TSTP Solution File: SWW529_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW529_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 : Fri May 19 12:24:59 EDT 2023
% Result : Theorem 12.17s 4.58s
% Output : Refutation 12.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 140
% Syntax : Number of formulae : 244 ( 80 unt; 38 typ; 0 def)
% Number of atoms : 1064 ( 168 equ; 0 cnn)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 4950 ( 54 ~; 24 |; 70 &;4639 @)
% ( 24 <=>; 139 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 34 usr; 11 con; 0-5 aty)
% Number of variables : 659 ( 0 ^; 610 !; 18 ?; 659 :)
% ( 31 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(code_term_type,type,
code_term: $tType ).
thf(code_code_numeral_type,type,
code_code_numeral: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(product_unit_type,type,
product_unit: $tType ).
thf(enum_type,type,
enum:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(combb_type,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ TB ) > ( fun @ TA @ TC ) > ( fun @ TA @ TB ) ) ).
thf(combc_type,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > TB > ( fun @ TC @ TA ) ) ).
thf(combk_type,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) ) ).
thf(combs_type,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ TC @ TB ) > ( fun @ TC @ TA ) ) ).
thf(finite_finite_type,type,
finite_finite:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > $o ) ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(huffma675207370phabet_type,type,
huffma675207370phabet:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > ( fun @ TA @ bool ) ) ).
thf(huffma1518433673istent_type,type,
huffma1518433673istent:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > $o ) ).
thf(huffma410068972_depth_type,type,
huffma410068972_depth:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > TA > nat ) ).
thf(huffma945805758height_type,type,
huffma945805758height:
!>[TA: $tType] : ( ( huffma1450048681e_tree @ TA ) > nat ) ).
thf(huffma1146269203erNode_type,type,
huffma1146269203erNode:
!>[TA: $tType] : ( nat > ( huffma1450048681e_tree @ TA ) > ( huffma1450048681e_tree @ TA ) > ( huffma1450048681e_tree @ TA ) ) ).
thf(huffma2021818691e_Leaf_type,type,
huffma2021818691e_Leaf:
!>[TA: $tType] : ( nat > TA > ( huffma1450048681e_tree @ TA ) ) ).
thf(inf_inf_type,type,
inf_inf:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(sup_sup_type,type,
sup_sup:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(bot_bot_type,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(fconj_type,type,
fconj: fun @ bool @ ( fun @ bool @ bool ) ).
thf(fdisj_type,type,
fdisj: fun @ bool @ ( fun @ bool @ bool ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(t_1_type,type,
t_1: huffma1450048681e_tree @ a ).
thf(t_2_type,type,
t_2: huffma1450048681e_tree @ a ).
thf(thesis_type,type,
thesis: $o ).
thf(w_type,type,
w: nat ).
thf(79,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(365,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(70,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_UnE) ).
thf(340,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(95,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_mem__def) ).
thf(417,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(34,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ A )
=> ( ( ord_less_eq @ nat @ A @ B )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_le__antisym) ).
thf(225,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ B @ A )
=> ( ( ord_less_eq @ nat @ A @ B )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(6,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: TA,E: nat] :
( ( huffma2021818691e_Leaf @ TA @ E @ D )
!= ( huffma1146269203erNode @ TA @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_tree_Osimps_I3_J) ).
thf(118,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: TA,E: nat] :
( ( huffma2021818691e_Leaf @ TA @ E @ D )
!= ( huffma1146269203erNode @ TA @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(89,axiom,
( ( huffma1518433673istent @ a @ t_2 )
=> ? [A: a] :
( ( pp @ ( aa @ ( fun @ a @ bool ) @ bool @ ( aa @ a @ ( fun @ ( fun @ a @ bool ) @ bool ) @ ( member @ a ) @ A ) @ ( huffma675207370phabet @ a @ t_2 ) ) )
& ( ( huffma410068972_depth @ a @ t_2 @ A )
= ( huffma945805758height @ a @ t_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_InnerNode_I2_J) ).
thf(399,plain,
( ( huffma1518433673istent @ a @ t_2 )
=> ? [A: a] :
( ( pp @ ( aa @ ( fun @ a @ bool ) @ bool @ ( aa @ a @ ( fun @ ( fun @ a @ bool ) @ bool ) @ ( member @ a ) @ A ) @ ( huffma675207370phabet @ a @ t_2 ) ) )
& ( ( huffma410068972_depth @ a @ t_2 @ A )
= ( huffma945805758height @ a @ t_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(92,axiom,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_emptyE) ).
thf(408,plain,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(101,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ B ) @ A )
= ( sup_sup @ ( fun @ TA @ bool ) @ C @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_Un__assoc) ).
thf(449,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ B ) @ A )
= ( sup_sup @ ( fun @ TA @ bool ) @ C @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(29,axiom,
! [TA: $tType,A: TA,B: nat] :
( ( huffma945805758height @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_height_Osimps_I1_J) ).
thf(202,plain,
! [TA: $tType,A: TA,B: nat] :
( ( huffma945805758height @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(5,axiom,
! [TA: $tType,A: TA,B: nat,C: TA,D: nat] :
( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
= ( huffma2021818691e_Leaf @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_tree_Osimps_I1_J) ).
thf(110,plain,
! [TA: $tType,A: TA,B: nat,C: TA,D: nat] :
( ( ( ( huffma2021818691e_Leaf @ TA @ D @ C )
= ( huffma2021818691e_Leaf @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( huffma2021818691e_Leaf @ TA @ D @ C )
= ( huffma2021818691e_Leaf @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(27,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(196,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(19,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
<=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_zero__le__double__add__iff__zero__le__single__add) ).
thf(157,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) )
& ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(26,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat] :
( ( huffma1518433673istent @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
<=> ( ( huffma1518433673istent @ TA @ B )
& ( huffma1518433673istent @ TA @ A )
& ( ( inf_inf @ ( fun @ TA @ bool ) @ ( huffma675207370phabet @ TA @ B ) @ ( huffma675207370phabet @ TA @ A ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_consistent_Osimps_I2_J) ).
thf(189,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat] :
( ( ( huffma1518433673istent @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
=> ( ( huffma1518433673istent @ TA @ B )
& ( huffma1518433673istent @ TA @ A )
& ( ( inf_inf @ ( fun @ TA @ bool ) @ ( huffma675207370phabet @ TA @ B ) @ ( huffma675207370phabet @ TA @ A ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
& ( ( ( huffma1518433673istent @ TA @ B )
& ( huffma1518433673istent @ TA @ A )
& ( ( inf_inf @ ( fun @ TA @ bool ) @ ( huffma675207370phabet @ TA @ B ) @ ( huffma675207370phabet @ TA @ A ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
=> ( huffma1518433673istent @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(284,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(35,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ A )
= ( plus_plus @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_nat__add__commute) ).
thf(228,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ A )
= ( plus_plus @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(43,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
<=> ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_double__add__le__zero__iff__single__add__le__zero) ).
thf(261,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) )
& ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(99,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_UnCI) ).
thf(443,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(64,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_IntD2) ).
thf(321,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(85,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) )
<=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_Un__iff) ).
thf(376,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) )
& ( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(7,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_double__zero__sym) ).
thf(121,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(73,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(348,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(75,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) )
<=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_empty__Collect__eq) ).
thf(353,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(16,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ( inf_inf @ ( fun @ TA @ bool ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Int__absorb2) ).
thf(147,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ( inf_inf @ ( fun @ TA @ bool ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(88,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(397,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(11,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ( sup_sup @ ( fun @ TA @ bool ) @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Un__absorb2) ).
thf(133,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ( sup_sup @ ( fun @ TA @ bool ) @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(59,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat] :
( ( huffma675207370phabet @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( sup_sup @ ( fun @ TA @ bool ) @ ( huffma675207370phabet @ TA @ B ) @ ( huffma675207370phabet @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_alphabet_Osimps_I2_J) ).
thf(307,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat] :
( ( huffma675207370phabet @ TA @ ( huffma1146269203erNode @ TA @ C @ B @ A ) )
= ( sup_sup @ ( fun @ TA @ bool ) @ ( huffma675207370phabet @ TA @ B ) @ ( huffma675207370phabet @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(53,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ B @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) )
= ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Un__left__absorb) ).
thf(292,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ B @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) )
= ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(40,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_nat__add__left__cancel) ).
thf(248,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(86,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ B ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
<=> ( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
& ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ B ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_ball__Un) ).
thf(380,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ B ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
=> ( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
& ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ B ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) ) )
& ( ( ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
& ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ B ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) )
=> ! [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ B ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(37,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( inf_inf @ ( fun @ TA @ bool ) @ B @ A )
= ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_Int__def) ).
thf(233,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( inf_inf @ ( fun @ TA @ bool ) @ B @ A )
= ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(102,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: nat,C: huffma1450048681e_tree @ TA,D: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( huffma675207370phabet @ TA @ C ) ) )
=> ( ( huffma410068972_depth @ TA @ ( huffma1146269203erNode @ TA @ B @ C @ A ) @ D )
= ( plus_plus @ nat @ ( huffma410068972_depth @ TA @ C @ D ) @ ( one_one @ nat ) ) ) )
& ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( huffma675207370phabet @ TA @ C ) ) )
=> ( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( huffma675207370phabet @ TA @ A ) ) )
=> ( ( huffma410068972_depth @ TA @ ( huffma1146269203erNode @ TA @ B @ C @ A ) @ D )
= ( plus_plus @ nat @ ( huffma410068972_depth @ TA @ A @ D ) @ ( one_one @ nat ) ) ) )
& ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( huffma675207370phabet @ TA @ A ) ) )
=> ( ( huffma410068972_depth @ TA @ ( huffma1146269203erNode @ TA @ B @ C @ A ) @ D )
= ( zero_zero @ nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_depth_Osimps_I2_J) ).
thf(452,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: nat,C: huffma1450048681e_tree @ TA,D: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( huffma675207370phabet @ TA @ C ) ) )
=> ( ( huffma410068972_depth @ TA @ ( huffma1146269203erNode @ TA @ B @ C @ A ) @ D )
= ( plus_plus @ nat @ ( huffma410068972_depth @ TA @ C @ D ) @ ( one_one @ nat ) ) ) )
& ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( huffma675207370phabet @ TA @ C ) ) )
=> ( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( huffma675207370phabet @ TA @ A ) ) )
=> ( ( huffma410068972_depth @ TA @ ( huffma1146269203erNode @ TA @ B @ C @ A ) @ D )
= ( plus_plus @ nat @ ( huffma410068972_depth @ TA @ A @ D ) @ ( one_one @ nat ) ) ) )
& ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( huffma675207370phabet @ TA @ A ) ) )
=> ( ( huffma410068972_depth @ TA @ ( huffma1146269203erNode @ TA @ B @ C @ A ) @ D )
= ( zero_zero @ nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(68,axiom,
! [TA: $tType,A: TA,B: huffma1450048681e_tree @ TA] : ( ord_less_eq @ nat @ ( huffma410068972_depth @ TA @ B @ A ) @ ( huffma945805758height @ TA @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_depth__le__height) ).
thf(334,plain,
! [TA: $tType,A: TA,B: huffma1450048681e_tree @ TA] : ( ord_less_eq @ nat @ ( huffma410068972_depth @ TA @ B @ A ) @ ( huffma945805758height @ TA @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(57,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(302,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(20,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool,D: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ D @ C )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ ( sup_sup @ ( fun @ TA @ bool ) @ D @ B ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Un__mono) ).
thf(160,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool,D: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ D @ C )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ ( sup_sup @ ( fun @ TA @ bool ) @ D @ B ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(97,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ B ) ) )
& ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
<=> ( ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
& ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
| ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ B ) )
& ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_bex__Un) ).
thf(424,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ B ) ) )
& ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
=> ( ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
& ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
| ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ B ) )
& ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) ) )
& ( ( ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
& ( pp @ ( aa @ TA @ bool @ A @ D ) ) )
| ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ B ) )
& ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) )
=> ? [D: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ B ) ) )
& ( pp @ ( aa @ TA @ bool @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(47,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_empty__subsetI) ).
thf(275,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(90,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Un__absorb) ).
thf(403,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(14,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ( inf_inf @ ( fun @ TA @ bool ) @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Int__absorb1) ).
thf(141,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ( inf_inf @ ( fun @ TA @ bool ) @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(96,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
<=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
& ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_Int__iff) ).
thf(420,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
& ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) )
& ( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
& ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(9,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_le0) ).
thf(129,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(82,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_UnI1) ).
thf(371,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(3,axiom,
! [TA: $tType,A: TA,B: nat] : ( huffma1518433673istent @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_consistent_Osimps_I1_J) ).
thf(105,plain,
! [TA: $tType,A: TA,B: nat] : ( huffma1518433673istent @ TA @ ( huffma2021818691e_Leaf @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(77,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_IntI) ).
thf(360,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(30,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_nat__add__left__commute) ).
thf(205,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(61,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_IntD1) ).
thf(311,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(55,axiom,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_empty__iff) ).
thf(298,plain,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(44,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_nat__add__right__cancel) ).
thf(264,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(49,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
<=> ( ( sup_sup @ ( fun @ TA @ bool ) @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_subset__Un__eq) ).
thf(279,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ( sup_sup @ ( fun @ TA @ bool ) @ B @ A )
= A ) )
& ( ( ( sup_sup @ ( fun @ TA @ bool ) @ B @ A )
= A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(24,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) )
<=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_subset__empty) ).
thf(180,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
& ( ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(84,axiom,
huffma1518433673istent @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_InnerNode_Oprems) ).
thf(375,plain,
huffma1518433673istent @ a @ ( huffma1146269203erNode @ a @ w @ t_1 @ t_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(62,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_ex__in__conv) ).
thf(313,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
& ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(15,axiom,
! [TA: $tType] :
( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fFalse ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_empty__def) ).
thf(144,plain,
! [TA: $tType] :
( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fFalse ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(38,axiom,
! [TA: $tType,A: TA,B: TA,C: nat] :
( ( huffma410068972_depth @ TA @ ( huffma2021818691e_Leaf @ TA @ C @ B ) @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_depth_Osimps_I1_J) ).
thf(236,plain,
! [TA: $tType,A: TA,B: TA,C: nat] :
( ( huffma410068972_depth @ TA @ ( huffma2021818691e_Leaf @ TA @ C @ B ) @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(74,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( inf_inf @ ( fun @ TA @ bool ) @ B @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) )
= ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Int__left__absorb) ).
thf(350,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( inf_inf @ ( fun @ TA @ bool ) @ B @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) )
= ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(91,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_UnI2) ).
thf(406,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( sup_sup @ ( fun @ TA @ bool ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(22,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ( sup_sup @ ( fun @ TA @ bool ) @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ B ) @ A )
= ( inf_inf @ ( fun @ TA @ bool ) @ C @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) )
<=> ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Un__Int__assoc__eq) ).
thf(172,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ( ( sup_sup @ ( fun @ TA @ bool ) @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ B ) @ A )
= ( inf_inf @ ( fun @ TA @ bool ) @ C @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ C ) )
& ( ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ C )
=> ( ( sup_sup @ ( fun @ TA @ bool ) @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ B ) @ A )
= ( inf_inf @ ( fun @ TA @ bool ) @ C @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(78,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( inf_inf @ ( fun @ TA @ bool ) @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Int__absorb) ).
thf(362,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( inf_inf @ ( fun @ TA @ bool ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(45,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_less__eq__nat_Osimps_I1_J) ).
thf(271,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(31,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Int__greatest) ).
thf(208,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(345,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(65,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( inf_inf @ ( fun @ TA @ bool ) @ C @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) )
= ( inf_inf @ ( fun @ TA @ bool ) @ B @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Int__left__commute) ).
thf(323,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( inf_inf @ ( fun @ TA @ bool ) @ C @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) )
= ( inf_inf @ ( fun @ TA @ bool ) @ B @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(18,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_Int__lower2) ).
thf(155,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(21,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: huffma1450048681e_tree @ TA,E: huffma1450048681e_tree @ TA,F: nat] :
( ( ( huffma1146269203erNode @ TA @ F @ E @ D )
= ( huffma1146269203erNode @ TA @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_tree_Osimps_I2_J) ).
thf(162,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA,B: huffma1450048681e_tree @ TA,C: nat,D: huffma1450048681e_tree @ TA,E: huffma1450048681e_tree @ TA,F: nat] :
( ( ( ( huffma1146269203erNode @ TA @ F @ E @ D )
= ( huffma1146269203erNode @ TA @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( huffma1146269203erNode @ TA @ F @ E @ D )
= ( huffma1146269203erNode @ TA @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(41,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ( sup_sup @ ( fun @ TA @ bool ) @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Un__absorb1) ).
thf(255,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ( sup_sup @ ( fun @ TA @ bool ) @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(342,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(54,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ~ ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_IntE) ).
thf(295,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ~ ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(17,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ C @ B ) @ ( plus_plus @ nat @ C @ A ) )
<=> ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_nat__add__left__cancel__le) ).
thf(150,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ C @ B ) @ ( plus_plus @ nat @ C @ A ) )
=> ( ord_less_eq @ nat @ B @ A ) )
& ( ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ nat @ ( plus_plus @ nat @ C @ B ) @ ( plus_plus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(94,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ C @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) )
= ( sup_sup @ ( fun @ TA @ bool ) @ B @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_Un__left__commute) ).
thf(414,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ C @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) )
= ( sup_sup @ ( fun @ TA @ bool ) @ B @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(60,axiom,
enum @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Enum_Oenum) ).
thf(310,plain,
enum @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(28,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Collect__def) ).
thf(199,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(23,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( inf_inf @ ( fun @ TA @ bool ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ B ) @ A )
= ( sup_sup @ ( fun @ TA @ bool ) @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ A ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_Int__Un__distrib2) ).
thf(177,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( inf_inf @ ( fun @ TA @ bool ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ B ) @ A )
= ( sup_sup @ ( fun @ TA @ bool ) @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ A ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(67,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( inf_inf @ ( fun @ TA @ bool ) @ B @ A )
= ( inf_inf @ ( fun @ TA @ bool ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Int__commute) ).
thf(331,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( inf_inf @ ( fun @ TA @ bool ) @ B @ A )
= ( inf_inf @ ( fun @ TA @ bool ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(81,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(370,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(8,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ B )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Un__least) ).
thf(127,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ C @ B )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ A @ B )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ ( sup_sup @ ( fun @ TA @ bool ) @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(69,axiom,
( ( huffma1518433673istent @ a @ t_1 )
=> ? [A: a] :
( ( pp @ ( aa @ ( fun @ a @ bool ) @ bool @ ( aa @ a @ ( fun @ ( fun @ a @ bool ) @ bool ) @ ( member @ a ) @ A ) @ ( huffma675207370phabet @ a @ t_1 ) ) )
& ( ( huffma410068972_depth @ a @ t_1 @ A )
= ( huffma945805758height @ a @ t_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_InnerNode_I1_J) ).
thf(336,plain,
( ( huffma1518433673istent @ a @ t_1 )
=> ? [A: a] :
( ( pp @ ( aa @ ( fun @ a @ bool ) @ bool @ ( aa @ a @ ( fun @ ( fun @ a @ bool ) @ bool ) @ ( member @ a ) @ A ) @ ( huffma675207370phabet @ a @ t_1 ) ) )
& ( ( huffma410068972_depth @ a @ t_1 @ A )
= ( huffma945805758height @ a @ t_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(100,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ B @ A )
= ( sup_sup @ ( fun @ TA @ bool ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Un__commute) ).
thf(446,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ B @ A )
= ( sup_sup @ ( fun @ TA @ bool ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(36,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool,D: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ D @ C )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ ( inf_inf @ ( fun @ TA @ bool ) @ D @ B ) @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Int__mono) ).
thf(231,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool,D: fun @ TA @ bool] :
( ( ord_less_eq @ ( fun @ TA @ bool ) @ D @ C )
=> ( ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ A )
=> ( ord_less_eq @ ( fun @ TA @ bool ) @ ( inf_inf @ ( fun @ TA @ bool ) @ D @ B ) @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(33,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
<=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_le__0__eq) ).
thf(218,plain,
! [A: nat] :
( ( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) )
& ( ( A
= ( zero_zero @ nat ) )
=> ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ thesis,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(104,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(80,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(368,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType] :
( ( ( enum @ TA )
& ( enum @ TB ) )
=> ( enum @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Enum_Oenum) ).
thf(319,plain,
! [TA: $tType,TB: $tType] :
( ( ( enum @ TA )
& ( enum @ TB ) )
=> ( enum @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(304,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(42,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( inf_inf @ ( fun @ TA @ bool ) @ C @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) )
= ( sup_sup @ ( fun @ TA @ bool ) @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ B ) @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_Int__Un__distrib) ).
thf(258,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( inf_inf @ ( fun @ TA @ bool ) @ C @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) )
= ( sup_sup @ ( fun @ TA @ bool ) @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ B ) @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(25,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
= ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_nat__add__assoc) ).
thf(186,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
= ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(13,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_Un__upper1) ).
thf(139,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ ( sup_sup @ ( fun @ TA @ bool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(52,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA] : ( finite_finite @ TA @ ( huffma675207370phabet @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_finite__alphabet) ).
thf(290,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA] : ( finite_finite @ TA @ ( huffma675207370phabet @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(51,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( inf_inf @ ( fun @ TA @ bool ) @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ B ) @ A )
= ( inf_inf @ ( fun @ TA @ bool ) @ C @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Int__assoc) ).
thf(287,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: fun @ TA @ bool] :
( ( inf_inf @ ( fun @ TA @ bool ) @ ( inf_inf @ ( fun @ TA @ bool ) @ C @ B ) @ A )
= ( inf_inf @ ( fun @ TA @ bool ) @ C @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(56,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(300,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(93,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_equals0D) ).
thf(410,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(46,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ ( sup_sup @ ( fun @ TA @ bool ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_Un__upper2) ).
thf(273,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ B @ ( sup_sup @ ( fun @ TA @ bool ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(83,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) )
| ( pp @ B )
| ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(373,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) )
| ( pp @ B )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(32,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( sup_sup @ ( fun @ TA @ bool ) @ B @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
<=> ( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
& ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_Un__empty) ).
thf(210,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( ( ( sup_sup @ ( fun @ TA @ bool ) @ B @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
& ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
& ( ( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
& ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
=> ( ( sup_sup @ ( fun @ TA @ bool ) @ B @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(39,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) )
<=> ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_add__is__0) ).
thf(239,plain,
! [A: nat,B: nat] :
( ( ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) )
=> ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) ) )
& ( ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) )
=> ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(12,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ B @ A )
= ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_Un__def) ).
thf(136,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( sup_sup @ ( fun @ TA @ bool ) @ B @ A )
= ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(76,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(358,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(98,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_all__not__in__conv) ).
thf(437,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
& ( ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(66,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
<=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_Collect__empty__eq) ).
thf(326,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: nat,C: huffma1450048681e_tree @ TA,D: huffma1450048681e_tree @ TA,E: nat] :
( ( huffma1146269203erNode @ TA @ E @ D @ C )
!= ( huffma2021818691e_Leaf @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_tree_Osimps_I4_J) ).
thf(107,plain,
! [TA: $tType,A: TA,B: nat,C: huffma1450048681e_tree @ TA,D: huffma1450048681e_tree @ TA,E: nat] :
( ( huffma1146269203erNode @ TA @ E @ D @ C )
!= ( huffma2021818691e_Leaf @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(87,axiom,
! [TA: $tType,A: huffma1450048681e_tree @ TA] :
? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( huffma675207370phabet @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_exists__in__alphabet) ).
thf(395,plain,
! [TA: $tType,A: huffma1450048681e_tree @ TA] :
? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( huffma675207370phabet @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(103,axiom,
! [A: a] :
( ( pp @ ( aa @ ( fun @ a @ bool ) @ bool @ ( aa @ a @ ( fun @ ( fun @ a @ bool ) @ bool ) @ ( member @ a ) @ A ) @ ( huffma675207370phabet @ a @ t_1 ) ) )
=> ( ( ( huffma410068972_depth @ a @ t_1 @ A )
= ( huffma945805758height @ a @ t_1 ) )
=> thesis ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(459,plain,
! [A: a] :
( ( pp @ ( aa @ ( fun @ a @ bool ) @ bool @ ( aa @ a @ ( fun @ ( fun @ a @ bool ) @ bool ) @ ( member @ a ) @ A ) @ ( huffma675207370phabet @ a @ t_1 ) ) )
=> ( ( ( huffma410068972_depth @ a @ t_1 @ A )
= ( huffma945805758height @ a @ t_1 ) )
=> thesis ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(10,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ C @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_le__trans) ).
thf(131,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ C @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( ord_less_eq @ nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(48,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_Int__lower1) ).
thf(277,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] : ( ord_less_eq @ ( fun @ TA @ bool ) @ ( inf_inf @ ( fun @ TA @ bool ) @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(462,plain,
$false,
inference(e,[status(thm)],[365,340,417,225,118,399,408,449,202,110,196,157,189,284,228,261,443,321,376,121,348,353,147,397,133,307,292,248,380,233,452,334,302,160,424,275,403,141,420,129,371,105,360,205,311,298,264,279,180,375,313,144,236,350,406,172,362,271,208,345,323,155,162,255,342,295,150,414,310,199,177,331,370,127,336,446,231,218,104,368,319,304,258,186,139,290,287,300,410,273,373,210,239,136,358,437,326,107,395,459,131,277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW529_5 : TPTP v8.1.2. Released v6.0.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n024.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 : Thu May 18 22:19:53 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.94/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.65/1.05 % [INFO] Parsing done (203ms).
% 1.65/1.06 % [INFO] Running in sequential loop mode.
% 2.30/1.26 % [INFO] eprover registered as external prover.
% 2.30/1.26 % [INFO] cvc4 registered as external prover.
% 2.30/1.27 % [INFO] Scanning for conjecture ...
% 2.63/1.37 % [INFO] Found a conjecture and 161 axioms. Running axiom selection ...
% 2.92/1.44 % [INFO] Axiom selection finished. Selected 101 axioms (removed 60 axioms).
% 3.37/1.58 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.37/1.60 % [INFO] Type checking passed.
% 3.37/1.60 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 4.17/1.91 % [INFO] [Domain constraints] Detected constraint on bool
% 4.17/1.91 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 12.17/4.58 % External prover 'e' found a proof!
% 12.17/4.58 % [INFO] Killing All external provers ...
% 12.17/4.58 % Time passed: 4066ms (effective reasoning time: 3523ms)
% 12.17/4.58 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 12.17/4.58 % Axioms used in derivation (101): fact_21_double__add__le__zero__iff__single__add__le__zero, fact_79_IntD1, fact_30_subset__empty, help_COMBS_1_1_U, fact_4_exists__in__alphabet, fact_2_InnerNode_I1_J, fact_24_Int__Un__distrib2, help_fconj_3_1_U, fact_78_IntD2, fact_83_Int__commute, fact_22_nat__add__left__cancel__le, fact_3_tree_Osimps_I2_J, fact_36_all__not__in__conv, fact_17_tree_Osimps_I3_J, fact_63_Un__Int__assoc__eq, fact_6_finite__alphabet, fact_38_nat__add__left__cancel, fact_37_nat__add__right__cancel, fact_56_Un__absorb1, fact_27_le__0__eq, fact_82_Int__left__absorb, fact_73_mem__def, fact_41_Int__iff, fact_74_Collect__def, fact_20_zero__le__double__add__iff__zero__le__single__add, fact_39_IntE, arity_fun___Enum_Oenum, fact_88_ball__Un, fact_91_Un__left__commute, fact_87_UnI1, fact_18_tree_Osimps_I4_J, help_fFalse_1_1_T, fact_57_Int__absorb1, fact_48_Un__empty, fact_90_Un__assoc, fact_35_empty__Collect__eq, help_COMBB_1_1_U, fact_16_consistent_Osimps_I1_J, fact_77_nat__add__commute, arity_HOL_Obool___Enum_Oenum, help_fdisj_1_1_U, fact_5_depth__le__height, fact_0_InnerNode_Oprems, fact_89_bex__Un, help_fconj_2_1_U, fact_44_Un__iff, fact_81_Int__left__commute, fact_84_Int__def, fact_94_Un__def, fact_49_add__is__0, fact_26_less__eq__nat_Osimps_I1_J, fact_31_empty__subsetI, fact_92_Un__left__absorb, fact_76_nat__add__left__commute, fact_50_Un__upper1, fact_71_empty__def, fact_58_Un__absorb2, fact_53_Int__lower2, fact_33_Collect__empty__eq, fact_55_Int__absorb2, fact_40_IntI, fact_25_le0, fact_80_Int__assoc, fact_9_height_Osimps_I1_J, fact_32_emptyE, fact_62_Un__mono, help_fdisj_2_1_U, help_COMBK_1_1_U, fact_93_Un__commute, fact_15_tree_Osimps_I1_J, help_COMBC_1_1_U, fact_69_equals0D, help_fconj_1_1_U, help_fdisj_3_1_U, fact_52_Int__lower1, fact_54_subset__Un__eq, fact_96_le__antisym, fact_8_depth_Osimps_I1_J, fact_95_Un__absorb, help_fFalse_1_1_U, fact_23_Int__Un__distrib, fact_60_Un__least, fact_51_Un__upper2, fact_47_double__zero__sym, fact_61_Int__mono, help_pp_1_1_U, fact_13_consistent_Osimps_I2_J, fact_1_InnerNode_I2_J, fact_86_UnI2, fact_34_empty__iff, fact_70_ex__in__conv, fact_59_Int__greatest, fact_10_depth_Osimps_I2_J, fact_42_UnCI, fact_43_UnE, conj_0, help_pp_2_1_U, fact_85_Int__absorb, fact_75_nat__add__assoc, fact_7_alphabet_Osimps_I2_J, fact_97_le__trans
% 12.17/4.58 % No. of inferences in proof: 206
% 12.17/4.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4066 ms resp. 3523 ms w/o parsing
% 12.65/4.66 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.65/4.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------