TSTP Solution File: SCT223_5 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SCT223_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 02:47:32 EDT 2024
% Result : Theorem 62.89s 35.18s
% Output : Refutation 63.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 161
% Syntax : Number of formulae : 278 ( 79 unt; 46 typ; 0 def)
% Number of atoms : 2650 ( 215 equ; 0 cnn)
% Maximal formula atoms : 138 ( 11 avg)
% Number of connectives : 10747 ( 164 ~; 33 |; 91 &;10147 @)
% ( 36 <=>; 276 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 12 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 46 usr; 17 con; 0-6 aty)
% Number of variables : 945 ( 0 ^ 872 !; 33 ?; 945 :)
% ( 40 !>; 0 ?*; 0 @-; 0 @+)
% 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(arrow_1958449194le_IIA_type,type,
arrow_1958449194le_IIA: ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) > $o ).
thf(arrow_1985332922le_Lin_type,type,
arrow_1985332922le_Lin: fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ).
thf(arrow_610318064e_Prof_type,type,
arrow_610318064e_Prof: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ bool ).
thf(arrow_1158827142_above_type,type,
arrow_1158827142_above: ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) > arrow_411405190le_alt > arrow_411405190le_alt > ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(arrow_319942042_below_type,type,
arrow_319942042_below: fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) ).
thf(arrow_987702531ctator_type,type,
arrow_987702531ctator: ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) > arrow_159774573e_indi > $o ).
thf(arrow_276188178_mkbot_type,type,
arrow_276188178_mkbot: ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) > arrow_411405190le_alt > ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(arrow_424895264_mktop_type,type,
arrow_424895264_mktop: ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) > arrow_411405190le_alt > ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(arrow_2069624013nimity_type,type,
arrow_2069624013nimity: ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) > $o ).
thf(combb_type,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ TB ) > ( fun @ TA @ TC ) > ( fun @ TA @ TB ) ) ).
thf(combc_type,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > TB > ( fun @ TC @ TA ) ) ).
thf(combi_type,type,
combi:
!>[TA: $tType] : ( fun @ TA @ TA ) ).
thf(combk_type,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) ) ).
thf(combs_type,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ TC @ TB ) > ( fun @ TC @ TA ) ) ).
thf(pi_type,type,
pi:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ bool ) > ( fun @ TB @ ( fun @ TA @ bool ) ) > ( fun @ ( fun @ TB @ TA ) @ bool ) ) ).
thf(distinct_type,type,
distinct:
!>[TA: $tType] : ( ( list @ TA ) > $o ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(lexord_type,type,
lexord:
!>[TA: $tType] : ( ( fun @ ( product_prod @ TA @ TA ) @ bool ) > ( fun @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ bool ) ) ).
thf(cons_type,type,
cons:
!>[TA: $tType] : ( TA > ( list @ TA ) > ( list @ TA ) ) ).
thf(nil_type,type,
nil:
!>[TA: $tType] : ( list @ TA ) ).
thf(list_case_type,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ ( fun @ ( list @ TA ) @ TB ) ) > ( list @ TA ) > TB ) ).
thf(list_all_type,type,
list_all:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > $o ) ).
thf(list_ex1_type,type,
list_ex1:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > $o ) ).
thf(partition_type,type,
partition:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( list @ TA ) > ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) ) ).
thf(splice_type,type,
splice:
!>[TA: $tType] : ( ( list @ TA ) > ( list @ TA ) > ( list @ TA ) ) ).
thf(product_Pair_type,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( product_prod @ TB @ TA ) ) ).
thf(product_curry_type,type,
product_curry:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ ( product_prod @ TC @ TB ) @ TA ) > TC > TB > TA ) ).
thf(produc1605651328_split_type,type,
produc1605651328_split:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(product_prod_rec_type,type,
product_prod_rec:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( product_prod @ TC @ TB ) > TA ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fNot_type,type,
fNot: fun @ bool @ bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(fdisj_type,type,
fdisj: fun @ bool @ ( fun @ bool @ bool ) ).
thf(fequal_type,type,
fequal:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(f_type,type,
f: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(p1_type,type,
p1: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(p_type,type,
p: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ).
thf(a_type,type,
a: arrow_411405190le_alt ).
thf(b_type,type,
b: arrow_411405190le_alt ).
thf(c_type,type,
c: arrow_411405190le_alt ).
thf(10,axiom,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ ( nil @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_splice_Osimps_I1_J) ).
thf(138,plain,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ ( nil @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
thf(550,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(301,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(9,axiom,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ A @ ( nil @ TA ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_splice__Nil2) ).
thf(135,plain,
! [TA: $tType,A: list @ TA] :
( ( splice @ TA @ A @ ( nil @ TA ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(50,axiom,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( arrow_1158827142_above @ A @ C @ B ) @ arrow_1985332922le_Lin ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_above__Lin) ).
thf(308,plain,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( arrow_1158827142_above @ A @ C @ B ) @ arrow_1985332922le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ TB ),D: TB] :
( ( list_case @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ ( list @ TA ) @ TB @ ( aa @ TA @ ( fun @ ( list @ TA ) @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_list_Osimps_I5_J) ).
thf(247,plain,
! [TA: $tType,TB: $tType,A: list @ TA,B: TA,C: fun @ TA @ ( fun @ ( list @ TA ) @ TB ),D: TB] :
( ( list_case @ TB @ TA @ D @ C @ ( cons @ TA @ B @ A ) )
= ( aa @ ( list @ TA ) @ TB @ ( aa @ TA @ ( fun @ ( list @ TA ) @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(41,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_prod__cases3) ).
thf(269,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TC @ ( product_prod @ TB @ TA )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ B @ ( product_Pair @ TB @ TA @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
( ( member @ ( fun @ TA @ TB ) @ D @ ( pi @ TA @ TB @ C @ B ) )
=> ( ( member @ TA @ A @ C )
=> ( member @ TB @ ( aa @ TA @ TB @ D @ A ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_Pi__mem) ).
thf(597,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
( ( member @ ( fun @ TA @ TB ) @ D @ ( pi @ TA @ TB @ C @ B ) )
=> ( ( member @ TA @ A @ C )
=> ( member @ TB @ ( aa @ TA @ TB @ D @ A ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( produc1605651328_split @ TC @ TA @ TB @ C @ ( product_Pair @ TC @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_internal__split__conv) ).
thf(389,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( produc1605651328_split @ TC @ TA @ TB @ C @ ( product_Pair @ TC @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(22,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct @ TA @ B )
=> ( distinct @ TA @ ( insert @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_distinct__insert) ).
thf(184,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( ( distinct @ TA @ B )
=> ( distinct @ TA @ ( insert @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(504,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(115,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( arrow_424895264_mktop @ B @ A ) )
<=> ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_in__mktop) ).
thf(619,plain,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( arrow_424895264_mktop @ B @ A ) )
=> ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) ) )
& ( ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( arrow_424895264_mktop @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(4,axiom,
arrow_2069624013nimity @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_u) ).
thf(125,plain,
arrow_2069624013nimity @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(61,axiom,
! [TA: $tType,A: fun @ ( list @ TA ) @ bool,B: list @ TA] :
( ( B
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ D ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ ( cons @ TA @ C @ D ) ) ) ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_list__nonempty__induct) ).
thf(357,plain,
! [TA: $tType,A: fun @ ( list @ TA ) @ bool,B: list @ TA] :
( ( B
!= ( nil @ TA ) )
=> ( ! [C: TA] : ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ ( cons @ TA @ C @ ( nil @ TA ) ) ) )
=> ( ! [C: TA,D: list @ TA] :
( ( D
!= ( nil @ TA ) )
=> ( ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ D ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ ( cons @ TA @ C @ D ) ) ) ) )
=> ( pp @ ( aa @ ( list @ TA ) @ bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(15,axiom,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_not__Cons__self) ).
thf(157,plain,
! [TA: $tType,A: TA,B: list @ TA] :
( B
!= ( cons @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) )
=> ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_curryI) ).
thf(559,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) )
=> ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(75,axiom,
! [A: arrow_159774573e_indi,B: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( arrow_987702531ctator @ B @ A )
<=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
=> ( ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C )
= ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_dictator__def) ).
thf(421,plain,
! [A: arrow_159774573e_indi,B: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( ( arrow_987702531ctator @ B @ A )
=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
=> ( ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C )
= ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) ) ) )
& ( ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
=> ( ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C )
= ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) ) )
=> ( arrow_987702531ctator @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(45,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(289,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(52,axiom,
member @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ f @ ( pi @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_610318064e_Prof @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_1985332922le_Lin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_assms_I1_J) ).
thf(321,plain,
member @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ f @ ( pi @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_610318064e_Prof @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_1985332922le_Lin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(59,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096a_A_126_061_Ab_096) ).
thf(353,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(73,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( arrow_276188178_mkbot @ B @ A ) )
<=> ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_in__mkbot) ).
thf(397,plain,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( arrow_276188178_mkbot @ B @ A ) )
=> ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) ) )
& ( ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ B ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( arrow_276188178_mkbot @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(85,axiom,
! [A: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_iff) ).
thf(507,plain,
! [A: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p1 @ A ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(86,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Pair__eq) ).
thf(512,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(93,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Pair__inject) ).
thf(534,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( product_Pair @ TB @ TA @ D @ C )
= ( product_Pair @ TB @ TA @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(67,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ bool] :
( ! [D: TA] :
( ( member @ TA @ D @ C )
=> ( member @ TB @ ( aa @ TA @ TB @ B @ D ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ D ) ) )
=> ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Pi__I) ).
thf(380,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ bool] :
( ! [D: TA] :
( ( member @ TA @ D @ C )
=> ( member @ TB @ ( aa @ TA @ TB @ B @ D ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ D ) ) )
=> ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(1,conjecture,
! [A: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ! [A: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(117,plain,
~ ! [A: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_prod__induct6) ).
thf(334,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) @ E @ ( product_Pair @ TD @ ( product_prod @ TE @ TF ) @ F @ ( product_Pair @ TE @ TF @ G @ H ) ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ ( product_prod @ TE @ TF ) ) ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ bool,C: fun @ TB @ bool,D: fun @ TB @ TA] :
( ( member @ ( fun @ TB @ TA ) @ D @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ B ) ) )
=> ( ( member @ TB @ A @ C )
=> ( member @ TA @ ( aa @ TB @ TA @ D @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_funcset__mem) ).
thf(260,plain,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ bool,C: fun @ TB @ bool,D: fun @ TB @ TA] :
( ( member @ ( fun @ TB @ TA ) @ D @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ B ) ) )
=> ( ( member @ TB @ A @ C )
=> ( member @ TA @ ( aa @ TB @ TA @ D @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(16,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_list__ex1__simps_I1_J) ).
thf(160,plain,
! [TA: $tType,A: fun @ TA @ bool] :
~ ( list_ex1 @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(103,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ bool] :
( ( list_ex1 @ TA @ C @ ( cons @ TA @ B @ A ) )
<=> ( ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( list_all @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj @ ( combb @ bool @ bool @ TA @ fNot @ C ) ) @ ( fequal @ TA @ B ) ) @ A ) )
& ( ~ ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( list_ex1 @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_list__ex1__simps_I2_J) ).
thf(561,plain,
! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ bool] :
( ( ( list_ex1 @ TA @ C @ ( cons @ TA @ B @ A ) )
=> ( ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( list_all @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj @ ( combb @ bool @ bool @ TA @ fNot @ C ) ) @ ( fequal @ TA @ B ) ) @ A ) )
& ( ~ ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( list_ex1 @ TA @ C @ A ) ) ) )
& ( ( ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( list_all @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj @ ( combb @ bool @ bool @ TA @ fNot @ C ) ) @ ( fequal @ TA @ B ) ) @ A ) )
& ( ~ ( pp @ ( aa @ TA @ bool @ C @ B ) )
=> ( list_ex1 @ TA @ C @ A ) ) )
=> ( list_ex1 @ TA @ C @ ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(71,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TB @ TA ) @ TC,B: TB,C: TA] :
( ( product_curry @ TB @ TA @ TC @ A @ B @ C )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_curry__def) ).
thf(392,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: fun @ ( product_prod @ TB @ TA ) @ TC,B: TB,C: TA] :
( ( product_curry @ TB @ TA @ TC @ A @ B @ C )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(18,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: TA] :
( ( distinct @ TA @ ( cons @ TA @ C @ ( cons @ TA @ B @ A ) ) )
<=> ( ( C != B )
& ( distinct @ TA @ ( cons @ TA @ C @ A ) )
& ( distinct @ TA @ ( cons @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_distinct__length__2__or__more) ).
thf(165,plain,
! [TA: $tType,A: list @ TA,B: TA,C: TA] :
( ( ( distinct @ TA @ ( cons @ TA @ C @ ( cons @ TA @ B @ A ) ) )
=> ( ( C != B )
& ( distinct @ TA @ ( cons @ TA @ C @ A ) )
& ( distinct @ TA @ ( cons @ TA @ B @ A ) ) ) )
& ( ( ( C != B )
& ( distinct @ TA @ ( cons @ TA @ C @ A ) )
& ( distinct @ TA @ ( cons @ TA @ B @ A ) ) )
=> ( distinct @ TA @ ( cons @ TA @ C @ ( cons @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_split__paired__All) ).
thf(522,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
=> ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) )
& ( ! [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) )
=> ! [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(80,axiom,
! [A: bool] :
( ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ fNot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(461,plain,
! [A: bool] :
( ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(54,axiom,
! [TA: $tType,A: TA] :
( ( aa @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(324,plain,
! [TA: $tType,A: TA] :
( ( aa @ TA @ TA @ ( combi @ TA ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(60,axiom,
member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) @ arrow_610318064e_Prof,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_058_AProf_096) ).
thf(356,plain,
member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) @ arrow_610318064e_Prof,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(11,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_list_Oinject) ).
thf(141,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( cons @ TA @ D @ C )
= ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(58,axiom,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
=> ( ! [G: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) ) )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23__C2_C) ).
thf(339,plain,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
=> ( ! [G: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) ) ) )
=> ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(26,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C )
=> ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_Lin__irrefl) ).
thf(193,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C )
=> ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(89,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_prod__induct5) ).
thf(526,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TD @ TE ) @ E @ ( product_Pair @ TD @ TE @ F @ G ) ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ ( product_prod @ TD @ TE ) ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(107,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: list @ TA] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) @ ( lexord @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_lexord__Nil__right) ).
thf(590,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: list @ TA] :
~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ ( nil @ TA ) ) @ ( lexord @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(98,axiom,
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_bc) ).
thf(547,plain,
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(32,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ ( arrow_1158827142_above @ C @ E @ D ) )
<=> ( ( B != A )
& ( ( B = D )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ E @ A ) @ C ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ E ) @ C ) ) )
& ( ( A != D )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_in__above) ).
thf(212,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ ( arrow_1158827142_above @ C @ E @ D ) )
=> ( ( B != A )
& ( ( B = D )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ E @ A ) @ C ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ E ) @ C ) ) )
& ( ( A != D )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ) ) ) )
& ( ( ( B != A )
& ( ( B = D )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ E @ A ) @ C ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ E ) @ C ) ) )
& ( ( A != D )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ ( arrow_1158827142_above @ C @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(78,axiom,
! [TA: $tType,A: list @ TA,B: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ! [C: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ C ) @ B )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ A ) @ ( lexord @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_lexord__irreflexive) ).
thf(457,plain,
! [TA: $tType,A: list @ TA,B: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ! [C: TA] :
~ ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ C @ C ) @ B )
=> ~ ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ A ) @ ( lexord @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(19,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_not__Cons__self2) ).
thf(173,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(8,axiom,
arrow_1958449194le_IIA @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_assms_I3_J) ).
thf(134,plain,
arrow_1958449194le_IIA @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_list_Osimps_I2_J) ).
thf(128,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( nil @ TA )
!= ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TB @ TA,C: fun @ TB @ bool] :
( ! [D: TB] :
( ( member @ TB @ D @ C )
=> ( member @ TA @ ( aa @ TB @ TA @ B @ D ) @ A ) )
=> ( member @ ( fun @ TB @ TA ) @ B @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_funcsetI) ).
thf(266,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: fun @ TB @ TA,C: fun @ TB @ bool] :
( ! [D: TB] :
( ( member @ TB @ D @ C )
=> ( member @ TA @ ( aa @ TB @ TA @ B @ D ) @ A ) )
=> ( member @ ( fun @ TB @ TA ) @ B @ ( pi @ TB @ TA @ C @ ( combk @ ( fun @ TA @ bool ) @ TB @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(51,axiom,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
=> ( ! [G: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) ) )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22__C1_C) ).
thf(311,plain,
! [A: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ),C: arrow_411405190le_alt,D: arrow_411405190le_alt,E: arrow_411405190le_alt,F: arrow_411405190le_alt] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ A @ arrow_610318064e_Prof )
=> ( ! [G: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ G ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ G ) ) ) )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ F @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ B ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ C ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ A ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_prod__cases4) ).
thf(430,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ B @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ C @ ( product_Pair @ TB @ TA @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ! [C: TA,D: TB] :
( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B )
<=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_pred__equals__eq2) ).
thf(573,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TA @ TB ) @ bool,B: fun @ ( product_prod @ TA @ TB ) @ bool] :
( ( ! [C: TA,D: TB] :
( ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
& ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ! [C: TA,D: TB] :
( ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A ) )
& ( ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ A )
=> ( member @ ( product_prod @ TA @ TB ) @ ( product_Pair @ TA @ TB @ C @ D ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(47,axiom,
! [A: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__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_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_096) ).
thf(296,plain,
! [A: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(12,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( list_all @ TA @ A @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_list__all__simps_I2_J) ).
thf(149,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( list_all @ TA @ A @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(65,axiom,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ A ) @ C ) @ B ) @ arrow_1985332922le_Lin ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_below__Lin) ).
thf(375,plain,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,B: arrow_411405190le_alt,C: arrow_411405190le_alt] :
( ( C != B )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ A ) @ C ) @ B ) @ arrow_1985332922le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(20,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(176,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(44,axiom,
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ p ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_ab) ).
thf(286,plain,
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ p ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ b ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(46,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( B != A )
=> ( ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_notin__Lin__iff) ).
thf(291,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( B != A )
=> ( ( ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ A @ B ) @ C ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ A @ B ) @ C )
=> ~ ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(97,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) )
| ( pp @ B )
| ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(545,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) )
| ( pp @ B )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(116,axiom,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( fequal @ TA @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(641,plain,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( fequal @ TA @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(82,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ C ) @ E ) @ D ) )
<=> ( ( B != A )
& ( ( A = E )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ D ) @ C ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ A ) @ C ) ) )
& ( ( B != E )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_in__below) ).
thf(466,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool,D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( E != D )
=> ( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
=> ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ C ) @ E ) @ D ) )
=> ( ( B != A )
& ( ( A = E )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ D ) @ C ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ A ) @ C ) ) )
& ( ( B != E )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ) ) ) )
& ( ( ( B != A )
& ( ( A = E )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ D ) @ C ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ A ) @ C ) ) )
& ( ( B != E )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ C ) @ E ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(95,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ bool] :
( ! [D: TA] :
( ( member @ TA @ D @ C )
=> ( member @ TB @ ( aa @ TA @ TB @ B @ D ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ D ) ) )
=> ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Pi__I_H) ).
thf(540,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ bool] :
( ! [D: TA] :
( ( member @ TA @ D @ C )
=> ( member @ TB @ ( aa @ TA @ TB @ B @ D ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ A @ D ) ) )
=> ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(24,axiom,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_insert__Nil) ).
thf(187,plain,
! [TA: $tType,A: TA] :
( ( insert @ TA @ A @ ( nil @ TA ) )
= ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(74,axiom,
? [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] : ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_linear__alt) ).
thf(419,plain,
? [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] : ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(111,axiom,
member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) @ arrow_610318064e_Prof,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096) ).
thf(599,plain,
member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) @ arrow_610318064e_Prof,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(63,axiom,
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_ac) ).
thf(367,plain,
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) @ b ) @ a ) ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ f @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(87,axiom,
! [TA: $tType,A: fun @ TA @ bool] : ( member @ ( fun @ TA @ TA ) @ ( combi @ TA ) @ ( pi @ TA @ TA @ A @ ( combk @ ( fun @ TA @ bool ) @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_funcset__id) ).
thf(520,plain,
! [TA: $tType,A: fun @ TA @ bool] : ( member @ ( fun @ TA @ TA ) @ ( combi @ TA ) @ ( pi @ TA @ TA @ A @ ( combk @ ( fun @ TA @ bool ) @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(30,axiom,
member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ p1 @ arrow_610318064e_Prof,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21__096P_H_A_058_AProf_096) ).
thf(209,plain,
member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ p1 @ arrow_610318064e_Prof,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(3,axiom,
! [TA: $tType,A: TA] : ( distinct @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_distinct__singleton) ).
thf(123,plain,
! [TA: $tType,A: TA] : ( distinct @ TA @ ( cons @ TA @ A @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(100,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_prod_Oexhaust) ).
thf(553,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(17,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_list_Osimps_I3_J) ).
thf(162,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( cons @ TA @ B @ A )
!= ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(91,axiom,
member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ p @ arrow_610318064e_Prof,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096P_A_058_AProf_096) ).
thf(531,plain,
member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ p @ arrow_610318064e_Prof,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ TB,D: fun @ TA @ bool] :
( ! [E: TA] :
( ( member @ TA @ E @ D )
=> ( ( aa @ TA @ TB @ C @ E )
= ( aa @ TA @ TB @ B @ E ) ) )
=> ( ( member @ ( fun @ TA @ TB ) @ C @ ( pi @ TA @ TB @ D @ A ) )
<=> ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Pi__cong) ).
thf(327,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ TB @ bool ),B: fun @ TA @ TB,C: fun @ TA @ TB,D: fun @ TA @ bool] :
( ! [E: TA] :
( ( member @ TA @ E @ D )
=> ( ( aa @ TA @ TB @ C @ E )
= ( aa @ TA @ TB @ B @ E ) ) )
=> ( ( ( member @ ( fun @ TA @ TB ) @ C @ ( pi @ TA @ TB @ D @ A ) )
=> ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ D @ A ) ) )
& ( ( member @ ( fun @ TA @ TB ) @ B @ ( pi @ TA @ TB @ D @ A ) )
=> ( member @ ( fun @ TA @ TB ) @ C @ ( pi @ TA @ TB @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(39,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_prod__cases6) ).
thf(263,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: product_prod @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( product_Pair @ TF @ ( product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) ) @ B @ ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ C @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ D @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ E @ ( product_Pair @ TB @ TA @ F @ G ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(28,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: list @ TA,C: TA,D: list @ TA,E: TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ E @ D ) @ ( cons @ TA @ C @ B ) ) @ ( lexord @ TA @ A ) )
<=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ C ) @ A )
| ( ( E = C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ D @ B ) @ ( lexord @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_lexord__cons__cons) ).
thf(199,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: list @ TA,C: TA,D: list @ TA,E: TA] :
( ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ E @ D ) @ ( cons @ TA @ C @ B ) ) @ ( lexord @ TA @ A ) )
=> ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ C ) @ A )
| ( ( E = C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ D @ B ) @ ( lexord @ TA @ A ) ) ) ) )
& ( ( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ C ) @ A )
| ( ( E = C )
& ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ D @ B ) @ ( lexord @ TA @ A ) ) ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( cons @ TA @ E @ D ) @ ( cons @ TA @ C @ B ) ) @ ( lexord @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(64,axiom,
! [A: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_096) ).
thf(370,plain,
! [A: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ a @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(81,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ TC] :
( ( product_curry @ TB @ TA @ TC @ C @ B @ A )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_curry__conv) ).
thf(463,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ TC] :
( ( product_curry @ TB @ TA @ TC @ C @ B @ A )
= ( aa @ ( product_prod @ TB @ TA ) @ TC @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(57,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(336,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(114,axiom,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: list @ TA] :
( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ B ) @ ( lexord @ TA @ A ) )
<=> ? [C: TA,D: list @ TA] :
( B
= ( cons @ TA @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_lexord__Nil__left) ).
thf(613,plain,
! [TA: $tType,A: fun @ ( product_prod @ TA @ TA ) @ bool,B: list @ TA] :
( ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ B ) @ ( lexord @ TA @ A ) )
=> ? [C: TA,D: list @ TA] :
( B
= ( cons @ TA @ C @ D ) ) )
& ( ? [C: TA,D: list @ TA] :
( B
= ( cons @ TA @ C @ D ) )
=> ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ B ) @ ( lexord @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(14,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_list_Oexhaust) ).
thf(154,plain,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
=> ~ ! [B: TA,C: list @ TA] :
( A
!= ( cons @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(112,axiom,
! [TA: $tType,A: list @ TA,B: list @ TA,C: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ! [D: TA,E: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ C )
| ( D = E )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ C ) )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ A ) @ ( lexord @ TA @ C ) )
| ( B = A )
| ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( lexord @ TA @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_lexord__linear) ).
thf(600,plain,
! [TA: $tType,A: list @ TA,B: list @ TA,C: fun @ ( product_prod @ TA @ TA ) @ bool] :
( ! [D: TA,E: TA] :
( ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ D @ E ) @ C )
| ( D = E )
| ( member @ ( product_prod @ TA @ TA ) @ ( product_Pair @ TA @ TA @ E @ D ) @ C ) )
=> ( ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ B @ A ) @ ( lexord @ TA @ C ) )
| ( B = A )
| ( member @ ( product_prod @ ( list @ TA ) @ ( list @ TA ) ) @ ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ A @ B ) @ ( lexord @ TA @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(386,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
( ( member @ ( fun @ TA @ TB ) @ D @ ( pi @ TA @ TB @ C @ B ) )
=> ( ~ ( member @ TB @ ( aa @ TA @ TB @ D @ A ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) )
=> ~ ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_PiE) ).
thf(595,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ ( fun @ TB @ bool ),C: fun @ TA @ bool,D: fun @ TA @ TB] :
( ( member @ ( fun @ TA @ TB ) @ D @ ( pi @ TA @ TB @ C @ B ) )
=> ( ~ ( member @ TB @ ( aa @ TA @ TB @ D @ A ) @ ( aa @ TA @ ( fun @ TB @ bool ) @ B @ A ) )
=> ~ ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
<=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_split__paired__Ex) ).
thf(250,plain,
! [TA: $tType,TB: $tType,A: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) )
=> ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) ) )
& ( ? [B: TB,C: TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ ( product_Pair @ TB @ TA @ B @ C ) ) )
=> ? [B: product_prod @ TB @ TA] : ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_prod__cases5) ).
thf(556,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: product_prod @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( product_Pair @ TE @ ( product_prod @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) ) @ B @ ( product_Pair @ TD @ ( product_prod @ TC @ ( product_prod @ TB @ TA ) ) @ C @ ( product_Pair @ TC @ ( product_prod @ TB @ TA ) @ D @ ( product_Pair @ TB @ TA @ E @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(94,axiom,
distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ a @ ( cons @ arrow_411405190le_alt @ b @ ( cons @ arrow_411405190le_alt @ c @ ( nil @ arrow_411405190le_alt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_dist) ).
thf(539,plain,
distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ a @ ( cons @ arrow_411405190le_alt @ b @ ( cons @ arrow_411405190le_alt @ c @ ( nil @ arrow_411405190le_alt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_prod__induct4) ).
thf(588,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) @ C @ ( product_Pair @ TB @ ( product_prod @ TC @ TD ) @ D @ ( product_Pair @ TC @ TD @ E @ F ) ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ ( product_prod @ TC @ TD ) ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(49,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ bool] :
( ( list_all @ TA @ C @ ( cons @ TA @ B @ A ) )
<=> ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
& ( list_all @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_list__all__simps_I1_J) ).
thf(304,plain,
! [TA: $tType,A: list @ TA,B: TA,C: fun @ TA @ bool] :
( ( ( list_all @ TA @ C @ ( cons @ TA @ B @ A ) )
=> ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
& ( list_all @ TA @ C @ A ) ) )
& ( ( ( pp @ ( aa @ TA @ bool @ C @ B ) )
& ( list_all @ TA @ C @ A ) )
=> ( list_all @ TA @ C @ ( cons @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(36,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( arrow_276188178_mkbot @ B @ A ) @ arrow_1985332922le_Lin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_mkbot__Lin) ).
thf(258,plain,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( arrow_276188178_mkbot @ B @ A ) @ arrow_1985332922le_Lin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(23,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(186,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(104,axiom,
! [A: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_096) ).
thf(568,plain,
! [A: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ a ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) ) @ a ) @ c ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ b @ c ) @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( aa @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( aa @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_319942042_below @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ p @ A ) ) @ c ) @ b ) ) @ b ) @ a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_curryD) ).
thf(378,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(77,axiom,
! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( arrow_1958449194le_IIA @ A )
<=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) )
<=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_IIA__def) ).
thf(433,plain,
! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( ( arrow_1958449194le_IIA @ A )
=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) ) ) )
=> ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) ) ) ) )
& ( ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ! [F: arrow_159774573e_indi] :
( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ F ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ F ) ) ) )
=> ( ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) ) )
& ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ C ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) ) ) )
=> ( arrow_1958449194le_IIA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ ( product_prod @ TB @ TC ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool] :
( ! [C: TA,D: TB,E: TC] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_prod__induct3) ).
thf(207,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: product_prod @ TA @ ( product_prod @ TB @ TC ),B: fun @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool] :
( ! [C: TA,D: TB,E: TC] : ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ ( product_Pair @ TA @ ( product_prod @ TB @ TC ) @ C @ ( product_Pair @ TB @ TC @ D @ E ) ) ) )
=> ( pp @ ( aa @ ( product_prod @ TA @ ( product_prod @ TB @ TC ) ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(42,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
& ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_complete__Lin) ).
thf(272,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ arrow_1985332922le_Lin )
& ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(68,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( partition @ TA @ A @ ( nil @ TA ) )
= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_partition_Osimps_I1_J) ).
thf(383,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( partition @ TA @ A @ ( nil @ TA ) )
= ( product_Pair @ ( list @ TA ) @ ( list @ TA ) @ ( nil @ TA ) @ ( nil @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(13,axiom,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( splice @ TA @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ D @ ( cons @ TA @ B @ ( splice @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_splice_Osimps_I3_J) ).
thf(151,plain,
! [TA: $tType,A: list @ TA,B: TA,C: list @ TA,D: TA] :
( ( splice @ TA @ ( cons @ TA @ D @ C ) @ ( cons @ TA @ B @ A ) )
= ( cons @ TA @ D @ ( cons @ TA @ B @ ( splice @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(38,axiom,
member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) @ arrow_610318064e_Prof,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096) ).
thf(262,plain,
member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( combc @ arrow_159774573e_indi @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combb @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( fun @ arrow_411405190le_alt @ ( fun @ arrow_411405190le_alt @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) ) @ arrow_159774573e_indi @ arrow_319942042_below @ p ) @ c ) @ b ) @ arrow_610318064e_Prof,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(25,axiom,
! [TA: $tType,A: list @ TA,B: TA] :
( ( splice @ TA @ ( cons @ TA @ B @ A ) @ ( nil @ TA ) )
= ( cons @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_splice_Osimps_I2_J) ).
thf(190,plain,
! [TA: $tType,A: list @ TA,B: TA] :
( ( splice @ TA @ ( cons @ TA @ B @ A ) @ ( nil @ TA ) )
= ( cons @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_curryE) ).
thf(210,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: fun @ ( product_prod @ TB @ TA ) @ bool] :
( ( pp @ ( product_curry @ TB @ TA @ bool @ C @ B @ A ) )
=> ( pp @ ( aa @ ( product_prod @ TB @ TA ) @ bool @ C @ ( product_Pair @ TB @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(5,axiom,
! [TA: $tType] : ( distinct @ TA @ ( nil @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_distinct_Osimps_I1_J) ).
thf(126,plain,
! [TA: $tType] : ( distinct @ TA @ ( nil @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(27,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( fequal @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(195,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( fequal @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(92,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(532,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(72,axiom,
? [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: arrow_411405190le_alt] : ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ A @ ( cons @ arrow_411405190le_alt @ B @ ( cons @ arrow_411405190le_alt @ C @ ( nil @ arrow_411405190le_alt ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_alt3) ).
thf(395,plain,
? [A: arrow_411405190le_alt,B: arrow_411405190le_alt,C: arrow_411405190le_alt] : ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ A @ ( cons @ arrow_411405190le_alt @ B @ ( cons @ arrow_411405190le_alt @ C @ ( nil @ arrow_411405190le_alt ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(90,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( product_prod_rec @ TC @ TA @ TB @ C @ ( product_Pair @ TC @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_prod_Orecs) ).
thf(528,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( product_prod_rec @ TC @ TA @ TB @ C @ ( product_Pair @ TC @ TA @ B @ A ) )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(79,axiom,
! [A: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ fNot @ A ) )
| ~ ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(459,plain,
! [A: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ fNot @ A ) )
| ~ ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ TA ),B: TA] :
( ( list_case @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_list_Osimps_I4_J) ).
thf(131,plain,
! [TA: $tType,TB: $tType,A: fun @ TB @ ( fun @ ( list @ TB ) @ TA ),B: TA] :
( ( list_case @ TA @ TB @ B @ A @ ( nil @ TB ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,axiom,
! [TA: $tType,A: list @ TA] :
( ( A
!= ( nil @ TA ) )
<=> ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_neq__Nil__conv) ).
thf(178,plain,
! [TA: $tType,A: list @ TA] :
( ( ( A
!= ( nil @ TA ) )
=> ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) ) )
& ( ? [B: TA,C: list @ TA] :
( A
= ( cons @ TA @ B @ C ) )
=> ( A
!= ( nil @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(43,axiom,
! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( arrow_2069624013nimity @ A )
<=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_unanimity__def) ).
thf(277,plain,
! [A: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( ( arrow_2069624013nimity @ A )
=> ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) ) )
& ( ! [B: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ arrow_610318064e_Prof )
=> ! [C: arrow_411405190le_alt,D: arrow_411405190le_alt] :
( ! [E: arrow_159774573e_indi] : ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ E ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ C @ D ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ B ) ) ) )
=> ( arrow_2069624013nimity @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(83,axiom,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: arrow_411405190le_alt] : ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ B @ ( cons @ arrow_411405190le_alt @ A @ ( cons @ arrow_411405190le_alt @ C @ ( nil @ arrow_411405190le_alt ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_third__alt) ).
thf(501,plain,
! [A: arrow_411405190le_alt,B: arrow_411405190le_alt] :
( ( B != A )
=> ? [C: arrow_411405190le_alt] : ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ B @ ( cons @ arrow_411405190le_alt @ A @ ( cons @ arrow_411405190le_alt @ C @ ( nil @ arrow_411405190le_alt ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(113,axiom,
! [A: arrow_159774573e_indi,B: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ ( pi @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_610318064e_Prof @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_1985332922le_Lin ) ) )
=> ( ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( D != E )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C ) ) ) ) )
=> ( arrow_987702531ctator @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_dictatorI) ).
thf(607,plain,
! [A: arrow_159774573e_indi,B: fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ B @ ( pi @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_610318064e_Prof @ ( combk @ ( fun @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ bool ) @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ arrow_1985332922le_Lin ) ) )
=> ( ! [C: fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool )] :
( ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ C @ arrow_610318064e_Prof )
=> ! [D: arrow_411405190le_alt,E: arrow_411405190le_alt] :
( ( D != E )
=> ( ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ C @ A ) )
=> ( member @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ ( product_Pair @ arrow_411405190le_alt @ arrow_411405190le_alt @ D @ E ) @ ( aa @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ C ) ) ) ) )
=> ( arrow_987702531ctator @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(35,axiom,
~ ! [A: arrow_411405190le_alt] :
~ ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ a @ ( cons @ arrow_411405190le_alt @ b @ ( cons @ arrow_411405190le_alt @ A @ ( nil @ arrow_411405190le_alt ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(254,plain,
~ ! [A: arrow_411405190le_alt] :
~ ( distinct @ arrow_411405190le_alt @ ( cons @ arrow_411405190le_alt @ a @ ( cons @ arrow_411405190le_alt @ b @ ( cons @ arrow_411405190le_alt @ A @ ( nil @ arrow_411405190le_alt ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(53,axiom,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( arrow_424895264_mktop @ B @ A ) @ arrow_1985332922le_Lin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_mktop__Lin) ).
thf(322,plain,
! [A: arrow_411405190le_alt,B: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ B @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ ( arrow_424895264_mktop @ B @ A ) @ arrow_1985332922le_Lin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(96,axiom,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combk @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_159774573e_indi @ A ) @ arrow_610318064e_Prof ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_const__Lin__Prof) ).
thf(543,plain,
! [A: fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool] :
( ( member @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ A @ arrow_1985332922le_Lin )
=> ( member @ ( fun @ arrow_159774573e_indi @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) ) @ ( combk @ ( fun @ ( product_prod @ arrow_411405190le_alt @ arrow_411405190le_alt ) @ bool ) @ arrow_159774573e_indi @ A ) @ arrow_610318064e_Prof ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_PairE) ).
thf(592,plain,
! [TA: $tType,TB: $tType,A: product_prod @ TB @ TA] :
~ ! [B: TB,C: TA] :
( A
!= ( product_Pair @ TB @ TA @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(62,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ A )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(364,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( member @ TA @ B @ A )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(644,plain,
$false,
inference(e,[status(thm)],[138,550,301,135,308,247,269,597,389,184,504,619,125,357,157,559,421,289,321,353,397,507,512,534,380,117,334,260,160,561,392,165,522,461,324,356,141,339,193,526,590,547,212,457,173,134,128,266,311,430,573,296,149,375,176,286,291,545,641,466,540,187,419,599,367,520,209,123,553,162,531,327,263,199,370,463,336,613,154,600,386,595,250,556,539,588,304,258,186,568,378,433,207,272,383,151,262,190,210,126,195,532,395,528,459,131,178,277,501,607,254,322,543,592,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SCT223_5 : TPTP v8.2.0. Released v6.0.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n032.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 20 00:00:54 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.27/1.17 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.22/1.53 % [INFO] Parsing done (352ms).
% 2.43/1.54 % [INFO] Running in sequential loop mode.
% 3.57/2.00 % [INFO] eprover registered as external prover.
% 3.57/2.01 % [INFO] cvc4 registered as external prover.
% 3.57/2.01 % [INFO] Scanning for conjecture ...
% 4.28/2.28 % [INFO] Found a conjecture (or negated_conjecture) and 114 axioms. Running axiom selection ...
% 4.84/2.44 % [INFO] Axiom selection finished. Selected 114 axioms (removed 0 axioms).
% 5.88/2.72 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.88/2.75 % [INFO] Type checking passed.
% 5.88/2.76 % [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 ...
% 62.89/35.17 % External prover 'e' found a proof!
% 62.89/35.17 % [INFO] Killing All external provers ...
% 62.89/35.17 % Time passed: 34624ms (effective reasoning time: 33625ms)
% 62.89/35.17 % 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)>
% 62.89/35.18 % Axioms used in derivation (114): help_fdisj_1_1_U, fact_42_above__Lin, fact_94_list__all__simps_I2_J, fact_60_alt3, fact_20_assms_I3_J, fact_78_prod__induct3, fact_91_list__ex1__simps_I2_J, fact_64_splice_Osimps_I2_J, help_COMBS_1_1_U, fact_15_ab, fact_18_in__below, fact_1__096a_A_126_061_Ab_096, fact_92_lexord__cons__cons, fact_29_notin__Lin__iff, fact_57_funcsetI, fact_83_internal__split__conv, fact_95_lexord__Nil__right, help_COMBI_1_1_U, fact_23__C2_C, fact_3_iff, fact_70_prod__induct6, fact_62_Pi__cong, fact_50_list_Oexhaust, fact_21__096P_H_A_058_AProf_096, fact_38_in__above, fact_69_list_Osimps_I5_J, fact_9_Pair__eq, fact_11__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_058_AProf_096, fact_8_split__paired__All, fact_5__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_096, fact_71_prod__cases6, fact_82_prod_Oexhaust, help_fNot_2_1_U, fact_32_distinct_Osimps_I1_J, fact_67_splice__Nil2, help_fNot_1_1_U, fact_73_prod__cases5, fact_39_prod_Orecs, fact_25_const__Lin__Prof, fact_52_funcset__mem, fact_14__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096, fact_34_split__paired__Ex, fact_44_list_Osimps_I2_J, fact_77_prod__induct4, fact_51_Pi__mem, fact_43_list_Osimps_I3_J, fact_12_in__mkbot, fact_87_curryD, fact_80_pred__equals__eq2, help_COMBB_1_1_U, fact_93_list__all__simps_I1_J, fact_99_partition_Osimps_I1_J, fact_97_lexord__irreflexive, fact_45_distinct__length__2__or__more, fact_98_lexord__linear, fact_89_list__ex1__simps_I1_J, fact_85_curryI, fact_90_list__nonempty__induct, fact_10__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096, fact_55_Pi__I, fact_41_not__Cons__self, fact_35_distinct__singleton, fact_30_below__Lin, fact_36_complete__Lin, fact_74_prod__cases4, fact_46_unanimity__def, help_fequal_1_1_T, fact_17_bc, fact_24_assms_I1_J, fact_47_IIA__def, fact_22__C1_C, fact_59_distinct__insert, fact_88_curry__def, fact_76_mem__def, fact_4__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_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_096, fact_2_dist, fact_0__096P_A_058_AProf_096, fact_54_dictator__def, help_fdisj_2_1_U, help_COMBK_1_1_U, fact_58_insert__Nil, fact_7__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_31_Pair__inject, fact_84_curry__conv, fact_53_funcset__id, help_COMBC_1_1_U, fact_56_neq__Nil__conv, help_fequal_2_1_T, fact_48_dictatorI, fact_26_mkbot__Lin, fact_68_splice_Osimps_I1_J, fact_79_prod__cases3, fact_16_ac, fact_27_mktop__Lin, help_fdisj_3_1_U, fact_37_list_Oinject, fact_49_PiE, fact_72_prod__induct5, fact_86_curryE, help_pp_1_1_U, fact_40_not__Cons__self2, fact_66_splice_Osimps_I3_J, fact_65_list_Osimps_I4_J, fact_81_PairE, fact_13_in__mktop, fact_75_ext, fact_6__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_096, help_pp_2_1_U, fact_19_u, fact_61_linear__alt, fact_28_Lin__irrefl, fact_33_third__alt, fact_63_Pi__I_H, fact_96_lexord__Nil__left
% 62.89/35.18 % No. of inferences in proof: 232
% 62.89/35.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 34624 ms resp. 33625 ms w/o parsing
% 63.91/35.40 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 63.91/35.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------