%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW535_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 : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:10:45 AM UTC 2026
% Result : Theorem 111.04s 35.33s
% Output : Refutation 111.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 123
% Number of leaves : 134
% Syntax : Number of formulae : 800 ( 157 unt; 0 typ; 1 def)
% Number of atoms : 8142 ( 838 equ; 0 cnn)
% Maximal formula atoms : 41 ( 10 avg)
% Number of connectives : 21732 ( 798 ~; 596 |; 54 &;20078 @)
% ( 20 <=>; 186 =>; 0 <=; 0 <~>)
% Maximal formula depth : 83 ( 16 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 49 usr; 10 con; 0-5 aty)
% Number of variables : 7191 ( 2 ^;7183 !; 5 ?;7191 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(bounded_lattice_decl,type,
bounded_lattice:
!>[TA: $tType] : $o ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(bot_decl,type,
bot:
!>[TA: $tType] : $o ).
thf(lattice_decl,type,
lattice:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(semiring_char_0_decl,type,
semiring_char_0:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_decl,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_decl,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(semilattice_inf_decl,type,
semilattice_inf:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(bounded_lattice_bot_decl,type,
bounded_lattice_bot:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(semiri456707255roduct_decl,type,
semiri456707255roduct:
!>[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(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(huffma1134658180e_cost_decl,type,
huffma1134658180e_cost:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > nat ) ).
thf(huffma410068972_depth_decl,type,
huffma410068972_depth:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > TA > nat ) ).
thf(huffma1352802255e_freq_decl,type,
huffma1352802255e_freq:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > TA > 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(huffma107959123e_case_decl,type,
huffma107959123e_case:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) @ ( nat @ fun ) ) > ( TA @ ( TB @ huffma1450048681e_tree @ fun ) @ ( TB @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ) ) > ( TB @ huffma1450048681e_tree ) > TA ) ).
thf(huffma1280178957ee_rec_decl,type,
huffma1280178957ee_rec:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) @ ( nat @ fun ) ) > ( TA @ ( TA @ fun ) @ ( TA @ fun ) @ ( TB @ huffma1450048681e_tree @ fun ) @ ( TB @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ) ) > ( TB @ huffma1450048681e_tree ) > TA ) ).
thf(huffma83463279weight_decl,type,
huffma83463279weight:
!>[TA: $tType] : ( ( TA @ huffma1450048681e_tree ) > nat ) ).
thf(inf_inf_decl,type,
inf_inf:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(semiring_1_of_nat_decl,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(bot_bot_decl,type,
bot_bot:
!>[TA: $tType] : TA ).
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(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(w_decl,type,
w: nat ).
thf(sk3_decl,type,
sk3:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > TA ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [TA: $tType,A: bool @ ( TA @ fun )] :
@+[B: TA] :
~ ~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ).
thf(8,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_33_tree_Osimps_I1_J) ).
thf(150,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)],[8]) ).
thf(151,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) )
| ( C != A )
| ( D != B ) )
& ( ( C = A )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) )
& ( ( D = B )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ) ),
inference(cnf,[status(esa)],[150]) ).
thf(153,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( C = A )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(cnfConj,[status(thm)],[151]) ).
thf(156,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( C = A )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(lifteq,[status(thm)],[153]) ).
thf(46,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(274,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(275,plain,
~ ( fFalse @ pp ),
inference(polarity_switch,[status(thm)],[274]) ).
thf(867,plain,
! [D: nat,C: $o,B: nat,A: $o] :
( ( A
!= ( fFalse @ pp ) )
| ~ C
| ( ( C @ ( D @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,275]) ).
thf(868,plain,
! [C: nat,B: $o,A: nat] :
( ~ B
| ( ( B @ ( C @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( fFalse @ pp @ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[867:[bind(A,$thf( fFalse @ pp )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(1475,plain,
! [C: nat,B: $o,A: nat] :
( ~ B
| ( ( B @ ( C @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( fFalse @ pp @ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[868]) ).
thf(2167,plain,
! [C: nat,B: $o,A: nat] :
( ~ B
| ( ( B @ ( C @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( $false @ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(rewrite,[status(thm)],[1475,275]) ).
thf(2186,plain,
! [D: $o,C: $o,B: nat,A: nat] :
( ~ ( D
| C )
| ( ( ( D
| C )
@ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( $false @ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(prim_subst,[status(thm)],[2167:[bind(A,$thf( A )),bind(B,$thf( E | D ))]]) ).
thf(2196,plain,
! [D: $o,C: $o,B: nat,A: nat] :
( ( ~ D
| ( ( ( D
| C )
@ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( $false @ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) )
& ( ~ C
| ( ( ( D
| C )
@ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( $false @ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ) ),
inference(cnf,[status(esa)],[2186]) ).
thf(2197,plain,
! [D: $o,C: $o,B: nat,A: nat] :
( ~ C
| ( ( ( D
| C )
@ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( $false @ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(cnfConj,[status(thm)],[2196]) ).
thf(2199,plain,
! [D: $o,C: $o,B: nat,A: nat] :
( ~ C
| ( ( ( D
| C )
@ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( $false @ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[2197]) ).
thf(68,axiom,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) )
= ( B @ ( A @ ( TA @ inf_inf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_inf__sup__aci_I1_J) ).
thf(347,plain,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) )
= ( B @ ( A @ ( TA @ inf_inf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(38,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(249,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)],[38]) ).
thf(72,axiom,
bool @ lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Olattice) ).
thf(363,plain,
bool @ lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ lattice )
=> ( TA @ ( TB @ fun ) @ lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Olattice) ).
thf(145,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ lattice )
=> ( TA @ ( TB @ fun ) @ lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(146,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ( TA @ fun ) @ lattice )
| ~ ( TB @ lattice ) ),
inference(cnf,[status(esa)],[145]) ).
thf(585,plain,
! [TA: $tType,TB: $tType] :
( ( ( bool @ lattice )
!= ( TB @ lattice ) )
| ( TB @ ( TA @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[363,146]) ).
thf(586,plain,
! [TA: $tType,TB: $tType] :
( ( ( bool @ lattice )
!= ( TB @ lattice ) )
| ( TB @ ( TA @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[585]) ).
thf(587,plain,
! [TA: $tType] : ( bool @ ( TA @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[586:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( bool ))]]) ).
thf(594,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( bool @ ( TA @ fun ) @ lattice )
!= ( TC @ lattice ) )
| ( TC @ ( TB @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[587,146]) ).
thf(595,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( bool @ ( TA @ fun ) @ lattice )
!= ( TC @ lattice ) )
| ( TC @ ( TB @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[594]) ).
thf(596,plain,
! [TA: $tType,TB: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[595:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( bool @ ( TA @ fun ) ))]]) ).
thf(600,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ lattice )
!= ( TD @ lattice ) )
| ( TD @ ( TC @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[596,146]) ).
thf(601,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ lattice )
!= ( TD @ lattice ) )
| ( TD @ ( TC @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[600]) ).
thf(602,plain,
! [TA: $tType,TB: $tType,TC: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[601:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) ))]]) ).
thf(613,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ lattice )
!= ( TE @ lattice ) )
| ( TE @ ( TD @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[602,146]) ).
thf(614,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ lattice )
!= ( TE @ lattice ) )
| ( TE @ ( TD @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[613]) ).
thf(615,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[614:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) ))]]) ).
thf(619,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ lattice )
!= ( TF @ lattice ) )
| ( TF @ ( TE @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[615,146]) ).
thf(620,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ lattice )
!= ( TF @ lattice ) )
| ( TF @ ( TE @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[619]) ).
thf(621,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[620:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) ))]]) ).
thf(634,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ lattice )
!= ( TG @ lattice ) )
| ( TG @ ( TF @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[621,146]) ).
thf(635,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ lattice )
!= ( TG @ lattice ) )
| ( TG @ ( TF @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[634]) ).
thf(636,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[635:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) ))]]) ).
thf(640,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ lattice )
!= ( TH @ lattice ) )
| ( TH @ ( TG @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[636,146]) ).
thf(641,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ lattice )
!= ( TH @ lattice ) )
| ( TH @ ( TG @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[640]) ).
thf(642,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[641:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) ))]]) ).
thf(649,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ lattice )
!= ( TI @ lattice ) )
| ( TI @ ( TH @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[642,146]) ).
thf(650,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ lattice )
!= ( TI @ lattice ) )
| ( TI @ ( TH @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[649]) ).
thf(651,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[650:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) ))]]) ).
thf(710,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ lattice )
!= ( TJ @ lattice ) )
| ( TJ @ ( TI @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[651,146]) ).
thf(711,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ lattice )
!= ( TJ @ lattice ) )
| ( TJ @ ( TI @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[710]) ).
thf(712,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[711:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) ))]]) ).
thf(716,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ lattice )
!= ( TK @ lattice ) )
| ( TK @ ( TJ @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[712,146]) ).
thf(717,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ lattice )
!= ( TK @ lattice ) )
| ( TK @ ( TJ @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[716]) ).
thf(718,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[717:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) ))]]) ).
thf(722,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ lattice )
!= ( TL @ lattice ) )
| ( TL @ ( TK @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[718,146]) ).
thf(723,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ lattice )
!= ( TL @ lattice ) )
| ( TL @ ( TK @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[722]) ).
thf(724,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[723:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) ))]]) ).
thf(1566,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ lattice )
!= ( TM @ lattice ) )
| ( TM @ ( TL @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[724,146]) ).
thf(1567,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ lattice )
!= ( TM @ lattice ) )
| ( TM @ ( TL @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[1566]) ).
thf(1568,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[1567:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) ))]]) ).
thf(1584,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ lattice )
!= ( TN @ lattice ) )
| ( TN @ ( TM @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1568,146]) ).
thf(1585,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ lattice )
!= ( TN @ lattice ) )
| ( TN @ ( TM @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[1584]) ).
thf(1586,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[1585:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) ))]]) ).
thf(1699,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ lattice )
!= ( TO @ lattice ) )
| ( TO @ ( TN @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1586,146]) ).
thf(1700,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ lattice )
!= ( TO @ lattice ) )
| ( TO @ ( TN @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[1699]) ).
thf(1701,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[1700:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) ))]]) ).
thf(1717,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ lattice )
!= ( TP @ lattice ) )
| ( TP @ ( TO @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1701,146]) ).
thf(1718,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ lattice )
!= ( TP @ lattice ) )
| ( TP @ ( TO @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[1717]) ).
thf(1719,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[1718:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) ))]]) ).
thf(1763,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ lattice )
!= ( TQ @ lattice ) )
| ( TQ @ ( TP @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1719,146]) ).
thf(1764,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ lattice )
!= ( TQ @ lattice ) )
| ( TQ @ ( TP @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[1763]) ).
thf(1765,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[1764:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) ))]]) ).
thf(2144,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ lattice )
!= ( TR @ lattice ) )
| ( TR @ ( TQ @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1765,146]) ).
thf(2145,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ lattice )
!= ( TR @ lattice ) )
| ( TR @ ( TQ @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[2144]) ).
thf(2146,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[2145:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) ))]]) ).
thf(2162,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ lattice )
!= ( TS @ lattice ) )
| ( TS @ ( TR @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2146,146]) ).
thf(2163,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ lattice )
!= ( TS @ lattice ) )
| ( TS @ ( TR @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[2162]) ).
thf(2164,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[2163:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) ))]]) ).
thf(2362,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ lattice )
!= ( TT @ lattice ) )
| ( TT @ ( TS @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2164,146]) ).
thf(2363,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ lattice )
!= ( TT @ lattice ) )
| ( TT @ ( TS @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[2362]) ).
thf(2364,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[2363:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) ))]]) ).
thf(2380,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ lattice )
!= ( TU @ lattice ) )
| ( TU @ ( TT @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2364,146]) ).
thf(2381,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ lattice )
!= ( TU @ lattice ) )
| ( TU @ ( TT @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[2380]) ).
thf(2382,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[2381:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) ))]]) ).
thf(2430,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ lattice )
!= ( TV @ lattice ) )
| ( TV @ ( TU @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2382,146]) ).
thf(2431,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ lattice )
!= ( TV @ lattice ) )
| ( TV @ ( TU @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[2430]) ).
thf(2432,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[2431:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) ))]]) ).
thf(2997,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ lattice )
!= ( TW @ lattice ) )
| ( TW @ ( TV @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2432,146]) ).
thf(2998,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ lattice )
!= ( TW @ lattice ) )
| ( TW @ ( TV @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[2997]) ).
thf(2999,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[2998:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) ))]]) ).
thf(3023,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ lattice )
!= ( TX @ lattice ) )
| ( TX @ ( TW @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2999,146]) ).
thf(3024,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ lattice )
!= ( TX @ lattice ) )
| ( TX @ ( TW @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[3023]) ).
thf(3025,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[3024:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) ))]]) ).
thf(3510,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ lattice )
!= ( TY @ lattice ) )
| ( TY @ ( TX @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3025,146]) ).
thf(3511,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ lattice )
!= ( TY @ lattice ) )
| ( TY @ ( TX @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[3510]) ).
thf(3512,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[3511:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) ))]]) ).
thf(3536,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ lattice )
!= ( TZ @ lattice ) )
| ( TZ @ ( TY @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3512,146]) ).
thf(3537,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ lattice )
!= ( TZ @ lattice ) )
| ( TZ @ ( TY @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[3536]) ).
thf(3538,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[3537:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) ))]]) ).
thf(3638,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ lattice )
!= ( TZA @ lattice ) )
| ( TZA @ ( TZ @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3538,146]) ).
thf(3639,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ lattice )
!= ( TZA @ lattice ) )
| ( TZA @ ( TZ @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[3638]) ).
thf(3640,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[3639:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) ))]]) ).
thf(4013,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ lattice )
!= ( TZB @ lattice ) )
| ( TZB @ ( TZA @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3640,146]) ).
thf(4014,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ lattice )
!= ( TZB @ lattice ) )
| ( TZB @ ( TZA @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[4013]) ).
thf(4015,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[4014:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) ))]]) ).
thf(130,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_5_nat__add__right__cancel) ).
thf(555,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)],[130]) ).
thf(152,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( D = B )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(cnfConj,[status(thm)],[151]) ).
thf(155,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( D = B )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(lifteq,[status(thm)],[152]) ).
thf(1,conjecture,
( ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) )
= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(135,plain,
( ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(136,plain,
( ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
inference(lifteq,[status(thm)],[135]) ).
thf(665,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( D
!= ( t_2 @ ( a @ huffma83463279weight ) ) )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( B @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[155,136]) ).
thf(666,plain,
! [TA: $tType,C: TA,B: nat,A: TA] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( B @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( t_2 @ ( a @ huffma83463279weight ) @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[665:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( t_2 @ ( a @ huffma83463279weight ) ))]]) ).
thf(27,axiom,
bool @ bounded_lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Obounded__lattice) ).
thf(214,plain,
bool @ bounded_lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bounded_lattice )
=> ( TA @ ( TB @ fun ) @ bounded_lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Obounded__lattice) ).
thf(178,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bounded_lattice )
=> ( TA @ ( TB @ fun ) @ bounded_lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(179,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ( TA @ fun ) @ bounded_lattice )
| ~ ( TB @ bounded_lattice ) ),
inference(cnf,[status(esa)],[178]) ).
thf(3986,plain,
! [TA: $tType,TB: $tType] :
( ( ( bool @ bounded_lattice )
!= ( TB @ bounded_lattice ) )
| ( TB @ ( TA @ fun ) @ bounded_lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,179]) ).
thf(3987,plain,
! [TA: $tType,TB: $tType] :
( ( ( bool @ bounded_lattice )
!= ( TB @ bounded_lattice ) )
| ( TB @ ( TA @ fun ) @ bounded_lattice ) ),
inference(simp,[status(thm)],[3986]) ).
thf(3988,plain,
! [TA: $tType] : ( bool @ ( TA @ fun ) @ bounded_lattice ),
inference(pattern_uni,[status(thm)],[3987:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( bool ))]]) ).
thf(4019,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( bool @ ( TA @ fun ) @ bounded_lattice )
!= ( TC @ bounded_lattice ) )
| ( TC @ ( TB @ fun ) @ bounded_lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3988,179]) ).
thf(4020,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( bool @ ( TA @ fun ) @ bounded_lattice )
!= ( TC @ bounded_lattice ) )
| ( TC @ ( TB @ fun ) @ bounded_lattice ) ),
inference(simp,[status(thm)],[4019]) ).
thf(4021,plain,
! [TA: $tType,TB: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ bounded_lattice ),
inference(pattern_uni,[status(thm)],[4020:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( bool @ ( TA @ fun ) ))]]) ).
thf(4539,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ bounded_lattice )
!= ( TD @ bounded_lattice ) )
| ( TD @ ( TC @ fun ) @ bounded_lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4021,179]) ).
thf(4540,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ bounded_lattice )
!= ( TD @ bounded_lattice ) )
| ( TD @ ( TC @ fun ) @ bounded_lattice ) ),
inference(simp,[status(thm)],[4539]) ).
thf(4541,plain,
! [TA: $tType,TB: $tType,TC: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ bounded_lattice ),
inference(pattern_uni,[status(thm)],[4540:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) ))]]) ).
thf(4583,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ bounded_lattice )
!= ( TE @ bounded_lattice ) )
| ( TE @ ( TD @ fun ) @ bounded_lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4541,179]) ).
thf(4584,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ bounded_lattice )
!= ( TE @ bounded_lattice ) )
| ( TE @ ( TD @ fun ) @ bounded_lattice ) ),
inference(simp,[status(thm)],[4583]) ).
thf(4585,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ bounded_lattice ),
inference(pattern_uni,[status(thm)],[4584:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) ))]]) ).
thf(5220,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ bounded_lattice )
!= ( TF @ bounded_lattice ) )
| ( TF @ ( TE @ fun ) @ bounded_lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4585,179]) ).
thf(5221,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ bounded_lattice )
!= ( TF @ bounded_lattice ) )
| ( TF @ ( TE @ fun ) @ bounded_lattice ) ),
inference(simp,[status(thm)],[5220]) ).
thf(5222,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ bounded_lattice ),
inference(pattern_uni,[status(thm)],[5221:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) ))]]) ).
thf(5732,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ bounded_lattice )
!= ( TG @ bounded_lattice ) )
| ( TG @ ( TF @ fun ) @ bounded_lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5222,179]) ).
thf(5733,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ bounded_lattice )
!= ( TG @ bounded_lattice ) )
| ( TG @ ( TF @ fun ) @ bounded_lattice ) ),
inference(simp,[status(thm)],[5732]) ).
thf(5734,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ bounded_lattice ),
inference(pattern_uni,[status(thm)],[5733:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) ))]]) ).
thf(6198,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ bounded_lattice )
!= ( TH @ bounded_lattice ) )
| ( TH @ ( TG @ fun ) @ bounded_lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5734,179]) ).
thf(6199,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ bounded_lattice )
!= ( TH @ bounded_lattice ) )
| ( TH @ ( TG @ fun ) @ bounded_lattice ) ),
inference(simp,[status(thm)],[6198]) ).
thf(6200,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ bounded_lattice ),
inference(pattern_uni,[status(thm)],[6199:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) ))]]) ).
thf(6664,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ bounded_lattice )
!= ( TI @ bounded_lattice ) )
| ( TI @ ( TH @ fun ) @ bounded_lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6200,179]) ).
thf(6665,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ bounded_lattice )
!= ( TI @ bounded_lattice ) )
| ( TI @ ( TH @ fun ) @ bounded_lattice ) ),
inference(simp,[status(thm)],[6664]) ).
thf(6666,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ bounded_lattice ),
inference(pattern_uni,[status(thm)],[6665:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) ))]]) ).
thf(6763,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ bounded_lattice )
!= ( TJ @ bounded_lattice ) )
| ( TJ @ ( TI @ fun ) @ bounded_lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6666,179]) ).
thf(6764,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ bounded_lattice )
!= ( TJ @ bounded_lattice ) )
| ( TJ @ ( TI @ fun ) @ bounded_lattice ) ),
inference(simp,[status(thm)],[6763]) ).
thf(6765,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ bounded_lattice ),
inference(pattern_uni,[status(thm)],[6764:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) ))]]) ).
thf(7211,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ bounded_lattice )
!= ( TK @ bounded_lattice ) )
| ( TK @ ( TJ @ fun ) @ bounded_lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6765,179]) ).
thf(7212,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ bounded_lattice )
!= ( TK @ bounded_lattice ) )
| ( TK @ ( TJ @ fun ) @ bounded_lattice ) ),
inference(simp,[status(thm)],[7211]) ).
thf(7213,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ bounded_lattice ),
inference(pattern_uni,[status(thm)],[7212:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) ))]]) ).
thf(7794,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ bounded_lattice )
!= ( TL @ bounded_lattice ) )
| ( TL @ ( TK @ fun ) @ bounded_lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7213,179]) ).
thf(7795,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ bounded_lattice )
!= ( TL @ bounded_lattice ) )
| ( TL @ ( TK @ fun ) @ bounded_lattice ) ),
inference(simp,[status(thm)],[7794]) ).
thf(7796,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ bounded_lattice ),
inference(pattern_uni,[status(thm)],[7795:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) ))]]) ).
thf(8340,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ bounded_lattice )
!= ( TM @ bounded_lattice ) )
| ( TM @ ( TL @ fun ) @ bounded_lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7796,179]) ).
thf(8341,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ bounded_lattice )
!= ( TM @ bounded_lattice ) )
| ( TM @ ( TL @ fun ) @ bounded_lattice ) ),
inference(simp,[status(thm)],[8340]) ).
thf(8342,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ bounded_lattice ),
inference(pattern_uni,[status(thm)],[8341:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) ))]]) ).
thf(8958,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ bounded_lattice )
!= ( TN @ bounded_lattice ) )
| ( TN @ ( TM @ fun ) @ bounded_lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8342,179]) ).
thf(8959,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ bounded_lattice )
!= ( TN @ bounded_lattice ) )
| ( TN @ ( TM @ fun ) @ bounded_lattice ) ),
inference(simp,[status(thm)],[8958]) ).
thf(8960,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ bounded_lattice ),
inference(pattern_uni,[status(thm)],[8959:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) ))]]) ).
thf(107,axiom,
! [TA: $tType,TB: $tType,A: TA,B: nat,C: TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ),D: TB @ ( TA @ fun ) @ ( nat @ fun )] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( C @ ( D @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) )
= ( A @ ( B @ ( D @ ( TB @ ( TA @ fun ) @ ( nat @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_tree_Orecs_I1_J) ).
thf(479,plain,
! [TA: $tType,TB: $tType,A: TA,B: nat,C: TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ),D: TB @ ( TA @ fun ) @ ( nat @ fun )] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( C @ ( D @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) )
= ( A @ ( B @ ( D @ ( TB @ ( TA @ fun ) @ ( nat @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(103,axiom,
nat @ lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Lattices_Olattice) ).
thf(463,plain,
nat @ lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(588,plain,
! [TA: $tType,TB: $tType] :
( ( ( nat @ lattice )
!= ( TB @ lattice ) )
| ( TB @ ( TA @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[463,146]) ).
thf(589,plain,
! [TA: $tType,TB: $tType] :
( ( ( nat @ lattice )
!= ( TB @ lattice ) )
| ( TB @ ( TA @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[588]) ).
thf(590,plain,
! [TA: $tType] : ( nat @ ( TA @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[589:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( nat ))]]) ).
thf(597,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( nat @ ( TA @ fun ) @ lattice )
!= ( TC @ lattice ) )
| ( TC @ ( TB @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[590,146]) ).
thf(598,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( nat @ ( TA @ fun ) @ lattice )
!= ( TC @ lattice ) )
| ( TC @ ( TB @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[597]) ).
thf(599,plain,
! [TA: $tType,TB: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[598:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( nat @ ( TA @ fun ) ))]]) ).
thf(603,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ lattice )
!= ( TD @ lattice ) )
| ( TD @ ( TC @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[599,146]) ).
thf(604,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ lattice )
!= ( TD @ lattice ) )
| ( TD @ ( TC @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[603]) ).
thf(605,plain,
! [TA: $tType,TB: $tType,TC: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[604:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) ))]]) ).
thf(616,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ lattice )
!= ( TE @ lattice ) )
| ( TE @ ( TD @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[605,146]) ).
thf(617,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ lattice )
!= ( TE @ lattice ) )
| ( TE @ ( TD @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[616]) ).
thf(618,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[617:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) ))]]) ).
thf(631,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ lattice )
!= ( TF @ lattice ) )
| ( TF @ ( TE @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[618,146]) ).
thf(632,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ lattice )
!= ( TF @ lattice ) )
| ( TF @ ( TE @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[631]) ).
thf(633,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[632:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) ))]]) ).
thf(637,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ lattice )
!= ( TG @ lattice ) )
| ( TG @ ( TF @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[633,146]) ).
thf(638,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ lattice )
!= ( TG @ lattice ) )
| ( TG @ ( TF @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[637]) ).
thf(639,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[638:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) ))]]) ).
thf(646,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ lattice )
!= ( TH @ lattice ) )
| ( TH @ ( TG @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[639,146]) ).
thf(647,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ lattice )
!= ( TH @ lattice ) )
| ( TH @ ( TG @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[646]) ).
thf(648,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[647:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) ))]]) ).
thf(652,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ lattice )
!= ( TI @ lattice ) )
| ( TI @ ( TH @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[648,146]) ).
thf(653,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ lattice )
!= ( TI @ lattice ) )
| ( TI @ ( TH @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[652]) ).
thf(654,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[653:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) ))]]) ).
thf(713,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ lattice )
!= ( TJ @ lattice ) )
| ( TJ @ ( TI @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[654,146]) ).
thf(714,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ lattice )
!= ( TJ @ lattice ) )
| ( TJ @ ( TI @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[713]) ).
thf(715,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[714:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) ))]]) ).
thf(719,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ lattice )
!= ( TK @ lattice ) )
| ( TK @ ( TJ @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[715,146]) ).
thf(720,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ lattice )
!= ( TK @ lattice ) )
| ( TK @ ( TJ @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[719]) ).
thf(721,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[720:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) ))]]) ).
thf(1557,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ lattice )
!= ( TL @ lattice ) )
| ( TL @ ( TK @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[721,146]) ).
thf(1558,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ lattice )
!= ( TL @ lattice ) )
| ( TL @ ( TK @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[1557]) ).
thf(1559,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[1558:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) ))]]) ).
thf(47,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_69_Int__commute) ).
thf(276,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)],[47]) ).
thf(1575,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ lattice )
!= ( TM @ lattice ) )
| ( TM @ ( TL @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1559,146]) ).
thf(1576,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ lattice )
!= ( TM @ lattice ) )
| ( TM @ ( TL @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[1575]) ).
thf(1577,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[1576:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) ))]]) ).
thf(1655,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ lattice )
!= ( TN @ lattice ) )
| ( TN @ ( TM @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1577,146]) ).
thf(1656,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ lattice )
!= ( TN @ lattice ) )
| ( TN @ ( TM @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[1655]) ).
thf(1657,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[1656:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) ))]]) ).
thf(1708,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ lattice )
!= ( TO @ lattice ) )
| ( TO @ ( TN @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1657,146]) ).
thf(1709,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ lattice )
!= ( TO @ lattice ) )
| ( TO @ ( TN @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[1708]) ).
thf(1710,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[1709:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) ))]]) ).
thf(1726,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ lattice )
!= ( TP @ lattice ) )
| ( TP @ ( TO @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1710,146]) ).
thf(1727,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ lattice )
!= ( TP @ lattice ) )
| ( TP @ ( TO @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[1726]) ).
thf(1728,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[1727:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) ))]]) ).
thf(2135,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ lattice )
!= ( TQ @ lattice ) )
| ( TQ @ ( TP @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1728,146]) ).
thf(2136,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ lattice )
!= ( TQ @ lattice ) )
| ( TQ @ ( TP @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[2135]) ).
thf(2137,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[2136:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) ))]]) ).
thf(2153,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ lattice )
!= ( TR @ lattice ) )
| ( TR @ ( TQ @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2137,146]) ).
thf(2154,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ lattice )
!= ( TR @ lattice ) )
| ( TR @ ( TQ @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[2153]) ).
thf(2155,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[2154:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) ))]]) ).
thf(2233,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ lattice )
!= ( TS @ lattice ) )
| ( TS @ ( TR @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2155,146]) ).
thf(2234,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ lattice )
!= ( TS @ lattice ) )
| ( TS @ ( TR @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[2233]) ).
thf(2235,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[2234:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) ))]]) ).
thf(2371,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ lattice )
!= ( TT @ lattice ) )
| ( TT @ ( TS @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2235,146]) ).
thf(2372,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ lattice )
!= ( TT @ lattice ) )
| ( TT @ ( TS @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[2371]) ).
thf(2373,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[2372:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) ))]]) ).
thf(2389,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ lattice )
!= ( TU @ lattice ) )
| ( TU @ ( TT @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2373,146]) ).
thf(2390,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ lattice )
!= ( TU @ lattice ) )
| ( TU @ ( TT @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[2389]) ).
thf(2391,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[2390:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) ))]]) ).
thf(2984,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ lattice )
!= ( TV @ lattice ) )
| ( TV @ ( TU @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2391,146]) ).
thf(2985,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ lattice )
!= ( TV @ lattice ) )
| ( TV @ ( TU @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[2984]) ).
thf(2986,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[2985:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) ))]]) ).
thf(3010,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ lattice )
!= ( TW @ lattice ) )
| ( TW @ ( TV @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2986,146]) ).
thf(3011,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ lattice )
!= ( TW @ lattice ) )
| ( TW @ ( TV @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[3010]) ).
thf(3012,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[3011:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) ))]]) ).
thf(44,axiom,
! [TA: $tType,A: TA,B: nat] : ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1518433673istent ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_consistent_Osimps_I1_J) ).
thf(269,plain,
! [TA: $tType,A: TA,B: nat] : ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1518433673istent ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(3112,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ lattice )
!= ( TX @ lattice ) )
| ( TX @ ( TW @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3012,146]) ).
thf(3113,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ lattice )
!= ( TX @ lattice ) )
| ( TX @ ( TW @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[3112]) ).
thf(3114,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[3113:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) ))]]) ).
thf(3523,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ lattice )
!= ( TY @ lattice ) )
| ( TY @ ( TX @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3114,146]) ).
thf(3524,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ lattice )
!= ( TY @ lattice ) )
| ( TY @ ( TX @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[3523]) ).
thf(3525,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[3524:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) ))]]) ).
thf(3549,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ lattice )
!= ( TZ @ lattice ) )
| ( TZ @ ( TY @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3525,146]) ).
thf(3550,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ lattice )
!= ( TZ @ lattice ) )
| ( TZ @ ( TY @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[3549]) ).
thf(3551,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[3550:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) ))]]) ).
thf(4000,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ lattice )
!= ( TZA @ lattice ) )
| ( TZA @ ( TZ @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3551,146]) ).
thf(4001,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ lattice )
!= ( TZA @ lattice ) )
| ( TZA @ ( TZ @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[4000]) ).
thf(4002,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[4001:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) ))]]) ).
thf(4038,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ lattice )
!= ( TZB @ lattice ) )
| ( TZB @ ( TZA @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4002,146]) ).
thf(4039,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ lattice )
!= ( TZB @ lattice ) )
| ( TZB @ ( TZA @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[4038]) ).
thf(4040,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[4039:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) ))]]) ).
thf(4564,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ lattice )
!= ( TZC @ lattice ) )
| ( TZC @ ( TZB @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4040,146]) ).
thf(4565,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ lattice )
!= ( TZC @ lattice ) )
| ( TZC @ ( TZB @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[4564]) ).
thf(4566,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[4565:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) ))]]) ).
thf(5198,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ lattice )
!= ( TZD @ lattice ) )
| ( TZD @ ( TZC @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4566,146]) ).
thf(5199,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ lattice )
!= ( TZD @ lattice ) )
| ( TZD @ ( TZC @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[5198]) ).
thf(5200,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[5199:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) ))]]) ).
thf(5710,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ lattice )
!= ( TZE @ lattice ) )
| ( TZE @ ( TZD @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5200,146]) ).
thf(5711,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ lattice )
!= ( TZE @ lattice ) )
| ( TZE @ ( TZD @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[5710]) ).
thf(5712,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[5711:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) ))]]) ).
thf(5846,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ lattice )
!= ( TZF @ lattice ) )
| ( TZF @ ( TZE @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5712,146]) ).
thf(5847,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ lattice )
!= ( TZF @ lattice ) )
| ( TZF @ ( TZE @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[5846]) ).
thf(5848,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[5847:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) ))]]) ).
thf(6226,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ lattice )
!= ( TZG @ lattice ) )
| ( TZG @ ( TZF @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5848,146]) ).
thf(6227,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ lattice )
!= ( TZG @ lattice ) )
| ( TZG @ ( TZF @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[6226]) ).
thf(6228,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[6227:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) ))]]) ).
thf(6692,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ lattice )
!= ( TZH @ lattice ) )
| ( TZH @ ( TZG @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6228,146]) ).
thf(6693,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ lattice )
!= ( TZH @ lattice ) )
| ( TZH @ ( TZG @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[6692]) ).
thf(6694,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[6693:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) ))]]) ).
thf(7189,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ lattice )
!= ( TZI @ lattice ) )
| ( TZI @ ( TZH @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6694,146]) ).
thf(7190,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ lattice )
!= ( TZI @ lattice ) )
| ( TZI @ ( TZH @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[7189]) ).
thf(7191,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[7190:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) ))]]) ).
thf(7772,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ lattice )
!= ( TZJ @ lattice ) )
| ( TZJ @ ( TZI @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7191,146]) ).
thf(7773,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ lattice )
!= ( TZJ @ lattice ) )
| ( TZJ @ ( TZI @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[7772]) ).
thf(7774,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[7773:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) ))]]) ).
thf(7918,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ lattice )
!= ( TZK @ lattice ) )
| ( TZK @ ( TZJ @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7774,146]) ).
thf(7919,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ lattice )
!= ( TZK @ lattice ) )
| ( TZK @ ( TZJ @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[7918]) ).
thf(7920,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[7919:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) ))]]) ).
thf(8368,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ lattice )
!= ( TZL @ lattice ) )
| ( TZL @ ( TZK @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7920,146]) ).
thf(8369,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ lattice )
!= ( TZL @ lattice ) )
| ( TZL @ ( TZK @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[8368]) ).
thf(8370,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[8369:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZK )),bind_type(TZL,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) ))]]) ).
thf(8986,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) @ lattice )
!= ( TZM @ lattice ) )
| ( TZM @ ( TZL @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8370,146]) ).
thf(8987,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) @ lattice )
!= ( TZM @ lattice ) )
| ( TZM @ ( TZL @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[8986]) ).
thf(8988,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) @ ( TZL @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[8987:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZK )),bind_type(TZL,$thf( TZL )),bind_type(TZM,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) ))]]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bounded_lattice )
=> ( TA @ ( TB @ fun ) @ bounded_lattice_bot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Obounded__lattice__bot) ).
thf(143,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bounded_lattice )
=> ( TA @ ( TB @ fun ) @ bounded_lattice_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(144,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ( TA @ fun ) @ bounded_lattice_bot )
| ~ ( TB @ bounded_lattice ) ),
inference(cnf,[status(esa)],[143]) ).
thf(4590,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ bounded_lattice )
!= ( TE @ bounded_lattice ) )
| ( TE @ ( TD @ fun ) @ bounded_lattice_bot )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4541,144]) ).
thf(4591,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ bounded_lattice )
!= ( TE @ bounded_lattice ) )
| ( TE @ ( TD @ fun ) @ bounded_lattice_bot ) ),
inference(simp,[status(thm)],[4590]) ).
thf(4592,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ bounded_lattice_bot ),
inference(pattern_uni,[status(thm)],[4591:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) ))]]) ).
thf(4127,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ lattice )
!= ( TZC @ lattice ) )
| ( TZC @ ( TZB @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4015,146]) ).
thf(4128,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ lattice )
!= ( TZC @ lattice ) )
| ( TZC @ ( TZB @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[4127]) ).
thf(4129,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[4128:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) ))]]) ).
thf(4577,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ lattice )
!= ( TZD @ lattice ) )
| ( TZD @ ( TZC @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4129,146]) ).
thf(4578,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ lattice )
!= ( TZD @ lattice ) )
| ( TZD @ ( TZC @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[4577]) ).
thf(4579,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[4578:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) ))]]) ).
thf(5214,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ lattice )
!= ( TZE @ lattice ) )
| ( TZE @ ( TZD @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4579,146]) ).
thf(5215,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ lattice )
!= ( TZE @ lattice ) )
| ( TZE @ ( TZD @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[5214]) ).
thf(5216,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[5215:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) ))]]) ).
thf(5726,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ lattice )
!= ( TZF @ lattice ) )
| ( TZF @ ( TZE @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5216,146]) ).
thf(5727,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ lattice )
!= ( TZF @ lattice ) )
| ( TZF @ ( TZE @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[5726]) ).
thf(5728,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[5727:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) ))]]) ).
thf(6192,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ lattice )
!= ( TZG @ lattice ) )
| ( TZG @ ( TZF @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5728,146]) ).
thf(6193,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ lattice )
!= ( TZG @ lattice ) )
| ( TZG @ ( TZF @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[6192]) ).
thf(6194,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[6193:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) ))]]) ).
thf(87,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ zero_zero @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_of__nat__0) ).
thf(408,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ zero_zero @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(12,axiom,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( TA @ one_one )
= A )
<=> ( A
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_one__reorient) ).
thf(170,plain,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( A
= ( TA @ one_one ) )
=> ( ( TA @ one_one )
= A ) )
& ( ( ( TA @ one_one )
= A )
=> ( A
= ( TA @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Collect__def) ).
thf(137,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(138,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(cnf,[status(esa)],[137]) ).
thf(139,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(lifteq,[status(thm)],[138]) ).
thf(31,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_46_Collect__empty__eq) ).
thf(229,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)],[31]) ).
thf(230,plain,
! [TA: $tType,B: TA,A: bool @ ( TA @ fun )] :
( ( ( ( A @ ( TA @ collect ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
| ( A @ ( TA @ sk3 ) @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( ( A @ ( TA @ collect ) )
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(cnf,[status(esa)],[229]) ).
thf(231,plain,
! [TA: $tType,B: TA,A: bool @ ( TA @ fun )] :
( ~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( ( A @ ( TA @ collect ) )
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
inference(cnfConj,[status(thm)],[230]) ).
thf(233,plain,
! [TA: $tType,B: TA,A: bool @ ( TA @ fun )] :
( ~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( ( A @ ( TA @ collect ) )
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
inference(lifteq,[status(thm)],[231]) ).
thf(609,plain,
! [TB: $tType,C: TB,B: bool @ ( TB @ fun ),A: bool @ ( TB @ fun )] :
( ( ( A @ ( TB @ collect ) )
!= ( B @ ( TB @ collect ) ) )
| ~ ( C @ ( B @ ( bool @ ( TB @ aa ) ) ) @ pp )
| ( A
!= ( bool @ ( TB @ fun ) @ bot_bot ) ) ),
inference(paramod_ordered,[status(thm)],[139,233]) ).
thf(610,plain,
! [TB: $tType,B: TB,A: bool @ ( TB @ fun )] :
( ~ ( B @ ( A @ ( bool @ ( TB @ aa ) ) ) @ pp )
| ( A
!= ( bool @ ( TB @ fun ) @ bot_bot ) ) ),
inference(pattern_uni,[status(thm)],[609:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(612,plain,
! [TA: $tType,A: TA] :
~ ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ pp ),
inference(simp,[status(thm)],[610]) ).
thf(911,plain,
! [TB: $tType,E: TB,D: nat,C: bool,B: nat,A: bool] :
( ( A
!= ( E @ ( bool @ ( TB @ fun ) @ bot_bot @ ( bool @ ( TB @ aa ) ) ) ) )
| ~ ( C @ pp )
| ( ( C @ ( D @ ( bool @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( bool @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,612]) ).
thf(912,plain,
! [TB: $tType,D: TB,C: nat,B: bool,A: nat] :
( ~ ( B @ pp )
| ( ( B @ ( C @ ( bool @ huffma2021818691e_Leaf ) ) )
!= ( D @ ( bool @ ( TB @ fun ) @ bot_bot @ ( bool @ ( TB @ aa ) ) ) @ ( A @ ( bool @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[911:[bind(A,$thf( G @ ( bool @ ( TB @ fun ) @ bot_bot @ ( bool @ ( TB @ aa ) ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G ))]]) ).
thf(1497,plain,
! [TA: $tType,D: TA,C: nat,B: bool,A: nat] :
( ~ ( B @ pp )
| ( ( B @ ( C @ ( bool @ huffma2021818691e_Leaf ) ) )
!= ( D @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ ( A @ ( bool @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[912]) ).
thf(4,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(140,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(141,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(cnf,[status(esa)],[140]) ).
thf(142,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(lifteq,[status(thm)],[141]) ).
thf(66,axiom,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ inf_inf ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_inf_Oidem) ).
thf(340,plain,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ inf_inf ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(931,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( C
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( A
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( C @ ( D @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,136]) ).
thf(932,plain,
! [C: nat,B: nat,A: nat] :
( ( A
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) @ ( C @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[931:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) )),bind(D,$thf( D ))]]) ).
thf(1507,plain,
! [B: nat,A: nat] :
( ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( A @ ( nat @ huffma2021818691e_Leaf ) ) ) ),
inference(simp,[status(thm)],[932]) ).
thf(7218,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ bounded_lattice )
!= ( TK @ bounded_lattice ) )
| ( TK @ ( TJ @ fun ) @ bounded_lattice_bot )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6765,144]) ).
thf(7219,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ bounded_lattice )
!= ( TK @ bounded_lattice ) )
| ( TK @ ( TJ @ fun ) @ bounded_lattice_bot ) ),
inference(simp,[status(thm)],[7218]) ).
thf(7220,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ bounded_lattice_bot ),
inference(pattern_uni,[status(thm)],[7219:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) ))]]) ).
thf(669,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( D
!= ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( B @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[155,136]) ).
thf(670,plain,
! [TA: $tType,C: TA,B: nat,A: TA] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( B @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[669:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ))]]) ).
thf(677,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( B
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( D
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[155,136]) ).
thf(678,plain,
! [TA: $tType,C: nat,B: TA,A: TA] :
( ( C
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( B @ ( C @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[677:[bind(A,$thf( A )),bind(B,$thf( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(698,plain,
! [TA: $tType,B: TA,A: TA] :
( ( B @ ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) @ ( TA @ huffma2021818691e_Leaf ) ) ) ),
inference(simp,[status(thm)],[678]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,A: TA,B: nat,C: TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ),D: TB @ ( TA @ fun ) @ ( nat @ fun )] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( C @ ( D @ ( TB @ ( TA @ huffma107959123e_case ) ) ) ) )
= ( A @ ( B @ ( D @ ( TB @ ( TA @ fun ) @ ( nat @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_tree_Osimps_I5_J) ).
thf(417,plain,
! [TA: $tType,TB: $tType,A: TA,B: nat,C: TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ),D: TB @ ( TA @ fun ) @ ( nat @ fun )] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( C @ ( D @ ( TB @ ( TA @ huffma107959123e_case ) ) ) ) )
= ( A @ ( B @ ( D @ ( TB @ ( TA @ fun ) @ ( nat @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(863,plain,
! [D: nat,C: $o,B: nat,A: $o] :
( ( C
!= ( fFalse @ pp ) )
| ~ A
| ( ( C @ ( D @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,275]) ).
thf(864,plain,
! [C: nat,B: nat,A: $o] :
( ~ A
| ( ( fFalse @ pp @ ( C @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[863:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( fFalse @ pp )),bind(D,$thf( D ))]]) ).
thf(1473,plain,
! [C: nat,B: nat,A: $o] :
( ~ A
| ( ( fFalse @ pp @ ( C @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[864]) ).
thf(1589,plain,
! [C: nat,B: nat,A: $o] :
( ~ A
| ( ( $false @ ( C @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(rewrite,[status(thm)],[1473,275]) ).
thf(1590,plain,
! [B: nat,A: nat] :
( ( $false @ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( $true @ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ),
inference(simp,[status(thm)],[1589]) ).
thf(1613,plain,
! [B: nat,A: nat] :
( ( $false @ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( $true @ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ),
inference(simp,[status(thm)],[1590]) ).
thf(1635,plain,
! [F: nat,E: nat,D: nat,C: $o @ huffma1450048681e_tree,B: nat,A: $o @ huffma1450048681e_tree] :
( ( A
!= ( $false @ ( F @ ( $o @ huffma2021818691e_Leaf ) ) ) )
| ( C
!= ( $true @ ( E @ ( $o @ huffma2021818691e_Leaf ) ) ) )
| ( ( C @ ( D @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,1613]) ).
thf(1636,plain,
! [E: nat,D: nat,C: nat,B: $o @ huffma1450048681e_tree,A: nat] :
( ( B
!= ( $true @ ( D @ ( $o @ huffma2021818691e_Leaf ) ) ) )
| ( ( B @ ( C @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( $false @ ( E @ ( $o @ huffma2021818691e_Leaf ) ) @ ( A @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1635:[bind(A,$thf( $false @ ( G @ ( $o @ huffma2021818691e_Leaf ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( G ))]]) ).
thf(1645,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( $true @ ( C @ ( $o @ huffma2021818691e_Leaf ) ) @ ( B @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( $false @ ( D @ ( $o @ huffma2021818691e_Leaf ) ) @ ( A @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ),
inference(simp,[status(thm)],[1636]) ).
thf(59,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(320,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(953,plain,
! [D: nat,C: a @ huffma1450048681e_tree,B: nat,A: a @ huffma1450048681e_tree] :
( ( C != t_2 )
| ( ( A @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,136]) ).
thf(954,plain,
! [C: nat,B: nat,A: a @ huffma1450048681e_tree] :
( ( ( A @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_2 @ ( C @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[953:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_2 ))]]) ).
thf(1518,plain,
! [C: nat,B: nat,A: a @ huffma1450048681e_tree] :
( ( ( A @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_2 @ ( C @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[954]) ).
thf(51,axiom,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ inf_inf ) ) @ ( TA @ inf_inf ) ) )
= ( A @ ( B @ ( TA @ inf_inf ) ) @ ( C @ ( TA @ inf_inf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_inf__assoc) ).
thf(288,plain,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ inf_inf ) ) @ ( TA @ inf_inf ) ) )
= ( A @ ( B @ ( TA @ inf_inf ) ) @ ( C @ ( TA @ inf_inf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(6328,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ lattice )
!= ( TZH @ lattice ) )
| ( TZH @ ( TZG @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6194,146]) ).
thf(6329,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ lattice )
!= ( TZH @ lattice ) )
| ( TZH @ ( TZG @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[6328]) ).
thf(6330,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[6329:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) ))]]) ).
thf(6708,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ lattice )
!= ( TZI @ lattice ) )
| ( TZI @ ( TZH @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6330,146]) ).
thf(6709,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ lattice )
!= ( TZI @ lattice ) )
| ( TZI @ ( TZH @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[6708]) ).
thf(6710,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[6709:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) ))]]) ).
thf(7205,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ lattice )
!= ( TZJ @ lattice ) )
| ( TZJ @ ( TZI @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6710,146]) ).
thf(7206,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ lattice )
!= ( TZJ @ lattice ) )
| ( TZJ @ ( TZI @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[7205]) ).
thf(7207,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[7206:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) ))]]) ).
thf(7788,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ lattice )
!= ( TZK @ lattice ) )
| ( TZK @ ( TZJ @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7207,146]) ).
thf(7789,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ lattice )
!= ( TZK @ lattice ) )
| ( TZK @ ( TZJ @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[7788]) ).
thf(7790,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[7789:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) ))]]) ).
thf(8965,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ bounded_lattice )
!= ( TN @ bounded_lattice ) )
| ( TN @ ( TM @ fun ) @ bounded_lattice_bot )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8342,144]) ).
thf(8966,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ bounded_lattice )
!= ( TN @ bounded_lattice ) )
| ( TN @ ( TM @ fun ) @ bounded_lattice_bot ) ),
inference(simp,[status(thm)],[8965]) ).
thf(8967,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ bounded_lattice_bot ),
inference(pattern_uni,[status(thm)],[8966:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) ))]]) ).
thf(16,axiom,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ inf_inf ) ) @ ( TA @ inf_inf ) ) )
= ( A @ ( B @ ( TA @ inf_inf ) ) @ ( C @ ( TA @ inf_inf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_inf__sup__aci_I2_J) ).
thf(184,plain,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ inf_inf ) ) @ ( TA @ inf_inf ) ) )
= ( A @ ( B @ ( TA @ inf_inf ) ) @ ( C @ ( TA @ inf_inf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_bot__apply) ).
thf(372,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(20,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_47_emptyE) ).
thf(196,plain,
! [TA: $tType,A: TA] :
~ ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(126,axiom,
nat @ comm_monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(542,plain,
nat @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(939,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( C
!= ( t_1 @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( A @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,136]) ).
thf(940,plain,
! [C: nat,B: nat,A: nat] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( A @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( C @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[939:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_1 @ ( a @ huffma1134658180e_cost ) )),bind(D,$thf( D ))]]) ).
thf(1511,plain,
! [C: nat,B: nat,A: nat] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( A @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( C @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[940]) ).
thf(685,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( B
!= ( t_1 @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( D @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[155,136]) ).
thf(686,plain,
! [TA: $tType,C: nat,B: TA,A: TA] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( C @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( B @ ( C @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[685:[bind(A,$thf( A )),bind(B,$thf( t_1 @ ( a @ huffma1134658180e_cost ) )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(702,plain,
! [TA: $tType,C: nat,B: TA,A: TA] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( C @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( B @ ( C @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[686]) ).
thf(50,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_40_IntE) ).
thf(284,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)],[50]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_bot__fun__def) ).
thf(325,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ bot_bot @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(945,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( C
!= ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( A @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,136]) ).
thf(946,plain,
! [C: nat,B: nat,A: nat] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( A @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[945:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )),bind(D,$thf( D ))]]) ).
thf(1514,plain,
! [C: nat,B: nat,A: nat] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( A @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[946]) ).
thf(18,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( 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_51_bot__empty__eq) ).
thf(189,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 )
=> ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( 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)],[18]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(421,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(7801,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ bounded_lattice )
!= ( TL @ bounded_lattice ) )
| ( TL @ ( TK @ fun ) @ bounded_lattice_bot )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7213,144]) ).
thf(7802,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ bounded_lattice )
!= ( TL @ bounded_lattice ) )
| ( TL @ ( TK @ fun ) @ bounded_lattice_bot ) ),
inference(simp,[status(thm)],[7801]) ).
thf(7803,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ bounded_lattice_bot ),
inference(pattern_uni,[status(thm)],[7802:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) ))]]) ).
thf(101,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_85_depth_Osimps_I2_J) ).
thf(448,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)],[101]) ).
thf(905,plain,
! [TB: $tType,E: TB,D: nat,C: bool,B: nat,A: bool] :
( ( C
!= ( E @ ( bool @ ( TB @ fun ) @ bot_bot @ ( bool @ ( TB @ aa ) ) ) ) )
| ~ ( A @ pp )
| ( ( C @ ( D @ ( bool @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( bool @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,612]) ).
thf(906,plain,
! [TB: $tType,D: TB,C: nat,B: nat,A: bool] :
( ~ ( A @ pp )
| ( ( D @ ( bool @ ( TB @ fun ) @ bot_bot @ ( bool @ ( TB @ aa ) ) ) @ ( C @ ( bool @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( bool @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[905:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( G @ ( bool @ ( TB @ fun ) @ bot_bot @ ( bool @ ( TB @ aa ) ) ) )),bind(D,$thf( D )),bind(E,$thf( G ))]]) ).
thf(1494,plain,
! [TA: $tType,D: TA,C: nat,B: nat,A: bool] :
( ~ ( A @ pp )
| ( ( D @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ aa ) ) ) @ ( C @ ( bool @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( bool @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[906]) ).
thf(105,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(475,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ lattice )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TA] :
( ( C @ ( A @ ( B @ ( TB @ ( TA @ fun ) @ inf_inf ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ inf_inf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_inf__fun__def) ).
thf(164,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ lattice )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TA] :
( ( C @ ( A @ ( B @ ( TB @ ( TA @ fun ) @ inf_inf ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ inf_inf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ lattice )
=> ( TA @ ( TB @ fun ) @ semilattice_inf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Lattices_Osemilattice__inf) ).
thf(376,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ lattice )
=> ( TA @ ( TB @ fun ) @ semilattice_inf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).
thf(211,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(117,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma83463279weight ) )
= ( A @ ( TA @ huffma83463279weight ) @ ( B @ ( TA @ huffma83463279weight ) @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_weight_Osimps_I2_J) ).
thf(514,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma83463279weight ) )
= ( A @ ( TA @ huffma83463279weight ) @ ( B @ ( TA @ huffma83463279weight ) @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(70,axiom,
! [TA: $tType] :
( ( TA @ semiring_char_0 )
=> ! [A: nat,B: nat] :
( ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_of__nat__eq__iff) ).
thf(353,plain,
! [TA: $tType] :
( ( TA @ semiring_char_0 )
=> ! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) ) )
& ( ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(7,axiom,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ inf_inf ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_inf__idem) ).
thf(147,plain,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ inf_inf ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(53,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_88_exists__in__alphabet) ).
thf(293,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)],[53]) ).
thf(6770,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ bounded_lattice )
!= ( TJ @ bounded_lattice ) )
| ( TJ @ ( TI @ fun ) @ bounded_lattice_bot )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6666,144]) ).
thf(6771,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ bounded_lattice )
!= ( TJ @ bounded_lattice ) )
| ( TJ @ ( TI @ fun ) @ bounded_lattice_bot ) ),
inference(simp,[status(thm)],[6770]) ).
thf(6772,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ bounded_lattice_bot ),
inference(pattern_uni,[status(thm)],[6771:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) ))]]) ).
thf(95,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(428,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(122,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_12_nat__add__left__commute) ).
thf(527,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)],[122]) ).
thf(24,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(206,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)],[24]) ).
thf(88,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_add__right__imp__eq) ).
thf(411,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(116,axiom,
( ( nat @ bot_bot )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_bot__nat__def) ).
thf(512,plain,
( ( nat @ bot_bot )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(80,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_add__left__cancel) ).
thf(381,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(74,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(366,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)],[74]) ).
thf(8334,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ lattice )
!= ( TZL @ lattice ) )
| ( TZL @ ( TZK @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7790,146]) ).
thf(8335,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ lattice )
!= ( TZL @ lattice ) )
| ( TZL @ ( TZK @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[8334]) ).
thf(8336,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[8335:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZK )),bind_type(TZL,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) ))]]) ).
thf(8480,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) @ lattice )
!= ( TZM @ lattice ) )
| ( TZM @ ( TZL @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8336,146]) ).
thf(8481,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) @ lattice )
!= ( TZM @ lattice ) )
| ( TZM @ ( TZL @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[8480]) ).
thf(8482,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) @ ( TZL @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[8481:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZK )),bind_type(TZL,$thf( TZL )),bind_type(TZM,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) ))]]) ).
thf(9002,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType,TZN: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) @ ( TZL @ fun ) @ lattice )
!= ( TZN @ lattice ) )
| ( TZN @ ( TZM @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8482,146]) ).
thf(9003,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType,TZN: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) @ ( TZL @ fun ) @ lattice )
!= ( TZN @ lattice ) )
| ( TZN @ ( TZM @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[9002]) ).
thf(9004,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) @ ( TZL @ fun ) @ ( TZM @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[9003:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZK )),bind_type(TZL,$thf( TZL )),bind_type(TZM,$thf( TZM )),bind_type(TZN,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) @ ( TZL @ fun ) ))]]) ).
thf(22,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Int__empty__right) ).
thf(201,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(93,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_add__left__imp__eq) ).
thf(424,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(1608,plain,
! [D: $o,C: $o,B: nat,A: nat] :
( ~ ( D
| C )
| ( ( $false @ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( ( D
| C )
@ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(prim_subst,[status(thm)],[1589:[bind(A,$thf( E | D ))]]) ).
thf(1616,plain,
! [D: $o,C: $o,B: nat,A: nat] :
( ( ~ D
| ( ( $false @ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( ( D
| C )
@ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) )
& ( ~ C
| ( ( $false @ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( ( D
| C )
@ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ) ),
inference(cnf,[status(esa)],[1608]) ).
thf(1617,plain,
! [D: $o,C: $o,B: nat,A: nat] :
( ~ C
| ( ( $false @ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( ( D
| C )
@ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(cnfConj,[status(thm)],[1616]) ).
thf(1619,plain,
! [D: $o,C: $o,B: nat,A: nat] :
( ~ C
| ( ( $false @ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( ( D
| C )
@ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[1617]) ).
thf(39,axiom,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) @ ( B @ ( TA @ inf_inf ) ) )
= ( A @ ( B @ ( TA @ inf_inf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_inf__left__idem) ).
thf(252,plain,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) @ ( B @ ( TA @ inf_inf ) ) )
= ( A @ ( B @ ( TA @ inf_inf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(197,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(cnf,[status(esa)],[196]) ).
thf(2198,plain,
! [D: $o,C: $o,B: nat,A: nat] :
( ~ D
| ( ( ( D
| C )
@ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( $false @ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(cnfConj,[status(thm)],[2196]) ).
thf(2200,plain,
! [D: $o,C: $o,B: nat,A: nat] :
( ~ D
| ( ( ( D
| C )
@ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( $false @ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[2198]) ).
thf(102,axiom,
! [TA: $tType,A: nat,B: TA,C: TA] :
( ( ( C != B )
=> ( ( C @ ( B @ ( A @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1352802255e_freq ) ) )
= ( nat @ zero_zero ) ) )
& ( ( C = B )
=> ( ( C @ ( B @ ( A @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1352802255e_freq ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_freq_Osimps_I1_J) ).
thf(456,plain,
! [TA: $tType,A: nat,B: TA,C: TA] :
( ( ( C != B )
=> ( ( C @ ( B @ ( A @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1352802255e_freq ) ) )
= ( nat @ zero_zero ) ) )
& ( ( C = B )
=> ( ( C @ ( B @ ( A @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1352802255e_freq ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(132,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_31_tree_Osimps_I3_J) ).
thf(566,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)],[132]) ).
thf(675,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( B != w )
| ( ( t_2 @ ( t_1 @ ( D @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[155,136]) ).
thf(676,plain,
! [TA: $tType,C: nat,B: TA,A: TA] :
( ( ( t_2 @ ( t_1 @ ( C @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( B @ ( C @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( w @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[675:[bind(A,$thf( A )),bind(B,$thf( w ))]]) ).
thf(697,plain,
! [TA: $tType,C: nat,B: TA,A: TA] :
( ( ( t_2 @ ( t_1 @ ( C @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( B @ ( C @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( w @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[676]) ).
thf(913,plain,
! [TB: $tType,E: TB,D: nat,C: bool @ ( TB @ fun ),B: nat,A: bool @ ( TB @ fun )] :
( ( A
!= ( bool @ ( TB @ fun ) @ bot_bot ) )
| ~ ( E @ ( C @ ( bool @ ( TB @ aa ) ) ) @ pp )
| ( ( C @ ( D @ ( bool @ ( TB @ fun ) @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( bool @ ( TB @ fun ) @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,612]) ).
thf(914,plain,
! [TB: $tType,D: TB,C: nat,B: bool @ ( TB @ fun ),A: nat] :
( ~ ( D @ ( B @ ( bool @ ( TB @ aa ) ) ) @ pp )
| ( ( B @ ( C @ ( bool @ ( TB @ fun ) @ huffma2021818691e_Leaf ) ) )
!= ( bool @ ( TB @ fun ) @ bot_bot @ ( A @ ( bool @ ( TB @ fun ) @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[913:[bind(A,$thf( bool @ ( TB @ fun ) @ bot_bot ))]]) ).
thf(1498,plain,
! [TA: $tType,D: TA,C: nat,B: bool @ ( TA @ fun ),A: nat] :
( ~ ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( ( B @ ( C @ ( bool @ ( TA @ fun ) @ huffma2021818691e_Leaf ) ) )
!= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[914]) ).
thf(17,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_inf1I) ).
thf(187,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun )] :
( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(188,plain,
! [TA: $tType,C: bool @ ( TA @ fun ),B: TA,A: bool @ ( TA @ fun )] :
( ( B @ ( A @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(cnf,[status(esa)],[187]) ).
thf(81,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_92_depth_Osimps_I1_J) ).
thf(388,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)],[81]) ).
thf(11,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_68_Int__def) ).
thf(167,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)],[11]) ).
thf(168,plain,
! [TA: $tType,B: bool @ ( TA @ fun ),A: 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(cnf,[status(esa)],[167]) ).
thf(169,plain,
! [TA: $tType,B: bool @ ( TA @ fun ),A: bool @ ( TA @ fun )] :
( ( 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 ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
inference(lifteq,[status(thm)],[168]) ).
thf(91,axiom,
nat @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(420,plain,
nat @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(62,axiom,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) @ ( B @ ( TA @ inf_inf ) ) )
= ( A @ ( B @ ( TA @ inf_inf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_inf__sup__aci_I4_J) ).
thf(328,plain,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) @ ( B @ ( TA @ inf_inf ) ) )
= ( A @ ( B @ ( TA @ inf_inf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(19,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_70_Int__left__absorb) ).
thf(193,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)],[19]) ).
thf(106,axiom,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_add__imp__eq) ).
thf(476,plain,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(691,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( B
!= ( t_1 @ ( a @ huffma83463279weight ) ) )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[155,136]) ).
thf(692,plain,
! [TA: $tType,C: nat,B: TA,A: TA] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( B @ ( C @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( t_1 @ ( a @ huffma83463279weight ) @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[691:[bind(A,$thf( A )),bind(B,$thf( t_1 @ ( a @ huffma83463279weight ) )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(706,plain,
! [TA: $tType,C: nat,B: TA,A: TA] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( B @ ( C @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( t_1 @ ( a @ huffma83463279weight ) @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[692]) ).
thf(683,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( B
!= ( t_2 @ ( a @ huffma83463279weight ) ) )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( D @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[155,136]) ).
thf(684,plain,
! [TA: $tType,C: nat,B: TA,A: TA] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( C @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( B @ ( C @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( t_2 @ ( a @ huffma83463279weight ) @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[683:[bind(A,$thf( A )),bind(B,$thf( t_2 @ ( a @ huffma83463279weight ) )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(701,plain,
! [TA: $tType,C: nat,B: TA,A: TA] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( C @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( B @ ( C @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( t_2 @ ( a @ huffma83463279weight ) @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[684]) ).
thf(6205,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ bounded_lattice )
!= ( TH @ bounded_lattice ) )
| ( TH @ ( TG @ fun ) @ bounded_lattice_bot )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5734,144]) ).
thf(6206,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ bounded_lattice )
!= ( TH @ bounded_lattice ) )
| ( TH @ ( TG @ fun ) @ bounded_lattice_bot ) ),
inference(simp,[status(thm)],[6205]) ).
thf(6207,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ bounded_lattice_bot ),
inference(pattern_uni,[status(thm)],[6206:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) ))]]) ).
thf(133,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ one_one @ ( TA @ semiring_1_of_nat ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_of__nat__1) ).
thf(569,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ one_one @ ( TA @ semiring_1_of_nat ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(113,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_of__nat__add) ).
thf(503,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(43,axiom,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) @ ( C @ ( TA @ inf_inf ) ) )
= ( A @ ( C @ ( TA @ inf_inf ) ) @ ( B @ ( TA @ inf_inf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_inf__left__commute) ).
thf(266,plain,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) @ ( C @ ( TA @ inf_inf ) ) )
= ( A @ ( C @ ( TA @ inf_inf ) ) @ ( B @ ( TA @ inf_inf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(23,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(204,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)],[23]) ).
thf(205,plain,
! [B: bool,A: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
inference(cnf,[status(esa)],[204]) ).
thf(114,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_30_tree_Osimps_I4_J) ).
thf(506,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)],[114]) ).
thf(507,plain,
! [TA: $tType,E: nat,D: TA @ huffma1450048681e_tree,C: TA @ huffma1450048681e_tree,B: nat,A: TA] :
( ( C @ ( D @ ( E @ ( TA @ huffma1146269203erNode ) ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ),
inference(cnf,[status(esa)],[506]) ).
thf(508,plain,
! [TA: $tType,E: nat,D: TA @ huffma1450048681e_tree,C: TA @ huffma1450048681e_tree,B: nat,A: TA] :
( ( C @ ( D @ ( E @ ( TA @ huffma1146269203erNode ) ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ),
inference(lifteq,[status(thm)],[507]) ).
thf(125,axiom,
t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1518433673istent ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_InnerNode_Oprems) ).
thf(541,plain,
t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1518433673istent ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(85,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(398,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(673,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( D
!= ( t_1 @ ( a @ huffma83463279weight ) ) )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[155,136]) ).
thf(674,plain,
! [TA: $tType,C: TA,B: nat,A: TA] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( t_1 @ ( a @ huffma83463279weight ) @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[673:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( t_1 @ ( a @ huffma83463279weight ) ))]]) ).
thf(947,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( C
!= ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) ) )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,136]) ).
thf(948,plain,
! [C: nat,B: nat,A: nat] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[947:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) )),bind(D,$thf( D ))]]) ).
thf(1515,plain,
! [C: nat,B: nat,A: nat] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[948]) ).
thf(123,axiom,
nat @ cancel146912293up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(530,plain,
nat @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(67,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_54_equals0D) ).
thf(343,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)],[67]) ).
thf(33,axiom,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) @ ( C @ ( TA @ inf_inf ) ) )
= ( A @ ( C @ ( TA @ inf_inf ) ) @ ( B @ ( TA @ inf_inf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_inf__sup__aci_I3_J) ).
thf(237,plain,
! [TA: $tType] :
( ( TA @ lattice )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) @ ( C @ ( TA @ inf_inf ) ) )
= ( A @ ( C @ ( TA @ inf_inf ) ) @ ( B @ ( TA @ inf_inf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(71,axiom,
! [TA: $tType] :
( ( TA @ bounded_lattice_bot )
=> ! [A: TA] :
( ( A @ ( TA @ bot_bot @ ( TA @ inf_inf ) ) )
= ( TA @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_inf__bot__left) ).
thf(360,plain,
! [TA: $tType] :
( ( TA @ bounded_lattice_bot )
=> ! [A: TA] :
( ( A @ ( TA @ bot_bot @ ( TA @ inf_inf ) ) )
= ( TA @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(661,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( D
!= ( t_2 @ ( a @ huffma1134658180e_cost ) ) )
| ( ( B @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[155,136]) ).
thf(662,plain,
! [TA: $tType,C: TA,B: nat,A: TA] :
( ( ( B @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[661:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( t_2 @ ( a @ huffma1134658180e_cost ) ))]]) ).
thf(55,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_44_empty__Collect__eq) ).
thf(298,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) ) )
& ( ( ( bool @ ( TA @ fun ) @ bot_bot )
= ( A @ ( TA @ collect ) ) )
=> ! [B: TA] :
~ ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(937,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( C
!= ( t_2 @ ( a @ huffma83463279weight ) ) )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( A @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,136]) ).
thf(938,plain,
! [C: nat,B: nat,A: nat] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( A @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_2 @ ( a @ huffma83463279weight ) @ ( C @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[937:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_2 @ ( a @ huffma83463279weight ) )),bind(D,$thf( D ))]]) ).
thf(1510,plain,
! [C: nat,B: nat,A: nat] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( A @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_2 @ ( a @ huffma83463279weight ) @ ( C @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[938]) ).
thf(165,plain,
! [TA: $tType,TB: $tType,C: TB,B: TA @ ( TB @ fun ),A: TA @ ( TB @ fun )] :
( ( ( C @ ( A @ ( B @ ( TA @ ( TB @ fun ) @ inf_inf ) ) @ ( TA @ ( TB @ aa ) ) ) )
= ( C @ ( A @ ( TA @ ( TB @ aa ) ) ) @ ( C @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ inf_inf ) ) ) )
| ~ ( TA @ lattice ) ),
inference(cnf,[status(esa)],[164]) ).
thf(166,plain,
! [TA: $tType,TB: $tType,C: TB,B: TA @ ( TB @ fun ),A: TA @ ( TB @ fun )] :
( ~ ( TA @ lattice )
| ( ( C @ ( A @ ( B @ ( TA @ ( TB @ fun ) @ inf_inf ) ) @ ( TA @ ( TB @ aa ) ) ) )
= ( C @ ( A @ ( TA @ ( TB @ aa ) ) ) @ ( C @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ inf_inf ) ) ) ) ),
inference(lifteq,[status(thm)],[165]) ).
thf(9,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_50_Int__iff) ).
thf(159,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)],[9]) ).
thf(160,plain,
! [TA: $tType,C: TA,B: bool @ ( TA @ fun ),A: bool @ ( TA @ fun )] :
( ( ( 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 ) )
& ( ( 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 ) )
& ( ( 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 ) ) ),
inference(cnf,[status(esa)],[159]) ).
thf(161,plain,
! [TA: $tType,C: TA,B: bool @ ( TA @ fun ),A: bool @ ( TA @ fun )] :
( ( 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 ) ),
inference(cnfConj,[status(thm)],[160]) ).
thf(48,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(279,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)],[48]) ).
thf(99,axiom,
nat @ ab_semigroup_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(444,plain,
nat @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(148,plain,
! [TA: $tType,A: TA] :
( ( ( A @ ( A @ ( TA @ inf_inf ) ) )
= A )
| ~ ( TA @ semilattice_inf ) ),
inference(cnf,[status(esa)],[147]) ).
thf(149,plain,
! [TA: $tType,A: TA] :
( ~ ( TA @ semilattice_inf )
| ( ( A @ ( A @ ( TA @ inf_inf ) ) )
= A ) ),
inference(lifteq,[status(thm)],[148]) ).
thf(77,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(375,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(14,axiom,
bool @ semilattice_inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Osemilattice__inf) ).
thf(180,plain,
bool @ semilattice_inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(582,plain,
! [TA: $tType,TB: $tType] :
( ( ( bool @ bounded_lattice )
!= ( TB @ bounded_lattice ) )
| ( TB @ ( TA @ fun ) @ bounded_lattice_bot )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,144]) ).
thf(583,plain,
! [TA: $tType,TB: $tType] :
( ( ( bool @ bounded_lattice )
!= ( TB @ bounded_lattice ) )
| ( TB @ ( TA @ fun ) @ bounded_lattice_bot ) ),
inference(simp,[status(thm)],[582]) ).
thf(584,plain,
! [TA: $tType] : ( bool @ ( TA @ fun ) @ bounded_lattice_bot ),
inference(pattern_uni,[status(thm)],[583:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( bool ))]]) ).
thf(8347,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ bounded_lattice )
!= ( TM @ bounded_lattice ) )
| ( TM @ ( TL @ fun ) @ bounded_lattice_bot )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7796,144]) ).
thf(8348,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ bounded_lattice )
!= ( TM @ bounded_lattice ) )
| ( TM @ ( TL @ fun ) @ bounded_lattice_bot ) ),
inference(simp,[status(thm)],[8347]) ).
thf(8349,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ bounded_lattice_bot ),
inference(pattern_uni,[status(thm)],[8348:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) ))]]) ).
thf(1618,plain,
! [D: $o,C: $o,B: nat,A: nat] :
( ~ D
| ( ( $false @ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( ( D
| C )
@ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(cnfConj,[status(thm)],[1616]) ).
thf(1620,plain,
! [D: $o,C: $o,B: nat,A: nat] :
( ~ D
| ( ( $false @ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( ( D
| C )
@ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[1618]) ).
thf(9112,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ bounded_lattice )
!= ( TO @ bounded_lattice ) )
| ( TO @ ( TN @ fun ) @ bounded_lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8960,179]) ).
thf(9113,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ bounded_lattice )
!= ( TO @ bounded_lattice ) )
| ( TO @ ( TN @ fun ) @ bounded_lattice ) ),
inference(simp,[status(thm)],[9112]) ).
thf(9114,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ bounded_lattice ),
inference(pattern_uni,[status(thm)],[9113:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) ))]]) ).
thf(52,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_inf1D1) ).
thf(291,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(49,axiom,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) )
= ( B @ ( A @ ( TA @ inf_inf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_inf__commute) ).
thf(281,plain,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) )
= ( B @ ( A @ ( TA @ inf_inf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(2168,plain,
! [B: nat,A: nat] :
( ( $true @ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( $false @ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ),
inference(simp,[status(thm)],[2167]) ).
thf(2193,plain,
! [B: nat,A: nat] :
( ( $true @ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( $false @ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ),
inference(simp,[status(thm)],[2168]) ).
thf(100,axiom,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(445,plain,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(9657,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType,TZN: $tType,TZO: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) @ ( TZL @ fun ) @ ( TZM @ fun ) @ lattice )
!= ( TZO @ lattice ) )
| ( TZO @ ( TZN @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9004,146]) ).
thf(9658,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType,TZN: $tType,TZO: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) @ ( TZL @ fun ) @ ( TZM @ fun ) @ lattice )
!= ( TZO @ lattice ) )
| ( TZO @ ( TZN @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[9657]) ).
thf(9659,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType,TZN: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) @ ( TZL @ fun ) @ ( TZM @ fun ) @ ( TZN @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[9658:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZK )),bind_type(TZL,$thf( TZL )),bind_type(TZM,$thf( TZM )),bind_type(TZN,$thf( TZN )),bind_type(TZO,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) @ ( TZL @ fun ) @ ( TZM @ fun ) ))]]) ).
thf(6671,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ bounded_lattice )
!= ( TI @ bounded_lattice ) )
| ( TI @ ( TH @ fun ) @ bounded_lattice_bot )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6200,144]) ).
thf(6672,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ bounded_lattice )
!= ( TI @ bounded_lattice ) )
| ( TI @ ( TH @ fun ) @ bounded_lattice_bot ) ),
inference(simp,[status(thm)],[6671]) ).
thf(6673,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ bounded_lattice_bot ),
inference(pattern_uni,[status(thm)],[6672:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) ))]]) ).
thf(64,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_72_Int__assoc) ).
thf(335,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)],[64]) ).
thf(15,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_71_Int__left__commute) ).
thf(181,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)],[15]) ).
thf(689,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( B
!= ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) ) )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[155,136]) ).
thf(690,plain,
! [TA: $tType,C: nat,B: TA,A: TA] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( B @ ( C @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[689:[bind(A,$thf( A )),bind(B,$thf( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(704,plain,
! [TA: $tType,C: nat,B: TA,A: TA] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( B @ ( C @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[690]) ).
thf(69,axiom,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ bot_bot )
= ( fFalse @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_empty__def) ).
thf(350,plain,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ bot_bot )
= ( fFalse @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(82,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TA] :
( ( D @ ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma1352802255e_freq ) ) )
= ( D @ ( A @ ( TA @ huffma1352802255e_freq ) ) @ ( D @ ( B @ ( TA @ huffma1352802255e_freq ) ) @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_freq_Osimps_I2_J) ).
thf(391,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TA] :
( ( D @ ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma1352802255e_freq ) ) )
= ( D @ ( A @ ( TA @ huffma1352802255e_freq ) ) @ ( D @ ( B @ ( TA @ huffma1352802255e_freq ) ) @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(923,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( C != w )
| ( ( t_2 @ ( t_1 @ ( A @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( C @ ( D @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,136]) ).
thf(924,plain,
! [C: nat,B: nat,A: nat] :
( ( ( t_2 @ ( t_1 @ ( A @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( w @ ( C @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[923:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( w ))]]) ).
thf(1503,plain,
! [C: nat,B: nat,A: nat] :
( ( ( t_2 @ ( t_1 @ ( A @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( w @ ( C @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[924]) ).
thf(134,axiom,
nat @ semiring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
thf(572,plain,
nat @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(671,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( D
!= ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) ) )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[155,136]) ).
thf(672,plain,
! [TA: $tType,C: TA,B: nat,A: TA] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[671:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) ))]]) ).
thf(36,axiom,
bool @ bounded_lattice_bot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Obounded__lattice__bot) ).
thf(245,plain,
bool @ bounded_lattice_bot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(115,axiom,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma1134658180e_cost ) )
= ( A @ ( TA @ huffma1134658180e_cost ) @ ( A @ ( TA @ huffma83463279weight ) @ ( B @ ( TA @ huffma1134658180e_cost ) @ ( B @ ( TA @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_cost_Osimps_I2_J) ).
thf(509,plain,
! [TA: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( TA @ huffma1134658180e_cost ) )
= ( A @ ( TA @ huffma1134658180e_cost ) @ ( A @ ( TA @ huffma83463279weight ) @ ( B @ ( TA @ huffma1134658180e_cost ) @ ( B @ ( TA @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(97,axiom,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA] :
( ( B
= ( A @ ( B @ ( TA @ plus_plus ) ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_add__0__iff) ).
thf(434,plain,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( B
= ( A @ ( B @ ( TA @ plus_plus ) ) ) ) )
& ( ( B
= ( A @ ( B @ ( TA @ plus_plus ) ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(45,axiom,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) @ ( B @ ( TA @ inf_inf ) ) )
= ( A @ ( B @ ( TA @ inf_inf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_inf_Oleft__idem) ).
thf(271,plain,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) @ ( B @ ( TA @ inf_inf ) ) )
= ( A @ ( B @ ( TA @ inf_inf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(207,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TA @ ( TB @ fun ) @ ( TC @ fun ),B: TB @ ( TC @ fun ),A: TC] :
( ( A @ ( B @ ( C @ ( TA @ ( TB @ ( TC @ combs ) ) ) ) @ ( TA @ ( TC @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TC @ aa ) ) ) @ ( A @ ( C @ ( TA @ ( TB @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ aa ) ) ) ) ),
inference(cnf,[status(esa)],[206]) ).
thf(208,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TA @ ( TB @ fun ) @ ( TC @ fun ),B: TB @ ( TC @ fun ),A: TC] :
( ( A @ ( B @ ( C @ ( TA @ ( TB @ ( TC @ combs ) ) ) ) @ ( TA @ ( TC @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TC @ aa ) ) ) @ ( A @ ( C @ ( TA @ ( TB @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ aa ) ) ) ) ),
inference(lifteq,[status(thm)],[207]) ).
thf(110,axiom,
nat @ semiri456707255roduct,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(494,plain,
nat @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(129,axiom,
! [TA: $tType,A: TA,B: nat] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1134658180e_cost ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_cost_Osimps_I1_J) ).
thf(552,plain,
! [TA: $tType,A: TA,B: nat] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma1134658180e_cost ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(4026,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( bool @ ( TA @ fun ) @ bounded_lattice )
!= ( TC @ bounded_lattice ) )
| ( TC @ ( TB @ fun ) @ bounded_lattice_bot )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3988,144]) ).
thf(4027,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( bool @ ( TA @ fun ) @ bounded_lattice )
!= ( TC @ bounded_lattice ) )
| ( TC @ ( TB @ fun ) @ bounded_lattice_bot ) ),
inference(simp,[status(thm)],[4026]) ).
thf(4028,plain,
! [TA: $tType,TB: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ bounded_lattice_bot ),
inference(pattern_uni,[status(thm)],[4027:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( bool @ ( TA @ fun ) ))]]) ).
thf(34,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_45_empty__iff) ).
thf(240,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)],[34]) ).
thf(21,axiom,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) )
= ( B @ ( A @ ( TA @ inf_inf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_inf_Ocommute) ).
thf(198,plain,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) )
= ( B @ ( A @ ( TA @ inf_inf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(60,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(323,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(681,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( B
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( D
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[155,136]) ).
thf(682,plain,
! [TA: $tType,C: nat,B: TA,A: TA] :
( ( C
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( B @ ( C @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[681:[bind(A,$thf( A )),bind(B,$thf( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(700,plain,
! [TA: $tType,B: TA,A: TA] :
( ( B @ ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( TA @ huffma2021818691e_Leaf ) ) ) ),
inference(simp,[status(thm)],[682]) ).
thf(119,axiom,
nat @ semilattice_inf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Lattices_Osemilattice__inf) ).
thf(520,plain,
nat @ semilattice_inf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(667,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( D
!= ( t_1 @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( B @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[155,136]) ).
thf(668,plain,
! [TA: $tType,C: TA,B: nat,A: TA] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( B @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[667:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( t_1 @ ( a @ huffma1134658180e_cost ) ))]]) ).
thf(120,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(521,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(865,plain,
! [D: nat,C: bool,B: nat,A: bool] :
( ( C != fFalse )
| ~ ( A @ pp )
| ( ( C @ ( D @ ( bool @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( bool @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,275]) ).
thf(866,plain,
! [C: nat,B: nat,A: bool] :
( ~ ( A @ pp )
| ( ( fFalse @ ( C @ ( bool @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( bool @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[865:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( fFalse ))]]) ).
thf(1474,plain,
! [C: nat,B: nat,A: bool] :
( ~ ( A @ pp )
| ( ( fFalse @ ( C @ ( bool @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( bool @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[866]) ).
thf(1631,plain,
! [F: nat,E: nat,D: nat,C: $o @ huffma1450048681e_tree,B: nat,A: $o @ huffma1450048681e_tree] :
( ( C
!= ( $true @ ( E @ ( $o @ huffma2021818691e_Leaf ) ) ) )
| ( A
!= ( $false @ ( F @ ( $o @ huffma2021818691e_Leaf ) ) ) )
| ( ( C @ ( D @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,1613]) ).
thf(1632,plain,
! [E: nat,D: nat,C: nat,B: nat,A: $o @ huffma1450048681e_tree] :
( ( A
!= ( $false @ ( D @ ( $o @ huffma2021818691e_Leaf ) ) ) )
| ( ( $true @ ( E @ ( $o @ huffma2021818691e_Leaf ) ) @ ( C @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1631:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( $true @ ( G @ ( $o @ huffma2021818691e_Leaf ) ) )),bind(D,$thf( D )),bind(E,$thf( G )),bind(F,$thf( F ))]]) ).
thf(1643,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( $true @ ( D @ ( $o @ huffma2021818691e_Leaf ) ) @ ( B @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( $false @ ( C @ ( $o @ huffma2021818691e_Leaf ) ) @ ( A @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ),
inference(simp,[status(thm)],[1632]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ lattice )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ inf_inf ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ inf_inf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_inf__apply) ).
thf(226,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ lattice )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ inf_inf ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ inf_inf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(96,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_nat__add__commute) ).
thf(431,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(657,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( D != w )
| ( ( t_2 @ ( t_1 @ ( B @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[155,136]) ).
thf(658,plain,
! [TA: $tType,C: TA,B: nat,A: TA] :
( ( ( t_2 @ ( t_1 @ ( B @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( C @ ( w @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[657:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( w ))]]) ).
thf(83,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(394,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(57,axiom,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) @ ( C @ ( TA @ inf_inf ) ) )
= ( A @ ( C @ ( TA @ inf_inf ) ) @ ( B @ ( TA @ inf_inf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_inf_Oleft__commute) ).
thf(306,plain,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ inf_inf ) ) @ ( C @ ( TA @ inf_inf ) ) )
= ( A @ ( C @ ( TA @ inf_inf ) ) @ ( B @ ( TA @ inf_inf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(131,axiom,
! [TA: $tType,A: TA,B: nat] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma83463279weight ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_weight_Osimps_I1_J) ).
thf(563,plain,
! [TA: $tType,A: TA,B: nat] :
( ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) @ ( TA @ huffma83463279weight ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(109,axiom,
! [A: a] :
( ( ( t_2 @ ( a @ huffma675207370phabet ) @ ( t_1 @ ( a @ huffma675207370phabet ) @ ( bool @ ( a @ fun ) @ inf_inf ) ) )
= ( bool @ ( a @ fun ) @ bot_bot ) )
=> ( ( t_2 @ ( a @ huffma675207370phabet ) @ ( A @ ( a @ member @ ( bool @ ( bool @ ( a @ fun ) @ fun ) @ ( a @ aa ) ) ) @ ( bool @ ( bool @ ( a @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma410068972_depth ) ) )
= ( nat @ one_one @ ( A @ ( t_2 @ ( a @ huffma410068972_depth ) ) @ ( nat @ plus_plus ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_d_092_060_094isub_0622) ).
thf(490,plain,
! [A: a] :
( ( ( t_2 @ ( a @ huffma675207370phabet ) @ ( t_1 @ ( a @ huffma675207370phabet ) @ ( bool @ ( a @ fun ) @ inf_inf ) ) )
= ( bool @ ( a @ fun ) @ bot_bot ) )
=> ( ( t_2 @ ( a @ huffma675207370phabet ) @ ( A @ ( a @ member @ ( bool @ ( bool @ ( a @ fun ) @ fun ) @ ( a @ aa ) ) ) @ ( bool @ ( bool @ ( a @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma410068972_depth ) ) )
= ( nat @ one_one @ ( A @ ( t_2 @ ( a @ huffma410068972_depth ) ) @ ( nat @ plus_plus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(851,plain,
! [TB: $tType,F: TB,E: bool @ ( TB @ fun ),D: nat,C: bool @ ( TB @ fun ),B: nat,A: bool @ ( TB @ fun )] :
( ( C
!= ( E @ ( TB @ collect ) ) )
| ~ ( F @ ( E @ ( bool @ ( TB @ aa ) ) ) @ pp )
| ( A
!= ( bool @ ( TB @ fun ) @ bot_bot ) )
| ( ( C @ ( D @ ( bool @ ( TB @ fun ) @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( bool @ ( TB @ fun ) @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,233]) ).
thf(852,plain,
! [TB: $tType,E: bool @ ( TB @ fun ),D: TB,C: nat,B: nat,A: bool @ ( TB @ fun )] :
( ~ ( D @ ( E @ ( bool @ ( TB @ aa ) ) ) @ pp )
| ( A
!= ( bool @ ( TB @ fun ) @ bot_bot ) )
| ( ( E @ ( TB @ collect ) @ ( C @ ( bool @ ( TB @ fun ) @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( bool @ ( TB @ fun ) @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[851:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( G @ ( TB @ collect ) )),bind(D,$thf( D )),bind(E,$thf( G ))]]) ).
thf(1467,plain,
! [TA: $tType,D: bool @ ( TA @ fun ),C: TA,B: nat,A: nat] :
( ~ ( C @ ( D @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( ( D @ ( TA @ collect ) @ ( B @ ( bool @ ( TA @ fun ) @ huffma2021818691e_Leaf ) ) )
!= ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[852]) ).
thf(40,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_53_ex__in__conv) ).
thf(255,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ? [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ? [B: TA] : ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(935,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( C
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( A
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,136]) ).
thf(936,plain,
! [C: nat,B: nat,A: nat] :
( ( A
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[935:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )),bind(D,$thf( D ))]]) ).
thf(1509,plain,
! [B: nat,A: nat] :
( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) @ ( A @ ( nat @ huffma2021818691e_Leaf ) ) ) ),
inference(simp,[status(thm)],[936]) ).
thf(162,plain,
! [TA: $tType,C: TA,B: bool @ ( TA @ fun ),A: bool @ ( TA @ fun )] :
( ( 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(cnfConj,[status(thm)],[160]) ).
thf(124,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_90_add__is__0) ).
thf(531,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)],[124]) ).
thf(25,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_73_IntD1) ).
thf(209,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)],[25]) ).
thf(5227,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ bounded_lattice )
!= ( TF @ bounded_lattice ) )
| ( TF @ ( TE @ fun ) @ bounded_lattice_bot )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4585,144]) ).
thf(5228,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ bounded_lattice )
!= ( TF @ bounded_lattice ) )
| ( TF @ ( TE @ fun ) @ bounded_lattice_bot ) ),
inference(simp,[status(thm)],[5227]) ).
thf(5229,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ bounded_lattice_bot ),
inference(pattern_uni,[status(thm)],[5228:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) ))]]) ).
thf(54,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(295,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)],[54]) ).
thf(2183,plain,
! [C: bool,B: nat,A: nat] :
( ~ ( C @ pp )
| ( ( C @ pp @ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( $false @ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(prim_subst,[status(thm)],[2167:[bind(A,$thf( A )),bind(B,$thf( D @ pp ))]]) ).
thf(2192,plain,
! [C: bool,B: nat,A: nat] :
( ~ ( C @ pp )
| ( ( C @ pp @ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( $false @ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[2183]) ).
thf(89,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_13_nat__add__assoc) ).
thf(414,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)],[89]) ).
thf(1639,plain,
! [F: nat,E: nat,D: nat,C: $o @ huffma1450048681e_tree,B: nat,A: $o @ huffma1450048681e_tree] :
( ( A
!= ( $true @ ( E @ ( $o @ huffma2021818691e_Leaf ) ) ) )
| ( C
!= ( $false @ ( F @ ( $o @ huffma2021818691e_Leaf ) ) ) )
| ( ( C @ ( D @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,1613]) ).
thf(1640,plain,
! [E: nat,D: nat,C: nat,B: $o @ huffma1450048681e_tree,A: nat] :
( ( B
!= ( $false @ ( D @ ( $o @ huffma2021818691e_Leaf ) ) ) )
| ( ( B @ ( C @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( $true @ ( E @ ( $o @ huffma2021818691e_Leaf ) ) @ ( A @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1639:[bind(A,$thf( $true @ ( G @ ( $o @ huffma2021818691e_Leaf ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G )),bind(F,$thf( F ))]]) ).
thf(1647,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( $false @ ( C @ ( $o @ huffma2021818691e_Leaf ) ) @ ( B @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( $true @ ( D @ ( $o @ huffma2021818691e_Leaf ) ) @ ( A @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ),
inference(simp,[status(thm)],[1640]) ).
thf(42,axiom,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ inf_inf ) ) @ ( TA @ inf_inf ) ) )
= ( A @ ( B @ ( TA @ inf_inf ) ) @ ( C @ ( TA @ inf_inf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_inf_Oassoc) ).
thf(263,plain,
! [TA: $tType] :
( ( TA @ semilattice_inf )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ inf_inf ) ) @ ( TA @ inf_inf ) ) )
= ( A @ ( B @ ( TA @ inf_inf ) ) @ ( C @ ( TA @ inf_inf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(949,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( C
!= ( t_1 @ ( a @ huffma83463279weight ) ) )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,136]) ).
thf(950,plain,
! [C: nat,B: nat,A: nat] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_1 @ ( a @ huffma83463279weight ) @ ( C @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[949:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_1 @ ( a @ huffma83463279weight ) )),bind(D,$thf( D ))]]) ).
thf(1516,plain,
! [C: nat,B: nat,A: nat] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( A @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_1 @ ( a @ huffma83463279weight ) @ ( C @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[950]) ).
thf(9119,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ bounded_lattice )
!= ( TO @ bounded_lattice ) )
| ( TO @ ( TN @ fun ) @ bounded_lattice_bot )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8960,144]) ).
thf(9120,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ bounded_lattice )
!= ( TO @ bounded_lattice ) )
| ( TO @ ( TN @ fun ) @ bounded_lattice_bot ) ),
inference(simp,[status(thm)],[9119]) ).
thf(9121,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ bounded_lattice_bot ),
inference(pattern_uni,[status(thm)],[9120:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) ))]]) ).
thf(63,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_75_mem__def) ).
thf(331,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)],[63]) ).
thf(98,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_add_Ocomm__neutral) ).
thf(441,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(112,axiom,
nat @ bot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Obot) ).
thf(502,plain,
nat @ bot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(65,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_77_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)],[65]) ).
thf(128,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_35_consistent_Osimps_I2_J) ).
thf(544,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)],[128]) ).
thf(687,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( B
!= ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( D @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[155,136]) ).
thf(688,plain,
! [TA: $tType,C: nat,B: TA,A: TA] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( C @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( B @ ( C @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[687:[bind(A,$thf( A )),bind(B,$thf( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(703,plain,
! [TA: $tType,C: nat,B: TA,A: TA] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( C @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( B @ ( C @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[688]) ).
thf(929,plain,
! [D: nat,C: a @ huffma1450048681e_tree,B: nat,A: a @ huffma1450048681e_tree] :
( ( C != t_2 )
| ( ( A @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( C @ ( D @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,136]) ).
thf(930,plain,
! [C: nat,B: nat,A: a @ huffma1450048681e_tree] :
( ( ( A @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( t_2 @ ( C @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[929:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_2 ))]]) ).
thf(1506,plain,
! [C: nat,B: nat,A: a @ huffma1450048681e_tree] :
( ( ( A @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( t_2 @ ( C @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[930]) ).
thf(925,plain,
! [D: nat,C: a @ huffma1450048681e_tree,B: nat,A: a @ huffma1450048681e_tree] :
( ( C != t_1 )
| ( ( t_2 @ ( A @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( C @ ( D @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,136]) ).
thf(926,plain,
! [C: nat,B: nat,A: a @ huffma1450048681e_tree] :
( ( ( t_2 @ ( A @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( t_1 @ ( C @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[925:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_1 ))]]) ).
thf(1504,plain,
! [C: nat,B: nat,A: a @ huffma1450048681e_tree] :
( ( ( t_2 @ ( A @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( t_1 @ ( C @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[926]) ).
thf(4546,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ bounded_lattice )
!= ( TD @ bounded_lattice ) )
| ( TD @ ( TC @ fun ) @ bounded_lattice_bot )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4021,144]) ).
thf(4547,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ bounded_lattice )
!= ( TD @ bounded_lattice ) )
| ( TD @ ( TC @ fun ) @ bounded_lattice_bot ) ),
inference(simp,[status(thm)],[4546]) ).
thf(4548,plain,
! [TA: $tType,TB: $tType,TC: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ bounded_lattice_bot ),
inference(pattern_uni,[status(thm)],[4547:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) ))]]) ).
thf(1627,plain,
! [F: nat,E: nat,D: nat,C: $o @ huffma1450048681e_tree,B: nat,A: $o @ huffma1450048681e_tree] :
( ( C
!= ( $false @ ( F @ ( $o @ huffma2021818691e_Leaf ) ) ) )
| ( A
!= ( $true @ ( E @ ( $o @ huffma2021818691e_Leaf ) ) ) )
| ( ( C @ ( D @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,1613]) ).
thf(1628,plain,
! [E: nat,D: nat,C: nat,B: nat,A: $o @ huffma1450048681e_tree] :
( ( A
!= ( $true @ ( D @ ( $o @ huffma2021818691e_Leaf ) ) ) )
| ( ( $false @ ( E @ ( $o @ huffma2021818691e_Leaf ) ) @ ( C @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1627:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( $false @ ( G @ ( $o @ huffma2021818691e_Leaf ) ) )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( G ))]]) ).
thf(1649,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( $false @ ( D @ ( $o @ huffma2021818691e_Leaf ) ) @ ( B @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( $true @ ( C @ ( $o @ huffma2021818691e_Leaf ) ) @ ( A @ ( $o @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ),
inference(simp,[status(thm)],[1628]) ).
thf(121,axiom,
! [TA: $tType,TB: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ),E: TB @ ( TA @ fun ) @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( D @ ( E @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) )
= ( A @ ( D @ ( E @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) @ ( B @ ( D @ ( E @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) @ ( A @ ( B @ ( C @ ( D @ ( TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_tree_Orecs_I2_J) ).
thf(524,plain,
! [TA: $tType,TB: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ),E: TB @ ( TA @ fun ) @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( D @ ( E @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) )
= ( A @ ( D @ ( E @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) @ ( B @ ( D @ ( E @ ( TB @ ( TA @ huffma1280178957ee_rec ) ) ) ) @ ( A @ ( B @ ( C @ ( D @ ( TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TB @ fun ) @ ( TA @ huffma1450048681e_tree @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(111,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_add__right__cancel) ).
thf(495,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(951,plain,
! [D: nat,C: a @ huffma1450048681e_tree,B: nat,A: a @ huffma1450048681e_tree] :
( ( C != t_2 )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( A @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,136]) ).
thf(952,plain,
! [C: nat,B: nat,A: a @ huffma1450048681e_tree] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( A @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_2 @ ( C @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[951:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_2 ))]]) ).
thf(1517,plain,
! [C: nat,B: nat,A: a @ huffma1450048681e_tree] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( A @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_2 @ ( C @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[952]) ).
thf(108,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_4_nat__add__left__cancel) ).
thf(482,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)],[108]) ).
thf(202,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
inference(cnf,[status(esa)],[201]) ).
thf(203,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( bool @ ( TA @ fun ) @ bot_bot @ ( A @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
inference(lifteq,[status(thm)],[202]) ).
thf(679,plain,
! [TA: $tType,D: nat,C: TA,B: nat,A: TA] :
( ( B
!= ( t_2 @ ( a @ huffma1134658180e_cost ) ) )
| ( ( D @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[155,136]) ).
thf(680,plain,
! [TA: $tType,C: nat,B: TA,A: TA] :
( ( ( C @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( B @ ( C @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[679:[bind(A,$thf( A )),bind(B,$thf( t_2 @ ( a @ huffma1134658180e_cost ) )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(699,plain,
! [TA: $tType,C: nat,B: TA,A: TA] :
( ( ( C @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( B @ ( C @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( TA @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[680]) ).
thf(869,plain,
! [D: nat,C: bool,B: nat,A: bool] :
( ( A != fFalse )
| ~ ( C @ pp )
| ( ( C @ ( D @ ( bool @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( bool @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,275]) ).
thf(870,plain,
! [C: nat,B: bool,A: nat] :
( ~ ( B @ pp )
| ( ( B @ ( C @ ( bool @ huffma2021818691e_Leaf ) ) )
!= ( fFalse @ ( A @ ( bool @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[869:[bind(A,$thf( fFalse ))]]) ).
thf(1476,plain,
! [C: nat,B: bool,A: nat] :
( ~ ( B @ pp )
| ( ( B @ ( C @ ( bool @ huffma2021818691e_Leaf ) ) )
!= ( fFalse @ ( A @ ( bool @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[870]) ).
thf(8374,plain,
! [TA: $tType,D: bool @ ( TA @ fun ),C: TA,B: nat,A: nat] :
( ~ ( C @ ( D @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( ( D @ ( TA @ collect ) )
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
| ( B != A ) ),
inference(simp,[status(thm)],[1467]) ).
thf(8424,plain,
! [TA: $tType,B: bool @ ( TA @ fun ),A: TA] :
( ~ ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( ( B @ ( TA @ collect ) )
!= ( bool @ ( TA @ fun ) @ bot_bot ) ) ),
inference(simp,[status(thm)],[8374]) ).
thf(8904,plain,
! [TA: $tType,D: bool @ ( TA @ fun ),C: TA,B: bool,A: bool] :
( ( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
!= ( C @ ( D @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
| ~ $true
| ( ( D @ ( TA @ collect ) )
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
inference(paramod_ordered,[status(thm)],[205,8424]) ).
thf(8905,plain,
! [TA: $tType,D: bool @ ( TA @ fun ),C: TA,B: bool,A: bool] :
( ( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
!= ( C @ ( D @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
| ( ( D @ ( TA @ collect ) )
!= ( bool @ ( TA @ fun ) @ bot_bot ) )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
inference(simp,[status(thm)],[8904]) ).
thf(8906,plain,
! [B: bool,A: bool] :
( ( ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ collect ) )
!= ( bool @ ( bool @ fun ) @ bot_bot ) )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
inference(pattern_uni,[status(thm)],[8905:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( F @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) )),bind_type(TA,$thf( bool ))]]) ).
thf(8930,plain,
! [B: bool,A: bool] :
( ( ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ collect ) )
!= ( bool @ ( bool @ fun ) @ bot_bot ) )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
inference(simp,[status(thm)],[8906]) ).
thf(9050,plain,
! [B: bool,A: bool] :
( ~ $true
| ( ( A @ pp )
!= ( B @ pp ) )
| ( ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ collect ) )
!= ( bool @ ( bool @ fun ) @ bot_bot ) )
| ~ ( B @ pp ) ),
inference(eqfactor_ordered,[status(thm)],[8930]) ).
thf(9051,plain,
! [A: bool] :
( ( ( A @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ collect ) )
!= ( bool @ ( bool @ fun ) @ bot_bot ) )
| ~ ( A @ pp ) ),
inference(pattern_uni,[status(thm)],[9050:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(9094,plain,
! [B: bool,A: bool @ ( bool @ fun )] :
( ( ( A @ ( bool @ collect ) )
!= ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ collect ) ) )
| ( A
!= ( bool @ ( bool @ fun ) @ bot_bot ) )
| ~ ( B @ pp ) ),
inference(paramod_ordered,[status(thm)],[139,9051]) ).
thf(9095,plain,
! [A: bool] :
( ( ( A @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) )
!= ( bool @ ( bool @ fun ) @ bot_bot ) )
| ~ ( A @ pp ) ),
inference(pattern_uni,[status(thm)],[9094:[bind(A,$thf( D @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) )),bind(B,$thf( D ))]]) ).
thf(9102,plain,
! [A: bool] :
( ( ( A @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) )
!= ( bool @ ( bool @ fun ) @ bot_bot ) )
| ~ ( A @ pp ) ),
inference(simp,[status(thm)],[9095]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ( TA @ ( TB @ fun ) @ bot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
thf(304,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ bot )
=> ( TA @ ( TB @ fun ) @ bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(933,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( C
!= ( t_2 @ ( a @ huffma1134658180e_cost ) ) )
| ( ( A @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,136]) ).
thf(934,plain,
! [C: nat,B: nat,A: nat] :
( ( ( A @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( C @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[933:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_2 @ ( a @ huffma1134658180e_cost ) )),bind(D,$thf( D ))]]) ).
thf(1508,plain,
! [C: nat,B: nat,A: nat] :
( ( ( A @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( C @ ( nat @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( nat @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[934]) ).
thf(185,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ( ( A @ ( B @ ( C @ ( TA @ inf_inf ) ) @ ( TA @ inf_inf ) ) )
= ( A @ ( B @ ( TA @ inf_inf ) ) @ ( C @ ( TA @ inf_inf ) ) ) )
| ~ ( TA @ lattice ) ),
inference(cnf,[status(esa)],[184]) ).
thf(186,plain,
! [TA: $tType,C: TA,B: TA,A: TA] :
( ~ ( TA @ lattice )
| ( ( A @ ( B @ ( C @ ( TA @ inf_inf ) ) @ ( TA @ inf_inf ) ) )
= ( A @ ( B @ ( TA @ inf_inf ) ) @ ( C @ ( TA @ inf_inf ) ) ) ) ),
inference(lifteq,[status(thm)],[185]) ).
thf(86,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_89_double__zero__sym) ).
thf(401,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)],[86]) ).
thf(118,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(517,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(567,plain,
! [TA: $tType,E: nat,D: TA,C: nat,B: TA @ huffma1450048681e_tree,A: TA @ huffma1450048681e_tree] :
( ( D @ ( E @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) ) ),
inference(cnf,[status(esa)],[566]) ).
thf(568,plain,
! [TA: $tType,E: nat,D: TA,C: nat,B: TA @ huffma1450048681e_tree,A: TA @ huffma1450048681e_tree] :
( ( D @ ( E @ ( TA @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) ) ),
inference(lifteq,[status(thm)],[567]) ).
thf(79,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(378,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(943,plain,
! [D: nat,C: a @ huffma1450048681e_tree,B: nat,A: a @ huffma1450048681e_tree] :
( ( C != t_1 )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( A @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,136]) ).
thf(944,plain,
! [C: nat,B: nat,A: a @ huffma1450048681e_tree] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( A @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_1 @ ( C @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[943:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_1 ))]]) ).
thf(1513,plain,
! [C: nat,B: nat,A: a @ huffma1450048681e_tree] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( A @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_1 @ ( C @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[944]) ).
thf(9641,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType,TZN: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) @ ( TZL @ fun ) @ lattice )
!= ( TZN @ lattice ) )
| ( TZN @ ( TZM @ fun ) @ lattice )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8988,146]) ).
thf(9642,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType,TZN: $tType] :
( ( ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) @ ( TZL @ fun ) @ lattice )
!= ( TZN @ lattice ) )
| ( TZN @ ( TZM @ fun ) @ lattice ) ),
inference(simp,[status(thm)],[9641]) ).
thf(9643,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType,TH: $tType,TI: $tType,TJ: $tType,TK: $tType,TL: $tType,TM: $tType,TN: $tType,TO: $tType,TP: $tType,TQ: $tType,TR: $tType,TS: $tType,TT: $tType,TU: $tType,TV: $tType,TW: $tType,TX: $tType,TY: $tType,TZ: $tType,TZA: $tType,TZB: $tType,TZC: $tType,TZD: $tType,TZE: $tType,TZF: $tType,TZG: $tType,TZH: $tType,TZI: $tType,TZJ: $tType,TZK: $tType,TZL: $tType,TZM: $tType] : ( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) @ ( TZL @ fun ) @ ( TZM @ fun ) @ lattice ),
inference(pattern_uni,[status(thm)],[9642:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( TG )),bind_type(TH,$thf( TH )),bind_type(TI,$thf( TI )),bind_type(TJ,$thf( TJ )),bind_type(TK,$thf( TK )),bind_type(TL,$thf( TL )),bind_type(TM,$thf( TM )),bind_type(TN,$thf( TN )),bind_type(TO,$thf( TO )),bind_type(TP,$thf( TP )),bind_type(TQ,$thf( TQ )),bind_type(TR,$thf( TR )),bind_type(TS,$thf( TS )),bind_type(TT,$thf( TT )),bind_type(TU,$thf( TU )),bind_type(TV,$thf( TV )),bind_type(TW,$thf( TW )),bind_type(TX,$thf( TX )),bind_type(TY,$thf( TY )),bind_type(TZ,$thf( TZ )),bind_type(TZA,$thf( TZA )),bind_type(TZB,$thf( TZB )),bind_type(TZC,$thf( TZC )),bind_type(TZD,$thf( TZD )),bind_type(TZE,$thf( TZE )),bind_type(TZF,$thf( TZF )),bind_type(TZG,$thf( TZG )),bind_type(TZH,$thf( TZH )),bind_type(TZI,$thf( TZI )),bind_type(TZJ,$thf( TZJ )),bind_type(TZK,$thf( TZK )),bind_type(TZL,$thf( TZL )),bind_type(TZM,$thf( TZM )),bind_type(TZN,$thf( nat @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ ( TG @ fun ) @ ( TH @ fun ) @ ( TI @ fun ) @ ( TJ @ fun ) @ ( TK @ fun ) @ ( TL @ fun ) @ ( TM @ fun ) @ ( TN @ fun ) @ ( TO @ fun ) @ ( TP @ fun ) @ ( TQ @ fun ) @ ( TR @ fun ) @ ( TS @ fun ) @ ( TT @ fun ) @ ( TU @ fun ) @ ( TV @ fun ) @ ( TW @ fun ) @ ( TX @ fun ) @ ( TY @ fun ) @ ( TZ @ fun ) @ ( TZA @ fun ) @ ( TZB @ fun ) @ ( TZC @ fun ) @ ( TZD @ fun ) @ ( TZE @ fun ) @ ( TZF @ fun ) @ ( TZG @ fun ) @ ( TZH @ fun ) @ ( TZI @ fun ) @ ( TZJ @ fun ) @ ( TZK @ fun ) @ ( TZL @ fun ) ))]]) ).
thf(32,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_inf1D2) ).
thf(235,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(37,axiom,
! [TA: $tType] :
( ( TA @ bounded_lattice_bot )
=> ! [A: TA] :
( ( TA @ bot_bot @ ( A @ ( TA @ inf_inf ) ) )
= ( TA @ bot_bot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_inf__bot__right) ).
thf(246,plain,
! [TA: $tType] :
( ( TA @ bounded_lattice_bot )
=> ! [A: TA] :
( ( TA @ bot_bot @ ( A @ ( TA @ inf_inf ) ) )
= ( TA @ bot_bot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1606,plain,
! [C: bool,B: nat,A: nat] :
( ~ ( C @ pp )
| ( ( $false @ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( C @ pp @ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(prim_subst,[status(thm)],[1589:[bind(A,$thf( D @ pp ))]]) ).
thf(1614,plain,
! [C: bool,B: nat,A: nat] :
( ~ ( C @ pp )
| ( ( $false @ ( B @ ( $o @ huffma2021818691e_Leaf ) ) )
!= ( C @ pp @ ( A @ ( $o @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[1606]) ).
thf(941,plain,
! [D: nat,C: a @ huffma1450048681e_tree,B: nat,A: a @ huffma1450048681e_tree] :
( ( C != t_1 )
| ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( A @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( C @ ( D @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,136]) ).
thf(942,plain,
! [C: nat,B: nat,A: a @ huffma1450048681e_tree] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( A @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_1 @ ( C @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[941:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_1 ))]]) ).
thf(1512,plain,
! [C: nat,B: nat,A: a @ huffma1450048681e_tree] :
( ( ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( A @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) )
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( a @ huffma1134658180e_cost ) ) )
| ( ( t_1 @ ( C @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[942]) ).
thf(41,axiom,
bool @ bot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
thf(262,plain,
bool @ bot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(182,plain,
! [TA: $tType,C: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),A: 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(cnf,[status(esa)],[181]) ).
thf(183,plain,
! [TA: $tType,C: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),A: 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(lifteq,[status(thm)],[182]) ).
thf(35,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Int__empty__left) ).
thf(242,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( bool @ ( TA @ fun ) @ bot_bot @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(907,plain,
! [TB: $tType,E: TB,D: nat,C: bool @ ( TB @ fun ),B: nat,A: bool @ ( TB @ fun )] :
( ( C
!= ( bool @ ( TB @ fun ) @ bot_bot ) )
| ~ ( E @ ( A @ ( bool @ ( TB @ aa ) ) ) @ pp )
| ( ( C @ ( D @ ( bool @ ( TB @ fun ) @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( bool @ ( TB @ fun ) @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,612]) ).
thf(908,plain,
! [TB: $tType,D: TB,C: nat,B: nat,A: bool @ ( TB @ fun )] :
( ~ ( D @ ( A @ ( bool @ ( TB @ aa ) ) ) @ pp )
| ( ( bool @ ( TB @ fun ) @ bot_bot @ ( C @ ( bool @ ( TB @ fun ) @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( bool @ ( TB @ fun ) @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[907:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( bool @ ( TB @ fun ) @ bot_bot ))]]) ).
thf(1495,plain,
! [TA: $tType,D: TA,C: nat,B: nat,A: bool @ ( TA @ fun )] :
( ~ ( D @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( ( bool @ ( TA @ fun ) @ bot_bot @ ( C @ ( bool @ ( TA @ fun ) @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( bool @ ( TA @ fun ) @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[908]) ).
thf(194,plain,
! [TA: $tType,B: bool @ ( TA @ fun ),A: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
inference(cnf,[status(esa)],[193]) ).
thf(195,plain,
! [TA: $tType,B: bool @ ( TA @ fun ),A: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) ) ),
inference(lifteq,[status(thm)],[194]) ).
thf(5739,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ bounded_lattice )
!= ( TG @ bounded_lattice ) )
| ( TG @ ( TF @ fun ) @ bounded_lattice_bot )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5222,144]) ).
thf(5740,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,TG: $tType] :
( ( ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ bounded_lattice )
!= ( TG @ bounded_lattice ) )
| ( TG @ ( TF @ fun ) @ bounded_lattice_bot ) ),
inference(simp,[status(thm)],[5739]) ).
thf(5741,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType] : ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) @ ( TF @ fun ) @ bounded_lattice_bot ),
inference(pattern_uni,[status(thm)],[5740:[bind_type(TA,$thf( TA )),bind_type(TB,$thf( TB )),bind_type(TC,$thf( TC )),bind_type(TD,$thf( TD )),bind_type(TE,$thf( TE )),bind_type(TF,$thf( TF )),bind_type(TG,$thf( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ ( TD @ fun ) @ ( TE @ fun ) ))]]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ),E: TB @ ( TA @ fun ) @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( D @ ( E @ ( TB @ ( TA @ huffma107959123e_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ aa ) ) ) @ ( TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ aa ) ) ) @ ( TB @ ( TA @ huffma1450048681e_tree @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_tree_Osimps_I6_J) ).
thf(395,plain,
! [TA: $tType,TB: $tType,A: TA @ huffma1450048681e_tree,B: TA @ huffma1450048681e_tree,C: nat,D: TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ fun ),E: TB @ ( TA @ fun ) @ ( nat @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ huffma1146269203erNode ) ) ) @ ( D @ ( E @ ( TB @ ( TA @ huffma107959123e_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ fun ) @ ( nat @ aa ) ) ) @ ( TB @ ( TA @ huffma1450048681e_tree @ fun ) @ ( TA @ huffma1450048681e_tree @ aa ) ) ) @ ( TB @ ( TA @ huffma1450048681e_tree @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(104,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_0_tree_Osimps_I2_J) ).
thf(464,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)],[104]) ).
thf(94,axiom,
nat @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(427,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(927,plain,
! [D: nat,C: a @ huffma1450048681e_tree,B: nat,A: a @ huffma1450048681e_tree] :
( ( C
!= ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) ) )
| ( ( A @ ( a @ huffma1134658180e_cost ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( C @ ( D @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,136]) ).
thf(928,plain,
! [C: nat,B: nat,A: a @ huffma1450048681e_tree] :
( ( ( A @ ( a @ huffma1134658180e_cost ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( C @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(pattern_uni,[status(thm)],[927:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) )),bind(D,$thf( D ))]]) ).
thf(1505,plain,
! [C: nat,B: nat,A: a @ huffma1450048681e_tree] :
( ( ( A @ ( a @ huffma1134658180e_cost ) )
!= ( t_2 @ ( a @ huffma1134658180e_cost ) @ ( t_2 @ ( a @ huffma83463279weight ) @ ( t_1 @ ( a @ huffma1134658180e_cost ) @ ( t_1 @ ( a @ huffma83463279weight ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) @ ( nat @ plus_plus ) ) ) )
| ( ( t_2 @ ( t_1 @ ( w @ ( a @ huffma1146269203erNode ) ) ) @ ( C @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) )
!= ( A @ ( B @ ( a @ huffma1450048681e_tree @ huffma2021818691e_Leaf ) ) ) ) ),
inference(simp,[status(thm)],[928]) ).
thf(75,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( A @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_Int__absorb) ).
thf(369,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( A @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(163,plain,
! [TA: $tType,C: TA,B: bool @ ( TA @ fun ),A: bool @ ( TA @ fun )] :
( ( 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(cnfConj,[status(thm)],[160]) ).
thf(199,plain,
! [TA: $tType,B: TA,A: TA] :
( ( ( A @ ( B @ ( TA @ inf_inf ) ) )
= ( B @ ( A @ ( TA @ inf_inf ) ) ) )
| ~ ( TA @ semilattice_inf ) ),
inference(cnf,[status(esa)],[198]) ).
thf(200,plain,
! [TA: $tType,B: TA,A: TA] :
( ~ ( TA @ semilattice_inf )
| ( ( A @ ( B @ ( TA @ inf_inf ) ) )
= ( B @ ( A @ ( TA @ inf_inf ) ) ) ) ),
inference(lifteq,[status(thm)],[199]) ).
thf(58,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
<=> ! [C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ! [D: TA] :
( ( A @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( C != D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_disjoint__iff__not__equal) ).
thf(309,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 )
=> ! [D: TA] :
( ( A @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( C != D ) ) )
=> ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) ) )
& ( ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ inf_inf ) ) )
= ( bool @ ( TA @ fun ) @ bot_bot ) )
=> ! [C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ! [D: TA] :
( ( A @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( C != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(127,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(543,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(28,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_43_all__not__in__conv) ).
thf(215,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)],[28]) ).
thf(29,axiom,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ~ ( ( A @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ~ ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_inf1E) ).
thf(222,plain,
! [TA: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ inf_inf ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ~ ( ( A @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ~ ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(73,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_41_IntI) ).
thf(364,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)],[73]) ).
thf(13172,plain,
$false,
inference(e,[status(thm)],[2199,347,249,4015,555,666,1586,8960,479,1559,276,1728,3012,269,8988,4592,6194,408,170,1497,142,715,8342,340,2146,1507,7220,670,8370,698,2432,417,1645,320,1518,651,288,1613,724,7790,8967,184,372,587,1577,5712,196,542,1511,702,2373,284,325,1568,1514,189,421,7803,448,1494,475,164,179,376,211,3525,514,353,602,147,293,2137,6772,4040,428,527,206,411,7213,233,512,381,366,2382,6200,9004,201,2364,2164,5734,424,2986,4021,275,1619,137,252,197,4585,2200,6666,456,229,566,697,1498,188,388,1719,169,420,156,615,328,7774,193,476,642,590,706,701,654,6207,721,569,503,605,266,205,508,541,398,674,1515,530,343,237,360,633,8482,662,718,2235,298,1510,618,2391,166,161,279,444,149,375,7920,6228,180,584,8349,1620,9114,291,1701,281,204,2193,445,9659,6673,144,335,1765,181,704,350,391,1503,572,7191,159,672,187,274,3551,5848,1589,5222,245,599,509,434,271,208,494,4541,552,4028,140,621,240,198,323,6710,700,520,668,155,521,1474,5216,636,1643,226,3512,2999,431,167,658,394,306,135,563,490,1467,255,1509,4566,145,162,531,648,209,3988,5229,712,295,150,2192,414,1647,263,3640,1516,9121,3114,331,441,502,7796,463,338,6330,544,703,7207,1506,1504,612,143,4548,1649,363,524,495,1517,482,203,699,1476,9102,304,1508,186,8336,401,139,6694,517,2167,568,378,1513,9643,235,246,214,1614,1512,5728,2155,262,146,183,9051,4579,242,136,1495,1657,506,195,8424,5741,5200,6765,1710,395,464,4129,3025,427,596,3538,178,1505,369,163,200,309,543,215,639,222,364,4002]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW535_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
% 0.13/0.38 % Computer : n004.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sat Sep 26 16:11:06 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 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
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.48/1.29 % [INFO] Parsing done (310ms).
% 1.97/1.30 % [INFO] Running in sequential loop mode.
% 2.40/1.70 % [INFO] eprover registered as external prover.
% 2.60/1.70 % [INFO] Scanning for conjecture ...
% 2.78/1.88 % [INFO] Found a conjecture (or negated_conjecture) and 132 axioms. Running axiom selection ...
% 2.97/2.01 % [INFO] Axiom selection finished. Selected 132 axioms (removed 0 axioms).
% 3.93/2.24 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.93/2.27 % [INFO] Type checking passed.
% 3.93/2.27 % [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 ...
% 4.65/2.54 % [INFO] [Domain constraints] Detected constraint on bool
% 4.65/2.55 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 111.04/35.32 % External prover 'e' found a proof!
% 111.04/35.32 % [INFO] Killing All external provers ...
% 111.04/35.32 % Time passed: 34790ms (effective reasoning time: 34014ms)
% 111.04/35.32 % 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)>
% 111.04/35.33 % Axioms used in derivation (132): arity_Nat_Onat___Orderings_Obot, fact_10_tree_Orecs_I2_J, fact_3_cost_Osimps_I2_J, fact_86_bot__fun__def, help_COMBS_1_1_U, fact_71_Int__left__commute, fact_15_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_29_weight_Osimps_I1_J, fact_36_one__reorient, fact_47_emptyE, help_fconj_3_1_U, fact_44_empty__Collect__eq, fact_63_inf__left__commute, arity_Nat_Onat___Rings_Osemiring__1, arity_fun___Orderings_Obot, fact_82_disjoint__iff__not__equal, fact_2_weight_Osimps_I2_J, fact_65_inf__sup__aci_I2_J, arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_64_inf_Oassoc, fact_81_Int__empty__right, fact_30_tree_Osimps_I4_J, fact_58_inf__sup__aci_I1_J, fact_75_mem__def, fact_84_inf__apply, fact_34_of__nat__1, fact_32_of__nat__eq__iff, fact_26_tree_Orecs_I1_J, fact_42_inf1I, arity_fun___Lattices_Olattice, fact_39_inf1E, fact_69_Int__commute, arity_HOL_Obool___Lattices_Obounded__lattice__bot, fact_96_add__0__iff, fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_78_inf1D1, arity_Nat_Onat___Groups_Ocomm__monoid__add, fact_70_Int__left__absorb, fact_80_Int__empty__left, fact_50_Int__iff, fact_87_bot__apply, help_fFalse_1_1_T, fact_66_inf__assoc, fact_9_tree_Osimps_I6_J, fact_74_ext, help_COMBB_1_1_U, fact_16_add__right__imp__eq, fact_8_freq_Osimps_I2_J, arity_HOL_Obool___Lattices_Osemilattice__inf, fact_22_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_1_InnerNode_Oprems, fact_37_inf__bot__right, fact_13_nat__add__assoc, fact_59_inf__commute, fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_76_Collect__def, help_fconj_2_1_U, fact_77_IntD2, fact_57_inf_Ocommute, fact_89_double__zero__sym, arity_Nat_Onat___Lattices_Olattice, fact_17_add__imp__eq, arity_fun___Lattices_Osemilattice__inf, fact_90_add__is__0, fact_33_tree_Osimps_I1_J, fact_38_inf__bot__left, fact_60_inf__sup__aci_I4_J, fact_52_empty__def, fact_6_add__left__cancel, fact_72_Int__assoc, fact_73_IntD1, fact_27_d_092_060_094isub_0622, fact_79_inf1D2, fact_67_Int__absorb, arity_Nat_Onat___Rings_Ocomm__semiring__1, arity_Nat_Onat___Groups_Ozero, arity_Nat_Onat___Lattices_Osemilattice__inf, fact_12_nat__add__left__commute, arity_HOL_Obool___Lattices_Obounded__lattice, fact_95_bot__nat__def, help_COMBK_1_1_U, fact_55_inf_Oidem, fact_88_exists__in__alphabet, fact_93_freq_Osimps_I1_J, help_COMBC_1_1_U, arity_HOL_Obool___Orderings_Obot, fact_85_depth_Osimps_I2_J, fact_21_ab__semigroup__add__class_Oadd__ac_I1_J, fact_54_equals0D, arity_Nat_Onat___Nat_Osemiring__char__0, help_fconj_1_1_U, fact_56_inf__idem, fact_43_all__not__in__conv, fact_92_depth_Osimps_I1_J, fact_11_nat__add__commute, arity_Nat_Onat___Groups_Oone, fact_5_nat__add__right__cancel, help_fFalse_1_1_U, fact_68_Int__def, fact_45_empty__iff, fact_62_inf__sup__aci_I3_J, arity_HOL_Obool___Lattices_Olattice, fact_61_inf_Oleft__commute, fact_7_add__right__cancel, fact_14_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_0_tree_Osimps_I2_J, fact_48_inf_Oleft__idem, help_pp_1_1_U, fact_51_bot__empty__eq, fact_25_consistent_Osimps_I1_J, arity_fun___Lattices_Obounded__lattice__bot, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_94_cost_Osimps_I1_J, fact_91_of__nat__0, fact_40_IntE, fact_23_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_53_ex__in__conv, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_28_of__nat__add, help_pp_2_1_U, fact_4_nat__add__left__cancel, arity_fun___Lattices_Obounded__lattice, fact_46_Collect__empty__eq, fact_18_add__left__imp__eq, fact_97_add_Ocomm__neutral, fact_31_tree_Osimps_I3_J, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_41_IntI, fact_35_consistent_Osimps_I2_J, fact_49_inf__left__idem, fact_24_tree_Osimps_I5_J, fact_83_inf__fun__def
% 111.04/35.33 % No. of inferences in proof: 799
% 111.04/35.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 34790 ms resp. 34014 ms w/o parsing
% 111.59/35.62 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 111.59/35.63 % [INFO] Killing All external provers ...
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