TSTP Solution File: DAT115^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT115^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:39:30 EDT 2024
% Result : Theorem 15.16s 4.67s
% Output : Refutation 15.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 234
% Syntax : Number of formulae : 443 ( 212 unt; 27 typ; 0 def)
% Number of atoms : 1362 ( 418 equ; 6 cnn)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 6764 ( 216 ~; 36 |; 106 &;5952 @)
% ( 0 <=>; 454 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 9 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 368 ( 368 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 8 con; 0-8 aty)
% Number of variables : 1910 ( 66 ^1754 !; 58 ?;1910 :)
% ( 32 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(coindu1928975208n_lset_type,type,
coindu1928975208n_lset:
!>[TA: $tType] : ( ( set @ TA ) > ( coindu1593790203_llist @ TA ) > ( set @ TA ) ) ).
thf(coindu268472904append_type,type,
coindu268472904append:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu1213758845finite_type,type,
coindu1213758845finite:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > $o ) ).
thf(coindu1121789889_LCons_type,type,
coindu1121789889_LCons:
!>[TA: $tType] : ( TA > ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu1598213697e_LNil_type,type,
coindu1598213697e_LNil:
!>[TA: $tType] : ( coindu1593790203_llist @ TA ) ).
thf(coindu882539134_llist_type,type,
coindu882539134_llist:
!>[TA: $tType,TB: $tType] : ( TB > ( TA > ( coindu1593790203_llist @ TA ) > TB ) > ( coindu1593790203_llist @ TA ) > TB ) ).
thf(coindu1244876290_llist_type,type,
coindu1244876290_llist:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TB > TA ) > ( TB > $o ) > ( TB > ( coindu1593790203_llist @ TA ) ) > ( TB > TB ) > TB > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu1046438764le_lhd_type,type,
coindu1046438764le_lhd:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > TA ) ).
thf(coindu987187967t_all2_type,type,
coindu987187967t_all2:
!>[TA: $tType,TB: $tType] : ( ( TB > TA > $o ) > ( coindu1593790203_llist @ TB ) > ( coindu1593790203_llist @ TA ) > $o ) ).
thf(coindu335574135_lnull_type,type,
coindu335574135_lnull:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > $o ) ).
thf(coindu1112613586e_lset_type,type,
coindu1112613586e_lset:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > ( set @ TA ) ) ).
thf(coindu1047225960le_ltl_type,type,
coindu1047225960le_ltl:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) ) ).
thf(coindu567634248member_type,type,
coindu567634248member:
!>[TA: $tType] : ( TA > ( coindu1593790203_llist @ TA ) > $o ) ).
thf(coindu1696667936prefix_type,type,
coindu1696667936prefix:
!>[TA: $tType] : ( ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o ) ).
thf(coindu1599971794_llist_type,type,
coindu1599971794_llist:
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TB > TA ) > ( TB > TB ) > TB > ( coindu1593790203_llist @ TA ) ) ).
thf(if_type,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(sup_sup_type,type,
sup_sup:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(produc2004651681e_prod_type,type,
produc2004651681e_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_rec_prod_type,type,
product_rec_prod:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TB > TA ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(xs_type,type,
xs: coindu1593790203_llist @ a ).
thf(ys_type,type,
ys: coindu1593790203_llist @ a ).
thf(zs_type,type,
zs: coindu1593790203_llist @ a ).
thf(92,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_Un__upper1) ).
thf(515,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(205,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu268472904append @ TA @ ( coindu268472904append @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ ( coindu1598213697e_LNil @ TA ) ) ) @ C )
= ( coindu268472904append @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_lappend__snocL1__conv__LCons2) ).
thf(892,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu268472904append @ TA @ ( coindu268472904append @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ ( coindu1598213697e_LNil @ TA ) ) ) @ C )
= ( coindu268472904append @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(125,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_subsetCE) ).
thf(629,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(83,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu1121789889_LCons @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_lset__intros_I2_J) ).
thf(479,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu1121789889_LCons @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(43,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: ( coindu1593790203_llist @ TA ) > $o] :
( ( coindu1213758845finite @ TA @ A )
=> ( ! [C: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ C )
=> ( B @ C ) )
=> ( ! [C: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ C )
=> ( ~ ( coindu335574135_lnull @ TA @ C )
=> ( ( B @ ( coindu1047225960le_ltl @ TA @ C ) )
=> ( B @ C ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_lfinite__induct) ).
thf(333,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: ( coindu1593790203_llist @ TA ) > $o] :
( ( coindu1213758845finite @ TA @ A )
=> ( ! [C: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ C )
=> ( B @ C ) )
=> ( ! [C: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ C )
=> ( ~ ( coindu335574135_lnull @ TA @ C )
=> ( ( B @ ( coindu1047225960le_ltl @ TA @ C ) )
=> ( B @ C ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B )
= ( coindu1121789889_LCons @ TB @ ( C @ B ) @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_unfold__llist_Octr_I2_J) ).
thf(234,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B )
= ( coindu1121789889_LCons @ TB @ ( C @ B ) @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(84,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_mem__Collect__eq) ).
thf(481,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_old_Oprod_Orec) ).
thf(408,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( product_rec_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(143,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_rev__subsetD) ).
thf(683,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(37,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Collect__mem__eq) ).
thf(308,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(157,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ A @ ( coindu268472904append @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_lprefix__lappend) ).
thf(741,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ A @ ( coindu268472904append @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(73,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( ( coindu1121789889_LCons @ TA @ A @ B )
= ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_llist_Oinject) ).
thf(449,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( ( coindu1121789889_LCons @ TA @ A @ B )
= ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coindu1593790203_llist @ TB,C: coindu1593790203_llist @ TA] :
( ( coindu987187967t_all2 @ TB @ TA @ A @ B @ C )
=> ( ( ( B
= ( coindu1598213697e_LNil @ TB ) )
=> ( C
!= ( coindu1598213697e_LNil @ TA ) ) )
=> ~ ! [D: TB,E: coindu1593790203_llist @ TB] :
( ( B
= ( coindu1121789889_LCons @ TB @ D @ E ) )
=> ! [F: TA,G: coindu1593790203_llist @ TA] :
( ( C
= ( coindu1121789889_LCons @ TA @ F @ G ) )
=> ( ( A @ D @ F )
=> ~ ( coindu987187967t_all2 @ TB @ TA @ A @ E @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_llist_Orel__cases) ).
thf(379,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coindu1593790203_llist @ TB,C: coindu1593790203_llist @ TA] :
( ( coindu987187967t_all2 @ TB @ TA @ A @ B @ C )
=> ( ( ( B
= ( coindu1598213697e_LNil @ TB ) )
=> ( C
!= ( coindu1598213697e_LNil @ TA ) ) )
=> ~ ! [D: TB,E: coindu1593790203_llist @ TB] :
( ( B
= ( coindu1121789889_LCons @ TB @ D @ E ) )
=> ! [F: TA,G: coindu1593790203_llist @ TA] :
( ( C
= ( coindu1121789889_LCons @ TA @ F @ G ) )
=> ( ( A @ D @ F )
=> ~ ( coindu987187967t_all2 @ TB @ TA @ A @ E @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(120,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_prod__cases3) ).
thf(614,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(111,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] : ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_lset__intros_I1_J) ).
thf(582,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] : ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(165,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu268472904append @ TA @ ( coindu1047225960le_ltl @ TA @ A ) @ B )
= ( coindu1047225960le_ltl @ TA @ ( coindu268472904append @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_lappend__ltl) ).
thf(762,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu268472904append @ TA @ ( coindu1047225960le_ltl @ TA @ A ) @ B )
= ( coindu1047225960le_ltl @ TA @ ( coindu268472904append @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(156,axiom,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ D @ E )
=> ( ? [F: coindu1593790203_llist @ TA] :
( ( D
= ( coindu1598213697e_LNil @ TA ) )
& ( E = F ) )
| ? [F: coindu1593790203_llist @ TA,G: coindu1593790203_llist @ TA,H: TA] :
( ( D
= ( coindu1121789889_LCons @ TA @ H @ F ) )
& ( E
= ( coindu1121789889_LCons @ TA @ H @ G ) )
& ( ( A @ F @ G )
| ( coindu1696667936prefix @ TA @ F @ G ) ) ) ) )
=> ( coindu1696667936prefix @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_lprefix_Ocoinduct) ).
thf(730,plain,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ D @ E )
=> ( ? [F: coindu1593790203_llist @ TA] :
( ( D
= ( coindu1598213697e_LNil @ TA ) )
& ( E = F ) )
| ? [F: coindu1593790203_llist @ TA,G: coindu1593790203_llist @ TA,H: TA] :
( ( D
= ( coindu1121789889_LCons @ TA @ H @ F ) )
& ( E
= ( coindu1121789889_LCons @ TA @ H @ G ) )
& ( ( A @ F @ G )
| ( coindu1696667936prefix @ TA @ F @ G ) ) ) ) )
=> ( coindu1696667936prefix @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(25,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_bex__Un) ).
thf(276,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ? [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
& ( C @ D ) ) )
= ( ? [D: TA] :
( ( member @ TA @ D @ A )
& ( C @ D ) )
| ? [D: TA] :
( ( member @ TA @ D @ B )
& ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(199,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
=> ~ ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_lprefix__not__lnullD) ).
thf(878,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
=> ~ ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(132,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu1047225960le_ltl @ TA @ A ) )
= ( coindu1213758845finite @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_lfinite__ltl) ).
thf(655,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu1047225960le_ltl @ TA @ A ) )
= ( coindu1213758845finite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(153,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_surj__pair) ).
thf(715,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
? [B: TB,C: TA] :
( A
= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(99,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( coindu1213758845finite @ TA @ ( coindu1121789889_LCons @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_lfinite__LConsI) ).
thf(538,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( coindu1213758845finite @ TA @ ( coindu1121789889_LCons @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(138,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1599971794_llist @ ( coindu1593790203_llist @ TA ) @ TA @ ( coindu335574135_lnull @ TA ) @ ( coindu1046438764le_lhd @ TA ) @ ( coindu1047225960le_ltl @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_unfold__llist__id) ).
thf(670,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1599971794_llist @ ( coindu1593790203_llist @ TA ) @ TA @ ( coindu335574135_lnull @ TA ) @ ( coindu1046438764le_lhd @ TA ) @ ( coindu1047225960le_ltl @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(207,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1047225960le_ltl @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( coindu1047225960le_ltl @ TA @ B ) ) )
& ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1047225960le_ltl @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( coindu268472904append @ TA @ ( coindu1047225960le_ltl @ TA @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ltl__lappend) ).
thf(898,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1047225960le_ltl @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( coindu1047225960le_ltl @ TA @ B ) ) )
& ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1047225960le_ltl @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( coindu268472904append @ TA @ ( coindu1047225960le_ltl @ TA @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(109,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > TA > $o] :
( ! [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ A ) )
=> ( B @ C @ C ) )
=> ( coindu987187967t_all2 @ TA @ TA @ B @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_llist_Orel__refl__strong) ).
thf(565,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA > TA > $o] :
( ! [C: TA] :
( ( member @ TA @ C @ ( coindu1112613586e_lset @ TA @ A ) )
=> ( B @ C @ C ) )
=> ( coindu987187967t_all2 @ TA @ TA @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( coindu1593790203_llist @ TB ),F: TA > TA] :
( ~ ( A @ B )
=> ~ ( coindu335574135_lnull @ TB @ ( coindu1244876290_llist @ TA @ TB @ A @ C @ D @ E @ F @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_llist_Ocorec__disc_I2_J) ).
thf(257,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( coindu1593790203_llist @ TB ),F: TA > TA] :
( ~ ( A @ B )
=> ~ ( coindu335574135_lnull @ TB @ ( coindu1244876290_llist @ TA @ TB @ A @ C @ D @ E @ F @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType] :
( ( coindu987187967t_all2 @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TB] :
( ( ( coindu335574135_lnull @ TA @ B )
= ( coindu335574135_lnull @ TB @ C ) )
& ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ~ ( coindu335574135_lnull @ TB @ C )
=> ( ( A @ ( coindu1046438764le_lhd @ TA @ B ) @ ( coindu1046438764le_lhd @ TB @ C ) )
& ( coindu987187967t_all2 @ TA @ TB @ A @ ( coindu1047225960le_ltl @ TA @ B ) @ ( coindu1047225960le_ltl @ TB @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_llist_Orel__sel) ).
thf(372,plain,
! [TA: $tType,TB: $tType] :
( ( coindu987187967t_all2 @ TA @ TB )
= ( ^ [A: TA > TB > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TB] :
( ( ( coindu335574135_lnull @ TA @ B )
= ( coindu335574135_lnull @ TB @ C ) )
& ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ~ ( coindu335574135_lnull @ TB @ C )
=> ( ( A @ ( coindu1046438764le_lhd @ TA @ B ) @ ( coindu1046438764le_lhd @ TB @ C ) )
& ( coindu987187967t_all2 @ TA @ TB @ A @ ( coindu1047225960le_ltl @ TA @ B ) @ ( coindu1047225960le_ltl @ TB @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TA,C: coindu1593790203_llist @ TA] :
~ ( coindu987187967t_all2 @ TB @ TA @ A @ ( coindu1598213697e_LNil @ TB ) @ ( coindu1121789889_LCons @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_llist_Orel__distinct_I1_J) ).
thf(344,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TA,C: coindu1593790203_llist @ TA] :
~ ( coindu987187967t_all2 @ TB @ TA @ A @ ( coindu1598213697e_LNil @ TB ) @ ( coindu1121789889_LCons @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > ( coindu1593790203_llist @ TA ) > TB,D: coindu1593790203_llist @ TA] :
( ( A @ ( coindu882539134_llist @ TB @ TA @ B @ C @ D ) )
= ( ( ( D
= ( coindu1598213697e_LNil @ TA ) )
=> ( A @ B ) )
& ( ( D
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) )
=> ( A @ ( C @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_llist_Osplit__sel) ).
thf(357,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > ( coindu1593790203_llist @ TA ) > TB,D: coindu1593790203_llist @ TA] :
( ( A @ ( coindu882539134_llist @ TB @ TA @ B @ C @ D ) )
= ( ( ( D
= ( coindu1598213697e_LNil @ TA ) )
=> ( A @ B ) )
& ( ( D
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) )
=> ( A @ ( C @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_old_Oprod_Oexhaust) ).
thf(542,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(150,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: ( coindu1593790203_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [D: coindu1593790203_llist @ TA] : ( C @ ( coindu1121789889_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ E ) )
=> ( ( C @ E )
=> ( C @ ( coindu1121789889_LCons @ TA @ D @ E ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_lset__induct_H) ).
thf(702,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: ( coindu1593790203_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [D: coindu1593790203_llist @ TA] : ( C @ ( coindu1121789889_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ E ) )
=> ( ( C @ E )
=> ( C @ ( coindu1121789889_LCons @ TA @ D @ E ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(161,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ ( coindu1598213697e_LNil @ TA ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_LNil__lprefix) ).
thf(751,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ ( coindu1598213697e_LNil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(183,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( ( A
= ( coindu1598213697e_LNil @ TA ) )
=> ! [C: coindu1593790203_llist @ TA] : ( B != C ) )
=> ~ ! [C: coindu1593790203_llist @ TA,D: coindu1593790203_llist @ TA,E: TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ E @ C ) )
=> ( ( B
= ( coindu1121789889_LCons @ TA @ E @ D ) )
=> ~ ( coindu1696667936prefix @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_lprefix_Ocases) ).
thf(817,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( ( A
= ( coindu1598213697e_LNil @ TA ) )
=> ! [C: coindu1593790203_llist @ TA] : ( B != C ) )
=> ~ ! [C: coindu1593790203_llist @ TA,D: coindu1593790203_llist @ TA,E: TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ E @ C ) )
=> ( ( B
= ( coindu1121789889_LCons @ TA @ E @ D ) )
=> ~ ( coindu1696667936prefix @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(107,axiom,
! [TA: $tType,A: set @ TA] :
( ( coindu1928975208n_lset @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_gen__lset__code_I1_J) ).
thf(559,plain,
! [TA: $tType,A: set @ TA] :
( ( coindu1928975208n_lset @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(117,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_prod__cases5) ).
thf(606,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_prod__cases) ).
thf(416,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(29,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_Un__iff) ).
thf(289,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( ( member @ TA @ A @ B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA] :
( ( ~ ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ D ) ) )
= ( ~ ( A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_unfold__llist_Odisc__iff_I2_J) ).
thf(261,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA] :
( ( ~ ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ D ) ) )
= ( ~ ( A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(5,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__cong) ).
thf(216,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(163,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( ( coindu335574135_lnull @ TA @ A )
& ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_lnull__lappend) ).
thf(756,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( ( coindu335574135_lnull @ TA @ A )
& ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(175,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu268472904append @ TA @ ( coindu1598213697e_LNil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_lappend__code_I1_J) ).
thf(789,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu268472904append @ TA @ ( coindu1598213697e_LNil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(115,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ( ( A @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1598213697e_LNil @ TB ) ) )
& ( ~ ( A @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_ltl__unfold__llist) ).
thf(591,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ( ( A @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1598213697e_LNil @ TB ) ) )
& ( ~ ( A @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(71,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_Un__absorb1) ).
thf(443,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(47,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA > ( coindu1593790203_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [D: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TA @ D )
=> ( C @ ( coindu1046438764le_lhd @ TA @ D ) @ D ) )
=> ( ! [D: coindu1593790203_llist @ TA,E: TA] :
( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ( member @ TA @ E @ ( coindu1112613586e_lset @ TA @ ( coindu1047225960le_ltl @ TA @ D ) ) )
=> ( ( C @ E @ ( coindu1047225960le_ltl @ TA @ D ) )
=> ( C @ E @ D ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_llist__set__induct) ).
thf(348,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA > ( coindu1593790203_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [D: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TA @ D )
=> ( C @ ( coindu1046438764le_lhd @ TA @ D ) @ D ) )
=> ( ! [D: coindu1593790203_llist @ TA,E: TA] :
( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ( member @ TA @ E @ ( coindu1112613586e_lset @ TA @ ( coindu1047225960le_ltl @ TA @ D ) ) )
=> ( ( C @ E @ ( coindu1047225960le_ltl @ TA @ D ) )
=> ( C @ E @ D ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(145,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1046438764le_lhd @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_lhd__LCons) ).
thf(687,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1046438764le_lhd @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(127,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1598213697e_LNil @ TA )
!= ( coindu1121789889_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_llist_Odistinct_I1_J) ).
thf(634,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1598213697e_LNil @ TA )
!= ( coindu1121789889_LCons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(57,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu1047225960le_ltl @ TA @ B ) ) )
=> ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_in__lset__ltlD) ).
thf(396,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu1047225960le_ltl @ TA @ B ) ) )
=> ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(134,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_prod__induct7) ).
thf(660,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF,I: TG] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ ( product_prod @ TF @ TG ) ) @ F @ ( product_Pair @ TE @ ( product_prod @ TF @ TG ) @ G @ ( product_Pair @ TF @ TG @ H @ I ) ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coindu1593790203_llist @ TB,C: coindu1593790203_llist @ TA,D: TB > TA > $o] :
( ( coindu987187967t_all2 @ TB @ TA @ A @ B @ C )
=> ( ! [E: TB,F: TA] :
( ( member @ TB @ E @ ( coindu1112613586e_lset @ TB @ B ) )
=> ( ( member @ TA @ F @ ( coindu1112613586e_lset @ TA @ C ) )
=> ( ( A @ E @ F )
=> ( D @ E @ F ) ) ) )
=> ( coindu987187967t_all2 @ TB @ TA @ D @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_llist_Orel__mono__strong) ).
thf(411,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: coindu1593790203_llist @ TB,C: coindu1593790203_llist @ TA,D: TB > TA > $o] :
( ( coindu987187967t_all2 @ TB @ TA @ A @ B @ C )
=> ( ! [E: TB,F: TA] :
( ( member @ TB @ E @ ( coindu1112613586e_lset @ TB @ B ) )
=> ( ( member @ TA @ F @ ( coindu1112613586e_lset @ TA @ C ) )
=> ( ( A @ E @ F )
=> ( D @ E @ F ) ) ) )
=> ( coindu987187967t_all2 @ TB @ TA @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( coindu987187967t_all2 @ TB @ TA @ A @ ( coindu1598213697e_LNil @ TB ) @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_llist_Octr__transfer_I1_J) ).
thf(243,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o] : ( coindu987187967t_all2 @ TB @ TA @ A @ ( coindu1598213697e_LNil @ TB ) @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TB > TA,D: TB > $o,E: TB > ( coindu1593790203_llist @ TA ),F: TB > TB] :
( ( A @ B )
=> ( ( coindu1244876290_llist @ TB @ TA @ A @ C @ D @ E @ F @ B )
= ( coindu1598213697e_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_llist_Ocorec_I1_J) ).
thf(265,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TB > TA,D: TB > $o,E: TB > ( coindu1593790203_llist @ TA ),F: TB > TB] :
( ( A @ B )
=> ( ( coindu1244876290_llist @ TB @ TA @ A @ C @ D @ E @ F @ B )
= ( coindu1598213697e_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(30,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
= ( ? [B: TA,C: coindu1593790203_llist @ TA] :
( A
= ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_neq__LNil__conv) ).
thf(292,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
= ( ? [B: TA,C: coindu1593790203_llist @ TA] :
( A
= ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(74,axiom,
! [TA: $tType] : ( coindu1213758845finite @ TA @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_lfinite__code_I1_J) ).
thf(452,plain,
! [TA: $tType] : ( coindu1213758845finite @ TA @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(16,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > $o,D: TA > ( coindu1593790203_llist @ TB ),E: TA > TA,F: TA] :
( ( ~ ( coindu335574135_lnull @ TB @ ( coindu1244876290_llist @ TA @ TB @ A @ B @ C @ D @ E @ F ) ) )
= ( ~ ( A @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_llist_Ocorec__disc__iff_I2_J) ).
thf(248,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > $o,D: TA > ( coindu1593790203_llist @ TB ),E: TA > TA,F: TA] :
( ( ~ ( coindu335574135_lnull @ TB @ ( coindu1244876290_llist @ TA @ TB @ A @ B @ C @ D @ E @ F ) ) )
= ( ~ ( A @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( coindu1593790203_llist @ TA ) > TB,C: TA,D: coindu1593790203_llist @ TA] :
( ( coindu882539134_llist @ TB @ TA @ A @ B @ ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_llist_Osimps_I5_J) ).
thf(512,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > ( coindu1593790203_llist @ TA ) > TB,C: TA,D: coindu1593790203_llist @ TA] :
( ( coindu882539134_llist @ TB @ TA @ A @ B @ ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(141,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_Un__left__commute) ).
thf(678,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
= ( sup_sup @ ( set @ TA ) @ B @ ( sup_sup @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(181,axiom,
( ( coindu1213758845finite @ a @ xs )
=> ( coindu1696667936prefix @ a @ ys @ zs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062lfinite_Axs_A_092_060longrightarrow_062_Ays_A_092_060sqsubseteq_062_Azs_092_060close_062) ).
thf(810,plain,
( ( coindu1213758845finite @ a @ xs )
=> ( coindu1696667936prefix @ a @ ys @ zs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(159,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
~ ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_lprefix__code_I2_J) ).
thf(746,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
~ ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(171,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ A )
| ~ ( coindu335574135_lnull @ TA @ B ) )
=> ~ ( coindu335574135_lnull @ TA @ ( coindu268472904append @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_lappend_Odisc_I2_J) ).
thf(778,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ A )
| ~ ( coindu335574135_lnull @ TA @ B ) )
=> ~ ( coindu335574135_lnull @ TA @ ( coindu268472904append @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(34,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_subsetD) ).
thf(302,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(194,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( ( coindu1213758845finite @ TA @ A )
& ( coindu1213758845finite @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_lfinite__lappend) ).
thf(862,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( ( coindu1213758845finite @ TA @ A )
& ( coindu1213758845finite @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_prod__cases6) ).
thf(297,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(147,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_lhd__LCons__ltl) ).
thf(693,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(85,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ( A
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_llist_Oexhaust__sel) ).
thf(484,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ( A
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(17,axiom,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA] :
( ! [C: TA] : ( A @ C @ C )
=> ( coindu987187967t_all2 @ TA @ TA @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_llist_Orel__refl) ).
thf(252,plain,
! [TA: $tType,A: TA > TA > $o,B: coindu1593790203_llist @ TA] :
( ! [C: TA] : ( A @ C @ C )
=> ( coindu987187967t_all2 @ TA @ TA @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(136,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_Collect__mono) ).
thf(665,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) )
=> ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(88,axiom,
! [TA: $tType,A: TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu567634248member @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( ( A = B )
| ( coindu567634248member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_lmember__code_I2_J) ).
thf(493,plain,
! [TA: $tType,A: TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu567634248member @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( ( A = B )
| ( coindu567634248member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_old_Oprod_Oinject) ).
thf(551,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(40,axiom,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_Un__absorb) ).
thf(324,plain,
! [TA: $tType,A: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > ( coindu1593790203_llist @ TA ) > TB,D: coindu1593790203_llist @ TA] :
( ( A @ ( coindu882539134_llist @ TB @ TA @ B @ C @ D ) )
= ( ~ ( ( ( D
= ( coindu1598213697e_LNil @ TA ) )
& ~ ( A @ B ) )
| ( ( D
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) )
& ~ ( A @ ( C @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_llist_Osplit__sel__asm) ).
thf(522,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TA > ( coindu1593790203_llist @ TA ) > TB,D: coindu1593790203_llist @ TA] :
( ( A @ ( coindu882539134_llist @ TB @ TA @ B @ C @ D ) )
= ( ~ ( ( ( D
= ( coindu1598213697e_LNil @ TA ) )
& ~ ( A @ B ) )
| ( ( D
= ( coindu1121789889_LCons @ TA @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) )
& ~ ( A @ ( C @ ( coindu1046438764le_lhd @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(184,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ ( coindu268472904append @ TA @ A @ B ) ) )
= ( ~ ( coindu335574135_lnull @ TA @ A )
| ~ ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_lappend_Odisc__iff_I2_J) ).
thf(830,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ ( coindu268472904append @ TA @ A @ B ) ) )
= ( ~ ( coindu335574135_lnull @ TA @ A )
| ~ ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(76,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_UnCI) ).
thf(456,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(188,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu335574135_lnull @ TA @ B )
=> ( ( coindu268472904append @ TA @ A @ B )
= ( coindu1598213697e_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_lappend_Octr_I1_J) ).
thf(842,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu335574135_lnull @ TA @ B )
=> ( ( coindu268472904append @ TA @ A @ B )
= ( coindu1598213697e_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(197,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: set @ ( product_prod @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) )] :
( ( member @ ( product_prod @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) ) @ ( product_Pair @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) @ A @ B ) @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( member @ ( product_prod @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) ) @ ( product_Pair @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) @ D @ E ) @ C )
=> ( ( coindu335574135_lnull @ TA @ D )
| ? [F: TA,G: coindu1593790203_llist @ TA,H: coindu1593790203_llist @ TA] :
( ( D
= ( coindu1121789889_LCons @ TA @ F @ G ) )
& ( E
= ( coindu1121789889_LCons @ TA @ F @ H ) )
& ( ( member @ ( product_prod @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) ) @ ( product_Pair @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) @ G @ H ) @ C )
| ( coindu1696667936prefix @ TA @ G @ H ) ) ) ) )
=> ( coindu1696667936prefix @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_lprefixI) ).
thf(869,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: set @ ( product_prod @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) )] :
( ( member @ ( product_prod @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) ) @ ( product_Pair @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) @ A @ B ) @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( member @ ( product_prod @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) ) @ ( product_Pair @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) @ D @ E ) @ C )
=> ( ( coindu335574135_lnull @ TA @ D )
| ? [F: TA,G: coindu1593790203_llist @ TA,H: coindu1593790203_llist @ TA] :
( ( D
= ( coindu1121789889_LCons @ TA @ F @ G ) )
& ( E
= ( coindu1121789889_LCons @ TA @ F @ H ) )
& ( ( member @ ( product_prod @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) ) @ ( product_Pair @ ( coindu1593790203_llist @ TA ) @ ( coindu1593790203_llist @ TA ) @ G @ H ) @ C )
| ( coindu1696667936prefix @ TA @ G @ H ) ) ) ) )
=> ( coindu1696667936prefix @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(65,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= ( coindu1213758845finite @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_lfinite__LCons) ).
thf(420,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= ( coindu1213758845finite @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(90,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: ( coindu1593790203_llist @ TA ) > $o] :
( ( coindu1213758845finite @ TA @ A )
=> ( ( B @ ( coindu1598213697e_LNil @ TA ) )
=> ( ! [C: coindu1593790203_llist @ TA,D: TA] :
( ( coindu1213758845finite @ TA @ C )
=> ( ( B @ C )
=> ( B @ ( coindu1121789889_LCons @ TA @ D @ C ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_lfinite_Oinducts) ).
thf(499,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: ( coindu1593790203_llist @ TA ) > $o] :
( ( coindu1213758845finite @ TA @ A )
=> ( ( B @ ( coindu1598213697e_LNil @ TA ) )
=> ( ! [C: coindu1593790203_llist @ TA,D: TA] :
( ( coindu1213758845finite @ TA @ C )
=> ( ( B @ C )
=> ( B @ ( coindu1121789889_LCons @ TA @ D @ C ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(80,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_prod__cases4) ).
thf(471,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(202,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ C )
= ( ? [D: coindu1593790203_llist @ TA] :
( ( C
= ( coindu1121789889_LCons @ TA @ A @ D ) )
& ( coindu1696667936prefix @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_LCons__lprefix__conv) ).
thf(884,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ C )
= ( ? [D: coindu1593790203_llist @ TA] :
( ( C
= ( coindu1121789889_LCons @ TA @ A @ D ) )
& ( coindu1696667936prefix @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > $o,D: TA > TB,E: TA > ( coindu1593790203_llist @ TB ),F: TA > TA] :
( ~ ( A @ B )
=> ( ( ( C @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1244876290_llist @ TA @ TB @ A @ D @ C @ E @ F @ B ) )
= ( E @ B ) ) )
& ( ~ ( C @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1244876290_llist @ TA @ TB @ A @ D @ C @ E @ F @ B ) )
= ( coindu1244876290_llist @ TA @ TB @ A @ D @ C @ E @ F @ ( F @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_llist_Ocorec__sel_I2_J) ).
thf(225,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > $o,D: TA > TB,E: TA > ( coindu1593790203_llist @ TB ),F: TA > TA] :
( ~ ( A @ B )
=> ( ( ( C @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1244876290_llist @ TA @ TB @ A @ D @ C @ E @ F @ B ) )
= ( E @ B ) ) )
& ( ~ ( C @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1244876290_llist @ TA @ TB @ A @ D @ C @ E @ F @ B ) )
= ( coindu1244876290_llist @ TA @ TB @ A @ D @ C @ E @ F @ ( F @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(128,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
= ( coindu335574135_lnull @ TA @ B ) )
=> ( ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ( ( coindu1046438764le_lhd @ TA @ A )
= ( coindu1046438764le_lhd @ TA @ B ) )
& ( ( coindu1047225960le_ltl @ TA @ A )
= ( coindu1047225960le_ltl @ TA @ B ) ) ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_llist_Oexpand) ).
thf(637,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
= ( coindu335574135_lnull @ TA @ B ) )
=> ( ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
=> ( ( ( coindu1046438764le_lhd @ TA @ A )
= ( coindu1046438764le_lhd @ TA @ B ) )
& ( ( coindu1047225960le_ltl @ TA @ A )
= ( coindu1047225960le_ltl @ TA @ B ) ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(151,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: ( coindu1593790203_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [D: coindu1593790203_llist @ TA] : ( C @ ( coindu1121789889_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ E ) )
=> ( ( A != D )
=> ( ( C @ E )
=> ( C @ ( coindu1121789889_LCons @ TA @ D @ E ) ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_lset__induct) ).
thf(706,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: ( coindu1593790203_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [D: coindu1593790203_llist @ TA] : ( C @ ( coindu1121789889_LCons @ TA @ A @ D ) )
=> ( ! [D: TA,E: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ E ) )
=> ( ( A != D )
=> ( ( C @ E )
=> ( C @ ( coindu1121789889_LCons @ TA @ D @ E ) ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(105,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ A ) )
= ( ? [B: TA,C: coindu1593790203_llist @ TA] :
( A
= ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_not__lnull__conv) ).
thf(554,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ A ) )
= ( ? [B: TA,C: coindu1593790203_llist @ TA] :
( A
= ( coindu1121789889_LCons @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(162,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( ( coindu1112613586e_lset @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ ( coindu1112613586e_lset @ TA @ A ) @ ( coindu1112613586e_lset @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_lset__lappend__lfinite) ).
thf(753,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( ( coindu1112613586e_lset @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ ( coindu1112613586e_lset @ TA @ A ) @ ( coindu1112613586e_lset @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA] :
( ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ D ) )
= ( A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_unfold__llist_Odisc__iff_I1_J) ).
thf(237,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA] :
( ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ D ) )
= ( A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(176,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1696667936prefix @ TA @ B @ A )
= ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_lprefix__lnull) ).
thf(792,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1696667936prefix @ TA @ B @ A )
= ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(49,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA > ( coindu1593790203_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [D: TA,E: coindu1593790203_llist @ TA] : ( C @ D @ ( coindu1121789889_LCons @ TA @ D @ E ) )
=> ( ! [D: TA,E: coindu1593790203_llist @ TA,F: TA] :
( ( member @ TA @ F @ ( coindu1112613586e_lset @ TA @ E ) )
=> ( ( C @ F @ E )
=> ( C @ F @ ( coindu1121789889_LCons @ TA @ D @ E ) ) ) )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_llist_Oset__induct) ).
thf(360,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA > ( coindu1593790203_llist @ TA ) > $o] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [D: TA,E: coindu1593790203_llist @ TA] : ( C @ D @ ( coindu1121789889_LCons @ TA @ D @ E ) )
=> ( ! [D: TA,E: coindu1593790203_llist @ TA,F: TA] :
( ( member @ TA @ F @ ( coindu1112613586e_lset @ TA @ E ) )
=> ( ( C @ F @ E )
=> ( C @ F @ ( coindu1121789889_LCons @ TA @ D @ E ) ) ) )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(38,axiom,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_set__eq__subset) ).
thf(311,plain,
! [TA: $tType] :
( ( (=) @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
& ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(166,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ C @ A ) @ ( coindu1121789889_LCons @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_Le__LCons) ).
thf(765,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ C @ A ) @ ( coindu1121789889_LCons @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(58,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_equalityD2) ).
thf(398,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_prod_Oinject) ).
thf(586,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(135,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_subset__antisym) ).
thf(662,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(154,axiom,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ D @ E )
=> ( ( ( coindu335574135_lnull @ TA @ E )
=> ( coindu335574135_lnull @ TA @ D ) )
& ( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ~ ( coindu335574135_lnull @ TA @ E )
=> ( ( ( coindu1046438764le_lhd @ TA @ D )
= ( coindu1046438764le_lhd @ TA @ E ) )
& ( ( A @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) )
| ( coindu1696667936prefix @ TA @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) ) ) ) ) ) ) )
=> ( coindu1696667936prefix @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_lprefix__coinduct) ).
thf(718,plain,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ D @ E )
=> ( ( ( coindu335574135_lnull @ TA @ E )
=> ( coindu335574135_lnull @ TA @ D ) )
& ( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ~ ( coindu335574135_lnull @ TA @ E )
=> ( ( ( coindu1046438764le_lhd @ TA @ D )
= ( coindu1046438764le_lhd @ TA @ E ) )
& ( ( A @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) )
| ( coindu1696667936prefix @ TA @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) ) ) ) ) ) ) )
=> ( coindu1696667936prefix @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(67,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_UnI2) ).
thf(425,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(192,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu268472904append @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_lappend__LNil2) ).
thf(856,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu268472904append @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(26,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ C ) )
=> ~ ( coindu335574135_lnull @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_llist_OdiscI_I2_J) ).
thf(279,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ C ) )
=> ~ ( coindu335574135_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(54,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( member @ TA @ B @ ( coindu1112613586e_lset @ TA @ ( coindu1047225960le_ltl @ TA @ A ) ) )
=> ( member @ TA @ B @ ( coindu1112613586e_lset @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_llist_Oset__sel_I2_J) ).
thf(375,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( member @ TA @ B @ ( coindu1112613586e_lset @ TA @ ( coindu1047225960le_ltl @ TA @ A ) ) )
=> ( member @ TA @ B @ ( coindu1112613586e_lset @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(112,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( coindu1112613586e_lset @ TA @ ( coindu1047225960le_ltl @ TA @ A ) ) @ ( coindu1112613586e_lset @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_lset__ltl) ).
thf(584,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( coindu1112613586e_lset @ TA @ ( coindu1047225960le_ltl @ TA @ A ) ) @ ( coindu1112613586e_lset @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType] :
( ( coindu1244876290_llist @ TA @ TB )
= ( ^ [A: TA > $o,B: TA > TB,C: TA > $o,D: TA > ( coindu1593790203_llist @ TB ),E: TA > TA,F: TA] : ( if @ ( coindu1593790203_llist @ TB ) @ ( A @ F ) @ ( coindu1598213697e_LNil @ TB ) @ ( coindu1121789889_LCons @ TB @ ( B @ F ) @ ( if @ ( coindu1593790203_llist @ TB ) @ ( C @ F ) @ ( D @ F ) @ ( coindu1244876290_llist @ TA @ TB @ A @ B @ C @ D @ E @ ( E @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_llist_Ocorec__code) ).
thf(562,plain,
! [TA: $tType,TB: $tType] :
( ( coindu1244876290_llist @ TA @ TB )
= ( ^ [A: TA > $o,B: TA > TB,C: TA > $o,D: TA > ( coindu1593790203_llist @ TB ),E: TA > TA,F: TA] : ( if @ ( coindu1593790203_llist @ TB ) @ ( A @ F ) @ ( coindu1598213697e_LNil @ TB ) @ ( coindu1121789889_LCons @ TB @ ( B @ F ) @ ( if @ ( coindu1593790203_llist @ TB ) @ ( C @ F ) @ ( D @ F ) @ ( coindu1244876290_llist @ TA @ TB @ A @ B @ C @ D @ E @ ( E @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(66,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_subset__trans) ).
thf(423,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( ord_less_eq @ ( set @ TA ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(59,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_subset__iff) ).
thf(402,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(169,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu1598213697e_LNil @ TA )
= ( coindu268472904append @ TA @ A @ B ) )
= ( ( A
= ( coindu1598213697e_LNil @ TA ) )
& ( B
= ( coindu1598213697e_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_LNil__eq__lappend__iff) ).
thf(772,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu1598213697e_LNil @ TA )
= ( coindu268472904append @ TA @ A @ B ) )
= ( ( A
= ( coindu1598213697e_LNil @ TA ) )
& ( B
= ( coindu1598213697e_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(28,axiom,
! [TA: $tType] :
( ( coindu1047225960le_ltl @ TA @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_ltl__simps_I1_J) ).
thf(286,plain,
! [TA: $tType] :
( ( coindu1047225960le_ltl @ TA @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(158,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu268472904append @ TA @ ( coindu268472904append @ TA @ A @ B ) @ C )
= ( coindu268472904append @ TA @ A @ ( coindu268472904append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_lappend__assoc) ).
thf(743,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu268472904append @ TA @ ( coindu268472904append @ TA @ A @ B ) @ C )
= ( coindu268472904append @ TA @ A @ ( coindu268472904append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(102,axiom,
! [TA: $tType] :
( ( coindu1928975208n_lset @ TA )
= ( ^ [A: set @ TA,B: coindu1593790203_llist @ TA] : ( sup_sup @ ( set @ TA ) @ A @ ( coindu1112613586e_lset @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_gen__lset__def) ).
thf(545,plain,
! [TA: $tType] :
( ( coindu1928975208n_lset @ TA )
= ( ^ [A: set @ TA,B: coindu1593790203_llist @ TA] : ( sup_sup @ ( set @ TA ) @ A @ ( coindu1112613586e_lset @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ~ ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_unfold__llist_Odisc_I2_J) ).
thf(259,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ~ ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(174,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( coindu1696667936prefix @ TA @ ( coindu268472904append @ TA @ C @ A ) @ ( coindu268472904append @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_lprefix__lappend__sameI) ).
thf(787,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( coindu1696667936prefix @ TA @ ( coindu268472904append @ TA @ C @ A ) @ ( coindu268472904append @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(78,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_Un__left__absorb) ).
thf(466,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(179,axiom,
! [TA: $tType] :
( ( coindu268472904append @ TA @ ( coindu1598213697e_LNil @ TA ) @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_lappend__LNil__LNil) ).
thf(804,plain,
! [TA: $tType] :
( ( coindu268472904append @ TA @ ( coindu1598213697e_LNil @ TA ) @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(100,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ ( sup_sup @ ( set @ TA ) @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_Un__mono) ).
thf(540,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA,D: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ D )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ ( sup_sup @ ( set @ TA ) @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(142,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_prod__induct4) ).
thf(681,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1046438764le_lhd @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_unfold__llist_Osimps_I3_J) ).
thf(219,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1046438764le_lhd @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(173,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu335574135_lnull @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_lprefix__LNil) ).
thf(784,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ ( coindu1598213697e_LNil @ TA ) )
= ( coindu335574135_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(55,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu1213758845finite @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_lnull__imp__lfinite) ).
thf(377,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu1213758845finite @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ( A @ B )
=> ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_unfold__llist_Odisc_I1_J) ).
thf(230,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ( A @ B )
=> ( coindu335574135_lnull @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [TA: $tType] :
( ( coindu987187967t_all2 @ TA @ TA @ ( (=) @ TA ) )
= ( (=) @ ( coindu1593790203_llist @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_llist_Orel__eq) ).
thf(245,plain,
! [TA: $tType] :
( ( coindu987187967t_all2 @ TA @ TA @ ( (=) @ TA ) )
= ( (=) @ ( coindu1593790203_llist @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: coindu1593790203_llist @ TB,E: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ( coindu987187967t_all2 @ TB @ TA @ A @ D @ E )
=> ( coindu987187967t_all2 @ TB @ TA @ A @ ( coindu1121789889_LCons @ TB @ B @ D ) @ ( coindu1121789889_LCons @ TA @ C @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_llist_Orel__intros_I2_J) ).
thf(271,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: TA,D: coindu1593790203_llist @ TB,E: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ( coindu987187967t_all2 @ TB @ TA @ A @ D @ E )
=> ( coindu987187967t_all2 @ TB @ TA @ A @ ( coindu1121789889_LCons @ TB @ B @ D ) @ ( coindu1121789889_LCons @ TA @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(200,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_lprefix__refl) ).
thf(880,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(130,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_ball__Un) ).
thf(649,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA > $o] :
( ( ! [D: TA] :
( ( member @ TA @ D @ ( sup_sup @ ( set @ TA ) @ A @ B ) )
=> ( C @ D ) ) )
= ( ! [D: TA] :
( ( member @ TA @ D @ A )
=> ( C @ D ) )
& ! [D: TA] :
( ( member @ TA @ D @ B )
=> ( C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(204,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ ( coindu1598213697e_LNil @ TA ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_lprefix__code_I1_J) ).
thf(890,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] : ( coindu1696667936prefix @ TA @ ( coindu1598213697e_LNil @ TA ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(82,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_UnE) ).
thf(477,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) )
=> ( ~ ( member @ TA @ A @ B )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(126,axiom,
! [TA: $tType] :
( ( coindu335574135_lnull @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
( A
= ( coindu1598213697e_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_lnull__def) ).
thf(631,plain,
! [TA: $tType] :
( ( coindu335574135_lnull @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
( A
= ( coindu1598213697e_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(51,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( A
= ( coindu1598213697e_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_llist_Ocollapse_I1_J) ).
thf(367,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( A
= ( coindu1598213697e_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(118,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_Un__subset__iff) ).
thf(609,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( ( ord_less_eq @ ( set @ TA ) @ A @ C )
& ( ord_less_eq @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > $o,D: TA > ( coindu1593790203_llist @ TB ),E: TA > TA,F: TA] :
( ( coindu335574135_lnull @ TB @ ( coindu1244876290_llist @ TA @ TB @ A @ B @ C @ D @ E @ F ) )
= ( A @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_llist_Ocorec__disc__iff_I1_J) ).
thf(213,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > $o,D: TA > ( coindu1593790203_llist @ TB ),E: TA > TA,F: TA] :
( ( coindu335574135_lnull @ TB @ ( coindu1244876290_llist @ TA @ TB @ A @ B @ C @ D @ E @ F ) )
= ( A @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(122,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
= ( coindu567634248member @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_lset__lmember) ).
thf(621,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
= ( coindu567634248member @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( coindu1593790203_llist @ TB ),F: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1046438764le_lhd @ TB @ ( coindu1244876290_llist @ TA @ TB @ A @ C @ D @ E @ F @ B ) )
= ( C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_llist_Ocorec__sel_I1_J) ).
thf(240,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( coindu1593790203_llist @ TB ),F: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1046438764le_lhd @ TB @ ( coindu1244876290_llist @ TA @ TB @ A @ C @ D @ E @ F @ B ) )
= ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(206,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_lprefix__antisym) ).
thf(895,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(168,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( ( A
= ( coindu1598213697e_LNil @ TA ) )
| ? [D: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ D ) )
& ( coindu1696667936prefix @ TA @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_lprefix__LCons__conv) ).
thf(769,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ ( coindu1121789889_LCons @ TA @ B @ C ) )
= ( ( A
= ( coindu1598213697e_LNil @ TA ) )
| ? [D: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ D ) )
& ( coindu1696667936prefix @ TA @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(137,axiom,
! [TA: $tType] : ( coindu1213758845finite @ TA @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_lfinite__LNil) ).
thf(668,plain,
! [TA: $tType] : ( coindu1213758845finite @ TA @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_internal__case__prod__conv) ).
thf(330,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC > TA > TB,B: TC,C: TA] :
( ( produc2004651681e_prod @ TC @ TA @ TB @ A @ ( product_Pair @ TC @ TA @ B @ C ) )
= ( A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(190,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu268472904append @ TA @ A @ B )
= ( coindu1598213697e_LNil @ TA ) )
= ( ( A
= ( coindu1598213697e_LNil @ TA ) )
& ( B
= ( coindu1598213697e_LNil @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_lappend__eq__LNil__iff) ).
thf(848,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu268472904append @ TA @ A @ B )
= ( coindu1598213697e_LNil @ TA ) )
= ( ( A
= ( coindu1598213697e_LNil @ TA ) )
& ( B
= ( coindu1598213697e_LNil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(149,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: coindu1593790203_llist @ TB] :
~ ( coindu987187967t_all2 @ TB @ TA @ A @ ( coindu1121789889_LCons @ TB @ B @ C ) @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_llist_Orel__distinct_I2_J) ).
thf(700,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: coindu1593790203_llist @ TB] :
~ ( coindu987187967t_all2 @ TB @ TA @ A @ ( coindu1121789889_LCons @ TB @ B @ C ) @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(144,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_UnI1) ).
thf(685,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( member @ TA @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_prod__induct5) ).
thf(306,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(191,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( coindu1046438764le_lhd @ TA @ B ) ) )
& ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( coindu1046438764le_lhd @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_lhd__lappend) ).
thf(851,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( coindu1046438764le_lhd @ TA @ B ) ) )
& ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1046438764le_lhd @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( coindu1046438764le_lhd @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(133,axiom,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_subset__refl) ).
thf(658,plain,
! [TA: $tType,A: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(114,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_Un__least) ).
thf(589,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ C @ B )
=> ( ord_less_eq @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(97,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [C: coindu1593790203_llist @ TA] :
( B
!= ( coindu1121789889_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_lset__cases) ).
thf(531,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [C: coindu1593790203_llist @ TA] :
( B
!= ( coindu1121789889_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(177,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ? [C: coindu1593790203_llist @ TA,D: coindu1593790203_llist @ TA] :
( ( B
= ( coindu268472904append @ TA @ C @ ( coindu1121789889_LCons @ TA @ A @ D ) ) )
& ( coindu1213758845finite @ TA @ C )
& ~ ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_split__llist__first) ).
thf(795,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ? [C: coindu1593790203_llist @ TA,D: coindu1593790203_llist @ TA] :
( ( B
= ( coindu268472904append @ TA @ C @ ( coindu1121789889_LCons @ TA @ A @ D ) ) )
& ( coindu1213758845finite @ TA @ C )
& ~ ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType] :
( ( coindu882539134_llist @ TA @ TB )
= ( ^ [A: TA,B: TB > ( coindu1593790203_llist @ TB ) > TA,C: coindu1593790203_llist @ TB] : ( if @ TA @ ( coindu335574135_lnull @ TB @ C ) @ A @ ( B @ ( coindu1046438764le_lhd @ TB @ C ) @ ( coindu1047225960le_ltl @ TB @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_llist_Ocase__eq__if) ).
thf(548,plain,
! [TA: $tType,TB: $tType] :
( ( coindu882539134_llist @ TA @ TB )
= ( ^ [A: TA,B: TB > ( coindu1593790203_llist @ TB ) > TA,C: coindu1593790203_llist @ TB] : ( if @ TA @ ( coindu335574135_lnull @ TB @ C ) @ A @ ( B @ ( coindu1046438764le_lhd @ TB @ C ) @ ( coindu1047225960le_ltl @ TB @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(182,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu1213758845finite @ TA @ A )
=> ( ( coindu1112613586e_lset @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ ( coindu1112613586e_lset @ TA @ A ) @ ( coindu1112613586e_lset @ TA @ B ) ) ) )
& ( ~ ( coindu1213758845finite @ TA @ A )
=> ( ( coindu1112613586e_lset @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( coindu1112613586e_lset @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_lset__lappend__conv) ).
thf(812,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu1213758845finite @ TA @ A )
=> ( ( coindu1112613586e_lset @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( sup_sup @ ( set @ TA ) @ ( coindu1112613586e_lset @ TA @ A ) @ ( coindu1112613586e_lset @ TA @ B ) ) ) )
& ( ~ ( coindu1213758845finite @ TA @ A )
=> ( ( coindu1112613586e_lset @ TA @ ( coindu268472904append @ TA @ A @ B ) )
= ( coindu1112613586e_lset @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(121,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_equalityD1) ).
thf(617,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(44,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( member @ TA @ C @ B )
=> ~ ( member @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_contra__subsetD) ).
thf(342,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ~ ( member @ TA @ C @ B )
=> ~ ( member @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(186,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ? [C: coindu1593790203_llist @ TA,D: coindu1593790203_llist @ TA] :
( ( B
= ( coindu268472904append @ TA @ C @ ( coindu1121789889_LCons @ TA @ A @ D ) ) )
& ( coindu1213758845finite @ TA @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_split__llist) ).
thf(836,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ? [C: coindu1593790203_llist @ TA,D: coindu1593790203_llist @ TA] :
( ( B
= ( coindu268472904append @ TA @ C @ ( coindu1121789889_LCons @ TA @ A @ D ) ) )
& ( coindu1213758845finite @ TA @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_prod__cases7) ).
thf(490,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,A: product_prod @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) )] :
~ ! [B: TG,C: TF,D: TE,E: TD,F: TC,G: TB,H: TA] :
( A
!= ( product_Pair @ TG @ ( product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) ) @ B @ ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ C @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ D @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ E @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ F @ ( product_Pair @ TB @ TA @ G @ H ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(140,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
=> ~ ( coindu335574135_lnull @ TA @ B ) )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
| ~ ( coindu335574135_lnull @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_lappend_Oexhaust) ).
thf(675,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ( coindu335574135_lnull @ TA @ A )
=> ~ ( coindu335574135_lnull @ TA @ B ) )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
| ~ ( coindu335574135_lnull @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(1,conjecture,
coindu1696667936prefix @ a @ ( coindu268472904append @ a @ xs @ ys ) @ ( coindu268472904append @ a @ xs @ zs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( coindu1696667936prefix @ a @ ( coindu268472904append @ a @ xs @ ys ) @ ( coindu268472904append @ a @ xs @ zs ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(209,plain,
~ ( coindu1696667936prefix @ a @ ( coindu268472904append @ a @ xs @ ys ) @ ( coindu268472904append @ a @ xs @ zs ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( coindu1593790203_llist @ TB ) > TA] :
( ( coindu882539134_llist @ TA @ TB @ A @ B @ ( coindu1598213697e_LNil @ TB ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_llist_Osimps_I4_J) ).
thf(487,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB > ( coindu1593790203_llist @ TB ) > TA] :
( ( coindu882539134_llist @ TA @ TB @ A @ B @ ( coindu1598213697e_LNil @ TB ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(95,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_Un__assoc) ).
thf(525,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ ( sup_sup @ ( set @ TA ) @ A @ B ) @ C )
= ( sup_sup @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(146,axiom,
! [TA: $tType] :
( ( coindu1213758845finite @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
| ? [B: coindu1593790203_llist @ TA,C: TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ C @ B ) )
& ( coindu1213758845finite @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_lfinite_Osimps) ).
thf(690,plain,
! [TA: $tType] :
( ( coindu1213758845finite @ TA )
= ( ^ [A: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
| ? [B: coindu1593790203_llist @ TA,C: TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ C @ B ) )
& ( coindu1213758845finite @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(31,axiom,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_set__rev__mp) ).
thf(295,plain,
! [TA: $tType,A: TA,B: set @ TA,C: set @ TA] :
( ( member @ TA @ A @ B )
=> ( ( ord_less_eq @ ( set @ TA ) @ B @ C )
=> ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(203,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( coindu1696667936prefix @ TA @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_LCons__lprefix__LCons) ).
thf(887,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA,D: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ ( coindu1121789889_LCons @ TA @ C @ D ) )
= ( ( A = C )
& ( coindu1696667936prefix @ TA @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(41,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_Un__absorb2) ).
thf(327,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( sup_sup @ ( set @ TA ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(152,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ~ ! [B: TA,C: coindu1593790203_llist @ TA] :
( A
!= ( coindu1121789889_LCons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_llist_Oexhaust) ).
thf(712,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ~ ! [B: TA,C: coindu1593790203_llist @ TA] :
( A
!= ( coindu1121789889_LCons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(106,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_Un__upper2) ).
thf(557,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] : ( ord_less_eq @ ( set @ TA ) @ A @ ( sup_sup @ ( set @ TA ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(139,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_in__mono) ).
thf(673,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_prod__induct6) ).
thf(441,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(52,axiom,
! [TA: $tType,A: TA] :
~ ( coindu567634248member @ TA @ A @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_lmember__code_I1_J) ).
thf(370,plain,
! [TA: $tType,A: TA] :
~ ( coindu567634248member @ TA @ A @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(187,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ C @ B )
=> ( ( coindu1696667936prefix @ TA @ A @ C )
| ( coindu1696667936prefix @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_lprefix__down__linear) ).
thf(840,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ C @ B )
=> ( ( coindu1696667936prefix @ TA @ A @ C )
| ( coindu1696667936prefix @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TB,C: coindu1593790203_llist @ TA,D: coindu1593790203_llist @ TA,E: TB > TA > $o,F: TB > TA > $o] :
( ( A = B )
=> ( ( C = D )
=> ( ! [G: TB,H: TA] :
( ( member @ TB @ G @ ( coindu1112613586e_lset @ TB @ B ) )
=> ( ( member @ TA @ H @ ( coindu1112613586e_lset @ TA @ D ) )
=> ( ( E @ G @ H )
= ( F @ G @ H ) ) ) )
=> ( ( coindu987187967t_all2 @ TB @ TA @ E @ A @ C )
= ( coindu987187967t_all2 @ TB @ TA @ F @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_llist_Orel__cong) ).
thf(314,plain,
! [TA: $tType,TB: $tType,A: coindu1593790203_llist @ TB,B: coindu1593790203_llist @ TB,C: coindu1593790203_llist @ TA,D: coindu1593790203_llist @ TA,E: TB > TA > $o,F: TB > TA > $o] :
( ( A = B )
=> ( ( C = D )
=> ( ! [G: TB,H: TA] :
( ( member @ TB @ G @ ( coindu1112613586e_lset @ TB @ B ) )
=> ( ( member @ TA @ H @ ( coindu1112613586e_lset @ TA @ D ) )
=> ( ( E @ G @ H )
= ( F @ G @ H ) ) ) )
=> ( ( coindu987187967t_all2 @ TB @ TA @ E @ A @ C )
= ( coindu987187967t_all2 @ TB @ TA @ F @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(119,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] : ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_llist_Oset__intros_I1_J) ).
thf(612,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] : ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(198,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( coindu1696667936prefix @ TA @ ( coindu1047225960le_ltl @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_lprefix__ltlI) ).
thf(876,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( coindu1696667936prefix @ TA @ ( coindu1047225960le_ltl @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(193,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1046438764le_lhd @ TA @ A )
= ( coindu1046438764le_lhd @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_lprefix__lhdD) ).
thf(859,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu1046438764le_lhd @ TA @ A )
= ( coindu1046438764le_lhd @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(72,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1047225960le_ltl @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_ltl__simps_I2_J) ).
thf(446,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1047225960le_ltl @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(110,axiom,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ D @ E )
=> ( ( ( coindu335574135_lnull @ TA @ D )
= ( coindu335574135_lnull @ TA @ E ) )
& ( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ~ ( coindu335574135_lnull @ TA @ E )
=> ( ( ( coindu1046438764le_lhd @ TA @ D )
= ( coindu1046438764le_lhd @ TA @ E ) )
& ( ( A @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) )
| ( ( coindu1047225960le_ltl @ TA @ D )
= ( coindu1047225960le_ltl @ TA @ E ) ) ) ) ) ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_llist_Ocoinduct__strong) ).
thf(571,plain,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ D @ E )
=> ( ( ( coindu335574135_lnull @ TA @ D )
= ( coindu335574135_lnull @ TA @ E ) )
& ( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ~ ( coindu335574135_lnull @ TA @ E )
=> ( ( ( coindu1046438764le_lhd @ TA @ D )
= ( coindu1046438764le_lhd @ TA @ E ) )
& ( ( A @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) )
| ( ( coindu1047225960le_ltl @ TA @ D )
= ( coindu1047225960le_ltl @ TA @ E ) ) ) ) ) ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(189,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu268472904append @ TA @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_lappend__lnull2) ).
thf(845,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu268472904append @ TA @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(124,axiom,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_old_Oprod_Oinducts) ).
thf(627,plain,
! [TA: $tType,TB: $tType,A: ( product_prod @ TA @ TB ) > $o,B: product_prod @ TA @ TB] :
( ! [C: TA,D: TB] : ( A @ ( product_Pair @ TA @ TB @ C @ D ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(208,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ B @ C )
=> ( coindu1696667936prefix @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_lprefix__trans) ).
thf(903,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu1696667936prefix @ TA @ B @ C )
=> ( coindu1696667936prefix @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(164,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu268472904append @ TA @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_lappend__lnull1) ).
thf(759,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu268472904append @ TA @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(93,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [C: coindu1593790203_llist @ TA] :
( B
!= ( coindu1121789889_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_llist_Oset__cases) ).
thf(517,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( ! [C: coindu1593790203_llist @ TA] :
( B
!= ( coindu1121789889_LCons @ TA @ A @ C ) )
=> ~ ! [C: TA,D: coindu1593790203_llist @ TA] :
( ( B
= ( coindu1121789889_LCons @ TA @ C @ D ) )
=> ~ ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(160,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu268472904append @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ C )
= ( coindu1121789889_LCons @ TA @ A @ ( coindu268472904append @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_lappend__code_I2_J) ).
thf(748,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( coindu268472904append @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) @ C )
= ( coindu1121789889_LCons @ TA @ A @ ( coindu268472904append @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_prod__induct3) ).
thf(304,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) > $o,B: product_prod @ TA @ ( product_prod @ TB @ TC )] :
( ! [C: TA,D: TB,E: TC] : ( A @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(131,axiom,
! [TA: $tType,TB: $tType] :
( ( coindu1599971794_llist @ TA @ TB )
= ( ^ [A: TA > $o,B: TA > TB,C: TA > TA,D: TA] : ( if @ ( coindu1593790203_llist @ TB ) @ ( A @ D ) @ ( coindu1598213697e_LNil @ TB ) @ ( coindu1121789889_LCons @ TB @ ( B @ D ) @ ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ ( C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_unfold__llist_Ocode) ).
thf(652,plain,
! [TA: $tType,TB: $tType] :
( ( coindu1599971794_llist @ TA @ TB )
= ( ^ [A: TA > $o,B: TA > TB,C: TA > TA,D: TA] : ( if @ ( coindu1593790203_llist @ TB ) @ ( A @ D ) @ ( coindu1598213697e_LNil @ TB ) @ ( coindu1121789889_LCons @ TB @ ( B @ D ) @ ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ ( C @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(64,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( member @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1112613586e_lset @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_llist_Oset__sel_I1_J) ).
thf(418,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ~ ( coindu335574135_lnull @ TA @ A )
=> ( member @ TA @ ( coindu1046438764le_lhd @ TA @ A ) @ ( coindu1112613586e_lset @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(172,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ~ ( coindu1213758845finite @ TA @ A )
=> ( ( coindu1696667936prefix @ TA @ A @ B )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_not__lfinite__lprefix__conv__eq) ).
thf(781,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ~ ( coindu1213758845finite @ TA @ A )
=> ( ( coindu1696667936prefix @ TA @ A @ B )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(46,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu1121789889_LCons @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_llist_Oset__intros_I2_J) ).
thf(346,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
=> ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu1121789889_LCons @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(98,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_set__mp) ).
thf(536,plain,
! [TA: $tType,A: set @ TA,B: set @ TA,C: TA] :
( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(178,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
& ( ( coindu1046438764le_lhd @ TA @ A )
= ( coindu1046438764le_lhd @ TA @ B ) )
& ( coindu1696667936prefix @ TA @ ( coindu1047225960le_ltl @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ) )
=> ( coindu1696667936prefix @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_lprefix__expand) ).
thf(800,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( ~ ( coindu335574135_lnull @ TA @ A )
=> ( ~ ( coindu335574135_lnull @ TA @ B )
& ( ( coindu1046438764le_lhd @ TA @ A )
= ( coindu1046438764le_lhd @ TA @ B ) )
& ( coindu1696667936prefix @ TA @ ( coindu1047225960le_ltl @ TA @ A ) @ ( coindu1047225960le_ltl @ TA @ B ) ) ) )
=> ( coindu1696667936prefix @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(33,axiom,
! [TA: $tType] : ( coindu335574135_lnull @ TA @ ( coindu1598213697e_LNil @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_llist_Odisc_I1_J) ).
thf(300,plain,
! [TA: $tType] : ( coindu335574135_lnull @ TA @ ( coindu1598213697e_LNil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(69,axiom,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ D @ E )
=> ( ( ( coindu335574135_lnull @ TA @ D )
= ( coindu335574135_lnull @ TA @ E ) )
& ( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ~ ( coindu335574135_lnull @ TA @ E )
=> ( ( ( coindu1046438764le_lhd @ TA @ D )
= ( coindu1046438764le_lhd @ TA @ E ) )
& ( A @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) ) ) ) ) ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_llist_Ocoinduct) ).
thf(432,plain,
! [TA: $tType,A: ( coindu1593790203_llist @ TA ) > ( coindu1593790203_llist @ TA ) > $o,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( A @ B @ C )
=> ( ! [D: coindu1593790203_llist @ TA,E: coindu1593790203_llist @ TA] :
( ( A @ D @ E )
=> ( ( ( coindu335574135_lnull @ TA @ D )
= ( coindu335574135_lnull @ TA @ E ) )
& ( ~ ( coindu335574135_lnull @ TA @ D )
=> ( ~ ( coindu335574135_lnull @ TA @ E )
=> ( ( ( coindu1046438764le_lhd @ TA @ D )
= ( coindu1046438764le_lhd @ TA @ E ) )
& ( A @ ( coindu1047225960le_ltl @ TA @ D ) @ ( coindu1047225960le_ltl @ TA @ E ) ) ) ) ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(185,axiom,
! [TA: $tType] :
( ( coindu1696667936prefix @ TA )
= ( ^ [A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ? [C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
& ( B = C ) )
| ? [C: coindu1593790203_llist @ TA,D: coindu1593790203_llist @ TA,E: TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ E @ C ) )
& ( B
= ( coindu1121789889_LCons @ TA @ E @ D ) )
& ( coindu1696667936prefix @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_lprefix_Osimps) ).
thf(833,plain,
! [TA: $tType] :
( ( coindu1696667936prefix @ TA )
= ( ^ [A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ? [C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
& ( B = C ) )
| ? [C: coindu1593790203_llist @ TA,D: coindu1593790203_llist @ TA,E: TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ E @ C ) )
& ( B
= ( coindu1121789889_LCons @ TA @ E @ D ) )
& ( coindu1696667936prefix @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( coindu1593790203_llist @ TB ),F: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1244876290_llist @ TA @ TB @ A @ C @ D @ E @ F @ B )
= ( coindu1121789889_LCons @ TB @ ( C @ B ) @ ( if @ ( coindu1593790203_llist @ TB ) @ ( D @ B ) @ ( E @ B ) @ ( coindu1244876290_llist @ TA @ TB @ A @ C @ D @ E @ F @ ( F @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_llist_Ocorec_I2_J) ).
thf(405,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( coindu1593790203_llist @ TB ),F: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1244876290_llist @ TA @ TB @ A @ C @ D @ E @ F @ B )
= ( coindu1121789889_LCons @ TB @ ( C @ B ) @ ( if @ ( coindu1593790203_llist @ TB ) @ ( D @ B ) @ ( E @ B ) @ ( coindu1244876290_llist @ TA @ TB @ A @ C @ D @ E @ F @ ( F @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(195,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( coindu1112613586e_lset @ TA @ ( coindu268472904append @ TA @ A @ B ) ) @ ( sup_sup @ ( set @ TA ) @ ( coindu1112613586e_lset @ TA @ A ) @ ( coindu1112613586e_lset @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_lset__lappend) ).
thf(865,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( coindu1112613586e_lset @ TA @ ( coindu268472904append @ TA @ A @ B ) ) @ ( sup_sup @ ( set @ TA ) @ ( coindu1112613586e_lset @ TA @ A ) @ ( coindu1112613586e_lset @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(196,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu335574135_lnull @ TA @ B )
=> ( coindu335574135_lnull @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_lprefix__lnullD) ).
thf(867,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu1696667936prefix @ TA @ A @ B )
=> ( ( coindu335574135_lnull @ TA @ B )
=> ( coindu335574135_lnull @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TB > TA,D: TB > TB] :
( ( A @ B )
=> ( ( coindu1599971794_llist @ TB @ TA @ A @ C @ D @ B )
= ( coindu1598213697e_LNil @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_unfold__llist_Octr_I1_J) ).
thf(273,plain,
! [TA: $tType,TB: $tType,A: TB > $o,B: TB,C: TB > TA,D: TB > TB] :
( ( A @ B )
=> ( ( coindu1599971794_llist @ TB @ TA @ A @ C @ D @ B )
= ( coindu1598213697e_LNil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA,E: TB,F: coindu1593790203_llist @ TB] :
( ( ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ D )
= ( coindu1121789889_LCons @ TB @ E @ F ) )
= ( ~ ( A @ D )
& ( E
= ( B @ D ) )
& ( F
= ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_unfold__llist__eq__LCons) ).
thf(210,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA > TB,C: TA > TA,D: TA,E: TB,F: coindu1593790203_llist @ TB] :
( ( ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ D )
= ( coindu1121789889_LCons @ TB @ E @ F ) )
= ( ~ ( A @ D )
& ( E
= ( B @ D ) )
& ( F
= ( coindu1599971794_llist @ TA @ TB @ A @ B @ C @ ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(22,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_unfold__llist_Osimps_I4_J) ).
thf(268,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > TA] :
( ~ ( A @ B )
=> ( ( coindu1047225960le_ltl @ TB @ ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ B ) )
= ( coindu1599971794_llist @ TA @ TB @ A @ C @ D @ ( D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(180,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ~ ( coindu1213758845finite @ TA @ A )
=> ( ( coindu268472904append @ TA @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_lappend__inf) ).
thf(807,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ~ ( coindu1213758845finite @ TA @ A )
=> ( ( coindu268472904append @ TA @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(148,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
=> ( coindu335574135_lnull @ TA @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_llist_OdiscI_I1_J) ).
thf(696,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1598213697e_LNil @ TA ) )
=> ( coindu335574135_lnull @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(27,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= ( coindu1213758845finite @ TA @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_lfinite__code_I2_J) ).
thf(283,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) )
= ( coindu1213758845finite @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(81,axiom,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_Un__commute) ).
thf(474,plain,
! [TA: $tType] :
( ( sup_sup @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] : ( sup_sup @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(167,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu335574135_lnull @ TA @ B )
=> ( coindu335574135_lnull @ TA @ ( coindu268472904append @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_lappend_Odisc_I1_J) ).
thf(767,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( ( coindu335574135_lnull @ TA @ B )
=> ( coindu335574135_lnull @ TA @ ( coindu268472904append @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(123,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_Collect__mono__iff) ).
thf(624,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ord_less_eq @ ( set @ TA ) @ ( collect @ TA @ A ) @ ( collect @ TA @ B ) )
= ( ! [C: TA] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(155,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( coindu1112613586e_lset @ TA @ A ) @ ( coindu1112613586e_lset @ TA @ ( coindu268472904append @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_lset__lappend1) ).
thf(728,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] : ( ord_less_eq @ ( set @ TA ) @ ( coindu1112613586e_lset @ TA @ A ) @ ( coindu1112613586e_lset @ TA @ ( coindu268472904append @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_Pair__inject) ).
thf(427,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB,D: TA] :
( ( ( product_Pair @ TB @ TA @ A @ B )
= ( product_Pair @ TB @ TA @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(116,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ C ) )
=> ( ( A
!= ( coindu1598213697e_LNil @ TA ) )
& ( ( coindu1046438764le_lhd @ TA @ A )
= B )
& ( ( coindu1047225960le_ltl @ TA @ A )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_eq__LConsD) ).
thf(596,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: TA,C: coindu1593790203_llist @ TA] :
( ( A
= ( coindu1121789889_LCons @ TA @ B @ C ) )
=> ( ( A
!= ( coindu1598213697e_LNil @ TA ) )
& ( ( coindu1046438764le_lhd @ TA @ A )
= B )
& ( ( coindu1047225960le_ltl @ TA @ A )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(96,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_subset__eq) ).
thf(528,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(129,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ~ ! [B: coindu1593790203_llist @ TA] :
( ? [C: TA] :
( A
= ( coindu1121789889_LCons @ TA @ C @ B ) )
=> ~ ( coindu1213758845finite @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_lfinite_Ocases) ).
thf(644,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu1213758845finite @ TA @ A )
=> ( ( A
!= ( coindu1598213697e_LNil @ TA ) )
=> ~ ! [B: coindu1593790203_llist @ TA] :
( ? [C: TA] :
( A
= ( coindu1121789889_LCons @ TA @ C @ B ) )
=> ~ ( coindu1213758845finite @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(77,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_equalityE) ).
thf(459,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ( A = B )
=> ~ ( ( ord_less_eq @ ( set @ TA ) @ A @ B )
=> ~ ( ord_less_eq @ ( set @ TA ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(79,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu335574135_lnull @ TA @ ( coindu1047225960le_ltl @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_lnull__ltlI) ).
thf(469,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu335574135_lnull @ TA @ ( coindu1047225960le_ltl @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(170,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu268472904append @ TA @ B @ C ) ) )
= ( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
| ( ( coindu1213758845finite @ TA @ B )
& ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_in__lset__lappend__iff) ).
thf(775,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA,C: coindu1593790203_llist @ TA] :
( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ ( coindu268472904append @ TA @ B @ C ) ) )
= ( ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ B ) )
| ( ( coindu1213758845finite @ TA @ B )
& ( member @ TA @ A @ ( coindu1112613586e_lset @ TA @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: coindu1593790203_llist @ TB,D: TA,E: coindu1593790203_llist @ TA] :
( ( coindu987187967t_all2 @ TB @ TA @ A @ ( coindu1121789889_LCons @ TB @ B @ C ) @ ( coindu1121789889_LCons @ TA @ D @ E ) )
= ( ( A @ B @ D )
& ( coindu987187967t_all2 @ TB @ TA @ A @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_llist_Orel__inject_I2_J) ).
thf(222,plain,
! [TA: $tType,TB: $tType,A: TB > TA > $o,B: TB,C: coindu1593790203_llist @ TB,D: TA,E: coindu1593790203_llist @ TA] :
( ( coindu987187967t_all2 @ TB @ TA @ A @ ( coindu1121789889_LCons @ TB @ B @ C ) @ ( coindu1121789889_LCons @ TA @ D @ E ) )
= ( ( A @ B @ D )
& ( coindu987187967t_all2 @ TB @ TA @ A @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(50,axiom,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_subset__Un__eq) ).
thf(364,plain,
! [TA: $tType] :
( ( ord_less_eq @ ( set @ TA ) )
= ( ^ [A: set @ TA,B: set @ TA] :
( ( sup_sup @ ( set @ TA ) @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( coindu1593790203_llist @ TB ),F: TA > TA] :
( ( A @ B )
=> ( coindu335574135_lnull @ TB @ ( coindu1244876290_llist @ TA @ TB @ A @ C @ D @ E @ F @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_llist_Ocorec__disc_I1_J) ).
thf(232,plain,
! [TA: $tType,TB: $tType,A: TA > $o,B: TA,C: TA > TB,D: TA > $o,E: TA > ( coindu1593790203_llist @ TB ),F: TA > TA] :
( ( A @ B )
=> ( coindu335574135_lnull @ TB @ ( coindu1244876290_llist @ TA @ TB @ A @ C @ D @ E @ F @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(201,axiom,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu1696667936prefix @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_lnull__lprefix) ).
thf(882,plain,
! [TA: $tType,A: coindu1593790203_llist @ TA,B: coindu1593790203_llist @ TA] :
( ( coindu335574135_lnull @ TA @ A )
=> ( coindu1696667936prefix @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(89,axiom,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_subsetI) ).
thf(496,plain,
! [TA: $tType,A: set @ TA,B: set @ TA] :
( ! [C: TA] :
( ( member @ TA @ C @ A )
=> ( member @ TA @ C @ B ) )
=> ( ord_less_eq @ ( set @ TA ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(75,axiom,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
~ ( coindu335574135_lnull @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_llist_Odisc_I2_J) ).
thf(454,plain,
! [TA: $tType,A: TA,B: coindu1593790203_llist @ TA] :
~ ( coindu335574135_lnull @ TA @ ( coindu1121789889_LCons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(905,plain,
$false,
inference(e,[status(thm)],[515,892,629,479,333,234,481,408,683,308,741,449,379,614,582,762,730,276,878,655,715,538,670,898,565,257,372,344,357,542,702,751,817,559,606,416,289,261,216,756,789,591,443,348,687,634,396,660,411,243,265,292,452,248,512,678,810,746,778,302,862,297,693,484,252,665,493,551,324,522,830,456,842,869,420,499,471,884,225,637,706,554,753,237,792,360,311,765,398,586,662,718,425,856,279,375,584,562,423,402,772,286,743,545,259,787,466,804,540,681,219,784,377,230,245,271,880,649,890,477,631,367,609,213,621,240,895,769,668,330,848,700,685,306,851,658,589,531,795,548,812,617,342,836,490,675,209,487,525,690,295,887,327,712,557,673,441,370,840,314,612,876,859,446,571,845,627,903,759,517,748,304,652,418,781,346,536,800,300,432,833,405,865,867,273,210,268,807,696,283,474,767,624,728,427,596,528,644,459,469,775,222,364,232,882,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT115^1 : TPTP v8.1.2. Released v7.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n004.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 6 11:29:54 EDT 2024
% 0.15/0.36 % CPUTime :
% 1.01/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.54/1.17 % [INFO] Parsing done (263ms).
% 1.54/1.18 % [INFO] Running in sequential loop mode.
% 2.65/1.38 % [INFO] eprover registered as external prover.
% 2.65/1.39 % [INFO] cvc4 registered as external prover.
% 2.65/1.39 % [INFO] Scanning for conjecture ...
% 2.85/1.48 % [INFO] Found a conjecture and 265 axioms. Running axiom selection ...
% 3.04/1.56 % [INFO] Axiom selection finished. Selected 206 axioms (removed 59 axioms).
% 3.59/1.76 % [INFO] Problem is higher-order (TPTP THF).
% 3.59/1.77 % [INFO] Type checking passed.
% 3.59/1.77 % [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 ...
% 15.16/4.66 % External prover 'e' found a proof!
% 15.16/4.66 % [INFO] Killing All external provers ...
% 15.16/4.66 % Time passed: 4142ms (effective reasoning time: 3483ms)
% 15.16/4.66 % 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)>
% 15.16/4.67 % Axioms used in derivation (206): fact_124_lfinite__induct, fact_176_ball__Un, fact_185_subsetI, fact_87_unfold__llist_Osimps_I4_J, fact_136_prod__cases, fact_82_lhd__LCons__ltl, fact_114_unfold__llist_Odisc_I1_J, fact_39_lnull__imp__lfinite, fact_53_lprefix__not__lnullD, fact_197_Un__absorb2, fact_91_llist_Oset__sel_I1_J, fact_10_lprefix__code_I1_J, fact_14_lappend__code_I2_J, fact_79_llist_Ocorec__disc__iff_I1_J, fact_121_llist_Ocorec_I1_J, fact_28_llist_OdiscI_I1_J, fact_188_Un__subset__iff, fact_12_lappend__inf, fact_16_lappend_Odisc__iff_I2_J, fact_181_internal__case__prod__conv, fact_89_llist_Ocorec__sel_I2_J, fact_119_llist_Ocorec__disc_I2_J, fact_83_llist__set__induct, fact_0_lprefix__refl, fact_108_lset__intros_I2_J, fact_241_set__mp, fact_69_split__llist__first, fact_193_Un__least, fact_101_llist_Oset__cases, fact_105_llist_Oset__intros_I1_J, fact_130_llist_Ocase__eq__if, fact_144_prod__induct4, fact_54_lprefix__lnullD, fact_78_unfold__llist__eq__LCons, fact_125_lprefix__lhdD, fact_49_lprefix_Ocoinduct, fact_98_lprefix__coinduct, fact_37_lfinite_Oinducts, fact_3_lprefix__trans, fact_110_ltl__simps_I2_J, fact_64_lappend__eq__LNil__iff, fact_174_Un__absorb, fact_1__092_060open_062lfinite_Axs_A_092_060longrightarrow_062_Ays_A_092_060sqsubseteq_062_Azs_092_060close_062, fact_173_Un__commute, fact_99_lprefix__expand, fact_94_llist_Oexpand, fact_151_old_Oprod_Orec, fact_196_Un__absorb1, fact_236_subset__eq, fact_234_equalityD2, fact_145_prod__induct5, fact_57_lprefix__lnull, fact_120_llist_Ocorec_I2_J, fact_25_llist_Odisc_I2_J, fact_122_in__lset__lappend__iff, fact_103_lset__induct, fact_74_ltl__lappend, fact_139_prod__cases4, fact_21_lfinite__code_I2_J, fact_88_llist_Ocorec__sel_I1_J, fact_84_lset__lmember, fact_51_lprefix_Ocases, fact_226_contra__subsetD, fact_231_rev__subsetD, fact_86_unfold__llist_Osimps_I3_J, fact_40_lfinite__LNil, fact_149_old_Oprod_Oinducts, fact_23_lfinite__code_I1_J, fact_102_lset__induct_H, fact_75_unfold__llist_Odisc__iff_I1_J, fact_133_llist_Osimps_I4_J, fact_195_Un__upper2, fact_112_lprefix__ltlI, fact_61_LCons__lprefix__conv, fact_177_bex__Un, fact_146_prod__induct6, fact_65_lmember__code_I1_J, fact_171_Un__left__commute, fact_60_lappend_Odisc_I2_J, fact_13_not__lfinite__lprefix__conv__eq, fact_117_unfold__llist_Octr_I1_J, fact_150_lset__lappend__conv, fact_59_lappend_Odisc_I1_J, fact_55_lappend__lnull2, fact_194_Un__upper1, fact_227_set__eq__subset, fact_245_llist_Octr__transfer_I1_J, fact_147_prod__induct7, fact_123_lappend__ltl, fact_183_llist_Orel__sel, fact_26_llist_Odisc_I1_J, fact_50_lprefix_Osimps, fact_81_unfold__llist__id, fact_38_lnull__def, fact_97_eq__LConsD, fact_116_unfold__llist_Octr_I2_J, fact_131_lset__lappend__lfinite, fact_148_old_Oprod_Oexhaust, fact_127_prod_Oinject, fact_237_equalityE, fact_238_subsetCE, fact_109_lnull__ltlI, fact_178_UnI2, fact_29_llist_Ocollapse_I1_J, fact_15_LCons__lprefix__LCons, fact_251_llist_Orel__distinct_I1_J, fact_70_lhd__lappend, fact_27_llist_OdiscI_I2_J, fact_143_prod__induct3, fact_17_lnull__lappend, fact_19_LNil__eq__lappend__iff, fact_43_lappend__snocL1__conv__LCons2, fact_198_subset__Un__eq, fact_8_lfinite__lappend, fact_31_lfinite_Ocases, fact_63_LNil__lprefix, fact_179_UnI1, fact_233_set__rev__mp, fact_129_llist_Osplit__sel, fact_240_in__mono, fact_58_lnull__lprefix, fact_253_lset__ltl, fact_230_subset__refl, fact_225_Collect__mono__iff, fact_5_lprefix__lappend, fact_192_Un__mono, fact_104_lset__cases, fact_152_UnCI, fact_52_lprefix__code_I2_J, fact_175_Un__assoc, fact_62_Le__LCons, fact_189_llist_Orel__inject_I2_J, fact_32_lfinite_Osimps, fact_96_llist_Oexhaust__sel, fact_73_unfold__llist_Ocode, fact_182_lset__lappend, fact_90_llist_Oset__sel_I2_J, fact_118_llist_Ocorec__disc_I1_J, fact_126_old_Oprod_Oinject, fact_76_unfold__llist_Odisc__iff_I2_J, fact_246_llist_Orel__refl__strong, fact_107_lset__intros_I1_J, fact_128_llist_Osplit__sel__asm, fact_232_subset__iff, fact_153_Un__iff, fact_56_lappend__lnull1, fact_2_lappend__assoc, fact_142_prod__cases7, fact_45_Collect__mem__eq, fact_113_lhd__LCons, fact_135_surj__pair, fact_239_subsetD, fact_9_lappend__code_I1_J, fact_30_llist_Odistinct_I1_J, fact_111_ltl__simps_I1_J, fact_243_llist_Orel__eq, fact_180_UnE, fact_138_prod__cases3, fact_228_subset__trans, fact_35_not__lnull__conv, fact_132_llist_Osimps_I5_J, fact_33_llist_Oexhaust, fact_254_lset__lappend1, fact_244_llist_Orel__refl, fact_106_llist_Oset__intros_I2_J, fact_248_llist_Orel__cong, fact_85_in__lset__ltlD, fact_68_split__llist, fact_77_lfinite__ltl, fact_184_subset__antisym, fact_92_llist_Ocoinduct__strong, fact_11_lappend__LNil2, fact_141_prod__cases6, fact_250_llist_Orel__distinct_I2_J, fact_22_lfinite__LCons, fact_71_gen__lset__code_I1_J, fact_18_lappend__LNil__LNil, fact_42_lappend_Octr_I1_J, fact_137_Pair__inject, fact_95_ltl__unfold__llist, fact_67_lprefixI, fact_252_llist_Orel__cases, fact_249_llist_Orel__intros_I2_J, fact_36_lappend_Oexhaust, fact_115_unfold__llist_Odisc_I2_J, fact_20_llist_Oinject, fact_48_lprefix__LCons__conv, fact_172_Un__left__absorb, fact_247_llist_Orel__mono__strong, fact_100_llist_Oset__induct, fact_41_lfinite__LConsI, fact_7_lprefix__lappend__sameI, fact_93_llist_Ocoinduct, fact_6_lprefix__down__linear, fact_66_lmember__code_I2_J, fact_140_prod__cases5, fact_134_gen__lset__def, fact_34_neq__LNil__conv, fact_24_lprefix__LNil, fact_4_lprefix__antisym, fact_72_llist_Ocorec__code, fact_46_Collect__cong, fact_44_mem__Collect__eq, fact_235_equalityD1, fact_80_llist_Ocorec__disc__iff_I2_J, fact_229_Collect__mono
% 15.16/4.67 % No. of inferences in proof: 416
% 15.16/4.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4142 ms resp. 3483 ms w/o parsing
% 15.82/4.80 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.82/4.80 % [INFO] Killing All external provers ...
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