TSTP Solution File: ITP144^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ITP144^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 : Tue May 7 07:48:12 EDT 2024
% Result : Theorem 8.83s 2.99s
% Output : Refutation 8.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 138
% Syntax : Number of formulae : 252 ( 109 unt; 26 typ; 0 def)
% Number of atoms : 536 ( 306 equ; 4 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 1469 ( 105 ~; 9 |; 52 &;1101 @)
% ( 0 <=>; 202 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 138 ( 138 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 5 con; 0-3 aty)
% Number of variables : 561 ( 72 ^ 459 !; 30 ?; 561 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_set_b_type,type,
set_set_b: $tType ).
thf(set_b_type,type,
set_b: $tType ).
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(bij_betw_b_b_type,type,
bij_betw_b_b: ( b > b ) > set_b > set_b > $o ).
thf(inj_on_b_set_b_type,type,
inj_on_b_set_b: ( b > set_b ) > set_b > $o ).
thf(inj_on_b_b_type,type,
inj_on_b_b: ( b > b ) > set_b > $o ).
thf(minus_minus_set_b_type,type,
minus_minus_set_b: set_b > set_b > set_b ).
thf(hilbert_Eps_b_type,type,
hilbert_Eps_b: ( b > $o ) > b ).
thf(hilbert_inv_into_b_b_type,type,
hilbert_inv_into_b_b: set_b > ( b > b ) > b > b ).
thf(bot_bot_b_o_type,type,
bot_bot_b_o: b > $o ).
thf(bot_bot_set_b_type,type,
bot_bot_set_b: set_b ).
thf(top_top_b_o_type,type,
top_top_b_o: b > $o ).
thf(top_top_set_b_type,type,
top_top_set_b: set_b ).
thf(collect_b_type,type,
collect_b: ( b > $o ) > set_b ).
thf(image_set_b_set_b_type,type,
image_set_b_set_b: ( set_b > set_b ) > set_set_b > set_set_b ).
thf(image_b_b_type,type,
image_b_b: ( b > b ) > set_b > set_b ).
thf(insert_b_type,type,
insert_b: b > set_b > set_b ).
thf(is_empty_b_type,type,
is_empty_b: set_b > $o ).
thf(is_singleton_b_type,type,
is_singleton_b: set_b > $o ).
thf(remove_b_type,type,
remove_b: b > set_b > set_b ).
thf(the_elem_b_type,type,
the_elem_b: set_b > b ).
thf(member_set_b_type,type,
member_set_b: set_b > set_set_b > $o ).
thf(member_b_type,type,
member_b: b > set_b > $o ).
thf(p_type,type,
p: a > $o ).
thf(q_type,type,
q: a > b > $o ).
thf(67,axiom,
! [A: b] : ( member_b @ A @ top_top_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_iso__tuple__UNIV__I) ).
thf(344,plain,
! [A: b] : ( member_b @ A @ top_top_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(65,axiom,
! [A: set_b] :
( ( ? [B: b] : ( member_b @ B @ A ) )
= ( A != bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_ex__in__conv) ).
thf(339,plain,
! [A: set_b] :
( ( ? [B: b] : ( member_b @ B @ A ) )
= ( A != bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(27,axiom,
( minus_minus_set_b
= ( ^ [A: set_b,B: set_b] :
( collect_b
@ ^ [C: b] :
( ( member_b @ C @ A )
& ~ ( member_b @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_set__diff__eq) ).
thf(204,plain,
( minus_minus_set_b
= ( ^ [A: set_b,B: set_b] :
( collect_b
@ ^ [C: b] :
( ( member_b @ C @ A )
& ~ ( member_b @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(97,axiom,
! [A: set_b,B: b > $o,C: b > $o] :
( ? [D: b] :
( ( member_b @ D @ A )
& ( B @ D ) )
=> ( ! [D: b] :
( ( ( member_b @ D @ A )
& ( B @ D ) )
=> ( C @ D ) )
=> ( C
@ ( hilbert_Eps_b
@ ^ [D: b] :
( ( member_b @ D @ A )
& ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_someI2__bex) ).
thf(441,plain,
! [A: set_b,B: b > $o,C: b > $o] :
( ? [D: b] :
( ( member_b @ D @ A )
& ( B @ D ) )
=> ( ! [D: b] :
( ( ( member_b @ D @ A )
& ( B @ D ) )
=> ( C @ D ) )
=> ( C
@ ( hilbert_Eps_b
@ ^ [D: b] :
( ( member_b @ D @ A )
& ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(8,axiom,
! [A: set_b] :
( ( minus_minus_set_b @ bot_bot_set_b @ A )
= bot_bot_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_empty__Diff) ).
thf(138,plain,
! [A: set_b] :
( ( minus_minus_set_b @ bot_bot_set_b @ A )
= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(63,axiom,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
=> ( member_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_DiffD1) ).
thf(333,plain,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
=> ( member_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(31,axiom,
! [A: b] :
( ( collect_b @ ( (=) @ b @ A ) )
= ( insert_b @ A @ bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_singleton__conv2) ).
thf(217,plain,
! [A: b] :
( ( collect_b @ ( (=) @ b @ A ) )
= ( insert_b @ A @ bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(4,axiom,
! [A: b > b,B: set_b,C: b,D: set_b] :
( ( inj_on_b_b @ A @ B )
=> ( ~ ( member_b @ C @ D )
=> ( ( ( insert_b @ C @ D )
= ( image_b_b @ A @ B ) )
=> ~ ! [E: b,F: set_b] :
( ~ ( member_b @ E @ F )
=> ( ( B
= ( insert_b @ E @ F ) )
=> ( ( C
= ( A @ E ) )
=> ( D
!= ( image_b_b @ A @ F ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_inj__img__insertE) ).
thf(120,plain,
! [A: b > b,B: set_b,C: b,D: set_b] :
( ( inj_on_b_b @ A @ B )
=> ( ~ ( member_b @ C @ D )
=> ( ( ( insert_b @ C @ D )
= ( image_b_b @ A @ B ) )
=> ~ ! [E: b,F: set_b] :
( ~ ( member_b @ E @ F )
=> ( ( B
= ( insert_b @ E @ F ) )
=> ( ( C
= ( A @ E ) )
=> ( D
!= ( image_b_b @ A @ F ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(40,axiom,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ~ ! [C: set_b] :
( ( B
= ( insert_b @ A @ C ) )
=> ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_Set_Oset__insert) ).
thf(247,plain,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ~ ! [C: set_b] :
( ( B
= ( insert_b @ A @ C ) )
=> ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(23,axiom,
! [A: b,B: set_b,C: b] :
( ( ~ ( member_b @ A @ B )
=> ( A = C ) )
=> ( member_b @ A @ ( insert_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_insertCI) ).
thf(189,plain,
! [A: b,B: set_b,C: b] :
( ( ~ ( member_b @ A @ B )
=> ( A = C ) )
=> ( member_b @ A @ ( insert_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(92,axiom,
! [A: b] :
( ( hilbert_Eps_b @ ( (=) @ b @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_some__sym__eq__trivial) ).
thf(421,plain,
! [A: b] :
( ( hilbert_Eps_b @ ( (=) @ b @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(49,axiom,
! [A: b,B: set_b] :
( ~ ( member_b @ A @ B )
=> ( ( minus_minus_set_b @ ( insert_b @ A @ B ) @ ( insert_b @ A @ bot_bot_set_b ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_Diff__insert__absorb) ).
thf(284,plain,
! [A: b,B: set_b] :
( ~ ( member_b @ A @ B )
=> ( ( minus_minus_set_b @ ( insert_b @ A @ B ) @ ( insert_b @ A @ bot_bot_set_b ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(12,axiom,
! [A: set_b,B: b,C: set_b] :
( ( minus_minus_set_b @ A @ ( insert_b @ B @ C ) )
= ( minus_minus_set_b @ ( minus_minus_set_b @ A @ C ) @ ( insert_b @ B @ bot_bot_set_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_Diff__insert) ).
thf(152,plain,
! [A: set_b,B: b,C: set_b] :
( ( minus_minus_set_b @ A @ ( insert_b @ B @ C ) )
= ( minus_minus_set_b @ ( minus_minus_set_b @ A @ C ) @ ( insert_b @ B @ bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(45,axiom,
! [A: b > $o,B: b] :
( ( ( A @ B )
=> ( ( collect_b
@ ^ [C: b] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_b @ B @ bot_bot_set_b ) ) )
& ( ~ ( A @ B )
=> ( ( collect_b
@ ^ [C: b] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_set_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_Collect__conv__if) ).
thf(261,plain,
! [A: b > $o,B: b] :
( ( ( A @ B )
=> ( ( collect_b
@ ^ [C: b] :
( ( C = B )
& ( A @ C ) ) )
= ( insert_b @ B @ bot_bot_set_b ) ) )
& ( ~ ( A @ B )
=> ( ( collect_b
@ ^ [C: b] :
( ( C = B )
& ( A @ C ) ) )
= bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(59,axiom,
( is_singleton_b
= ( ^ [A: set_b] :
? [B: b] :
( A
= ( insert_b @ B @ bot_bot_set_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_is__singleton__def) ).
thf(321,plain,
( is_singleton_b
= ( ^ [A: set_b] :
? [B: b] :
( A
= ( insert_b @ B @ bot_bot_set_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(42,axiom,
! [A: b] : ( is_singleton_b @ ( insert_b @ A @ bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_is__singletonI) ).
thf(253,plain,
! [A: b] : ( is_singleton_b @ ( insert_b @ A @ bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(70,axiom,
! [A: b,B: b] :
( ( member_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_singletonD) ).
thf(353,plain,
! [A: b,B: b] :
( ( member_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(11,axiom,
! [A: b,B: set_b,C: b,D: b > b] :
( ( member_b @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_b @ C @ ( image_b_b @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_rev__image__eqI) ).
thf(147,plain,
! [A: b,B: set_b,C: b,D: b > b] :
( ( member_b @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_b @ C @ ( image_b_b @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,axiom,
! [A: b > $o] :
( ( bot_bot_set_b
= ( collect_b @ A ) )
= ( ! [B: b] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_empty__Collect__eq) ).
thf(133,plain,
! [A: b > $o] :
( ( bot_bot_set_b
= ( collect_b @ A ) )
= ( ! [B: b] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(94,axiom,
! [A: b] :
( ( hilbert_Eps_b
@ ^ [B: b] : ( B = A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_some__eq__trivial) ).
thf(428,plain,
! [A: b] :
( ( hilbert_Eps_b
@ ^ [B: b] : ( B = A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(28,axiom,
! [A: b,B: set_b,C: b,D: set_b] :
( ~ ( member_b @ A @ B )
=> ( ~ ( member_b @ C @ D )
=> ( ( ( insert_b @ A @ B )
= ( insert_b @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_b] :
( ( B
= ( insert_b @ C @ E ) )
& ~ ( member_b @ C @ E )
& ( D
= ( insert_b @ A @ E ) )
& ~ ( member_b @ A @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_insert__eq__iff) ).
thf(206,plain,
! [A: b,B: set_b,C: b,D: set_b] :
( ~ ( member_b @ A @ B )
=> ( ~ ( member_b @ C @ D )
=> ( ( ( insert_b @ A @ B )
= ( insert_b @ C @ D ) )
= ( ( ( A = C )
=> ( B = D ) )
& ( ( A != C )
=> ? [E: set_b] :
( ( B
= ( insert_b @ C @ E ) )
& ~ ( member_b @ C @ E )
& ( D
= ( insert_b @ A @ E ) )
& ~ ( member_b @ A @ E ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(56,axiom,
! [A: set_b,B: b] :
( ( ( A = bot_bot_set_b )
=> ( ( image_b_b
@ ^ [C: b] : B
@ A )
= bot_bot_set_b ) )
& ( ( A != bot_bot_set_b )
=> ( ( image_b_b
@ ^ [C: b] : B
@ A )
= ( insert_b @ B @ bot_bot_set_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_image__constant__conv) ).
thf(307,plain,
! [A: set_b,B: b] :
( ( ( A = bot_bot_set_b )
=> ( ( image_b_b
@ ^ [C: b] : B
@ A )
= bot_bot_set_b ) )
& ( ( A != bot_bot_set_b )
=> ( ( image_b_b
@ ^ [C: b] : B
@ A )
= ( insert_b @ B @ bot_bot_set_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(36,axiom,
! [A: b > b,B: b,C: set_b] :
( ( inj_on_b_b @ A @ top_top_set_b )
=> ( ( member_b @ ( A @ B ) @ ( image_b_b @ A @ C ) )
= ( member_b @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_inj__image__mem__iff) ).
thf(233,plain,
! [A: b > b,B: b,C: set_b] :
( ( inj_on_b_b @ A @ top_top_set_b )
=> ( ( member_b @ ( A @ B ) @ ( image_b_b @ A @ C ) )
= ( member_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(80,axiom,
( bot_bot_b_o
= ( ^ [A: b] : ( member_b @ A @ bot_bot_set_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_bot__empty__eq) ).
thf(380,plain,
( bot_bot_b_o
= ( ^ [A: b] : ( member_b @ A @ bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(3,axiom,
! [A: b] :
( ( the_elem_b @ ( insert_b @ A @ bot_bot_set_b ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_the__elem__eq) ).
thf(117,plain,
! [A: b] :
( ( the_elem_b @ ( insert_b @ A @ bot_bot_set_b ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(113,axiom,
! [A: b > $o,B: b] :
( ? [C: b] :
( ( A @ C )
& ! [D: b] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ( A @ B )
=> ( ( hilbert_Eps_b @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_some1__equality) ).
thf(512,plain,
! [A: b > $o,B: b] :
( ? [C: b] :
( ( A @ C )
& ! [D: b] :
( ( A @ D )
=> ( D = C ) ) )
=> ( ( A @ B )
=> ( ( hilbert_Eps_b @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(96,axiom,
( ( '!' @ b )
= ( ^ [A: b > $o] :
( A
@ ( hilbert_Eps_b
@ ^ [B: b] :
~ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_verit__sko__forall) ).
thf(439,plain,
( ( '!' @ b )
= ( ^ [A: b > $o] :
( A
@ ( hilbert_Eps_b
@ ^ [B: b] :
~ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(32,axiom,
! [A: b,B: b > b,C: set_b] :
( ( member_b @ A @ ( image_b_b @ B @ C ) )
=> ~ ! [D: b] :
( ( A
= ( B @ D ) )
=> ~ ( member_b @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_imageE) ).
thf(220,plain,
! [A: b,B: b > b,C: set_b] :
( ( member_b @ A @ ( image_b_b @ B @ C ) )
=> ~ ! [D: b] :
( ( A
= ( B @ D ) )
=> ~ ( member_b @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(74,axiom,
! [A: set_b] :
( inj_on_b_set_b
@ ^ [B: b] : ( insert_b @ B @ bot_bot_set_b )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_inj__singleton) ).
thf(366,plain,
! [A: set_b] :
( inj_on_b_set_b
@ ^ [B: b] : ( insert_b @ B @ bot_bot_set_b )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(15,axiom,
! [A: b > $o] :
( ( ( collect_b @ A )
= bot_bot_set_b )
= ( ! [B: b] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Collect__empty__eq) ).
thf(160,plain,
! [A: b > $o] :
( ( ( collect_b @ A )
= bot_bot_set_b )
= ( ! [B: b] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(53,axiom,
! [A: b > b,B: set_b] :
( ( bot_bot_set_b
= ( image_b_b @ A @ B ) )
= ( B = bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_empty__is__image) ).
thf(297,plain,
! [A: b > b,B: set_b] :
( ( bot_bot_set_b
= ( image_b_b @ A @ B ) )
= ( B = bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(93,axiom,
! [A: b,B: b > $o] :
( ( A
= ( hilbert_Eps_b @ B ) )
=> ( ( ? [C: b] : ( B @ C ) )
= ( B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_verit__sko__ex__indirect) ).
thf(424,plain,
! [A: b,B: b > $o] :
( ( A
= ( hilbert_Eps_b @ B ) )
=> ( ( ? [C: b] : ( B @ C ) )
= ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(47,axiom,
( remove_b
= ( ^ [A: b,B: set_b] : ( minus_minus_set_b @ B @ ( insert_b @ A @ bot_bot_set_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_remove__def) ).
thf(275,plain,
( remove_b
= ( ^ [A: b,B: set_b] : ( minus_minus_set_b @ B @ ( insert_b @ A @ bot_bot_set_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(102,axiom,
! [A: b > $o] :
( ? [B: b] : ( A @ B )
=> ( A @ ( hilbert_Eps_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_someI__ex) ).
thf(467,plain,
! [A: b > $o] :
( ? [B: b] : ( A @ B )
=> ( A @ ( hilbert_Eps_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(25,axiom,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
= ( ( member_b @ A @ B )
& ~ ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_Diff__iff) ).
thf(197,plain,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
= ( ( member_b @ A @ B )
& ~ ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(73,axiom,
! [A: set_b,B: b] :
( ( A = bot_bot_set_b )
=> ~ ( member_b @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_equals0D) ).
thf(361,plain,
! [A: set_b,B: b] :
( ( A = bot_bot_set_b )
=> ~ ( member_b @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(33,axiom,
! [A: b > b,B: b,C: set_b] :
( ( inj_on_b_b @ A @ ( insert_b @ B @ C ) )
= ( ( inj_on_b_b @ A @ C )
& ~ ( member_b @ ( A @ B ) @ ( image_b_b @ A @ ( minus_minus_set_b @ C @ ( insert_b @ B @ bot_bot_set_b ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_inj__on__insert) ).
thf(224,plain,
! [A: b > b,B: b,C: set_b] :
( ( inj_on_b_b @ A @ ( insert_b @ B @ C ) )
= ( ( inj_on_b_b @ A @ C )
& ~ ( member_b @ ( A @ B ) @ ( image_b_b @ A @ ( minus_minus_set_b @ C @ ( insert_b @ B @ bot_bot_set_b ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(87,axiom,
! [A: set_set_b,B: b,C: set_b] :
( ! [D: set_b] :
( ( member_set_b @ D @ A )
=> ~ ( member_b @ B @ D ) )
=> ( ( member_set_b @ C @ ( image_set_b_set_b @ ( insert_b @ B ) @ A ) )
= ( ( member_b @ B @ C )
& ( member_set_b @ ( minus_minus_set_b @ C @ ( insert_b @ B @ bot_bot_set_b ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_in__image__insert__iff) ).
thf(403,plain,
! [A: set_set_b,B: b,C: set_b] :
( ! [D: set_b] :
( ( member_set_b @ D @ A )
=> ~ ( member_b @ B @ D ) )
=> ( ( member_set_b @ C @ ( image_set_b_set_b @ ( insert_b @ B ) @ A ) )
= ( ( member_b @ B @ C )
& ( member_set_b @ ( minus_minus_set_b @ C @ ( insert_b @ B @ bot_bot_set_b ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(71,axiom,
( top_top_b_o
= ( ^ [A: b] : ( member_b @ A @ top_top_set_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_top__empty__eq) ).
thf(356,plain,
( top_top_b_o
= ( ^ [A: b] : ( member_b @ A @ top_top_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(18,axiom,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ B )
=> ( ( minus_minus_set_b @ ( insert_b @ A @ C ) @ B )
= ( minus_minus_set_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_insert__Diff1) ).
thf(169,plain,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ B )
=> ( ( minus_minus_set_b @ ( insert_b @ A @ C ) @ B )
= ( minus_minus_set_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(9,axiom,
! [A: b > b] :
( ( image_b_b @ A @ bot_bot_set_b )
= bot_bot_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_image__empty) ).
thf(141,plain,
! [A: b > b] :
( ( image_b_b @ A @ bot_bot_set_b )
= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(83,axiom,
? [A: b] : ( member_b @ A @ top_top_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_UNIV__witness) ).
thf(393,plain,
? [A: b] : ( member_b @ A @ top_top_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(100,axiom,
! [A: b,B: b > $o,C: b > $o] :
( ( A
= ( hilbert_Eps_b
@ ^ [D: b] :
~ ( B @ D ) ) )
=> ( ! [D: b] :
( ( B @ D )
= ( C @ D ) )
=> ( ( ! [D: b] : ( C @ D ) )
= ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_verit__sko__forall__indirect2) ).
thf(457,plain,
! [A: b,B: b > $o,C: b > $o] :
( ( A
= ( hilbert_Eps_b
@ ^ [D: b] :
~ ( B @ D ) ) )
=> ( ! [D: b] :
( ( B @ D )
= ( C @ D ) )
=> ( ( ! [D: b] : ( C @ D ) )
= ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(19,axiom,
! [A: b,B: set_b,C: set_b] :
( ( ( member_b @ A @ B )
=> ( ( minus_minus_set_b @ ( insert_b @ A @ C ) @ B )
= ( minus_minus_set_b @ C @ B ) ) )
& ( ~ ( member_b @ A @ B )
=> ( ( minus_minus_set_b @ ( insert_b @ A @ C ) @ B )
= ( insert_b @ A @ ( minus_minus_set_b @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_insert__Diff__if) ).
thf(173,plain,
! [A: b,B: set_b,C: set_b] :
( ( ( member_b @ A @ B )
=> ( ( minus_minus_set_b @ ( insert_b @ A @ C ) @ B )
= ( minus_minus_set_b @ C @ B ) ) )
& ( ~ ( member_b @ A @ B )
=> ( ( minus_minus_set_b @ ( insert_b @ A @ C ) @ B )
= ( insert_b @ A @ ( minus_minus_set_b @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(76,axiom,
! [A: b] : ( member_b @ A @ top_top_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_UNIV__I) ).
thf(371,plain,
! [A: b] : ( member_b @ A @ top_top_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(37,axiom,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
=> ~ ( member_b @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_DiffD2) ).
thf(237,plain,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
=> ~ ( member_b @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(39,axiom,
! [A: set_b] :
( ( collect_b
@ ^ [B: b] : ( member_b @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_Collect__mem__eq) ).
thf(244,plain,
! [A: set_b] :
( ( collect_b
@ ^ [B: b] : ( member_b @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(85,axiom,
! [A: set_b] :
( ! [B: b] : ( member_b @ B @ A )
=> ( top_top_set_b = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_UNIV__eq__I) ).
thf(398,plain,
! [A: set_b] :
( ! [B: b] : ( member_b @ B @ A )
=> ( top_top_set_b = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(89,axiom,
! [A: a] :
( ( p @ A )
=> ? [B: b] : ( q @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(412,plain,
! [A: a] :
( ( p @ A )
=> ? [B: b] : ( q @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(17,axiom,
! [A: b > $o] :
( ( ( collect_b @ A )
= bot_bot_set_b )
= ( A = bot_bot_b_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_Collect__empty__eq__bot) ).
thf(166,plain,
! [A: b > $o] :
( ( ( collect_b @ A )
= bot_bot_set_b )
= ( A = bot_bot_b_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(20,axiom,
! [A: b,B: set_b] :
( ( insert_b @ A @ ( minus_minus_set_b @ B @ ( insert_b @ A @ bot_bot_set_b ) ) )
= ( insert_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_insert__Diff__single) ).
thf(180,plain,
! [A: b,B: set_b] :
( ( insert_b @ A @ ( minus_minus_set_b @ B @ ( insert_b @ A @ bot_bot_set_b ) ) )
= ( insert_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(78,axiom,
! [A: set_b] :
( ( ! [B: b] :
~ ( member_b @ B @ A ) )
= ( A = bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_all__not__in__conv) ).
thf(375,plain,
! [A: set_b] :
( ( ! [B: b] :
~ ( member_b @ B @ A ) )
= ( A = bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(81,axiom,
! [A: set_b] :
( ( A != bot_bot_set_b )
=> ( ! [B: b,C: b] :
( ( member_b @ B @ A )
=> ( ( member_b @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_is__singletonI_H) ).
thf(382,plain,
! [A: set_b] :
( ( A != bot_bot_set_b )
=> ( ! [B: b,C: b] :
( ( member_b @ B @ A )
=> ( ( member_b @ C @ A )
=> ( B = C ) ) )
=> ( is_singleton_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(10,axiom,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ( ( insert_b @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_insert__absorb) ).
thf(144,plain,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ( ( insert_b @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(110,axiom,
! [A: b > $o,B: b,C: b] :
( ( A @ B )
=> ( ~ ( A @ C )
=> ( ( ( hilbert_Eps_b @ A )
= C )
=> ( ( hilbert_Eps_b @ A )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_Nitpick_OEps__psimp) ).
thf(498,plain,
! [A: b > $o,B: b,C: b] :
( ( A @ B )
=> ( ~ ( A @ C )
=> ( ( ( hilbert_Eps_b @ A )
= C )
=> ( ( hilbert_Eps_b @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(69,axiom,
! [A: b] :
~ ( member_b @ A @ bot_bot_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_empty__iff) ).
thf(350,plain,
! [A: b] :
~ ( member_b @ A @ bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(35,axiom,
! [A: b > b,B: set_b,C: b > $o] :
( ( collect_b
@ ^ [D: b] :
( ( member_b @ D @ ( image_b_b @ A @ B ) )
& ( C @ D ) ) )
= ( image_b_b @ A
@ ( collect_b
@ ^ [D: b] :
( ( member_b @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_Compr__image__eq) ).
thf(230,plain,
! [A: b > b,B: set_b,C: b > $o] :
( ( collect_b
@ ^ [D: b] :
( ( member_b @ D @ ( image_b_b @ A @ B ) )
& ( C @ D ) ) )
= ( image_b_b @ A
@ ( collect_b
@ ^ [D: b] :
( ( member_b @ D @ B )
& ( C @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(112,axiom,
! [A: b > $o] :
( ( A @ ( hilbert_Eps_b @ A ) )
= ( ? [B: b] : ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_some__eq__ex) ).
thf(509,plain,
! [A: b > $o] :
( ( A @ ( hilbert_Eps_b @ A ) )
= ( ? [B: b] : ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(105,axiom,
! [A: b,B: b > $o,C: b > $o] :
( ( A
= ( hilbert_Eps_b @ B ) )
=> ( ! [D: b] :
( ( B @ D )
= ( C @ D ) )
=> ( ( ? [D: b] : ( C @ D ) )
= ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_verit__sko__ex__indirect2) ).
thf(477,plain,
! [A: b,B: b > $o,C: b > $o] :
( ( A
= ( hilbert_Eps_b @ B ) )
=> ( ! [D: b] :
( ( B @ D )
= ( C @ D ) )
=> ( ( ? [D: b] : ( C @ D ) )
= ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(109,axiom,
! [A: b > $o,B: $o] :
( ( ( A
@ ( hilbert_Eps_b
@ ^ [C: b] :
~ ( A @ C ) ) )
= B )
=> ( ( ! [C: b] : ( A @ C ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_verit__sko__forall_H) ).
thf(494,plain,
! [A: b > $o,B: $o] :
( ( ( A
@ ( hilbert_Eps_b
@ ^ [C: b] :
~ ( A @ C ) ) )
= B )
=> ( ( ! [C: b] : ( A @ C ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(60,axiom,
! [A: b,B: set_b,C: b] :
( ( member_b @ A @ B )
=> ( ( image_b_b
@ ^ [D: b] : C
@ B )
= ( insert_b @ C @ bot_bot_set_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_image__constant) ).
thf(323,plain,
! [A: b,B: set_b,C: b] :
( ( member_b @ A @ B )
=> ( ( image_b_b
@ ^ [D: b] : C
@ B )
= ( insert_b @ C @ bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(30,axiom,
! [A: b,B: set_b] :
( ( insert_b @ A @ B )
!= bot_bot_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_insert__not__empty) ).
thf(213,plain,
! [A: b,B: set_b] :
( ( insert_b @ A @ B )
!= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(41,axiom,
! [A: b,B: set_b] : ( member_b @ A @ ( insert_b @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_insertI1) ).
thf(251,plain,
! [A: b,B: set_b] : ( member_b @ A @ ( insert_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(13,axiom,
! [A: b,B: b] :
( ( ( insert_b @ A @ bot_bot_set_b )
= ( insert_b @ B @ bot_bot_set_b ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_singleton__inject) ).
thf(155,plain,
! [A: b,B: b] :
( ( ( insert_b @ A @ bot_bot_set_b )
= ( insert_b @ B @ bot_bot_set_b ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(62,axiom,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
=> ~ ( ( member_b @ A @ B )
=> ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_DiffE) ).
thf(330,plain,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ ( minus_minus_set_b @ B @ C ) )
=> ~ ( ( member_b @ A @ B )
=> ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(101,axiom,
! [A: b > $o,B: b] :
( ( A @ B )
=> ( ! [C: b] :
( ( A @ C )
=> ( C = B ) )
=> ( ( hilbert_Eps_b @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_some__equality) ).
thf(462,plain,
! [A: b > $o,B: b] :
( ( A @ B )
=> ( ! [C: b] :
( ( A @ C )
=> ( C = B ) )
=> ( ( hilbert_Eps_b @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(5,axiom,
! [A: b,B: b,C: b,D: b] :
( ( ( insert_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
= ( insert_b @ C @ ( insert_b @ D @ bot_bot_set_b ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_doubleton__eq__iff) ).
thf(130,plain,
! [A: b,B: b,C: b,D: b] :
( ( ( insert_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
= ( insert_b @ C @ ( insert_b @ D @ bot_bot_set_b ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(95,axiom,
! [A: b > $o,B: b,C: b] :
( ( ( hilbert_Eps_b @ A )
= B )
=> ( ( A @ C )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_some__eq__imp) ).
thf(431,plain,
! [A: b > $o,B: b,C: b] :
( ( ( hilbert_Eps_b @ A )
= B )
=> ( ( A @ C )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(108,axiom,
! [A: b > $o,B: b,C: b > $o] :
( ( A @ B )
=> ( ! [D: b] :
( ( A @ D )
=> ( C @ D ) )
=> ( C @ ( hilbert_Eps_b @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_someI2) ).
thf(490,plain,
! [A: b > $o,B: b,C: b > $o] :
( ( A @ B )
=> ( ! [D: b] :
( ( A @ D )
=> ( C @ D ) )
=> ( C @ ( hilbert_Eps_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(43,axiom,
! [A: b] :
( ( collect_b
@ ^ [B: b] : ( B = A ) )
= ( insert_b @ A @ bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_singleton__conv) ).
thf(255,plain,
! [A: b] :
( ( collect_b
@ ^ [B: b] : ( B = A ) )
= ( insert_b @ A @ bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(66,axiom,
! [A: b,B: b > b,C: set_b] :
( ( member_b @ A @ ( image_b_b @ B @ C ) )
=> ( member_b @ ( hilbert_inv_into_b_b @ C @ B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_inv__into__into) ).
thf(342,plain,
! [A: b,B: b > b,C: set_b] :
( ( member_b @ A @ ( image_b_b @ B @ C ) )
=> ( member_b @ ( hilbert_inv_into_b_b @ C @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(24,axiom,
! [A: set_b] :
( ( minus_minus_set_b @ A @ top_top_set_b )
= bot_bot_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Diff__UNIV) ).
thf(194,plain,
! [A: set_b] :
( ( minus_minus_set_b @ A @ top_top_set_b )
= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(90,axiom,
! [A: b,B: b > $o] :
( ( A
= ( hilbert_Eps_b
@ ^ [C: b] :
~ ( B @ C ) ) )
=> ( ( ! [C: b] : ( B @ C ) )
= ( B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_verit__sko__forall__indirect) ).
thf(414,plain,
! [A: b,B: b > $o] :
( ( A
= ( hilbert_Eps_b
@ ^ [C: b] :
~ ( B @ C ) ) )
=> ( ( ! [C: b] : ( B @ C ) )
= ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(61,axiom,
! [A: b > b,B: set_b] :
( ( ( image_b_b @ A @ B )
= bot_bot_set_b )
= ( B = bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_image__is__empty) ).
thf(327,plain,
! [A: b > b,B: set_b] :
( ( ( image_b_b @ A @ B )
= bot_bot_set_b )
= ( B = bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(88,axiom,
bot_bot_set_b != top_top_set_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_empty__not__UNIV) ).
thf(409,plain,
bot_bot_set_b != top_top_set_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(64,axiom,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ( ( insert_b @ A @ ( minus_minus_set_b @ B @ ( insert_b @ A @ bot_bot_set_b ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_insert__Diff) ).
thf(336,plain,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ( ( insert_b @ A @ ( minus_minus_set_b @ B @ ( insert_b @ A @ bot_bot_set_b ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(98,axiom,
! [A: b > $o,B: b] :
( ? [C: b] : ( A @ C )
=> ( ( B
= ( hilbert_Eps_b @ A ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_exE__some) ).
thf(446,plain,
! [A: b > $o,B: b] :
( ? [C: b] : ( A @ C )
=> ( ( B
= ( hilbert_Eps_b @ A ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(106,axiom,
! [A: b > $o,B: b > $o] :
( ? [C: b] : ( A @ C )
=> ( ! [C: b] :
( ( A @ C )
=> ( B @ C ) )
=> ( B @ ( hilbert_Eps_b @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_someI2__ex) ).
thf(482,plain,
! [A: b > $o,B: b > $o] :
( ? [C: b] : ( A @ C )
=> ( ! [C: b] :
( ( A @ C )
=> ( B @ C ) )
=> ( B @ ( hilbert_Eps_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(75,axiom,
! [A: b > b,B: set_b] :
( ( bij_betw_b_b @ A @ B @ bot_bot_set_b )
=> ( B = bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_bij__betw__empty2) ).
thf(368,plain,
! [A: b > b,B: set_b] :
( ( bij_betw_b_b @ A @ B @ bot_bot_set_b )
=> ( B = bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(58,axiom,
( bot_bot_set_b
= ( collect_b @ bot_bot_b_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_bot__set__def) ).
thf(319,plain,
( bot_bot_set_b
= ( collect_b @ bot_bot_b_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(55,axiom,
! [A: b,B: set_b,C: b] :
( ( member_b @ A @ B )
=> ( member_b @ A @ ( insert_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_insertI2) ).
thf(304,plain,
! [A: b,B: set_b,C: b] :
( ( member_b @ A @ B )
=> ( member_b @ A @ ( insert_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(44,axiom,
! [A: set_b] :
( ( minus_minus_set_b @ A @ A )
= bot_bot_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_Diff__cancel) ).
thf(258,plain,
! [A: set_b] :
( ( minus_minus_set_b @ A @ A )
= bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(14,axiom,
( insert_b
= ( ^ [A: b,B: set_b] :
( collect_b
@ ^ [C: b] :
( ( C = A )
| ( member_b @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_insert__compr) ).
thf(158,plain,
( insert_b
= ( ^ [A: b,B: set_b] :
( collect_b
@ ^ [C: b] :
( ( C = A )
| ( member_b @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(82,axiom,
! [A: b > b,B: set_b] :
( ( bij_betw_b_b @ A @ bot_bot_set_b @ B )
=> ( B = bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_bij__betw__empty1) ).
thf(390,plain,
! [A: b > b,B: set_b] :
( ( bij_betw_b_b @ A @ bot_bot_set_b @ B )
=> ( B = bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(22,axiom,
! [A: set_b] :
( ( minus_minus_set_b @ A @ bot_bot_set_b )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Diff__empty) ).
thf(186,plain,
! [A: set_b] :
( ( minus_minus_set_b @ A @ bot_bot_set_b )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1,conjecture,
! [A: a] :
( ~ ( p @ A )
| ( q @ A @ ( hilbert_Eps_b @ ( q @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ! [A: a] :
( ~ ( p @ A )
| ( q @ A @ ( hilbert_Eps_b @ ( q @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(114,plain,
~ ! [A: a] :
( ~ ( p @ A )
| ( q @ A @ ( hilbert_Eps_b @ ( q @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(86,axiom,
( is_empty_b
= ( ^ [A: set_b] : ( A = bot_bot_set_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Set_Ois__empty__def) ).
thf(401,plain,
( is_empty_b
= ( ^ [A: set_b] : ( A = bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(91,axiom,
! [A: b > $o,B: b > $o] :
( ! [C: b] :
( ( A @ C )
= ( B @ C ) )
=> ( ( hilbert_Eps_b @ A )
= ( hilbert_Eps_b @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Eps__cong) ).
thf(418,plain,
! [A: b > $o,B: b > $o] :
( ! [C: b] :
( ( A @ C )
= ( B @ C ) )
=> ( ( hilbert_Eps_b @ A )
= ( hilbert_Eps_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(68,axiom,
! [A: set_b] :
( ! [B: b] :
~ ( member_b @ B @ A )
=> ( A = bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_equals0I) ).
thf(346,plain,
! [A: set_b] :
( ! [B: b] :
~ ( member_b @ B @ A )
=> ( A = bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(50,axiom,
! [A: set_b,B: b,C: set_b] :
( ( minus_minus_set_b @ A @ ( insert_b @ B @ C ) )
= ( minus_minus_set_b @ ( minus_minus_set_b @ A @ ( insert_b @ B @ bot_bot_set_b ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_Diff__insert2) ).
thf(287,plain,
! [A: set_b,B: b,C: set_b] :
( ( minus_minus_set_b @ A @ ( insert_b @ B @ C ) )
= ( minus_minus_set_b @ ( minus_minus_set_b @ A @ ( insert_b @ B @ bot_bot_set_b ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(51,axiom,
! [A: b,B: set_b,C: set_b] :
( ~ ( member_b @ A @ B )
=> ( ~ ( member_b @ A @ C )
=> ( ( ( insert_b @ A @ B )
= ( insert_b @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_insert__ident) ).
thf(290,plain,
! [A: b,B: set_b,C: set_b] :
( ~ ( member_b @ A @ B )
=> ( ~ ( member_b @ A @ C )
=> ( ( ( insert_b @ A @ B )
= ( insert_b @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(79,axiom,
! [A: b] : ( member_b @ A @ ( insert_b @ A @ bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_singletonI) ).
thf(378,plain,
! [A: b] : ( member_b @ A @ ( insert_b @ A @ bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(54,axiom,
! [A: set_b] :
( ( is_singleton_b @ A )
=> ~ ! [B: b] :
( A
!= ( insert_b @ B @ bot_bot_set_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_is__singletonE) ).
thf(300,plain,
! [A: set_b] :
( ( is_singleton_b @ A )
=> ~ ! [B: b] :
( A
!= ( insert_b @ B @ bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(57,axiom,
! [A: b,B: set_b,C: set_b] :
( ~ ( member_b @ A @ B )
=> ( ( minus_minus_set_b @ B @ ( insert_b @ A @ C ) )
= ( minus_minus_set_b @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_Diff__insert0) ).
thf(315,plain,
! [A: b,B: set_b,C: set_b] :
( ~ ( member_b @ A @ B )
=> ( ( minus_minus_set_b @ B @ ( insert_b @ A @ C ) )
= ( minus_minus_set_b @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(21,axiom,
! [A: b,B: b,C: set_b] :
( ( member_b @ A @ ( insert_b @ B @ C ) )
=> ( ( A != B )
=> ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_insertE) ).
thf(183,plain,
! [A: b,B: b,C: set_b] :
( ( member_b @ A @ ( insert_b @ B @ C ) )
=> ( ( A != B )
=> ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(77,axiom,
( bot_bot_set_b
= ( collect_b
@ ^ [A: b] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_empty__def) ).
thf(373,plain,
( bot_bot_set_b
= ( collect_b
@ ^ [A: b] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(29,axiom,
! [A: b,B: b > $o] :
( ( member_b @ A @ ( collect_b @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_mem__Collect__eq) ).
thf(210,plain,
! [A: b,B: b > $o] :
( ( member_b @ A @ ( collect_b @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(38,axiom,
! [A: b,B: b > b,C: b,D: set_b] :
( ( A
= ( B @ C ) )
=> ( ( member_b @ C @ D )
=> ( member_b @ A @ ( image_b_b @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_image__eqI) ).
thf(239,plain,
! [A: b,B: b > b,C: b,D: set_b] :
( ( A
= ( B @ C ) )
=> ( ( member_b @ C @ D )
=> ( member_b @ A @ ( image_b_b @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(72,axiom,
! [A: b] :
~ ( member_b @ A @ bot_bot_set_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_emptyE) ).
thf(358,plain,
! [A: b] :
~ ( member_b @ A @ bot_bot_set_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(104,axiom,
! [A: b > $o,B: b] :
( ( A @ B )
=> ( A @ ( hilbert_Eps_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_someI) ).
thf(474,plain,
! [A: b > $o,B: b] :
( ( A @ B )
=> ( A @ ( hilbert_Eps_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(52,axiom,
! [A: b,B: b,C: set_b] :
( ( member_b @ A @ ( insert_b @ B @ C ) )
= ( ( A = B )
| ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_insert__iff) ).
thf(294,plain,
! [A: b,B: b,C: set_b] :
( ( member_b @ A @ ( insert_b @ B @ C ) )
= ( ( A = B )
| ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(7,axiom,
( is_singleton_b
= ( ^ [A: set_b] :
( A
= ( insert_b @ ( the_elem_b @ A ) @ bot_bot_set_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_is__singleton__the__elem) ).
thf(136,plain,
( is_singleton_b
= ( ^ [A: set_b] :
( A
= ( insert_b @ ( the_elem_b @ A ) @ bot_bot_set_b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(111,axiom,
! [A: b > $o,B: b] :
( ( A @ B )
=> ( A @ ( hilbert_Eps_b @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_tfl__some) ).
thf(506,plain,
! [A: b > $o,B: b] :
( ( A @ B )
=> ( A @ ( hilbert_Eps_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(46,axiom,
! [A: b > $o,B: b] :
( ( ( A @ B )
=> ( ( collect_b
@ ^ [C: b] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_b @ B @ bot_bot_set_b ) ) )
& ( ~ ( A @ B )
=> ( ( collect_b
@ ^ [C: b] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_set_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_Collect__conv__if2) ).
thf(268,plain,
! [A: b > $o,B: b] :
( ( ( A @ B )
=> ( ( collect_b
@ ^ [C: b] :
( ( B = C )
& ( A @ C ) ) )
= ( insert_b @ B @ bot_bot_set_b ) ) )
& ( ~ ( A @ B )
=> ( ( collect_b
@ ^ [C: b] :
( ( B = C )
& ( A @ C ) ) )
= bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(84,axiom,
! [A: b,B: b] :
( ( member_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_singleton__iff) ).
thf(395,plain,
! [A: b,B: b] :
( ( member_b @ A @ ( insert_b @ B @ bot_bot_set_b ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(48,axiom,
! [A: $o] :
( ( A
=> ( ( collect_b
@ ^ [B: b] : A )
= top_top_set_b ) )
& ( ~ A
=> ( ( collect_b
@ ^ [B: b] : A )
= bot_bot_set_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_Collect__const) ).
thf(277,plain,
! [A: $o] :
( ( A
=> ( ( collect_b
@ ^ [B: b] : A )
= top_top_set_b ) )
& ( ~ A
=> ( ( collect_b
@ ^ [B: b] : A )
= bot_bot_set_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(16,axiom,
! [A: b,B: set_b,C: b > b] :
( ( member_b @ A @ B )
=> ( member_b @ ( C @ A ) @ ( image_b_b @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_imageI) ).
thf(163,plain,
! [A: b,B: set_b,C: b > b] :
( ( member_b @ A @ B )
=> ( member_b @ ( C @ A ) @ ( image_b_b @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(26,axiom,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ? [C: set_b] :
( ( B
= ( insert_b @ A @ C ) )
& ~ ( member_b @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_mk__disjoint__insert) ).
thf(200,plain,
! [A: b,B: set_b] :
( ( member_b @ A @ B )
=> ? [C: set_b] :
( ( B
= ( insert_b @ A @ C ) )
& ~ ( member_b @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(34,axiom,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ B )
=> ( ~ ( member_b @ A @ C )
=> ( member_b @ A @ ( minus_minus_set_b @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_DiffI) ).
thf(227,plain,
! [A: b,B: set_b,C: set_b] :
( ( member_b @ A @ B )
=> ( ~ ( member_b @ A @ C )
=> ( member_b @ A @ ( minus_minus_set_b @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(107,axiom,
! [A: b > $o,B: $o] :
( ( ( A @ ( hilbert_Eps_b @ A ) )
= B )
=> ( ( ? [C: b] : ( A @ C ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_verit__sko__ex_H) ).
thf(486,plain,
! [A: b > $o,B: $o] :
( ( ( A @ ( hilbert_Eps_b @ A ) )
= B )
=> ( ( ? [C: b] : ( A @ C ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(103,axiom,
! [A: b,B: b,C: b > $o] :
( ( A = B )
=> ( ( ( hilbert_Eps_b @ C )
= B )
= ( ( hilbert_Eps_b @ C )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_verit__sko__forall_H_H) ).
thf(469,plain,
! [A: b,B: b,C: b > $o] :
( ( A = B )
=> ( ( ( hilbert_Eps_b @ C )
= B )
= ( ( hilbert_Eps_b @ C )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(99,axiom,
! [A: set_b] :
( ( member_b
@ ( hilbert_Eps_b
@ ^ [B: b] : ( member_b @ B @ A ) )
@ A )
= ( A != bot_bot_set_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_some__in__eq) ).
thf(454,plain,
! [A: set_b] :
( ( member_b
@ ( hilbert_Eps_b
@ ^ [B: b] : ( member_b @ B @ A ) )
@ A )
= ( A != bot_bot_set_b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(521,plain,
$false,
inference(e,[status(thm)],[344,339,204,441,138,333,217,120,247,189,421,284,152,261,321,253,353,147,133,428,206,307,233,380,117,512,439,220,366,160,297,424,275,467,197,361,224,403,356,169,141,393,457,173,371,237,244,398,412,166,180,375,382,144,498,350,230,509,477,494,323,213,251,155,330,462,130,431,490,255,342,194,414,327,409,336,446,482,368,319,304,258,158,390,186,114,401,418,346,287,290,378,300,315,183,373,210,239,358,474,294,136,506,268,395,277,163,200,227,486,469,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10 % Problem : ITP144^1 : TPTP v8.1.2. Released v7.5.0.
% 0.10/0.12 % Command : run_Leo-III %s %d
% 0.13/0.32 % Computer : n009.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 6 14:32:09 EDT 2024
% 0.13/0.32 % CPUTime :
% 0.85/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/1.00 % [INFO] Parsing done (190ms).
% 1.52/1.01 % [INFO] Running in sequential loop mode.
% 1.93/1.24 % [INFO] eprover registered as external prover.
% 1.93/1.24 % [INFO] cvc4 registered as external prover.
% 1.93/1.24 % [INFO] Scanning for conjecture ...
% 2.00/1.32 % [INFO] Found a conjecture and 111 axioms. Running axiom selection ...
% 2.36/1.40 % [INFO] Axiom selection finished. Selected 111 axioms (removed 0 axioms).
% 2.63/1.51 % [INFO] Problem is higher-order (TPTP THF).
% 2.80/1.52 % [INFO] Type checking passed.
% 2.80/1.52 % [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 ...
% 8.79/2.99 % External prover 'e' found a proof!
% 8.79/2.99 % [INFO] Killing All external provers ...
% 8.83/2.99 % Time passed: 2491ms (effective reasoning time: 1976ms)
% 8.83/2.99 % 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)>
% 8.83/2.99 % Axioms used in derivation (111): fact_109_remove__def, conj_0, fact_11_some__eq__ex, fact_22_some__in__eq, fact_51_singleton__conv2, fact_79_rev__image__eqI, fact_7_verit__sko__forall_H_H, fact_19_verit__sko__ex__indirect2, fact_105_DiffD1, fact_3_verit__sko__ex_H, fact_91_Diff__iff, fact_29_Collect__mem__eq, fact_75_empty__is__image, fact_86_inj__singleton, fact_57_Set_Oset__insert, fact_4_verit__sko__forall, fact_40_UNIV__I, fact_53_insert__eq__iff, fact_66_singletonD, fact_55_insert__ident, fact_27_empty__iff, fact_95_insert__Diff1, fact_15_someI, fact_101_insert__Diff, fact_37_Collect__empty__eq__bot, fact_61_top__empty__eq, fact_72_the__elem__eq, fact_76_image__empty, fact_74_image__is__empty, fact_94_Diff__cancel, fact_98_Diff__UNIV, fact_68_Collect__conv__if2, fact_30_bot__set__def, fact_97_insert__Diff__single, fact_64_doubleton__eq__iff, fact_100_Diff__insert2, fact_92_Diff__empty, fact_70_is__singletonE, fact_90_DiffI, fact_93_empty__Diff, fact_43_UNIV__witness, fact_8_someI__ex, fact_78_imageI, fact_26_all__not__in__conv, fact_0_some__equality, fact_81_inv__into__into, fact_71_is__singleton__the__elem, fact_21_Nitpick_OEps__psimp, fact_35_empty__def, fact_59_insertI1, fact_33_equals0I, fact_108_insert__Diff__if, fact_62_singleton__inject, fact_38_bot__empty__eq, fact_104_DiffE, fact_13_tfl__some, fact_85_bij__betw__empty1, fact_73_image__eqI, fact_9_someI2__ex, fact_18_some1__equality, fact_6_verit__sko__forall_H, fact_42_UNIV__eq__I, fact_2_some__sym__eq__trivial, fact_46_is__singletonI, fact_87_inj__img__insertE, fact_25_Collect__empty__eq, fact_60_insertE, fact_39_is__singletonI_H, fact_17_verit__sko__forall__indirect, fact_24_empty__Collect__eq, fact_48_insertCI, fact_20_verit__sko__ex__indirect, fact_80_Compr__image__eq, fact_56_insert__compr, fact_54_insert__absorb, fact_14_Eps__cong, fact_103_in__image__insert__iff, fact_65_singleton__iff, fact_31_emptyE, fact_47_insert__iff, fact_23_exE__some, fact_99_Diff__insert__absorb, fact_67_Collect__conv__if, fact_107_set__diff__eq, fact_28_mem__Collect__eq, fact_16_verit__sko__forall__indirect2, fact_10_someI2__bex, fact_63_insert__not__empty, fact_49_singletonI, fact_102_Diff__insert, fact_77_imageE, fact_88_inj__image__mem__iff, fact_1_some__eq__trivial, fact_36_Set_Ois__empty__def, fact_69_is__singleton__def, fact_5_someI2, fact_32_equals0D, fact_50_singleton__conv, fact_106_DiffD2, fact_83_image__constant__conv, fact_41_Collect__const, fact_44_empty__not__UNIV, fact_89_inj__on__insert, fact_52_mk__disjoint__insert, fact_34_ex__in__conv, fact_82_image__constant, fact_58_insertI2, fact_96_Diff__insert0, fact_12_some__eq__imp, fact_84_bij__betw__empty2, fact_45_iso__tuple__UNIV__I
% 8.83/2.99 % No. of inferences in proof: 226
% 8.83/2.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2491 ms resp. 1976 ms w/o parsing
% 8.96/3.09 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.96/3.09 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------