TSTP Solution File: ITP028^1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : ITP028^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% 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 : Mon Jun 24 09:23:47 EDT 2024
% Result : Theorem 6.78s 2.56s
% Output : Refutation 7.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 101
% Syntax : Number of formulae : 204 ( 80 unt; 0 typ; 0 def)
% Number of atoms : 544 ( 164 equ; 14 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1348 ( 10 ~; 8 |; 30 &;1046 @)
% ( 0 <=>; 254 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 16 ( 15 usr)
% Number of type conns : 194 ( 194 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 22 usr; 11 con; 0-3 aty)
% Number of variables : 498 ( 38 ^ 442 !; 18 ?; 498 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_Pr1710391469_a_a_e_type,type,
set_Pr1710391469_a_a_e: $tType ).
thf(produc169085773_a_a_e_type,type,
produc169085773_a_a_e: $tType ).
thf(set_se821189730_a_a_e_type,type,
set_se821189730_a_a_e: $tType ).
thf(set_Pr2045688071_set_a_type,type,
set_Pr2045688071_set_a: $tType ).
thf(set_Pr204296108_a_a_e_type,type,
set_Pr204296108_a_a_e: $tType ).
thf(set_Pr305929312_set_a_type,type,
set_Pr305929312_set_a: $tType ).
thf(produc1691597095_set_a_type,type,
produc1691597095_set_a: $tType ).
thf(produc715398134_a_a_e_type,type,
produc715398134_a_a_e: $tType ).
thf(produc1965228714_set_a_type,type,
produc1965228714_set_a: $tType ).
thf(set_set_set_a_type,type,
set_set_set_a: $tType ).
thf(set_set_a_type,type,
set_set_a: $tType ).
thf(set_a_e_type,type,
set_a_e: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(e_type,type,
e: $tType ).
thf(a_type,type,
a: $tType ).
thf(ord_less_eq_o_set_a_type,type,
ord_less_eq_o_set_a: ( $o > set_a ) > ( $o > set_a ) > $o ).
thf(ord_less_eq_set_a_type,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(order_Greatest_set_a_type,type,
order_Greatest_set_a: ( set_a > $o ) > set_a ).
thf(top_to2000253225_a_e_o_type,type,
top_to2000253225_a_e_o: produc715398134_a_a_e > $o ).
thf(top_top_set_a_o_type,type,
top_top_set_a_o: set_a > $o ).
thf(top_to1601855068_a_a_e_type,type,
top_to1601855068_a_a_e: set_Pr204296108_a_a_e ).
thf(top_top_set_set_a_type,type,
top_top_set_set_a: set_set_a ).
thf(top_top_set_a_type,type,
top_top_set_a: set_a ).
thf(produc1443219402_e_a_e_type,type,
produc1443219402_e_a_e: ( set_a > set_a ) > ( ( a > e ) > a > e ) > produc715398134_a_a_e > produc715398134_a_a_e ).
thf(produc1040928388_a_a_e_type,type,
produc1040928388_a_a_e: produc715398134_a_a_e > set_a ).
thf(domain_set_a_a_e_type,type,
domain_set_a_a_e: set_Pr204296108_a_a_e > set_set_a ).
thf(collect_set_a_type,type,
collect_set_a: ( set_a > $o ) > set_set_a ).
thf(collect_a_type,type,
collect_a: ( a > $o ) > set_a ).
thf(pow_a_type,type,
pow_a: set_a > set_set_a ).
thf(image_64240033_set_a_type,type,
image_64240033_set_a: ( produc715398134_a_a_e > set_a ) > set_Pr204296108_a_a_e > set_set_a ).
thf(member1258382221_a_a_e_type,type,
member1258382221_a_a_e: produc715398134_a_a_e > set_Pr204296108_a_a_e > $o ).
thf(member_set_a_type,type,
member_set_a: set_a > set_set_a > $o ).
thf(c_type,type,
c: set_Pr204296108_a_a_e ).
thf(a1_type,type,
a1: set_a ).
thf(a2_type,type,
a2: set_a ).
thf(a3_type,type,
a3: set_a ).
thf(thesis_type,type,
thesis: $o ).
thf(55,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_order__class_Oorder_Oantisym) ).
thf(292,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(52,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( member_set_a @ A @ ( pow_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_PowI) ).
thf(285,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( member_set_a @ A @ ( pow_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(63,axiom,
( top_top_set_a_o
= ( ^ [A: set_a] : ( member_set_a @ A @ top_top_set_set_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_top__empty__eq) ).
thf(317,plain,
( top_top_set_a_o
= ( ^ [A: set_a] : ( member_set_a @ A @ top_top_set_set_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(11,axiom,
! [A: set_Pr204296108_a_a_e,B: set_Pr204296108_a_a_e,C: produc715398134_a_a_e > set_a,D: produc715398134_a_a_e > set_a,E: set_set_a > set_a] :
( ( A = B )
=> ( ! [F: produc715398134_a_a_e] :
( ( member1258382221_a_a_e @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_64240033_set_a @ C @ A ) )
= ( E @ ( image_64240033_set_a @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_Inf_OINF__cong) ).
thf(129,plain,
! [A: set_Pr204296108_a_a_e,B: set_Pr204296108_a_a_e,C: produc715398134_a_a_e > set_a,D: produc715398134_a_a_e > set_a,E: set_set_a > set_a] :
( ( A = B )
=> ( ! [F: produc715398134_a_a_e] :
( ( member1258382221_a_a_e @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_64240033_set_a @ C @ A ) )
= ( E @ ( image_64240033_set_a @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(76,axiom,
! [A: set_a,B: set_a] :
( ( member_set_a @ A @ ( pow_a @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_PowD) ).
thf(360,plain,
! [A: set_a,B: set_a] :
( ( member_set_a @ A @ ( pow_a @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(56,axiom,
! [A: produc715398134_a_a_e,B: set_Pr204296108_a_a_e,C: produc715398134_a_a_e > set_a] :
( ( member1258382221_a_a_e @ A @ B )
=> ( member_set_a @ ( C @ A ) @ ( image_64240033_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_imageI) ).
thf(295,plain,
! [A: produc715398134_a_a_e,B: set_Pr204296108_a_a_e,C: produc715398134_a_a_e > set_a] :
( ( member1258382221_a_a_e @ A @ B )
=> ( member_set_a @ ( C @ A ) @ ( image_64240033_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(61,axiom,
member_set_a @ a1 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_A_I1_J) ).
thf(314,plain,
member_set_a @ a1 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(71,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_order_Otrans) ).
thf(347,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(37,axiom,
! [A: set_Pr204296108_a_a_e,B: produc715398134_a_a_e > set_a,C: set_set_a,D: produc715398134_a_a_e] :
( ! [E: produc715398134_a_a_e] :
( ( member1258382221_a_a_e @ E @ A )
=> ( member_set_a @ ( B @ E ) @ C ) )
=> ( ( member1258382221_a_a_e @ D @ A )
=> ( member_set_a @ ( B @ D ) @ ( image_64240033_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_mem__in__image1) ).
thf(234,plain,
! [A: set_Pr204296108_a_a_e,B: produc715398134_a_a_e > set_a,C: set_set_a,D: produc715398134_a_a_e] :
( ! [E: produc715398134_a_a_e] :
( ( member1258382221_a_a_e @ E @ A )
=> ( member_set_a @ ( B @ E ) @ C ) )
=> ( ( member1258382221_a_a_e @ D @ A )
=> ( member_set_a @ ( B @ D ) @ ( image_64240033_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(73,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_antisym__conv) ).
thf(352,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(21,axiom,
! [A: set_Pr204296108_a_a_e,B: set_Pr204296108_a_a_e,C: produc715398134_a_a_e > set_a,D: produc715398134_a_a_e > set_a,E: set_set_a > set_a] :
( ( A = B )
=> ( ! [F: produc715398134_a_a_e] :
( ( member1258382221_a_a_e @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_64240033_set_a @ C @ A ) )
= ( E @ ( image_64240033_set_a @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_Sup_OSUP__cong) ).
thf(170,plain,
! [A: set_Pr204296108_a_a_e,B: set_Pr204296108_a_a_e,C: produc715398134_a_a_e > set_a,D: produc715398134_a_a_e > set_a,E: set_set_a > set_a] :
( ( A = B )
=> ( ! [F: produc715398134_a_a_e] :
( ( member1258382221_a_a_e @ F @ B )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( E @ ( image_64240033_set_a @ C @ A ) )
= ( E @ ( image_64240033_set_a @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(100,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_eq__iff) ).
thf(440,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(31,axiom,
! [A: produc715398134_a_a_e > set_a,B: set_a] :
( ( ( image_64240033_set_a @ A @ top_to1601855068_a_a_e )
= top_top_set_set_a )
=> ? [C: produc715398134_a_a_e] :
( B
= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_surjD) ).
thf(217,plain,
! [A: produc715398134_a_a_e > set_a,B: set_a] :
( ( ( image_64240033_set_a @ A @ top_to1601855068_a_a_e )
= top_top_set_set_a )
=> ? [C: produc715398134_a_a_e] :
( B
= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(49,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_ge__convert) ).
thf(276,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(82,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ B @ A )
& ( ord_less_eq_set_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_dual__order_Oeq__iff) ).
thf(385,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ B @ A )
& ( ord_less_eq_set_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(13,axiom,
! [A: $o > set_a,B: $o > set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
=> ( ( ord_less_eq_o_set_a @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_dual__order_Oantisym) ).
thf(142,plain,
! [A: $o > set_a,B: $o > set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
=> ( ( ord_less_eq_o_set_a @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(98,axiom,
! [A: set_a] : ( member_set_a @ A @ ( pow_a @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_Pow__top) ).
thf(436,plain,
! [A: set_a] : ( member_set_a @ A @ ( pow_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(44,axiom,
! [A: set_a > set_a,B: ( a > e ) > a > e,C: produc715398134_a_a_e] :
( ( produc1040928388_a_a_e @ ( produc1443219402_e_a_e @ A @ B @ C ) )
= ( A @ ( produc1040928388_a_a_e @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_fst__map__prod) ).
thf(257,plain,
! [A: set_a > set_a,B: ( a > e ) > a > e,C: produc715398134_a_a_e] :
( ( produc1040928388_a_a_e @ ( produc1443219402_e_a_e @ A @ B @ C ) )
= ( A @ ( produc1040928388_a_a_e @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(70,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_dual__order_Oantisym) ).
thf(344,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(26,axiom,
! [A: $o > set_a,B: $o > set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
=> ( ( ord_less_eq_o_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_antisym) ).
thf(196,plain,
! [A: $o > set_a,B: $o > set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
=> ( ( ord_less_eq_o_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(66,axiom,
! [A: set_a,B: produc715398134_a_a_e > set_a,C: produc715398134_a_a_e] :
( ( A
= ( B @ C ) )
=> ( member_set_a @ A @ ( image_64240033_set_a @ B @ top_to1601855068_a_a_e ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_range__eqI) ).
thf(325,plain,
! [A: set_a,B: produc715398134_a_a_e > set_a,C: produc715398134_a_a_e] :
( ( A
= ( B @ C ) )
=> ( member_set_a @ A @ ( image_64240033_set_a @ B @ top_to1601855068_a_a_e ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(35,axiom,
( ( (=) @ ( $o > set_a ) )
= ( ^ [A: $o > set_a,B: $o > set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
& ( ord_less_eq_o_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_order__class_Oorder_Oeq__iff) ).
thf(228,plain,
( ( (=) @ ( $o > set_a ) )
= ( ^ [A: $o > set_a,B: $o > set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
& ( ord_less_eq_o_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(19,axiom,
! [A: set_Pr204296108_a_a_e] :
( ! [B: produc715398134_a_a_e] : ( member1258382221_a_a_e @ B @ A )
=> ( top_to1601855068_a_a_e = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_UNIV__eq__I) ).
thf(164,plain,
! [A: set_Pr204296108_a_a_e] :
( ! [B: produc715398134_a_a_e] : ( member1258382221_a_a_e @ B @ A )
=> ( top_to1601855068_a_a_e = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(80,axiom,
! [A: set_a > $o,B: set_a,C: set_a > $o] :
( ( A @ B )
=> ( ! [D: set_a] :
( ( A @ D )
=> ( ord_less_eq_set_a @ D @ B ) )
=> ( ! [D: set_a] :
( ( A @ D )
=> ( ! [E: set_a] :
( ( A @ E )
=> ( ord_less_eq_set_a @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_Greatest_set_a @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_GreatestI2__order) ).
thf(376,plain,
! [A: set_a > $o,B: set_a,C: set_a > $o] :
( ( A @ B )
=> ( ! [D: set_a] :
( ( A @ D )
=> ( ord_less_eq_set_a @ D @ B ) )
=> ( ! [D: set_a] :
( ( A @ D )
=> ( ! [E: set_a] :
( ( A @ E )
=> ( ord_less_eq_set_a @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_Greatest_set_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(4,axiom,
( ( (=) @ ( $o > set_a ) )
= ( ^ [A: $o > set_a,B: $o > set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
& ( ord_less_eq_o_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_eq__iff) ).
thf(106,plain,
( ( (=) @ ( $o > set_a ) )
= ( ^ [A: $o > set_a,B: $o > set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
& ( ord_less_eq_o_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(38,axiom,
( ord_less_eq_o_set_a
= ( ^ [A: $o > set_a,B: $o > set_a] :
( ( ord_less_eq_set_a @ ( A @ $false ) @ ( B @ $false ) )
& ( ord_less_eq_set_a @ ( A @ $true ) @ ( B @ $true ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_le__rel__bool__arg__iff) ).
thf(238,plain,
( ord_less_eq_o_set_a
= ( ^ [A: $o > set_a,B: $o > set_a] :
( ( ord_less_eq_set_a @ ( A @ $false ) @ ( B @ $false ) )
& ( ord_less_eq_set_a @ ( A @ $true ) @ ( B @ $true ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(15,axiom,
! [A: $o > set_a,B: $o > set_a,C: ( $o > set_a ) > set_a,D: set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: $o > set_a,F: $o > set_a] :
( ( ord_less_eq_o_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_ord__le__eq__subst) ).
thf(147,plain,
! [A: $o > set_a,B: $o > set_a,C: ( $o > set_a ) > set_a,D: set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: $o > set_a,F: $o > set_a] :
( ( ord_less_eq_o_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(86,axiom,
! [A: set_set_a] :
( ( collect_set_a
@ ^ [B: set_a] : ( member_set_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_Collect__mem__eq) ).
thf(397,plain,
! [A: set_set_a] :
( ( collect_set_a
@ ^ [B: set_a] : ( member_set_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(32,axiom,
? [A: set_a] : ( member_set_a @ A @ top_top_set_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_UNIV__witness) ).
thf(221,plain,
? [A: set_a] : ( member_set_a @ A @ top_top_set_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(8,axiom,
! [A: $o > set_a,B: ( $o > set_a ) > $o > set_a,C: $o > set_a,D: $o > set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_o_set_a @ C @ D )
=> ( ! [E: $o > set_a,F: $o > set_a] :
( ( ord_less_eq_o_set_a @ E @ F )
=> ( ord_less_eq_o_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_o_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_ord__eq__le__subst) ).
thf(116,plain,
! [A: $o > set_a,B: ( $o > set_a ) > $o > set_a,C: $o > set_a,D: $o > set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_o_set_a @ C @ D )
=> ( ! [E: $o > set_a,F: $o > set_a] :
( ( ord_less_eq_o_set_a @ E @ F )
=> ( ord_less_eq_o_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_o_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(46,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ top_top_set_a @ A )
=> ( A = top_top_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_top_Oextremum__uniqueI) ).
thf(265,plain,
! [A: set_a] :
( ( ord_less_eq_set_a @ top_top_set_a @ A )
=> ( A = top_top_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(58,axiom,
! [A: produc715398134_a_a_e > set_a,B: set_Pr204296108_a_a_e,C: set_a > $o] :
( ? [D: set_a] :
( ( member_set_a @ D @ ( image_64240033_set_a @ A @ B ) )
& ( C @ D ) )
=> ? [D: produc715398134_a_a_e] :
( ( member1258382221_a_a_e @ D @ B )
& ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_bex__imageD) ).
thf(302,plain,
! [A: produc715398134_a_a_e > set_a,B: set_Pr204296108_a_a_e,C: set_a > $o] :
( ? [D: set_a] :
( ( member_set_a @ D @ ( image_64240033_set_a @ A @ B ) )
& ( C @ D ) )
=> ? [D: produc715398134_a_a_e] :
( ( member1258382221_a_a_e @ D @ B )
& ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(45,axiom,
! [A: produc715398134_a_a_e,B: set_Pr204296108_a_a_e,C: set_a,D: produc715398134_a_a_e > set_a] :
( ( member1258382221_a_a_e @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_set_a @ C @ ( image_64240033_set_a @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_rev__image__eqI) ).
thf(260,plain,
! [A: produc715398134_a_a_e,B: set_Pr204296108_a_a_e,C: set_a,D: produc715398134_a_a_e > set_a] :
( ( member1258382221_a_a_e @ A @ B )
=> ( ( C
= ( D @ A ) )
=> ( member_set_a @ C @ ( image_64240033_set_a @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(18,axiom,
! [A: $o > set_a,B: $o > set_a] :
( ( A = B )
=> ( ord_less_eq_o_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_eq__refl) ).
thf(160,plain,
! [A: $o > set_a,B: $o > set_a] :
( ( A = B )
=> ( ord_less_eq_o_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(85,axiom,
? [A: set_a] :
( ( member_set_a @ A @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
& ( ord_less_eq_set_a @ a1 @ A )
& ( ord_less_eq_set_a @ a2 @ A )
& ( ord_less_eq_set_a @ a3 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062_092_060exists_062a_092_060in_062fst_A_096_AC_O_Aa1_A_092_060subseteq_062_Aa_A_092_060and_062_Aa2_A_092_060subseteq_062_Aa_A_092_060and_062_Aa3_A_092_060subseteq_062_Aa_092_060close_062) ).
thf(392,plain,
? [A: set_a] :
( ( member_set_a @ A @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
& ( ord_less_eq_set_a @ a1 @ A )
& ( ord_less_eq_set_a @ a2 @ A )
& ( ord_less_eq_set_a @ a3 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(94,axiom,
! [A: produc715398134_a_a_e,B: set_Pr204296108_a_a_e,C: produc715398134_a_a_e > set_a] :
( ( member1258382221_a_a_e @ A @ B )
=> ( member_set_a @ ( C @ A ) @ ( image_64240033_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_mem__in__image2) ).
thf(424,plain,
! [A: produc715398134_a_a_e,B: set_Pr204296108_a_a_e,C: produc715398134_a_a_e > set_a] :
( ( member1258382221_a_a_e @ A @ B )
=> ( member_set_a @ ( C @ A ) @ ( image_64240033_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(89,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_Collect__mono) ).
thf(407,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(12,axiom,
! [A: $o > set_a,B: $o > set_a,C: $o > set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_o_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_ord__le__eq__trans) ).
thf(137,plain,
! [A: $o > set_a,B: $o > set_a,C: $o > set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_o_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
( top_to2000253225_a_e_o
= ( ^ [A: produc715398134_a_a_e] : ( member1258382221_a_a_e @ A @ top_to1601855068_a_a_e ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_top__empty__eq) ).
thf(124,plain,
( top_to2000253225_a_e_o
= ( ^ [A: produc715398134_a_a_e] : ( member1258382221_a_a_e @ A @ top_to1601855068_a_a_e ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(34,axiom,
! [A: $o > set_a,B: $o > set_a,C: $o > set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
=> ( ( ord_less_eq_o_set_a @ C @ A )
=> ( ord_less_eq_o_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_dual__order_Otrans) ).
thf(225,plain,
! [A: $o > set_a,B: $o > set_a,C: $o > set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
=> ( ( ord_less_eq_o_set_a @ C @ A )
=> ( ord_less_eq_o_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(57,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_eq__refl) ).
thf(298,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(91,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_eq_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_equalityE) ).
thf(412,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_eq_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(96,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_order__subst1) ).
thf(430,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(79,axiom,
member_set_a @ a3 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_A_I3_J) ).
thf(375,plain,
member_set_a @ a3 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(88,axiom,
! [A: set_a > $o,B: set_a] :
( ( A @ B )
=> ( ! [C: set_a] :
( ( A @ C )
=> ( ord_less_eq_set_a @ C @ B ) )
=> ( ( order_Greatest_set_a @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_Greatest__equality) ).
thf(402,plain,
! [A: set_a > $o,B: set_a] :
( ( A @ B )
=> ( ! [C: set_a] :
( ( A @ C )
=> ( ord_less_eq_set_a @ C @ B ) )
=> ( ( order_Greatest_set_a @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(50,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_dual__order_Orefl) ).
thf(281,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(28,axiom,
! [A: $o > set_a,B: $o > set_a,C: $o > set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
=> ( ( ord_less_eq_o_set_a @ B @ C )
=> ( ord_less_eq_o_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_order__trans) ).
thf(204,plain,
! [A: $o > set_a,B: $o > set_a,C: $o > set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
=> ( ( ord_less_eq_o_set_a @ B @ C )
=> ( ord_less_eq_o_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(84,axiom,
member_set_a @ a2 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_A_I2_J) ).
thf(391,plain,
member_set_a @ a2 @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(102,axiom,
! [A: set_a] :
( ( member_set_a @ A @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
=> ( ( ord_less_eq_set_a @ a1 @ A )
=> ( ( ord_less_eq_set_a @ a2 @ A )
=> ( ( ord_less_eq_set_a @ a3 @ A )
=> thesis ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(445,plain,
! [A: set_a] :
( ( member_set_a @ A @ ( image_64240033_set_a @ produc1040928388_a_a_e @ c ) )
=> ( ( ord_less_eq_set_a @ a1 @ A )
=> ( ( ord_less_eq_set_a @ a2 @ A )
=> ( ( ord_less_eq_set_a @ a3 @ A )
=> thesis ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(72,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ top_top_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_subset__UNIV) ).
thf(350,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ top_top_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(7,axiom,
! [A: produc715398134_a_a_e > set_a] :
( ( ( image_64240033_set_a @ A @ top_to1601855068_a_a_e )
= top_top_set_set_a )
= ( ! [B: set_a] :
? [C: produc715398134_a_a_e] :
( B
= ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_surj__def) ).
thf(113,plain,
! [A: produc715398134_a_a_e > set_a] :
( ( ( image_64240033_set_a @ A @ top_to1601855068_a_a_e )
= top_top_set_set_a )
= ( ! [B: set_a] :
? [C: produc715398134_a_a_e] :
( B
= ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(92,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_subset__antisym) ).
thf(419,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(36,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_equalityD2) ).
thf(230,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(77,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_ord__eq__le__trans) ).
thf(362,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(41,axiom,
! [A: set_a,B: produc715398134_a_a_e > set_a,C: produc715398134_a_a_e,D: set_Pr204296108_a_a_e] :
( ( A
= ( B @ C ) )
=> ( ( member1258382221_a_a_e @ C @ D )
=> ( member_set_a @ A @ ( image_64240033_set_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_image__eqI) ).
thf(245,plain,
! [A: set_a,B: produc715398134_a_a_e > set_a,C: produc715398134_a_a_e,D: set_Pr204296108_a_a_e] :
( ( A
= ( B @ C ) )
=> ( ( member1258382221_a_a_e @ C @ D )
=> ( member_set_a @ A @ ( image_64240033_set_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(97,axiom,
! [A: produc715398134_a_a_e > set_a,B: produc715398134_a_a_e] : ( member_set_a @ ( A @ B ) @ ( image_64240033_set_a @ A @ top_to1601855068_a_a_e ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_rangeI) ).
thf(434,plain,
! [A: produc715398134_a_a_e > set_a,B: produc715398134_a_a_e] : ( member_set_a @ ( A @ B ) @ ( image_64240033_set_a @ A @ top_to1601855068_a_a_e ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(83,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_eqsets__sub) ).
thf(387,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(78,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_ord__le__eq__subst) ).
thf(367,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(1,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ thesis,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(103,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(39,axiom,
( ( ord_less_eq_set_a @ a1 @ a3 )
| ( ord_less_eq_set_a @ a3 @ a1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__092_060open_062a1_A_092_060subseteq_062_Aa3_A_092_060or_062_Aa3_A_092_060subseteq_062_Aa1_092_060close_062) ).
thf(240,plain,
( ( ord_less_eq_set_a @ a1 @ a3 )
| ( ord_less_eq_set_a @ a3 @ a1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(16,axiom,
! [A: set_set_a] :
( ! [B: set_a] : ( member_set_a @ B @ A )
=> ( top_top_set_set_a = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_UNIV__eq__I) ).
thf(155,plain,
! [A: set_set_a] :
( ! [B: set_a] : ( member_set_a @ B @ A )
=> ( top_top_set_set_a = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(5,axiom,
! [A: $o > set_a,B: $o > set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
=> ( ( ord_less_eq_o_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_order__class_Oorder_Oantisym) ).
thf(108,plain,
! [A: $o > set_a,B: $o > set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
=> ( ( ord_less_eq_o_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(67,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_ord__eq__le__subst) ).
thf(330,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(33,axiom,
! [A: $o > set_a] : ( ord_less_eq_o_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_dual__order_Orefl) ).
thf(223,plain,
! [A: $o > set_a] : ( ord_less_eq_o_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(99,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_order__refl) ).
thf(438,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(20,axiom,
! [A: $o > set_a,B: $o > set_a,C: $o > set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
=> ( ( ord_less_eq_o_set_a @ B @ C )
=> ( ord_less_eq_o_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_order_Otrans) ).
thf(167,plain,
! [A: $o > set_a,B: $o > set_a,C: $o > set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
=> ( ( ord_less_eq_o_set_a @ B @ C )
=> ( ord_less_eq_o_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(74,axiom,
! [A: produc715398134_a_a_e > set_a,B: set_Pr204296108_a_a_e,C: set_a > $o] :
( ! [D: set_a] :
( ( member_set_a @ D @ ( image_64240033_set_a @ A @ B ) )
=> ( C @ D ) )
=> ! [D: produc715398134_a_a_e] :
( ( member1258382221_a_a_e @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_ball__imageD) ).
thf(355,plain,
! [A: produc715398134_a_a_e > set_a,B: set_Pr204296108_a_a_e,C: set_a > $o] :
( ! [D: set_a] :
( ( member_set_a @ D @ ( image_64240033_set_a @ A @ B ) )
=> ( C @ D ) )
=> ! [D: produc715398134_a_a_e] :
( ( member1258382221_a_a_e @ D @ B )
=> ( C @ ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(25,axiom,
( ( (=) @ ( $o > set_a ) )
= ( ^ [A: $o > set_a,B: $o > set_a] :
( ( ord_less_eq_o_set_a @ B @ A )
& ( ord_less_eq_o_set_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_dual__order_Oeq__iff) ).
thf(194,plain,
( ( (=) @ ( $o > set_a ) )
= ( ^ [A: $o > set_a,B: $o > set_a] :
( ( ord_less_eq_o_set_a @ B @ A )
& ( ord_less_eq_o_set_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(14,axiom,
! [A: $o > set_a] : ( ord_less_eq_o_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_order__refl) ).
thf(145,plain,
! [A: $o > set_a] : ( ord_less_eq_o_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(27,axiom,
! [A: $o > set_a,B: $o > set_a,C: $o > set_a] :
( ( A = B )
=> ( ( ord_less_eq_o_set_a @ B @ C )
=> ( ord_less_eq_o_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_ord__eq__le__trans) ).
thf(199,plain,
! [A: $o > set_a,B: $o > set_a,C: $o > set_a] :
( ( A = B )
=> ( ( ord_less_eq_o_set_a @ B @ C )
=> ( ord_less_eq_o_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(23,axiom,
! [A: set_a,B: set_a,C: set_a > $o > set_a,D: $o > set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_o_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_o_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_ord__le__eq__subst) ).
thf(182,plain,
! [A: set_a,B: set_a,C: set_a > $o > set_a,D: $o > set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_o_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_o_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(68,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_Collect__mono__iff) ).
thf(338,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(42,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_order__subst2) ).
thf(250,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(3,axiom,
( ( image_64240033_set_a @ produc1040928388_a_a_e @ top_to1601855068_a_a_e )
= top_top_set_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_range__fst) ).
thf(104,plain,
( ( image_64240033_set_a @ produc1040928388_a_a_e @ top_to1601855068_a_a_e )
= top_top_set_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(64,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ top_top_set_a @ A )
= ( A = top_top_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_top_Oextremum__unique) ).
thf(319,plain,
! [A: set_a] :
( ( ord_less_eq_set_a @ top_top_set_a @ A )
= ( A = top_top_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(17,axiom,
? [A: produc715398134_a_a_e] : ( member1258382221_a_a_e @ A @ top_to1601855068_a_a_e ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_UNIV__witness) ).
thf(158,plain,
? [A: produc715398134_a_a_e] : ( member1258382221_a_a_e @ A @ top_to1601855068_a_a_e ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(54,axiom,
( ( ord_less_eq_set_a @ a2 @ a3 )
| ( ord_less_eq_set_a @ a3 @ a2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__092_060open_062a2_A_092_060subseteq_062_Aa3_A_092_060or_062_Aa3_A_092_060subseteq_062_Aa2_092_060close_062) ).
thf(290,plain,
( ( ord_less_eq_set_a @ a2 @ a3 )
| ( ord_less_eq_set_a @ a3 @ a2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(29,axiom,
! [A: set_Pr204296108_a_a_e,B: set_Pr204296108_a_a_e,C: produc715398134_a_a_e > set_a,D: produc715398134_a_a_e > set_a] :
( ( A = B )
=> ( ! [E: produc715398134_a_a_e] :
( ( member1258382221_a_a_e @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image_64240033_set_a @ C @ A )
= ( image_64240033_set_a @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_image__cong) ).
thf(207,plain,
! [A: set_Pr204296108_a_a_e,B: set_Pr204296108_a_a_e,C: produc715398134_a_a_e > set_a,D: produc715398134_a_a_e > set_a] :
( ( A = B )
=> ( ! [E: produc715398134_a_a_e] :
( ( member1258382221_a_a_e @ E @ B )
=> ( ( C @ E )
= ( D @ E ) ) )
=> ( ( image_64240033_set_a @ C @ A )
= ( image_64240033_set_a @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(81,axiom,
! [A: produc715398134_a_a_e] :
( ( member1258382221_a_a_e @ A @ c )
=> ! [B: produc715398134_a_a_e] :
( ( member1258382221_a_a_e @ B @ c )
=> ( ( ord_less_eq_set_a @ ( produc1040928388_a_a_e @ A ) @ ( produc1040928388_a_a_e @ B ) )
| ( ord_less_eq_set_a @ ( produc1040928388_a_a_e @ B ) @ ( produc1040928388_a_a_e @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062_092_060forall_062a_092_060in_062C_O_A_092_060forall_062b_092_060in_062C_O_Afst_Aa_A_092_060subseteq_062_Afst_Ab_A_092_060or_062_Afst_Ab_A_092_060subseteq_062_Afst_Aa_092_060close_062) ).
thf(383,plain,
! [A: produc715398134_a_a_e] :
( ( member1258382221_a_a_e @ A @ c )
=> ! [B: produc715398134_a_a_e] :
( ( member1258382221_a_a_e @ B @ c )
=> ( ( ord_less_eq_set_a @ ( produc1040928388_a_a_e @ A ) @ ( produc1040928388_a_a_e @ B ) )
| ( ord_less_eq_set_a @ ( produc1040928388_a_a_e @ B ) @ ( produc1040928388_a_a_e @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(53,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_dual__order_Otrans) ).
thf(287,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(62,axiom,
( ( ord_less_eq_set_a @ a1 @ a2 )
| ( ord_less_eq_set_a @ a2 @ a1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062a1_A_092_060subseteq_062_Aa2_A_092_060or_062_Aa2_A_092_060subseteq_062_Aa1_092_060close_062) ).
thf(315,plain,
( ( ord_less_eq_set_a @ a1 @ a2 )
| ( ord_less_eq_set_a @ a2 @ a1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(90,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ top_top_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_top__greatest) ).
thf(410,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ top_top_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(24,axiom,
! [A: produc715398134_a_a_e > set_a,B: set_a > produc715398134_a_a_e] :
( ! [C: set_a] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_64240033_set_a @ A @ top_to1601855068_a_a_e )
= top_top_set_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_surjI) ).
thf(190,plain,
! [A: produc715398134_a_a_e > set_a,B: set_a > produc715398134_a_a_e] :
( ! [C: set_a] :
( ( A @ ( B @ C ) )
= C )
=> ( ( image_64240033_set_a @ A @ top_to1601855068_a_a_e )
= top_top_set_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(93,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_set__eq__subset) ).
thf(422,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(48,axiom,
! [A: set_a,B: produc715398134_a_a_e > set_a,C: set_Pr204296108_a_a_e] :
( ( member_set_a @ A @ ( image_64240033_set_a @ B @ C ) )
= ( ? [D: produc715398134_a_a_e] :
( ( member1258382221_a_a_e @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_image__iff) ).
thf(273,plain,
! [A: set_a,B: produc715398134_a_a_e > set_a,C: set_Pr204296108_a_a_e] :
( ( member_set_a @ A @ ( image_64240033_set_a @ B @ C ) )
= ( ? [D: produc715398134_a_a_e] :
( ( member1258382221_a_a_e @ D @ C )
& ( A
= ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(59,axiom,
! [A: set_a,B: produc715398134_a_a_e > set_a,C: set_Pr204296108_a_a_e] :
( ( member_set_a @ A @ ( image_64240033_set_a @ B @ C ) )
=> ? [D: produc715398134_a_a_e] :
( ( member1258382221_a_a_e @ D @ C )
& ( A
= ( B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_mem__in__image3) ).
thf(305,plain,
! [A: set_a,B: produc715398134_a_a_e > set_a,C: set_Pr204296108_a_a_e] :
( ( member_set_a @ A @ ( image_64240033_set_a @ B @ C ) )
=> ? [D: produc715398134_a_a_e] :
( ( member1258382221_a_a_e @ D @ C )
& ( A
= ( B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(40,axiom,
! [A: set_a,B: set_a > $o] :
( ( member_set_a @ A @ ( collect_set_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_mem__Collect__eq) ).
thf(242,plain,
! [A: set_a,B: set_a > $o] :
( ( member_set_a @ A @ ( collect_set_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(10,axiom,
! [A: $o > set_a,B: $o > set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
=> ( ( ord_less_eq_o_set_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_antisym__conv) ).
thf(126,plain,
! [A: $o > set_a,B: $o > set_a] :
( ( ord_less_eq_o_set_a @ A @ B )
=> ( ( ord_less_eq_o_set_a @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(69,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_antisym) ).
thf(341,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(47,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_ord__le__eq__trans) ).
thf(268,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(75,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_subset__self) ).
thf(358,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(87,axiom,
( domain_set_a_a_e
= ( image_64240033_set_a @ produc1040928388_a_a_e ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_Domain__fst) ).
thf(400,plain,
( domain_set_a_a_e
= ( image_64240033_set_a @ produc1040928388_a_a_e ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(51,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_order__class_Oorder_Oeq__iff) ).
thf(283,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(95,axiom,
! [A: set_Pr204296108_a_a_e] :
( ( image_64240033_set_a @ produc1040928388_a_a_e @ A )
= ( domain_set_a_a_e @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_fst__eq__Domain) ).
thf(427,plain,
! [A: set_Pr204296108_a_a_e] :
( ( image_64240033_set_a @ produc1040928388_a_a_e @ A )
= ( domain_set_a_a_e @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(22,axiom,
! [A: produc715398134_a_a_e > set_a,B: set_a] :
( ( ( image_64240033_set_a @ A @ top_to1601855068_a_a_e )
= top_top_set_set_a )
=> ~ ! [C: produc715398134_a_a_e] :
( B
!= ( A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_surjE) ).
thf(178,plain,
! [A: produc715398134_a_a_e > set_a,B: set_a] :
( ( ( image_64240033_set_a @ A @ top_to1601855068_a_a_e )
= top_top_set_set_a )
=> ~ ! [C: produc715398134_a_a_e] :
( B
!= ( A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(101,axiom,
! [A: set_a,B: set_a] :
( ( member_set_a @ A @ ( pow_a @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_Pow__iff) ).
thf(442,plain,
! [A: set_a,B: set_a] :
( ( member_set_a @ A @ ( pow_a @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(6,axiom,
! [A: set_a] : ( member_set_a @ A @ top_top_set_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_UNIV__I) ).
thf(111,plain,
! [A: set_a] : ( member_set_a @ A @ top_top_set_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(43,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_order__trans) ).
thf(254,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(65,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_subset__trans) ).
thf(322,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(60,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ A @ C )
=> ( ord_less_eq_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_le__convert) ).
thf(309,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ A @ C )
=> ( ord_less_eq_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(30,axiom,
! [A: produc715398134_a_a_e] : ( member1258382221_a_a_e @ A @ top_to1601855068_a_a_e ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_UNIV__I) ).
thf(215,plain,
! [A: produc715398134_a_a_e] : ( member1258382221_a_a_e @ A @ top_to1601855068_a_a_e ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(453,plain,
$false,
inference(e,[status(thm)],[292,285,317,129,360,295,314,347,234,352,170,440,217,276,385,142,436,257,344,196,325,228,164,376,106,238,147,397,221,116,265,302,260,160,392,424,407,137,124,225,298,412,430,375,402,281,204,391,445,350,113,419,230,362,245,434,387,367,103,240,155,108,330,223,438,167,355,194,145,199,182,338,250,104,319,158,290,207,383,287,315,410,190,422,273,305,242,126,341,268,358,400,283,427,178,442,111,254,322,309,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ITP028^1 : TPTP v8.2.0. Released v7.5.0.
% 0.10/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n009.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Jun 19 00:09:25 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.98/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.68/1.12 % [INFO] Parsing done (243ms).
% 1.68/1.13 % [INFO] Running in sequential loop mode.
% 2.66/1.34 % [INFO] eprover registered as external prover.
% 2.66/1.34 % [INFO] Scanning for conjecture ...
% 2.78/1.43 % [INFO] Found a conjecture (or negated_conjecture) and 353 axioms. Running axiom selection ...
% 2.99/1.50 % [INFO] Axiom selection finished. Selected 100 axioms (removed 253 axioms).
% 3.30/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 3.30/1.60 % [INFO] Type checking passed.
% 3.30/1.60 % [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 ...
% 6.78/2.55 % External prover 'e' found a proof!
% 6.78/2.56 % [INFO] Killing All external provers ...
% 6.78/2.56 % Time passed: 2012ms (effective reasoning time: 1422ms)
% 6.78/2.56 % 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)>
% 6.78/2.56 % Axioms used in derivation (100): fact_161_ord__le__eq__subst, fact_147_antisym, fact_107_order__trans, fact_20_subset__antisym, fact_258_Pow__iff, fact_263_le__rel__bool__arg__iff, fact_113_order__class_Oorder_Oantisym, fact_132_antisym__conv, fact_267_fst__eq__Domain, fact_102_dual__order_Orefl, fact_245_subset__self, fact_328_UNIV__eq__I, fact_268_Domain__fst, fact_133_antisym__conv, fact_233_mem__in__image2, fact_182_image__iff, fact_194_equalityD2, fact_259_Pow__top, fact_330_UNIV__witness, fact_171_mem__Collect__eq, fact_1__092_060open_062_092_060exists_062a_092_060in_062fst_A_096_AC_O_Aa1_A_092_060subseteq_062_Aa_A_092_060and_062_Aa2_A_092_060subseteq_062_Aa_A_092_060and_062_Aa3_A_092_060subseteq_062_Aa_092_060close_062, fact_169_order__subst2, fact_3__092_060open_062a1_A_092_060subseteq_062_Aa3_A_092_060or_062_Aa3_A_092_060subseteq_062_Aa1_092_060close_062, fact_260_PowD, fact_187_Collect__mono__iff, fact_315_surjD, fact_317_top_Oextremum__uniqueI, fact_158_ord__le__eq__subst, fact_329_UNIV__eq__I, fact_122_ord__eq__le__trans, fact_179_ball__imageD, fact_92_dual__order_Oeq__iff, fact_331_UNIV__witness, fact_4__092_060open_062a2_A_092_060subseteq_062_Aa3_A_092_060or_062_Aa3_A_092_060subseteq_062_Aa2_092_060close_062, fact_2__092_060open_062a1_A_092_060subseteq_062_Aa2_A_092_060or_062_Aa2_A_092_060subseteq_062_Aa1_092_060close_062, fact_173_Collect__mem__eq, fact_123_ord__eq__le__trans, fact_98_dual__order_Otrans, fact_97_dual__order_Otrans, fact_312_surj__def, fact_5_A_I3_J, fact_180_image__cong, fact_320_subset__UNIV, fact_305_fst__map__prod, fact_339_top__empty__eq, fact_229_ge__convert, fact_153_eq__iff, fact_223_eqsets__sub, fact_309_range__fst, fact_189_subset__trans, fact_138_order_Otrans, fact_236_mem__in__image1, fact_310_rangeI, fact_127_order__class_Oorder_Oeq__iff, fact_6_A_I2_J, fact_190_Collect__mono, fact_170_order__subst1, fact_128_order__class_Oorder_Oeq__iff, fact_188_set__eq__subset, fact_117_ord__le__eq__trans, fact_311_range__eqI, fact_143_eq__refl, fact_7_A_I1_J, fact_154_ord__le__eq__subst, fact_148_antisym, fact_185_imageI, fact_177_rev__image__eqI, fact_93_dual__order_Oeq__iff, fact_34_order__refl, fact_302_UNIV__I, fact_253_Sup_OSUP__cong, fact_152_eq__iff, fact_318_top_Oextremum__unique, fact_88_dual__order_Oantisym, fact_228_le__convert, fact_257_PowI, fact_198_equalityE, fact_35_order__refl, fact_338_top__empty__eq, fact_314_surjE, fact_213_Greatest__equality, fact_230_mem__in__image3, fact_313_surjI, fact_319_top__greatest, fact_87_dual__order_Oantisym, fact_254_Inf_OINF__cong, fact_303_UNIV__I, fact_181_bex__imageD, fact_168_ord__eq__le__subst, fact_118_ord__le__eq__trans, fact_112_order__class_Oorder_Oantisym, fact_23_image__eqI, fact_214_GreatestI2__order, fact_103_dual__order_Orefl, fact_167_ord__eq__le__subst, fact_0__092_060open_062_092_060forall_062a_092_060in_062C_O_A_092_060forall_062b_092_060in_062C_O_Afst_Aa_A_092_060subseteq_062_Afst_Ab_A_092_060or_062_Afst_Ab_A_092_060subseteq_062_Afst_Aa_092_060close_062, conj_0, fact_108_order__trans, fact_142_eq__refl, fact_137_order_Otrans
% 6.78/2.56 % No. of inferences in proof: 204
% 6.78/2.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2012 ms resp. 1422 ms w/o parsing
% 7.10/2.64 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.10/2.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------