%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP004^7 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:16 AM UTC 2026
% Result : Theorem 23.65s 6.79s
% Output : Refutation 25.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 136
% Syntax : Number of formulae : 281 ( 189 unt; 0 typ; 1 def)
% Number of atoms : 1110 ( 316 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 2506 ( 83 ~; 14 |; 98 &;2249 @)
% ( 0 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 446 ( 446 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 1 con; 0-5 aty)
% Number of variables : 898 ( 8 ^; 867 !; 22 ?; 898 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Emin_2Eind_type,type,
tyop_2Emin_2Eind: $tType ).
thf(tyop_2Enum_2Enum_type,type,
tyop_2Enum_2Enum: $tType ).
thf(tyop_2Eone_2Eone_type,type,
tyop_2Eone_2Eone: $tType ).
thf(skt1_type,type,
skt1: $tType ).
thf(c_2Ebool_2EIN_decl,type,
c_2Ebool_2EIN:
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf(c_2Ebool_2ERES__ABSTRACT_decl,type,
c_2Ebool_2ERES__ABSTRACT:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TB > TA ) > TB > TA ) ).
thf(c_2Enum_2ESUC_decl,type,
c_2Enum_2ESUC: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Epred__set_2ECHOICE_decl,type,
c_2Epred__set_2ECHOICE:
!>[TA: $tType] : ( ( TA > $o ) > TA ) ).
thf(c_2Epred__set_2EDELETE_decl,type,
c_2Epred__set_2EDELETE:
!>[TA: $tType] : ( ( TA > $o ) > TA > TA > $o ) ).
thf(c_2Epred__set_2EDIFF_decl,type,
c_2Epred__set_2EDIFF:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA > $o ) ).
thf(c_2Epred__set_2EDISJOINT_decl,type,
c_2Epred__set_2EDISJOINT:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > $o ) ).
thf(c_2Epred__set_2EEMPTY_decl,type,
c_2Epred__set_2EEMPTY:
!>[TA: $tType] : ( TA > $o ) ).
thf(c_2Epred__set_2EINSERT_decl,type,
c_2Epred__set_2EINSERT:
!>[TA: $tType] : ( TA > ( TA > $o ) > TA > $o ) ).
thf(c_2Epred__set_2EINTER_decl,type,
c_2Epred__set_2EINTER:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA > $o ) ).
thf(c_2Epred__set_2EPSUBSET_decl,type,
c_2Epred__set_2EPSUBSET:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > $o ) ).
thf(c_2Epred__set_2EREST_decl,type,
c_2Epred__set_2EREST:
!>[TA: $tType] : ( ( TA > $o ) > TA > $o ) ).
thf(c_2Epred__set_2ESUBSET_decl,type,
c_2Epred__set_2ESUBSET:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > $o ) ).
thf(c_2Epred__set_2EUNION_decl,type,
c_2Epred__set_2EUNION:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA > $o ) ).
thf(c_2Epred__set_2EUNIV_decl,type,
c_2Epred__set_2EUNIV:
!>[TA: $tType] : ( TA > $o ) ).
thf(sk1_decl,type,
sk1: skt1 > $o ).
thf(sk8_decl,type,
sk8:
!>[TA: $tType] : TA ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1 > $o] :
~ ( c_2Epred__set_2ESUBSET @ skt1 @ ( c_2Epred__set_2EREST @ skt1 @ A ) @ A ) ) ) ).
thf(1,conjecture,
! [TA: $tType,A: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EREST @ TA @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__SUBSET) ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EREST @ TA @ A ) @ A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(137,plain,
~ ! [TA: $tType,A: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EREST @ TA @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(138,plain,
~ ( c_2Epred__set_2ESUBSET @ skt1 @ ( c_2Epred__set_2EREST @ skt1 @ sk1 ) @ sk1 ),
inference(cnf,[status(esa)],[137]) ).
thf(35,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EDISJOINT @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ C )
= ( ( c_2Epred__set_2EDISJOINT @ TA @ A @ C )
& ( c_2Epred__set_2EDISJOINT @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDISJOINT__UNION) ).
thf(249,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EDISJOINT @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ C )
= ( ( c_2Epred__set_2EDISJOINT @ TA @ A @ C )
& ( c_2Epred__set_2EDISJOINT @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(117,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( ( c_2Epred__set_2EDISJOINT @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ C @ B ) )
=> ( c_2Epred__set_2EDISJOINT @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDISJOINT__SUBSET) ).
thf(518,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( ( c_2Epred__set_2EDISJOINT @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ C @ B ) )
=> ( c_2Epred__set_2EDISJOINT @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(103,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
=> ! [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ A )
=> ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__THM) ).
thf(468,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
=> ! [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ A )
=> ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(30,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ~ ( c_2Ebool_2EIN @ TA @ B @ A )
=> ( ( c_2Epred__set_2EDELETE @ TA @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDELETE__NON__ELEMENT__RWT) ).
thf(234,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ~ ( c_2Ebool_2EIN @ TA @ B @ A )
=> ( ( c_2Epred__set_2EDELETE @ TA @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(108,axiom,
! [TA: $tType,A: TA > $o] :
( ( A
!= ( c_2Epred__set_2EEMPTY @ TA ) )
=> ( ( c_2Epred__set_2EINSERT @ TA @ ( c_2Epred__set_2ECHOICE @ TA @ A ) @ ( c_2Epred__set_2EREST @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ECHOICE__INSERT__REST) ).
thf(481,plain,
! [TA: $tType,A: TA > $o] :
( ( A
!= ( c_2Epred__set_2EEMPTY @ TA ) )
=> ( ( c_2Epred__set_2EINSERT @ TA @ ( c_2Epred__set_2ECHOICE @ TA @ A ) @ ( c_2Epred__set_2EREST @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(11,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EDISJOINT @ TA @ A @ B )
= ( ! [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ A )
=> ~ ( c_2Ebool_2EIN @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDISJOINT__ALT) ).
thf(170,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EDISJOINT @ TA @ A @ B )
= ( ! [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ A )
=> ~ ( c_2Ebool_2EIN @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(119,axiom,
! [TA: $tType] :
( ! [A: TA > $o,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EINTER @ TA @ A @ B ) @ A )
& ! [A: TA > $o,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EINTER @ TA @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__SUBSET) ).
thf(523,plain,
! [TA: $tType] :
( ! [A: TA > $o,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EINTER @ TA @ A @ B ) @ A )
& ! [A: TA > $o,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EINTER @ TA @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(56,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EDISJOINT @ TA @ A @ B )
= ( c_2Epred__set_2EDISJOINT @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDISJOINT__SYM) ).
thf(308,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EDISJOINT @ TA @ A @ B )
= ( c_2Epred__set_2EDISJOINT @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(98,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Epred__set_2EDELETE @ TA @ ( c_2Epred__set_2EDELETE @ TA @ B @ A ) @ A )
= ( c_2Epred__set_2EDELETE @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDELETE__DELETE) ).
thf(449,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Epred__set_2EDELETE @ TA @ ( c_2Epred__set_2EDELETE @ TA @ B @ A ) @ A )
= ( c_2Epred__set_2EDELETE @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(95,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ ( c_2Epred__set_2EINTER @ TA @ A @ B ) )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
& ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__INTER) ).
thf(440,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ ( c_2Epred__set_2EINTER @ TA @ A @ B ) )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
& ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(25,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( ( c_2Epred__set_2EDISJOINT @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ C )
= ( ( c_2Epred__set_2EDISJOINT @ TA @ A @ C )
& ( c_2Epred__set_2EDISJOINT @ TA @ B @ C ) ) )
& ( ( c_2Epred__set_2EDISJOINT @ TA @ C @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) )
= ( ( c_2Epred__set_2EDISJOINT @ TA @ A @ C )
& ( c_2Epred__set_2EDISJOINT @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDISJOINT__UNION__BOTH) ).
thf(217,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( ( c_2Epred__set_2EDISJOINT @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ C )
= ( ( c_2Epred__set_2EDISJOINT @ TA @ A @ C )
& ( c_2Epred__set_2EDISJOINT @ TA @ B @ C ) ) )
& ( ( c_2Epred__set_2EDISJOINT @ TA @ C @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) )
= ( ( c_2Epred__set_2EDISJOINT @ TA @ A @ C )
& ( c_2Epred__set_2EDISJOINT @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(44,axiom,
! [TA: $tType,A: TA > $o] :
~ ( c_2Epred__set_2EPSUBSET @ TA @ ( c_2Epred__set_2EUNIV @ TA ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ENOT__UNIV__PSUBSET) ).
thf(276,plain,
! [TA: $tType,A: TA > $o] :
~ ( c_2Epred__set_2EPSUBSET @ TA @ ( c_2Epred__set_2EUNIV @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(80,axiom,
! [TA: $tType] :
( ! [A: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EUNIV @ TA ) @ A )
= A )
& ! [A: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ ( c_2Epred__set_2EUNIV @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__UNIV) ).
thf(385,plain,
! [TA: $tType] :
( ! [A: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EUNIV @ TA ) @ A )
= A )
& ! [A: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ ( c_2Epred__set_2EUNIV @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(4,axiom,
! [A: tyop_2Enum_2Enum] :
( ( c_2Enum_2ESUC @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2ESUC__ID) ).
thf(142,plain,
! [A: tyop_2Enum_2Enum] :
( ( c_2Enum_2ESUC @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(124,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EINTER @ TA @ B @ C ) )
= ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__INTER) ).
thf(538,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EINTER @ TA @ B @ C ) )
= ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(85,axiom,
! [TA: $tType,A: TA,B: TA,C: TA > $o] :
( ( c_2Epred__set_2EINSERT @ TA @ B @ C @ A )
= ( ( A = B )
| ( c_2Ebool_2EIN @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EINSERT__applied) ).
thf(404,plain,
! [TA: $tType,A: TA,B: TA,C: TA > $o] :
( ( c_2Epred__set_2EINSERT @ TA @ B @ C @ A )
= ( ( A = B )
| ( c_2Ebool_2EIN @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(60,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) )
=> ( A @ D ) ) )
= ( ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ B )
=> ( A @ D ) )
& ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ C )
=> ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EFORALL__IN__UNION) ).
thf(320,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) )
=> ( A @ D ) ) )
= ( ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ B )
=> ( A @ D ) )
& ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ C )
=> ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(16,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__IDEMPOT) ).
thf(184,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(72,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Epred__set_2EUNION @ TA @ A @ B @ C )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
| ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__applied) ).
thf(357,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Epred__set_2EUNION @ TA @ A @ B @ C )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
| ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(28,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EEMPTY @ TA ) @ A )
= ( c_2Epred__set_2EEMPTY @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EEMPTY__DIFF) ).
thf(228,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EEMPTY @ TA ) @ A )
= ( c_2Epred__set_2EEMPTY @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(49,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EDISJOINT @ TA @ A @ A )
= ( A
= ( c_2Epred__set_2EEMPTY @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDISJOINT__EMPTY__REFL__RWT) ).
thf(289,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EDISJOINT @ TA @ A @ A )
= ( A
= ( c_2Epred__set_2EEMPTY @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(39,axiom,
! [TA: $tType,A: TA > $o] :
( ( A
= ( c_2Epred__set_2EEMPTY @ TA ) )
= ( c_2Epred__set_2EDISJOINT @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDISJOINT__EMPTY__REFL) ).
thf(261,plain,
! [TA: $tType,A: TA > $o] :
( ( A
= ( c_2Epred__set_2EEMPTY @ TA ) )
= ( c_2Epred__set_2EDISJOINT @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(106,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EPSUBSET @ TA @ A @ B )
= ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ? [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ B )
& ~ ( c_2Ebool_2EIN @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EPSUBSET__MEMBER) ).
thf(475,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EPSUBSET @ TA @ A @ B )
= ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ? [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ B )
& ~ ( c_2Ebool_2EIN @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(9,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Ebool_2EIN @ TA @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__ABS) ).
thf(164,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Ebool_2EIN @ TA @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(96,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( c_2Ebool_2EIN @ TA @ B @ A )
= ( ? [C: TA > $o] :
( ( A
= ( c_2Epred__set_2EINSERT @ TA @ B @ C ) )
& ~ ( c_2Ebool_2EIN @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDECOMPOSITION) ).
thf(443,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( c_2Ebool_2EIN @ TA @ B @ A )
= ( ? [C: TA > $o] :
( ( A
= ( c_2Epred__set_2EINSERT @ TA @ B @ C ) )
& ~ ( c_2Ebool_2EIN @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(77,axiom,
! [TA: $tType,A: TA] : ( c_2Ebool_2EIN @ TA @ A @ ( c_2Epred__set_2EUNIV @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__UNIV) ).
thf(376,plain,
! [TA: $tType,A: TA] : ( c_2Ebool_2EIN @ TA @ A @ ( c_2Epred__set_2EUNIV @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(69,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EINSERT @ TA @ C @ B ) )
= ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EDELETE @ TA @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__INSERT) ).
thf(348,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EINSERT @ TA @ C @ B ) )
= ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EDELETE @ TA @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(31,axiom,
! [TA: $tType] :
( ( c_2Epred__set_2EUNIV @ TA )
!= ( c_2Epred__set_2EEMPTY @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EUNIV__NOT__EMPTY) ).
thf(237,plain,
! [TA: $tType] :
( ( c_2Epred__set_2EUNIV @ TA )
!= ( c_2Epred__set_2EEMPTY @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(238,plain,
! [TA: $tType] :
( ( c_2Epred__set_2EUNIV @ TA )
!= ( c_2Epred__set_2EEMPTY @ TA ) ),
inference(cnf,[status(esa)],[237]) ).
thf(239,plain,
! [TA: $tType] :
( ( c_2Epred__set_2EUNIV @ TA )
!= ( c_2Epred__set_2EEMPTY @ TA ) ),
inference(lifteq,[status(thm)],[238]) ).
thf(574,plain,
! [TA: $tType] :
( ( c_2Epred__set_2EUNIV @ TA @ ( sk8 @ TA ) )
!= ( c_2Epred__set_2EEMPTY @ TA @ ( sk8 @ TA ) ) ),
inference(func_ext,[status(esa)],[239]) ).
thf(33,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EDISJOINT @ TA @ A @ B )
= ( ~ ? [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ A )
& ( c_2Ebool_2EIN @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__DISJOINT) ).
thf(243,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EDISJOINT @ TA @ A @ B )
= ( ~ ? [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ A )
& ( c_2Ebool_2EIN @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(91,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Epred__set_2EINTER @ TA @ A @ B @ C )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
& ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__applied) ).
thf(428,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Epred__set_2EINTER @ TA @ A @ B @ C )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
& ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(50,axiom,
! [TA: $tType,A: TA] : ( c_2Epred__set_2EUNIV @ TA @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EUNIV__applied) ).
thf(292,plain,
! [TA: $tType,A: TA] : ( c_2Epred__set_2EUNIV @ TA @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(99,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ A )
= ( c_2Epred__set_2EEMPTY @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__EQ__EMPTY) ).
thf(452,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ A )
= ( c_2Epred__set_2EEMPTY @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(115,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ B @ A )
=> ( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__DIFF__SUBSET) ).
thf(512,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ B @ A )
=> ( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(42,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ C )
= ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__COMM) ).
thf(270,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ C )
= ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(21,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EDISJOINT @ TA @ A @ B )
= ( ( c_2Epred__set_2EINTER @ TA @ A @ B )
= ( c_2Epred__set_2EEMPTY @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDISJOINT__DEF) ).
thf(201,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EDISJOINT @ TA @ A @ B )
= ( ( c_2Epred__set_2EINTER @ TA @ A @ B )
= ( c_2Epred__set_2EEMPTY @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(79,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EDISJOINT @ TA @ B @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) )
& ( c_2Epred__set_2EDISJOINT @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDISJOINT__DIFF) ).
thf(381,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EDISJOINT @ TA @ B @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) )
& ( c_2Epred__set_2EDISJOINT @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(75,axiom,
! [TA: $tType] :
( ! [A: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EEMPTY @ TA ) @ A )
= A )
& ! [A: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__EMPTY) ).
thf(366,plain,
! [TA: $tType] :
( ! [A: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EEMPTY @ TA ) @ A )
= A )
& ! [A: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(122,axiom,
! [TA: $tType,A: TA > $o] :
~ ( c_2Ebool_2EIN @ TA @ ( c_2Epred__set_2ECHOICE @ TA @ A ) @ ( c_2Epred__set_2EREST @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ECHOICE__NOT__IN__REST) ).
thf(534,plain,
! [TA: $tType,A: TA > $o] :
~ ( c_2Ebool_2EIN @ TA @ ( c_2Epred__set_2ECHOICE @ TA @ A ) @ ( c_2Epred__set_2EREST @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(54,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ A )
= ( c_2Ebool_2EIN @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EEXTENSION) ).
thf(302,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ A )
= ( c_2Ebool_2EIN @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(133,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__SUBSET) ).
thf(561,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(81,axiom,
! [TA: $tType] :
( ( c_2Ebool_2EIN @ TA )
= ( ^ [A: TA,B: TA > $o] : ( B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIN__DEF) ).
thf(392,plain,
! [TA: $tType] :
( ( c_2Ebool_2EIN @ TA )
= ( ^ [A: TA,B: TA > $o] : ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(86,axiom,
! [TA: $tType,A: TA] :
( ( c_2Epred__set_2EINSERT @ TA @ A @ ( c_2Epred__set_2EUNIV @ TA ) )
= ( c_2Epred__set_2EUNIV @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EINSERT__UNIV) ).
thf(407,plain,
! [TA: $tType,A: TA] :
( ( c_2Epred__set_2EINSERT @ TA @ A @ ( c_2Epred__set_2EUNIV @ TA ) )
= ( c_2Epred__set_2EUNIV @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(36,axiom,
! [TA: $tType,A: TA,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EDISJOINT @ TA @ ( c_2Epred__set_2EINSERT @ TA @ A @ B ) @ C )
= ( ( c_2Epred__set_2EDISJOINT @ TA @ B @ C )
& ~ ( c_2Ebool_2EIN @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDISJOINT__INSERT) ).
thf(252,plain,
! [TA: $tType,A: TA,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EDISJOINT @ TA @ ( c_2Epred__set_2EINSERT @ TA @ A @ B ) @ C )
= ( ( c_2Epred__set_2EDISJOINT @ TA @ B @ C )
& ~ ( c_2Ebool_2EIN @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(63,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ ( c_2Epred__set_2EINTER @ TA @ B @ C ) )
= ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ ( c_2Epred__set_2EUNION @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__OVER__UNION) ).
thf(329,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ ( c_2Epred__set_2EINTER @ TA @ B @ C ) )
= ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ ( c_2Epred__set_2EUNION @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(111,axiom,
! [TA: $tType] :
( ! [A: TA > $o,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) )
& ! [A: TA > $o,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__UNION) ).
thf(493,plain,
! [TA: $tType] :
( ! [A: TA > $o,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) )
& ! [A: TA > $o,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(129,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
=> ( ( c_2Epred__set_2EINTER @ TA @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__INTER2) ).
thf(551,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
=> ( ( c_2Epred__set_2EINTER @ TA @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(135,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ A ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__SUBSET__EQ) ).
thf(566,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ A ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(109,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Ebool_2EIN @ TA @ A @ ( c_2Epred__set_2EREST @ TA @ B ) )
= ( ( c_2Ebool_2EIN @ TA @ A @ B )
& ( A
!= ( c_2Epred__set_2ECHOICE @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__REST) ).
thf(484,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Ebool_2EIN @ TA @ A @ ( c_2Epred__set_2EREST @ TA @ B ) )
= ( ( c_2Ebool_2EIN @ TA @ A @ B )
& ( A
!= ( c_2Epred__set_2ECHOICE @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(59,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( ~ ( c_2Ebool_2EIN @ TA @ A @ B ) )
= ( ( c_2Epred__set_2EDELETE @ TA @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDELETE__NON__ELEMENT) ).
thf(317,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( ~ ( c_2Ebool_2EIN @ TA @ A @ B ) )
= ( ( c_2Epred__set_2EDELETE @ TA @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(88,axiom,
! [TA: $tType,A: TA > $o] :
( ( ? [B: TA] : ( c_2Ebool_2EIN @ TA @ B @ A ) )
= ( A
!= ( c_2Epred__set_2EEMPTY @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EMEMBER__NOT__EMPTY) ).
thf(420,plain,
! [TA: $tType,A: TA > $o] :
( ( ? [B: TA] : ( c_2Ebool_2EIN @ TA @ B @ A ) )
= ( A
!= ( c_2Epred__set_2EEMPTY @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(130,axiom,
! [TA: $tType,A: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__REFL) ).
thf(554,plain,
! [TA: $tType,A: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(18,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
~ ( c_2Ebool_2EIN @ TA @ A @ ( c_2Epred__set_2EDELETE @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EELT__IN__DELETE) ).
thf(193,plain,
! [TA: $tType,A: TA,B: TA > $o] :
~ ( c_2Ebool_2EIN @ TA @ A @ ( c_2Epred__set_2EDELETE @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(116,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EUNIV @ TA ) @ A )
= ( A
= ( c_2Epred__set_2EUNIV @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EUNIV__SUBSET) ).
thf(515,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EUNIV @ TA ) @ A )
= ( A
= ( c_2Epred__set_2EUNIV @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(12,axiom,
! [TA: $tType,A: TA,B: TA > $o] : ( c_2Ebool_2EIN @ TA @ A @ ( c_2Epred__set_2EINSERT @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ECOMPONENT) ).
thf(173,plain,
! [TA: $tType,A: TA,B: TA > $o] : ( c_2Ebool_2EIN @ TA @ A @ ( c_2Epred__set_2EINSERT @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(136,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EREST @ TA @ A )
= ( c_2Epred__set_2EDELETE @ TA @ A @ ( c_2Epred__set_2ECHOICE @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__DEF) ).
thf(569,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EREST @ TA @ A )
= ( c_2Epred__set_2EDELETE @ TA @ A @ ( c_2Epred__set_2ECHOICE @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(73,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) )
= ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__ASSOC) ).
thf(360,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) )
= ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(57,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EUNIV @ TA ) )
= ( c_2Epred__set_2EEMPTY @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__UNIV) ).
thf(311,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EUNIV @ TA ) )
= ( c_2Epred__set_2EEMPTY @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(125,axiom,
! [TA: $tType,A: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EEMPTY @ TA ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EEMPTY__SUBSET) ).
thf(541,plain,
! [TA: $tType,A: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EEMPTY @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(83,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
& ~ ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__DIFF) ).
thf(398,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
& ~ ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(132,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ C )
= ( ( c_2Epred__set_2ESUBSET @ TA @ A @ C )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__SUBSET) ).
thf(558,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ C )
= ( ( c_2Epred__set_2ESUBSET @ TA @ A @ C )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(90,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A != B )
= ( ? [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ B )
= ( ~ ( c_2Ebool_2EIN @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ENOT__EQUAL__SETS) ).
thf(425,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A != B )
= ( ? [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ B )
= ( ~ ( c_2Ebool_2EIN @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(40,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Epred__set_2EDISJOINT @ TA @ ( c_2Epred__set_2EDELETE @ TA @ A @ C ) @ B )
= ( c_2Epred__set_2EDISJOINT @ TA @ ( c_2Epred__set_2EDELETE @ TA @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDISJOINT__DELETE__SYM) ).
thf(264,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Epred__set_2EDISJOINT @ TA @ ( c_2Epred__set_2EDELETE @ TA @ A @ C ) @ B )
= ( c_2Epred__set_2EDISJOINT @ TA @ ( c_2Epred__set_2EDELETE @ TA @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(8,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EPSUBSET @ TA @ A @ ( c_2Epred__set_2EUNIV @ TA ) )
= ( ? [B: TA] :
~ ( c_2Ebool_2EIN @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EPSUBSET__UNIV) ).
thf(161,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EPSUBSET @ TA @ A @ ( c_2Epred__set_2EUNIV @ TA ) )
= ( ? [B: TA] :
~ ( c_2Ebool_2EIN @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(52,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ B )
= ( c_2Epred__set_2EDIFF @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__DIFF) ).
thf(296,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ B )
= ( c_2Epred__set_2EDIFF @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(89,axiom,
! [TA: $tType,A: TA > $o] :
~ ( c_2Epred__set_2EPSUBSET @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ENOT__PSUBSET__EMPTY) ).
thf(423,plain,
! [TA: $tType,A: TA > $o] :
~ ( c_2Epred__set_2EPSUBSET @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(48,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ ( c_2Epred__set_2EINTER @ TA @ B @ C ) )
= ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EINTER @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__ASSOC) ).
thf(286,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ ( c_2Epred__set_2EINTER @ TA @ B @ C ) )
= ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EINTER @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(127,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
= ( ! [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ A )
=> ( c_2Ebool_2EIN @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__DEF) ).
thf(545,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
= ( ! [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ A )
=> ( c_2Ebool_2EIN @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(46,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( ( c_2Epred__set_2EPSUBSET @ TA @ A @ B )
& ( c_2Epred__set_2EPSUBSET @ TA @ B @ C ) )
=> ( c_2Epred__set_2EPSUBSET @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EPSUBSET__TRANS) ).
thf(281,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( ( c_2Epred__set_2EPSUBSET @ TA @ A @ B )
& ( c_2Epred__set_2EPSUBSET @ TA @ B @ C ) )
=> ( c_2Epred__set_2EPSUBSET @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(22,axiom,
! [TA: $tType,A: TA > $o] :
( ( ! [B: TA] : ( c_2Ebool_2EIN @ TA @ B @ A ) )
= ( A
= ( c_2Epred__set_2EUNIV @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EEQ__UNIV) ).
thf(204,plain,
! [TA: $tType,A: TA > $o] :
( ( ! [B: TA] : ( c_2Ebool_2EIN @ TA @ B @ A ) )
= ( A
= ( c_2Epred__set_2EUNIV @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(112,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
=> ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EEQ__SUBSET__SUBSET) ).
thf(498,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
=> ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(65,axiom,
! [TA: $tType,A: TA,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EDISJOINT @ TA @ C @ ( c_2Epred__set_2EINSERT @ TA @ A @ B ) )
= ( ( c_2Epred__set_2EDISJOINT @ TA @ C @ B )
& ~ ( c_2Ebool_2EIN @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDISJOINT__INSERT_27) ).
thf(335,plain,
! [TA: $tType,A: TA,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EDISJOINT @ TA @ C @ ( c_2Epred__set_2EINSERT @ TA @ A @ B ) )
= ( ( c_2Epred__set_2EDISJOINT @ TA @ C @ B )
& ~ ( c_2Ebool_2EIN @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(15,axiom,
! [TA: $tType,A: TA,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EINSERT @ TA @ A @ B ) @ C )
= ( ( c_2Ebool_2EIN @ TA @ A @ C )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EINSERT__SUBSET) ).
thf(181,plain,
! [TA: $tType,A: TA,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EINSERT @ TA @ A @ B ) @ C )
= ( ( c_2Ebool_2EIN @ TA @ A @ C )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(17,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ A )
= ( c_2Epred__set_2EDIFF @ TA @ B @ A ) )
& ( ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ B )
= ( c_2Epred__set_2EDIFF @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__SAME__UNION) ).
thf(187,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ A )
= ( c_2Epred__set_2EDIFF @ TA @ B @ A ) )
& ( ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) @ B )
= ( c_2Epred__set_2EDIFF @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(114,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Epred__set_2EREST @ TA @ B @ A )
= ( ( c_2Ebool_2EIN @ TA @ A @ B )
& ( A
!= ( c_2Epred__set_2ECHOICE @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__applied) ).
thf(509,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Epred__set_2EREST @ TA @ B @ A )
= ( ( c_2Ebool_2EIN @ TA @ A @ B )
& ( A
!= ( c_2Epred__set_2ECHOICE @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(93,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__IDEMPOT) ).
thf(434,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(68,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__EMPTY) ).
thf(345,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(61,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ B )
= ( c_2Epred__set_2EINTER @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__COMM) ).
thf(323,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ B )
= ( c_2Epred__set_2EINTER @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(118,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) )
= ( A
= ( c_2Epred__set_2EEMPTY @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__EMPTY) ).
thf(520,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) )
= ( A
= ( c_2Epred__set_2EEMPTY @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(32,axiom,
! [TA: $tType,A: TA,B: TA,C: TA > $o] :
( ( c_2Epred__set_2EINSERT @ TA @ A @ ( c_2Epred__set_2EINSERT @ TA @ B @ C ) )
= ( c_2Epred__set_2EINSERT @ TA @ B @ ( c_2Epred__set_2EINSERT @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EINSERT__COMM) ).
thf(240,plain,
! [TA: $tType,A: TA,B: TA,C: TA > $o] :
( ( c_2Epred__set_2EINSERT @ TA @ A @ ( c_2Epred__set_2EINSERT @ TA @ B @ C ) )
= ( c_2Epred__set_2EINSERT @ TA @ B @ ( c_2Epred__set_2EINSERT @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(20,axiom,
! [TA: $tType,A: tyop_2Enum_2Enum > TA > $o,B: tyop_2Enum_2Enum > TA > $o,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
( ( ! [E: tyop_2Enum_2Enum] : ( c_2Epred__set_2ESUBSET @ TA @ ( B @ E ) @ ( B @ ( c_2Enum_2ESUC @ E ) ) )
& ! [E: tyop_2Enum_2Enum] :
( ( A @ E )
= ( c_2Epred__set_2EDIFF @ TA @ ( B @ ( c_2Enum_2ESUC @ E ) ) @ ( B @ E ) ) )
& ( C != D ) )
=> ( c_2Epred__set_2EDISJOINT @ TA @ ( A @ C ) @ ( A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDISJOINT__DIFFS) ).
thf(198,plain,
! [TA: $tType,A: tyop_2Enum_2Enum > TA > $o,B: tyop_2Enum_2Enum > TA > $o,C: tyop_2Enum_2Enum,D: tyop_2Enum_2Enum] :
( ( ! [E: tyop_2Enum_2Enum] : ( c_2Epred__set_2ESUBSET @ TA @ ( B @ E ) @ ( B @ ( c_2Enum_2ESUC @ E ) ) )
& ! [E: tyop_2Enum_2Enum] :
( ( A @ E )
= ( c_2Epred__set_2EDIFF @ TA @ ( B @ ( c_2Enum_2ESUC @ E ) ) @ ( B @ E ) ) )
& ( C != D ) )
=> ( c_2Epred__set_2EDISJOINT @ TA @ ( A @ C ) @ ( A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(102,axiom,
! [TA: $tType,A: TA > $o] :
( ( A
= ( c_2Epred__set_2EEMPTY @ TA ) )
| ? [B: TA,C: TA > $o] :
( ( A
= ( c_2Epred__set_2EINSERT @ TA @ B @ C ) )
& ~ ( c_2Ebool_2EIN @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESET__CASES) ).
thf(462,plain,
! [TA: $tType,A: TA > $o] :
( ( A
= ( c_2Epred__set_2EEMPTY @ TA ) )
| ? [B: TA,C: TA > $o] :
( ( A
= ( c_2Epred__set_2EINSERT @ TA @ B @ C ) )
& ~ ( c_2Ebool_2EIN @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(45,axiom,
! [TA: $tType,A: TA > $o] :
( ( A
!= ( c_2Epred__set_2EEMPTY @ TA ) )
=> ( c_2Ebool_2EIN @ TA @ ( c_2Epred__set_2ECHOICE @ TA @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ECHOICE__DEF) ).
thf(278,plain,
! [TA: $tType,A: TA > $o] :
( ( A
!= ( c_2Epred__set_2EEMPTY @ TA ) )
=> ( c_2Ebool_2EIN @ TA @ ( c_2Epred__set_2ECHOICE @ TA @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(100,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA] :
( ( ( c_2Ebool_2EIN @ TA @ B @ A )
= ( c_2Ebool_2EIN @ TA @ C @ A ) )
= ( ( c_2Ebool_2EIN @ TA @ B @ ( c_2Epred__set_2EDELETE @ TA @ A @ C ) )
= ( c_2Ebool_2EIN @ TA @ C @ ( c_2Epred__set_2EDELETE @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__DELETE__EQ) ).
thf(455,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA] :
( ( ( c_2Ebool_2EIN @ TA @ B @ A )
= ( c_2Ebool_2EIN @ TA @ C @ A ) )
= ( ( c_2Ebool_2EIN @ TA @ B @ ( c_2Epred__set_2EDELETE @ TA @ A @ C ) )
= ( c_2Ebool_2EIN @ TA @ C @ ( c_2Epred__set_2EDELETE @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(26,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2EUNION @ TA @ A @ B )
= ( c_2Epred__set_2EEMPTY @ TA ) )
= ( ( A
= ( c_2Epred__set_2EEMPTY @ TA ) )
& ( B
= ( c_2Epred__set_2EEMPTY @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EEMPTY__UNION) ).
thf(223,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2EUNION @ TA @ A @ B )
= ( c_2Epred__set_2EEMPTY @ TA ) )
= ( ( A
= ( c_2Epred__set_2EEMPTY @ TA ) )
& ( B
= ( c_2Epred__set_2EEMPTY @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(393,plain,
! [TA: $tType] :
( ( c_2Ebool_2EIN @ TA )
= ( ^ [A: TA,B: TA > $o] : ( B @ A ) ) ),
inference(cnf,[status(esa)],[392]) ).
thf(394,plain,
! [TA: $tType] :
( ( c_2Ebool_2EIN @ TA )
= ( ^ [A: TA,B: TA > $o] : ( B @ A ) ) ),
inference(lifteq,[status(thm)],[393]) ).
thf(134,axiom,
! [TA: $tType,A: TA,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ B @ ( c_2Epred__set_2EINSERT @ TA @ A @ C ) )
= ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EDELETE @ TA @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__INSERT__DELETE) ).
thf(563,plain,
! [TA: $tType,A: TA,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ B @ ( c_2Epred__set_2EINSERT @ TA @ A @ C ) )
= ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EDELETE @ TA @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(53,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Epred__set_2EINSERT @ TA @ A @ ( c_2Epred__set_2EINSERT @ TA @ A @ B ) )
= ( c_2Epred__set_2EINSERT @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EINSERT__INSERT) ).
thf(299,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Epred__set_2EINSERT @ TA @ A @ ( c_2Epred__set_2EINSERT @ TA @ A @ B ) )
= ( c_2Epred__set_2EINSERT @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(27,axiom,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2EIN @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ENOT__IN__EMPTY) ).
thf(226,plain,
! [TA: $tType,A: TA] :
~ ( c_2Ebool_2EIN @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(41,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EINTER @ TA @ B @ A ) )
= ( c_2Epred__set_2EDIFF @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__INTER2) ).
thf(267,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EINTER @ TA @ B @ A ) )
= ( c_2Epred__set_2EDIFF @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(92,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( c_2Epred__set_2EDELETE @ TA @ A @ B )
= ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EINSERT @ TA @ B @ ( c_2Epred__set_2EEMPTY @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDELETE__DEF) ).
thf(431,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( c_2Epred__set_2EDELETE @ TA @ A @ B )
= ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EINSERT @ TA @ B @ ( c_2Epred__set_2EEMPTY @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(10,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Epred__set_2EEMPTY @ TA )
!= ( c_2Epred__set_2EINSERT @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ENOT__EMPTY__INSERT) ).
thf(167,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Epred__set_2EEMPTY @ TA )
!= ( c_2Epred__set_2EINSERT @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(105,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ C ) )
=> ( c_2Epred__set_2ESUBSET @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__TRANS) ).
thf(473,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ C ) )
=> ( c_2Epred__set_2ESUBSET @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(121,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__applied) ).
thf(531,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(128,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EPSUBSET @ TA @ A @ B )
= ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EPSUBSET__DEF) ).
thf(548,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EPSUBSET @ TA @ A @ B )
= ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(37,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) )
= ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__UNION) ).
thf(255,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) )
= ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(110,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ B @ A )
=> ( ( ( c_2Epred__set_2EUNION @ TA @ B @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) )
= A )
& ( ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__DIFF) ).
thf(487,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ B @ A )
=> ( ( ( c_2Epred__set_2EUNION @ TA @ B @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) )
= A )
& ( ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(67,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) )
= ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EINTER @ TA @ A @ B ) @ ( c_2Epred__set_2EINTER @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__OVER__INTER) ).
thf(342,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) )
= ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EINTER @ TA @ A @ B ) @ ( c_2Epred__set_2EINTER @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(101,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EDISJOINT @ TA @ ( c_2Epred__set_2EEMPTY @ TA ) @ A )
& ( c_2Epred__set_2EDISJOINT @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDISJOINT__EMPTY) ).
thf(458,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EDISJOINT @ TA @ ( c_2Epred__set_2EEMPTY @ TA ) @ A )
& ( c_2Epred__set_2EDISJOINT @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(66,axiom,
! [TA: $tType,A: TA > $o] :
( ( A
= ( c_2Epred__set_2EUNIV @ TA ) )
=> ! [B: TA] : ( c_2Ebool_2EIN @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__EQ__UNIV__IMP) ).
thf(338,plain,
! [TA: $tType,A: TA > $o] :
( ( A
= ( c_2Epred__set_2EUNIV @ TA ) )
=> ! [B: TA] : ( c_2Ebool_2EIN @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(104,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
=> ( ( c_2Epred__set_2EINTER @ TA @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__INTER1) ).
thf(470,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
=> ( ( c_2Epred__set_2EINTER @ TA @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(576,plain,
! [TA: $tType] :
( ( c_2Epred__set_2EUNIV @ TA @ ( sk8 @ TA ) )
| ( c_2Epred__set_2EEMPTY @ TA @ ( sk8 @ TA ) ) ),
inference(bool_ext,[status(thm)],[574]) ).
thf(13,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ B @ C )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
& ~ ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__applied) ).
thf(175,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Epred__set_2EDIFF @ TA @ A @ B @ C )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
& ~ ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(58,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA] :
( ( c_2Ebool_2EIN @ TA @ B @ ( c_2Epred__set_2EDELETE @ TA @ A @ C ) )
= ( ( c_2Ebool_2EIN @ TA @ B @ A )
& ( B != C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__DELETE) ).
thf(314,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA] :
( ( c_2Ebool_2EIN @ TA @ B @ ( c_2Epred__set_2EDELETE @ TA @ A @ C ) )
= ( ( c_2Ebool_2EIN @ TA @ B @ A )
& ( B != C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(97,axiom,
! [TA: $tType] :
( ( c_2Epred__set_2EEMPTY @ TA )
!= ( c_2Epred__set_2EUNIV @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EEMPTY__NOT__UNIV) ).
thf(446,plain,
! [TA: $tType] :
( ( c_2Epred__set_2EEMPTY @ TA )
!= ( c_2Epred__set_2EUNIV @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(29,axiom,
! [TA: $tType,A: TA] :
( ( c_2Epred__set_2EDELETE @ TA @ ( c_2Epred__set_2EEMPTY @ TA ) @ A )
= ( c_2Epred__set_2EEMPTY @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EEMPTY__DELETE) ).
thf(231,plain,
! [TA: $tType,A: TA] :
( ( c_2Epred__set_2EDELETE @ TA @ ( c_2Epred__set_2EEMPTY @ TA ) @ A )
= ( c_2Epred__set_2EEMPTY @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(74,axiom,
! [TA: $tType,A: TA,B: TA,C: TA > $o] :
( ( c_2Epred__set_2EDELETE @ TA @ ( c_2Epred__set_2EDELETE @ TA @ C @ A ) @ B )
= ( c_2Epred__set_2EDELETE @ TA @ ( c_2Epred__set_2EDELETE @ TA @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDELETE__COMM) ).
thf(363,plain,
! [TA: $tType,A: TA,B: TA,C: TA > $o] :
( ( c_2Epred__set_2EDELETE @ TA @ ( c_2Epred__set_2EDELETE @ TA @ C @ A ) @ B )
= ( c_2Epred__set_2EDELETE @ TA @ ( c_2Epred__set_2EDELETE @ TA @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(131,axiom,
! [TA: $tType,A: TA,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EDELETE @ TA @ B @ A ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDELETE__SUBSET) ).
thf(556,plain,
! [TA: $tType,A: TA,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EDELETE @ TA @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(38,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
| ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__UNION) ).
thf(258,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ ( c_2Epred__set_2EUNION @ TA @ A @ B ) )
= ( ( c_2Ebool_2EIN @ TA @ C @ A )
| ( c_2Ebool_2EIN @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(84,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA] :
( ( c_2Epred__set_2EDELETE @ TA @ A @ C @ B )
= ( ( c_2Ebool_2EIN @ TA @ B @ A )
& ( B != C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDELETE__applied) ).
thf(401,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA] :
( ( c_2Epred__set_2EDELETE @ TA @ A @ C @ B )
= ( ( c_2Ebool_2EIN @ TA @ B @ A )
& ( B != C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(3,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Enum_2ESUC @ A )
= ( c_2Enum_2ESUC @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2EINV__SUC__EQ) ).
thf(139,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Enum_2ESUC @ A )
= ( c_2Enum_2ESUC @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [TA: $tType,A: TA,B: TA,C: TA > $o] :
( ( c_2Ebool_2EIN @ TA @ A @ ( c_2Epred__set_2EINSERT @ TA @ B @ C ) )
= ( ( A = B )
| ( c_2Ebool_2EIN @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__INSERT) ).
thf(158,plain,
! [TA: $tType,A: TA,B: TA,C: TA > $o] :
( ( c_2Ebool_2EIN @ TA @ A @ ( c_2Epred__set_2EINSERT @ TA @ B @ C ) )
= ( ( A = B )
| ( c_2Ebool_2EIN @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(70,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( ? [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ ( c_2Epred__set_2EINSERT @ TA @ B @ C ) )
& ( A @ D ) ) )
= ( ( A @ B )
| ? [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ C )
& ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EEXISTS__IN__INSERT) ).
thf(351,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( ? [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ ( c_2Epred__set_2EINSERT @ TA @ B @ C ) )
& ( A @ D ) ) )
= ( ( A @ B )
| ? [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ C )
& ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(78,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Epred__set_2EINSERT @ TA @ A @ B )
!= ( c_2Epred__set_2EEMPTY @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ENOT__INSERT__EMPTY) ).
thf(378,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Epred__set_2EINSERT @ TA @ A @ B )
!= ( c_2Epred__set_2EEMPTY @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(34,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Ebool_2EIN @ TA @ A @ B )
= ( ( c_2Epred__set_2EINSERT @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EABSORPTION) ).
thf(246,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Ebool_2EIN @ TA @ A @ B )
= ( ( c_2Epred__set_2EINSERT @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(23,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EPSUBSET @ TA @ A @ B )
= ( ? [C: TA] :
( ~ ( c_2Ebool_2EIN @ TA @ C @ A )
& ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EINSERT @ TA @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EPSUBSET__INSERT__SUBSET) ).
thf(207,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EPSUBSET @ TA @ A @ B )
= ( ? [C: TA] :
( ~ ( c_2Ebool_2EIN @ TA @ C @ A )
& ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EINSERT @ TA @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(107,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__ANTISYM) ).
thf(478,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(123,axiom,
! [TA: $tType,A: TA,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ B @ ( c_2Epred__set_2EINSERT @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__OF__INSERT) ).
thf(536,plain,
! [TA: $tType,A: TA,B: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ B @ ( c_2Epred__set_2EINSERT @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(6,axiom,
! [TA: $tType] :
( ! [A: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EUNIV @ TA ) @ A )
= ( c_2Epred__set_2EUNIV @ TA ) )
& ! [A: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ ( c_2Epred__set_2EUNIV @ TA ) )
= ( c_2Epred__set_2EUNIV @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__UNIV) ).
thf(151,plain,
! [TA: $tType] :
( ! [A: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EUNIV @ TA ) @ A )
= ( c_2Epred__set_2EUNIV @ TA ) )
& ! [A: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ ( c_2Epred__set_2EUNIV @ TA ) )
= ( c_2Epred__set_2EUNIV @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType] :
( ! [A: TB > $o,B: TB > TA,C: TB] :
( ( c_2Ebool_2EIN @ TB @ C @ A )
=> ( ( c_2Ebool_2ERES__ABSTRACT @ TB @ TA @ A @ B @ C )
= ( B @ C ) ) )
& ! [A: TB > $o,B: TB > TA,C: TB > TA] :
( ! [D: TB] :
( ( c_2Ebool_2EIN @ TB @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( c_2Ebool_2ERES__ABSTRACT @ TB @ TA @ A @ B )
= ( c_2Ebool_2ERES__ABSTRACT @ TB @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ERES__ABSTRACT__DEF) ).
thf(410,plain,
! [TA: $tType,TB: $tType] :
( ! [A: TB > $o,B: TB > TA,C: TB] :
( ( c_2Ebool_2EIN @ TB @ C @ A )
=> ( ( c_2Ebool_2ERES__ABSTRACT @ TB @ TA @ A @ B @ C )
= ( B @ C ) ) )
& ! [A: TB > $o,B: TB > TA,C: TB > TA] :
( ! [D: TB] :
( ( c_2Ebool_2EIN @ TB @ D @ A )
=> ( ( B @ D )
= ( C @ D ) ) )
=> ( ( c_2Ebool_2ERES__ABSTRACT @ TB @ TA @ A @ B )
= ( c_2Ebool_2ERES__ABSTRACT @ TB @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(5,axiom,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Enum_2ESUC @ A )
= ( c_2Enum_2ESUC @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enum_2EINV__SUC) ).
thf(146,plain,
! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( ( c_2Enum_2ESUC @ A )
= ( c_2Enum_2ESUC @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(43,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Ebool_2EIN @ TA @ A @ B )
=> ( ( c_2Epred__set_2EINSERT @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EABSORPTION__RWT) ).
thf(273,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Ebool_2EIN @ TA @ A @ B )
=> ( ( c_2Epred__set_2EINSERT @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(76,axiom,
! [TA: $tType,A: TA,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ B @ ( c_2Epred__set_2EDELETE @ TA @ C @ A ) )
= ( ~ ( c_2Ebool_2EIN @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__DELETE) ).
thf(373,plain,
! [TA: $tType,A: TA,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ B @ ( c_2Epred__set_2EDELETE @ TA @ C @ A ) )
= ( ~ ( c_2Ebool_2EIN @ TA @ A @ B )
& ( c_2Epred__set_2ESUBSET @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(55,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ ( c_2Epred__set_2EINSERT @ TA @ B @ C ) )
=> ( A @ D ) ) )
= ( ( A @ B )
& ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ C )
=> ( A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EFORALL__IN__INSERT) ).
thf(305,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > $o] :
( ( ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ ( c_2Epred__set_2EINSERT @ TA @ B @ C ) )
=> ( A @ D ) ) )
= ( ( A @ B )
& ! [D: TA] :
( ( c_2Ebool_2EIN @ TA @ D @ C )
=> ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(24,axiom,
! [TA: $tType] :
( ! [A: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EEMPTY @ TA ) @ A )
= ( c_2Epred__set_2EEMPTY @ TA ) )
& ! [A: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) )
= ( c_2Epred__set_2EEMPTY @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__EMPTY) ).
thf(210,plain,
! [TA: $tType] :
( ! [A: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EEMPTY @ TA ) @ A )
= ( c_2Epred__set_2EEMPTY @ TA ) )
& ! [A: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ A @ ( c_2Epred__set_2EEMPTY @ TA ) )
= ( c_2Epred__set_2EEMPTY @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(62,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ B )
= ( c_2Epred__set_2EUNION @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__COMM) ).
thf(326,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ A @ B )
= ( c_2Epred__set_2EUNION @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(51,axiom,
! [TA: $tType,A: TA > $o] :
~ ( c_2Epred__set_2EPSUBSET @ TA @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EPSUBSET__IRREFL) ).
thf(294,plain,
! [TA: $tType,A: TA > $o] :
~ ( c_2Epred__set_2EPSUBSET @ TA @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(113,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
= ( ( c_2Epred__set_2EINTER @ TA @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__INTER__ABSORPTION) ).
thf(506,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
= ( ( c_2Epred__set_2EINTER @ TA @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(19,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EDELETE @ TA @ A @ C ) @ B )
= ( c_2Epred__set_2EDELETE @ TA @ ( c_2Epred__set_2EINTER @ TA @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDELETE__INTER) ).
thf(195,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA] :
( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EDELETE @ TA @ A @ C ) @ B )
= ( c_2Epred__set_2EDELETE @ TA @ ( c_2Epred__set_2EINTER @ TA @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(94,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ~ ( c_2Ebool_2EIN @ TA @ A @ B )
=> ! [C: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ B @ ( c_2Epred__set_2EINSERT @ TA @ A @ C ) )
= ( c_2Epred__set_2ESUBSET @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__INSERT) ).
thf(437,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ~ ( c_2Ebool_2EIN @ TA @ A @ B )
=> ! [C: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ B @ ( c_2Epred__set_2EINSERT @ TA @ A @ C ) )
= ( c_2Epred__set_2ESUBSET @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(47,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Ebool_2EIN @ TA @ A @ B )
=> ( ( c_2Epred__set_2EINSERT @ TA @ A @ ( c_2Epred__set_2EDELETE @ TA @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EINSERT__DELETE) ).
thf(283,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Ebool_2EIN @ TA @ A @ B )
=> ( ( c_2Epred__set_2EINSERT @ TA @ A @ ( c_2Epred__set_2EDELETE @ TA @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(82,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Ebool_2EIN @ TA @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__APP) ).
thf(395,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( c_2Ebool_2EIN @ TA @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(64,axiom,
! [TA: $tType,A: TA,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EINSERT @ TA @ A @ B ) @ C )
= ( c_2Epred__set_2EINSERT @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EINSERT__UNION__EQ) ).
thf(332,plain,
! [TA: $tType,A: TA,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EUNION @ TA @ ( c_2Epred__set_2EINSERT @ TA @ A @ B ) @ C )
= ( c_2Epred__set_2EINSERT @ TA @ A @ ( c_2Epred__set_2EUNION @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(575,plain,
! [TA: $tType] :
( ~ ( c_2Epred__set_2EUNIV @ TA @ ( sk8 @ TA ) )
| ~ ( c_2Epred__set_2EEMPTY @ TA @ ( sk8 @ TA ) ) ),
inference(bool_ext,[status(thm)],[574]) ).
thf(120,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
= ( ( c_2Epred__set_2EUNION @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__UNION__ABSORPTION) ).
thf(528,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
= ( ( c_2Epred__set_2EUNION @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(14,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ C )
= ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EINTER @ TA @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EDIFF__INTER) ).
thf(178,plain,
! [TA: $tType,A: TA > $o,B: TA > $o,C: TA > $o] :
( ( c_2Epred__set_2EINTER @ TA @ ( c_2Epred__set_2EDIFF @ TA @ A @ B ) @ C )
= ( c_2Epred__set_2EDIFF @ TA @ ( c_2Epred__set_2EINTER @ TA @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(71,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( c_2Ebool_2EIN @ TA @ B @ A )
= ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESPECIFICATION) ).
thf(354,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( c_2Ebool_2EIN @ TA @ B @ A )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(126,axiom,
! [TA: $tType,A: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EUNIV @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__UNIV) ).
thf(543,plain,
! [TA: $tType,A: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ A @ ( c_2Epred__set_2EUNIV @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(597,plain,
$false,
inference(e,[status(thm)],[138,249,518,468,234,481,170,523,308,449,440,217,276,385,142,538,404,320,184,357,228,289,261,475,164,443,376,348,574,243,428,292,452,512,270,201,381,366,534,302,561,392,407,137,252,329,493,551,566,484,317,420,554,193,515,173,569,237,360,311,541,398,558,425,264,161,296,423,286,545,281,204,498,335,181,187,509,434,345,323,520,240,198,462,278,455,223,394,563,299,226,267,431,167,473,531,548,255,487,342,458,338,470,576,175,314,446,231,363,556,258,401,139,158,351,378,246,207,478,536,151,410,146,273,373,305,210,326,239,294,506,195,437,283,395,332,575,528,178,354,543]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP004^7 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.10 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.24/0.29 % Computer : n017.cluster.edu
% 0.24/0.29 % Model : x86_64 x86_64
% 0.24/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.29 % Memory : 8046.5625MB
% 0.24/0.29 % OS : Linux 6.8.0-71-generic
% 0.24/0.29 % CPULimit : 300
% 0.24/0.29 % WCLimit : 300
% 0.24/0.29 % DateTime : Tue Sep 29 19:16:22 UTC 2026
% 0.24/0.29 % CPUTime :
% 0.24/0.29 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.12/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 5.49/2.10 % [INFO] Parsing done (1095ms).
% 5.49/2.12 % [INFO] Running in sequential loop mode.
% 6.78/2.60 % [INFO] eprover registered as external prover.
% 6.78/2.61 % [INFO] Scanning for conjecture ...
% 7.72/2.97 % [INFO] Found a conjecture (or negated_conjecture) and 1996 axioms. Running axiom selection ...
% 8.11/3.12 % [INFO] Axiom selection finished. Selected 134 axioms (removed 1862 axioms).
% 9.19/3.32 % [INFO] Problem is higher-order (TPTP THF).
% 9.19/3.34 % [INFO] Type checking passed.
% 9.19/3.34 % [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 ...
% 23.65/6.78 % External prover 'e' found a proof!
% 23.65/6.78 % [INFO] Killing All external provers ...
% 23.65/6.78 % Time passed: 6302ms (effective reasoning time: 4650ms)
% 23.65/6.78 % 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)>
% 23.65/6.78 % Axioms used in derivation (134): thm_2Epred__set_2EDISJOINT__INSERT, thm_2Epred__set_2EEMPTY__UNION, thm_2Epred__set_2EINTER__ASSOC, thm_2Epred__set_2EIN__ABS, thm_2Epred__set_2EUNION__DIFF, thm_2Epred__set_2ENOT__PSUBSET__EMPTY, thm_2Epred__set_2EIN__UNION, thm_2Eprim__rec_2EINV__SUC__EQ, thm_2Epred__set_2EEMPTY__NOT__UNIV, thm_2Epred__set_2EDIFF__EMPTY, thm_2Epred__set_2EDELETE__INTER, thm_2Epred__set_2EINSERT__UNIV, thm_2Epred__set_2EREST__DEF, thm_2Epred__set_2ESUBSET__DELETE, thm_2Epred__set_2ESUBSET__THM, thm_2Epred__set_2EUNION__applied, thm_2Epred__set_2EABSORPTION__RWT, thm_2Epred__set_2EINTER__applied, thm_2Epred__set_2ECHOICE__DEF, thm_2Epred__set_2EIN__DISJOINT, thm_2Epred__set_2EDIFF__INTER, thm_2Ebool_2EIN__DEF, thm_2Epred__set_2EFORALL__IN__UNION, thm_2Epred__set_2EEMPTY__DELETE, thm_2Epred__set_2ESUBSET__OF__INSERT, thm_2Epred__set_2EDISJOINT__DELETE__SYM, thm_2Epred__set_2EDISJOINT__INSERT_27, thm_2Epred__set_2ESUBSET__ANTISYM, thm_2Epred__set_2EDELETE__applied, thm_2Epred__set_2EUNIV__applied, thm_2Epred__set_2EEXISTS__IN__INSERT, thm_2Epred__set_2EDELETE__DEF, thm_2Epred__set_2EDIFF__SUBSET, thm_2Epred__set_2ENOT__EMPTY__INSERT, thm_2Epred__set_2EDIFF__applied, thm_2Epred__set_2EUNION__OVER__INTER, thm_2Epred__set_2ENOT__UNIV__PSUBSET, thm_2Epred__set_2EIN__DIFF, thm_2Epred__set_2EDELETE__NON__ELEMENT, thm_2Epred__set_2EINSERT__INSERT, thm_2Epred__set_2EIN__EQ__UNIV__IMP, thm_2Epred__set_2EIN__DELETE__EQ, thm_2Ebool_2ERES__ABSTRACT__DEF, thm_2Epred__set_2ESPECIFICATION, thm_2Epred__set_2EINSERT__SUBSET, thm_2Epred__set_2EEMPTY__DIFF, thm_2Epred__set_2EDIFF__DIFF__SUBSET, thm_2Epred__set_2EDIFF__SAME__UNION, thm_2Epred__set_2EMEMBER__NOT__EMPTY, thm_2Epred__set_2EUNIV__SUBSET, thm_2Eprim__rec_2ESUC__ID, thm_2Epred__set_2ESUBSET__TRANS, thm_2Epred__set_2EIN__INSERT, thm_2Epred__set_2EDISJOINT__SYM, thm_2Epred__set_2EREST__applied, thm_2Epred__set_2EDISJOINT__EMPTY, thm_2Epred__set_2EDIFF__COMM, thm_2Epred__set_2EINTER__IDEMPOT, thm_2Epred__set_2ESUBSET__INTER2, thm_2Epred__set_2EIN__REST, thm_2Epred__set_2EINSERT__COMM, thm_2Epred__set_2ESUBSET__UNION, thm_2Epred__set_2EPSUBSET__IRREFL, thm_2Epred__set_2EINSERT__applied, thm_2Epred__set_2EDISJOINT__SUBSET, thm_2Epred__set_2EDIFF__INTER2, thm_2Epred__set_2EINSERT__DELETE, thm_2Epred__set_2EUNION__COMM, thm_2Epred__set_2EUNION__ASSOC, thm_2Epred__set_2ESUBSET__INSERT__DELETE, thm_2Epred__set_2EFORALL__IN__INSERT, thm_2Epred__set_2EIN__APP, thm_2Epred__set_2ESET__CASES, thm_2Epred__set_2EEQ__SUBSET__SUBSET, thm_2Epred__set_2EUNION__SUBSET, thm_2Epred__set_2EDELETE__NON__ELEMENT__RWT, thm_2Epred__set_2EINSERT__UNION__EQ, thm_2Epred__set_2ESUBSET__REFL, thm_2Epred__set_2EPSUBSET__TRANS, thm_2Epred__set_2EINTER__EMPTY, thm_2Enum_2EINV__SUC, thm_2Epred__set_2EPSUBSET__MEMBER, thm_2Epred__set_2EDIFF__EQ__EMPTY, thm_2Epred__set_2EDIFF__UNIV, thm_2Epred__set_2EEQ__UNIV, thm_2Epred__set_2EDISJOINT__DEF, thm_2Epred__set_2EPSUBSET__UNIV, thm_2Epred__set_2EIN__UNIV, thm_2Epred__set_2EINTER__OVER__UNION, thm_2Epred__set_2EDELETE__COMM, thm_2Epred__set_2EDELETE__DELETE, thm_2Epred__set_2EPSUBSET__DEF, thm_2Epred__set_2ESUBSET__INTER1, thm_2Epred__set_2ENOT__IN__EMPTY, thm_2Epred__set_2EIN__DELETE, thm_2Epred__set_2ESUBSET__UNION__ABSORPTION, thm_2Epred__set_2ESUBSET__INSERT, thm_2Epred__set_2ECHOICE__INSERT__REST, thm_2Epred__set_2EEXTENSION, thm_2Epred__set_2EUNION__EMPTY, thm_2Epred__set_2EINTER__UNIV, thm_2Epred__set_2ENOT__INSERT__EMPTY, thm_2Epred__set_2EDISJOINT__DIFF, thm_2Epred__set_2EDISJOINT__ALT, thm_2Epred__set_2EDELETE__SUBSET, thm_2Epred__set_2ECOMPONENT, thm_2Epred__set_2ESUBSET__UNIV, thm_2Epred__set_2EDIFF__DIFF, thm_2Epred__set_2EDIFF__UNION, thm_2Epred__set_2EDIFF__INSERT, thm_2Epred__set_2EPSUBSET__INSERT__SUBSET, thm_2Epred__set_2EINTER__SUBSET, thm_2Epred__set_2EELT__IN__DELETE, thm_2Epred__set_2EABSORPTION, thm_2Epred__set_2EDISJOINT__DIFFS, thm_2Epred__set_2ESUBSET__applied, thm_2Epred__set_2ESUBSET__DEF, thm_2Epred__set_2ESUBSET__EMPTY, thm_2Epred__set_2EDISJOINT__UNION__BOTH, thm_2Epred__set_2EUNION__UNIV, thm_2Epred__set_2EIN__INTER, thm_2Epred__set_2ENOT__EQUAL__SETS, thm_2Epred__set_2EDISJOINT__UNION, thm_2Epred__set_2ESUBSET__SUBSET__EQ, thm_2Epred__set_2EDISJOINT__EMPTY__REFL__RWT, thm_2Epred__set_2EUNION__IDEMPOT, thm_2Epred__set_2EDECOMPOSITION, thm_2Epred__set_2EINTER__COMM, thm_2Epred__set_2EEMPTY__SUBSET, thm_2Epred__set_2EDISJOINT__EMPTY__REFL, thm_2Epred__set_2ESUBSET__INTER__ABSORPTION, thm_2Epred__set_2ESUBSET__INTER, thm_2Epred__set_2EUNIV__NOT__EMPTY, thm_2Epred__set_2ECHOICE__NOT__IN__REST
% 23.65/6.78 % No. of inferences in proof: 280
% 23.65/6.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6302 ms resp. 4650 ms w/o parsing
% 25.33/7.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.33/7.11 % [INFO] Killing All external provers ...
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