%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM095_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:58:01 AM UTC 2026
% Result : Theorem 23.93s 13.05s
% Output : Refutation 24.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 117
% Syntax : Number of formulae : 236 ( 102 unt; 0 typ; 0 def)
% Number of atoms : 955 ( 221 equ; 0 cnn)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 4354 ( 85 ~; 15 |; 71 &;4012 @)
% ( 22 <=>; 149 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 8 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 49 usr; 12 con; 0-6 aty)
% Number of variables : 815 ( 0 ^; 780 !; 35 ?; 815 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(atom_type,type,
atom: $tType ).
thf(enum_decl,type,
enum:
!>[TA: $tType] : $o ).
thf(cl_HOL_Oequal_decl,type,
cl_HOL_Oequal:
!>[TA: $tType] : $o ).
thf(ring_decl,type,
ring:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(n_lists_decl,type,
n_lists:
!>[TA: $tType] : ( nat > ( TA @ list ) > ( TA @ list @ list ) ) ).
thf(product_decl,type,
product:
!>[TA: $tType,TB: $tType] : ( ( TB @ list ) > ( TA @ list ) > ( TA @ ( TB @ product_prod ) @ list ) ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(equal_equal_decl,type,
equal_equal:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(iprod_decl,type,
iprod:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) > TA ) ).
thf(zipwith0_decl,type,
zipwith0:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TC @ list ) > ( TB @ list ) > ( TA @ list ) ) ).
thf(listMem_decl,type,
listMem:
!>[TA: $tType] : ( TA > ( TA @ list ) > $o ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(lexord_decl,type,
lexord:
!>[TA: $tType] : ( ( bool @ ( TA @ ( TA @ product_prod ) @ fun ) ) > ( bool @ ( TA @ list @ ( TA @ list @ product_prod ) @ fun ) ) ) ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( TA @ list ) ).
thf(list_case_decl,type,
list_case:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ list @ fun ) @ ( TA @ fun ) ) > ( TA @ list ) > TB ) ).
thf(list_rec_decl,type,
list_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ) ) > ( TA @ list ) > TB ) ).
thf(list_size_decl,type,
list_size:
!>[TA: $tType] : ( ( nat @ ( TA @ fun ) ) > ( TA @ list ) > nat ) ).
thf(list_ex1_decl,type,
list_ex1:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(member1_decl,type,
member1:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( TA @ list @ fun ) ) ).
thf(null_decl,type,
null:
!>[TA: $tType] : ( ( TA @ list ) > $o ) ).
thf(remdups_decl,type,
remdups:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) ) ).
thf(rotate1_decl,type,
rotate1:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) ) ).
thf(set_decl,type,
set:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( TA @ list @ fun ) ) ).
thf(splice_decl,type,
splice:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) > ( TA @ list ) ) ).
thf(sublist_decl,type,
sublist:
!>[TA: $tType] : ( ( TA @ list ) > ( bool @ ( nat @ fun ) ) > ( TA @ list ) ) ).
thf(transpose_decl,type,
transpose:
!>[TA: $tType] : ( ( TA @ list @ list ) > ( TA @ list @ list ) ) ).
thf(i_Z_decl,type,
i_Z: atom > ( int @ list ) > $o ).
thf(divisor_decl,type,
divisor: atom > int ).
thf(lbounds_decl,type,
lbounds: ( atom @ list ) > ( int @ list @ ( int @ product_prod ) @ list ) ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( TA @ ( TB @ product_prod ) ) ) ).
thf(product_curry_decl,type,
product_curry:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ ( TC @ product_prod ) @ fun ) ) > TC > TB > TA ) ).
thf(produc1605651328_split_decl,type,
produc1605651328_split:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ product_prod ) ) > TA ) ).
thf(product_prod_rec_decl,type,
product_prod_rec:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ product_prod ) ) > TA ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fequal_decl,type,
fequal:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(a_decl,type,
a: atom ).
thf(as_decl,type,
as: atom @ list ).
thf(li_decl,type,
li: int ).
thf(lks_decl,type,
lks: int @ list ).
thf(x_decl,type,
x: int ).
thf(xs_decl,type,
xs: int @ list ).
thf(110,axiom,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons ) ) @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( ( A @ ( B @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_member__rec_I1_J) ).
thf(503,plain,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( ( ( A @ ( B @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( C = A ) )
=> ( A @ ( B @ ( C @ ( TA @ cons ) ) @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( C @ ( TA @ cons ) ) @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(103,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TA @ zero ) )
=> ! [A: TA @ list,B: TA,C: TC @ list,D: TC,E: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TC @ cons ) ) @ ( E @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) )
= ( A @ ( C @ ( E @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) @ ( B @ ( D @ ( E @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_zipwith0_Osimps_I2_J) ).
thf(462,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TA @ zero ) )
=> ! [A: TA @ list,B: TA,C: TC @ list,D: TC,E: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TC @ cons ) ) @ ( E @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) )
= ( A @ ( C @ ( E @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) @ ( B @ ( D @ ( E @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(7,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( ( A @ ( B @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( B @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_List_Omember__def) ).
thf(130,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( ( ( B @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ member ) ) )
=> ( A @ ( B @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(66,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( H @ ( G @ ( TF @ ( TE @ product_Pair ) ) ) @ ( F @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( E @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_prod__induct6) ).
thf(336,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE,H: TF] : ( H @ ( G @ ( TF @ ( TE @ product_Pair ) ) ) @ ( F @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( E @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TF @ ( TE @ product_prod ) @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(75,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ iprod ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_iprod__Nil) ).
thf(365,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ iprod ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(71,axiom,
atom @ cl_HOL_Oequal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_PresArith_Oatom___HOL_Oequal) ).
thf(352,plain,
atom @ cl_HOL_Oequal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(116,axiom,
! [TA: $tType,A: TA,B: bool @ ( nat @ fun )] :
( ( ~ ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil ) ) )
& ( ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_sublist__singleton) ).
thf(523,plain,
! [TA: $tType,A: TA,B: bool @ ( nat @ fun )] :
( ( ~ ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil ) ) )
& ( ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(99,axiom,
! [A: atom] :
( ( as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( A @ ( atom @ member ) ) )
=> ( xs @ ( x @ ( int @ cons ) ) @ ( A @ i_Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_x) ).
thf(449,plain,
! [A: atom] :
( ( as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( A @ ( atom @ member ) ) )
=> ( xs @ ( x @ ( int @ cons ) ) @ ( A @ i_Z ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(111,axiom,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( B @ ( C @ ( TA @ listMem ) ) )
=> ( B @ ( A @ ( TA @ cons ) ) @ ( C @ ( TA @ listMem ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_insert) ).
thf(511,plain,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( B @ ( C @ ( TA @ listMem ) ) )
=> ( B @ ( A @ ( TA @ cons ) ) @ ( C @ ( TA @ listMem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(30,axiom,
bool @ enum,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Enum_Oenum) ).
thf(217,plain,
bool @ enum,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(47,axiom,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( A @ ( B @ ( TA @ list @ equal_equal @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_equal__list__def) ).
thf(276,plain,
! [TA: $tType,A: TA @ list,B: TA @ list] :
( ( ( B = A )
=> ( A @ ( B @ ( TA @ list @ equal_equal @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ list @ equal_equal @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(3,axiom,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ( ( TA @ equal_equal )
= ( TA @ fequal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_equal) ).
thf(120,plain,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ( ( TA @ equal_equal )
= ( TA @ fequal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_PairE) ).
thf(247,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(80,axiom,
! [TA: $tType,A: TA @ list @ list] :
( ( A @ ( TA @ nil @ ( TA @ list @ cons ) ) @ ( TA @ transpose ) )
= ( A @ ( TA @ transpose ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_transpose_Osimps_I2_J) ).
thf(385,plain,
! [TA: $tType,A: TA @ list @ list] :
( ( A @ ( TA @ nil @ ( TA @ list @ cons ) ) @ ( TA @ transpose ) )
= ( A @ ( TA @ transpose ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) @ ( A @ ( B @ ( C @ ( TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_list_Orecs_I2_J) ).
thf(500,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ ( TB @ list_rec ) ) ) ) @ ( A @ ( B @ ( C @ ( TB @ ( TB @ fun ) @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_prod )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( G @ ( F @ ( TA @ ( TB @ product_Pair ) ) ) @ ( E @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_prod__cases6) ).
thf(185,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,TF: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_prod )] :
~ ! [B: TF,C: TE,D: TD,E: TC,F: TB,G: TA] :
( A
!= ( G @ ( F @ ( TA @ ( TB @ product_Pair ) ) ) @ ( E @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod ) @ ( TF @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(90,axiom,
! [TA: $tType,A: TA @ list,B: TA] : ( A @ ( B @ ( TA @ cons ) ) @ ( B @ ( TA @ listMem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_elem) ).
thf(417,plain,
! [TA: $tType,A: TA @ list,B: TA] : ( A @ ( B @ ( TA @ cons ) ) @ ( B @ ( TA @ listMem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(49,axiom,
nat @ cl_HOL_Oequal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___HOL_Oequal) ).
thf(288,plain,
nat @ cl_HOL_Oequal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(19,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_prod_Orecs) ).
thf(174,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(85,axiom,
! [A: atom] :
( ( as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( A @ ( atom @ member ) ) )
=> ( ( A @ divisor )
!= ( int @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_norm) ).
thf(404,plain,
! [A: atom] :
( ( as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( A @ ( atom @ member ) ) )
=> ( ( A @ divisor )
!= ( int @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType,A: TB @ list] :
( ( A @ ( TA @ nil @ ( TB @ ( TA @ product ) ) ) )
= ( TB @ ( TA @ product_prod ) @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_product_Osimps_I1_J) ).
thf(372,plain,
! [TA: $tType,TB: $tType,A: TB @ list] :
( ( A @ ( TA @ nil @ ( TB @ ( TA @ product ) ) ) )
= ( TB @ ( TA @ product_prod ) @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_curryE) ).
thf(344,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(14,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_zero__reorient) ).
thf(157,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= A ) )
& ( ( ( TA @ zero_zero )
= A )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(62,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ rotate1 ) @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) )
= ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_set__rotate1) ).
thf(325,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ rotate1 ) @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) )
= ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(50,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_splice__Nil2) ).
thf(289,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(58,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(316,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(108,axiom,
! [TA: $tType,A: bool @ ( TA @ list @ fun ),B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ! [C: TA] : ( TA @ nil @ ( C @ ( TA @ cons ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: TA @ list] :
( ( D
!= ( TA @ nil ) )
=> ( ( D @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ cons ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_list__nonempty__induct) ).
thf(492,plain,
! [TA: $tType,A: bool @ ( TA @ list @ fun ),B: TA @ list] :
( ( B
!= ( TA @ nil ) )
=> ( ! [C: TA] : ( TA @ nil @ ( C @ ( TA @ cons ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( ! [C: TA,D: TA @ list] :
( ( D
!= ( TA @ nil ) )
=> ( ( D @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( D @ ( C @ ( TA @ cons ) ) @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(21,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ listMem ) ) )
<=> ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_ListMem__iff) ).
thf(179,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( A @ ( B @ ( TA @ listMem ) ) ) )
& ( ( A @ ( B @ ( TA @ listMem ) ) )
=> ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(98,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ~ ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_List_Oinsert__def) ).
thf(443,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ~ ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(42,axiom,
! [TA: $tType,A: TA @ list] :
( ( ( TA @ nil )
= ( A @ ( TA @ remdups ) ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_remdups__eq__nil__right__iff) ).
thf(253,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( ( TA @ nil )
= ( A @ ( TA @ remdups ) ) ) )
& ( ( ( TA @ nil )
= ( A @ ( TA @ remdups ) ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(72,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( TA @ remdups ) @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ insert ) ) @ ( TA @ remdups ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_insert__remdups) ).
thf(353,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( TA @ remdups ) @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ insert ) ) @ ( TA @ remdups ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType] : ( TA @ ( TB @ product_prod ) @ cl_HOL_Oequal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod___HOL_Oequal) ).
thf(307,plain,
! [TA: $tType,TB: $tType] : ( TA @ ( TB @ product_prod ) @ cl_HOL_Oequal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(51,axiom,
! [TA: $tType] :
( ( TA @ member1 )
= ( TA @ set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_member__set) ).
thf(292,plain,
! [TA: $tType] :
( ( TA @ member1 )
= ( TA @ set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: TC @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TA @ ( TB @ product_curry ) ) ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( TC @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_curry__conv) ).
thf(233,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB,C: TC @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TA @ ( TB @ product_curry ) ) ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( TC @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(117,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( C @ ( TA @ splice ) ) @ ( B @ ( TA @ cons ) ) @ ( D @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_splice_Osimps_I3_J) ).
thf(529,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( C @ ( TA @ splice ) ) @ ( B @ ( TA @ cons ) ) @ ( D @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_curryI) ).
thf(334,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ? [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
<=> ? [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_split__paired__Ex) ).
thf(302,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( ? [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ? [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) )
& ( ? [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ? [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(86,axiom,
? [A: int] :
! [B: atom] :
( ( as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( B @ ( atom @ member ) ) )
=> ( xs @ ( A @ ( int @ cons ) ) @ ( B @ i_Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096EX_Ax_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_096) ).
thf(407,plain,
? [A: int] :
! [B: atom] :
( ( as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( B @ ( atom @ member ) ) )
=> ( xs @ ( A @ ( int @ cons ) ) @ ( B @ i_Z ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(9,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ list @ equal_equal @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
<=> ( A @ ( TA @ null ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_equal__Nil__null) ).
thf(137,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ null ) )
=> ( TA @ nil @ ( A @ ( TA @ list @ equal_equal @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ list @ aa ) ) ) @ pp ) )
& ( ( TA @ nil @ ( A @ ( TA @ list @ equal_equal @ ( bool @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ list @ aa ) ) ) @ pp )
=> ( A @ ( TA @ null ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [TA: $tType] :
( ( TA @ list @ nil @ ( TA @ transpose ) )
= ( TA @ list @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_transpose_Osimps_I1_J) ).
thf(165,plain,
! [TA: $tType] :
( ( TA @ list @ nil @ ( TA @ transpose ) )
= ( TA @ list @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(43,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mem__def) ).
thf(260,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member ) ) ) )
& ( ( A @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).
thf(349,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ enum ) )
=> ( TA @ ( TB @ fun ) @ enum ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Enum_Oenum) ).
thf(229,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ enum ) )
=> ( TA @ ( TB @ fun ) @ enum ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ enum ) )
=> ( TA @ ( TB @ product_prod ) @ enum ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod___Enum_Oenum) ).
thf(197,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ enum ) )
=> ( TA @ ( TB @ product_prod ) @ enum ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(115,axiom,
as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( a @ ( atom @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096a_A_058_Aset_Aas_096) ).
thf(522,plain,
as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( a @ ( atom @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(114,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) )
=> ( ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) )
| ( C = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_set__ConsD) ).
thf(519,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) )
=> ( ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) )
| ( C = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(59,axiom,
! [TA: $tType,A: bool @ ( nat @ fun ),B: TA @ list,C: TA] :
( ~ ( B @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) )
=> ~ ( A @ ( B @ ( TA @ sublist ) ) @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_notin__set__sublistI) ).
thf(317,plain,
! [TA: $tType,A: bool @ ( nat @ fun ),B: TA @ list,C: TA] :
( ~ ( B @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) )
=> ~ ( A @ ( B @ ( TA @ sublist ) ) @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( F @ ( E @ ( TA @ ( TB @ product_Pair ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_prod__cases5) ).
thf(188,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_prod )] :
~ ! [B: TE,C: TD,D: TC,E: TB,F: TA] :
( A
!= ( F @ ( E @ ( TA @ ( TB @ product_Pair ) ) ) @ ( D @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod ) @ ( TE @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(81,axiom,
! [TA: $tType,A: nat] :
( ( ( A
!= ( nat @ zero_zero ) )
=> ( ( TA @ nil @ ( A @ ( TA @ n_lists ) ) )
= ( TA @ list @ nil ) ) )
& ( ( A
= ( nat @ zero_zero ) )
=> ( ( TA @ nil @ ( A @ ( TA @ n_lists ) ) )
= ( TA @ list @ nil @ ( TA @ nil @ ( TA @ list @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_n__lists__Nil) ).
thf(388,plain,
! [TA: $tType,A: nat] :
( ( ( A
!= ( nat @ zero_zero ) )
=> ( ( TA @ nil @ ( A @ ( TA @ n_lists ) ) )
= ( TA @ list @ nil ) ) )
& ( ( A
= ( nat @ zero_zero ) )
=> ( ( TA @ nil @ ( A @ ( TA @ n_lists ) ) )
= ( TA @ list @ nil @ ( TA @ nil @ ( TA @ list @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC] : ( E @ ( D @ ( TC @ ( TB @ product_Pair ) ) ) @ ( C @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_prod__induct3) ).
thf(356,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC] : ( E @ ( D @ ( TC @ ( TB @ product_Pair ) ) ) @ ( C @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TC @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_list_Osimps_I4_J) ).
thf(141,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_case ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(92,axiom,
( ( as @ lbounds )
!= ( int @ list @ ( int @ product_prod ) @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20__096lbounds_Aas_A_126_061_A_091_093_096) ).
thf(420,plain,
( ( as @ lbounds )
!= ( int @ list @ ( int @ product_prod ) @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(63,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TB @ zero ) )
=> ! [A: TA @ ( TC @ fun ) @ ( TB @ fun )] :
( ( TC @ nil @ ( TB @ nil @ ( A @ ( TA @ ( TC @ ( TB @ zipwith0 ) ) ) ) ) )
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_zipwith0_Osimps_I1_J) ).
thf(328,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TB @ zero ) )
=> ! [A: TA @ ( TC @ fun ) @ ( TB @ fun )] :
( ( TC @ nil @ ( TB @ nil @ ( A @ ( TA @ ( TC @ ( TB @ zipwith0 ) ) ) ) ) )
= ( TA @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(106,axiom,
as @ lbounds @ ( int @ list @ ( int @ product_prod ) @ set @ ( bool @ ( int @ list @ ( int @ product_prod ) @ fun ) @ ( int @ list @ ( int @ product_prod ) @ list @ aa ) ) ) @ ( lks @ ( li @ ( int @ list @ ( int @ product_Pair ) ) ) @ ( int @ list @ ( int @ product_prod ) @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_calculation_I1_J) ).
thf(488,plain,
as @ lbounds @ ( int @ list @ ( int @ product_prod ) @ set @ ( bool @ ( int @ list @ ( int @ product_prod ) @ fun ) @ ( int @ list @ ( int @ product_prod ) @ list @ aa ) ) ) @ ( lks @ ( li @ ( int @ list @ ( int @ product_Pair ) ) ) @ ( int @ list @ ( int @ product_prod ) @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(32,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(225,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(107,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil @ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_splice_Osimps_I2_J) ).
thf(489,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil @ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ splice ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(28,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_list__ex1__simps_I1_J) ).
thf(212,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TA @ fun ) @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_rec ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_list_Orecs_I1_J) ).
thf(134,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TA @ fun ) @ ( TB @ list @ fun ) @ ( TB @ fun ),B: TA] :
( ( TB @ nil @ ( A @ ( B @ ( TB @ ( TA @ list_rec ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_curryD) ).
thf(128,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( A @ ( B @ ( C @ ( bool @ ( TA @ ( TB @ product_curry ) ) ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(39,axiom,
! [TA: $tType,A: bool @ ( nat @ fun )] :
( ( A @ ( TA @ nil @ ( TA @ sublist ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_sublist__nil) ).
thf(244,plain,
! [TA: $tType,A: bool @ ( nat @ fun )] :
( ( A @ ( TA @ nil @ ( TA @ sublist ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(83,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( nat @ zero_zero @ ( TA @ n_lists ) ) )
= ( TA @ list @ nil @ ( TA @ nil @ ( TA @ list @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_n__lists_Osimps_I1_J) ).
thf(398,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( nat @ zero_zero @ ( TA @ n_lists ) ) )
= ( TA @ list @ nil @ ( TA @ nil @ ( TA @ list @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(53,axiom,
! [TA: $tType,A: bool @ ( nat @ fun ),B: TA @ list,C: TA] :
( ( A @ ( B @ ( TA @ sublist ) ) @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) )
=> ( B @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_in__set__sublistD) ).
thf(298,plain,
! [TA: $tType,A: bool @ ( nat @ fun ),B: TA @ list,C: TA] :
( ( A @ ( B @ ( TA @ sublist ) ) @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) )
=> ( B @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_list_Osimps_I5_J) ).
thf(412,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ list @ fun ) @ ( TA @ fun ),D: TB] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ ( TB @ list_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ list @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(13,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Pair__eq) ).
thf(148,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(44,axiom,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ rotate1 ) )
= ( TA @ nil ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_rotate1__is__Nil__conv) ).
thf(264,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( ( A @ ( TA @ rotate1 ) )
= ( TA @ nil ) ) )
& ( ( ( A @ ( TA @ rotate1 ) )
= ( TA @ nil ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(78,axiom,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ equal_equal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_equal__eq) ).
thf(375,plain,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( A @ ( B @ ( TA @ equal_equal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ equal_equal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(112,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_not__Cons__self) ).
thf(513,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(95,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_not__Cons__self2) ).
thf(430,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(93,axiom,
~ ! [A: int] :
~ ! [B: atom] :
( ( as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( B @ ( atom @ member ) ) )
=> ( xs @ ( A @ ( int @ cons ) ) @ ( B @ i_Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096_B_Bthesis_O_A_I_B_Bx_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(423,plain,
~ ! [A: int] :
~ ! [B: atom] :
( ( as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( B @ ( atom @ member ) ) )
=> ( xs @ ( A @ ( int @ cons ) ) @ ( B @ i_Z ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Pair__inject) ).
thf(191,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(79,axiom,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_insert__Nil) ).
thf(382,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(11,axiom,
bool @ cl_HOL_Oequal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___HOL_Oequal) ).
thf(144,plain,
bool @ cl_HOL_Oequal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ produc1605651328_split ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_internal__split__conv) ).
thf(236,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ produc1605651328_split ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ cl_HOL_Oequal ) )
=> ( TA @ ( TB @ fun ) @ cl_HOL_Oequal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___HOL_Oequal) ).
thf(172,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ cl_HOL_Oequal ) )
=> ( TA @ ( TB @ fun ) @ cl_HOL_Oequal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(46,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(274,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(91,axiom,
int @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(419,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(100,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
<=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_neq__Nil__conv) ).
thf(451,plain,
! [TA: $tType,A: TA @ list] :
( ( ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) )
=> ( A
!= ( TA @ nil ) ) )
& ( ( A
!= ( TA @ nil ) )
=> ? [B: TA,C: TA @ list] :
( A
= ( C @ ( B @ ( TA @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(97,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_list_Oinject) ).
thf(434,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(45,axiom,
! [TA: $tType,A: nat @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ list_size ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_list_Osize_I1_J) ).
thf(271,plain,
! [TA: $tType,A: nat @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ list_size ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(113,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_list_Oexhaust) ).
thf(516,plain,
! [TA: $tType,A: TA @ list] :
( ( A
!= ( TA @ nil ) )
=> ~ ! [B: TA,C: TA @ list] :
( A
!= ( C @ ( B @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(4,axiom,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ( ( TA @ fequal )
= ( TA @ equal_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_eq__equal) ).
thf(123,plain,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ( ( TA @ fequal )
= ( TA @ equal_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(101,axiom,
int @ cl_HOL_Oequal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___HOL_Oequal) ).
thf(458,plain,
int @ cl_HOL_Oequal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(12,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ iprod ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_iprod__Nil2) ).
thf(145,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ iprod ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(52,axiom,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ remdups ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_remdups_Osimps_I1_J) ).
thf(295,plain,
! [TA: $tType] :
( ( TA @ nil @ ( TA @ remdups ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(87,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TA @ zero ) )
=> ! [A: TC @ list,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( TA @ nil @ ( A @ ( B @ ( TC @ cons ) ) @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) )
= ( TA @ nil @ ( A @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) @ ( TA @ zero_zero @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_zipwith0_Osimps_I3_J) ).
thf(409,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TA @ zero ) )
=> ! [A: TC @ list,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( TA @ nil @ ( A @ ( B @ ( TC @ cons ) ) @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) )
= ( TA @ nil @ ( A @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) @ ( TA @ zero_zero @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(27,axiom,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ list_ex1 ) ) )
<=> ? [C: TA] :
( ! [D: TA] :
( ( ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ member ) ) ) )
=> ( D = C ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_list__ex1__iff) ).
thf(199,plain,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( ? [C: TA] :
( ! [D: TA] :
( ( ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ member ) ) ) )
=> ( D = C ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) ) )
=> ( A @ ( B @ ( TA @ list_ex1 ) ) ) )
& ( ( A @ ( B @ ( TA @ list_ex1 ) ) )
=> ? [C: TA] :
( ! [D: TA] :
( ( ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ member ) ) ) )
=> ( D = C ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(20,axiom,
! [TA: $tType] : ( TA @ nil @ ( TA @ null ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_null__rec_I2_J) ).
thf(177,plain,
! [TA: $tType] : ( TA @ nil @ ( TA @ null ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(64,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ remdups ) @ ( TA @ remdups ) )
= ( A @ ( TA @ remdups ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_remdups__remdups) ).
thf(331,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ remdups ) @ ( TA @ remdups ) )
= ( A @ ( TA @ remdups ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(67,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list] :
( ! [C: TA] :
( ( B @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) )
=> ( C
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ iprod ) ) )
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_iprod0__if__coeffs0) ).
thf(338,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list] :
( ! [C: TA] :
( ( B @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) )
=> ( C
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ iprod ) ) )
= ( TA @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(105,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ~ ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ remdups ) )
= ( A @ ( TA @ remdups ) @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ remdups ) )
= ( A @ ( TA @ remdups ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_remdups_Osimps_I2_J) ).
thf(482,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ~ ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ remdups ) )
= ( A @ ( TA @ remdups ) @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ remdups ) )
= ( A @ ( TA @ remdups ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(31,axiom,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ remdups ) )
= ( TA @ nil ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_remdups__eq__nil__iff) ).
thf(218,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( ( A @ ( TA @ remdups ) )
= ( TA @ nil ) ) )
& ( ( ( A @ ( TA @ remdups ) )
= ( TA @ nil ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(76,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_in__set__member) ).
thf(368,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ( B @ ( A @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) ) )
& ( ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(41,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_in__set__insert) ).
thf(250,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(104,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ listMem ) ) )
<=> ( ? [C: TA,D: TA @ list,E: TA] :
( ( D @ ( C @ ( TA @ listMem ) ) )
& ( A
= ( D @ ( E @ ( TA @ cons ) ) ) )
& ( B = C ) )
| ? [C: TA,D: TA @ list] :
( ( A
= ( D @ ( C @ ( TA @ cons ) ) ) )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_ListMem_Osimps) ).
thf(465,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ( ? [C: TA,D: TA @ list,E: TA] :
( ( D @ ( C @ ( TA @ listMem ) ) )
& ( A
= ( D @ ( E @ ( TA @ cons ) ) ) )
& ( B = C ) )
| ? [C: TA,D: TA @ list] :
( ( A
= ( D @ ( C @ ( TA @ cons ) ) ) )
& ( B = C ) ) )
=> ( A @ ( B @ ( TA @ listMem ) ) ) )
& ( ( A @ ( B @ ( TA @ listMem ) ) )
=> ( ? [C: TA,D: TA @ list,E: TA] :
( ( D @ ( C @ ( TA @ listMem ) ) )
& ( A
= ( D @ ( E @ ( TA @ cons ) ) ) )
& ( B = C ) )
| ? [C: TA,D: TA @ list] :
( ( A
= ( D @ ( C @ ( TA @ cons ) ) ) )
& ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(34,axiom,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ! [A: TA] : ( A @ ( A @ ( TA @ equal_equal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_equal__refl) ).
thf(231,plain,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ! [A: TA] : ( A @ ( A @ ( TA @ equal_equal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(60,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ remdups ) @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) )
= ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_set__remdups) ).
thf(319,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ remdups ) @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) )
= ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(84,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_list_Osimps_I3_J) ).
thf(401,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(17,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(171,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,conjecture,
xs @ ( x @ ( int @ cons ) ) @ ( a @ i_Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( xs @ ( x @ ( int @ cons ) ) @ ( a @ i_Z ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(119,plain,
~ ( xs @ ( x @ ( int @ cons ) ) @ ( a @ i_Z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(96,axiom,
int @ ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(433,plain,
int @ ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(69,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( E @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_prod__cases4) ).
thf(346,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_prod )] :
~ ! [B: TD,C: TC,D: TB,E: TA] :
( A
!= ( E @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) @ ( C @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_prod ) @ ( TD @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_prod_Oexhaust) ).
thf(214,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ product_prod )] :
~ ! [B: TB,C: TA] :
( A
!= ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(54,axiom,
! [TA: $tType,A: TA] :
~ ( A @ ( TA @ nil @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_member__rec_I2_J) ).
thf(300,plain,
! [TA: $tType,A: TA] :
~ ( A @ ( TA @ nil @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(16,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(168,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(22,axiom,
! [TA: $tType] : ( TA @ list @ cl_HOL_Oequal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List_Olist___HOL_Oequal) ).
thf(183,plain,
! [TA: $tType] : ( TA @ list @ cl_HOL_Oequal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(5,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( G @ ( F @ ( TE @ ( TD @ product_Pair ) ) ) @ ( E @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_prod__induct5) ).
thf(126,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD,G: TE] : ( G @ ( F @ ( TE @ ( TD @ product_Pair ) ) ) @ ( E @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_Pair ) ) ) @ ( D @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TE @ ( TD @ product_prod ) @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(74,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ null ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_List_Onull__def) ).
thf(358,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A
= ( TA @ nil ) )
=> ( A @ ( TA @ null ) ) )
& ( ( A @ ( TA @ null ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(118,axiom,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA @ list,C: TA,D: TA @ list,E: TA] :
( ( A @ ( TA @ lexord ) @ ( B @ ( C @ ( TA @ cons ) ) @ ( D @ ( E @ ( TA @ cons ) ) @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) )
<=> ( ( ( A @ ( TA @ lexord ) @ ( B @ ( D @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) )
& ( E = C ) )
| ( A @ ( C @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_lexord__cons__cons) ).
thf(532,plain,
! [TA: $tType,A: bool @ ( TA @ ( TA @ product_prod ) @ fun ),B: TA @ list,C: TA,D: TA @ list,E: TA] :
( ( ( ( ( A @ ( TA @ lexord ) @ ( B @ ( D @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) )
& ( E = C ) )
| ( A @ ( C @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) )
=> ( A @ ( TA @ lexord ) @ ( B @ ( C @ ( TA @ cons ) ) @ ( D @ ( E @ ( TA @ cons ) ) @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) ) )
& ( ( A @ ( TA @ lexord ) @ ( B @ ( C @ ( TA @ cons ) ) @ ( D @ ( E @ ( TA @ cons ) ) @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) )
=> ( ( ( A @ ( TA @ lexord ) @ ( B @ ( D @ ( TA @ list @ ( TA @ list @ product_Pair ) ) ) @ ( TA @ list @ ( TA @ list @ product_prod ) @ member ) ) )
& ( E = C ) )
| ( A @ ( C @ ( E @ ( TA @ ( TA @ product_Pair ) ) ) @ ( TA @ ( TA @ product_prod ) @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(48,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ! [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
<=> ! [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_split__paired__All) ).
thf(283,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ ( TB @ product_prod ) @ fun )] :
( ( ! [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ! [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) )
& ( ! [B: TA @ ( TB @ product_prod )] : ( B @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp )
=> ! [B: TB,C: TA] : ( C @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) @ ( A @ ( bool @ ( TA @ ( TB @ product_prod ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(89,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
~ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ null ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_null__rec_I1_J) ).
thf(415,plain,
! [TA: $tType,A: TA @ list,B: TA] :
~ ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ null ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( D @ ( C @ ( TA @ ( TB @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_prod__cases3) ).
thf(239,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA @ ( TB @ product_prod ) @ ( TC @ product_prod )] :
~ ! [B: TC,C: TB,D: TA] :
( A
!= ( D @ ( C @ ( TA @ ( TB @ product_Pair ) ) ) @ ( B @ ( TA @ ( TB @ product_prod ) @ ( TC @ product_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( F @ ( E @ ( TD @ ( TC @ product_Pair ) ) ) @ ( D @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_prod__induct4) ).
thf(242,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,A: TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ),B: bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ fun )] :
( ! [C: TA,D: TB,E: TC,F: TD] : ( F @ ( E @ ( TD @ ( TC @ product_Pair ) ) ) @ ( D @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_Pair ) ) ) @ ( C @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_Pair ) ) ) @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TD @ ( TC @ product_prod ) @ ( TB @ product_prod ) @ ( TA @ product_prod ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TA @ zero ) )
=> ! [A: TA @ list,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TC @ nil @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) )
= ( A @ ( TC @ nil @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) @ ( B @ ( TC @ zero_zero @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_zipwith0_Osimps_I4_J) ).
thf(395,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TA @ zero ) )
=> ! [A: TA @ list,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TC @ nil @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) )
= ( A @ ( TC @ nil @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) ) ) @ ( B @ ( TC @ zero_zero @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(94,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_list_Osimps_I2_J) ).
thf(427,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(102,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ~ ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_not__in__set__insert) ).
thf(459,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ~ ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(61,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_splice_Osimps_I1_J) ).
thf(322,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(57,axiom,
! [TA: $tType,A: TA @ list] :
( ( A
= ( TA @ nil ) )
<=> ( A @ ( TA @ null ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_eq__Nil__null) ).
thf(309,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ null ) )
=> ( A
= ( TA @ nil ) ) )
& ( ( A
= ( TA @ nil ) )
=> ( A @ ( TA @ null ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(715,plain,
$false,
inference(e,[status(thm)],[503,462,130,336,365,352,523,449,511,217,276,120,247,385,500,185,417,288,174,404,372,344,157,325,289,316,492,179,443,253,353,307,292,233,529,334,302,407,137,165,260,349,229,197,522,519,317,188,388,356,141,420,328,488,225,489,212,134,128,244,398,298,412,148,264,375,513,430,423,191,382,144,236,172,274,419,451,434,271,516,123,458,145,295,409,199,177,331,338,482,218,368,250,465,231,319,401,171,119,433,346,214,300,168,183,126,358,532,283,415,239,242,395,427,459,322,309]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COM095_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.08/0.33 % Computer : n012.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Sat Sep 26 23:28:20 UTC 2026
% 0.08/0.33 % CPUTime :
% 0.08/0.33 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.50/0.65 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.00/0.82 % [INFO] Parsing done (164ms).
% 1.00/0.82 % [INFO] Running in sequential loop mode.
% 1.55/1.03 % [INFO] eprover registered as external prover.
% 1.55/1.04 % [INFO] Scanning for conjecture ...
% 1.55/1.13 % [INFO] Found a conjecture (or negated_conjecture) and 116 axioms. Running axiom selection ...
% 1.77/1.20 % [INFO] Axiom selection finished. Selected 116 axioms (removed 0 axioms).
% 2.34/1.33 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.34/1.35 % [INFO] Type checking passed.
% 2.34/1.35 % [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 ...
% 23.93/13.04 % External prover 'e' found a proof!
% 23.93/13.04 % [INFO] Killing All external provers ...
% 23.93/13.04 % Time passed: 12628ms (effective reasoning time: 12216ms)
% 23.93/13.04 % 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)>
% 23.93/13.05 % Axioms used in derivation (116): fact_68_prod__cases5, fact_1_x, fact_89_product_Osimps_I1_J, fact_78_internal__split__conv, arity_Int_Oint___HOL_Oequal, fact_35_insert__Nil, fact_79_curry__conv, fact_94_n__lists__Nil, fact_61_split__paired__All, fact_11_null__rec_I1_J, fact_84_in__set__sublistD, fact_20__096lbounds_Aas_A_126_061_A_091_093_096, fact_24_remdups_Osimps_I2_J, fact_87_list_Osize_I1_J, arity_prod___HOL_Oequal, fact_15_member__set, fact_18_in__set__member, fact_52_neq__Nil__conv, fact_19_insert, fact_37_zipwith0_Osimps_I4_J, arity_fun___HOL_Oequal, arity_PresArith_Oatom___HOL_Oequal, fact_69_prod__induct5, fact_21_not__in__set__insert, fact_27_set__rotate1, fact_28_set__remdups, fact_38_remdups__remdups, fact_67_prod__cases6, fact_81_curryI, fact_82_sublist__nil, fact_44_splice__Nil2, fact_0__096a_A_058_Aset_Aas_096, arity_Nat_Onat___HOL_Oequal, fact_75_mem__def, arity_Int_Oint___Rings_Oring, fact_92_equal__eq, fact_57_iprod__Nil2, arity_HOL_Obool___HOL_Oequal, fact_34_list__ex1__simps_I1_J, fact_42_list_Osimps_I4_J, fact_16_List_Omember__def, fact_63_Pair__inject, arity_fun___Enum_Oenum, fact_74_ext, fact_59_zero__reorient, fact_90_equal, fact_29_remdups_Osimps_I1_J, fact_13_elem, fact_65_prod_Orecs, fact_58_equal__list__def, fact_85_curryE, fact_6_not__Cons__self2, arity_HOL_Obool___Enum_Oenum, fact_25_ListMem_Osimps, arity_List_Olist___HOL_Oequal, fact_45_splice_Osimps_I1_J, fact_39_insert__remdups, fact_91_eq__equal, fact_72_prod__induct3, fact_62_Pair__eq, fact_50_in__set__insert, fact_43_eq__Nil__null, fact_23_norm, fact_76_prod_Oexhaust, fact_4_list_Oinject, fact_5_not__Cons__self, fact_9_splice_Osimps_I3_J, fact_40_list_Osimps_I2_J, fact_60_iprod0__if__coeffs0, arity_prod___Enum_Oenum, fact_17_ListMem__iff, help_fequal_1_1_T, fact_66_prod__induct6, fact_70_prod__induct4, fact_53_list_Oexhaust, fact_88_list__nonempty__induct, arity_Nat_Onat___Groups_Ozero, fact_33_zipwith0_Osimps_I1_J, fact_46_member__rec_I2_J, fact_30_remdups__eq__nil__right__iff, fact_32_rotate1__is__Nil__conv, fact_26_list__ex1__iff, fact_73_prod__cases3, fact_80_sublist__singleton, fact_51_splice_Osimps_I2_J, fact_7_set__ConsD, fact_54_calculation_I1_J, fact_93_equal__refl, fact_55_equal__Nil__null, help_fequal_2_1_T, fact_41_list_Osimps_I3_J, fact_22_List_Oinsert__def, fact_48_null__rec_I2_J, fact_10_list_Orecs_I2_J, fact_14_member__rec_I1_J, fact_31_remdups__eq__nil__iff, fact_95_n__lists_Osimps_I1_J, fact_86_curryD, fact_64_split__paired__Ex, fact_12_zipwith0_Osimps_I2_J, help_pp_1_1_U, fact_36_zipwith0_Osimps_I3_J, fact_2__096EX_Ax_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_096, fact_71_prod__cases4, fact_56_iprod__Nil, fact_97_lexord__cons__cons, fact_98_transpose_Osimps_I1_J, arity_Int_Oint___Groups_Ozero, fact_96_transpose_Osimps_I2_J, fact_49_list_Orecs_I1_J, fact_8_list_Osimps_I5_J, help_pp_2_1_U, fact_3__096_B_Bthesis_O_A_I_B_Bx_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_77_PairE, fact_47_List_Onull__def, fact_83_notin__set__sublistI
% 23.93/13.05 % No. of inferences in proof: 236
% 23.93/13.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 12628 ms resp. 12216 ms w/o parsing
% 24.39/13.17 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.39/13.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------