%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW529_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:10:45 AM UTC 2026
% Result : Theorem 14.63s 5.79s
% Output : Refutation 15.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 102
% Syntax : Number of formulae : 206 ( 80 unt; 0 typ; 0 def)
% Number of atoms : 1064 ( 168 equ; 0 cnn)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 4894 ( 54 ~; 24 |; 70 &;4583 @)
% ( 24 <=>; 139 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 34 usr; 11 con; 0-5 aty)
% Number of variables : 628 ( 0 ^; 610 !; 18 ?; 628 :)
% 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_decl,type,
enum:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(combb_decl,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TB @ ( TC @ fun ) ) > ( TC @ ( TA @ fun ) ) > ( TB @ ( TA @ fun ) ) ) ).
thf(combc_decl,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > TB > ( TA @ ( TC @ fun ) ) ) ).
thf(combk_decl,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ fun ) ) ) ).
thf(combs_decl,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ fun ) ) > ( TA @ ( TC @ fun ) ) ) ).
thf(finite_finite_decl,type,
finite_finite:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > $o ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(huffma675207370phabet_decl,type,
huffma675207370phabet:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > ( bool @ ( TA @ fun ) ) ) ).
thf(huffma1518433673istent_decl,type,
huffma1518433673istent:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > $o ) ).
thf(huffma410068972_depth_decl,type,
huffma410068972_depth:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > TA > nat ) ).
thf(huffma945805758height_decl,type,
huffma945805758height:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > nat ) ).
thf(huffma1146269203erNode_decl,type,
huffma1146269203erNode:
!>[TA: $tType] : ( nat > ( TA @ huffma1450048681e_tree ) > ( TA @ huffma1450048681e_tree ) > ( TA @ huffma1450048681e_tree ) ) ).
thf(huffma2021818691e_Leaf_decl,type,
huffma2021818691e_Leaf:
!>[TA: $tType] : ( nat > TA > ( TA @ huffma1450048681e_tree ) ) ).
thf(inf_inf_decl,type,
inf_inf:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(sup_sup_decl,type,
sup_sup:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fconj_decl,type,
fconj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(fdisj_decl,type,
fdisj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ fun ) ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(t_1_decl,type,
t_1: a @ huffma1450048681e_tree ).
thf(t_2_decl,type,
t_2: a @ huffma1450048681e_tree ).
thf(thesis_decl,type,
thesis: $o ).
thf(w_decl,type,
w: nat ).
thf(90,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Un__absorb) ).
thf(426,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(12,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_Un__def) ).
thf(138,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(39,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) )
<=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_add__is__0) ).
thf(249,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) )
=> ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) )
=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(68,axiom,
! [TA: $tType,A: TA,B: TA @ huffma1450048681e_tree] : ( B @ ( TA @ huffma945805758height ) @ ( A @ ( B @ ( TA @ huffma410068972_depth ) ) @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_depth__le__height) ).
thf(352,plain,
! [TA: $tType,A: TA,B: TA @ huffma1450048681e_tree] : ( B @ ( TA @ huffma945805758height ) @ ( A @ ( B @ ( TA @ huffma410068972_depth ) ) @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(97,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ? [D: TA] :
( ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( B @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
<=> ( ? [D: TA] :
( ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( B @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
| ? [D: TA] :
( ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( C @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_bex__Un) ).
thf(449,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( ( ? [D: TA] :
( ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( B @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
| ? [D: TA] :
( ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( C @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) )
=> ? [D: TA] :
( ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( B @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) )
& ( ? [D: TA] :
( ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( B @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( ? [D: TA] :
( ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( B @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
| ? [D: TA] :
( ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( C @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(95,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_mem__def) ).
thf(440,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(79,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(385,plain,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(65,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Int__left__commute) ).
thf(340,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(87,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree] :
? [B: TA] : ( A @ ( TA @ huffma675207370phabet ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_exists__in__alphabet) ).
thf(417,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree] :
? [B: TA] : ( A @ ( TA @ huffma675207370phabet ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(320,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(75,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) )
<=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_empty__Collect__eq) ).
thf(372,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) ) )
& ( ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) )
=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(5,axiom,
! [TA: $tType,A: TA,B: nat,C: TA,D: nat] :
( ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
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] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(26,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma1518433673istent ) )
<=> ( ( ( A @ ( TA @ huffma675207370phabet ) @ ( B @ ( TA @ huffma675207370phabet ) @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
& ( A @ ( TA @ huffma1518433673istent ) )
& ( B @ ( TA @ huffma1518433673istent ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_consistent_Osimps_I2_J) ).
thf(196,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat] :
( ( ( ( ( A @ ( TA @ huffma675207370phabet ) @ ( B @ ( TA @ huffma675207370phabet ) @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
& ( A @ ( TA @ huffma1518433673istent ) )
& ( B @ ( TA @ huffma1518433673istent ) ) )
=> ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma1518433673istent ) ) )
& ( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma1518433673istent ) )
=> ( ( ( A @ ( TA @ huffma675207370phabet ) @ ( B @ ( TA @ huffma675207370phabet ) @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
& ( A @ ( TA @ huffma1518433673istent ) )
& ( B @ ( TA @ huffma1518433673istent ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(89,axiom,
( ( t_2 @ ( a @ huffma1518433673istent ) )
=> ? [A: a] :
( ( ( A @ ( t_2 @ ( a @ huffma410068972_depth ) ) )
= ( t_2 @ ( a @ huffma945805758height ) ) )
& ( t_2 @ ( a @ huffma675207370phabet ) @ ( A @ ( a @ member @ ( bool @ ( bool @ ( a @ fun ) @ fun ) @ ( a @ aa ) ) ) @ ( bool @ ( bool @ ( a @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_InnerNode_I2_J) ).
thf(421,plain,
( ( t_2 @ ( a @ huffma1518433673istent ) )
=> ? [A: a] :
( ( ( A @ ( t_2 @ ( a @ huffma410068972_depth ) ) )
= ( t_2 @ ( a @ huffma945805758height ) ) )
& ( t_2 @ ( a @ huffma675207370phabet ) @ ( A @ ( a @ member @ ( bool @ ( bool @ ( a @ fun ) @ fun ) @ ( a @ aa ) ) ) @ ( bool @ ( bool @ ( a @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(17,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_nat__add__left__cancel__le) ).
thf(152,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less_eq ) ) ) )
& ( ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(47,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_empty__subsetI) ).
thf(289,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(56,axiom,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(316,plain,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(31,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Int__greatest) ).
thf(216,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(20,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: bool @ ( TA @ fun )] :
( ( C @ ( D @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( B @ ( D @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Un__mono) ).
thf(164,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: bool @ ( TA @ fun )] :
( ( C @ ( D @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( B @ ( D @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(35,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_nat__add__commute) ).
thf(238,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(102,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: nat,C: TA @ huffma1450048681e_tree,D: TA] :
( ( ~ ( C @ ( TA @ huffma675207370phabet ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( ~ ( A @ ( TA @ huffma675207370phabet ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( D @ ( A @ ( C @ ( B @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma410068972_depth ) ) )
= ( nat @ zero_zero ) ) )
& ( ( A @ ( TA @ huffma675207370phabet ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( D @ ( A @ ( C @ ( B @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma410068972_depth ) ) )
= ( nat @ one_one @ ( D @ ( A @ ( TA @ huffma410068972_depth ) ) @ ( nat @ plus_plus ) ) ) ) ) ) )
& ( ( C @ ( TA @ huffma675207370phabet ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( D @ ( A @ ( C @ ( B @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma410068972_depth ) ) )
= ( nat @ one_one @ ( D @ ( C @ ( TA @ huffma410068972_depth ) ) @ ( nat @ plus_plus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_depth_Osimps_I2_J) ).
thf(480,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: nat,C: TA @ huffma1450048681e_tree,D: TA] :
( ( ~ ( C @ ( TA @ huffma675207370phabet ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( ~ ( A @ ( TA @ huffma675207370phabet ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( D @ ( A @ ( C @ ( B @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma410068972_depth ) ) )
= ( nat @ zero_zero ) ) )
& ( ( A @ ( TA @ huffma675207370phabet ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( D @ ( A @ ( C @ ( B @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma410068972_depth ) ) )
= ( nat @ one_one @ ( D @ ( A @ ( TA @ huffma410068972_depth ) ) @ ( nat @ plus_plus ) ) ) ) ) ) )
& ( ( C @ ( TA @ huffma675207370phabet ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( D @ ( A @ ( C @ ( B @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma410068972_depth ) ) )
= ( nat @ one_one @ ( D @ ( C @ ( TA @ huffma410068972_depth ) ) @ ( nat @ plus_plus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(49,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
<=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_subset__Un__eq) ).
thf(293,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= A )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(85,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
| ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_Un__iff) ).
thf(396,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
| ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
| ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(10,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_le__trans) ).
thf(133,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(37,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_Int__def) ).
thf(243,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(53,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Un__left__absorb) ).
thf(307,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(77,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_IntI) ).
thf(380,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(42,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_Int__Un__distrib) ).
thf(270,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(51,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Int__assoc) ).
thf(302,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(67,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( B @ ( A @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Int__commute) ).
thf(349,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( B @ ( A @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(19,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_zero__le__double__add__iff__zero__le__single__add) ).
thf(160,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(91,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_UnI2) ).
thf(429,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(361,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(62,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ? [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_ex__in__conv) ).
thf(329,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ? [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ? [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(45,axiom,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_less__eq__nat_Osimps_I1_J) ).
thf(285,plain,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(80,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(388,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(13,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] : ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_Un__upper1) ).
thf(141,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] : ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(103,axiom,
! [A: a] :
( ( t_1 @ ( a @ huffma675207370phabet ) @ ( A @ ( a @ member @ ( bool @ ( bool @ ( a @ fun ) @ fun ) @ ( a @ aa ) ) ) @ ( bool @ ( bool @ ( a @ fun ) @ aa ) ) ) @ pp )
=> ( ( ( A @ ( t_1 @ ( a @ huffma410068972_depth ) ) )
= ( t_1 @ ( a @ huffma945805758height ) ) )
=> thesis ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(488,plain,
! [A: a] :
( ( t_1 @ ( a @ huffma675207370phabet ) @ ( A @ ( a @ member @ ( bool @ ( bool @ ( a @ fun ) @ fun ) @ ( a @ aa ) ) ) @ ( bool @ ( bool @ ( a @ fun ) @ aa ) ) ) @ pp )
=> ( ( ( A @ ( t_1 @ ( a @ huffma410068972_depth ) ) )
= ( t_1 @ ( a @ huffma945805758height ) ) )
=> thesis ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(25,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_nat__add__assoc) ).
thf(193,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(83,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ( B @ pp )
| ~ ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(393,plain,
! [A: bool,B: bool] :
( ( A @ pp )
| ( B @ pp )
| ~ ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(8,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B @ ( A @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Un__least) ).
thf(129,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( B @ ( A @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(66,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
<=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_Collect__empty__eq) ).
thf(343,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(3,axiom,
! [TA: $tType,A: TA,B: nat] : ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1518433673istent ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_consistent_Osimps_I1_J) ).
thf(105,plain,
! [TA: $tType,A: TA,B: nat] : ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1518433673istent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(21,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TA @ huffma1450048681e_tree,E: TA @ huffma1450048681e_tree,F: nat] :
( ( ( D @ ( E @ ( F @ ( TA @ huffma1146269203erNode ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_tree_Osimps_I2_J) ).
thf(166,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TA @ huffma1450048681e_tree,E: TA @ huffma1450048681e_tree,F: nat] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ ( TA @ huffma1146269203erNode ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ ( TA @ huffma1146269203erNode ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(96,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_Int__iff) ).
thf(444,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(16,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Int__absorb2) ).
thf(149,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(48,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] : ( B @ ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_Int__lower1) ).
thf(291,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] : ( B @ ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(27,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(204,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(40,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_nat__add__left__cancel) ).
thf(259,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(82,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_UnI1) ).
thf(391,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(78,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( A @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Int__absorb) ).
thf(382,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( A @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(88,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(419,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(57,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(318,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(101,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_Un__assoc) ).
thf(477,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(73,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(367,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(59,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma675207370phabet ) )
= ( A @ ( TA @ huffma675207370phabet ) @ ( B @ ( TA @ huffma675207370phabet ) @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_alphabet_Osimps_I2_J) ).
thf(323,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma675207370phabet ) )
= ( A @ ( TA @ huffma675207370phabet ) @ ( B @ ( TA @ huffma675207370phabet ) @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(30,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_nat__add__left__commute) ).
thf(213,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(11,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Un__absorb2) ).
thf(135,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(50,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(299,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(41,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Un__absorb1) ).
thf(267,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(92,axiom,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_emptyE) ).
thf(431,plain,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(36,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: bool @ ( TA @ fun )] :
( ( C @ ( D @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( B @ ( D @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_Int__mono) ).
thf(241,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: bool @ ( TA @ fun )] :
( ( C @ ( D @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( B @ ( D @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(61,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_IntD1) ).
thf(327,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(54,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_IntE) ).
thf(310,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(22,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) )
<=> ( C @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Un__Int__assoc__eq) ).
thf(177,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( ( C @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ) )
& ( ( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) )
=> ( C @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(98,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_all__not__in__conv) ).
thf(463,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ! [B: TA] :
~ ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(64,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_IntD2) ).
thf(338,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(99,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( ~ ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( B @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_UnCI) ).
thf(470,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( ~ ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( B @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(70,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ~ ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_UnE) ).
thf(359,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ~ ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ enum ) )
=> ( TA @ ( TB @ fun ) @ enum ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Enum_Oenum) ).
thf(336,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ enum ) )
=> ( TA @ ( TB @ fun ) @ enum ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(55,axiom,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_empty__iff) ).
thf(314,plain,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(14,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Int__absorb1) ).
thf(143,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(32,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
<=> ( ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) )
& ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_Un__empty) ).
thf(218,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) )
& ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) )
& ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
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(18,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] : ( A @ ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_Int__lower2) ).
thf(158,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] : ( A @ ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(81,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(390,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(24,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
<=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_subset__empty) ).
thf(186,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ) )
& ( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A
= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(86,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ! [D: TA] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
<=> ( ! [D: TA] :
( ( B @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ! [D: TA] :
( ( C @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_ball__Un) ).
thf(401,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( ( ! [D: TA] :
( ( B @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ! [D: TA] :
( ( C @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) )
=> ! [D: TA] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) )
& ( ! [D: TA] :
( ( B @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( ! [D: TA] :
( ( B @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ! [D: TA] :
( ( C @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(93,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ~ ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_equals0D) ).
thf(433,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun )] :
( ( B
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ~ ( B @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(28,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Collect__def) ).
thf(207,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(46,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] : ( B @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_Un__upper2) ).
thf(287,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] : ( B @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( B @ ( bool @ ( TA @ fun ) @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(6,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TA,E: nat] :
( ( D @ ( E @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_tree_Osimps_I3_J) ).
thf(119,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TA,E: nat] :
( ( D @ ( E @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(76,axiom,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(378,plain,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(34,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_le__antisym) ).
thf(235,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(38,axiom,
! [TA: $tType,A: TA,B: TA,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma410068972_depth ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_depth_Osimps_I1_J) ).
thf(246,plain,
! [TA: $tType,A: TA,B: TA,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma410068972_depth ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(15,axiom,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ bot_bot )
= ( fFalse @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_empty__def) ).
thf(146,plain,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ bot_bot )
= ( fFalse @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(23,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( A @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_Int__Un__distrib2) ).
thf(183,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( A @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(43,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_double__add__le__zero__iff__single__add__le__zero) ).
thf(273,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(52,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree] : ( A @ ( TA @ huffma675207370phabet ) @ ( TA @ finite_finite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_finite__alphabet) ).
thf(305,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree] : ( A @ ( TA @ huffma675207370phabet ) @ ( TA @ finite_finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(29,axiom,
! [TA: $tType,A: TA,B: nat] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma945805758height ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_height_Osimps_I1_J) ).
thf(210,plain,
! [TA: $tType,A: TA,B: nat] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma945805758height ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(94,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( A @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_Un__left__commute) ).
thf(437,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( A @ ( C @ ( bool @ ( TA @ fun ) @ sup_sup ) ) @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(100,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( B @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Un__commute) ).
thf(474,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ sup_sup ) ) )
= ( B @ ( A @ ( bool @ ( TA @ fun ) @ sup_sup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(60,axiom,
bool @ enum,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Enum_Oenum) ).
thf(326,plain,
bool @ enum,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: nat,C: TA @ huffma1450048681e_tree,D: TA @ huffma1450048681e_tree,E: nat] :
( ( C @ ( D @ ( E @ ( TA @ huffma1146269203erNode ) ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_tree_Osimps_I4_J) ).
thf(107,plain,
! [TA: $tType,A: TA,B: nat,C: TA @ huffma1450048681e_tree,D: TA @ huffma1450048681e_tree,E: nat] :
( ( C @ ( D @ ( E @ ( TA @ huffma1146269203erNode ) ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(84,axiom,
t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1518433673istent ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_InnerNode_Oprems) ).
thf(395,plain,
t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1518433673istent ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(9,axiom,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_le0) ).
thf(131,plain,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(44,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_nat__add__right__cancel) ).
thf(277,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(74,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Int__left__absorb) ).
thf(369,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(33,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_le__0__eq) ).
thf(227,plain,
! [A: nat] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) ) )
& ( ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(7,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_double__zero__sym) ).
thf(122,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(69,axiom,
( ( t_1 @ ( a @ huffma1518433673istent ) )
=> ? [A: a] :
( ( ( A @ ( t_1 @ ( a @ huffma410068972_depth ) ) )
= ( t_1 @ ( a @ huffma945805758height ) ) )
& ( t_1 @ ( a @ huffma675207370phabet ) @ ( A @ ( a @ member @ ( bool @ ( bool @ ( a @ fun ) @ fun ) @ ( a @ aa ) ) ) @ ( bool @ ( bool @ ( a @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_InnerNode_I1_J) ).
thf(354,plain,
( ( t_1 @ ( a @ huffma1518433673istent ) )
=> ? [A: a] :
( ( ( A @ ( t_1 @ ( a @ huffma410068972_depth ) ) )
= ( t_1 @ ( a @ huffma945805758height ) ) )
& ( t_1 @ ( a @ huffma675207370phabet ) @ ( A @ ( a @ member @ ( bool @ ( bool @ ( a @ fun ) @ fun ) @ ( a @ aa ) ) ) @ ( bool @ ( bool @ ( a @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(364,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(533,plain,
$false,
inference(e,[status(thm)],[426,138,249,352,449,440,385,340,417,320,372,110,196,421,152,289,316,216,164,238,480,293,396,133,243,307,380,270,302,349,160,429,361,329,285,388,141,488,193,393,129,343,105,166,444,149,291,204,259,391,382,419,318,477,367,323,213,135,299,267,431,241,327,310,177,463,338,470,359,336,314,143,218,104,158,390,186,401,433,207,287,119,378,235,246,146,183,273,305,210,437,474,326,107,395,131,277,369,227,122,354,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW529_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.40 % Computer : n010.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sat Sep 26 16:11:31 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.82/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.43/1.27 % [INFO] Parsing done (293ms).
% 1.43/1.28 % [INFO] Running in sequential loop mode.
% 2.44/1.66 % [INFO] eprover registered as external prover.
% 2.44/1.67 % [INFO] Scanning for conjecture ...
% 2.82/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 161 axioms. Running axiom selection ...
% 3.05/1.94 % [INFO] Axiom selection finished. Selected 101 axioms (removed 60 axioms).
% 4.02/2.14 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.02/2.17 % [INFO] Type checking passed.
% 4.02/2.17 % [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 ...
% 5.36/2.66 % [INFO] [Domain constraints] Detected constraint on bool
% 5.36/2.66 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 14.63/5.79 % External prover 'e' found a proof!
% 14.63/5.79 % [INFO] Killing All external provers ...
% 14.63/5.79 % Time passed: 5246ms (effective reasoning time: 4506ms)
% 14.63/5.79 % 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)>
% 14.63/5.79 % 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
% 14.63/5.79 % No. of inferences in proof: 206
% 14.63/5.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5246 ms resp. 4506 ms w/o parsing
% 15.68/5.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.68/5.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------