%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM183^1 : TPTP v9.3.1. Released v7.0.0.
% 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 : n003.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 07:46:19 AM UTC 2026
% Result : Theorem 12.46s 4.21s
% Output : Refutation 12.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 116
% Syntax : Number of formulae : 234 ( 106 unt; 0 typ; 0 def)
% Number of atoms : 904 ( 166 equ; 2 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 2837 ( 60 ~; 6 |; 20 &;2571 @)
% ( 0 <=>; 180 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 7 con; 0-3 aty)
% Number of variables : 750 ( 26 ^; 716 !; 8 ?; 750 :)
% Comments :
%------------------------------------------------------------------------------
thf(dtree_type,type,
dtree: $tType ).
thf(t_type,type,
t: $tType ).
thf(n_type,type,
n: $tType ).
thf(root_decl,type,
root: dtree > n ).
thf(gram_L861583724lle_Fr_decl,type,
gram_L861583724lle_Fr: ( set @ n ) > dtree > ( set @ t ) ).
thf(gram_L1333338417e_inFr_decl,type,
gram_L1333338417e_inFr: ( set @ n ) > dtree > t > $o ).
thf(gram_L805317441_inFr2_decl,type,
gram_L805317441_inFr2: ( set @ n ) > dtree > t > $o ).
thf(gram_L830233218_inItr_decl,type,
gram_L830233218_inItr: ( set @ n ) > dtree > n > $o ).
thf(gram_L716654942_subtr_decl,type,
gram_L716654942_subtr: ( set @ n ) > dtree > dtree > $o ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(uminus_uminus_decl,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(sup_sup_decl,type,
sup_sup:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(pairwise_decl,type,
pairwise:
!>[TA: $tType] : ( ( TA > TA > $o ) > ( set @ TA ) > $o ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(ns_decl,type,
ns: set @ n ).
thf(tr1_decl,type,
tr1: dtree ).
thf(tr2_decl,type,
tr2: dtree ).
thf(tr3_decl,type,
tr3: dtree ).
thf(90,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_Un__left__absorb) ).
thf(365,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(43,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_Diff__subset) ).
thf(234,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(85,axiom,
! [A: dtree,B: set @ n] :
( ( member @ n @ ( root @ A ) @ B )
=> ( gram_L830233218_inItr @ B @ A @ ( root @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_inItr_OBase) ).
thf(352,plain,
! [A: dtree,B: set @ n] :
( ( member @ n @ ( root @ A ) @ B )
=> ( gram_L830233218_inItr @ B @ A @ ( root @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(105,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_insert__subset) ).
thf(408,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( ( member @ TA @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(70,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_subset__Un__eq) ).
thf(308,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(48,axiom,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Un__commute) ).
thf(247,plain,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(36,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_UnE) ).
thf(217,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(58,axiom,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_ex__in__conv) ).
thf(276,plain,
! [TA: $tType,A: set @ TA] :
( ( ? [B: TA] : ( member @ TA @ B @ A ) )
= ( A
!= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(97,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ ( sup_sup @ ( set @ TA ) @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_Un__mono) ).
thf(384,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ ( sup_sup @ ( set @ TA ) @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(81,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ D ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_Diff__mono) ).
thf(340,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ D ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(14,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_empty__Collect__eq) ).
thf(153,plain,
! [TA: $tType,A: TA > $o] :
( ( ( bot_bot @ ( set @ TA ) )
= ( collect @ TA @ A ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(103,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_subsetCE) ).
thf(404,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(25,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(185,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(108,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Un__absorb1) ).
thf(417,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(63,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( insert @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_Un__insert__left) ).
thf(288,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( insert @ TA @ A @ B ) @ C )
= ( insert @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(74,axiom,
! [A: set @ n,B: dtree,C: t,D: set @ n] :
( ( gram_L805317441_inFr2 @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ n ) @ A @ D )
=> ( gram_L805317441_inFr2 @ D @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_inFr2__mono) ).
thf(320,plain,
! [A: set @ n,B: dtree,C: t,D: set @ n] :
( ( gram_L805317441_inFr2 @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ n ) @ A @ D )
=> ( gram_L805317441_inFr2 @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(93,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_Collect__mono) ).
thf(372,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(5,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_Diff__cancel) ).
thf(125,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(41,axiom,
! [A: set @ n,B: dtree,C: t,D: set @ n] :
( ( gram_L1333338417e_inFr @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ n ) @ A @ D )
=> ( gram_L1333338417e_inFr @ D @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_inFr__mono) ).
thf(228,plain,
! [A: set @ n,B: dtree,C: t,D: set @ n] :
( ( gram_L1333338417e_inFr @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ n ) @ A @ D )
=> ( gram_L1333338417e_inFr @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(53,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_subsetI) ).
thf(261,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(23,axiom,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_Collect__empty__eq) ).
thf(179,plain,
! [TA: $tType,A: TA > $o] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( set @ TA ) ) )
= ( ! [B: TA] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(94,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_set__mp) ).
thf(376,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(50,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_emptyE) ).
thf(253,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(38,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_Un__empty__right) ).
thf(221,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(106,axiom,
! [A: dtree,B: set @ n] :
( ~ ( member @ n @ ( root @ A ) @ B )
=> ( ( gram_L861583724lle_Fr @ B @ A )
= ( bot_bot @ ( set @ t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_not__root__Fr) ).
thf(411,plain,
! [A: dtree,B: set @ n] :
( ~ ( member @ n @ ( root @ A ) @ B )
=> ( ( gram_L861583724lle_Fr @ B @ A )
= ( bot_bot @ ( set @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(54,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_Un__subset__iff) ).
thf(265,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(56,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Un__absorb) ).
thf(270,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(96,axiom,
! [TA: $tType] :
( ( pairwise @ TA )
= ( ^ [A: TA > TA > $o,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ B )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ( C != D )
=> ( A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_pairwise__def) ).
thf(381,plain,
! [TA: $tType] :
( ( pairwise @ TA )
= ( ^ [A: TA > TA > $o,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ B )
=> ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( ( C != D )
=> ( A @ C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(68,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_equals0I) ).
thf(302,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(66,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
=> ~ ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_ComplD) ).
thf(297,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
=> ~ ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(111,axiom,
! [A: set @ n,B: dtree,C: dtree] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( member @ n @ ( root @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_subtr__rootR__in) ).
thf(424,plain,
! [A: set @ n,B: dtree,C: dtree] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( member @ n @ ( root @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(8,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_Compl__Diff__eq) ).
thf(137,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(18,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_insert__absorb2) ).
thf(165,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( insert @ TA @ A @ ( insert @ TA @ A @ B ) )
= ( insert @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(29,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_Un__Diff) ).
thf(197,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ C ) @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(89,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_equals0D) ).
thf(361,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( A
= ( bot_bot @ ( set @ TA ) ) )
=> ~ ( member @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(77,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_Un__left__commute) ).
thf(329,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(39,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_ComplI) ).
thf(224,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(73,axiom,
! [A: set @ n,B: dtree,C: t] :
( ( gram_L805317441_inFr2 @ A @ B @ C )
=> ( member @ n @ ( root @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_inFr2__root__in) ).
thf(317,plain,
! [A: set @ n,B: dtree,C: t] :
( ( gram_L805317441_inFr2 @ A @ B @ C )
=> ( member @ n @ ( root @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(15,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_insert__iff) ).
thf(156,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(26,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( uminus_uminus @ ( set @ TA ) @ A )
= ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_Compl__eq__Compl__iff) ).
thf(188,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( uminus_uminus @ ( set @ TA ) @ A )
= ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(99,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_empty__subsetI) ).
thf(388,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(87,axiom,
! [A: dtree,B: set @ n,C: t] :
( ~ ( member @ n @ ( root @ A ) @ B )
=> ~ ( gram_L1333338417e_inFr @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_not__root__inFr) ).
thf(356,plain,
! [A: dtree,B: set @ n,C: t] :
( ~ ( member @ n @ ( root @ A ) @ B )
=> ~ ( gram_L1333338417e_inFr @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(109,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_Un__least) ).
thf(420,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(101,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_equalityE) ).
thf(393,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(21,axiom,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_subset__Compl__self__eq) ).
thf(173,plain,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(6,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_Diff__idemp) ).
thf(128,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( minus_minus @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(47,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_Un__empty) ).
thf(244,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( sup_sup @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ( A
= ( bot_bot @ ( set @ TA ) ) )
& ( B
= ( bot_bot @ ( set @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(71,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_ball__Un) ).
thf(311,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(114,axiom,
gram_L716654942_subtr @ ns @ tr1 @ tr2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_assms_I1_J) ).
thf(430,plain,
gram_L716654942_subtr @ ns @ tr1 @ tr2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(59,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_in__mono) ).
thf(279,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(12,axiom,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_singletonI) ).
thf(149,plain,
! [TA: $tType,A: TA] : ( member @ TA @ A @ ( insert @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(22,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_Diff__empty) ).
thf(176,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(27,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_Un__iff) ).
thf(191,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(62,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_empty__iff) ).
thf(286,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(64,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_UnCI) ).
thf(291,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(1,conjecture,
gram_L716654942_subtr @ ns @ tr1 @ tr3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( gram_L716654942_subtr @ ns @ tr1 @ tr3 ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(118,plain,
~ ( gram_L716654942_subtr @ ns @ tr1 @ tr3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(60,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_DiffD1) ).
thf(281,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ( member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(31,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Collect__mono__iff) ).
thf(204,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(79,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_subsetD) ).
thf(335,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(44,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Un__assoc) ).
thf(236,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(84,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_subset__refl) ).
thf(350,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(16,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( minus_minus @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_insert__Diff1) ).
thf(159,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ ( insert @ TA @ A @ C ) @ B )
= ( minus_minus @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(104,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_set__rev__mp) ).
thf(406,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(37,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Un__upper1) ).
thf(219,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(116,axiom,
! [A: set @ n,B: dtree,C: dtree,D: set @ n] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ n ) @ A @ D )
=> ( gram_L716654942_subtr @ D @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_subtr__mono) ).
thf(434,plain,
! [A: set @ n,B: dtree,C: dtree,D: set @ n] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ n ) @ A @ D )
=> ( gram_L716654942_subtr @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(75,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_Un__Diff__cancel2) ).
thf(323,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ B )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(9,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(140,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(34,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_DiffD2) ).
thf(213,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( member @ TA @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(67,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Un__absorb2) ).
thf(299,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(40,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_UnI2) ).
thf(226,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(115,axiom,
! [A: set @ n,B: dtree,C: dtree] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( member @ n @ ( root @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_subtr__rootL__in) ).
thf(431,plain,
! [A: set @ n,B: dtree,C: dtree] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( member @ n @ ( root @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(112,axiom,
gram_L716654942_subtr @ ( sup_sup @ ( set @ n ) @ ns @ ns ) @ tr1 @ tr3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062subtr_A_Ins_A_092_060union_062_Ans_J_Atr1_Atr3_092_060close_062) ).
thf(426,plain,
gram_L716654942_subtr @ ( sup_sup @ ( set @ n ) @ ns @ ns ) @ tr1 @ tr3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(17,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_Diff__insert0) ).
thf(162,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ~ ( member @ TA @ A @ B )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( insert @ TA @ A @ C ) )
= ( minus_minus @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(51,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( minus_minus @ ( set @ TA ) @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_double__diff) ).
thf(255,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ( minus_minus @ ( set @ TA ) @ B @ ( minus_minus @ ( set @ TA ) @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(82,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_DiffE) ).
thf(342,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
=> ~ ( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(28,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_bex__Un) ).
thf(194,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(65,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_DiffI) ).
thf(295,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ~ ( member @ TA @ A @ C )
=> ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(107,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_Compl__subset__Compl__iff) ).
thf(414,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(24,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A = C )
& ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_singleton__insert__inj__eq_H) ).
thf(182,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ( insert @ TA @ A @ B )
= ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) )
= ( ( A = C )
& ( ord_less_eq @ ( set @ TA ) @ B @ ( insert @ TA @ C @ ( bot_bot @ ( set @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(92,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_rev__subsetD) ).
thf(370,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(88,axiom,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_subset__emptyI) ).
thf(359,plain,
! [TA: $tType,A: set @ TA] :
( ! [B: TA] :
~ ( member @ TA @ B @ A )
=> ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(98,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_Un__upper2) ).
thf(386,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(72,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ A ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_Un__Diff__cancel) ).
thf(314,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ A ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(10,axiom,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_empty__Diff) ).
thf(143,plain,
! [TA: $tType,A: set @ TA] :
( ( minus_minus @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(91,axiom,
! [TA: $tType,A: TA > TA > $o,B: set @ TA,C: set @ TA] :
( ( pairwise @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( pairwise @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_pairwise__subset) ).
thf(368,plain,
! [TA: $tType,A: TA > TA > $o,B: set @ TA,C: set @ TA] :
( ( pairwise @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( pairwise @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(49,axiom,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_all__not__in__conv) ).
thf(250,plain,
! [TA: $tType,A: set @ TA] :
( ( ! [B: TA] :
~ ( member @ TA @ B @ A ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(42,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_subset__eq) ).
thf(231,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(52,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_Diff__partition) ).
thf(258,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ A @ ( minus_minus @ ( set @ TA ) @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(100,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_Un__empty__left) ).
thf(390,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( bot_bot @ ( set @ TA ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(102,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ C )
= ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_Diff__subset__conv) ).
thf(401,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( minus_minus @ ( set @ TA ) @ A @ B ) @ C )
= ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(20,axiom,
gram_L1333338417e_inFr = gram_L805317441_inFr2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_inFr__inFr2) ).
thf(171,plain,
gram_L1333338417e_inFr = gram_L805317441_inFr2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(32,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_subset__antisym) ).
thf(207,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(83,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_equalityD1) ).
thf(346,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(3,axiom,
! [TA: $tType,A: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_double__complement) ).
thf(119,plain,
! [TA: $tType,A: set @ TA] :
( ( uminus_uminus @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(95,axiom,
! [A: set @ n,B: dtree,C: n] :
( ( gram_L830233218_inItr @ A @ B @ C )
=> ( member @ n @ ( root @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_inItr__root__in) ).
thf(378,plain,
! [A: set @ n,B: dtree,C: n] :
( ( gram_L830233218_inItr @ A @ B @ C )
=> ( member @ n @ ( root @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(13,axiom,
! [TA: $tType,A: TA > TA > $o] : ( pairwise @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_pairwise__empty) ).
thf(151,plain,
! [TA: $tType,A: TA > TA > $o] : ( pairwise @ TA @ A @ ( bot_bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(19,axiom,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ~ ( member @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_subset__Compl__singleton) ).
thf(168,plain,
! [TA: $tType,A: set @ TA,B: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( uminus_uminus @ ( set @ TA ) @ ( insert @ TA @ B @ ( bot_bot @ ( set @ TA ) ) ) ) )
= ( ~ ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(11,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(146,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(110,axiom,
! [A: dtree,B: set @ n] :
( ( member @ n @ ( root @ A ) @ B )
=> ( gram_L716654942_subtr @ B @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Refl) ).
thf(422,plain,
! [A: dtree,B: set @ n] :
( ( member @ n @ ( root @ A ) @ B )
=> ( gram_L716654942_subtr @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(57,axiom,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_subset__empty) ).
thf(273,plain,
! [TA: $tType,A: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ ( bot_bot @ ( set @ TA ) ) )
= ( A
= ( bot_bot @ ( set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(69,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_Diff__iff) ).
thf(305,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( minus_minus @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
& ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(33,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_set__eq__subset) ).
thf(210,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(76,axiom,
! [A: set @ n,B: dtree,C: t] :
( ( gram_L1333338417e_inFr @ A @ B @ C )
=> ( member @ n @ ( root @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_inFr__root__in) ).
thf(326,plain,
! [A: set @ n,B: dtree,C: t] :
( ( gram_L1333338417e_inFr @ A @ B @ C )
=> ( member @ n @ ( root @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(55,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_subset__trans) ).
thf(268,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(117,axiom,
gram_L716654942_subtr @ ns @ tr2 @ tr3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I2_J) ).
thf(437,plain,
gram_L716654942_subtr @ ns @ tr2 @ tr3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(61,axiom,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ~ ( member @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_Compl__iff) ).
thf(283,plain,
! [TA: $tType,A: TA,B: set @ TA] :
( ( member @ TA @ A @ ( uminus_uminus @ ( set @ TA ) @ B ) )
= ( ~ ( member @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(45,axiom,
! [A: set @ n,B: dtree,C: n,D: set @ n] :
( ( gram_L830233218_inItr @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ n ) @ A @ D )
=> ( gram_L830233218_inItr @ D @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_inItr__mono) ).
thf(239,plain,
! [A: set @ n,B: dtree,C: n,D: set @ n] :
( ( gram_L830233218_inItr @ A @ B @ C )
=> ( ( ord_less_eq @ ( set @ n ) @ A @ D )
=> ( gram_L830233218_inItr @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(46,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ B ) @ ( uminus_uminus @ ( set @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_Compl__anti__mono) ).
thf(242,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( uminus_uminus @ ( set @ TA ) @ B ) @ ( uminus_uminus @ ( set @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(78,axiom,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_Un__insert__right) ).
thf(332,plain,
! [TA: $tType,A: set @ TA,B: TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( insert @ TA @ B @ C ) )
= ( insert @ TA @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(113,axiom,
! [A: set @ n,B: dtree,C: dtree,D: set @ n,E: dtree] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( ( gram_L716654942_subtr @ D @ C @ E )
=> ( gram_L716654942_subtr @ ( sup_sup @ ( set @ n ) @ A @ D ) @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_subtr__trans__Un) ).
thf(427,plain,
! [A: set @ n,B: dtree,C: dtree,D: set @ n,E: dtree] :
( ( gram_L716654942_subtr @ A @ B @ C )
=> ( ( gram_L716654942_subtr @ D @ C @ E )
=> ( gram_L716654942_subtr @ ( sup_sup @ ( set @ n ) @ A @ D ) @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(7,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_insertCI) ).
thf(131,plain,
! [TA: $tType,A: TA,B: set @ TA,C: TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( A = C ) )
=> ( member @ TA @ A @ ( insert @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(30,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_equalityD2) ).
thf(200,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(86,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_UnI1) ).
thf(354,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(35,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( member @ TA @ C @ B )
=> ~ ( member @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_contra__subsetD) ).
thf(215,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( member @ TA @ C @ B )
=> ~ ( member @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(80,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_subset__iff) ).
thf(337,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(4,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( minus_minus @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_Diff__eq__empty__iff) ).
thf(122,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ( minus_minus @ ( set @ TA ) @ A @ B )
= ( bot_bot @ ( set @ TA ) ) )
= ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(448,plain,
$false,
inference(e,[status(thm)],[365,234,352,408,308,247,217,276,384,340,153,404,185,417,288,320,372,125,228,261,179,376,253,221,411,265,270,381,302,297,424,137,165,197,361,329,224,317,156,188,388,356,420,393,173,128,244,311,430,279,149,176,191,286,291,118,281,204,335,236,350,159,406,219,434,323,140,213,299,226,431,426,162,255,342,194,295,414,182,370,359,386,314,143,368,250,231,258,390,401,171,207,346,119,378,151,168,146,422,273,305,210,326,268,437,283,239,242,332,427,131,200,354,215,337,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM183^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % 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
% 0.08/0.20 % Computer : n003.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Sep 29 17:51:43 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.85/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.01/1.19 % [INFO] Parsing done (404ms).
% 2.34/1.20 % [INFO] Running in sequential loop mode.
% 3.01/1.58 % [INFO] eprover registered as external prover.
% 3.01/1.59 % [INFO] Scanning for conjecture ...
% 3.38/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 296 axioms. Running axiom selection ...
% 3.57/1.87 % [INFO] Axiom selection finished. Selected 115 axioms (removed 181 axioms).
% 4.20/2.06 % [INFO] Problem is higher-order (TPTP THF).
% 4.20/2.08 % [INFO] Type checking passed.
% 4.20/2.08 % [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 ...
% 12.46/4.21 % External prover 'e' found a proof!
% 12.46/4.21 % [INFO] Killing All external provers ...
% 12.46/4.21 % Time passed: 3868ms (effective reasoning time: 3001ms)
% 12.46/4.21 % 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)>
% 12.46/4.21 % Axioms used in derivation (115): fact_215_Un__empty__right, fact_0__092_060open_062subtr_A_Ins_A_092_060union_062_Ans_J_Atr1_Atr3_092_060close_062, fact_37_set__mp, fact_144_Un__Diff__cancel2, fact_95_Un__upper1, fact_25_Collect__mono, fact_255_singleton__insert__inj__eq_H, fact_221_equals0D, fact_31_equalityD1, fact_35_subsetD, fact_173_Compl__eq__Compl__iff, fact_8_Un__subset__iff, fact_146_Diff__mono, fact_216_Un__empty__left, fact_175_ComplI, fact_55_Un__commute, fact_57_Un__assoc, fact_246_insert__absorb2, fact_24_subset__trans, fact_152_DiffD1, fact_33_equalityE, fact_131_inFr2__root__in, fact_91_subset__Un__eq, fact_34_subsetCE, fact_191_Un__empty, fact_150_pairwise__def, fact_97_Un__mono, fact_166_empty__Collect__eq, fact_20_subsetI, fact_249_singletonI, fact_141_Diff__idemp, fact_92_Un__absorb2, fact_153_DiffE, fact_46_Collect__mem__eq, fact_23_set__eq__subset, fact_193_empty__Diff, fact_247_insert__iff, fact_219_ex__in__conv, fact_123_inItr__mono, fact_137_pairwise__subset, fact_167_Collect__empty__eq, fact_62_UnE, fact_60_UnI2, fact_151_DiffD2, fact_54_Un__left__absorb, fact_53_Un__left__commute, fact_248_insertCI, fact_192_Diff__cancel, fact_138_Diff__subset__conv, fact_19_subset__antisym, fact_169_empty__iff, fact_190_subset__empty, fact_128_inFr__inFr2, fact_244_subset__Compl__singleton, fact_26_subset__refl, fact_12_Un__iff, fact_218_double__complement, fact_196_Compl__anti__mono, fact_56_Un__absorb, fact_6_subtr__rootL__in, fact_228_subset__emptyI, fact_45_mem__Collect__eq, fact_251_Un__insert__right, fact_220_equals0I, fact_230_not__root__Fr, fact_254_Diff__insert0, fact_125_inFr__mono, fact_61_UnI1, fact_164_Compl__Diff__eq, fact_1_assms_I2_J, fact_207_pairwise__empty, fact_148_double__diff, fact_47_Collect__cong, fact_223_ComplD, fact_168_all__not__in__conv, fact_124_inFr2__mono, fact_189_empty__subsetI, fact_32_subset__eq, fact_59_bex__Un, fact_195_Compl__subset__Compl__iff, fact_130_inFr__root__in, fact_133_inItr_OBase, fact_22_contra__subsetD, fact_145_Un__Diff__cancel, fact_3_subtr__trans__Un, fact_174_Compl__iff, fact_58_ball__Un, fact_11_UnCI, fact_27_rev__subsetD, fact_28_subset__iff, fact_96_Un__least, fact_143_DiffI, fact_30_equalityD2, fact_21_Collect__mono__iff, fact_222_emptyE, fact_139_Diff__partition, fact_36_in__mono, fact_29_set__rev__mp, fact_162_Diff__eq__empty__iff, fact_129_not__root__inFr, fact_253_insert__Diff1, fact_194_Diff__empty, fact_2_assms_I1_J, fact_93_Un__absorb1, fact_154_Un__Diff, fact_132_inItr__root__in, fact_142_Diff__iff, fact_252_Un__insert__left, fact_5_Refl, fact_250_insert__subset, fact_94_Un__upper2, fact_4_subtr__mono, fact_208_subset__Compl__self__eq, fact_7_subtr__rootR__in, fact_147_Diff__subset
% 12.46/4.21 % No. of inferences in proof: 234
% 12.46/4.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3868 ms resp. 3001 ms w/o parsing
% 12.46/4.29 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.46/4.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------