF).
% 4.95/2.39 % [INFO] Type checking passed.
% 5.16/2.39 % [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 ...
% 26.99/13.00 % External prover 'e' found a proof!
% 26.99/13.00 % [INFO] Killing All external provers ...
% 26.99/13.00 % Time passed: 12483ms (effective reasoning time: 11569ms)
% 26.99/13.00 % 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)>
% 26.99/13.00 % Axioms used in derivation (182): fact_4_inf__bot__left, tcon_Set_Oset___Lattices_Obounded__lattice__bot_19, subcl_Topological__Spaces_Olinorder__topology___Topological__Spaces_Ot2__space, tcon_HOL_Obool___Topological__Spaces_Ot2__space_32, fact_217_Diff__mono, fact_97_is__singletonI, fact_200_Diff__eq__empty__iff, subcl_Topological__Spaces_Olinorder__topology___Topological__Spaces_Ot1__space, fact_240_equalityD2, tfree_0, fact_41_Int__left__absorb, subcl_Topological__Spaces_Olinorder__topology___Topological__Spaces_Otopological__space, fact_85_Int__insert__left__if1, fact_233_member__remove, fact_72_insert__disjoint_I2_J, fact_140_insert__Diff, fact_146_is__singletonE, fact_204_insert__mono, fact_95_disjoint__insert_I1_J, fact_194_empty__subsetI, fact_71_insert__disjoint_I1_J, fact_87_Int__insert__right__if0, fact_188_open__delete, fact_201_subset__insertI2, fact_225_subset__insert__iff, fact_202_subset__insertI, fact_239_equalityD1, fact_107_insert__eq__iff, fact_65_totally__bounded__empty, fact_155_Diff__Int2, fact_219_subset__singletonD, fact_214_topological__space__class_OopenI, fact_59_Int__empty__left, fact_109_insert__commute, fact_158_Diff__Int__distrib2, fact_157_Diff__Int__distrib, fact_79_Diff__iff, fact_212_first__countable__basis, tcon_fun___Topological__Spaces_Otopological__space, fact_224_Diff__single__insert, fact_106_insert__absorb, fact_186_not__open__singleton, fact_154_Int__Diff, fact_232_subset__antisym, fact_195_subset__empty, fact_229_remove__def, fact_0__092_060open_062A_A_092_060noteq_062_Af_Ax0_092_060close_062, fact_58_Int__empty__right, fact_103_insertI2, fact_93_insert__Diff1, fact_152_Int__insert__left, fact_23_ex__in__conv, tcon_HOL_Obool___Topological__Spaces_Odiscrete__topology_30, fact_92_Diff__insert0, fact_94_disjoint__insert_I2_J, fact_98_DiffE, fact_6_hausdorff, fact_43_Int__absorb, fact_80_Diff__idemp, fact_46_Collect__mem__eq, fact_22_bot__set__def, fact_218_totally__bounded__subset, fact_248_at__discrete, fact_235_in__mono, fact_244_subset__trans, fact_76_insert__iff, fact_42_Int__commute, fact_54_separation__t0, fact_57_disjoint__iff__not__equal, fact_247_at__le, fact_138_Diff__insert__absorb, fact_189_Int__Diff__disjoint, fact_16_all__not__in__conv, fact_49_IntD2, fact_88_Int__insert__right__if1, fact_2_open__Int, fact_53_separation__t1, fact_111_mk__disjoint__insert, fact_63_calculation, fact_83_singletonI, fact_86_insert__inter__insert, fact_207_Int__absorb2, fact_208_Int__absorb1, fact_149_doubleton__eq__iff, fact_150_insert__not__empty, fact_151_singleton__inject, fact_199_singleton__insert__inj__eq_H, fact_234_at__within__empty, fact_243_Collect__mono, fact_17_empty__iff, fact_66_Collect__empty__eq__bot, fact_50_IntD1, subcl_Topological__Spaces_Olinorder__topology___Topological__Spaces_Ot0__space, fact_51_IntE, fact_108_insert__Diff__if, fact_237_equalityE, fact_196_insert__subset, fact_40_Int__left__commute, tfree_2, fact_45_mem__Collect__eq, fact_56_t0__space, tcon_HOL_Obool___Topological__Spaces_Ot1__space_33, fact_190_is__singleton__the__elem, fact_5_inf__bot__right, fact_67_bot__empty__eq, fact_61_Int__emptyI, fact_209_Int__lower2, fact_141_Diff__insert, fact_187_Diff__triv, subcl_Topological__Spaces_Ofirst__countable__topology___Topological__Spaces_Otopological__space, fact_221_subset__Diff__insert, fact_210_Int__lower1, fact_55_t1__space, fact_26_emptyE, fact_9_Int__iff, fact_105_insert__ident, fact_47_Collect__cong, fact_24_equals0I, fact_191_ball__insert, fact_231_subsetI, fact_14_empty__Collect__eq, fact_206_Int__greatest, fact_211_Int__mono, fact_15_Collect__empty__eq, fact_147_singletonD, fact_78_DiffI, fact_197_Int__subset__iff, fact_44_Int__assoc, fact_25_equals0D, fact_148_singleton__iff, fact_84_Int__insert__left__if0, 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_156_Diff__Diff__Int, fact_236_subsetD, fact_75_insertCI, fact_102_insertI1, tfree_1, fact_69_is__singletonI_H, fact_213_open__subopen, fact_241_subset__iff, fact_230_at__within__nhd, fact_216_Diff__subset, fact_100_DiffD2, fact_7_separation__t2, fact_242_subset__refl, fact_215_double__diff, fact_145_is__singleton__def, fact_249_insert__subsetI, tcon_HOL_Obool___Topological__Spaces_Ot0__space_34, fact_101_insertE, fact_153_Int__insert__right, fact_89_Diff__empty, fact_8_IntI, tcon_HOL_Obool___Lattices_Obounded__lattice__bot_31, fact_198_singleton__insert__inj__eq, fact_139_Diff__insert2, fact_104_Set_Oset__insert, fact_77_insert__absorb2, fact_3_open__empty, fact_205_Int__Collect__mono, fact_254_UNIV__I, fact_91_Diff__cancel, fact_99_DiffD1, fact_96_insert__Diff__single, fact_60_disjoint__iff, conj_0, fact_245_set__eq__subset, fact_192_the__elem__eq, subcl_Complete__Lattices_Ocomplete__linorder___Lattices_Obounded__lattice__bot, fact_220_subset__singleton__iff, fact_52_open__discrete, fact_64_Set_Ois__empty__def, fact_70_Diff__disjoint, tcon_HOL_Obool___Topological__Spaces_Otopological__space_29, fact_251_at__eq__bot__iff, fact_21__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, tcon_Filter_Ofilter___Lattices_Obounded__lattice__bot_45, fact_250_subset__emptyI, fact_238_subset__eq, fact_203_subset__insert, fact_246_Collect__mono__iff, fact_90_empty__Diff
% 26.99/13.00 % No. of inferences in proof: 368
% 26.99/13.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 12483 ms resp. 11569 ms w/o parsing
% 27.85/13.12 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 27.85/13.12 % [INFO] Killing All external provers ...
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