%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP162^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n004.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 08:07:00 AM UTC 2026
% Result : Theorem 22.59s 5.98s
% Output : Refutation 24.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 352
% Syntax : Number of formulae : 706 ( 314 unt; 0 typ; 0 def)
% Number of atoms : 2053 ( 580 equ; 22 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 5708 ( 84 ~; 3 |; 73 &;4646 @)
% ( 0 <=>; 902 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 750 ( 750 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 27 usr; 8 con; 0-4 aty)
% Number of variables : 2116 ( 209 ^;1903 !; 4 ?;2116 :)
% Comments :
%------------------------------------------------------------------------------
thf(refine424419629nres_a_type,type,
refine424419629nres_a: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(a_type,type,
a: $tType ).
thf(if_a_o_decl,type,
if_a_o: $o > ( a > $o ) > ( a > $o ) > a > $o ).
thf(if_Ref1724547303nres_a_decl,type,
if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
thf(inf_inf_a_o_decl,type,
inf_inf_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
thf(inf_inf_o_decl,type,
inf_inf_o: $o > $o > $o ).
thf(inf_in262696383nres_a_decl,type,
inf_in262696383nres_a: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).
thf(inf_inf_set_a_decl,type,
inf_inf_set_a: set_a > set_a > set_a ).
thf(bot_bo529555393nres_a_decl,type,
bot_bo529555393nres_a: refine424419629nres_a ).
thf(bot_bot_set_a_decl,type,
bot_bot_set_a: set_a ).
thf(ord_less_eq_a_o_decl,type,
ord_less_eq_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(ord_less_eq_o_decl,type,
ord_less_eq_o: $o > $o > $o ).
thf(ord_le519537037nres_a_decl,type,
ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).
thf(ord_less_eq_set_a_decl,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(order_1714329108nres_a_decl,type,
order_1714329108nres_a: ( refine424419629nres_a > $o ) > refine424419629nres_a ).
thf(top_to231829469nres_a_decl,type,
top_to231829469nres_a: refine424419629nres_a ).
thf(refine2063221604TURN_a_decl,type,
refine2063221604TURN_a: a > refine424419629nres_a ).
thf(refine436832838nd_a_a_decl,type,
refine436832838nd_a_a: refine424419629nres_a > ( a > refine424419629nres_a ) > refine424419629nres_a ).
thf(refine1001002027nres_a_decl,type,
refine1001002027nres_a: refine424419629nres_a > a > $o ).
thf(refine1312857699nres_a_decl,type,
refine1312857699nres_a: refine424419629nres_a > a > $o ).
thf(refine412683989fail_a_decl,type,
refine412683989fail_a: refine424419629nres_a > $o ).
thf(refine464223677AILi_a_decl,type,
refine464223677AILi_a: refine424419629nres_a ).
thf(refine1198353288_RES_a_decl,type,
refine1198353288_RES_a: set_a > refine424419629nres_a ).
thf(refine1822134885_RES_a_decl,type,
refine1822134885_RES_a: refine424419629nres_a > set_a ).
thf(collect_a_decl,type,
collect_a: ( a > $o ) > set_a ).
thf(member_a_decl,type,
member_a: a > set_a > $o ).
thf(a2_decl,type,
a2: refine424419629nres_a ).
thf(p_decl,type,
p: a > $o ).
thf(q_decl,type,
q: a > $o ).
thf(347,axiom,
! [A: a] :
( ( refine1198353288_RES_a
@ ( collect_a
@ ^ [B: a] : ( B = A ) ) )
= ( refine2063221604TURN_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_SPEC__eq__is__RETURN_I2_J) ).
thf(1665,plain,
! [A: a] :
( ( refine1198353288_RES_a
@ ( collect_a
@ ^ [B: a] : ( B = A ) ) )
= ( refine2063221604TURN_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(203,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ A @ C )
=> ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_inf__greatest) ).
thf(1036,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ A @ C )
=> ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(276,axiom,
! [A: refine424419629nres_a > refine424419629nres_a > $o,B: refine424419629nres_a,C: refine424419629nres_a] :
( ! [D: refine424419629nres_a] : ( A @ refine464223677AILi_a @ D )
=> ( ! [D: set_a] : ( A @ ( refine1198353288_RES_a @ D ) @ refine464223677AILi_a )
=> ( ! [D: set_a,E: set_a] : ( A @ ( refine1198353288_RES_a @ D ) @ ( refine1198353288_RES_a @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_less__nres_Oinduct) ).
thf(1337,plain,
! [A: refine424419629nres_a > refine424419629nres_a > $o,B: refine424419629nres_a,C: refine424419629nres_a] :
( ! [D: refine424419629nres_a] : ( A @ refine464223677AILi_a @ D )
=> ( ! [D: set_a] : ( A @ ( refine1198353288_RES_a @ D ) @ refine464223677AILi_a )
=> ( ! [D: set_a,E: set_a] : ( A @ ( refine1198353288_RES_a @ D ) @ ( refine1198353288_RES_a @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(303,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ A @ C )
=> ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_inf_OboundedI) ).
thf(1469,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ A @ C )
=> ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(7,axiom,
( ord_less_eq_a_o
= ( ^ [A: a > $o,B: a > $o] :
( ( inf_inf_a_o @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_le__iff__inf) ).
thf(365,plain,
( ord_less_eq_a_o
= ( ^ [A: a > $o,B: a > $o] :
( ( inf_inf_a_o @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(297,axiom,
! [A: set_a,B: set_a] :
( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_nres__order__simps_I5_J) ).
thf(1454,plain,
! [A: set_a,B: set_a] :
( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(325,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_Collect__mono) ).
thf(1559,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(254,axiom,
! [A: set_a] :
( ( inf_in262696383nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ A ) )
= ( refine1198353288_RES_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_inf__nres_Osimps_I2_J) ).
thf(1237,plain,
! [A: set_a] :
( ( inf_in262696383nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ A ) )
= ( refine1198353288_RES_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(158,axiom,
! [A: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ bot_bo529555393nres_a )
= bot_bo529555393nres_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_inf__bot__right) ).
thf(893,plain,
! [A: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ bot_bo529555393nres_a )
= bot_bo529555393nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(91,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( A = B )
=> ( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_ord__eq__le__trans) ).
thf(666,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( A = B )
=> ( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(322,axiom,
! [A: refine424419629nres_a,B: ( a > $o ) > refine424419629nres_a,C: a > $o,D: a > $o] :
( ( ord_le519537037nres_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_order__subst1) ).
thf(1549,plain,
! [A: refine424419629nres_a,B: ( a > $o ) > refine424419629nres_a,C: a > $o,D: a > $o] :
( ( ord_le519537037nres_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(180,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ C @ A )
=> ( ord_less_eq_a_o @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_dual__order_Otrans) ).
thf(962,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ C @ A )
=> ( ord_less_eq_a_o @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(34,axiom,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_inf__sup__ord_I1_J) ).
thf(468,plain,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(323,axiom,
( refine412683989fail_a
= ( ^ [A: refine424419629nres_a] :
? [B: set_a] :
( A
= ( refine1198353288_RES_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_nofail__RES__conv) ).
thf(1554,plain,
( refine412683989fail_a
= ( ^ [A: refine424419629nres_a] :
? [B: set_a] :
( A
= ( refine1198353288_RES_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(222,axiom,
! [A: set_a,B: set_a,C: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ A
@ ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: a] :
( ( member_a @ D @ A )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_subset__Collect__iff) ).
thf(1110,plain,
! [A: set_a,B: set_a,C: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ A
@ ( collect_a
@ ^ [D: a] :
( ( member_a @ D @ B )
& ( C @ D ) ) ) )
= ( ! [D: a] :
( ( member_a @ D @ A )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(245,axiom,
! [A: set_a] :
( ( bot_bo529555393nres_a
= ( refine1198353288_RES_a @ A ) )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_nres__more__simps_I1_J) ).
thf(1200,plain,
! [A: set_a] :
( ( bot_bo529555393nres_a
= ( refine1198353288_RES_a @ A ) )
= ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(17,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( inf_inf_set_a @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_inf_Oabsorb2) ).
thf(408,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( inf_inf_set_a @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(96,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_inf_OboundedE) ).
thf(683,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(213,axiom,
! [A: set_a,B: refine424419629nres_a > set_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_order__subst1) ).
thf(1068,plain,
! [A: set_a,B: refine424419629nres_a > set_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(328,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
= ( ( ord_le519537037nres_a @ A @ B )
& ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_inf_Obounded__iff) ).
thf(1569,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
= ( ( ord_le519537037nres_a @ A @ B )
& ( ord_le519537037nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(214,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Collect__cong) ).
thf(1073,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(88,axiom,
! [A: a > $o,B: a > $o,C: a > $o,D: a > $o] :
( ( A
= ( inf_inf_a_o @ B @ C ) )
=> ( ( inf_inf_a_o @ A @ D )
= ( inf_inf_a_o @ B @ ( inf_inf_a_o @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_boolean__algebra__cancel_Oinf1) ).
thf(655,plain,
! [A: a > $o,B: a > $o,C: a > $o,D: a > $o] :
( ( A
= ( inf_inf_a_o @ B @ C ) )
=> ( ( inf_inf_a_o @ A @ D )
= ( inf_inf_a_o @ B @ ( inf_inf_a_o @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(94,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_order_Otrans) ).
thf(677,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(73,axiom,
! [A: a > $o,B: a > $o,C: ( a > $o ) > a > $o,D: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_a_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a_o @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_ord__le__eq__subst) ).
thf(597,plain,
! [A: a > $o,B: a > $o,C: ( a > $o ) > a > $o,D: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_a_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a_o @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(238,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( refine412683989fail_a @ B )
=> ( refine412683989fail_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_pwD1) ).
thf(1173,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( refine412683989fail_a @ B )
=> ( refine412683989fail_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(234,axiom,
! [A: set_a,B: set_a,C: a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ! [E: a] :
( ( member_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ ( collect_a @ C ) ) @ ( inf_inf_set_a @ B @ ( collect_a @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_Int__Collect__mono) ).
thf(1158,plain,
! [A: set_a,B: set_a,C: a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ! [E: a] :
( ( member_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ ( collect_a @ C ) ) @ ( inf_inf_set_a @ B @ ( collect_a @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(122,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( A
= ( inf_inf_a_o @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_inf_OorderE) ).
thf(762,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( A
= ( inf_inf_a_o @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(154,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( inf_inf_set_a @ B @ C ) )
=> ~ ( ( member_a @ A @ B )
=> ~ ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_IntE) ).
thf(873,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( inf_inf_set_a @ B @ C ) )
=> ~ ( ( member_a @ A @ B )
=> ~ ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(29,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( inf_in262696383nres_a @ ( inf_in262696383nres_a @ A @ B ) @ C )
= ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_inf_Oassoc) ).
thf(449,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( inf_in262696383nres_a @ ( inf_in262696383nres_a @ A @ B ) @ C )
= ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(349,axiom,
! [A: refine424419629nres_a,B: a > refine424419629nres_a,C: a > $o] :
( ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ B ) @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) )
= ( ord_le519537037nres_a @ A
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [D: a] : ( ord_le519537037nres_a @ ( B @ D ) @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_bind__rule__complete) ).
thf(1671,plain,
! [A: refine424419629nres_a,B: a > refine424419629nres_a,C: a > $o] :
( ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ B ) @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) )
= ( ord_le519537037nres_a @ A
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [D: a] : ( ord_le519537037nres_a @ ( B @ D ) @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(174,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_dual__order_Orefl) ).
thf(945,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(55,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
= ( inf_in262696383nres_a @ B @ ( inf_in262696383nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_inf__sup__aci_I3_J) ).
thf(538,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
= ( inf_in262696383nres_a @ B @ ( inf_in262696383nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(250,axiom,
! [A: refine424419629nres_a,B: a > refine424419629nres_a,C: refine424419629nres_a] :
( ( refine412683989fail_a @ A )
=> ( ! [D: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ D ) @ A )
=> ( ord_le519537037nres_a @ ( B @ D ) @ C ) )
=> ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_bind__le__nofailI) ).
thf(1222,plain,
! [A: refine424419629nres_a,B: a > refine424419629nres_a,C: refine424419629nres_a] :
( ( refine412683989fail_a @ A )
=> ( ! [D: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ D ) @ A )
=> ( ord_le519537037nres_a @ ( B @ D ) @ C ) )
=> ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(235,axiom,
( inf_inf_set_a
= ( ^ [A: set_a,B: set_a] :
( collect_a
@ ( inf_inf_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_inf__set__def) ).
thf(1164,plain,
( inf_inf_set_a
= ( ^ [A: set_a,B: set_a] :
( collect_a
@ ( inf_inf_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(133,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
= ( inf_in262696383nres_a @ B @ ( inf_in262696383nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_inf_Oleft__commute) ).
thf(797,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
= ( inf_in262696383nres_a @ B @ ( inf_in262696383nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(278,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_Collect__mem__eq) ).
thf(1342,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(163,axiom,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( A
= ( inf_inf_set_a @ B @ C ) )
=> ( ( inf_inf_set_a @ D @ A )
= ( inf_inf_set_a @ B @ ( inf_inf_set_a @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_boolean__algebra__cancel_Oinf2) ).
thf(913,plain,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( A
= ( inf_inf_set_a @ B @ C ) )
=> ( ( inf_inf_set_a @ D @ A )
= ( inf_inf_set_a @ B @ ( inf_inf_set_a @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(142,axiom,
! [A: a > $o,B: a > $o] :
( ( inf_inf_a_o @ ( inf_inf_a_o @ A @ B ) @ B )
= ( inf_inf_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_inf_Oright__idem) ).
thf(829,plain,
! [A: a > $o,B: a > $o] :
( ( inf_inf_a_o @ ( inf_inf_a_o @ A @ B ) @ B )
= ( inf_inf_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(160,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
= ( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_le__inf__iff) ).
thf(898,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
= ( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(284,axiom,
! [A: a,B: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine2063221604TURN_a @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_nres__order__simps_I20_J) ).
thf(1391,plain,
! [A: a,B: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine2063221604TURN_a @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(129,axiom,
! [A: a > $o,B: ( a > $o ) > a > $o,C: a > $o,D: a > $o] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_a_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a_o @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_ord__eq__le__subst) ).
thf(782,plain,
! [A: a > $o,B: ( a > $o ) > a > $o,C: a > $o,D: a > $o] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_a_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a_o @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(207,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ C ) @ ( inf_in262696383nres_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_inf__mono) ).
thf(1046,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ C ) @ ( inf_in262696383nres_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(282,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_inf__le2) ).
thf(1386,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(63,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_order__trans) ).
thf(565,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(260,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
= ( ( ord_le519537037nres_a @ A @ B )
& ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_le__inf__iff) ).
thf(1254,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
= ( ( ord_le519537037nres_a @ A @ B )
& ( ord_le519537037nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(109,axiom,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_inf_Ocobounded1) ).
thf(724,plain,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(107,axiom,
! [A: a > $o,B: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_inf__le1) ).
thf(719,plain,
! [A: a > $o,B: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(46,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_antisym) ).
thf(504,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(264,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > a > $o,D: a > $o] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_a_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a_o @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_ord__le__eq__subst) ).
thf(1264,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > a > $o,D: a > $o] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_a_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a_o @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(135,axiom,
! [A: a > $o,B: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_inf__le2) ).
thf(802,plain,
! [A: a > $o,B: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(331,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_inf__sup__ord_I2_J) ).
thf(1577,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(211,axiom,
! [A: set_a,B: set_a,C: a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ! [E: a] :
( ( member_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq_set_a
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ A )
& ( C @ E ) ) )
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ B )
& ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_subset__CollectI) ).
thf(1059,plain,
! [A: set_a,B: set_a,C: a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ! [E: a] :
( ( member_a @ E @ A )
=> ( ( C @ E )
=> ( D @ E ) ) )
=> ( ord_less_eq_set_a
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ A )
& ( C @ E ) ) )
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ B )
& ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(33,axiom,
! [A: $o,B: a > $o,C: a > $o,D: a > $o,E: a > $o] :
( ( A
=> ( ord_less_eq_a_o @ B @ C ) )
=> ( ( ~ A
=> ( ord_less_eq_a_o @ D @ E ) )
=> ( ord_less_eq_a_o @ ( if_a_o @ A @ B @ D ) @ ( if_a_o @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Refine__Misc_Oif__mono) ).
thf(460,plain,
! [A: $o,B: a > $o,C: a > $o,D: a > $o,E: a > $o] :
( ( A
=> ( ord_less_eq_a_o @ B @ C ) )
=> ( ( ~ A
=> ( ord_less_eq_a_o @ D @ E ) )
=> ( ord_less_eq_a_o @ ( if_a_o @ A @ B @ D ) @ ( if_a_o @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(274,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_ord__le__eq__subst) ).
thf(1323,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(78,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_ord__le__eq__trans) ).
thf(619,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(314,axiom,
! [A: refine424419629nres_a > $o,B: refine424419629nres_a,C: refine424419629nres_a > $o] :
( ( A @ B )
=> ( ! [D: refine424419629nres_a] :
( ( A @ D )
=> ( ord_le519537037nres_a @ D @ B ) )
=> ( ! [D: refine424419629nres_a] :
( ( A @ D )
=> ( ! [E: refine424419629nres_a] :
( ( A @ E )
=> ( ord_le519537037nres_a @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_1714329108nres_a @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_GreatestI2__order) ).
thf(1511,plain,
! [A: refine424419629nres_a > $o,B: refine424419629nres_a,C: refine424419629nres_a > $o] :
( ( A @ B )
=> ( ! [D: refine424419629nres_a] :
( ( A @ D )
=> ( ord_le519537037nres_a @ D @ B ) )
=> ( ! [D: refine424419629nres_a] :
( ( A @ D )
=> ( ! [E: refine424419629nres_a] :
( ( A @ E )
=> ( ord_le519537037nres_a @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_1714329108nres_a @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(101,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_order__class_Oorder_Oeq__iff) ).
thf(702,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(118,axiom,
( inf_inf_a_o
= ( ^ [A: a > $o,B: a > $o] : ( inf_inf_a_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_inf__commute) ).
thf(751,plain,
( inf_inf_a_o
= ( ^ [A: a > $o,B: a > $o] : ( inf_inf_a_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(61,axiom,
! [A: a > $o,B: a > $o] :
( ( inf_inf_a_o @ A @ ( inf_inf_a_o @ A @ B ) )
= ( inf_inf_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_inf__sup__aci_I4_J) ).
thf(559,plain,
! [A: a > $o,B: a > $o] :
( ( inf_inf_a_o @ A @ ( inf_inf_a_o @ A @ B ) )
= ( inf_inf_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(83,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_ord__le__eq__trans) ).
thf(638,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(230,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_order_Otrans) ).
thf(1147,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(258,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_inf_Ocobounded2) ).
thf(1247,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(153,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( inf_in262696383nres_a @ ( inf_in262696383nres_a @ A @ B ) @ B )
= ( inf_in262696383nres_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_inf__right__idem) ).
thf(870,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( inf_in262696383nres_a @ ( inf_in262696383nres_a @ A @ B ) @ B )
= ( inf_in262696383nres_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(306,axiom,
! [A: refine424419629nres_a,B: set_a > refine424419629nres_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_ord__eq__le__subst) ).
thf(1479,plain,
! [A: refine424419629nres_a,B: set_a > refine424419629nres_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(310,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > a > $o,D: a > $o] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_less_eq_a_o @ ( C @ B ) @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_a_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a_o @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_order__subst2) ).
thf(1494,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > a > $o,D: a > $o] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_less_eq_a_o @ ( C @ B ) @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_a_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a_o @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(182,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( inf_inf_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
= ( inf_inf_a_o @ B @ ( inf_inf_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_inf_Oleft__commute) ).
thf(969,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( inf_inf_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
= ( inf_inf_a_o @ B @ ( inf_inf_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(74,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( inf_inf_a_o @ ( inf_inf_a_o @ A @ B ) @ C )
= ( inf_inf_a_o @ A @ ( inf_inf_a_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_inf__assoc) ).
thf(606,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( inf_inf_a_o @ ( inf_inf_a_o @ A @ B ) @ C )
= ( inf_inf_a_o @ A @ ( inf_inf_a_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(329,axiom,
( ( (=) @ refine424419629nres_a )
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
& ( ord_le519537037nres_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_order__class_Oorder_Oeq__iff) ).
thf(1572,plain,
( ( (=) @ refine424419629nres_a )
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
& ( ord_le519537037nres_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(286,axiom,
! [A: set_a,B: a > $o] :
( ord_less_eq_set_a
@ ( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_Collect__subset) ).
thf(1398,plain,
! [A: set_a,B: a > $o] :
( ord_less_eq_set_a
@ ( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(156,axiom,
! [A: a > $o,B: set_a > a > $o,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_a_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a_o @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_ord__eq__le__subst) ).
thf(881,plain,
! [A: a > $o,B: set_a > a > $o,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_a_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a_o @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(20,axiom,
! [A: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ refine464223677AILi_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_inf__nres_Osimps_I1_J) ).
thf(416,plain,
! [A: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ refine464223677AILi_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(290,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_inf_OcoboundedI2) ).
thf(1415,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(205,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ A )
=> ( ord_le519537037nres_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_dual__order_Otrans) ).
thf(1040,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ A )
=> ( ord_le519537037nres_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(11,axiom,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( A
= ( inf_inf_set_a @ B @ C ) )
=> ( ( inf_inf_set_a @ A @ D )
= ( inf_inf_set_a @ B @ ( inf_inf_set_a @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_boolean__algebra__cancel_Oinf1) ).
thf(376,plain,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( A
= ( inf_inf_set_a @ B @ C ) )
=> ( ( inf_inf_set_a @ A @ D )
= ( inf_inf_set_a @ B @ ( inf_inf_set_a @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(291,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ~ ( ord_le519537037nres_a @ A @ B )
=> ( ! [C: set_a] :
( ( A
= ( refine1198353288_RES_a @ C ) )
=> ! [D: set_a] :
( ( B
= ( refine1198353288_RES_a @ D ) )
=> ( ord_less_eq_set_a @ C @ D ) ) )
=> ~ ( ( A = refine464223677AILi_a )
=> ! [C: set_a] :
( B
!= ( refine1198353288_RES_a @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_less__eq__nres_Oelims_I3_J) ).
thf(1418,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ~ ( ord_le519537037nres_a @ A @ B )
=> ( ! [C: set_a] :
( ( A
= ( refine1198353288_RES_a @ C ) )
=> ! [D: set_a] :
( ( B
= ( refine1198353288_RES_a @ D ) )
=> ( ord_less_eq_set_a @ C @ D ) ) )
=> ~ ( ( A = refine464223677AILi_a )
=> ! [C: set_a] :
( B
!= ( refine1198353288_RES_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(85,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( inf_inf_set_a @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_inf_Oabsorb1) ).
thf(646,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( inf_inf_set_a @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(353,axiom,
! [A: $o,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
=> ( ord_le519537037nres_a @ B @ C ) )
=> ( ( ~ A
=> ( ord_le519537037nres_a @ D @ C ) )
=> ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ A @ B @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_lhs__step__If) ).
thf(1682,plain,
! [A: $o,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
=> ( ord_le519537037nres_a @ B @ C ) )
=> ( ( ~ A
=> ( ord_le519537037nres_a @ D @ C ) )
=> ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ A @ B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(171,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( inf_in262696383nres_a @ ( inf_in262696383nres_a @ A @ B ) @ B )
= ( inf_in262696383nres_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_inf_Oright__idem) ).
thf(937,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( inf_in262696383nres_a @ ( inf_in262696383nres_a @ A @ B ) @ B )
= ( inf_in262696383nres_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(199,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( inf_in262696383nres_a @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_inf_Oabsorb1) ).
thf(1020,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( inf_in262696383nres_a @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(351,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
=> ( ord_le519537037nres_a @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_le__infD2) ).
thf(1677,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
=> ( ord_le519537037nres_a @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(333,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_inf_Ocobounded1) ).
thf(1581,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(241,axiom,
! [A: refine424419629nres_a,B: a > refine424419629nres_a,C: a > $o] :
( ( ord_le519537037nres_a @ A
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [D: a] : ( ord_le519537037nres_a @ ( B @ D ) @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ) )
=> ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ B ) @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_bind__rule) ).
thf(1183,plain,
! [A: refine424419629nres_a,B: a > refine424419629nres_a,C: a > $o] :
( ( ord_le519537037nres_a @ A
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [D: a] : ( ord_le519537037nres_a @ ( B @ D ) @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ) )
=> ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ B ) @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(38,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_dual__order_Oantisym) ).
thf(480,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(271,axiom,
! [A: refine424419629nres_a > $o,B: refine424419629nres_a] :
( ( A @ B )
=> ( ! [C: refine424419629nres_a] :
( ( A @ C )
=> ( ord_le519537037nres_a @ C @ B ) )
=> ( ( order_1714329108nres_a @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_Greatest__equality) ).
thf(1302,plain,
! [A: refine424419629nres_a > $o,B: refine424419629nres_a] :
( ( A @ B )
=> ( ! [C: refine424419629nres_a] :
( ( A @ C )
=> ( ord_le519537037nres_a @ C @ B ) )
=> ( ( order_1714329108nres_a @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(120,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ A @ B ) )
= ( inf_in262696383nres_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_inf__sup__aci_I4_J) ).
thf(756,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ A @ B ) )
= ( inf_in262696383nres_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(97,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( inf_inf_set_a @ B @ C ) )
=> ( member_a @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_IntD2) ).
thf(687,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( inf_inf_set_a @ B @ C ) )
=> ( member_a @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(155,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
=> ~ ( ( ord_less_eq_a_o @ A @ B )
=> ~ ( ord_less_eq_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_inf_OboundedE) ).
thf(877,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
=> ~ ( ( ord_less_eq_a_o @ A @ B )
=> ~ ( ord_less_eq_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(178,axiom,
! [A: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_inf_Oidem) ).
thf(956,plain,
! [A: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(285,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ( refine412683989fail_a @ A )
=> ( ord_le519537037nres_a @ B @ A ) )
=> ( ord_le519537037nres_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_le__nofailI) ).
thf(1394,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ( refine412683989fail_a @ A )
=> ( ord_le519537037nres_a @ B @ A ) )
=> ( ord_le519537037nres_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(281,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ( inf_in262696383nres_a @ A @ B )
= C )
=> ( ( ( B = refine464223677AILi_a )
=> ( C != A ) )
=> ( ( ( A = refine464223677AILi_a )
=> ! [D: set_a] :
( ( B
= ( refine1198353288_RES_a @ D ) )
=> ( C
!= ( refine1198353288_RES_a @ D ) ) ) )
=> ~ ! [D: set_a] :
( ( A
= ( refine1198353288_RES_a @ D ) )
=> ! [E: set_a] :
( ( B
= ( refine1198353288_RES_a @ E ) )
=> ( C
!= ( refine1198353288_RES_a @ ( inf_inf_set_a @ D @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_inf__nres_Oelims) ).
thf(1351,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ( inf_in262696383nres_a @ A @ B )
= C )
=> ( ( ( B = refine464223677AILi_a )
=> ( C != A ) )
=> ( ( ( A = refine464223677AILi_a )
=> ! [D: set_a] :
( ( B
= ( refine1198353288_RES_a @ D ) )
=> ( C
!= ( refine1198353288_RES_a @ D ) ) ) )
=> ~ ! [D: set_a] :
( ( A
= ( refine1198353288_RES_a @ D ) )
=> ! [E: set_a] :
( ( B
= ( refine1198353288_RES_a @ E ) )
=> ( C
!= ( refine1198353288_RES_a @ ( inf_inf_set_a @ D @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(89,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
= ( inf_in262696383nres_a @ B @ ( inf_in262696383nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_inf__left__commute) ).
thf(660,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
= ( inf_in262696383nres_a @ B @ ( inf_in262696383nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(292,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_le__infI1) ).
thf(1433,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(338,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_order__trans) ).
thf(1600,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(47,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
= ( inf_in262696383nres_a @ B @ C ) )
=> ( ( inf_in262696383nres_a @ D @ A )
= ( inf_in262696383nres_a @ B @ ( inf_in262696383nres_a @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_boolean__algebra__cancel_Oinf2) ).
thf(507,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
= ( inf_in262696383nres_a @ B @ C ) )
=> ( ( inf_in262696383nres_a @ D @ A )
= ( inf_in262696383nres_a @ B @ ( inf_in262696383nres_a @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(225,axiom,
ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_assms_I2_J) ).
thf(1119,plain,
ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(126,axiom,
! [A: a > $o] : ( ord_less_eq_a_o @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_dual__order_Orefl) ).
thf(774,plain,
! [A: a > $o] : ( ord_less_eq_a_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(18,axiom,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_inf__le2) ).
thf(411,plain,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(279,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( inf_in262696383nres_a @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_inf__absorb2) ).
thf(1345,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( inf_in262696383nres_a @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(189,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_in__mono) ).
thf(988,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(220,axiom,
! [A: a > $o,B: a] :
( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) @ ( refine2063221604TURN_a @ B ) )
= ( refine1198353288_RES_a
@ ( collect_a
@ ^ [C: a] :
( ( C = B )
& ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_inf__RETURN__SPEC_I2_J) ).
thf(1104,plain,
! [A: a > $o,B: a] :
( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) @ ( refine2063221604TURN_a @ B ) )
= ( refine1198353288_RES_a
@ ( collect_a
@ ^ [C: a] :
( ( C = B )
& ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(256,axiom,
! [A: refine424419629nres_a > refine424419629nres_a > $o,B: refine424419629nres_a,C: refine424419629nres_a] :
( ! [D: refine424419629nres_a] : ( A @ D @ refine464223677AILi_a )
=> ( ! [D: set_a] : ( A @ refine464223677AILi_a @ ( refine1198353288_RES_a @ D ) )
=> ( ! [D: set_a,E: set_a] : ( A @ ( refine1198353288_RES_a @ D ) @ ( refine1198353288_RES_a @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_sup__nres_Oinduct) ).
thf(1242,plain,
! [A: refine424419629nres_a > refine424419629nres_a > $o,B: refine424419629nres_a,C: refine424419629nres_a] :
( ! [D: refine424419629nres_a] : ( A @ D @ refine464223677AILi_a )
=> ( ! [D: set_a] : ( A @ refine464223677AILi_a @ ( refine1198353288_RES_a @ D ) )
=> ( ! [D: set_a,E: set_a] : ( A @ ( refine1198353288_RES_a @ D ) @ ( refine1198353288_RES_a @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(146,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_less__eq__set__def) ).
thf(849,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(342,axiom,
( ( (=) @ refine424419629nres_a )
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ B @ A )
& ( ord_le519537037nres_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_dual__order_Oeq__iff) ).
thf(1651,plain,
( ( (=) @ refine424419629nres_a )
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ B @ A )
& ( ord_le519537037nres_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(30,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ( inf_in262696383nres_a @ A @ B )
= top_to231829469nres_a )
= ( ( A = top_to231829469nres_a )
& ( B = top_to231829469nres_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_inf__top_Oeq__neutr__iff) ).
thf(452,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ( inf_in262696383nres_a @ A @ B )
= top_to231829469nres_a )
= ( ( A = top_to231829469nres_a )
& ( B = top_to231829469nres_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(165,axiom,
! [A: set_a] :
( ( inf_inf_set_a @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_inf__idem) ).
thf(920,plain,
! [A: set_a] :
( ( inf_inf_set_a @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(138,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ C )
= ( inf_inf_set_a @ A @ ( inf_inf_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_inf__sup__aci_I2_J) ).
thf(810,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ C )
= ( inf_inf_set_a @ A @ ( inf_inf_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(12,axiom,
! [A: set_a,B: set_a,C: set_a > a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_a_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a_o @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_ord__le__eq__subst) ).
thf(381,plain,
! [A: set_a,B: set_a,C: set_a > a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_a_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a_o @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(48,axiom,
! [A: a > $o] :
( ( inf_inf_a_o @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_inf__idem) ).
thf(512,plain,
! [A: a > $o] :
( ( inf_inf_a_o @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(173,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
= ( ( ord_less_eq_a_o @ A @ B )
& ( ord_less_eq_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_le__inf__iff) ).
thf(942,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
= ( ( ord_less_eq_a_o @ A @ B )
& ( ord_less_eq_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(58,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_order__subst2) ).
thf(546,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(131,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( A
= ( inf_inf_set_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_inf_Oorder__iff) ).
thf(793,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( A
= ( inf_inf_set_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(272,axiom,
! [A: a,B: set_a,C: refine424419629nres_a,D: a > refine424419629nres_a] :
( ( member_a @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ ( D @ A ) )
=> ( ord_le519537037nres_a @ C @ ( refine436832838nd_a_a @ ( refine1198353288_RES_a @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_RES__bind__choose) ).
thf(1311,plain,
! [A: a,B: set_a,C: refine424419629nres_a,D: a > refine424419629nres_a] :
( ( member_a @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ ( D @ A ) )
=> ( ord_le519537037nres_a @ C @ ( refine436832838nd_a_a @ ( refine1198353288_RES_a @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(53,axiom,
( inf_inf_a_o
= ( ^ [A: a > $o,B: a > $o] : ( inf_inf_a_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_inf_Ocommute) ).
thf(534,plain,
( inf_inf_a_o
= ( ^ [A: a > $o,B: a > $o] : ( inf_inf_a_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(162,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ B )
=> ( ( member_a @ A @ C )
=> ( member_a @ A @ ( inf_inf_set_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_IntI) ).
thf(910,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ B )
=> ( ( member_a @ A @ C )
=> ( member_a @ A @ ( inf_inf_set_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(117,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_order__subst1) ).
thf(746,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(150,axiom,
( inf_inf_a_o
= ( ^ [A: a > $o,B: a > $o,C: a] : ( inf_inf_o @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_inf__fun__def) ).
thf(862,plain,
( inf_inf_a_o
= ( ^ [A: a > $o,B: a > $o,C: a] : ( inf_inf_o @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(312,axiom,
! [A: refine424419629nres_a > $o,B: refine424419629nres_a] :
( ( A @ refine464223677AILi_a )
=> ( ! [C: set_a] : ( A @ ( refine1198353288_RES_a @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_nres_Oinduct) ).
thf(1502,plain,
! [A: refine424419629nres_a > $o,B: refine424419629nres_a] :
( ( A @ refine464223677AILi_a )
=> ( ! [C: set_a] : ( A @ ( refine1198353288_RES_a @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(111,axiom,
! [A: set_a,B: set_a] :
( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ B )
= ( inf_inf_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_inf__right__idem) ).
thf(729,plain,
! [A: set_a,B: set_a] :
( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ B )
= ( inf_inf_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(201,axiom,
( ord_le519537037nres_a
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_le__iff__inf) ).
thf(1032,plain,
( ord_le519537037nres_a
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(5,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T) ).
thf(361,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,axiom,
! [A: a > $o] :
( ( inf_inf_a_o @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_inf_Oidem) ).
thf(435,plain,
! [A: a > $o] :
( ( inf_inf_a_o @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(269,axiom,
! [A: set_a,B: set_a] :
( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( refine1198353288_RES_a @ ( inf_inf_set_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_inf__nres_Osimps_I3_J) ).
thf(1296,plain,
! [A: set_a,B: set_a] :
( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( refine1198353288_RES_a @ ( inf_inf_set_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(298,axiom,
( ( (=) @ refine424419629nres_a )
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
& ( ord_le519537037nres_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_eq__iff) ).
thf(1457,plain,
( ( (=) @ refine424419629nres_a )
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
& ( ord_le519537037nres_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(244,axiom,
! [A: refine424419629nres_a,B: set_a > refine424419629nres_a,C: set_a,D: set_a] :
( ( ord_le519537037nres_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_order__subst1) ).
thf(1195,plain,
! [A: refine424419629nres_a,B: set_a > refine424419629nres_a,C: set_a,D: set_a] :
( ( ord_le519537037nres_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(59,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ A @ C )
=> ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_inf__greatest) ).
thf(551,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ A @ C )
=> ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(184,axiom,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_inf__sup__ord_I2_J) ).
thf(974,plain,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(198,axiom,
! [A: a,B: set_a] :
( ( ( member_a @ A @ B )
=> ( ( inf_in262696383nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( refine2063221604TURN_a @ A ) ) )
& ( ~ ( member_a @ A @ B )
=> ( ( inf_in262696383nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= bot_bo529555393nres_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_inf__RETURN__RES_I1_J) ).
thf(1012,plain,
! [A: a,B: set_a] :
( ( ( member_a @ A @ B )
=> ( ( inf_in262696383nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( refine2063221604TURN_a @ A ) ) )
& ( ~ ( member_a @ A @ B )
=> ( ( inf_in262696383nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= bot_bo529555393nres_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(68,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ A @ C )
=> ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_inf_OboundedI) ).
thf(583,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ A @ C )
=> ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(51,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
= ( ( ord_less_eq_a_o @ A @ B )
& ( ord_less_eq_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_inf_Obounded__iff) ).
thf(522,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
= ( ( ord_less_eq_a_o @ A @ B )
& ( ord_less_eq_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(248,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( inf_in262696383nres_a @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_inf__absorb1) ).
thf(1210,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( inf_in262696383nres_a @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(344,axiom,
! [A: a > $o] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_SUCCEED__rule) ).
thf(1656,plain,
! [A: a > $o] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(268,axiom,
! [A: a > $o,B: refine424419629nres_a > a > $o,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_less_eq_a_o @ A @ ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_a_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a_o @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_order__subst1) ).
thf(1291,plain,
! [A: a > $o,B: refine424419629nres_a > a > $o,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_less_eq_a_o @ A @ ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_a_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a_o @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(104,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ ( inf_inf_set_a @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_le__infI2) ).
thf(710,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ ( inf_inf_set_a @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(262,axiom,
( ord_le519537037nres_a
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_inf_Oabsorb__iff1) ).
thf(1259,plain,
( ord_le519537037nres_a
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(317,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a,E: $o] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ E @ A @ C ) @ ( if_Ref1724547303nres_a @ E @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_order__mono__setup_Omono__if) ).
thf(1534,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a,E: $o] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ E @ A @ C ) @ ( if_Ref1724547303nres_a @ E @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(77,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_le__infE) ).
thf(615,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(251,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
=> ~ ( ( ord_le519537037nres_a @ A @ B )
=> ~ ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_le__infE) ).
thf(1227,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
=> ~ ( ( ord_le519537037nres_a @ A @ B )
=> ~ ( ord_le519537037nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(319,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_antisym) ).
thf(1540,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(229,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > set_a,D: set_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_ord__le__eq__subst) ).
thf(1138,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > set_a,D: set_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(149,axiom,
! [A: a > $o,B: a > $o,C: ( a > $o ) > set_a,D: set_a] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_order__subst2) ).
thf(857,plain,
! [A: a > $o,B: a > $o,C: ( a > $o ) > set_a,D: set_a] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(217,axiom,
! [A: set_a,B: refine424419629nres_a > set_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_ord__eq__le__subst) ).
thf(1089,plain,
! [A: set_a,B: refine424419629nres_a > set_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(253,axiom,
! [A: set_a] :
~ ( ord_le519537037nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_less__eq__nres_Osimps_I3_J) ).
thf(1234,plain,
! [A: set_a] :
~ ( ord_le519537037nres_a @ refine464223677AILi_a @ ( refine1198353288_RES_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(300,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_dual__order_Orefl) ).
thf(1461,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(161,axiom,
! [A: ( a > $o ) > ( a > $o ) > a > $o,B: a > $o,C: a > $o] :
( ! [D: a > $o,E: a > $o] : ( ord_less_eq_a_o @ ( A @ D @ E ) @ D )
=> ( ! [D: a > $o,E: a > $o] : ( ord_less_eq_a_o @ ( A @ D @ E ) @ E )
=> ( ! [D: a > $o,E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ D @ E )
=> ( ( ord_less_eq_a_o @ D @ F )
=> ( ord_less_eq_a_o @ D @ ( A @ E @ F ) ) ) )
=> ( ( inf_inf_a_o @ B @ C )
= ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_inf__unique) ).
thf(901,plain,
! [A: ( a > $o ) > ( a > $o ) > a > $o,B: a > $o,C: a > $o] :
( ! [D: a > $o,E: a > $o] : ( ord_less_eq_a_o @ ( A @ D @ E ) @ D )
=> ( ! [D: a > $o,E: a > $o] : ( ord_less_eq_a_o @ ( A @ D @ E ) @ E )
=> ( ! [D: a > $o,E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ D @ E )
=> ( ( ord_less_eq_a_o @ D @ F )
=> ( ord_less_eq_a_o @ D @ ( A @ E @ F ) ) ) )
=> ( ( inf_inf_a_o @ B @ C )
= ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(41,axiom,
! [A: set_a,B: set_a,C: set_a > a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_a_o @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_a_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a_o @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_order__subst2) ).
thf(489,plain,
! [A: set_a,B: set_a,C: set_a > a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_a_o @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_a_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a_o @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(247,axiom,
! [A: a,B: set_a,C: a > $o] :
( ( member_a @ A @ ( inf_inf_set_a @ B @ ( collect_a @ C ) ) )
= ( ( member_a @ A @ B )
& ( C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_Int__Collect) ).
thf(1207,plain,
! [A: a,B: set_a,C: a > $o] :
( ( member_a @ A @ ( inf_inf_set_a @ B @ ( collect_a @ C ) ) )
= ( ( member_a @ A @ B )
& ( C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(60,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
= ( inf_in262696383nres_a @ B @ C ) )
=> ( ( inf_in262696383nres_a @ A @ D )
= ( inf_in262696383nres_a @ B @ ( inf_in262696383nres_a @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_boolean__algebra__cancel_Oinf1) ).
thf(554,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
= ( inf_in262696383nres_a @ B @ C ) )
=> ( ( inf_in262696383nres_a @ A @ D )
= ( inf_in262696383nres_a @ B @ ( inf_in262696383nres_a @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(119,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_order__trans) ).
thf(753,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(340,axiom,
! [A: set_a,B: a > $o] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( B @ C ) )
=> ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_RES__rule) ).
thf(1612,plain,
! [A: set_a,B: a > $o] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( B @ C ) )
=> ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(204,axiom,
ord_le519537037nres_a @ a2 @ ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ ( collect_a @ p ) ) @ ( refine1198353288_RES_a @ ( collect_a @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__092_060open_062A_A_092_060le_062_Ainf_A_ISPEC_AP_J_A_ISPEC_AQ_J_092_060close_062) ).
thf(1039,plain,
ord_le519537037nres_a @ a2 @ ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ ( collect_a @ p ) ) @ ( refine1198353288_RES_a @ ( collect_a @ q ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(144,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_antisym__conv) ).
thf(837,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(223,axiom,
( inf_inf_set_a
= ( ^ [A: set_a,B: set_a] :
( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
& ( member_a @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_Int__def) ).
thf(1114,plain,
( inf_inf_set_a
= ( ^ [A: set_a,B: set_a] :
( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
& ( member_a @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(296,axiom,
! [A: refine424419629nres_a] :
( ( refine412683989fail_a @ A )
=> ( ( refine1198353288_RES_a @ ( refine1822134885_RES_a @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_the__RES__inv) ).
thf(1451,plain,
! [A: refine424419629nres_a] :
( ( refine412683989fail_a @ A )
=> ( ( refine1198353288_RES_a @ ( refine1822134885_RES_a @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(316,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
=> ~ ( ( ord_le519537037nres_a @ A @ B )
=> ~ ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_inf_OboundedE) ).
thf(1530,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
=> ~ ( ( ord_le519537037nres_a @ A @ B )
=> ~ ( ord_le519537037nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(252,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_le__infI2) ).
thf(1231,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(348,axiom,
! [A: set_a] :
( ( refine1822134885_RES_a @ ( refine1198353288_RES_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_the__RES_Osimps) ).
thf(1668,plain,
! [A: set_a] :
( ( refine1822134885_RES_a @ ( refine1198353288_RES_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(108,axiom,
! [A: a > $o,B: a > $o,C: a > $o,D: a > $o,E: $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ord_less_eq_a_o @ ( if_a_o @ E @ A @ C ) @ ( if_a_o @ E @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_order__mono__setup_Omono__if) ).
thf(721,plain,
! [A: a > $o,B: a > $o,C: a > $o,D: a > $o,E: $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ord_less_eq_a_o @ ( if_a_o @ E @ A @ C ) @ ( if_a_o @ E @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(194,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] : ( ord_less_eq_o @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_le__funI) ).
thf(1002,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] : ( ord_less_eq_o @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(128,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( inf_inf_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
= ( inf_inf_a_o @ B @ ( inf_inf_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_inf__sup__aci_I3_J) ).
thf(779,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( inf_inf_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
= ( inf_inf_a_o @ B @ ( inf_inf_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(335,axiom,
! [A: refine424419629nres_a,B: a] :
( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ ( (=) @ a @ B ) ) ) )
=> ( ord_le519537037nres_a @ A @ ( refine2063221604TURN_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_RETURN__to__SPEC__rule) ).
thf(1588,plain,
! [A: refine424419629nres_a,B: a] :
( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ ( (=) @ a @ B ) ) ) )
=> ( ord_le519537037nres_a @ A @ ( refine2063221604TURN_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(188,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( inf_inf_a_o @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_inf_Oabsorb2) ).
thf(985,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( inf_inf_a_o @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(49,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_subset__iff) ).
thf(515,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(231,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ refine464223677AILi_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_less__eq__nres_Osimps_I1_J) ).
thf(1150,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ refine464223677AILi_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(259,axiom,
! [A: a > $o,B: a > $o,C: ( a > $o ) > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_le519537037nres_a @ ( C @ B ) @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_order__subst2) ).
thf(1249,plain,
! [A: a > $o,B: a > $o,C: ( a > $o ) > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_le519537037nres_a @ ( C @ B ) @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(56,axiom,
( ( (=) @ ( a > $o ) )
= ( ^ [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
& ( ord_less_eq_a_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_eq__iff) ).
thf(541,plain,
( ( (=) @ ( a > $o ) )
= ( ^ [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
& ( ord_less_eq_a_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(326,axiom,
! [A: set_a,B: set_a] :
( ( ( refine1198353288_RES_a @ A )
= ( refine1198353288_RES_a @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_nres__more__simps_I4_J) ).
thf(1563,plain,
! [A: set_a,B: set_a] :
( ( ( refine1198353288_RES_a @ A )
= ( refine1198353288_RES_a @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(123,axiom,
! [A: a > $o] : ( ord_less_eq_a_o @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_order__mono__setup_Orefl) ).
thf(765,plain,
! [A: a > $o] : ( ord_less_eq_a_o @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(302,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
=> ( ord_le519537037nres_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_le__infD1) ).
thf(1466,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) )
=> ( ord_le519537037nres_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(341,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: $o] :
( ( ( ord_le519537037nres_a @ A @ B )
= C )
=> ( ( ( B = refine464223677AILi_a )
=> ~ C )
=> ( ! [D: set_a] :
( ( A
= ( refine1198353288_RES_a @ D ) )
=> ! [E: set_a] :
( ( B
= ( refine1198353288_RES_a @ E ) )
=> ( C
= ( ~ ( ord_less_eq_set_a @ D @ E ) ) ) ) )
=> ~ ( ( A = refine464223677AILi_a )
=> ( ? [D: set_a] :
( B
= ( refine1198353288_RES_a @ D ) )
=> C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_less__eq__nres_Oelims_I1_J) ).
thf(1616,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: $o] :
( ( ( ord_le519537037nres_a @ A @ B )
= C )
=> ( ( ( B = refine464223677AILi_a )
=> ~ C )
=> ( ! [D: set_a] :
( ( A
= ( refine1198353288_RES_a @ D ) )
=> ! [E: set_a] :
( ( B
= ( refine1198353288_RES_a @ E ) )
=> ( C
= ( ~ ( ord_less_eq_set_a @ D @ E ) ) ) ) )
=> ~ ( ( A = refine464223677AILi_a )
=> ( ? [D: set_a] :
( B
= ( refine1198353288_RES_a @ D ) )
=> C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(69,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ A @ C )
=> ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_le__infI) ).
thf(586,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ A @ C )
=> ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(167,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
= ( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_inf_Obounded__iff) ).
thf(926,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
= ( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(243,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( B != refine464223677AILi_a )
=> ~ ! [C: set_a] :
( ( A
= ( refine1198353288_RES_a @ C ) )
=> ! [D: set_a] :
( ( B
= ( refine1198353288_RES_a @ D ) )
=> ~ ( ord_less_eq_set_a @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_less__eq__nres_Oelims_I2_J) ).
thf(1187,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( B != refine464223677AILi_a )
=> ~ ! [C: set_a] :
( ( A
= ( refine1198353288_RES_a @ C ) )
=> ! [D: set_a] :
( ( B
= ( refine1198353288_RES_a @ D ) )
=> ~ ( ord_less_eq_set_a @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(93,axiom,
! [A: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_inf__idem) ).
thf(674,plain,
! [A: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(177,axiom,
! [A: a > $o,B: a > $o,C: a] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ord_less_eq_o @ ( A @ C ) @ ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_le__funE) ).
thf(953,plain,
! [A: a > $o,B: a > $o,C: a] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ord_less_eq_o @ ( A @ C ) @ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(242,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_nres__order__simps_I1_J) ).
thf(1185,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(266,axiom,
! [A: set_a,B: refine424419629nres_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ C ) @ B ) )
=> ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_lhs__step__RES) ).
thf(1278,plain,
! [A: set_a,B: refine424419629nres_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ C ) @ B ) )
=> ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(181,axiom,
! [A: a > $o,B: a > $o] :
( ( A = B )
=> ( ord_less_eq_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_eq__refl) ).
thf(965,plain,
! [A: a > $o,B: a > $o] :
( ( A = B )
=> ( ord_less_eq_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(265,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_order__subst1) ).
thf(1273,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(337,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > set_a,D: set_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_order__subst2) ).
thf(1595,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > set_a,D: set_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_less_eq_set_a @ ( C @ B ) @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(65,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_order__mono__setup_Orefl) ).
thf(573,plain,
! [A: set_a] : ( ord_less_eq_set_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(98,axiom,
( ( (=) @ ( a > $o ) )
= ( ^ [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
& ( ord_less_eq_a_o @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_order__class_Oorder_Oeq__iff) ).
thf(689,plain,
( ( (=) @ ( a > $o ) )
= ( ^ [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
& ( ord_less_eq_a_o @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(27,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ord_less_eq_a_o @ ( inf_inf_a_o @ C @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_le__infI2) ).
thf(444,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ord_less_eq_a_o @ ( inf_inf_a_o @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(62,axiom,
! [A: a > $o,B: a > $o] :
( ( A
= ( inf_inf_a_o @ A @ B ) )
=> ( ord_less_eq_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_inf_OorderI) ).
thf(562,plain,
! [A: a > $o,B: a > $o] :
( ( A
= ( inf_inf_a_o @ A @ B ) )
=> ( ord_less_eq_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(22,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_dual__order_Otrans) ).
thf(423,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ A )
=> ( ord_less_eq_set_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(15,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_pred__subset__eq) ).
thf(402,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(112,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_order__class_Oorder_Oantisym) ).
thf(732,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(227,axiom,
! [A: $o,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a,E: refine424419629nres_a] :
( ( A
=> ( ord_le519537037nres_a @ B @ C ) )
=> ( ( ~ A
=> ( ord_le519537037nres_a @ D @ E ) )
=> ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ A @ B @ D ) @ ( if_Ref1724547303nres_a @ A @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_Refine__Misc_Oif__mono) ).
thf(1125,plain,
! [A: $o,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a,E: refine424419629nres_a] :
( ( A
=> ( ord_le519537037nres_a @ B @ C ) )
=> ( ( ~ A
=> ( ord_le519537037nres_a @ D @ E ) )
=> ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ A @ B @ D ) @ ( if_Ref1724547303nres_a @ A @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(125,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ B @ A )
& ( ord_less_eq_set_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_dual__order_Oeq__iff) ).
thf(772,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ B @ A )
& ( ord_less_eq_set_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(283,axiom,
! [A: a > $o,B: a > $o] :
( ( collect_a
@ ^ [C: a] :
( ( A @ C )
& ( B @ C ) ) )
= ( inf_inf_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_Collect__conj__eq) ).
thf(1388,plain,
! [A: a > $o,B: a > $o] :
( ( collect_a
@ ^ [C: a] :
( ( A @ C )
& ( B @ C ) ) )
= ( inf_inf_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(116,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( inf_inf_set_a @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_inf__absorb2) ).
thf(743,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( inf_inf_set_a @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(307,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( A
= ( inf_in262696383nres_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_inf_OorderE) ).
thf(1488,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( A
= ( inf_in262696383nres_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(19,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ( inf_in262696383nres_a @ A @ B )
= top_to231829469nres_a )
= ( ( A = top_to231829469nres_a )
& ( B = top_to231829469nres_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_inf__eq__top__iff) ).
thf(413,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ( inf_in262696383nres_a @ A @ B )
= top_to231829469nres_a )
= ( ( A = top_to231829469nres_a )
& ( B = top_to231829469nres_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(196,axiom,
( inf_in262696383nres_a
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] : ( inf_in262696383nres_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_inf__sup__aci_I1_J) ).
thf(1007,plain,
( inf_in262696383nres_a
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] : ( inf_in262696383nres_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(100,axiom,
! [A: $o,B: a > $o,C: a > $o,D: a > $o] :
( ( A
=> ( ord_less_eq_a_o @ B @ C ) )
=> ( ( ~ A
=> ( ord_less_eq_a_o @ D @ C ) )
=> ( ord_less_eq_a_o @ ( if_a_o @ A @ B @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_lhs__step__If) ).
thf(694,plain,
! [A: $o,B: a > $o,C: a > $o,D: a > $o] :
( ( A
=> ( ord_less_eq_a_o @ B @ C ) )
=> ( ( ~ A
=> ( ord_less_eq_a_o @ D @ C ) )
=> ( ord_less_eq_a_o @ ( if_a_o @ A @ B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(221,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ A @ C )
=> ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_le__infI) ).
thf(1107,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ A @ C )
=> ( ord_le519537037nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(275,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A = B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ( C = D )
=> ( ord_le519537037nres_a @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_ord__eq__le__eq__trans) ).
thf(1332,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A = B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ( C = D )
=> ( ord_le519537037nres_a @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(136,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
=> ~ ( ( ord_less_eq_a_o @ A @ B )
=> ~ ( ord_less_eq_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_le__infE) ).
thf(804,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
=> ~ ( ( ord_less_eq_a_o @ A @ B )
=> ~ ( ord_less_eq_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(102,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T) ).
thf(704,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(175,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( inf_inf_a_o @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_inf_Oabsorb1) ).
thf(947,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( inf_inf_a_o @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(105,axiom,
! [A: refine424419629nres_a] :
( ( inf_in262696383nres_a @ top_to231829469nres_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_inf__top_Oleft__neutral) ).
thf(713,plain,
! [A: refine424419629nres_a] :
( ( inf_in262696383nres_a @ top_to231829469nres_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(44,axiom,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ C ) @ ( inf_inf_set_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_inf__mono) ).
thf(498,plain,
! [A: set_a,B: set_a,C: set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ C ) @ ( inf_inf_set_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(186,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( refine412683989fail_a @ ( inf_in262696383nres_a @ A @ B ) )
= ( ( refine412683989fail_a @ A )
| ( refine412683989fail_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_pw__inf__nofail) ).
thf(979,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( refine412683989fail_a @ ( inf_in262696383nres_a @ A @ B ) )
= ( ( refine412683989fail_a @ A )
| ( refine412683989fail_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(267,axiom,
! [A: refine424419629nres_a,B: ( a > $o ) > refine424419629nres_a,C: a > $o,D: a > $o] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_ord__eq__le__subst) ).
thf(1282,plain,
! [A: refine424419629nres_a,B: ( a > $o ) > refine424419629nres_a,C: a > $o,D: a > $o] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(192,axiom,
! [A: set_a,B: set_a] :
( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
= ( inf_inf_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_inf_Oleft__idem) ).
thf(996,plain,
! [A: set_a,B: set_a] :
( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
= ( inf_inf_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(6,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( inf_inf_set_a @ B @ C ) )
= ( ( member_a @ A @ B )
& ( member_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_Int__iff) ).
thf(362,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( inf_inf_set_a @ B @ C ) )
= ( ( member_a @ A @ B )
& ( member_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(114,axiom,
( inf_inf_a_o
= ( ^ [A: a > $o,B: a > $o,C: a] : ( inf_inf_o @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_inf__apply) ).
thf(737,plain,
( inf_inf_a_o
= ( ^ [A: a > $o,B: a > $o,C: a] : ( inf_inf_o @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(294,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_ord__eq__le__subst) ).
thf(1439,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a > refine424419629nres_a,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le519537037nres_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_le519537037nres_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(239,axiom,
! [A: refine424419629nres_a,B: a > $o,C: a > $o] :
( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) )
=> ( ! [D: a] :
( ( B @ D )
=> ( C @ D ) )
=> ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_SPEC__cons__rule) ).
thf(1175,plain,
! [A: refine424419629nres_a,B: a > $o,C: a > $o] :
( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) )
=> ( ! [D: a] :
( ( B @ D )
=> ( C @ D ) )
=> ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(330,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > $o] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) )
=> ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_SPEC__trans) ).
thf(1574,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > $o] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) )
=> ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(21,axiom,
! [A: set_a,B: set_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_subsetI) ).
thf(419,plain,
! [A: set_a,B: set_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(309,axiom,
( refine2063221604TURN_a
= ( ^ [A: a] :
( refine1198353288_RES_a
@ ( collect_a
@ ^ [B: a] : ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_RETURN__SPEC__conv) ).
thf(1492,plain,
( refine2063221604TURN_a
= ( ^ [A: a] :
( refine1198353288_RES_a
@ ( collect_a
@ ^ [B: a] : ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(339,axiom,
! [A: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ! [D: refine424419629nres_a,E: refine424419629nres_a] : ( ord_le519537037nres_a @ ( A @ D @ E ) @ D )
=> ( ! [D: refine424419629nres_a,E: refine424419629nres_a] : ( ord_le519537037nres_a @ ( A @ D @ E ) @ E )
=> ( ! [D: refine424419629nres_a,E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ D @ E )
=> ( ( ord_le519537037nres_a @ D @ F )
=> ( ord_le519537037nres_a @ D @ ( A @ E @ F ) ) ) )
=> ( ( inf_in262696383nres_a @ B @ C )
= ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_inf__unique) ).
thf(1603,plain,
! [A: refine424419629nres_a > refine424419629nres_a > refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ! [D: refine424419629nres_a,E: refine424419629nres_a] : ( ord_le519537037nres_a @ ( A @ D @ E ) @ D )
=> ( ! [D: refine424419629nres_a,E: refine424419629nres_a] : ( ord_le519537037nres_a @ ( A @ D @ E ) @ E )
=> ( ! [D: refine424419629nres_a,E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ D @ E )
=> ( ( ord_le519537037nres_a @ D @ F )
=> ( ord_le519537037nres_a @ D @ ( A @ E @ F ) ) ) )
=> ( ( inf_in262696383nres_a @ B @ C )
= ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(86,axiom,
! [A: refine424419629nres_a] :
( ( inf_in262696383nres_a @ top_to231829469nres_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_inf__top__left) ).
thf(649,plain,
! [A: refine424419629nres_a] :
( ( inf_in262696383nres_a @ top_to231829469nres_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(206,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_antisym__conv) ).
thf(1043,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(157,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( inf_in262696383nres_a @ ( inf_in262696383nres_a @ A @ B ) @ C )
= ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_inf__sup__aci_I2_J) ).
thf(890,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( inf_in262696383nres_a @ ( inf_in262696383nres_a @ A @ B ) @ C )
= ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(42,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( inf_inf_set_a @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_le__iff__inf) ).
thf(494,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
( ( inf_inf_set_a @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(8,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_le__infD1) ).
thf(367,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(75,axiom,
! [A: refine424419629nres_a] :
( ( inf_in262696383nres_a @ bot_bo529555393nres_a @ A )
= bot_bo529555393nres_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_inf__bot__left) ).
thf(609,plain,
! [A: refine424419629nres_a] :
( ( inf_in262696383nres_a @ bot_bo529555393nres_a @ A )
= bot_bo529555393nres_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(72,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( top_to231829469nres_a
= ( inf_in262696383nres_a @ A @ B ) )
= ( ( A = top_to231829469nres_a )
& ( B = top_to231829469nres_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_top__eq__inf__iff) ).
thf(594,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( top_to231829469nres_a
= ( inf_in262696383nres_a @ A @ B ) )
= ( ( A = top_to231829469nres_a )
& ( B = top_to231829469nres_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(110,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ C )
= ( inf_inf_set_a @ A @ ( inf_inf_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_inf_Oassoc) ).
thf(726,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ C )
= ( inf_inf_set_a @ A @ ( inf_inf_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(39,axiom,
! [A: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ top_to231829469nres_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_inf__top__right) ).
thf(483,plain,
! [A: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ top_to231829469nres_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(324,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( inf_in262696383nres_a @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_inf_Oabsorb2) ).
thf(1556,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( inf_in262696383nres_a @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(169,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( inf_inf_a_o @ ( inf_inf_a_o @ A @ B ) @ C )
= ( inf_inf_a_o @ A @ ( inf_inf_a_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_inf__sup__aci_I2_J) ).
thf(932,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( inf_inf_a_o @ ( inf_inf_a_o @ A @ B ) @ C )
= ( inf_inf_a_o @ A @ ( inf_inf_a_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(237,axiom,
! [A: set_a,B: a > $o] :
( ord_less_eq_set_a
@ ( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
& ( B @ C ) ) )
@ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_Collect__restrict) ).
thf(1171,plain,
! [A: set_a,B: a > $o] :
( ord_less_eq_set_a
@ ( collect_a
@ ^ [C: a] :
( ( member_a @ C @ A )
& ( B @ C ) ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(14,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ A @ B ) )
= ( inf_in262696383nres_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_inf_Oleft__idem) ).
thf(399,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ A @ B ) )
= ( inf_in262696383nres_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(305,axiom,
! [A: set_a,B: set_a,C: set_a > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_le519537037nres_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_order__subst2) ).
thf(1474,plain,
! [A: set_a,B: set_a,C: set_a > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_le519537037nres_a @ ( C @ B ) @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(179,axiom,
! [A: set_a,B: set_a] :
( ( A
= ( inf_inf_set_a @ A @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_inf_OorderI) ).
thf(959,plain,
! [A: set_a,B: set_a] :
( ( A
= ( inf_inf_set_a @ A @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(257,axiom,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_RETURN__rule) ).
thf(1245,plain,
! [A: a > $o,B: a] :
( ( A @ B )
=> ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ B ) @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(31,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ A @ B ) )
= ( inf_in262696383nres_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_inf__left__idem) ).
thf(455,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ A @ B ) )
= ( inf_in262696383nres_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(147,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_subsetD) ).
thf(851,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(25,axiom,
! [A: a > $o,B: a > $o,C: a] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ord_less_eq_o @ ( A @ C ) @ ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_le__funD) ).
thf(438,plain,
! [A: a > $o,B: a > $o,C: a] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ord_less_eq_o @ ( A @ C ) @ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(249,axiom,
! [A: set_a,B: set_a,C: set_a > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_ord__le__eq__subst) ).
thf(1213,plain,
! [A: set_a,B: set_a,C: set_a > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(141,axiom,
( ( (=) @ ( a > $o ) )
= ( ^ [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ B @ A )
& ( ord_less_eq_a_o @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_dual__order_Oeq__iff) ).
thf(827,plain,
( ( (=) @ ( a > $o ) )
= ( ^ [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ B @ A )
& ( ord_less_eq_a_o @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(202,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_bot_Oextremum) ).
thf(1034,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ bot_bo529555393nres_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(334,axiom,
! [A: refine424419629nres_a,B: a > $o,C: a > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) )
=> ( ! [E: a] :
( ( B @ E )
=> ( ord_le519537037nres_a @ ( C @ E ) @ D ) )
=> ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_specify__left) ).
thf(1583,plain,
! [A: refine424419629nres_a,B: a > $o,C: a > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) )
=> ( ! [E: a] :
( ( B @ E )
=> ( ord_le519537037nres_a @ ( C @ E ) @ D ) )
=> ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(346,axiom,
! [A: set_a,B: set_a] :
( ( ( refine1198353288_RES_a @ A )
= ( refine1198353288_RES_a @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_nres_Oinject) ).
thf(1662,plain,
! [A: set_a,B: set_a] :
( ( ( refine1198353288_RES_a @ A )
= ( refine1198353288_RES_a @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(90,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( inf_inf_a_o @ ( inf_inf_a_o @ A @ B ) @ C )
= ( inf_inf_a_o @ A @ ( inf_inf_a_o @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_inf_Oassoc) ).
thf(663,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( inf_inf_a_o @ ( inf_inf_a_o @ A @ B ) @ C )
= ( inf_inf_a_o @ A @ ( inf_inf_a_o @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(216,axiom,
! [A: $o,B: refine424419629nres_a,C: a > $o,D: refine424419629nres_a] :
( ( A
=> ( ord_le519537037nres_a @ B @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) )
=> ( ( ~ A
=> ( ord_le519537037nres_a @ D @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) )
=> ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ A @ B @ D ) @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_if__rule) ).
thf(1081,plain,
! [A: $o,B: refine424419629nres_a,C: a > $o,D: refine424419629nres_a] :
( ( A
=> ( ord_le519537037nres_a @ B @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) )
=> ( ( ~ A
=> ( ord_le519537037nres_a @ D @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) )
=> ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ A @ B @ D ) @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(277,axiom,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_order__mono__setup_Orefl) ).
thf(1340,plain,
! [A: refine424419629nres_a] : ( ord_le519537037nres_a @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(304,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_inf__le1) ).
thf(1472,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(3,axiom,
! [A: a > $o,B: a > $o] :
( ( if_a_o @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001_062_Itf__a_M_Eo_J_T) ).
thf(355,plain,
! [A: a > $o,B: a > $o] :
( ( if_a_o @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(32,axiom,
( inf_inf_a_o
= ( ^ [A: a > $o,B: a > $o] : ( inf_inf_a_o @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_inf__sup__aci_I1_J) ).
thf(458,plain,
( inf_inf_a_o
= ( ^ [A: a > $o,B: a > $o] : ( inf_inf_a_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(208,axiom,
! [A: refine424419629nres_a > refine424419629nres_a > $o,B: refine424419629nres_a,C: refine424419629nres_a] :
( ! [D: refine424419629nres_a] : ( A @ D @ refine464223677AILi_a )
=> ( ! [D: set_a,E: set_a] : ( A @ ( refine1198353288_RES_a @ D ) @ ( refine1198353288_RES_a @ E ) )
=> ( ! [D: set_a] : ( A @ refine464223677AILi_a @ ( refine1198353288_RES_a @ D ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_less__eq__nres_Oinduct) ).
thf(1049,plain,
! [A: refine424419629nres_a > refine424419629nres_a > $o,B: refine424419629nres_a,C: refine424419629nres_a] :
( ! [D: refine424419629nres_a] : ( A @ D @ refine464223677AILi_a )
=> ( ! [D: set_a,E: set_a] : ( A @ ( refine1198353288_RES_a @ D ) @ ( refine1198353288_RES_a @ E ) )
=> ( ! [D: set_a] : ( A @ refine464223677AILi_a @ ( refine1198353288_RES_a @ D ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(36,axiom,
! [A: set_a,B: ( a > $o ) > set_a,C: a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_order__subst1) ).
thf(473,plain,
! [A: set_a,B: ( a > $o ) > set_a,C: a > $o,D: a > $o] :
( ( ord_less_eq_set_a @ A @ ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(215,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ ( C @ B ) @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_order__subst2) ).
thf(1076,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ ( C @ B ) @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(23,axiom,
! [A: set_a > set_a > set_a,B: set_a,C: set_a] :
( ! [D: set_a,E: set_a] : ( ord_less_eq_set_a @ ( A @ D @ E ) @ D )
=> ( ! [D: set_a,E: set_a] : ( ord_less_eq_set_a @ ( A @ D @ E ) @ E )
=> ( ! [D: set_a,E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ D @ E )
=> ( ( ord_less_eq_set_a @ D @ F )
=> ( ord_less_eq_set_a @ D @ ( A @ E @ F ) ) ) )
=> ( ( inf_inf_set_a @ B @ C )
= ( A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_inf__unique) ).
thf(426,plain,
! [A: set_a > set_a > set_a,B: set_a,C: set_a] :
( ! [D: set_a,E: set_a] : ( ord_less_eq_set_a @ ( A @ D @ E ) @ D )
=> ( ! [D: set_a,E: set_a] : ( ord_less_eq_set_a @ ( A @ D @ E ) @ E )
=> ( ! [D: set_a,E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ D @ E )
=> ( ( ord_less_eq_set_a @ D @ F )
=> ( ord_less_eq_set_a @ D @ ( A @ E @ F ) ) ) )
=> ( ( inf_inf_set_a @ B @ C )
= ( A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(236,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( A = B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ord__eq__le__trans) ).
thf(1166,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( A = B )
=> ( ( ord_le519537037nres_a @ B @ C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(246,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_SPEC__rule) ).
thf(1203,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(70,axiom,
! [A: set_a,B: set_a] :
( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ B )
= ( inf_inf_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_inf_Oright__idem) ).
thf(589,plain,
! [A: set_a,B: set_a] :
( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ B )
= ( inf_inf_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(132,axiom,
( inf_in262696383nres_a
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] : ( inf_in262696383nres_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_inf__commute) ).
thf(795,plain,
( inf_in262696383nres_a
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] : ( inf_in262696383nres_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(95,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
= ( inf_inf_set_a @ B @ ( inf_inf_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_inf_Oleft__commute) ).
thf(680,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
= ( inf_inf_set_a @ B @ ( inf_inf_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(127,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( inf_in262696383nres_a @ ( inf_in262696383nres_a @ A @ B ) @ C )
= ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_inf__assoc) ).
thf(776,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( inf_in262696383nres_a @ ( inf_in262696383nres_a @ A @ B ) @ C )
= ( inf_in262696383nres_a @ A @ ( inf_in262696383nres_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(52,axiom,
! [A: a > $o,B: a > $o,C: ( a > $o ) > set_a,D: set_a] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_ord__le__eq__subst) ).
thf(525,plain,
! [A: a > $o,B: a > $o,C: ( a > $o ) > set_a,D: set_a] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(67,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( inf_inf_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
= ( inf_inf_a_o @ B @ ( inf_inf_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_inf__left__commute) ).
thf(580,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( inf_inf_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
= ( inf_inf_a_o @ B @ ( inf_inf_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(233,axiom,
( ord_le519537037nres_a
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( inf_in262696383nres_a @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_inf_Oabsorb__iff2) ).
thf(1156,plain,
( ord_le519537037nres_a
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( inf_in262696383nres_a @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(327,axiom,
! [A: a,B: a > $o] :
( ( inf_in262696383nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) )
= ( refine1198353288_RES_a
@ ( collect_a
@ ^ [C: a] :
( ( C = A )
& ( B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_inf__RETURN__SPEC_I1_J) ).
thf(1566,plain,
! [A: a,B: a > $o] :
( ( inf_in262696383nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) )
= ( refine1198353288_RES_a
@ ( collect_a
@ ^ [C: a] :
( ( C = A )
& ( B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(115,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_eq__refl) ).
thf(739,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(218,axiom,
! [A: a,B: set_a,C: set_a,D: a > $o] :
( ( member_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_prop__restrict) ).
thf(1098,plain,
! [A: a,B: set_a,C: set_a,D: a > $o] :
( ( member_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B
@ ( collect_a
@ ^ [E: a] :
( ( member_a @ E @ C )
& ( D @ E ) ) ) )
=> ( D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(191,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_antisym__conv) ).
thf(993,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(287,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( A = B )
=> ( ord_le519537037nres_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_eq__refl) ).
thf(1400,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( A = B )
=> ( ord_le519537037nres_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(103,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( top_to231829469nres_a
= ( inf_in262696383nres_a @ A @ B ) )
= ( ( A = top_to231829469nres_a )
& ( B = top_to231829469nres_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_inf__top_Oneutr__eq__iff) ).
thf(707,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( top_to231829469nres_a
= ( inf_in262696383nres_a @ A @ B ) )
= ( ( A = top_to231829469nres_a )
& ( B = top_to231829469nres_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(311,axiom,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ bot_bo529555393nres_a )
=> ( A = bot_bo529555393nres_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_bot_Oextremum__uniqueI) ).
thf(1499,plain,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ bot_bo529555393nres_a )
=> ( A = bot_bo529555393nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(130,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
=> ( ord_less_eq_set_a @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_le__infD2) ).
thf(791,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
=> ( ord_less_eq_set_a @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(26,axiom,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( inf_inf_set_a @ B @ C ) )
=> ( member_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_IntD1) ).
thf(441,plain,
! [A: a,B: set_a,C: set_a] :
( ( member_a @ A @ ( inf_inf_set_a @ B @ C ) )
=> ( member_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(9,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_antisym) ).
thf(370,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(145,axiom,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_ord__eq__le__subst) ).
thf(840,plain,
! [A: set_a,B: set_a > set_a,C: set_a,D: set_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(137,axiom,
! [A: a > $o,B: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_inf__sup__ord_I2_J) ).
thf(808,plain,
! [A: a > $o,B: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(352,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( A
= ( inf_in262696383nres_a @ A @ B ) )
=> ( ord_le519537037nres_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_inf_OorderI) ).
thf(1679,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( A
= ( inf_in262696383nres_a @ A @ B ) )
=> ( ord_le519537037nres_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(332,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_inf__sup__ord_I1_J) ).
thf(1579,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] : ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(84,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_dual__order_Oantisym) ).
thf(643,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(35,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_order__class_Oorder_Oantisym) ).
thf(470,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(345,axiom,
! [A: refine424419629nres_a] :
( ( A != refine464223677AILi_a )
=> ~ ! [B: set_a] :
( A
!= ( refine1198353288_RES_a @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_nres_Oexhaust) ).
thf(1658,plain,
! [A: refine424419629nres_a] :
( ( A != refine464223677AILi_a )
=> ~ ! [B: set_a] :
( A
!= ( refine1198353288_RES_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(288,axiom,
! [A: a,B: set_a] :
( ( ( member_a @ A @ B )
=> ( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ B ) @ ( refine2063221604TURN_a @ A ) )
= ( refine2063221604TURN_a @ A ) ) )
& ( ~ ( member_a @ A @ B )
=> ( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ B ) @ ( refine2063221604TURN_a @ A ) )
= bot_bo529555393nres_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_inf__RETURN__RES_I2_J) ).
thf(1404,plain,
! [A: a,B: set_a] :
( ( ( member_a @ A @ B )
=> ( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ B ) @ ( refine2063221604TURN_a @ A ) )
= ( refine2063221604TURN_a @ A ) ) )
& ( ~ ( member_a @ A @ B )
=> ( ( inf_in262696383nres_a @ ( refine1198353288_RES_a @ B ) @ ( refine2063221604TURN_a @ A ) )
= bot_bo529555393nres_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(320,axiom,
! [A: a > $o,B: a,C: refine424419629nres_a,D: a > refine424419629nres_a] :
( ( A @ B )
=> ( ( ord_le519537037nres_a @ C @ ( D @ B ) )
=> ( ord_le519537037nres_a @ C @ ( refine436832838nd_a_a @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_le__SPEC__bindI) ).
thf(1543,plain,
! [A: a > $o,B: a,C: refine424419629nres_a,D: a > refine424419629nres_a] :
( ( A @ B )
=> ( ( ord_le519537037nres_a @ C @ ( D @ B ) )
=> ( ord_le519537037nres_a @ C @ ( refine436832838nd_a_a @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(261,axiom,
( ord_le519537037nres_a
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( A
= ( inf_in262696383nres_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_inf_Oorder__iff) ).
thf(1257,plain,
( ord_le519537037nres_a
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] :
( A
= ( inf_in262696383nres_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(200,axiom,
! [A: a > $o,B: refine424419629nres_a > a > $o,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_a_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a_o @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_ord__eq__le__subst) ).
thf(1023,plain,
! [A: a > $o,B: refine424419629nres_a > a > $o,C: refine424419629nres_a,D: refine424419629nres_a] :
( ( A
= ( B @ C ) )
=> ( ( ord_le519537037nres_a @ C @ D )
=> ( ! [E: refine424419629nres_a,F: refine424419629nres_a] :
( ( ord_le519537037nres_a @ E @ F )
=> ( ord_less_eq_a_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a_o @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(209,axiom,
! [A: set_a] :
( refine464223677AILi_a
!= ( refine1198353288_RES_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_nres_Odistinct_I1_J) ).
thf(1052,plain,
! [A: set_a] :
( refine464223677AILi_a
!= ( refine1198353288_RES_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(151,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ A @ C )
=> ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_inf__greatest) ).
thf(864,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ A @ C )
=> ( ord_less_eq_set_a @ A @ ( inf_inf_set_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(76,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
= ( inf_inf_set_a @ B @ ( inf_inf_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_inf__left__commute) ).
thf(612,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
= ( inf_inf_set_a @ B @ ( inf_inf_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(255,axiom,
! [A: refine424419629nres_a,B: a > $o,C: a > $o] :
( ( ord_le519537037nres_a @ A
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [D: a] :
( ( B @ D )
=> ( C @ D ) ) ) ) )
=> ( ( ord_le519537037nres_a @ A
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [D: a] :
( ~ ( B @ D )
=> ~ ( C @ D ) ) ) ) )
=> ( ord_le519537037nres_a @ A
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [D: a] :
( ( B @ D )
= ( C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_SPEC__iff) ).
thf(1240,plain,
! [A: refine424419629nres_a,B: a > $o,C: a > $o] :
( ( ord_le519537037nres_a @ A
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [D: a] :
( ( B @ D )
=> ( C @ D ) ) ) ) )
=> ( ( ord_le519537037nres_a @ A
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [D: a] :
( ~ ( B @ D )
=> ~ ( C @ D ) ) ) ) )
=> ( ord_le519537037nres_a @ A
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [D: a] :
( ( B @ D )
= ( C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(190,axiom,
( inf_inf_set_a
= ( ^ [A: set_a,B: set_a] : ( inf_inf_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_inf__commute) ).
thf(991,plain,
( inf_inf_set_a
= ( ^ [A: set_a,B: set_a] : ( inf_inf_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(80,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_ord__eq__le__trans) ).
thf(627,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( A = B )
=> ( ( ord_less_eq_set_a @ B @ C )
=> ( ord_less_eq_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(299,axiom,
! [A: set_a] : ( refine412683989fail_a @ ( refine1198353288_RES_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_nofail__simps_I2_J) ).
thf(1459,plain,
! [A: set_a] : ( refine412683989fail_a @ ( refine1198353288_RES_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(240,axiom,
! [A: refine424419629nres_a,B: set_a] :
( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ B ) )
=> ( refine412683989fail_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_le__RES__nofailI) ).
thf(1180,plain,
! [A: refine424419629nres_a,B: set_a] :
( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ B ) )
=> ( refine412683989fail_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(92,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T) ).
thf(671,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( if_Ref1724547303nres_a @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(185,axiom,
! [A: set_a] :
( ( inf_inf_set_a @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_inf_Oidem) ).
thf(976,plain,
! [A: set_a] :
( ( inf_inf_set_a @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(289,axiom,
! [A: a,B: set_a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( member_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_nres__order__simps_I21_J) ).
thf(1412,plain,
! [A: a,B: set_a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( member_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(121,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
= ( inf_inf_set_a @ B @ ( inf_inf_set_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_inf__sup__aci_I3_J) ).
thf(759,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ B @ C ) )
= ( inf_inf_set_a @ B @ ( inf_inf_set_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(295,axiom,
! [A: refine424419629nres_a,B: a > $o,C: a > $o] :
( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) )
=> ( ( ord_le519537037nres_a @ A
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [D: a] :
( ( B @ D )
=> ( C @ D ) ) ) ) )
=> ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_use__spec__rule) ).
thf(1448,plain,
! [A: refine424419629nres_a,B: a > $o,C: a > $o] :
( ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ B ) ) )
=> ( ( ord_le519537037nres_a @ A
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [D: a] :
( ( B @ D )
=> ( C @ D ) ) ) ) )
=> ( ord_le519537037nres_a @ A @ ( refine1198353288_RES_a @ ( collect_a @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(336,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ! [D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ D @ A )
=> ( ( ord_le519537037nres_a @ D @ B )
=> ( ord_le519537037nres_a @ D @ C ) ) )
=> ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_inf__leI) ).
thf(1590,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ! [D: refine424419629nres_a] :
( ( ord_le519537037nres_a @ D @ A )
=> ( ( ord_le519537037nres_a @ D @ B )
=> ( ord_le519537037nres_a @ D @ C ) ) )
=> ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(139,axiom,
! [A: a > $o,B: a > $o,C: a > $o,D: a > $o] :
( ( A
= ( inf_inf_a_o @ B @ C ) )
=> ( ( inf_inf_a_o @ D @ A )
= ( inf_inf_a_o @ B @ ( inf_inf_a_o @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_boolean__algebra__cancel_Oinf2) ).
thf(813,plain,
! [A: a > $o,B: a > $o,C: a > $o,D: a > $o] :
( ( A
= ( inf_inf_a_o @ B @ C ) )
=> ( ( inf_inf_a_o @ D @ A )
= ( inf_inf_a_o @ B @ ( inf_inf_a_o @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(50,axiom,
! [A: a > $o,B: a > $o,C: ( a > $o ) > a > $o,D: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ ( C @ B ) @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_a_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a_o @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_order__subst2) ).
thf(517,plain,
! [A: a > $o,B: a > $o,C: ( a > $o ) > a > $o,D: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ ( C @ B ) @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_a_o @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_a_o @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(159,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
=> ( ord_less_eq_a_o @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_le__infD2) ).
thf(896,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
=> ( ord_less_eq_a_o @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(350,axiom,
! [A: a > $o,B: a] :
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) @ B )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_nf__inres__SPEC) ).
thf(1674,plain,
! [A: a > $o,B: a] :
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) @ B )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(313,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_inf_OcoboundedI1) ).
thf(1508,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ord_le519537037nres_a @ ( inf_in262696383nres_a @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(219,axiom,
! [A: set_a,B: a > $o,C: a > $o] :
( ( ord_less_eq_set_a @ A
@ ( collect_a
@ ^ [D: a] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq_set_a @ A @ ( collect_a @ B ) )
& ( ord_less_eq_set_a @ A @ ( collect_a @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_conj__subset__def) ).
thf(1101,plain,
! [A: set_a,B: a > $o,C: a > $o] :
( ( ord_less_eq_set_a @ A
@ ( collect_a
@ ^ [D: a] :
( ( B @ D )
& ( C @ D ) ) ) )
= ( ( ord_less_eq_set_a @ A @ ( collect_a @ B ) )
& ( ord_less_eq_set_a @ A @ ( collect_a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(87,axiom,
! [A: a > $o,B: a > $o] :
( ( inf_inf_a_o @ A @ ( inf_inf_a_o @ A @ B ) )
= ( inf_inf_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_inf_Oleft__idem) ).
thf(652,plain,
! [A: a > $o,B: a > $o] :
( ( inf_inf_a_o @ A @ ( inf_inf_a_o @ A @ B ) )
= ( inf_inf_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(13,axiom,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_ord__le__eq__subst) ).
thf(390,plain,
! [A: set_a,B: set_a,C: set_a > set_a,D: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_set_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_set_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(81,axiom,
! [A: set_a,B: set_a] :
( ( inf_inf_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) )
= ( ^ [C: a] : ( member_a @ C @ ( inf_inf_set_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_inf__Int__eq) ).
thf(632,plain,
! [A: set_a,B: set_a] :
( ( inf_inf_a_o
@ ^ [C: a] : ( member_a @ C @ A )
@ ^ [C: a] : ( member_a @ C @ B ) )
= ( ^ [C: a] : ( member_a @ C @ ( inf_inf_set_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(308,axiom,
ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_assms_I1_J) ).
thf(1491,plain,
ord_le519537037nres_a @ a2 @ ( refine1198353288_RES_a @ ( collect_a @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(64,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ! [D: a > $o] :
( ( ord_less_eq_a_o @ D @ A )
=> ( ( ord_less_eq_a_o @ D @ B )
=> ( ord_less_eq_a_o @ D @ C ) ) )
=> ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_inf__leI) ).
thf(568,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ! [D: a > $o] :
( ( ord_less_eq_a_o @ D @ A )
=> ( ( ord_less_eq_a_o @ D @ B )
=> ( ord_less_eq_a_o @ D @ C ) ) )
=> ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(168,axiom,
! [A: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ top_to231829469nres_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_inf__top_Oright__neutral) ).
thf(929,plain,
! [A: refine424419629nres_a] :
( ( inf_in262696383nres_a @ A @ top_to231829469nres_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(37,axiom,
( inf_in262696383nres_a
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] : ( inf_in262696383nres_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_inf_Ocommute) ).
thf(478,plain,
( inf_in262696383nres_a
= ( ^ [A: refine424419629nres_a,B: refine424419629nres_a] : ( inf_in262696383nres_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(143,axiom,
! [A: a > $o,B: ( a > $o ) > a > $o,C: a > $o,D: a > $o] :
( ( ord_less_eq_a_o @ A @ ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_a_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a_o @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_order__subst1) ).
thf(832,plain,
! [A: a > $o,B: ( a > $o ) > a > $o,C: a > $o,D: a > $o] :
( ( ord_less_eq_a_o @ A @ ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_a_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a_o @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(54,axiom,
! [A: a > $o,B: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_inf_Ocobounded2) ).
thf(536,plain,
! [A: a > $o,B: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(106,axiom,
! [A: a > $o,B: a > $o] :
( ( inf_inf_a_o @ A @ ( inf_inf_a_o @ A @ B ) )
= ( inf_inf_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_inf__left__idem) ).
thf(716,plain,
! [A: a > $o,B: a > $o] :
( ( inf_inf_a_o @ A @ ( inf_inf_a_o @ A @ B ) )
= ( inf_inf_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(134,axiom,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_eq__iff) ).
thf(800,plain,
( ( (=) @ set_a )
= ( ^ [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
& ( ord_less_eq_set_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(224,axiom,
! [A: refine424419629nres_a,B: a > refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ B ) @ C )
= ( ord_le519537037nres_a @ A
@ ( if_Ref1724547303nres_a @ ( refine412683989fail_a @ C )
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [D: a] : ( ord_le519537037nres_a @ ( B @ D ) @ C ) ) )
@ top_to231829469nres_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_bind__le__shift) ).
thf(1116,plain,
! [A: refine424419629nres_a,B: a > refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ B ) @ C )
= ( ord_le519537037nres_a @ A
@ ( if_Ref1724547303nres_a @ ( refine412683989fail_a @ C )
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [D: a] : ( ord_le519537037nres_a @ ( B @ D ) @ C ) ) )
@ top_to231829469nres_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(228,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( B = C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_ord__le__eq__trans) ).
thf(1133,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( B = C )
=> ( ord_le519537037nres_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(280,axiom,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
= ( A = top_to231829469nres_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_nres__order__simps_I4_J) ).
thf(1348,plain,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ top_to231829469nres_a @ A )
= ( A = top_to231829469nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(193,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ A @ C )
=> ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_le__infI) ).
thf(999,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ A @ C )
=> ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(28,axiom,
( inf_inf_set_a
= ( ^ [A: set_a,B: set_a] : ( inf_inf_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_inf_Ocommute) ).
thf(447,plain,
( inf_inf_set_a
= ( ^ [A: set_a,B: set_a] : ( inf_inf_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(176,axiom,
! [A: set_a,B: set_a] :
( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
= ( inf_inf_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_inf__sup__aci_I4_J) ).
thf(950,plain,
! [A: set_a,B: set_a] :
( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
= ( inf_inf_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(321,axiom,
! [A: set_a,B: set_a] :
( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_less__eq__nres_Osimps_I2_J) ).
thf(1546,plain,
! [A: set_a,B: set_a] :
( ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ A ) @ ( refine1198353288_RES_a @ B ) )
= ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(140,axiom,
! [A: set_a,B: ( a > $o ) > set_a,C: a > $o,D: a > $o] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_ord__eq__le__subst) ).
thf(818,plain,
! [A: set_a,B: ( a > $o ) > set_a,C: a > $o,D: a > $o] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_less_eq_set_a @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_set_a @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(16,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ A @ C )
=> ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_inf_OboundedI) ).
thf(405,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ A @ C )
=> ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(148,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_order_Otrans) ).
thf(854,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ B @ C )
=> ( ord_less_eq_a_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(315,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_dual__order_Oantisym) ).
thf(1527,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(152,axiom,
! [A: a > $o,B: a > $o] :
( ( inf_inf_a_o @ ( inf_inf_a_o @ A @ B ) @ B )
= ( inf_inf_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_inf__right__idem) ).
thf(867,plain,
! [A: a > $o,B: a > $o] :
( ( inf_inf_a_o @ ( inf_inf_a_o @ A @ B ) @ B )
= ( inf_inf_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(10,axiom,
! [A: set_a,B: set_a] :
( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
= ( inf_inf_set_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_inf__left__idem) ).
thf(373,plain,
! [A: set_a,B: set_a] :
( ( inf_inf_set_a @ A @ ( inf_inf_set_a @ A @ B ) )
= ( inf_inf_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(113,axiom,
( ord_less_eq_a_o
= ( ^ [A: a > $o,B: a > $o] :
! [C: a] : ( ord_less_eq_o @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_le__fun__def) ).
thf(735,plain,
( ord_less_eq_a_o
= ( ^ [A: a > $o,B: a > $o] :
! [C: a] : ( ord_less_eq_o @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(293,axiom,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ bot_bo529555393nres_a )
= ( A = bot_bo529555393nres_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_nres__order__simps_I2_J) ).
thf(1436,plain,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ bot_bo529555393nres_a )
= ( A = bot_bo529555393nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(164,axiom,
( ord_less_eq_a_o
= ( ^ [A: a > $o,B: a > $o] :
( A
= ( inf_inf_a_o @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_inf_Oorder__iff) ).
thf(918,plain,
( ord_less_eq_a_o
= ( ^ [A: a > $o,B: a > $o] :
( A
= ( inf_inf_a_o @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(273,axiom,
! [A: a > $o,B: a > $o,C: ( a > $o ) > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_ord__le__eq__subst) ).
thf(1314,plain,
! [A: a > $o,B: a > $o,C: ( a > $o ) > refine424419629nres_a,D: refine424419629nres_a] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: a > $o,F: a > $o] :
( ( ord_less_eq_a_o @ E @ F )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_le519537037nres_a @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(4,axiom,
! [A: a > $o,B: a > $o] :
( ( if_a_o @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001_062_Itf__a_M_Eo_J_T) ).
thf(358,plain,
! [A: a > $o,B: a > $o] :
( ( if_a_o @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(124,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ! [D: set_a] :
( ( ord_less_eq_set_a @ D @ A )
=> ( ( ord_less_eq_set_a @ D @ B )
=> ( ord_less_eq_set_a @ D @ C ) ) )
=> ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_inf__leI) ).
thf(767,plain,
! [A: set_a,B: set_a,C: set_a] :
( ! [D: set_a] :
( ( ord_less_eq_set_a @ D @ A )
=> ( ( ord_less_eq_set_a @ D @ B )
=> ( ord_less_eq_set_a @ D @ C ) ) )
=> ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(210,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_order__class_Oorder_Oantisym) ).
thf(1056,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ( ord_le519537037nres_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(82,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( A
= ( inf_inf_set_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_inf_OorderE) ).
thf(635,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( A
= ( inf_inf_set_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(212,axiom,
! [A: set_a] :
( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ A ) )
= ( ^ [B: a] : ( member_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_inres__simps_I2_J) ).
thf(1065,plain,
! [A: set_a] :
( ( refine1001002027nres_a @ ( refine1198353288_RES_a @ A ) )
= ( ^ [B: a] : ( member_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(79,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ C )
= ( inf_inf_set_a @ A @ ( inf_inf_set_a @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_inf__assoc) ).
thf(624,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( inf_inf_set_a @ ( inf_inf_set_a @ A @ B ) @ C )
= ( inf_inf_set_a @ A @ ( inf_inf_set_a @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(263,axiom,
! [A: set_a,B: a > $o] :
( ( ord_less_eq_set_a @ A @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( member_a @ C @ A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_subset__Collect__conv) ).
thf(1261,plain,
! [A: set_a,B: a > $o] :
( ( ord_less_eq_set_a @ A @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( member_a @ C @ A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(66,axiom,
! [A: a > $o,B: set_a > a > $o,C: set_a,D: set_a] :
( ( ord_less_eq_a_o @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_a_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a_o @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_order__subst1) ).
thf(575,plain,
! [A: a > $o,B: set_a > a > $o,C: set_a,D: set_a] :
( ( ord_less_eq_a_o @ A @ ( B @ C ) )
=> ( ( ord_less_eq_set_a @ C @ D )
=> ( ! [E: set_a,F: set_a] :
( ( ord_less_eq_set_a @ E @ F )
=> ( ord_less_eq_a_o @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_a_o @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(232,axiom,
! [A: a > $o,B: refine424419629nres_a] :
( ! [C: a] :
( ( A @ C )
=> ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ C ) @ B ) )
=> ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_lhs__step__SPEC) ).
thf(1152,plain,
! [A: a > $o,B: refine424419629nres_a] :
( ! [C: a] :
( ( A @ C )
=> ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ C ) @ B ) )
=> ( ord_le519537037nres_a @ ( refine1198353288_RES_a @ ( collect_a @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(318,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_Collect__mono__iff) ).
thf(1537,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_set_a @ ( collect_a @ A ) @ ( collect_a @ B ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(270,axiom,
! [A: set_a,B: a] :
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ A ) @ B )
= ( member_a @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_nf__inres__RES) ).
thf(1299,plain,
! [A: set_a,B: a] :
( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ A ) @ B )
= ( member_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(99,axiom,
! [A: a > $o,B: a > $o,C: a > $o,D: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ C ) @ ( inf_inf_a_o @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_inf__mono) ).
thf(691,plain,
! [A: a > $o,B: a > $o,C: a > $o,D: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( ord_less_eq_a_o @ C @ D )
=> ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ C ) @ ( inf_inf_a_o @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(226,axiom,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine424419629nres_a,D: a > refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ! [E: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ E ) @ A )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ C ) @ ( refine436832838nd_a_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J) ).
thf(1120,plain,
! [A: refine424419629nres_a,B: refine424419629nres_a,C: a > refine424419629nres_a,D: a > refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ B )
=> ( ! [E: a] :
( ( ord_le519537037nres_a @ ( refine2063221604TURN_a @ E ) @ A )
=> ( ord_le519537037nres_a @ ( C @ E ) @ ( D @ E ) ) )
=> ( ord_le519537037nres_a @ ( refine436832838nd_a_a @ A @ C ) @ ( refine436832838nd_a_a @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(45,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( inf_inf_a_o @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_inf__absorb1) ).
thf(501,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( inf_inf_a_o @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(187,axiom,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_le__infI1) ).
thf(982,plain,
! [A: set_a,B: set_a,C: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(195,axiom,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( inf_inf_a_o @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_inf__absorb2) ).
thf(1004,plain,
! [A: a > $o,B: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ( inf_inf_a_o @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(40,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_le__infI1) ).
thf(486,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ B )
=> ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1,conjecture,
( ord_le519537037nres_a @ a2
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [A: a] :
( ( p @ A )
& ( q @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_le519537037nres_a @ a2
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [A: a] :
( ( p @ A )
& ( q @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(354,plain,
~ ( ord_le519537037nres_a @ a2
@ ( refine1198353288_RES_a
@ ( collect_a
@ ^ [A: a] :
( ( p @ A )
& ( q @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(166,axiom,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
=> ( ord_less_eq_a_o @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_le__infD1) ).
thf(923,plain,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ord_less_eq_a_o @ A @ ( inf_inf_a_o @ B @ C ) )
=> ( ord_less_eq_a_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(301,axiom,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ bot_bo529555393nres_a )
= ( A = bot_bo529555393nres_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_bot_Oextremum__unique) ).
thf(1463,plain,
! [A: refine424419629nres_a] :
( ( ord_le519537037nres_a @ A @ bot_bo529555393nres_a )
= ( A = bot_bo529555393nres_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(57,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( inf_inf_set_a @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_inf__absorb1) ).
thf(543,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( inf_inf_set_a @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(71,axiom,
! [A: a > $o,B: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_inf__sup__ord_I1_J) ).
thf(592,plain,
! [A: a > $o,B: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(43,axiom,
( inf_inf_set_a
= ( ^ [A: set_a,B: set_a] : ( inf_inf_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_inf__sup__aci_I1_J) ).
thf(496,plain,
( inf_inf_set_a
= ( ^ [A: set_a,B: set_a] : ( inf_inf_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(183,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_subset__eq) ).
thf(972,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(343,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_mem__Collect__eq) ).
thf(1653,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(172,axiom,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_inf__le1) ).
thf(940,plain,
! [A: set_a,B: set_a] : ( ord_less_eq_set_a @ ( inf_inf_set_a @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(170,axiom,
! [A: a > $o,B: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_inf_Ocobounded1) ).
thf(935,plain,
! [A: a > $o,B: a > $o] : ( ord_less_eq_a_o @ ( inf_inf_a_o @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(197,axiom,
! [A: a] :
( ( refine1198353288_RES_a @ ( collect_a @ ( (=) @ a @ A ) ) )
= ( refine2063221604TURN_a @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_SPEC__eq__is__RETURN_I1_J) ).
thf(1009,plain,
! [A: a] :
( ( refine1198353288_RES_a @ ( collect_a @ ( (=) @ a @ A ) ) )
= ( refine2063221604TURN_a @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(1944,plain,
$false,
inference(e,[status(thm)],[1665,1036,1337,1469,365,1454,1559,1237,893,666,1549,962,468,1554,1110,1200,408,683,1068,1569,1073,655,677,597,1173,1158,762,873,449,1671,945,538,1222,1164,797,1342,913,829,898,1391,782,1046,1386,565,1254,724,719,504,1264,802,1577,1059,460,1323,619,1511,702,751,559,638,1147,1247,870,1479,1494,969,606,1572,1398,881,416,1415,1040,376,1418,646,1682,937,1020,1677,1581,1183,480,1302,756,687,877,956,1394,1351,660,1433,1600,507,1119,774,411,1345,988,1104,1242,849,1651,452,920,810,381,512,942,546,793,1311,534,910,746,862,1502,729,1032,361,435,1296,1457,1195,551,974,1012,583,522,1210,1656,1291,710,1259,1534,615,1227,1540,1138,857,1089,1234,1461,901,489,1207,554,753,1612,1039,837,1114,1451,1530,1231,1668,721,1002,779,1588,985,515,1150,1249,541,1563,765,1466,1616,586,926,1187,674,953,1185,1278,965,1273,1595,573,689,444,562,423,402,732,1125,772,1388,743,1488,413,1007,694,1107,1332,804,704,947,713,498,979,1282,996,362,737,1439,1175,1574,419,1492,1603,649,1043,890,494,367,609,594,726,483,1556,932,1171,399,1474,959,1245,455,851,438,1213,827,1034,1583,1662,663,1081,1340,1472,355,458,1049,473,1076,426,1166,1203,589,795,680,776,525,580,1156,1566,739,1098,993,1400,707,1499,791,441,370,840,808,1679,1579,643,470,1658,1404,1543,1257,1023,1052,864,612,1240,991,627,1459,1180,671,976,1412,759,1448,1590,813,517,896,1674,1508,1101,652,390,632,1491,568,929,478,832,536,716,800,1116,1133,1348,999,447,950,1546,818,405,854,1527,867,373,735,1436,918,1314,358,767,1056,635,1065,624,1261,575,1152,1537,1299,691,1120,501,982,1004,486,354,923,1463,543,592,496,972,1653,940,935,1009]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP162^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.19 % Computer : n004.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 20:04:07 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.92/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.45/1.26 % [INFO] Parsing done (486ms).
% 2.45/1.27 % [INFO] Running in sequential loop mode.
% 3.92/1.61 % [INFO] eprover registered as external prover.
% 3.92/1.62 % [INFO] Scanning for conjecture ...
% 3.92/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 356 axioms. Running axiom selection ...
% 4.54/1.81 % [INFO] Axiom selection finished. Selected 351 axioms (removed 5 axioms).
% 5.00/2.01 % [INFO] Problem is higher-order (TPTP THF).
% 5.00/2.03 % [INFO] Type checking passed.
% 5.00/2.03 % [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 ...
% 22.59/5.98 % External prover 'e' found a proof!
% 22.59/5.98 % [INFO] Killing All external provers ...
% 22.59/5.98 % Time passed: 5647ms (effective reasoning time: 4696ms)
% 22.59/5.98 % 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)>
% 22.59/5.98 % Axioms used in derivation (351): fact_26_Refine__Misc_Oif__mono, fact_68_order__class_Oorder_Oantisym, fact_232_inf__absorb1, fact_187_inf__sup__ord_I2_J, fact_158_inf_Ocommute, fact_227_inf_Oabsorb1, fact_203_le__infI, fact_240_inf_OboundedI, fact_104_ord__le__eq__subst, fact_293_less__nres_Oinduct, fact_207_le__infI1, fact_136_inf_Oleft__idem, fact_129_inf__apply, fact_306_nres__order__simps_I21_J, fact_80_antisym__conv, fact_225_inf_Oabsorb1, fact_220_inf__unique, fact_289_nres_Odistinct_I1_J, fact_143_inf_Oright__idem, fact_180_inf__sup__aci_I3_J, fact_284_subset__Collect__conv, fact_282_Collect__restrict, fact_95_eq__iff, fact_161_inf__assoc, fact_236_inf__absorb2, fact_14_SPEC__cons__rule, fact_213_inf_OorderE, fact_132_inf_Oidem, fact_127_le__inf__iff, fact_212_le__infI2, fact_292_sup__nres_Oinduct, fact_144_inf_Oright__idem, fact_243_inf__greatest, fact_255_inf_Oabsorb__iff2, fact_290_nres_Oinduct, fact_174_inf__sup__aci_I1_J, fact_108_ord__eq__le__subst, fact_100_ord__le__eq__subst, fact_268_Int__def, fact_42_le__infD1, fact_333_bind__rule__complete, fact_215_inf_OorderE, fact_192_inf__le1, fact_246_inf_Oorder__iff, fact_189_inf__sup__ord_I1_J, fact_23_le__funI, fact_223_le__iff__inf, fact_97_ord__le__eq__subst, fact_305_nres__order__simps_I20_J, fact_70_ord__le__eq__trans, fact_64_order__trans, fact_190_inf__sup__ord_I1_J, fact_241_inf_OboundedI, fact_280_subset__Collect__iff, fact_183_inf__sup__aci_I4_J, fact_228_inf_Oabsorb2, fact_221_inf__unique, fact_239_inf_OboundedE, fact_286_inf__nres_Oelims, fact_311_SPEC__eq__is__RETURN_I1_J, help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T, fact_230_inf_Oabsorb2, fact_18_the__RES_Osimps, fact_178_inf__sup__aci_I2_J, fact_76_order__class_Oorder_Oeq__iff, fact_134_inf__idem, fact_343_inf__top_Oleft__neutral, fact_300_less__eq__nres_Oelims_I3_J, fact_67_order__class_Oorder_Oantisym, fact_259_Collect__subset, fact_16_order__mono__setup_Orefl, fact_340_inf__eq__top__iff, fact_173_inf__fun__def, fact_118_order__subst2, fact_288_inf__nres_Osimps_I1_J, fact_31_order__subst1, fact_181_inf__sup__aci_I3_J, fact_152_inf_Oleft__commute, fact_211_le__infI2, fact_264_Int__iff, fact_278_subsetD, fact_275_Collect__mono, fact_162_inf__assoc, fact_62_dual__order_Orefl, fact_78_antisym__conv, fact_7_SPEC__iff, fact_112_ord__eq__le__subst, fact_146_inf__right__idem, fact_66_order__class_Oorder_Oantisym, fact_209_le__infI1, fact_179_inf__sup__aci_I2_J, fact_307_inf__RETURN__SPEC_I2_J, fact_120_order__subst2, fact_121_order__subst2, fact_135_inf__idem, fact_140_inf__left__idem, fact_226_inf_Oabsorb1, fact_341_top__eq__inf__iff, fact_51_dual__order_Oantisym, fact_323_inf__bot__left, fact_149_inf__left__commute, fact_322_inf__bot__right, fact_262_conj__subset__def, fact_93_eq__iff, fact_165_inf_Oassoc, fact_344_inf__top_Oneutr__eq__iff, fact_172_boolean__algebra__cancel_Oinf1, fact_46_less__eq__nres_Osimps_I2_J, fact_332_nres__order__simps_I1_J, fact_12_lhs__step__If, fact_274_Collect__mono__iff, fact_32_order__subst1, fact_131_inf_Oidem, fact_194_inf__le1, fact_266_IntD1, fact_198_le__infE, fact_164_inf_Oassoc, fact_176_inf__sup__aci_I1_J, fact_167_boolean__algebra__cancel_Oinf2, fact_124_inf_Obounded__iff, fact_237_inf_OboundedE, fact_265_IntE, fact_298_less__eq__nres_Oelims_I1_J, fact_186_inf__sup__ord_I2_J, fact_58_dual__order_Otrans, fact_317_lhs__step__RES, fact_301_Greatest__equality, fact_50_order__mono__setup_Omono__if, fact_217_inf_OorderI, fact_175_inf__sup__aci_I1_J, fact_117_order__subst2, fact_87_eq__refl, fact_40_le__infD1, fact_345_inf__top_Oright__neutral, fact_130_inf_Oidem, fact_69_ord__le__eq__trans, fact_85_order_Otrans, fact_35_order__subst1, fact_328_SUCCEED__rule, fact_258_subsetI, fact_37_le__infD2, fact_294_less__eq__nres_Oinduct, fact_155_inf__commute, fact_251_inf_Ocobounded1, fact_21_le__funD, fact_244_inf__greatest, fact_197_inf__le2, fact_45_inf__leI, fact_347_nres__order__simps_I4_J, fact_57_dual__order_Otrans, fact_210_le__infI2, fact_253_inf_Ocobounded2, fact_75_order__class_Oorder_Oeq__iff, fact_206_inf__mono, fact_249_inf_Ocobounded1, fact_109_ord__eq__le__subst, fact_91_antisym, fact_299_less__eq__nres_Oelims_I2_J, fact_267_IntD2, fact_77_order__class_Oorder_Oeq__iff, fact_324_nres__order__simps_I2_J, fact_156_inf__commute, fact_54_dual__order_Oeq__iff, fact_53_dual__order_Oantisym, fact_218_inf_OorderI, fact_20_nf__inres__SPEC, fact_41_le__infD1, fact_295_less__eq__nres_Osimps_I1_J, fact_15_order__mono__setup_Orefl, fact_334_specify__left, fact_119_order__subst2, fact_92_antisym, fact_276_subset__iff, fact_222_le__iff__inf, fact_202_le__infI, fact_90_antisym, fact_154_inf_Oleft__commute, fact_339_inf__top__right, fact_71_ord__le__eq__trans, fact_248_inf_Oorder__iff, fact_63_order__trans, fact_142_inf_Oright__idem, fact_56_dual__order_Oeq__iff, fact_216_inf_OorderI, fact_138_inf_Oleft__idem, fact_320_inf__RETURN__RES_I2_J, fact_326_le__SPEC__bindI, fact_269_Int__Collect, fact_22_le__funE, fact_231_inf__absorb1, fact_151_inf__left__commute, fact_208_le__infI1, fact_34_order__subst1, fact_123_inf_Obounded__iff, fact_28_order__subst1, fact_205_inf__mono, fact_273_Int__Collect__mono, fact_245_inf__greatest, help_If_1_1_If_001_062_Itf__a_M_Eo_J_T, fact_133_inf__idem, fact_193_inf__le1, fact_169_boolean__algebra__cancel_Oinf2, fact_336_bind__le__nofailI, fact_261_pred__subset__eq, fact_283_ord__eq__le__eq__trans, fact_297_inf__nres_Osimps_I2_J, fact_327_RES__bind__choose, fact_348_nres__more__simps_I1_J, fact_148_inf__nres_Osimps_I3_J, fact_177_inf__sup__aci_I2_J, fact_147_inf__right__idem, fact_106_ord__eq__le__subst, fact_98_ord__le__eq__subst, fact_145_inf__right__idem, fact_1_nres_Oinject, fact_36_order__subst1, fact_60_dual__order_Orefl, fact_25_Refine__Misc_Oif__mono, fact_5_if__rule, fact_110_ord__eq__le__subst, fact_277_subset__eq, fact_44_inf__leI, fact_116_order__subst2, fact_242_inf_OboundedI, fact_99_ord__le__eq__subst, fact_113_ord__eq__le__subst, fact_199_le__infE, fact_279_in__mono, fact_107_ord__eq__le__subst, fact_287_GreatestI2__order, fact_86_order_Otrans, fact_114_order__subst2, fact_263_IntI, fact_2_assms_I2_J, fact_188_inf__sup__ord_I2_J, fact_4__092_060open_062A_A_092_060le_062_Ainf_A_ISPEC_AP_J_A_ISPEC_AQ_J_092_060close_062, fact_9_SPEC__trans, fact_157_inf__commute, fact_272_Collect__conj__eq, fact_254_inf_Oabsorb__iff1, fact_171_boolean__algebra__cancel_Oinf1, fact_233_inf__absorb1, fact_315_le__RES__nofailI, fact_82_Collect__mem__eq, fact_219_inf__unique, fact_27_le__fun__def, fact_19_nf__inres__RES, fact_159_inf_Ocommute, fact_43_inf__leI, fact_335_bind__rule, fact_319_lhs__step__SPEC, fact_252_inf_Ocobounded2, fact_303_inf__RETURN__SPEC_I1_J, fact_3_assms_I1_J, fact_325_Refine__Basic__Mirabelle__kwjuvthmas_Obind__mono_I1_J, fact_150_inf__left__commute, fact_79_antisym__conv, fact_337_bind__le__shift, fact_308_pwD1, fact_271_inf__Int__eq, fact_141_inf__left__idem, fact_318_RETURN__to__SPEC__rule, fact_257_inf_OcoboundedI2, fact_102_ord__le__eq__subst, fact_302_the__RES__inv, fact_170_boolean__algebra__cancel_Oinf1, fact_304_nofail__simps_I2_J, fact_346_inres__simps_I2_J, fact_338_inf__top__left, fact_122_order__subst2, fact_247_inf_Oorder__iff, fact_168_boolean__algebra__cancel_Oinf2, fact_201_le__infI, help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T, fact_238_inf_OboundedE, fact_126_le__inf__iff, fact_163_inf__assoc, fact_65_order__trans, fact_59_dual__order_Otrans, fact_195_inf__le2, fact_200_le__infE, fact_309_le__nofailI, fact_125_inf_Obounded__iff, help_If_3_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T, fact_96_ord__le__eq__subst, fact_89_eq__refl, fact_281_subset__CollectI, fact_115_order__subst2, fact_94_eq__iff, fact_11_lhs__step__If, fact_103_ord__le__eq__subst, fact_88_eq__refl, fact_61_dual__order_Orefl, fact_160_inf_Ocommute, fact_72_ord__eq__le__trans, fact_137_inf_Oleft__idem, fact_29_order__subst1, fact_39_le__infD2, fact_33_order__subst1, fact_55_dual__order_Oeq__iff, fact_331_bot_Oextremum, fact_139_inf__left__idem, fact_81_mem__Collect__eq, fact_153_inf_Oleft__commute, fact_49_order__mono__setup_Omono__if, fact_234_inf__absorb2, fact_314_pw__inf__nofail, fact_111_ord__eq__le__subst, fact_17_order__mono__setup_Orefl, fact_330_bot_Oextremum__unique, fact_296_less__eq__nres_Osimps_I3_J, fact_47_nres__order__simps_I5_J, fact_196_inf__le2, fact_0_nres__more__simps_I4_J, fact_235_inf__absorb2, fact_312_RETURN__SPEC__conv, fact_342_inf__top_Oeq__neutr__iff, fact_316_RETURN__rule, fact_73_ord__eq__le__trans, fact_166_inf_Oassoc, fact_250_inf_Ocobounded1, fact_224_le__iff__inf, fact_229_inf_Oabsorb2, fact_74_ord__eq__le__trans, fact_270_inf__set__def, fact_204_inf__mono, fact_38_le__infD2, fact_191_inf__sup__ord_I1_J, fact_52_dual__order_Oantisym, fact_30_order__subst1, fact_6_RES__rule, fact_105_ord__eq__le__subst, fact_321_inf__RETURN__RES_I1_J, fact_182_inf__sup__aci_I3_J, fact_101_ord__le__eq__subst, fact_256_inf_OcoboundedI1, fact_8_SPEC__rule, fact_291_nres_Oexhaust, fact_184_inf__sup__aci_I4_J, fact_214_inf_OorderE, fact_285_prop__restrict, fact_83_Collect__cong, fact_260_less__eq__set__def, fact_329_bot_Oextremum__uniqueI, fact_185_inf__sup__aci_I4_J, fact_13_use__spec__rule, fact_310_nofail__RES__conv, help_If_2_1_If_001_062_Itf__a_M_Eo_J_T, fact_128_le__inf__iff, fact_84_order_Otrans, fact_313_SPEC__eq__is__RETURN_I2_J
% 22.59/5.98 % No. of inferences in proof: 706
% 22.59/5.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5647 ms resp. 4696 ms w/o parsing
% 24.41/6.32 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 24.41/6.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------