%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT209_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n006.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 08:27:33 AM UTC 2026
% Result : Theorem 110.46s 88.53s
% Output : Refutation 111.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 118
% Syntax : Number of formulae : 238 ( 77 unt; 0 typ; 0 def)
% Number of atoms : 2838 ( 203 equ; 0 cnn)
% Maximal formula atoms : 154 ( 11 avg)
% Number of connectives : 11445 ( 131 ~; 22 |; 63 &;10965 @)
% ( 22 <=>; 242 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 12 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 40 usr; 15 con; 0-6 aty)
% Number of variables : 964 ( 0 ^; 951 !; 13 ?; 964 :)
% Comments :
%------------------------------------------------------------------------------
thf(arrow_411405190le_alt_type,type,
arrow_411405190le_alt: $tType ).
thf(arrow_159774573e_indi_type,type,
arrow_159774573e_indi: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(top_decl,type,
top:
!>[TA: $tType] : $o ).
thf(arrow_1958449194le_IIA_decl,type,
arrow_1958449194le_IIA: ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) ) > $o ).
thf(arrow_1985332922le_Lin_decl,type,
arrow_1985332922le_Lin: bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) ).
thf(arrow_610318064e_Prof_decl,type,
arrow_610318064e_Prof: bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) ).
thf(arrow_1158827142_above_decl,type,
arrow_1158827142_above: ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ) > arrow_411405190le_alt > arrow_411405190le_alt > ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ) ).
thf(arrow_319942042_below_decl,type,
arrow_319942042_below: ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ) > arrow_411405190le_alt > arrow_411405190le_alt > ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ) ).
thf(arrow_987702531ctator_decl,type,
arrow_987702531ctator: ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) ) > arrow_159774573e_indi > $o ).
thf(arrow_276188178_mkbot_decl,type,
arrow_276188178_mkbot: ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ) > arrow_411405190le_alt > ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ) ).
thf(arrow_424895264_mktop_decl,type,
arrow_424895264_mktop: ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ) > arrow_411405190le_alt > ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) ) ).
thf(arrow_2069624013nimity_decl,type,
arrow_2069624013nimity: ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) ) > $o ).
thf(combb_decl,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TB @ ( TC @ fun ) ) > ( TB @ ( TA @ fun ) @ ( TC @ ( TA @ fun ) @ fun ) ) ) ).
thf(combi_decl,type,
combi:
!>[TA: $tType] : ( TA @ ( TA @ fun ) ) ).
thf(combk_decl,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ fun ) ) ) ).
thf(pi_decl,type,
pi:
!>[TA: $tType,TB: $tType] : ( ( bool @ ( TB @ fun ) ) > ( bool @ ( TA @ fun ) @ ( TB @ fun ) ) > ( bool @ ( TA @ ( TB @ fun ) @ fun ) ) ) ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( bool > TA > TA > TA ) ).
thf(top_top_decl,type,
top_top:
!>[TA: $tType] : TA ).
thf(inv_imagep_decl,type,
inv_imagep:
!>[TA: $tType,TB: $tType] : ( ( bool @ ( TB @ fun ) @ ( TB @ fun ) ) > ( TB @ ( TA @ fun ) ) > TA > TA > $o ) ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ fun ) ) ).
thf(product_curry_decl,type,
product_curry:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ ( TC @ product_prod ) @ fun ) ) > ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) ) ).
thf(produc1605651328_split_decl,type,
produc1605651328_split:
!>[TA: $tType,TB: $tType,TC: $tType] : ( TA @ ( TB @ ( TC @ product_prod ) @ fun ) @ ( TA @ ( TB @ fun ) @ ( TC @ fun ) @ fun ) ) ).
thf(product_prod_case_decl,type,
product_prod_case:
!>[TA: $tType,TB: $tType,TC: $tType] : ( TA @ ( TB @ ( TC @ product_prod ) @ fun ) @ ( TA @ ( TB @ fun ) @ ( TC @ fun ) @ fun ) ) ).
thf(product_prod_rec_decl,type,
product_prod_rec:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ product_prod ) ) > 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 @ ( bool @ fun ) ) ).
thf(fequal_decl,type,
fequal:
!>[TA: $tType] : ( TA > TA > bool ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(f_decl,type,
f: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) ).
thf(p1_decl,type,
p1: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) ).
thf(p_decl,type,
p: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) ).
thf(q_decl,type,
q: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) ).
thf(a1_decl,type,
a1: arrow_411405190le_alt ).
thf(a_decl,type,
a: arrow_411405190le_alt ).
thf(b_decl,type,
b: arrow_411405190le_alt ).
thf(b1_decl,type,
b1: arrow_411405190le_alt ).
thf(10,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(138,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_curryD) ).
thf(479,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(32,axiom,
! [A: arrow_411405190le_alt,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_1985332922le_Lin @ ( A @ ( B @ arrow_276188178_mkbot ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_mkbot__Lin) ).
thf(234,plain,
! [A: arrow_411405190le_alt,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_1985332922le_Lin @ ( A @ ( B @ arrow_276188178_mkbot ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(79,axiom,
a != b1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_d1_I1_J) ).
thf(481,plain,
a != b1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ! [D: TA] :
( ( C @ ( D @ ( TA @ member ) ) )
=> ( D @ ( A @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ pi ) ) ) @ ( B @ ( TB @ ( TA @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_Pi__I) ).
thf(308,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ! [D: TA] :
( ( C @ ( D @ ( TA @ member ) ) )
=> ( D @ ( A @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ pi ) ) ) @ ( B @ ( TB @ ( TA @ fun ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(1,conjecture,
q @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b @ ( b1 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( q @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b @ ( b1 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(120,plain,
~ ( q @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b @ ( b1 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_prod )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( G @ ( F @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( E @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ fun ) @ ( TD @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ fun ) @ ( TE @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ aa ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ fun ) @ ( TF @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_prod__cases6) ).
thf(538,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_prod )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( G @ ( F @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( E @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ fun ) @ ( TD @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ fun ) @ ( TE @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ aa ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ fun ) @ ( TF @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(16,axiom,
bool @ top,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Otop) ).
thf(153,plain,
bool @ top,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(15,axiom,
arrow_1985332922le_Lin @ ( q @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__096F_AQ_A_058_ALin_096) ).
thf(152,plain,
arrow_1985332922le_Lin @ ( q @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ produc1605651328_split ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_internal__split__conv) ).
thf(228,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ produc1605651328_split ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(39,axiom,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_iso__tuple__UNIV__I) ).
thf(261,plain,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_curryI) ).
thf(492,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(71,axiom,
! [A: arrow_159774573e_indi] : ( A @ ( q @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( b @ ( b1 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__096_B_Bi_O_Ab_A_060_092_060_094bsub_062Q_Ai_092_060_094esub_062_Ab_H_096) ).
thf(443,plain,
! [A: arrow_159774573e_indi] : ( A @ ( q @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( b @ ( b1 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(3,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fFalse @ ( TA @ if ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(121,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fFalse @ ( TA @ if ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(61,axiom,
? [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] : ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_linear__alt) ).
thf(348,plain,
? [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] : ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TA @ ( TB @ product_prod ) @ fun ),B: TB,C: TA] :
( ( C @ ( B @ ( A @ ( TC @ ( TA @ ( TB @ product_curry ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( A @ ( TC @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_curry__def) ).
thf(280,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TA @ ( TB @ product_prod ) @ fun ),B: TB,C: TA] :
( ( C @ ( B @ ( A @ ( TC @ ( TA @ ( TB @ product_curry ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( A @ ( TC @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(56,axiom,
! [A: arrow_411405190le_alt,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( A @ ( B @ arrow_424895264_mktop ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( ( ( C != A )
=> ( B @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( C = A )
=> ( D != C ) )
& ( D != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_in__mktop) ).
thf(312,plain,
! [A: arrow_411405190le_alt,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( ( ( ( C != A )
=> ( B @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( C = A )
=> ( D != C ) )
& ( D != A ) )
=> ( A @ ( B @ arrow_424895264_mktop ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( A @ ( B @ arrow_424895264_mktop ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( ( ( C != A )
=> ( B @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( C = A )
=> ( D != C ) )
& ( D != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(50,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(292,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(74,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ fconj @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(452,plain,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ fconj @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(91,axiom,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_1985332922le_Lin @ ( B @ ( C @ ( A @ arrow_319942042_below ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_below__Lin) ).
thf(512,plain,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_1985332922le_Lin @ ( B @ ( C @ ( A @ arrow_319942042_below ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(97,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_splitI) ).
thf(529,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(104,axiom,
a1 != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_d1_I2_J) ).
thf(546,plain,
a1 != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( F @ ( E @ ( TD @ ( TC @ product_Pair ) @ ( TD @ ( TC @ product_prod ) @ ( TD @ fun ) @ ( TC @ aa ) ) ) @ ( TD @ ( TC @ product_prod ) @ ( TD @ aa ) ) ) @ ( D @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_Pair ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TD @ ( TC @ product_prod ) @ fun ) @ ( TB @ aa ) ) ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TD @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ fun ) @ ( TA @ aa ) ) ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ aa ) ) ) @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_prod__induct4) ).
thf(534,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( F @ ( E @ ( TD @ ( TC @ product_Pair ) @ ( TD @ ( TC @ product_prod ) @ ( TD @ fun ) @ ( TC @ aa ) ) ) @ ( TD @ ( TC @ product_prod ) @ ( TD @ aa ) ) ) @ ( D @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_Pair ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TD @ ( TC @ product_prod ) @ fun ) @ ( TB @ aa ) ) ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TD @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ fun ) @ ( TA @ aa ) ) ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ aa ) ) ) @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(64,axiom,
( ( a != a1 )
=> ( q @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( a @ ( a1 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_calculation_I2_J) ).
thf(392,plain,
( ( a != a1 )
=> ( q @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( a @ ( a1 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(119,axiom,
arrow_1985332922le_Lin @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ ( bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ combk ) ) @ ( arrow_610318064e_Prof @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ pi ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_assms_I1_J) ).
thf(630,plain,
arrow_1985332922le_Lin @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ ( bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ combk ) ) @ ( arrow_610318064e_Prof @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ pi ) ) ) @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(43,axiom,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_610318064e_Prof @ ( A @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combk ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_const__Lin__Prof) ).
thf(275,plain,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_610318064e_Prof @ ( A @ ( arrow_159774573e_indi @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ combk ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(80,axiom,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ fconj @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(484,plain,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ fconj @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(47,axiom,
! [A: arrow_411405190le_alt,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_1985332922le_Lin @ ( A @ ( B @ arrow_424895264_mktop ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_mktop__Lin) ).
thf(285,plain,
! [A: arrow_411405190le_alt,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_1985332922le_Lin @ ( A @ ( B @ arrow_424895264_mktop ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(29,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(224,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member ) ) ) )
& ( ( A @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: bool @ ( TC @ fun ) @ ( TA @ fun ) @ ( TB @ fun ),D: TC] :
( ( A @ ( B @ ( C @ ( bool @ ( TC @ fun ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TC @ fun ) @ ( TA @ aa ) ) ) @ ( D @ ( TC @ member ) ) )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TC @ fun ) @ ( TA @ ( TB @ product_prod_case ) ) @ ( bool @ ( TC @ fun ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TC @ fun ) @ ( TA @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TC @ fun ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( D @ ( TC @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_mem__splitI) ).
thf(403,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: bool @ ( TC @ fun ) @ ( TA @ fun ) @ ( TB @ fun ),D: TC] :
( ( A @ ( B @ ( C @ ( bool @ ( TC @ fun ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TC @ fun ) @ ( TA @ aa ) ) ) @ ( D @ ( TC @ member ) ) )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TC @ fun ) @ ( TA @ ( TB @ product_prod_case ) ) @ ( bool @ ( TC @ fun ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TC @ fun ) @ ( TA @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TC @ fun ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( D @ ( TC @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(11,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(141,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(113,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC] : ( E @ ( D @ ( TC @ ( TB @ product_Pair ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ aa ) ) ) @ ( C @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_Pair ) @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TC @ ( TB @ product_prod ) @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TC @ ( TB @ product_prod ) @ aa ) ) ) @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_prod__induct3) ).
thf(610,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC] : ( E @ ( D @ ( TC @ ( TB @ product_Pair ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ aa ) ) ) @ ( C @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_Pair ) @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TC @ ( TB @ product_prod ) @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TC @ ( TB @ product_prod ) @ aa ) ) ) @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(87,axiom,
b1 != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__096b_A_126_061_Ab_H_096) ).
thf(499,plain,
b1 != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(82,axiom,
p @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b1 @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12__096a_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_096) ).
thf(488,plain,
p @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b1 @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(124,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: bool @ ( TB @ fun ) @ ( TB @ fun ),C: TA,D: TA] :
( ( D @ ( C @ ( A @ ( B @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) )
<=> ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_inv__imagep__def) ).
thf(339,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: bool @ ( TB @ fun ) @ ( TB @ fun ),C: TA,D: TA] :
( ( ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( A @ ( B @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) ) )
& ( ( D @ ( C @ ( A @ ( B @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) )
=> ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_case ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_split__conv) ).
thf(489,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_case ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(92,axiom,
arrow_610318064e_Prof @ ( p1 @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22__096P_H_A_058_AProf_096) ).
thf(515,plain,
arrow_610318064e_Prof @ ( p1 @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_curry ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_curry__split) ).
thf(173,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_curry ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(8,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(134,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(37,axiom,
! [A: arrow_159774573e_indi,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ ( bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ combk ) ) @ ( arrow_610318064e_Prof @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ pi ) ) ) @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) @ member ) ) )
=> ( ! [C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( D != E )
=> ( ( A @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( C @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) )
=> ( A @ ( B @ arrow_987702531ctator ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_dictatorI) ).
thf(244,plain,
! [A: arrow_159774573e_indi,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ ( bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ combk ) ) @ ( arrow_610318064e_Prof @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ pi ) ) ) @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun ) @ member ) ) )
=> ( ! [C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( D != E )
=> ( ( A @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( C @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) )
=> ( A @ ( B @ arrow_987702531ctator ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ),C: TB @ ( TC @ product_prod )] :
( ! [D: TC,E: TB] :
( ( ( E @ ( D @ ( TB @ ( TC @ product_Pair ) @ ( TB @ ( TC @ product_prod ) @ ( TB @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TC @ product_prod ) @ ( TB @ aa ) ) ) )
= C )
=> ( A @ ( E @ ( D @ ( B @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( C @ ( B @ ( bool @ ( TA @ fun ) @ ( TB @ ( TC @ product_prod_case ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ ( TC @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ ( TC @ product_prod ) @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_splitI2_H) ).
thf(266,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ),C: TB @ ( TC @ product_prod )] :
( ! [D: TC,E: TB] :
( ( ( E @ ( D @ ( TB @ ( TC @ product_Pair ) @ ( TB @ ( TC @ product_prod ) @ ( TB @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TC @ product_prod ) @ ( TB @ aa ) ) ) )
= C )
=> ( A @ ( E @ ( D @ ( B @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( C @ ( B @ ( bool @ ( TA @ fun ) @ ( TB @ ( TC @ product_prod_case ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ ( TC @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ ( TC @ product_prod ) @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(102,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/sandbox2/benchmark/theBenchmark.p',fact_75_ext) ).
thf(541,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)],[102]) ).
thf(107,axiom,
! [TA: $tType,A: TA] : ( A @ ( bool @ ( TA @ fun ) @ top_top @ ( bool @ ( TA @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_top1I) ).
thf(558,plain,
! [TA: $tType,A: TA] : ( A @ ( bool @ ( TA @ fun ) @ top_top @ ( bool @ ( TA @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(60,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TC @ product_prod ),B: bool @ ( TB @ fun ) @ ( TA @ fun ) @ ( TC @ fun ),C: TB] :
( ( A @ ( B @ ( bool @ ( TB @ fun ) @ ( TA @ ( TC @ product_prod_case ) ) @ ( bool @ ( TB @ fun ) @ ( TA @ ( TC @ product_prod ) @ fun ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ fun ) @ ( TA @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( TB @ member ) ) )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( E @ ( D @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) ) )
=> ~ ( E @ ( D @ ( B @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( C @ ( TB @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_mem__splitE) ).
thf(343,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TC @ product_prod ),B: bool @ ( TB @ fun ) @ ( TA @ fun ) @ ( TC @ fun ),C: TB] :
( ( A @ ( B @ ( bool @ ( TB @ fun ) @ ( TA @ ( TC @ product_prod_case ) ) @ ( bool @ ( TB @ fun ) @ ( TA @ ( TC @ product_prod ) @ fun ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ fun ) @ ( TA @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( TB @ member ) ) )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( E @ ( D @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) ) )
=> ~ ( E @ ( D @ ( B @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( C @ ( TB @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(34,axiom,
( arrow_610318064e_Prof
= ( arrow_1985332922le_Lin @ ( arrow_159774573e_indi @ ( bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ combk ) ) @ ( bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ pi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_Prof__def) ).
thf(237,plain,
( arrow_610318064e_Prof
= ( arrow_1985332922le_Lin @ ( arrow_159774573e_indi @ ( bool @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ fun ) @ combk ) ) @ ( bool @ ( arrow_159774573e_indi @ fun ) @ top_top @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ pi ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod ),B: bool @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ~ ! [C: TB,D: TA] :
( ( A
= ( D @ ( C @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) )
=> ~ ( D @ ( C @ ( B @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_splitE) ).
thf(298,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod ),B: bool @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ~ ! [C: TB,D: TA] :
( ( A
= ( D @ ( C @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) )
=> ~ ( D @ ( C @ ( B @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(69,axiom,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun )] :
( ( A @ arrow_1958449194le_IIA )
<=> ! [B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( F @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( F @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
=> ( ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( C @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_IIA__def) ).
thf(412,plain,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun )] :
( ( ! [B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( ( F @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( F @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( F @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( F @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
=> ( ( ( C @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( C @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) )
=> ( A @ arrow_1958449194le_IIA ) )
& ( ( A @ arrow_1958449194le_IIA )
=> ! [B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( ( F @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( F @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( F @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( F @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
=> ( ( ( C @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( C @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( E @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(20,axiom,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TB @ fun ) @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ pi ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ member ) ) )
=> ( ~ ( A @ ( B @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member ) ) )
=> ~ ( C @ ( A @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_PiE) ).
thf(176,plain,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TB @ fun ) @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ pi ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ member ) ) )
=> ( ~ ( A @ ( B @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member ) ) )
=> ~ ( C @ ( A @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: TA @ ( TB @ fun ),C: bool @ ( TB @ fun )] :
( ! [D: TB] :
( ( C @ ( D @ ( TB @ member ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ member ) ) ) )
=> ( A @ ( TB @ ( bool @ ( TA @ fun ) @ combk ) ) @ ( C @ ( TA @ ( TB @ pi ) ) ) @ ( B @ ( TA @ ( TB @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_funcsetI) ).
thf(204,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: TA @ ( TB @ fun ),C: bool @ ( TB @ fun )] :
( ! [D: TB] :
( ( C @ ( D @ ( TB @ member ) ) )
=> ( A @ ( D @ ( B @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ member ) ) ) )
=> ( A @ ( TB @ ( bool @ ( TA @ fun ) @ combk ) ) @ ( C @ ( TA @ ( TB @ pi ) ) ) @ ( B @ ( TA @ ( TB @ fun ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(72,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: bool @ ( TC @ fun ) @ ( TB @ fun ) @ ( TA @ fun ),B: TC,C: TB @ ( TA @ product_prod )] :
( ! [D: TA,E: TB] :
( ( C
= ( E @ ( D @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) ) )
=> ( E @ ( D @ ( A @ ( bool @ ( TC @ fun ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( B @ ( TC @ member ) ) ) )
=> ( C @ ( A @ ( bool @ ( TC @ fun ) @ ( TB @ ( TA @ product_prod_case ) ) @ ( bool @ ( TC @ fun ) @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( bool @ ( TC @ fun ) @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TC @ fun ) @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) @ ( B @ ( TC @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_mem__splitI2) ).
thf(445,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: bool @ ( TC @ fun ) @ ( TB @ fun ) @ ( TA @ fun ),B: TC,C: TB @ ( TA @ product_prod )] :
( ! [D: TA,E: TB] :
( ( C
= ( E @ ( D @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) ) )
=> ( E @ ( D @ ( A @ ( bool @ ( TC @ fun ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( B @ ( TC @ member ) ) ) )
=> ( C @ ( A @ ( bool @ ( TC @ fun ) @ ( TB @ ( TA @ product_prod_case ) ) @ ( bool @ ( TC @ fun ) @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( bool @ ( TC @ fun ) @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TC @ fun ) @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) @ ( B @ ( TC @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(12,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(144,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ top )
=> ( TA @ ( TB @ fun ) @ top ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Otop) ).
thf(335,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ top )
=> ( TA @ ( TB @ fun ) @ top ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(33,axiom,
f @ arrow_1958449194le_IIA,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_assms_I3_J) ).
thf(236,plain,
f @ arrow_1958449194le_IIA,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(22,axiom,
! [A: arrow_411405190le_alt,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( A @ ( B @ arrow_276188178_mkbot ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( ( ( D != A )
=> ( B @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( D = A )
=> ( D != C ) )
& ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_in__mkbot) ).
thf(181,plain,
! [A: arrow_411405190le_alt,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( ( ( ( D != A )
=> ( B @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( D = A )
=> ( D != C ) )
& ( C != A ) )
=> ( A @ ( B @ arrow_276188178_mkbot ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( A @ ( B @ arrow_276188178_mkbot ) @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( ( ( D != A )
=> ( B @ ( C @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( D = A )
=> ( D != C ) )
& ( C != A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(62,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( D @ ( E @ ( C @ arrow_1158827142_above ) ) @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( ( ( B != D )
=> ( ( ( A != D )
=> ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( A = D )
=> ( ( C @ ( E @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( B = E ) ) ) ) )
& ( ( B = D )
=> ( C @ ( A @ ( E @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( B != A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_in__above) ).
thf(350,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( ( ( ( B != D )
=> ( ( ( A != D )
=> ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( A = D )
=> ( ( C @ ( E @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( B = E ) ) ) ) )
& ( ( B = D )
=> ( C @ ( A @ ( E @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( B != A ) )
=> ( D @ ( E @ ( C @ arrow_1158827142_above ) ) @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( D @ ( E @ ( C @ arrow_1158827142_above ) ) @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( ( ( B != D )
=> ( ( ( A != D )
=> ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( A = D )
=> ( ( C @ ( E @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( B = E ) ) ) ) )
& ( ( B = D )
=> ( C @ ( A @ ( E @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( B != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_PairE) ).
thf(604,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ top )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ top_top @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ top_top ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_top__apply) ).
thf(219,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ top )
=> ! [A: TB] :
( ( A @ ( TA @ ( TB @ fun ) @ top_top @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ top_top ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(53,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_case ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_prod_Osimps_I2_J) ).
thf(303,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_case ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TC @ product_prod ),B: TB @ ( TA @ fun ) @ ( TC @ fun ),C: bool @ ( TB @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ ( TC @ product_prod_case ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( E @ ( D @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) ) )
=> ~ ( E @ ( D @ ( B @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_splitE2) ).
thf(599,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TC @ product_prod ),B: TB @ ( TA @ fun ) @ ( TC @ fun ),C: bool @ ( TB @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ ( TC @ product_prod_case ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ fun ) @ ( TB @ ( TA @ fun ) @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ~ ! [D: TC,E: TA] :
( ( A
= ( E @ ( D @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) ) )
=> ~ ( E @ ( D @ ( B @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(42,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ! [D: TA] :
( ( C @ ( D @ ( TA @ member ) ) )
=> ( D @ ( A @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ pi ) ) ) @ ( B @ ( TB @ ( TA @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Pi__I_H) ).
thf(271,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: bool @ ( TA @ fun )] :
( ! [D: TA] :
( ( C @ ( D @ ( TA @ member ) ) )
=> ( D @ ( A @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ pi ) ) ) @ ( B @ ( TB @ ( TA @ fun ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(24,axiom,
f @ arrow_2069624013nimity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_u) ).
thf(208,plain,
f @ arrow_2069624013nimity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(85,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB,D: bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ product_Pair ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ aa ) ) ) @ ( D @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod ) @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( D @ ( bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_splitD_H) ).
thf(494,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB,D: bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ product_Pair ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ aa ) ) ) @ ( D @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod ) @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( D @ ( bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_Pair__inject) ).
thf(552,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(117,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_complete__Lin) ).
thf(621,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
& ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(38,axiom,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun )] :
( ( A @ arrow_2069624013nimity )
<=> ! [B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( E @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( D @ ( C @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( D @ ( C @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_unanimity__def) ).
thf(251,plain,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun )] :
( ( ! [B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( E @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( D @ ( C @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( D @ ( C @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) )
=> ( A @ arrow_2069624013nimity ) )
& ( ( A @ arrow_2069624013nimity )
=> ! [B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( E @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( D @ ( C @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( B @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( D @ ( C @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_prod_Oexhaust) ).
thf(521,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(6,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(130,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(75,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_prod_Orecs) ).
thf(455,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TC @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(54,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ~ ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_Lin__irrefl) ).
thf(306,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ~ ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(89,axiom,
q @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b1 @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_calculation_I1_J) ).
thf(505,plain,
q @ ( f @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) @ ( b1 @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(36,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 @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(241,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 @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(9,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fTrue @ ( TA @ if ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(135,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fTrue @ ( TA @ if ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(109,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( D @ ( E @ ( C @ arrow_319942042_below ) ) @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( B = E )
=> ( ( C @ ( A @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( D @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( B != A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_in__below) ).
thf(563,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( B = E )
=> ( ( C @ ( A @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( D @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( B != A ) )
=> ( D @ ( E @ ( C @ arrow_319942042_below ) ) @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( D @ ( E @ ( C @ arrow_319942042_below ) ) @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( ( ( A != E )
=> ( ( ( B != E )
=> ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( B = E )
=> ( ( C @ ( A @ ( D @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
| ( A = D ) ) ) ) )
& ( ( A = E )
=> ( C @ ( D @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( B != A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( E @ ( D @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ fun ) @ ( TD @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_prod__cases4) ).
thf(531,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( E @ ( D @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ fun ) @ ( TD @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ fun ) @ ( TA @ fun ),B: bool,C: TB @ ( TA @ product_prod )] :
( ( C @ ( A @ ( B @ fconj @ ( TB @ ( bool @ ( bool @ combb ) ) ) @ ( TA @ ( bool @ ( TB @ fun ) @ ( bool @ ( TB @ fun ) @ combb ) ) ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ product_prod_case ) ) @ ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
<=> ( ( C @ ( A @ ( bool @ ( TB @ ( TA @ product_prod_case ) ) @ ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
& ( B @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_split__part) ).
thf(209,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ fun ) @ ( TA @ fun ),B: bool,C: TB @ ( TA @ product_prod )] :
( ( ( ( C @ ( A @ ( bool @ ( TB @ ( TA @ product_prod_case ) ) @ ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
& ( B @ pp ) )
=> ( C @ ( A @ ( B @ fconj @ ( TB @ ( bool @ ( bool @ combb ) ) ) @ ( TA @ ( bool @ ( TB @ fun ) @ ( bool @ ( TB @ fun ) @ combb ) ) ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ product_prod_case ) ) @ ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) )
& ( ( C @ ( A @ ( B @ fconj @ ( TB @ ( bool @ ( bool @ combb ) ) ) @ ( TA @ ( bool @ ( TB @ fun ) @ ( bool @ ( TB @ fun ) @ combb ) ) ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ product_prod_case ) ) @ ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( ( C @ ( A @ ( bool @ ( TB @ ( TA @ product_prod_case ) ) @ ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
& ( B @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC @ ( TB @ product_prod ),C: bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod ) @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ~ ! [D: TB,E: TC] :
( ( B
= ( E @ ( D @ ( TC @ ( TB @ product_Pair ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ aa ) ) ) ) )
=> ~ ( A @ ( E @ ( D @ ( C @ ( bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_splitE_H) ).
thf(458,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC @ ( TB @ product_prod ),C: bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ ( TB @ product_prod ) @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ~ ! [D: TB,E: TC] :
( ( B
= ( E @ ( D @ ( TC @ ( TB @ product_Pair ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( TC @ ( TB @ product_prod ) @ ( TC @ aa ) ) ) ) )
=> ~ ( A @ ( E @ ( D @ ( C @ ( bool @ ( TA @ fun ) @ ( TC @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(115,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TC @ ( TB @ ( TA @ product_curry ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_split__curry) ).
thf(617,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( A @ ( TC @ ( TB @ ( TA @ product_curry ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ! [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
<=> ! [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_split__paired__All) ).
thf(516,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( ! [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ! [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) )
& ( ! [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ! [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB @ ( TA @ fun ),D: bool @ ( TB @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) )
<=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_in__inv__imagep) ).
thf(525,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: TB @ ( TA @ fun ),D: bool @ ( TB @ fun ) @ ( TB @ fun )] :
( ( ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TB @ inv_imagep ) ) ) ) ) )
=> ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( bool @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( TB @ ( TA @ product_Pair ) @ ( A @ ( TB @ ( TC @ ( TB @ ( TA @ product_prod ) @ combb ) ) ) @ ( TA @ ( TC @ ( TB @ fun ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ combb ) ) ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_split__eta) ).
thf(295,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( TB @ ( TA @ product_Pair ) @ ( A @ ( TB @ ( TC @ ( TB @ ( TA @ product_prod ) @ combb ) ) ) @ ( TA @ ( TC @ ( TB @ fun ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ combb ) ) ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(14,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_curryE) ).
thf(150,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ ( TA @ product_prod ) @ fun ),B: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ! [C: TA,D: TB] :
( ( D @ ( C @ ( B @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) )
= ( D @ ( C @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) @ ( A @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) ) )
=> ( ( B @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_cond__split__eta) ).
thf(409,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ ( TA @ product_prod ) @ fun ),B: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ! [C: TA,D: TB] :
( ( D @ ( C @ ( B @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) )
= ( D @ ( C @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) @ ( A @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) ) )
=> ( ( B @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: TC @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TA @ ( TB @ product_curry ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_curry__conv) ).
thf(263,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: TC @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TA @ ( TB @ product_curry ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(502,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)],[88]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB] :
( ( B @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
<=> ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_pred__equals__eq2) ).
thf(463,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ ( TA @ product_prod ) @ fun ),B: bool @ ( TB @ ( TA @ product_prod ) @ fun )] :
( ( ( B = A )
=> ! [C: TA,D: TB] :
( ( ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) )
& ( ( B @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) ) ) )
& ( ! [C: TA,D: TB] :
( ( ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( B @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) )
& ( ( B @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) )
=> ( A @ ( D @ ( C @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ member ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( TC @ ( TB @ ( TA @ produc1605651328_split ) ) )
= ( TC @ ( TB @ ( TA @ product_prod_case ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_internal__split__def) ).
thf(127,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( TC @ ( TB @ ( TA @ produc1605651328_split ) ) )
= ( TC @ ( TB @ ( TA @ product_prod_case ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_prod__caseI) ).
thf(544,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Pair__eq) ).
thf(154,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(63,axiom,
! [A: arrow_159774573e_indi] :
( ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( b1 @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( A @ ( q @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( b1 @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062Q_Ai_092_060_094esub_062_Ab_J_096) ).
thf(386,plain,
! [A: arrow_159774573e_indi] :
( ( ( A @ ( q @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( b1 @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( b1 @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( b1 @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( A @ ( q @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( b1 @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ product_prod )] :
( ! [C: TA,D: TB] :
( ( B
= ( D @ ( C @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) ) )
=> ( D @ ( C @ ( A @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) )
=> ( B @ ( A @ ( bool @ ( TB @ ( TA @ product_prod_case ) ) @ ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_splitI2) ).
thf(612,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ product_prod )] :
( ! [C: TA,D: TB] :
( ( B
= ( D @ ( C @ ( TB @ ( TA @ product_Pair ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ product_prod ) @ ( TB @ aa ) ) ) ) )
=> ( D @ ( C @ ( A @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TB @ aa ) ) ) @ pp ) )
=> ( B @ ( A @ ( bool @ ( TB @ ( TA @ product_prod_case ) ) @ ( bool @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(31,axiom,
b1 != a1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_d2_I2_J) ).
thf(231,plain,
b1 != a1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(118,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun )] :
( ( bool @ ( TB @ fun ) @ top_top @ ( TA @ ( bool @ ( TB @ fun ) @ combk ) ) @ ( A @ ( TB @ ( TA @ pi ) ) ) )
= ( bool @ ( TB @ ( TA @ fun ) @ fun ) @ top_top ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_Pi__UNIV) ).
thf(627,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun )] :
( ( bool @ ( TB @ fun ) @ top_top @ ( TA @ ( bool @ ( TB @ fun ) @ combk ) ) @ ( A @ ( TB @ ( TA @ pi ) ) ) )
= ( bool @ ( TB @ ( TA @ fun ) @ fun ) @ top_top ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( G @ ( F @ ( TE @ ( TD @ product_Pair ) @ ( TE @ ( TD @ product_prod ) @ ( TE @ fun ) @ ( TD @ aa ) ) ) @ ( TE @ ( TD @ product_prod ) @ ( TE @ aa ) ) ) @ ( E @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_Pair ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ aa ) ) ) @ ( D @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ fun ) @ ( TB @ aa ) ) ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ fun ) @ ( TA @ aa ) ) ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ aa ) ) ) @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_prod__induct5) ).
thf(450,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( G @ ( F @ ( TE @ ( TD @ product_Pair ) @ ( TE @ ( TD @ product_prod ) @ ( TE @ fun ) @ ( TD @ aa ) ) ) @ ( TE @ ( TD @ product_prod ) @ ( TE @ aa ) ) ) @ ( E @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_Pair ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ aa ) ) ) @ ( D @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ fun ) @ ( TB @ aa ) ) ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ fun ) @ ( TA @ aa ) ) ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ aa ) ) ) @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(95,axiom,
arrow_610318064e_Prof @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096P_A_058_AProf_096) ).
thf(524,plain,
arrow_610318064e_Prof @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(49,axiom,
! [TA: $tType,TB: $tType,A: TB,B: bool @ ( TA @ fun ),C: bool @ ( TB @ fun ),D: TA @ ( TB @ fun )] :
( ( B @ ( TB @ ( bool @ ( TA @ fun ) @ combk ) ) @ ( C @ ( TA @ ( TB @ pi ) ) ) @ ( D @ ( TA @ ( TB @ fun ) @ member ) ) )
=> ( ( C @ ( A @ ( TB @ member ) ) )
=> ( B @ ( A @ ( D @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_funcset__mem) ).
thf(290,plain,
! [TA: $tType,TB: $tType,A: TB,B: bool @ ( TA @ fun ),C: bool @ ( TB @ fun ),D: TA @ ( TB @ fun )] :
( ( B @ ( TB @ ( bool @ ( TA @ fun ) @ combk ) ) @ ( C @ ( TA @ ( TB @ pi ) ) ) @ ( D @ ( TA @ ( TB @ fun ) @ member ) ) )
=> ( ( C @ ( A @ ( TB @ member ) ) )
=> ( B @ ( A @ ( D @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(105,axiom,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_1985332922le_Lin @ ( B @ ( C @ ( A @ arrow_1158827142_above ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_above__Lin) ).
thf(549,plain,
! [A: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ),B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( arrow_1985332922le_Lin @ ( A @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( arrow_1985332922le_Lin @ ( B @ ( C @ ( A @ arrow_1158827142_above ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( H @ ( G @ ( TF @ ( TE @ product_Pair ) @ ( TF @ ( TE @ product_prod ) @ ( TF @ fun ) @ ( TE @ aa ) ) ) @ ( TF @ ( TE @ product_prod ) @ ( TF @ aa ) ) ) @ ( F @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_Pair ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ fun ) @ ( TD @ aa ) ) ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ aa ) ) ) @ ( E @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_Pair ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ aa ) ) ) @ ( D @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ fun ) @ ( TB @ aa ) ) ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ fun ) @ ( TA @ aa ) ) ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ aa ) ) ) @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_prod__induct6) ).
thf(536,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( H @ ( G @ ( TF @ ( TE @ product_Pair ) @ ( TF @ ( TE @ product_prod ) @ ( TF @ fun ) @ ( TE @ aa ) ) ) @ ( TF @ ( TE @ product_prod ) @ ( TF @ aa ) ) ) @ ( F @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_Pair ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ fun ) @ ( TD @ aa ) ) ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ aa ) ) ) @ ( E @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_Pair ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ aa ) ) ) @ ( D @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ fun ) @ ( TB @ aa ) ) ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ aa ) ) ) @ ( C @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ fun ) @ ( TA @ aa ) ) ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ aa ) ) ) @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ? [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
<=> ? [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_split__paired__Ex) ).
thf(214,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( ? [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ? [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) )
& ( ? [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ? [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(48,axiom,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_d2_I1_J) ).
thf(287,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(116,axiom,
arrow_610318064e_Prof @ ( q @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096Q_A_058_AProf_096) ).
thf(620,plain,
arrow_610318064e_Prof @ ( q @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(13,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal ) ) @ pp )
| ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(146,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal ) ) @ pp )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ product_prod ),C: TB @ ( TA @ product_prod )] :
( ( C = B )
=> ( ( C @ ( A @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) )
= ( B @ ( A @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_split__weak__cong) ).
thf(405,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ product_prod ),C: TB @ ( TA @ product_prod )] :
( ( C = B )
=> ( ( C @ ( A @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) )
= ( B @ ( A @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_splitD) ).
thf(239,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ fun ) @ ( TB @ fun )] :
( ( A @ ( B @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod_case ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( bool @ ( TA @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( bool @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(90,axiom,
! [A: arrow_159774573e_indi] :
( ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( b1 @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( A @ ( p1 @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( b @ ( a1 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19__C1_C) ).
thf(506,plain,
! [A: arrow_159774573e_indi] :
( ( ( A @ ( p1 @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( b @ ( a1 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( b1 @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( b1 @ ( a @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( A @ ( p1 @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( b @ ( a1 @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(70,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( B != A )
=> ( ~ ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
<=> ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_notin__Lin__iff) ).
thf(437,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun )] :
( ( arrow_1985332922le_Lin @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ member ) ) )
=> ( ( B != A )
=> ( ( ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ~ ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) )
& ( ~ ( C @ ( A @ ( B @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) )
=> ( C @ ( B @ ( A @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_Pair ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ fun ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ ( arrow_411405190le_alt @ aa ) ) ) @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ member ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(46,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ ( bool @ ( TA @ fun ) @ combk ) ) @ ( A @ ( TA @ ( TA @ pi ) ) ) @ ( TA @ combi @ ( TA @ ( TA @ fun ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_funcset__id) ).
thf(283,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( A @ ( TA @ ( bool @ ( TA @ fun ) @ combk ) ) @ ( A @ ( TA @ ( TA @ pi ) ) ) @ ( TA @ combi @ ( TA @ ( TA @ fun ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun ),D: bool @ ( TA @ fun )] :
( ! [E: TA] :
( ( D @ ( E @ ( TA @ member ) ) )
=> ( ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) )
= ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) ) ) )
=> ( ( A @ ( D @ ( TB @ ( TA @ pi ) ) ) @ ( C @ ( TB @ ( TA @ fun ) @ member ) ) )
<=> ( A @ ( D @ ( TB @ ( TA @ pi ) ) ) @ ( B @ ( TB @ ( TA @ fun ) @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_Pi__cong) ).
thf(395,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun ),D: bool @ ( TA @ fun )] :
( ! [E: TA] :
( ( D @ ( E @ ( TA @ member ) ) )
=> ( ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) )
= ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) ) ) )
=> ( ( ( A @ ( D @ ( TB @ ( TA @ pi ) ) ) @ ( B @ ( TB @ ( TA @ fun ) @ member ) ) )
=> ( A @ ( D @ ( TB @ ( TA @ pi ) ) ) @ ( C @ ( TB @ ( TA @ fun ) @ member ) ) ) )
& ( ( A @ ( D @ ( TB @ ( TA @ pi ) ) ) @ ( C @ ( TB @ ( TA @ fun ) @ member ) ) )
=> ( A @ ( D @ ( TB @ ( TA @ pi ) ) ) @ ( B @ ( TB @ ( TA @ fun ) @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(7,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(131,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(18,axiom,
! [A: arrow_159774573e_indi,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun )] :
( ( A @ ( B @ arrow_987702531ctator ) )
<=> ! [C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ( C @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) )
= ( A @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_dictator__def) ).
thf(163,plain,
! [A: arrow_159774573e_indi,B: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ fun )] :
( ( ! [C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ( C @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) )
= ( A @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) ) ) )
=> ( A @ ( B @ arrow_987702531ctator ) ) )
& ( ( A @ ( B @ arrow_987702531ctator ) )
=> ! [C: bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun )] :
( ( arrow_610318064e_Prof @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ member ) ) )
=> ( ( C @ ( B @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ fun ) @ aa ) ) ) )
= ( A @ ( C @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(21,axiom,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ top_top )
= ( fTrue @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_UNIV__def) ).
thf(178,plain,
! [TA: $tType] :
( ( bool @ ( TA @ fun ) @ top_top )
= ( fTrue @ ( TA @ ( bool @ combk ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(44,axiom,
! [A: arrow_159774573e_indi] :
( ( A @ ( q @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) )
= ( b @ ( b1 @ ( a @ ( a1 @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ arrow_319942042_below ) ) @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( a1 @ ( a @ ( arrow_411405190le_alt @ fequal ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if ) ) ) @ arrow_1158827142_above ) ) @ ( a @ ( a1 @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ arrow_319942042_below ) ) @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( a1 @ ( a @ ( arrow_411405190le_alt @ fequal ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if ) ) ) @ ( b @ ( b1 @ ( arrow_411405190le_alt @ fequal ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_Q__def) ).
thf(277,plain,
! [A: arrow_159774573e_indi] :
( ( A @ ( q @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) )
= ( b @ ( b1 @ ( a @ ( a1 @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ arrow_319942042_below ) ) @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( a1 @ ( a @ ( arrow_411405190le_alt @ fequal ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if ) ) ) @ arrow_1158827142_above ) ) @ ( a @ ( a1 @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ arrow_319942042_below ) ) @ ( A @ ( p @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ ( arrow_159774573e_indi @ aa ) ) ) @ ( a1 @ ( a @ ( arrow_411405190le_alt @ fequal ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if ) ) ) @ ( b @ ( b1 @ ( arrow_411405190le_alt @ fequal ) ) @ ( bool @ ( arrow_411405190le_alt @ ( arrow_411405190le_alt @ product_prod ) @ fun ) @ if ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(112,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( F @ ( E @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ fun ) @ ( TD @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ aa ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ fun ) @ ( TE @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_prod__cases5) ).
thf(607,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( F @ ( E @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ fun ) @ ( TD @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ aa ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ fun ) @ ( TE @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TB @ fun ) @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ pi ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ member ) ) )
=> ( ( C @ ( A @ ( TA @ member ) ) )
=> ( A @ ( B @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_Pi__mem) ).
thf(486,plain,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TB @ fun ) @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ pi ) ) ) @ ( D @ ( TB @ ( TA @ fun ) @ member ) ) )
=> ( ( C @ ( A @ ( TA @ member ) ) )
=> ( A @ ( B @ ( bool @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(58,axiom,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_UNIV__I) ).
thf(337,plain,
! [TA: $tType,A: TA] : ( bool @ ( TA @ fun ) @ top_top @ ( A @ ( TA @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TB @ ( TA @ product_prod ),B: TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ ( TA @ fun ),C: TC @ ( TD @ fun ) @ ( TE @ fun )] :
( ( A @ ( B @ ( TD @ ( TE @ product_prod ) @ ( TB @ ( TA @ product_prod_case ) ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) @ ( C @ ( TC @ ( TD @ ( TE @ product_prod_case ) ) @ ( TC @ ( TD @ ( TE @ product_prod ) @ fun ) @ ( TC @ ( TD @ fun ) @ ( TE @ fun ) @ aa ) ) ) @ ( TC @ ( TD @ ( TE @ product_prod ) @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TC @ ( TD @ ( TE @ product_prod_case ) ) @ ( TC @ ( TD @ ( TE @ product_prod ) @ fun ) @ ( TC @ ( TD @ fun ) @ ( TE @ fun ) @ aa ) ) ) @ ( TB @ ( TC @ ( TD @ ( TE @ product_prod ) @ combb ) ) ) @ ( TA @ ( TC @ ( TB @ fun ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ combb ) ) ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_split__twice) ).
thf(560,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TB @ ( TA @ product_prod ),B: TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ ( TA @ fun ),C: TC @ ( TD @ fun ) @ ( TE @ fun )] :
( ( A @ ( B @ ( TD @ ( TE @ product_prod ) @ ( TB @ ( TA @ product_prod_case ) ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) @ ( C @ ( TC @ ( TD @ ( TE @ product_prod_case ) ) @ ( TC @ ( TD @ ( TE @ product_prod ) @ fun ) @ ( TC @ ( TD @ fun ) @ ( TE @ fun ) @ aa ) ) ) @ ( TC @ ( TD @ ( TE @ product_prod ) @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TC @ ( TD @ ( TE @ product_prod_case ) ) @ ( TC @ ( TD @ ( TE @ product_prod ) @ fun ) @ ( TC @ ( TD @ fun ) @ ( TE @ fun ) @ aa ) ) ) @ ( TB @ ( TC @ ( TD @ ( TE @ product_prod ) @ combb ) ) ) @ ( TA @ ( TC @ ( TB @ fun ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ combb ) ) ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(28,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ fconj @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(222,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ fconj @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( D @ ( C @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_prod__cases3) ).
thf(496,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( D @ ( C @ ( TA @ ( TB @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TA @ aa ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ fun ) @ ( TC @ aa ) ) ) @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(631,plain,
$false,
inference(e,[status(thm)],[138,479,234,481,308,120,538,153,152,228,261,492,443,121,348,280,312,292,452,512,529,546,534,392,630,275,484,285,224,403,141,610,499,488,124,339,489,515,173,134,244,266,541,558,343,237,298,412,176,204,445,144,335,236,181,350,604,219,303,599,271,208,494,552,621,251,521,130,455,306,505,241,135,563,531,209,458,617,516,525,295,150,409,263,502,463,127,544,154,386,612,231,627,450,524,290,549,536,214,287,620,146,405,239,506,437,283,395,131,163,178,277,607,486,337,560,222,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT209_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.36 % Computer : n006.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 06:42:10 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.89/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.98/1.32 % [INFO] Parsing done (354ms).
% 1.98/1.34 % [INFO] Running in sequential loop mode.
% 3.13/1.73 % [INFO] eprover registered as external prover.
% 3.13/1.74 % [INFO] Scanning for conjecture ...
% 3.55/1.94 % [INFO] Found a conjecture (or negated_conjecture) and 117 axioms. Running axiom selection ...
% 4.01/2.09 % [INFO] Axiom selection finished. Selected 117 axioms (removed 0 axioms).
% 4.89/2.38 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.16/2.42 % [INFO] Type checking passed.
% 5.16/2.42 % [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 ...
% 6.00/2.69 % [INFO] [Domain constraints] Detected constraint on bool
% 6.30/2.70 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 6.30/2.71 % [INFO] [Domain constraints] Detected constraint on bool
% 6.30/2.71 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 110.46/88.53 % External prover 'e' found a proof!
% 110.46/88.53 % [INFO] Killing All external provers ...
% 110.46/88.53 % Time passed: 88018ms (effective reasoning time: 87188ms)
% 110.46/88.53 % 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)>
% 110.46/88.53 % Axioms used in derivation (117): fact_34_assms_I1_J, fact_79_split__curry, fact_85_split__twice, fact_45_prod__cases5, fact_89_mem__splitE, fact_63_curryI, fact_51_funcset__id, fact_99_top__apply, fact_73_split__conv, fact_50_prod__cases3, fact_88_splitI2_H, fact_22__096P_H_A_058_AProf_096, fact_98_splitE2, fact_2__096Q_A_058_AProf_096, fact_82_prod_Osimps_I2_J, help_fconj_3_1_U, fact_90_split__part, fact_30_prod_Orecs, fact_7_d1_I2_J, fact_61_curry__conv, fact_46_prod__cases4, fact_66_in__inv__imagep, fact_16__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062Q_Ai_092_060_094esub_062_Ab_J_096, help_COMBI_1_1_U, fact_55_funcsetI, fact_24_mktop__Lin, fact_43_prod__induct5, fact_4__096b_A_126_061_Ab_H_096, help_fTrue_1_1_T, fact_40_pred__equals__eq2, fact_21_unanimity__def, fact_36_below__Lin, fact_5__096_B_Bi_O_Ab_A_060_092_060_094bsub_062Q_Ai_092_060_094esub_062_Ab_H_096, fact_72_top1I, help_fTrue_1_1_U, fact_44_dictatorI, fact_20_Pair__inject, fact_65_curryE, fact_41_prod__induct6, fact_9_d2_I1_J, fact_29_complete__Lin, fact_68_internal__split__def, fact_3_assms_I3_J, help_COMBB_1_1_U, help_If_1_1_T, fact_64_curryD, fact_26_notin__Lin__iff, fact_32_in__below, fact_8_d1_I1_J, fact_42_prod__cases6, fact_62_curry__def, fact_15_calculation_I2_J, fact_13_split__paired__All, fact_54_Pi__I, fact_33_in__above, help_fconj_2_1_U, fact_39_linear__alt, fact_27_IIA__def, fact_37_above__Lin, fact_19__C1_C, fact_92_splitI2, fact_83_splitD_H, fact_10__096F_AQ_A_058_ALin_096, arity_HOL_Obool___Orderings_Otop, fact_84_splitD, fact_60_internal__split__conv, help_fequal_1_1_T, fact_28_split__paired__Ex, fact_76_mem__def, fact_0__096P_A_058_AProf_096, fact_93_splitE, fact_96_UNIV__I, help_If_3_1_T, fact_23_mkbot__Lin, fact_95_iso__tuple__UNIV__I, fact_56_Pi__I_H, fact_78_curry__split, help_If_2_1_T, help_COMBK_1_1_U, fact_6_d2_I2_J, fact_18_in__mktop, fact_35_const__Lin__Prof, fact_67_Prof__def, fact_48_PiE, fact_17_in__mkbot, fact_74_Pi__UNIV, fact_47_prod__induct4, fact_86_inv__imagep__def, help_fequal_2_1_T, fact_97_UNIV__def, fact_49_prod__induct3, fact_1_u, fact_69_mem__splitI, help_fconj_1_1_U, fact_70_splitI, fact_14_Pair__eq, fact_81_split__weak__cong, fact_87_mem__splitI2, fact_53_funcset__mem, fact_38_dictator__def, fact_31_Q__def, fact_80_split__eta, fact_77_Collect__def, fact_94_cond__split__eta, help_pp_1_1_U, fact_71_prod__caseI, fact_57_Pi__cong, fact_75_ext, arity_fun___Orderings_Otop, fact_11_calculation_I1_J, fact_52_Pi__mem, help_pp_2_1_U, fact_91_splitE_H, fact_58_PairE, fact_59_prod_Oexhaust, fact_25_Lin__irrefl, fact_12__096a_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_096
% 110.46/88.53 % No. of inferences in proof: 238
% 110.46/88.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 88018 ms resp. 87188 ms w/o parsing
% 111.37/88.70 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 111.37/88.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------