%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM088_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 : n018.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 06:58:00 AM UTC 2026
% Result : Theorem 36.85s 26.99s
% Output : Refutation 38.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 131
% Syntax : Number of formulae : 264 ( 91 unt; 0 typ; 0 def)
% Number of atoms : 1861 ( 211 equ; 0 cnn)
% Maximal formula atoms : 49 ( 7 avg)
% Number of connectives : 7947 ( 91 ~; 28 |; 68 &;7525 @)
% ( 17 <=>; 218 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 50 usr; 12 con; 0-5 aty)
% Number of variables : 812 ( 0 ^; 794 !; 18 ?; 812 :)
% 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(ring_decl,type,
ring:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(cl_Groups_Ominus_decl,type,
cl_Groups_Ominus:
!>[TA: $tType] : $o ).
thf(group_add_decl,type,
group_add:
!>[TA: $tType] : $o ).
thf(finite_finite1_decl,type,
finite_finite1:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(combb_decl,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( TB @ ( TA @ fun ) @ ( TC @ ( TA @ fun ) @ fun ) @ ( TB @ ( TC @ fun ) @ fun ) ) ).
thf(combc_decl,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > TB > ( TA @ ( TC @ fun ) ) ) ).
thf(combi_decl,type,
combi:
!>[TA: $tType] : ( TA @ ( TA @ fun ) ) ).
thf(combs_decl,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ fun ) ) > ( TA @ ( TC @ fun ) ) ) ).
thf(finite_finite_decl,type,
finite_finite:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > $o ) ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(iprod_decl,type,
iprod:
!>[TA: $tType] : ( TA @ ( TA @ list @ fun ) @ ( TA @ list @ fun ) ) ).
thf(zipwith0_decl,type,
zipwith0:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TA @ list @ ( TB @ list @ fun ) @ ( TC @ list @ fun ) ) ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(linord2118332866rt_key_decl,type,
linord2118332866rt_key:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > ( TB @ list ) > ( TB @ list ) ) ).
thf(linorder_insort_key_decl,type,
linorder_insort_key:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > ( TB @ list ) > ( TB @ list ) ) ).
thf(linorder_sort_key_decl,type,
linorder_sort_key:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > ( TB @ list ) > ( TB @ list ) ) ).
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_size_decl,type,
list_size:
!>[TA: $tType] : ( ( nat @ ( TA @ fun ) ) > ( TA @ list ) > nat ) ).
thf(list_all_decl,type,
list_all:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(list_ex1_decl,type,
list_ex1:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(set_decl,type,
set:
!>[TA: $tType] : ( ( TA @ list ) > ( bool @ ( TA @ 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(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(produc1605651328_split_decl,type,
produc1605651328_split:
!>[TA: $tType,TB: $tType,TC: $tType] : ( TA @ ( TB @ ( TC @ product_prod ) @ fun ) @ ( TA @ ( TB @ fun ) @ ( TC @ fun ) @ fun ) ) ).
thf(product_prod_case_decl,type,
product_prod_case:
!>[TA: $tType,TB: $tType,TC: $tType] : ( TA @ ( TB @ ( TC @ product_prod ) @ fun ) @ ( TA @ ( TB @ fun ) @ ( TC @ fun ) @ fun ) ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
thf(image_decl,type,
image:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > ( bool @ ( TB @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fNot_decl,type,
fNot: bool @ ( bool @ fun ) ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fconj_decl,type,
fconj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(fdisj_decl,type,
fdisj: bool @ ( bool @ fun ) @ ( bool @ fun ) ).
thf(fequal_decl,type,
fequal:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ fun ) ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(as_decl,type,
as: atom @ list ).
thf(x_decl,type,
x: int ).
thf(xs_decl,type,
xs: int @ list ).
thf(118,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(515,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)],[118]) ).
thf(19,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_list_Osimps_I3_J) ).
thf(177,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(17,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_61_splice_Osimps_I2_J) ).
thf(171,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)],[17]) ).
thf(63,axiom,
! [TA: $tType] :
( ( TA @ finite_finite1 )
=> ! [A: bool @ ( TA @ fun )] : ( A @ ( TA @ finite_finite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_finite) ).
thf(347,plain,
! [TA: $tType] :
( ( TA @ finite_finite1 )
=> ! [A: bool @ ( TA @ fun )] : ( A @ ( TA @ finite_finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(119,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Diff__idemp) ).
thf(518,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(105,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 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( TA @ nil @ ( A @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ zero_zero @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_zipwith0_Osimps_I3_J) ).
thf(468,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 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( TA @ nil @ ( A @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ zero_zero @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(65,axiom,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(352,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(75,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(385,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)],[75]) ).
thf(123,axiom,
! [TA: $tType,A: bool @ ( nat @ fun ),B: TA @ list,C: TA] :
( ( A @ ( B @ ( TA @ sublist ) ) @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_in__set__sublistD) ).
thf(533,plain,
! [TA: $tType,A: bool @ ( nat @ fun ),B: TA @ list,C: TA] :
( ( A @ ( B @ ( TA @ sublist ) ) @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(18,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_not__Cons__self) ).
thf(174,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(47,axiom,
! [A: nat] :
( ( A @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_diff__self__eq__0) ).
thf(288,plain,
! [A: nat] :
( ( A @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(55,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA @ list,B: TA,C: TB @ ( TA @ fun )] :
( ~ ( A @ ( TA @ set ) @ ( C @ ( TB @ ( TA @ image ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( C @ ( TB @ ( TA @ linord2118332866rt_key ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_insort__insert__insort__key) ).
thf(320,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA @ list,B: TA,C: TB @ ( TA @ fun )] :
( ~ ( A @ ( TA @ set ) @ ( C @ ( TB @ ( TA @ image ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( C @ ( TB @ ( TA @ linord2118332866rt_key ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(76,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( TC @ ( TB @ ( TA @ produc1605651328_split ) ) )
= ( TC @ ( TB @ ( TA @ product_prod_case ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_internal__split__def) ).
thf(389,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( TC @ ( TB @ ( TA @ produc1605651328_split ) ) )
= ( TC @ ( TB @ ( TA @ product_prod_case ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(131,axiom,
! [TA: $tType,A: bool @ ( nat @ fun ),B: TA @ list,C: TA] :
( ~ ( B @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( A @ ( B @ ( TA @ sublist ) ) @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_notin__set__sublistI) ).
thf(570,plain,
! [TA: $tType,A: bool @ ( nat @ fun ),B: TA @ list,C: TA] :
( ~ ( B @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( A @ ( B @ ( TA @ sublist ) ) @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(115,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ( B @ pp )
| ~ ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(504,plain,
! [A: bool,B: bool] :
( ( A @ pp )
| ( B @ pp )
| ~ ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(344,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(68,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_diff__commute) ).
thf(357,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(102,axiom,
! [A: atom] :
( ( as @ ( atom @ set ) @ ( A @ ( atom @ member @ ( bool @ ( bool @ ( atom @ fun ) @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( bool @ ( atom @ fun ) @ aa ) ) ) @ pp )
=> ( xs @ ( x @ ( int @ cons ) ) @ ( A @ i_Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_x) ).
thf(460,plain,
! [A: atom] :
( ( as @ ( atom @ set ) @ ( A @ ( atom @ member @ ( bool @ ( bool @ ( atom @ fun ) @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( bool @ ( atom @ fun ) @ aa ) ) ) @ pp )
=> ( xs @ ( x @ ( int @ cons ) ) @ ( A @ i_Z ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA @ list,B: TA,C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TB @ ( TA @ linorder_sort_key ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ linorder_sort_key ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_sort__key__simps_I2_J) ).
thf(157,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA @ list,B: TA,C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TB @ ( TA @ linorder_sort_key ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ linorder_sort_key ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(129,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( ( D = C )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_diff__eq__diff__eq) ).
thf(559,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( ( ( B = A )
=> ( D = C ) )
& ( ( D = C )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(22,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(189,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(85,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA @ list,B: TA] :
( ~ ( A @ ( TA @ set ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ combi @ ( TA @ ( TA @ linord2118332866rt_key ) ) ) ) )
= ( A @ ( B @ ( TA @ combi @ ( TA @ ( TA @ linorder_insort_key ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_insort__insert__insort) ).
thf(416,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA @ list,B: TA] :
( ~ ( A @ ( TA @ set ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ combi @ ( TA @ ( TA @ linord2118332866rt_key ) ) ) ) )
= ( A @ ( B @ ( TA @ combi @ ( TA @ ( TA @ linorder_insort_key ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(35,axiom,
int @ cl_Groups_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ominus) ).
thf(228,plain,
int @ cl_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(54,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ~ ( B @ ( TA @ finite_finite ) )
=> ( ( B @ ( A @ ( TB @ ( TA @ image ) ) ) @ ( TB @ finite_finite ) )
=> ? [C: TA] :
( ~ ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( TB @ fequal @ ( TA @ ( bool @ ( TB @ fun ) @ ( TB @ combb ) ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( bool @ ( TB @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ combc ) ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) @ ( TA @ finite_finite ) )
& ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_pigeonhole__infinite) ).
thf(316,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ~ ( B @ ( TA @ finite_finite ) )
=> ( ( B @ ( A @ ( TB @ ( TA @ image ) ) ) @ ( TB @ finite_finite ) )
=> ? [C: TA] :
( ~ ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( TB @ fequal @ ( TA @ ( bool @ ( TB @ fun ) @ ( TB @ combb ) ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( bool @ ( TB @ fun ) @ ( TB @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ fun ) @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TB @ ( TA @ combc ) ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) @ ( TA @ finite_finite ) )
& ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(33,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_29_list_Oinject) ).
thf(216,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)],[33]) ).
thf(72,axiom,
! [TA: $tType,A: TA @ list] : ( A @ ( TA @ set ) @ ( TA @ finite_finite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_finite__set) ).
thf(376,plain,
! [TA: $tType,A: TA @ list] : ( A @ ( TA @ set ) @ ( TA @ finite_finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(30,axiom,
bool @ finite_finite1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
thf(211,plain,
bool @ finite_finite1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(109,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) )
=> ( ( ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_diffs0__imp__equal) ).
thf(480,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) )
=> ( ( ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(8,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(147,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(99,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ list @ minus_minus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ iprod @ ( TA @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ iprod @ ( TA @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ aa ) ) ) @ ( A @ ( C @ ( TA @ iprod @ ( TA @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ aa ) ) ) @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_iprod__left__diff__distrib) ).
thf(453,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ list @ minus_minus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ iprod @ ( TA @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ iprod @ ( TA @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ aa ) ) ) @ ( A @ ( C @ ( TA @ iprod @ ( TA @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ aa ) ) ) @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(1,conjecture,
as @ lbounds @ ( int @ list @ ( int @ product_prod ) @ set ) @ ( xs @ ( int @ iprod @ ( int @ ( int @ list @ ( int @ list @ combc ) ) ) ) @ ( int @ minus_minus @ ( int @ list @ ( int @ ( int @ combb ) ) @ ( int @ ( int @ ( int @ list @ fun ) @ ( int @ ( int @ list @ fun ) @ fun ) @ ( int @ ( int @ fun ) @ combb ) ) @ ( int @ ( int @ list @ fun ) @ ( int @ ( int @ list @ fun ) @ fun ) @ ( int @ fun ) @ ( int @ ( int @ fun ) @ ( int @ fun ) @ fun ) @ ( int @ ( int @ list @ fun ) @ ( int @ ( int @ list @ fun ) @ fun ) @ ( int @ ( int @ fun ) @ fun ) @ aa ) ) ) @ ( int @ ( int @ list @ fun ) @ ( int @ ( int @ list @ fun ) @ fun ) @ ( int @ fun ) @ ( int @ ( int @ fun ) @ ( int @ fun ) @ aa ) ) ) @ ( int @ ( int @ list @ fun ) @ ( int @ ( int @ list @ fun ) @ ( int @ combc ) ) ) ) @ ( int @ ( int @ list @ ( int @ product_prod_case ) ) @ ( int @ ( int @ list @ ( int @ product_prod ) @ fun ) @ ( int @ ( int @ list @ fun ) @ ( int @ fun ) @ aa ) ) ) @ ( int @ ( int @ list @ ( int @ product_prod ) @ image ) ) ) @ ( int @ finite_finite ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( as @ lbounds @ ( int @ list @ ( int @ product_prod ) @ set ) @ ( xs @ ( int @ iprod @ ( int @ ( int @ list @ ( int @ list @ combc ) ) ) ) @ ( int @ minus_minus @ ( int @ list @ ( int @ ( int @ combb ) ) @ ( int @ ( int @ ( int @ list @ fun ) @ ( int @ ( int @ list @ fun ) @ fun ) @ ( int @ ( int @ fun ) @ combb ) ) @ ( int @ ( int @ list @ fun ) @ ( int @ ( int @ list @ fun ) @ fun ) @ ( int @ fun ) @ ( int @ ( int @ fun ) @ ( int @ fun ) @ fun ) @ ( int @ ( int @ list @ fun ) @ ( int @ ( int @ list @ fun ) @ fun ) @ ( int @ ( int @ fun ) @ fun ) @ aa ) ) ) @ ( int @ ( int @ list @ fun ) @ ( int @ ( int @ list @ fun ) @ fun ) @ ( int @ fun ) @ ( int @ ( int @ fun ) @ ( int @ fun ) @ aa ) ) ) @ ( int @ ( int @ list @ fun ) @ ( int @ ( int @ list @ fun ) @ ( int @ combc ) ) ) ) @ ( int @ ( int @ list @ ( int @ product_prod_case ) ) @ ( int @ ( int @ list @ ( int @ product_prod ) @ fun ) @ ( int @ ( int @ list @ fun ) @ ( int @ fun ) @ aa ) ) ) @ ( int @ ( int @ list @ ( int @ product_prod ) @ image ) ) ) @ ( int @ finite_finite ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(133,plain,
~ ( as @ lbounds @ ( int @ list @ ( int @ product_prod ) @ set ) @ ( xs @ ( int @ iprod @ ( int @ ( int @ list @ ( int @ list @ combc ) ) ) ) @ ( int @ minus_minus @ ( int @ list @ ( int @ ( int @ combb ) ) @ ( int @ ( int @ ( int @ list @ fun ) @ ( int @ ( int @ list @ fun ) @ fun ) @ ( int @ ( int @ fun ) @ combb ) ) @ ( int @ ( int @ list @ fun ) @ ( int @ ( int @ list @ fun ) @ fun ) @ ( int @ fun ) @ ( int @ ( int @ fun ) @ ( int @ fun ) @ fun ) @ ( int @ ( int @ list @ fun ) @ ( int @ ( int @ list @ fun ) @ fun ) @ ( int @ ( int @ fun ) @ fun ) @ aa ) ) ) @ ( int @ ( int @ list @ fun ) @ ( int @ ( int @ list @ fun ) @ fun ) @ ( int @ fun ) @ ( int @ ( int @ fun ) @ ( int @ fun ) @ aa ) ) ) @ ( int @ ( int @ list @ fun ) @ ( int @ ( int @ list @ fun ) @ ( int @ combc ) ) ) ) @ ( int @ ( int @ list @ ( int @ product_prod_case ) ) @ ( int @ ( int @ list @ ( int @ product_prod ) @ fun ) @ ( int @ ( int @ list @ fun ) @ ( int @ fun ) @ aa ) ) ) @ ( int @ ( int @ list @ ( int @ product_prod ) @ image ) ) ) @ ( int @ finite_finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(90,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_DiffE) ).
thf(428,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(46,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA @ list,D: TA @ list] :
( ( D = C )
=> ( ! [E: TA] :
( ( C @ ( TA @ set ) @ ( E @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( E @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) )
=> ( ( D @ ( B @ ( TA @ list_all ) ) )
<=> ( C @ ( A @ ( TA @ list_all ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_list__all__cong) ).
thf(265,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA @ list,D: TA @ list] :
( ( D = C )
=> ( ! [E: TA] :
( ( C @ ( TA @ set ) @ ( E @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( E @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( E @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( E @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) )
=> ( ( ( C @ ( A @ ( TA @ list_all ) ) )
=> ( D @ ( B @ ( TA @ list_all ) ) ) )
& ( ( D @ ( B @ ( TA @ list_all ) ) )
=> ( C @ ( A @ ( TA @ list_all ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(52,axiom,
! [TA: $tType] :
( ( ( TA @ zero )
& ( TA @ cl_Groups_Ominus ) )
=> ! [A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ list @ minus_minus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ list @ minus_minus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( D @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_list__diff__Cons__Cons) ).
thf(307,plain,
! [TA: $tType] :
( ( ( TA @ zero )
& ( TA @ cl_Groups_Ominus ) )
=> ! [A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ list @ minus_minus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ list @ minus_minus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( D @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(41,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ~ ( A @ ( TA @ set ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_not__in__set__insert) ).
thf(248,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ~ ( A @ ( TA @ set ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(74,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_Diff__iff) ).
thf(380,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( ( ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
& ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(94,axiom,
( ( as @ lbounds )
!= ( int @ list @ ( int @ product_prod ) @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096lbounds_Aas_A_126_061_A_091_093_096) ).
thf(439,plain,
( ( as @ lbounds )
!= ( int @ list @ ( int @ product_prod ) @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(64,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(349,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(13,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_splice_Osimps_I1_J) ).
thf(160,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(77,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list] :
( ! [C: TA] :
( ( B @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( C
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ iprod @ ( TA @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ aa ) ) ) )
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_iprod0__if__coeffs0) ).
thf(392,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list] :
( ! [C: TA] :
( ( B @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( C
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ iprod @ ( TA @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ aa ) ) ) )
= ( TA @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(50,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ finite_finite ) )
=> ? [B: TA @ list] :
( ( B @ ( TA @ set ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_finite__list) ).
thf(297,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ finite_finite ) )
=> ? [B: TA @ list] :
( ( B @ ( TA @ set ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(82,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_set__diff__eq) ).
thf(407,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ ( TA @ combc ) ) ) ) @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(4,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_list_Osimps_I2_J) ).
thf(137,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(36,axiom,
! [TA: $tType] :
( ( ( TA @ cl_Groups_Ominus )
& ( TA @ zero ) )
=> ( TA @ list @ cl_Groups_Ominus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_List_Olist___Groups_Ominus) ).
thf(229,plain,
! [TA: $tType] :
( ( ( TA @ cl_Groups_Ominus )
& ( TA @ zero ) )
=> ( TA @ list @ cl_Groups_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(58,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: bool @ ( TA @ fun )] :
( ( D = C )
=> ( ! [E: TA] :
( ( C @ ( E @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( E @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) )
=> ( ( D @ ( B @ ( TB @ ( TA @ image ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ image ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_image__cong) ).
thf(329,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: bool @ ( TA @ fun ),D: bool @ ( TA @ fun )] :
( ( D = C )
=> ( ! [E: TA] :
( ( C @ ( E @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( E @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) )
=> ( ( D @ ( B @ ( TB @ ( TA @ image ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ image ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(100,axiom,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(456,plain,
! [A: bool,B: bool] :
( ( B @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(67,axiom,
int @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(356,plain,
int @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(16,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ list_all ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_list__all__simps_I2_J) ).
thf(169,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] : ( TA @ nil @ ( A @ ( TA @ list_all ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(87,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ iprod @ ( TA @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_iprod__Nil) ).
thf(420,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list] :
( ( A @ ( TA @ nil @ ( TA @ iprod @ ( TA @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(113,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(499,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: bool @ ( TA @ fun ),B: TC @ ( TA @ fun ),C: TB @ ( TC @ fun )] :
( ( A @ ( B @ ( TC @ ( TA @ image ) ) ) @ ( C @ ( TB @ ( TC @ image ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( TB @ ( TC @ combb ) ) @ ( TB @ ( TA @ fun ) @ ( TC @ ( TA @ fun ) @ fun ) @ ( TB @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ fun ) @ ( TC @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ image ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_image__image) ).
thf(471,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: bool @ ( TA @ fun ),B: TC @ ( TA @ fun ),C: TB @ ( TC @ fun )] :
( ( A @ ( B @ ( TC @ ( TA @ image ) ) ) @ ( C @ ( TB @ ( TC @ image ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( TB @ ( TC @ combb ) ) @ ( TB @ ( TA @ fun ) @ ( TC @ ( TA @ fun ) @ fun ) @ ( TB @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ fun ) @ ( TC @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ image ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(111,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TB] :
( ( A @ ( B @ ( TB @ ( TA @ image ) ) ) @ ( C @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp )
<=> ? [D: TA] :
( ( C
= ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) ) )
& ( A @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_image__iff) ).
thf(488,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TB] :
( ( ? [D: TA] :
( ( C
= ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) ) )
& ( A @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( TB @ ( TA @ image ) ) ) @ ( C @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TB @ ( TA @ image ) ) ) @ ( C @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp )
=> ? [D: TA] :
( ( C
= ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) ) )
& ( A @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ cl_Groups_Ominus )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ minus_minus @ ( TB @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ minus_minus @ ( TB @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_minus__apply) ).
thf(225,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ cl_Groups_Ominus )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ minus_minus @ ( TB @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ minus_minus @ ( TB @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(60,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(339,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( A @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(31,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(212,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(24,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_49_neq__Nil__conv) ).
thf(193,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)],[24]) ).
thf(125,axiom,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TB @ ( TA @ product_prod ),B: TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ ( TA @ fun ),C: TC @ ( TD @ fun ) @ ( TE @ fun )] :
( ( A @ ( B @ ( TD @ ( TE @ product_prod ) @ ( TB @ ( TA @ product_prod_case ) ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) @ ( C @ ( TC @ ( TD @ ( TE @ product_prod_case ) ) @ ( TC @ ( TD @ ( TE @ product_prod ) @ fun ) @ ( TC @ ( TD @ fun ) @ ( TE @ fun ) @ aa ) ) ) @ ( TC @ ( TD @ ( TE @ product_prod ) @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TC @ ( TD @ ( TE @ product_prod_case ) ) @ ( TC @ ( TD @ ( TE @ product_prod ) @ fun ) @ ( TC @ ( TD @ fun ) @ ( TE @ fun ) @ aa ) ) ) @ ( TB @ ( TC @ ( TD @ ( TE @ product_prod ) @ combb ) ) @ ( TC @ ( TB @ fun ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ fun ) @ ( TC @ ( TD @ ( TE @ product_prod ) @ fun ) @ aa ) ) ) @ ( TA @ ( TC @ ( TB @ fun ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ combb ) ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_split__twice) ).
thf(537,plain,
! [TA: $tType,TB: $tType,TC: $tType,TD: $tType,TE: $tType,A: TB @ ( TA @ product_prod ),B: TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ ( TA @ fun ),C: TC @ ( TD @ fun ) @ ( TE @ fun )] :
( ( A @ ( B @ ( TD @ ( TE @ product_prod ) @ ( TB @ ( TA @ product_prod_case ) ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) @ ( C @ ( TC @ ( TD @ ( TE @ product_prod_case ) ) @ ( TC @ ( TD @ ( TE @ product_prod ) @ fun ) @ ( TC @ ( TD @ fun ) @ ( TE @ fun ) @ aa ) ) ) @ ( TC @ ( TD @ ( TE @ product_prod ) @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TC @ ( TD @ ( TE @ product_prod_case ) ) @ ( TC @ ( TD @ ( TE @ product_prod ) @ fun ) @ ( TC @ ( TD @ fun ) @ ( TE @ fun ) @ aa ) ) ) @ ( TB @ ( TC @ ( TD @ ( TE @ product_prod ) @ combb ) ) @ ( TC @ ( TB @ fun ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ fun ) @ ( TC @ ( TD @ ( TE @ product_prod ) @ fun ) @ aa ) ) ) @ ( TA @ ( TC @ ( TB @ fun ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ combb ) ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ ( TA @ fun ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ ( TD @ ( TE @ product_prod ) @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(3,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA @ list,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ combi @ ( TA @ ( TA @ linorder_insort_key ) ) ) ) @ ( C @ ( TA @ combi @ ( TA @ ( TA @ linorder_insort_key ) ) ) ) )
= ( A @ ( C @ ( TA @ combi @ ( TA @ ( TA @ linorder_insort_key ) ) ) ) @ ( B @ ( TA @ combi @ ( TA @ ( TA @ linorder_insort_key ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_insort__left__comm) ).
thf(134,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA @ list,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ combi @ ( TA @ ( TA @ linorder_insort_key ) ) ) ) @ ( C @ ( TA @ combi @ ( TA @ ( TA @ linorder_insort_key ) ) ) ) )
= ( A @ ( C @ ( TA @ combi @ ( TA @ ( TA @ linorder_insort_key ) ) ) ) @ ( B @ ( TA @ combi @ ( TA @ ( TA @ linorder_insort_key ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(69,axiom,
~ ! [A: int] :
~ ! [B: atom] :
( ( as @ ( atom @ set ) @ ( B @ ( atom @ member @ ( bool @ ( bool @ ( atom @ fun ) @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( bool @ ( atom @ fun ) @ aa ) ) ) @ pp )
=> ( xs @ ( A @ ( int @ cons ) ) @ ( B @ i_Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37__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(360,plain,
~ ! [A: int] :
~ ! [B: atom] :
( ( as @ ( atom @ set ) @ ( B @ ( atom @ member @ ( bool @ ( bool @ ( atom @ fun ) @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( bool @ ( atom @ fun ) @ aa ) ) ) @ pp )
=> ( xs @ ( A @ ( int @ cons ) ) @ ( B @ i_Z ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(117,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_right__minus__eq) ).
thf(508,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ cl_Groups_Ominus )
=> ( TA @ ( TB @ fun ) @ cl_Groups_Ominus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Groups_Ominus) ).
thf(398,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ cl_Groups_Ominus )
=> ( TA @ ( TB @ fun ) @ cl_Groups_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(15,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA @ list,B: TA,C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) )
!= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_insort__not__Nil) ).
thf(166,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA @ list,B: TA,C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) )
!= ( TA @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(9,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA,B: TB @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( B @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_insort__key_Osimps_I1_J) ).
thf(148,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA,B: TB @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( B @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(20,axiom,
bool @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(180,plain,
bool @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(96,axiom,
! [A: bool] :
( ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( A @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(444,plain,
! [A: bool] :
( ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ( A @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(88,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_diff__self) ).
thf(423,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(80,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 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( E @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( D @ ( E @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_zipwith0_Osimps_I2_J) ).
thf(402,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 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( E @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( D @ ( E @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(48,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(291,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)],[48]) ).
thf(27,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_not__Cons__self2) ).
thf(204,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(44,axiom,
! [TA: $tType] :
( ( ( TA @ zero )
& ( TA @ cl_Groups_Ominus ) )
=> ( ( TA @ list @ minus_minus )
= ( TA @ minus_minus @ ( TA @ ( TA @ ( TA @ zipwith0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_list__diff__def) ).
thf(259,plain,
! [TA: $tType] :
( ( ( TA @ zero )
& ( TA @ cl_Groups_Ominus ) )
=> ( ( TA @ list @ minus_minus )
= ( TA @ minus_minus @ ( TA @ ( TA @ ( TA @ zipwith0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(413,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(132,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( TA @ set ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_in__set__insert) ).
thf(572,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( TA @ set ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(38,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( A @ ( TA @ collect ) @ ( TA @ finite_finite ) )
| ( B @ ( TA @ collect ) @ ( TA @ finite_finite ) ) )
=> ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) @ ( TA @ finite_finite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_finite__Collect__conjI) ).
thf(236,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( A @ ( TA @ collect ) @ ( TA @ finite_finite ) )
| ( B @ ( TA @ collect ) @ ( TA @ finite_finite ) ) )
=> ( A @ ( B @ ( fconj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) @ ( TA @ finite_finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(21,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_zero__reorient) ).
thf(181,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)],[21]) ).
thf(126,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 ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( D = C ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_list__ex1__iff) ).
thf(540,plain,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( ? [C: TA] :
( ! [D: TA] :
( ( ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( D = C ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( TA @ list_ex1 ) ) ) )
& ( ( A @ ( B @ ( TA @ list_ex1 ) ) )
=> ? [C: TA] :
( ! [D: TA] :
( ( ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set ) @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
=> ( D = C ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(86,axiom,
int @ group_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ogroup__add) ).
thf(419,plain,
int @ group_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(130,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_41_list_Osimps_I5_J) ).
thf(567,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)],[130]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB,C: bool @ ( TA @ fun ),D: TA] :
( ( C @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( B
= ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( C @ ( A @ ( TB @ ( TA @ image ) ) ) @ ( B @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_rev__image__eqI) ).
thf(434,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB,C: bool @ ( TA @ fun ),D: TA] :
( ( C @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( B
= ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( C @ ( A @ ( TB @ ( TA @ image ) ) ) @ ( B @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(29,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_64_splice_Osimps_I3_J) ).
thf(208,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)],[29]) ).
thf(108,axiom,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_diff__0__eq__0) ).
thf(477,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(124,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_DiffD2) ).
thf(535,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ product_prod ),C: TB @ ( TA @ product_prod )] :
( ( C = B )
=> ( ( C @ ( A @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) )
= ( B @ ( A @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_split__weak__cong) ).
thf(323,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC @ ( TB @ fun ) @ ( TA @ fun ),B: TB @ ( TA @ product_prod ),C: TB @ ( TA @ product_prod )] :
( ( C = B )
=> ( ( C @ ( A @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) )
= ( B @ ( A @ ( TC @ ( TB @ ( TA @ product_prod_case ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ fun ) @ ( TC @ ( TB @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TC @ ( TB @ ( TA @ product_prod ) @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(5,axiom,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_insert__Nil) ).
thf(140,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TB] :
( ( A @ ( B @ ( TB @ ( TA @ image ) ) ) @ ( C @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp )
=> ~ ! [D: TA] :
( ( C
= ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) ) )
=> ~ ( A @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_imageE) ).
thf(483,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TB] :
( ( A @ ( B @ ( TB @ ( TA @ image ) ) ) @ ( C @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp )
=> ~ ! [D: TA] :
( ( C
= ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) ) )
=> ~ ( A @ ( D @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(103,axiom,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(462,plain,
! [A: bool,B: bool] :
( ( A @ pp )
| ~ ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(39,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ~ ( A @ ( TA @ set ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( A @ ( TA @ set ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_List_Oinsert__def) ).
thf(240,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ~ ( A @ ( TA @ set ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( A @ ( TA @ set ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(42,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ iprod @ ( TA @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_iprod__Nil2) ).
thf(251,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ iprod @ ( TA @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ ( TA @ list @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(120,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
| ( C = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_set__ConsD) ).
thf(521,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
| ( C = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(93,axiom,
int @ ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(438,plain,
int @ ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(89,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ finite_finite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_finite__Diff) ).
thf(426,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite ) )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ finite_finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(66,axiom,
int @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(355,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(127,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ list @ minus_minus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_list__diff__Nil2) ).
thf(553,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ list @ minus_minus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ finite_finite1 )
& ( TA @ finite_finite1 ) )
=> ( TA @ ( TB @ fun ) @ finite_finite1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).
thf(458,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ finite_finite1 )
& ( TA @ finite_finite1 ) )
=> ( TA @ ( TB @ fun ) @ finite_finite1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(57,axiom,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(327,plain,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ aa ) ) ) @ ( bool @ ( bool @ aa ) ) ) @ pp )
| ~ ( B @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(53,axiom,
! [TA: $tType,A: TA,B: bool @ ( nat @ fun )] :
( ( ~ ( B @ ( nat @ zero_zero @ ( nat @ member @ ( bool @ ( bool @ ( nat @ fun ) @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( bool @ ( nat @ fun ) @ aa ) ) ) @ pp )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil ) ) )
& ( ( B @ ( nat @ zero_zero @ ( nat @ member @ ( bool @ ( bool @ ( nat @ fun ) @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( bool @ ( nat @ fun ) @ aa ) ) ) @ pp )
=> ( ( 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(310,plain,
! [TA: $tType,A: TA,B: bool @ ( nat @ fun )] :
( ( ~ ( B @ ( nat @ zero_zero @ ( nat @ member @ ( bool @ ( bool @ ( nat @ fun ) @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( bool @ ( nat @ fun ) @ aa ) ) ) @ pp )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil ) ) )
& ( ( B @ ( nat @ zero_zero @ ( nat @ member @ ( bool @ ( bool @ ( nat @ fun ) @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( bool @ ( nat @ fun ) @ aa ) ) ) @ pp )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(11,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(154,plain,
! [TA: $tType,A: bool @ ( nat @ fun )] :
( ( A @ ( TA @ nil @ ( TA @ sublist ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(97,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite ) )
=> ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ finite_finite ) )
<=> ( A @ ( TA @ finite_finite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_finite__Diff2) ).
thf(446,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite ) )
=> ( ( ( A @ ( TA @ finite_finite ) )
=> ( B @ ( A @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ finite_finite ) ) )
& ( ( B @ ( A @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TA @ finite_finite ) )
=> ( A @ ( TA @ finite_finite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(6,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Collect__def) ).
thf(143,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA @ list,B: TA,C: TA,D: TB @ ( TA @ fun )] :
( ( ( C @ ( D @ ( TB @ ( TA @ aa ) ) ) )
!= ( B @ ( D @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( C @ ( D @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) @ ( B @ ( D @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) )
= ( A @ ( B @ ( D @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) @ ( C @ ( D @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_insort__key__left__comm) ).
thf(450,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA @ list,B: TA,C: TA,D: TB @ ( TA @ fun )] :
( ( ( C @ ( D @ ( TB @ ( TA @ aa ) ) ) )
!= ( B @ ( D @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( C @ ( D @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) @ ( B @ ( D @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) )
= ( A @ ( B @ ( D @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) @ ( C @ ( D @ ( TB @ ( TA @ linorder_insort_key ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(128,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_minus__nat_Odiff__0) ).
thf(556,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(26,axiom,
bool @ cl_Groups_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ominus) ).
thf(203,plain,
bool @ cl_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(121,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: TA,C: TB @ ( TA @ fun ),D: TB] :
( ( D
= ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TB @ ( TA @ image ) ) ) @ ( D @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_image__eqI) ).
thf(524,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: TA,C: TB @ ( TA @ fun ),D: TB] :
( ( D
= ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TB @ ( TA @ image ) ) ) @ ( D @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(71,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ list_ex1 ) ) )
<=> ( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ list_ex1 ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( C @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ list_all ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_list__ex1__simps_I2_J) ).
thf(368,plain,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( ( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ list_ex1 ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( C @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ list_all ) ) ) ) )
=> ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ list_ex1 ) ) ) )
& ( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ list_ex1 ) ) )
=> ( ( ~ ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( C @ ( TA @ list_ex1 ) ) ) )
& ( ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( C @ ( fNot @ ( TA @ ( bool @ ( bool @ combb ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ list_all ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(104,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ image ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_image__ident) ).
thf(465,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ image ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(37,axiom,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ list_all ) ) )
<=> ! [C: TA] :
( ( A @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_list__all__iff) ).
thf(231,plain,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( ! [C: TA] :
( ( A @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( TA @ list_all ) ) ) )
& ( ( A @ ( B @ ( TA @ list_all ) ) )
=> ! [C: TA] :
( ( A @ ( TA @ set ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(73,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_DiffI) ).
thf(378,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ~ ( A @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(40,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ finite_finite1 )
& ( TA @ finite_finite1 ) )
=> ( TA @ ( TB @ product_prod ) @ finite_finite1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod___Finite__Set_Ofinite) ).
thf(246,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ finite_finite1 )
& ( TA @ finite_finite1 ) )
=> ( TA @ ( TB @ product_prod ) @ finite_finite1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(28,axiom,
nat @ cl_Groups_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ominus) ).
thf(207,plain,
nat @ cl_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(32,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_list__ex1__simps_I1_J) ).
thf(214,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(10,axiom,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_splice__Nil2) ).
thf(151,plain,
! [TA: $tType,A: TA @ list] :
( ( TA @ nil @ ( A @ ( TA @ splice ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(51,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( B = A )
<=> ( ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_eq__iff__diff__eq__0) ).
thf(300,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite ) )
=> ( B @ ( A @ ( TB @ ( TA @ image ) ) ) @ ( TB @ finite_finite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_finite__imageI) ).
thf(432,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( B @ ( TA @ finite_finite ) )
=> ( B @ ( A @ ( TB @ ( TA @ image ) ) ) @ ( TB @ finite_finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(83,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 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( TC @ nil @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TC @ zero_zero @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_zipwith0_Osimps_I4_J) ).
thf(410,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 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( TC @ nil @ ( C @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( TC @ zero_zero @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ cl_Groups_Ominus )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TA] :
( ( C @ ( A @ ( B @ ( TB @ ( TA @ fun ) @ minus_minus @ ( TB @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ minus_minus @ ( TB @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_fun__diff__def) ).
thf(262,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ cl_Groups_Ominus )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TA] :
( ( C @ ( A @ ( B @ ( TB @ ( TA @ fun ) @ minus_minus @ ( TB @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ minus_minus @ ( TB @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(7,axiom,
nat @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(146,plain,
nat @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(81,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_DiffD1) ).
thf(405,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( A @ ( B @ ( bool @ ( TA @ fun ) @ minus_minus @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(23,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_24_list_Osimps_I4_J) ).
thf(190,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)],[23]) ).
thf(49,axiom,
! [A: atom] :
( ( as @ ( atom @ set ) @ ( A @ ( atom @ member @ ( bool @ ( bool @ ( atom @ fun ) @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( bool @ ( atom @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ divisor )
!= ( int @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_norm) ).
thf(294,plain,
! [A: atom] :
( ( as @ ( atom @ set ) @ ( A @ ( atom @ member @ ( bool @ ( bool @ ( atom @ fun ) @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( bool @ ( atom @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ divisor )
!= ( int @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(61,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_diff__0__right) ).
thf(341,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TB @ ( TA @ image ) ) ) @ ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_imageI) ).
thf(506,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: bool @ ( TA @ fun ),C: TA] :
( ( B @ ( C @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( TB @ ( TA @ image ) ) ) @ ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(107,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA @ list,B: TA] :
( ( A @ ( TA @ set ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ combi @ ( TA @ ( TA @ linord2118332866rt_key ) ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_insort__insert__triv) ).
thf(474,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA @ list,B: TA] :
( ( A @ ( TA @ set ) @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ combi @ ( TA @ ( TA @ linord2118332866rt_key ) ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(79,axiom,
! [TA: $tType] :
( ( TA @ finite_finite1 )
=> ! [A: bool @ ( TA @ fun )] : ( A @ ( TA @ finite_finite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_finite__code) ).
thf(400,plain,
! [TA: $tType] :
( ( TA @ finite_finite1 )
=> ! [A: bool @ ( TA @ fun )] : ( A @ ( TA @ finite_finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(122,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ list_all ) ) )
<=> ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_list__all__simps_I1_J) ).
thf(528,plain,
! [TA: $tType,A: TA @ list,B: TA,C: bool @ ( TA @ fun )] :
( ( ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ list_all ) ) ) )
& ( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TA @ list_all ) ) )
=> ( ( A @ ( C @ ( TA @ list_all ) ) )
& ( B @ ( C @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(95,axiom,
! [A: bool] :
( ~ ( A @ pp )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(442,plain,
! [A: bool] :
( ~ ( A @ pp )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(114,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA @ list,B: TA,C: TB @ ( TA @ fun )] :
( ( A @ ( TA @ set ) @ ( C @ ( TB @ ( TA @ image ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( C @ ( TB @ ( TA @ linord2118332866rt_key ) ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_insort__insert__key__triv) ).
thf(501,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ linorder )
=> ! [A: TA @ list,B: TA,C: TB @ ( TA @ fun )] :
( ( A @ ( TA @ set ) @ ( C @ ( TB @ ( TA @ image ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ member @ ( bool @ ( bool @ ( TB @ fun ) @ fun ) @ ( TB @ aa ) ) ) @ ( bool @ ( bool @ ( TB @ fun ) @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( C @ ( TB @ ( TA @ linord2118332866rt_key ) ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(14,axiom,
! [TA: $tType,A: nat @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ list_size ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_list_Osize_I1_J) ).
thf(163,plain,
! [TA: $tType,A: nat @ ( TA @ fun )] :
( ( TA @ nil @ ( A @ ( TA @ list_size ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(25,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_48_list_Oexhaust) ).
thf(200,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)],[25]) ).
thf(43,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) @ ( TA @ finite_finite ) )
<=> ( ( A @ ( TA @ collect ) @ ( TA @ finite_finite ) )
& ( B @ ( TA @ collect ) @ ( TA @ finite_finite ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_finite__Collect__disjI) ).
thf(254,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: bool @ ( TA @ fun )] :
( ( ( ( A @ ( TA @ collect ) @ ( TA @ finite_finite ) )
& ( B @ ( TA @ collect ) @ ( TA @ finite_finite ) ) )
=> ( A @ ( B @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) @ ( TA @ finite_finite ) ) )
& ( ( A @ ( B @ ( fdisj @ ( TA @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ fun ) @ ( TA @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ combs ) ) ) ) @ ( TA @ collect ) @ ( TA @ finite_finite ) )
=> ( ( A @ ( TA @ collect ) @ ( TA @ finite_finite ) )
& ( B @ ( TA @ collect ) @ ( TA @ finite_finite ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(59,axiom,
? [A: int] :
! [B: atom] :
( ( as @ ( atom @ set ) @ ( B @ ( atom @ member @ ( bool @ ( bool @ ( atom @ fun ) @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( bool @ ( atom @ fun ) @ aa ) ) ) @ pp )
=> ( xs @ ( A @ ( int @ cons ) ) @ ( B @ i_Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27__096EX_Ax_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_096) ).
thf(337,plain,
? [A: int] :
! [B: atom] :
( ( as @ ( atom @ set ) @ ( B @ ( atom @ member @ ( bool @ ( bool @ ( atom @ fun ) @ fun ) @ ( atom @ aa ) ) ) @ ( bool @ ( bool @ ( atom @ fun ) @ aa ) ) ) @ pp )
=> ( xs @ ( A @ ( int @ cons ) ) @ ( B @ i_Z ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(112,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 @ list @ ( TC @ list @ fun ) @ ( TB @ list @ aa ) ) ) @ ( TA @ list @ ( TC @ list @ aa ) ) ) )
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_zipwith0_Osimps_I1_J) ).
thf(496,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 @ list @ ( TC @ list @ fun ) @ ( TB @ list @ aa ) ) ) @ ( TA @ list @ ( TC @ list @ aa ) ) ) )
= ( TA @ nil ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(70,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mem__def) ).
thf(364,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ member @ ( bool @ ( bool @ ( TA @ fun ) @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(575,plain,
$false,
inference(e,[status(thm)],[515,177,171,347,518,468,352,385,533,174,288,320,389,570,504,344,357,460,157,559,189,416,228,316,216,376,211,480,147,453,133,428,265,307,248,380,439,349,160,392,297,407,137,229,329,456,356,169,420,499,471,488,225,339,212,193,537,134,360,508,398,166,148,180,444,423,402,291,204,259,413,572,236,181,540,419,567,434,208,477,535,323,140,483,462,240,251,521,438,426,355,553,458,327,310,154,446,143,450,556,203,524,368,465,231,378,246,207,214,151,300,432,410,262,146,405,190,294,341,506,474,400,528,442,501,163,200,254,337,496,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COM088_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.09 % 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
% 0.17/5.43 % Computer : n018.cluster.edu
% 0.17/5.43 % Model : x86_64 x86_64
% 0.17/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.43 % Memory : 8046.5625MB
% 0.17/5.43 % OS : Linux 6.8.0-71-generic
% 0.17/5.43 % CPULimit : 300
% 0.17/5.43 % WCLimit : 300
% 0.17/5.43 % DateTime : Sat Sep 26 23:30:28 UTC 2026
% 0.17/5.43 % CPUTime :
% 0.17/5.43 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
% 0.20/6.03 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.74/6.37 % [INFO] Parsing done (345ms).
% 1.74/6.39 % [INFO] Running in sequential loop mode.
% 2.92/6.78 % [INFO] eprover registered as external prover.
% 2.92/6.78 % [INFO] Scanning for conjecture ...
% 3.30/6.99 % [INFO] Found a conjecture (or negated_conjecture) and 130 axioms. Running axiom selection ...
% 3.62/7.12 % [INFO] Axiom selection finished. Selected 130 axioms (removed 0 axioms).
% 5.23/7.41 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.23/7.44 % [INFO] Type checking passed.
% 5.23/7.45 % [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 ...
% 36.85/26.98 % External prover 'e' found a proof!
% 36.85/26.98 % [INFO] Killing All external provers ...
% 36.85/26.98 % Time passed: 21406ms (effective reasoning time: 20586ms)
% 36.85/26.98 % 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)>
% 36.85/26.99 % Axioms used in derivation (130): help_COMBS_1_1_U, arity_Int_Oint___Groups_Ominus, fact_54_list__all__simps_I1_J, fact_47_list__ex1__iff, fact_19_image__iff, arity_HOL_Obool___Finite__Set_Ofinite, fact_44_set__ConsD, help_fconj_3_1_U, fact_45_list_Osimps_I3_J, fact_41_list_Osimps_I5_J, fact_4_finite__Collect__conjI, help_COMBI_1_1_U, fact_9_image__image, fact_58_List_Oinsert__def, fact_30_Diff__iff, fact_95_insort__key__left__comm, arity_HOL_Obool___Groups_Ominus, fact_37__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_12_split__weak__cong, fact_77_right__minus__eq, fact_91_list_Osize_I1_J, fact_82_sublist__nil, fact_75_mem__def, fact_43_DiffD2, arity_Int_Oint___Rings_Oring, fact_56_list__all__iff, fact_87_diff__0__eq__0, fact_67_zipwith0_Osimps_I4_J, fact_33_DiffE, help_fNot_2_1_U, fact_1_finite__imageI, fact_36_list__diff__Cons__Cons, fact_93_insort__key_Osimps_I1_J, help_fNot_1_1_U, fact_2_finite__set, arity_HOL_Obool___Orderings_Olinorder, fact_7_iprod__left__diff__distrib, fact_74_ext, fact_98_sort__key__simps_I2_J, fact_38_not__Cons__self, fact_26_list__diff__def, arity_List_Olist___Groups_Ominus, fact_0__096lbounds_Aas_A_126_061_A_091_093_096, help_COMBB_1_1_U, fact_42_DiffD1, arity_Nat_Onat___Orderings_Olinorder, help_fdisj_1_1_U, fact_32_DiffI, fact_76_Collect__def, help_fconj_2_1_U, fact_28_list__ex1__simps_I1_J, fact_81_insort__insert__key__triv, fact_55_list__all__simps_I2_J, fact_90_diffs0__imp__equal, fact_97_insort__insert__insort, fact_34_zipwith0_Osimps_I2_J, fact_15_finite__Diff2, fact_8_split__twice, fact_66_iprod__Nil2, fact_3_finite__Collect__disjI, fact_51_minus__apply, fact_48_list_Oexhaust, fact_29_list_Oinject, fact_83_in__set__sublistD, fact_57_in__set__insert, fact_59_not__in__set__insert, arity_Int_Oint___Orderings_Olinorder, fact_96_insort__left__comm, fact_23_image__cong, help_fequal_1_1_T, arity_fun___Finite__Set_Ofinite, fact_49_neq__Nil__conv, arity_Nat_Onat___Groups_Ozero, fact_79_diff__0__right, help_fdisj_2_1_U, fact_61_splice_Osimps_I2_J, fact_68_splice__Nil2, fact_24_list_Osimps_I4_J, fact_46_list_Osimps_I2_J, fact_69_splice_Osimps_I1_J, fact_63_zipwith0_Osimps_I3_J, arity_Int_Oint___Groups_Ogroup__add, fact_80_sublist__singleton, fact_85_insort__insert__triv, fact_14_list__diff__Nil2, fact_62_norm, help_COMBC_1_1_U, fact_92_insort__insert__insort__key, fact_89_minus__nat_Odiff__0, fact_53_list__ex1__simps_I2_J, fact_17_rev__image__eqI, fact_70_diff__self, fact_31_Diff__idemp, fact_11_pigeonhole__infinite, fact_21_finite__list, arity_prod___Finite__Set_Ofinite, fact_6_finite__code, help_fequal_2_1_T, help_fconj_1_1_U, fact_25_x, help_fdisj_3_1_U, fact_72_zero__reorient, fact_16_finite, fact_86_diff__self__eq__0, fact_88_diff__commute, fact_84_notin__set__sublistI, fact_60_list__all__cong, fact_13_finite__Diff, fact_65_iprod__Nil, fact_39_not__Cons__self2, fact_52_insert__Nil, fact_20_imageE, fact_18_imageI, help_pp_1_1_U, fact_50_fun__diff__def, arity_Int_Oint___Groups_Ozero, fact_78_eq__iff__diff__eq__0, fact_94_insort__not__Nil, help_pp_2_1_U, fact_35_zipwith0_Osimps_I1_J, arity_Nat_Onat___Groups_Ominus, fact_71_iprod0__if__coeffs0, fact_64_splice_Osimps_I3_J, arity_fun___Groups_Ominus, fact_10_image__ident, fact_73_diff__eq__diff__eq, fact_22_internal__split__def, fact_40_set__diff__eq, fact_5_image__eqI, fact_27__096EX_Ax_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_096
% 36.85/26.99 % No. of inferences in proof: 264
% 36.85/26.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 21406 ms resp. 20586 ms w/o parsing
% 38.04/27.14 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 38.04/27.14 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------