%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM122_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 : n011.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 06:58:03 AM UTC 2026
% Result : Theorem 23.55s 10.36s
% Output : Refutation 24.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 116
% Syntax : Number of formulae : 234 ( 90 unt; 0 typ; 0 def)
% Number of atoms : 699 ( 259 equ; 0 cnn)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 3113 ( 88 ~; 10 |; 69 &;2712 @)
% ( 31 <=>; 203 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 46 usr; 9 con; 0-4 aty)
% Number of variables : 512 ( 0 ^; 481 !; 31 ?; 512 :)
% 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(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(ring_1_decl,type,
ring_1:
!>[TA: $tType] : $o ).
thf(sgn_if_decl,type,
sgn_if:
!>[TA: $tType] : $o ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(zero_neq_one_decl,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linordered_semidom_decl,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(combi_decl,type,
combi:
!>[TA: $tType] : ( TA @ ( TA @ fun ) ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(sgn_sgn_decl,type,
sgn_sgn:
!>[TA: $tType] : ( TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(iszero_decl,type,
iszero:
!>[TA: $tType] : ( TA > $o ) ).
thf(ring_1_of_int_decl,type,
ring_1_of_int:
!>[TA: $tType] : ( int > TA ) ).
thf(listMem_decl,type,
listMem:
!>[TA: $tType] : ( TA > ( TA @ list ) > $o ) ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(nil_decl,type,
nil:
!>[TA: $tType] : ( TA @ list ) ).
thf(list_ex1_decl,type,
list_ex1:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( TA @ list ) > $o ) ).
thf(map_decl,type,
map:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > ( TB @ list ) > ( TA @ list ) ) ).
thf(member1_decl,type,
member1:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( TA @ list @ fun ) ) ).
thf(set_decl,type,
set:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( TA @ list @ fun ) ) ).
thf(sublist_decl,type,
sublist:
!>[TA: $tType] : ( ( TA @ list ) > ( bool @ ( nat @ fun ) ) > ( TA @ list ) ) ).
thf(semiring_1_Nats_decl,type,
semiring_1_Nats:
!>[TA: $tType] : ( bool @ ( TA @ fun ) ) ).
thf(size_size_decl,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(asubst_decl,type,
asubst: int > ( int @ list ) > atom > atom ).
thf(dvd_decl,type,
dvd: int > int > ( int @ list ) > atom ).
thf(atom_size_decl,type,
atom_size: atom > nat ).
thf(decr_Z_decl,type,
decr_Z: atom > atom ).
thf(divisor_decl,type,
divisor: atom > int ).
thf(hd_coeff_decl,type,
hd_coeff: int @ ( atom @ fun ) ).
thf(hd_coeff1_decl,type,
hd_coeff1: int > ( atom @ ( atom @ fun ) ) ).
thf(zlcms_decl,type,
zlcms: ( int @ list ) > int ).
thf(qEpres1907640072oeffs1_decl,type,
qEpres1907640072oeffs1: ( atom @ list ) > ( atom @ list ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(a_decl,type,
a: atom ).
thf(as_decl,type,
as: atom @ list ).
thf(b_decl,type,
b: atom ).
thf(1,conjecture,
( ( b @ ( hd_coeff @ ( int @ ( atom @ aa ) ) ) )
!= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( ( b @ ( hd_coeff @ ( int @ ( atom @ aa ) ) ) )
!= ( int @ zero_zero ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(118,plain,
~ ( ( ( b @ ( hd_coeff @ ( int @ ( atom @ aa ) ) ) )
!= ( int @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( TA @ semiring_1_Nats @ ( TA @ one_one @ ( TA @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Nats__1) ).
thf(140,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( TA @ semiring_1_Nats @ ( TA @ one_one @ ( TA @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
nat @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(145,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(36,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(249,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(65,axiom,
int @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(365,plain,
int @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(8,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_list__ex1__simps_I1_J) ).
thf(138,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
~ ( TA @ nil @ ( A @ ( TA @ list_ex1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(69,axiom,
! [A: atom] :
( ( ( A @ ( hd_coeff @ ( int @ ( atom @ aa ) ) ) )
= ( int @ zero_zero ) )
=> ( ( ( A @ divisor )
!= ( int @ zero_zero ) )
=> ( ( A @ decr_Z @ divisor )
!= ( int @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Z_Oanormal__decr) ).
thf(379,plain,
! [A: atom] :
( ( ( A @ ( hd_coeff @ ( int @ ( atom @ aa ) ) ) )
= ( int @ zero_zero ) )
=> ( ( ( A @ divisor )
!= ( int @ zero_zero ) )
=> ( ( A @ decr_Z @ divisor )
!= ( int @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(41,axiom,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ map ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_map__ident) ).
thf(269,plain,
! [TA: $tType,A: TA @ list] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ map ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(27,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(217,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(44,axiom,
! [TA: $tType] :
( ( TA @ ring_char_0 )
=> ! [A: int] :
( ( ( TA @ zero_zero )
= ( A @ ( TA @ ring_1_of_int ) ) )
<=> ( A
= ( int @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_of__int__0__eq__iff) ).
thf(276,plain,
! [TA: $tType] :
( ( TA @ ring_char_0 )
=> ! [A: int] :
( ( ( A
= ( int @ zero_zero ) )
=> ( ( TA @ zero_zero )
= ( A @ ( TA @ ring_1_of_int ) ) ) )
& ( ( ( TA @ zero_zero )
= ( A @ ( TA @ ring_1_of_int ) ) )
=> ( A
= ( int @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(108,axiom,
! [A: int @ list] :
( ( ( A @ zlcms )
= ( int @ zero_zero ) )
<=> ( A @ ( int @ set @ ( bool @ ( int @ fun ) @ ( int @ list @ aa ) ) ) @ ( int @ zero_zero @ ( int @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_zlcms0__iff) ).
thf(550,plain,
! [A: int @ list] :
( ( ( A @ ( int @ set @ ( bool @ ( int @ fun ) @ ( int @ list @ aa ) ) ) @ ( int @ zero_zero @ ( int @ member ) ) )
=> ( ( A @ zlcms )
= ( int @ zero_zero ) ) )
& ( ( ( A @ zlcms )
= ( int @ zero_zero ) )
=> ( A @ ( int @ set @ ( bool @ ( int @ fun ) @ ( int @ list @ aa ) ) ) @ ( int @ zero_zero @ ( int @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(10,axiom,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_linorder__neqE__nat) ).
thf(142,plain,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ( ( int @ one_one @ ( TA @ ring_1_of_int ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_of__int__1) ).
thf(472,plain,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ( ( int @ one_one @ ( TA @ ring_1_of_int ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(74,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(404,plain,
! [TA: $tType,A: TA] :
( ( A @ ( TA @ combi @ ( TA @ ( TA @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(47,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( TA @ zero_zero @ ( TA @ iszero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_iszero__0) ).
thf(288,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( TA @ zero_zero @ ( TA @ iszero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(22,axiom,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( B @ ( C @ ( TA @ listMem ) ) )
=> ( B @ ( A @ ( TA @ cons ) ) @ ( C @ ( TA @ listMem ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_insert) ).
thf(184,plain,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( B @ ( C @ ( TA @ listMem ) ) )
=> ( B @ ( A @ ( TA @ cons ) ) @ ( C @ ( TA @ listMem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(115,axiom,
! [A: atom @ list] :
( ( A @ qEpres1907640072oeffs1 )
= ( A @ ( A @ ( hd_coeff @ ( int @ ( atom @ map ) ) ) @ zlcms @ hd_coeff1 @ ( atom @ ( atom @ map ) ) ) @ ( int @ nil @ ( int @ one_one @ ( int @ cons ) ) @ ( int @ zero_zero @ ( A @ ( hd_coeff @ ( int @ ( atom @ map ) ) ) @ zlcms @ dvd ) ) @ ( atom @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_hd__coeffs1__def) ).
thf(587,plain,
! [A: atom @ list] :
( ( A @ qEpres1907640072oeffs1 )
= ( A @ ( A @ ( hd_coeff @ ( int @ ( atom @ map ) ) ) @ zlcms @ hd_coeff1 @ ( atom @ ( atom @ map ) ) ) @ ( int @ nil @ ( int @ one_one @ ( int @ cons ) ) @ ( int @ zero_zero @ ( A @ ( hd_coeff @ ( int @ ( atom @ map ) ) ) @ zlcms @ dvd ) ) @ ( atom @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(16,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_33_list_Oinject) ).
thf(157,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)],[16]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ fun )] :
( ( TB @ nil @ ( A @ ( TA @ ( TB @ map ) ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_map_Osimps_I1_J) ).
thf(189,plain,
! [TA: $tType,TB: $tType,A: TA @ ( TB @ fun )] :
( ( TB @ nil @ ( A @ ( TA @ ( TB @ map ) ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(77,axiom,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ one_one )
!= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_one__neq__zero) ).
thf(416,plain,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ one_one )
!= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(55,axiom,
! [A: atom] :
( ( as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( A @ ( atom @ member ) ) )
=> ( ( A @ divisor )
!= ( int @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_div0) ).
thf(325,plain,
! [A: atom] :
( ( as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( A @ ( atom @ member ) ) )
=> ( ( A @ divisor )
!= ( int @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(32,axiom,
! [A: atom,B: int @ list,C: int] :
( ( A @ ( B @ ( C @ asubst ) ) @ divisor )
= ( A @ divisor ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_divisor__asubst) ).
thf(228,plain,
! [A: atom,B: int @ list,C: int] :
( ( A @ ( B @ ( C @ asubst ) ) @ divisor )
= ( A @ divisor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(38,axiom,
! [TA: $tType,A: TA @ list,B: TA] : ( A @ ( B @ ( TA @ cons ) ) @ ( B @ ( TA @ listMem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_elem) ).
thf(261,plain,
! [TA: $tType,A: TA @ list,B: TA] : ( A @ ( B @ ( TA @ cons ) ) @ ( B @ ( TA @ listMem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(93,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_less__nat__zero__code) ).
thf(475,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun ),C: TB @ list,D: TB] :
( ( ( C @ ( D @ ( TB @ cons ) ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) ) ) ) )
<=> ? [E: TA,F: TA @ list] :
( ( C
= ( F @ ( B @ ( TB @ ( TA @ map ) ) ) ) )
& ( D
= ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) ) )
& ( A
= ( F @ ( E @ ( TA @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Cons__eq__map__conv) ).
thf(492,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun ),C: TB @ list,D: TB] :
( ( ? [E: TA,F: TA @ list] :
( ( C
= ( F @ ( B @ ( TB @ ( TA @ map ) ) ) ) )
& ( D
= ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) ) )
& ( A
= ( F @ ( E @ ( TA @ cons ) ) ) ) )
=> ( ( C @ ( D @ ( TB @ cons ) ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TB @ cons ) ) )
= ( A @ ( B @ ( TB @ ( TA @ map ) ) ) ) )
=> ? [E: TA,F: TA @ list] :
( ( C
= ( F @ ( B @ ( TB @ ( TA @ map ) ) ) ) )
& ( D
= ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) ) )
& ( A
= ( F @ ( E @ ( TA @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(20,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_72_list_Oexhaust) ).
thf(179,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)],[20]) ).
thf(34,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_less__not__refl) ).
thf(238,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(3,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_not__Cons__self) ).
thf(121,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(29,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_less__irrefl__nat) ).
thf(221,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(49,axiom,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ list_ex1 ) ) )
<=> ? [C: TA] :
( ! [D: TA] :
( ( ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ member ) ) ) )
=> ( D = C ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_list__ex1__iff) ).
thf(293,plain,
! [TA: $tType,A: TA @ list,B: bool @ ( TA @ fun )] :
( ( ? [C: TA] :
( ! [D: TA] :
( ( ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ member ) ) ) )
=> ( D = C ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) ) )
=> ( A @ ( B @ ( TA @ list_ex1 ) ) ) )
& ( ( A @ ( B @ ( TA @ list_ex1 ) ) )
=> ? [C: TA] :
( ! [D: TA] :
( ( ( D @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ member ) ) ) )
=> ( D = C ) )
& ( C @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp )
& ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TA @ list,D: TA @ list] :
( ( D = C )
=> ( ! [E: TA] :
( ( C @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( E @ ( TA @ member ) ) )
=> ( ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( E @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) )
=> ( ( D @ ( B @ ( TB @ ( TA @ map ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ map ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_map__cong) ).
thf(396,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TA @ list,D: TA @ list] :
( ( D = C )
=> ( ! [E: TA] :
( ( C @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( E @ ( TA @ member ) ) )
=> ( ( E @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( E @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) )
=> ( ( D @ ( B @ ( TB @ ( TA @ map ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ map ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(100,axiom,
! [TA: $tType,A: TA @ ( TA @ fun ),B: TA @ list] :
( ! [C: TA] :
( ( B @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) )
=> ( ( C @ ( A @ ( TA @ ( TA @ aa ) ) ) )
= C ) )
=> ( ( B @ ( A @ ( TA @ ( TA @ map ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_map__idI) ).
thf(507,plain,
! [TA: $tType,A: TA @ ( TA @ fun ),B: TA @ list] :
( ! [C: TA] :
( ( B @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) )
=> ( ( C @ ( A @ ( TA @ ( TA @ aa ) ) ) )
= C ) )
=> ( ( B @ ( A @ ( TA @ ( TA @ map ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(66,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ~ ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_not__in__set__insert) ).
thf(366,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ~ ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(104,axiom,
! [A: int,B: int,C: int] :
( ( int @ nil @ ( A @ ( B @ dvd ) ) @ ( C @ hd_coeff1 @ ( atom @ ( atom @ aa ) ) ) )
= ( int @ nil @ ( A @ ( B @ dvd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_hd__coeff1_Osimps_I5_J) ).
thf(534,plain,
! [A: int,B: int,C: int] :
( ( int @ nil @ ( A @ ( B @ dvd ) ) @ ( C @ hd_coeff1 @ ( atom @ ( atom @ aa ) ) ) )
= ( int @ nil @ ( A @ ( B @ dvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(58,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_sgn__pos) ).
thf(334,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ one_one ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(81,axiom,
( a
= ( b @ ( as @ ( hd_coeff @ ( int @ ( atom @ map ) ) ) @ zlcms @ hd_coeff1 @ ( atom @ ( atom @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__096a_A_061_Ahd__coeff1_A_Izlcms_A_Imap_Ahd__coeff_Aas_J_J_Ab_096) ).
thf(429,plain,
( a
= ( b @ ( as @ ( hd_coeff @ ( int @ ( atom @ map ) ) ) @ zlcms @ hd_coeff1 @ ( atom @ ( atom @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(25,axiom,
! [A: int @ list,B: int,C: int,D: int @ list,E: int,F: int] :
( ( ( D @ ( E @ ( F @ dvd ) ) )
= ( A @ ( B @ ( C @ dvd ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_atom_Osimps_I2_J) ).
thf(192,plain,
! [A: int @ list,B: int,C: int,D: int @ list,E: int,F: int] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ dvd ) ) )
= ( A @ ( B @ ( C @ dvd ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ dvd ) ) )
= ( A @ ( B @ ( C @ dvd ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(75,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_neq0__conv) ).
thf(407,plain,
! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) )
& ( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(43,axiom,
int @ linordered_semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
thf(275,plain,
int @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(7,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(137,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(95,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_mem__def) ).
thf(484,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member ) ) ) )
& ( ( A @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(64,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ listMem ) ) )
<=> ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_ListMem__iff) ).
thf(361,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( A @ ( B @ ( TA @ listMem ) ) ) )
& ( ( A @ ( B @ ( TA @ listMem ) ) )
=> ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(87,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_not__less0) ).
thf(461,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(46,axiom,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ( ( int @ zero_zero @ ( TA @ ring_1_of_int ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_of__int__0) ).
thf(285,plain,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ( ( int @ zero_zero @ ( TA @ ring_1_of_int ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(30,axiom,
nat @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(224,plain,
nat @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(62,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_zero__less__one) ).
thf(356,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(117,axiom,
as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( b @ ( atom @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096b_A_058_Aset_Aas_096) ).
thf(593,plain,
as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( b @ ( atom @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(79,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_gr__implies__not0) ).
thf(420,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(56,axiom,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ dvd ) ) @ atom_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_atom_Osize_I2_J) ).
thf(328,plain,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ dvd ) ) @ atom_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(96,axiom,
int @ sgn_if,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Osgn__if) ).
thf(488,plain,
int @ sgn_if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(105,axiom,
~ ! [A: atom] :
( ( as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( A @ ( atom @ member ) ) )
=> ( a
!= ( A @ ( as @ ( hd_coeff @ ( int @ ( atom @ map ) ) ) @ zlcms @ hd_coeff1 @ ( atom @ ( atom @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__096_B_Bthesis_O_A_I_B_Bb_O_A_091_124_Ab_A_058_Aset_Aas_059_Aa_A_061_Ahd__coeff1_A_Izlcms_A_Imap_Ahd__coeff_Aas_J_J_Ab_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(537,plain,
~ ! [A: atom] :
( ( as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( A @ ( atom @ member ) ) )
=> ( a
!= ( A @ ( as @ ( hd_coeff @ ( int @ ( atom @ map ) ) ) @ zlcms @ hd_coeff1 @ ( atom @ ( atom @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(97,axiom,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ dvd ) ) @ ( atom @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_atom_Osize_I5_J) ).
thf(489,plain,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ dvd ) ) @ ( atom @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(116,axiom,
! [TA: $tType,A: TA @ list,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) )
=> ( ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) )
| ( C = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_set__ConsD) ).
thf(590,plain,
! [TA: $tType,A: TA @ list,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) )
=> ( ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ member ) ) )
| ( C = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(4,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ sgn_sgn ) @ ( TA @ sgn_sgn ) )
= ( A @ ( TA @ sgn_sgn ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_sgn__sgn) ).
thf(124,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ sgn_sgn ) @ ( TA @ sgn_sgn ) )
= ( A @ ( TA @ sgn_sgn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(31,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_list_Osimps_I2_J) ).
thf(225,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( TA @ nil )
!= ( A @ ( B @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(68,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_zero__reorient) ).
thf(371,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)],[68]) ).
thf(99,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( ( A @ ( B @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( B @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_List_Omember__def) ).
thf(503,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( ( ( B @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ member ) ) )
=> ( A @ ( B @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( A @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(6,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_linorder__neqE__linordered__idom) ).
thf(134,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(60,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_sgn__0__0) ).
thf(343,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(40,axiom,
! [TA: $tType] :
( ( TA @ member1 )
= ( TA @ set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_member__set) ).
thf(266,plain,
! [TA: $tType] :
( ( TA @ member1 )
= ( TA @ set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(51,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_in__set__member) ).
thf(311,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ( B @ ( A @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) ) )
& ( ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ list] :
( ? [C: TA @ list] :
( B
= ( C @ ( A @ ( TB @ ( TA @ map ) ) ) ) )
<=> ! [C: TB] :
( ( B @ ( TB @ set @ ( bool @ ( TB @ fun ) @ ( TB @ list @ aa ) ) ) @ ( C @ ( TB @ member ) ) )
=> ? [D: TA] :
( C
= ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_ex__map__conv) ).
thf(558,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ list] :
( ( ! [C: TB] :
( ( B @ ( TB @ set @ ( bool @ ( TB @ fun ) @ ( TB @ list @ aa ) ) ) @ ( C @ ( TB @ member ) ) )
=> ? [D: TA] :
( C
= ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) )
=> ? [C: TA @ list] :
( B
= ( C @ ( A @ ( TB @ ( TA @ map ) ) ) ) ) )
& ( ? [C: TA @ list] :
( B
= ( C @ ( A @ ( TB @ ( TA @ map ) ) ) ) )
=> ! [C: TB] :
( ( B @ ( TB @ set @ ( bool @ ( TB @ fun ) @ ( TB @ list @ aa ) ) ) @ ( C @ ( TB @ member ) ) )
=> ? [D: TA] :
( C
= ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(80,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: int,B: int] :
( ( A @ ( TA @ ring_1_of_int ) @ ( B @ ( TA @ ring_1_of_int ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_of__int__less__iff) ).
thf(425,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( TA @ ring_1_of_int ) @ ( B @ ( TA @ ring_1_of_int ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ ring_1_of_int ) @ ( B @ ( TA @ ring_1_of_int ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(101,axiom,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ cons ) ) @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( ( A @ ( B @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_member__rec_I1_J) ).
thf(513,plain,
! [TA: $tType,A: TA,B: TA @ list,C: TA] :
( ( ( ( A @ ( B @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( C = A ) )
=> ( A @ ( B @ ( C @ ( TA @ cons ) ) @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( C @ ( TA @ cons ) ) @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( ( A @ ( B @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(17,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(166,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(112,axiom,
! [A: int,B: int,C: int @ list,D: int] :
( ( int @ nil @ ( A @ ( B @ dvd ) ) @ ( C @ ( D @ asubst ) ) )
= ( int @ nil @ ( A @ ( B @ dvd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_asubst_Osimps_I5_J) ).
thf(573,plain,
! [A: int,B: int,C: int @ list,D: int] :
( ( int @ nil @ ( A @ ( B @ dvd ) ) @ ( C @ ( D @ asubst ) ) )
= ( int @ nil @ ( A @ ( B @ dvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(84,axiom,
! [TA: $tType,A: TA] :
~ ( A @ ( TA @ nil @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_member__rec_I2_J) ).
thf(444,plain,
! [TA: $tType,A: TA] :
~ ( A @ ( TA @ nil @ ( TA @ member1 @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(72,axiom,
! [A: int @ list] :
( ! [B: int] :
( ( A @ ( int @ set @ ( bool @ ( int @ fun ) @ ( int @ list @ aa ) ) ) @ ( B @ ( int @ member ) ) )
=> ( B
!= ( int @ zero_zero ) ) )
=> ( A @ zlcms @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_zlcms__pos) ).
thf(391,plain,
! [A: int @ list] :
( ! [B: int] :
( ( A @ ( int @ set @ ( bool @ ( int @ fun ) @ ( int @ list @ aa ) ) ) @ ( B @ ( int @ member ) ) )
=> ( B
!= ( int @ zero_zero ) ) )
=> ( A @ zlcms @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TA @ list,C: TB @ ( TA @ fun )] :
( ( ( B @ ( C @ ( TB @ ( TA @ map ) ) ) )
= ( B @ ( A @ ( TB @ ( TA @ map ) ) ) ) )
<=> ! [D: TA] :
( ( B @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ member ) ) )
=> ( ( D @ ( C @ ( TB @ ( TA @ aa ) ) ) )
= ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_map__eq__conv) ).
thf(382,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TA @ list,C: TB @ ( TA @ fun )] :
( ( ! [D: TA] :
( ( B @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ member ) ) )
=> ( ( D @ ( C @ ( TB @ ( TA @ aa ) ) ) )
= ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) )
=> ( ( B @ ( C @ ( TB @ ( TA @ map ) ) ) )
= ( B @ ( A @ ( TB @ ( TA @ map ) ) ) ) ) )
& ( ( ( B @ ( C @ ( TB @ ( TA @ map ) ) ) )
= ( B @ ( A @ ( TB @ ( TA @ map ) ) ) ) )
=> ! [D: TA] :
( ( B @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ member ) ) )
=> ( ( D @ ( C @ ( TB @ ( TA @ aa ) ) ) )
= ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(111,axiom,
as @ qEpres1907640072oeffs1 @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( a @ ( atom @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_a) ).
thf(572,plain,
as @ qEpres1907640072oeffs1 @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( a @ ( atom @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(90,axiom,
! [A: atom] :
( ( as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( A @ ( atom @ member ) ) )
=> ( ( A @ ( hd_coeff @ ( int @ ( atom @ aa ) ) ) )
!= ( int @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_hd0) ).
thf(466,plain,
! [A: atom] :
( ( as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( A @ ( atom @ member ) ) )
=> ( ( A @ ( hd_coeff @ ( int @ ( atom @ aa ) ) ) )
!= ( int @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(61,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ~ ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_List_Oinsert__def) ).
thf(350,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( ~ ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(78,axiom,
int @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(419,plain,
int @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ sgn_sgn ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_sgn__greater) ).
thf(318,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( TA @ sgn_sgn ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ sgn_sgn ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ list,D: TA @ ( TB @ fun )] :
( ( ( C @ ( D @ ( TA @ ( TB @ map ) ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
<=> ? [E: TB,F: TB @ list] :
( ( ( F @ ( D @ ( TA @ ( TB @ map ) ) ) )
= A )
& ( ( E @ ( D @ ( TA @ ( TB @ aa ) ) ) )
= B )
& ( C
= ( F @ ( E @ ( TB @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_map__eq__Cons__conv) ).
thf(521,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ list,D: TA @ ( TB @ fun )] :
( ( ? [E: TB,F: TB @ list] :
( ( ( F @ ( D @ ( TA @ ( TB @ map ) ) ) )
= A )
& ( ( E @ ( D @ ( TA @ ( TB @ aa ) ) ) )
= B )
& ( C
= ( F @ ( E @ ( TB @ cons ) ) ) ) )
=> ( ( C @ ( D @ ( TA @ ( TB @ map ) ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ ( TB @ map ) ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
=> ? [E: TB,F: TB @ list] :
( ( ( F @ ( D @ ( TA @ ( TB @ map ) ) ) )
= A )
& ( ( E @ ( D @ ( TA @ ( TB @ aa ) ) ) )
= B )
& ( C
= ( F @ ( E @ ( TB @ cons ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(50,axiom,
? [A: atom] :
( ( a
= ( A @ ( as @ ( hd_coeff @ ( int @ ( atom @ map ) ) ) @ zlcms @ hd_coeff1 @ ( atom @ ( atom @ aa ) ) ) ) )
& ( as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( A @ ( atom @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096EX_Ab_058set_Aas_O_Aa_A_061_Ahd__coeff1_A_Izlcms_A_Imap_Ahd__coeff_Aas_J_J_Ab_096) ).
thf(306,plain,
? [A: atom] :
( ( a
= ( A @ ( as @ ( hd_coeff @ ( int @ ( atom @ map ) ) ) @ zlcms @ hd_coeff1 @ ( atom @ ( atom @ aa ) ) ) ) )
& ( as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( A @ ( atom @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TA @ list] :
( ! [D: TA] :
( ( C @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ member ) ) )
=> ( ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) )
=> ( ( C @ ( B @ ( TB @ ( TA @ map ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ map ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_map__ext) ).
thf(431,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TA @ list] :
( ! [D: TA] :
( ( C @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( D @ ( TA @ member ) ) )
=> ( ( D @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( D @ ( A @ ( TB @ ( TA @ aa ) ) ) ) ) )
=> ( ( C @ ( B @ ( TB @ ( TA @ map ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ map ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(35,axiom,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( TA @ one_one )
= A )
<=> ( A
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_one__reorient) ).
thf(241,plain,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( A
= ( TA @ one_one ) )
=> ( ( TA @ one_one )
= A ) )
& ( ( ( TA @ one_one )
= A )
=> ( A
= ( TA @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(114,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ iszero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_iszero__def) ).
thf(580,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( A @ ( TA @ iszero ) ) )
& ( ( A @ ( TA @ iszero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(13,axiom,
nat @ linordered_semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(150,plain,
nat @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(39,axiom,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ dvd ) ) @ divisor )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_divisor_Osimps_I2_J) ).
thf(263,plain,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ dvd ) ) @ divisor )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(21,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ~ ( TA @ one_one @ ( TA @ iszero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_not__iszero__1) ).
thf(182,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ~ ( TA @ one_one @ ( TA @ iszero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(57,axiom,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ zero_zero )
!= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_zero__neq__one) ).
thf(331,plain,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ zero_zero )
!= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(5,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_75_neq__Nil__conv) ).
thf(127,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)],[5]) ).
thf(113,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: int] :
( ( A @ ( TA @ ring_1_of_int ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_of__int__0__less__iff) ).
thf(576,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: int] :
( ( ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( A @ ( TA @ ring_1_of_int ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ ring_1_of_int ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(15,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_not__Cons__self2) ).
thf(154,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(19,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_less__not__refl3) ).
thf(175,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(85,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: int] :
( ( TA @ zero_zero @ ( A @ ( TA @ ring_1_of_int ) @ ( TA @ ord_less ) ) )
<=> ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_of__int__less__0__iff) ).
thf(446,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: int] :
( ( ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ring_1_of_int ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( TA @ ring_1_of_int ) @ ( TA @ ord_less ) ) )
=> ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(86,axiom,
! [A: bool @ ( nat @ fun ) @ ( nat @ fun ),B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C @ ( B @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_nat__less__cases) ).
thf(450,plain,
! [A: bool @ ( nat @ fun ) @ ( nat @ fun ),B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C @ ( B @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(28,axiom,
! [TA: $tType,A: bool @ ( nat @ fun )] :
( ( A @ ( TA @ nil @ ( TA @ sublist ) ) )
= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_sublist__nil) ).
thf(218,plain,
! [TA: $tType,A: bool @ ( nat @ fun )] :
( ( A @ ( TA @ nil @ ( TA @ sublist ) ) )
= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(37,axiom,
! [A: nat,B: nat] :
( ( B != A )
<=> ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_nat__neq__iff) ).
thf(250,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(89,axiom,
int @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(465,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(33,axiom,
! [TA: $tType] :
( ( TA @ ring_char_0 )
=> ! [A: int,B: int] :
( ( ( B @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ ring_1_of_int ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_of__int__eq__iff) ).
thf(231,plain,
! [TA: $tType] :
( ( TA @ ring_char_0 )
=> ! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ ring_1_of_int ) ) ) )
& ( ( ( B @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ ring_1_of_int ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(71,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(390,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(23,axiom,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_insert__Nil) ).
thf(186,plain,
! [TA: $tType,A: TA] :
( ( TA @ nil @ ( A @ ( TA @ insert ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(110,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ sgn_sgn ) @ ( TA @ ord_less ) ) )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_sgn__less) ).
thf(568,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ sgn_sgn ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( TA @ sgn_sgn ) @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(48,axiom,
! [TA: $tType] :
( ( TA @ sgn_if )
=> ( ( TA @ zero_zero @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_sgn0) ).
thf(290,plain,
! [TA: $tType] :
( ( TA @ sgn_if )
=> ( ( TA @ zero_zero @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(94,axiom,
! [TA: $tType,A: TA,B: bool @ ( nat @ fun )] :
( ( ~ ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil ) ) )
& ( ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_sublist__singleton) ).
thf(478,plain,
! [TA: $tType,A: TA,B: bool @ ( nat @ fun )] :
( ( ~ ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil ) ) )
& ( ( B @ ( nat @ zero_zero @ ( nat @ member ) ) )
=> ( ( B @ ( TA @ nil @ ( A @ ( TA @ cons ) ) @ ( TA @ sublist ) ) )
= ( TA @ nil @ ( A @ ( TA @ cons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(42,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_73_ext) ).
thf(272,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)],[42]) ).
thf(107,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(549,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(14,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_list_Osimps_I3_J) ).
thf(151,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= ( TA @ nil ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TB @ ( TA @ map ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ map ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_map_Osimps_I2_J) ).
thf(315,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TA,C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( TB @ ( TA @ map ) ) ) )
= ( A @ ( C @ ( TB @ ( TA @ map ) ) ) @ ( B @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( ( TB @ nil )
= ( A @ ( B @ ( TB @ ( TA @ map ) ) ) ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_Nil__is__map__conv) ).
thf(168,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( ( A
= ( TA @ nil ) )
=> ( ( TB @ nil )
= ( A @ ( B @ ( TB @ ( TA @ map ) ) ) ) ) )
& ( ( ( TB @ nil )
= ( A @ ( B @ ( TB @ ( TA @ map ) ) ) ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(12,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_less__not__refl2) ).
thf(146,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(26,axiom,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( ( A @ ( B @ ( TB @ ( TA @ map ) ) ) )
= ( TB @ nil ) )
<=> ( A
= ( TA @ nil ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_map__is__Nil__conv) ).
thf(210,plain,
! [TA: $tType,TB: $tType,A: TA @ list,B: TB @ ( TA @ fun )] :
( ( ( A
= ( TA @ nil ) )
=> ( ( A @ ( B @ ( TB @ ( TA @ map ) ) ) )
= ( TB @ nil ) ) )
& ( ( ( A @ ( B @ ( TB @ ( TA @ map ) ) ) )
= ( TB @ nil ) )
=> ( A
= ( TA @ nil ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(63,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_less__zeroE) ).
thf(358,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(83,axiom,
! [TA: $tType] :
( ( TA @ ring_char_0 )
=> ! [A: int] :
( ( ( A @ ( TA @ ring_1_of_int ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( int @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_of__int__eq__0__iff) ).
thf(437,plain,
! [TA: $tType] :
( ( TA @ ring_char_0 )
=> ! [A: int] :
( ( ( A
= ( int @ zero_zero ) )
=> ( ( A @ ( TA @ ring_1_of_int ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( TA @ ring_1_of_int ) )
= ( TA @ zero_zero ) )
=> ( A
= ( int @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(103,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ~ ( TA @ zero_zero @ ( TA @ one_one @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_not__one__less__zero) ).
thf(532,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ~ ( TA @ zero_zero @ ( TA @ one_one @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(45,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( TA @ semiring_1_Nats @ ( TA @ zero_zero @ ( TA @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_Nats__0) ).
thf(283,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( TA @ semiring_1_Nats @ ( TA @ zero_zero @ ( TA @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(76,axiom,
int @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(415,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(88,axiom,
int @ ring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1) ).
thf(464,plain,
int @ ring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(67,axiom,
( ( int @ nil @ zlcms )
= ( int @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_zlcms_Osimps_I1_J) ).
thf(369,plain,
( ( int @ nil @ zlcms )
= ( int @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(54,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_in__set__insert) ).
thf(322,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( TA @ set @ ( bool @ ( TA @ fun ) @ ( TA @ list @ aa ) ) ) @ ( B @ ( TA @ member ) ) )
=> ( ( A @ ( B @ ( TA @ insert ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(59,axiom,
( ? [A: atom] :
( ( a
= ( A @ ( as @ ( hd_coeff @ ( int @ ( atom @ map ) ) ) @ zlcms @ hd_coeff1 @ ( atom @ ( atom @ aa ) ) ) ) )
& ( as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( A @ ( atom @ member ) ) ) )
| ( a
= ( int @ nil @ ( int @ one_one @ ( int @ cons ) ) @ ( int @ zero_zero @ ( as @ ( hd_coeff @ ( int @ ( atom @ map ) ) ) @ zlcms @ dvd ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26__096a_A_061_ADvd_A_Izlcms_A_Imap_Ahd__coeff_Aas_J_J_A0_A_0911_093_A_124_IEX_Ab_058set_Aas_O_Aa_A_061_Ahd__coeff1_A_Izlcms_A_Imap_Ahd__coeff_Aas_J_J_Ab_J_096) ).
thf(337,plain,
( ? [A: atom] :
( ( a
= ( A @ ( as @ ( hd_coeff @ ( int @ ( atom @ map ) ) ) @ zlcms @ hd_coeff1 @ ( atom @ ( atom @ aa ) ) ) ) )
& ( as @ ( atom @ set @ ( bool @ ( atom @ fun ) @ ( atom @ list @ aa ) ) ) @ ( A @ ( atom @ member ) ) ) )
| ( a
= ( int @ nil @ ( int @ one_one @ ( int @ cons ) ) @ ( int @ zero_zero @ ( as @ ( hd_coeff @ ( int @ ( atom @ map ) ) ) @ zlcms @ dvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(91,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_gr0I) ).
thf(469,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(106,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ one_one ) )
<=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_sgn__1__pos) ).
thf(543,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ one_one ) ) )
& ( ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ one_one ) )
=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(687,plain,
$false,
inference(e,[status(thm)],[118,140,145,249,365,138,379,269,217,276,550,142,472,404,288,184,587,157,189,416,325,228,261,475,492,179,238,121,221,293,396,507,366,534,334,429,192,407,275,137,484,361,461,285,224,356,593,420,328,488,537,489,590,124,225,371,503,134,343,266,311,558,425,513,166,573,444,391,382,572,466,350,419,318,521,306,431,241,580,150,263,182,331,127,576,154,175,446,450,218,250,465,231,390,186,568,290,478,272,549,151,315,168,146,210,358,437,532,283,415,464,369,322,337,469,543]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM122_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40 % Computer : n011.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sat Sep 26 23:31:31 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 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
% 0.69/0.73 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.03/1.03 % [INFO] Parsing done (294ms).
% 1.58/1.04 % [INFO] Running in sequential loop mode.
% 2.19/1.43 % [INFO] eprover registered as external prover.
% 2.19/1.43 % [INFO] Scanning for conjecture ...
% 2.54/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 115 axioms. Running axiom selection ...
% 2.75/1.72 % [INFO] Axiom selection finished. Selected 115 axioms (removed 0 axioms).
% 3.07/1.89 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.33/1.92 % [INFO] Type checking passed.
% 3.33/1.92 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 23.55/10.36 % External prover 'e' found a proof!
% 23.55/10.36 % [INFO] Killing All external provers ...
% 23.55/10.36 % Time passed: 9864ms (effective reasoning time: 9313ms)
% 23.55/10.36 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 23.55/10.36 % Axioms used in derivation (115): fact_94_sublist__singleton, arity_Int_Oint___Rings_Ozero__neq__one, fact_76_less__zeroE, fact_78_neq0__conv, fact_12_sgn0, fact_3__096b_A_058_Aset_Aas_096, fact_29_in__set__member, arity_Int_Oint___Groups_Oone, fact_54_not__Cons__self2, fact_63_set__ConsD, arity_Int_Oint___Rings_Olinordered__idom, fact_5__096EX_Ab_058set_Aas_O_Aa_A_061_Ahd__coeff1_A_Izlcms_A_Imap_Ahd__coeff_Aas_J_J_Ab_096, arity_Nat_Onat___Rings_Osemiring__1, arity_Int_Oint___Int_Oring__char__0, fact_91_in__set__insert, fact_92_List_Oinsert__def, fact_14_iszero__0, fact_97_sublist__nil, fact_38_map__is__Nil__conv, fact_53_elem, fact_45_of__int__less__0__iff, fact_9_of__int__eq__0__iff, fact_81_not__less0, help_COMBI_1_1_U, fact_93_not__in__set__insert, fact_89_nat__neq__iff, fact_19_sgn__0__0, fact_87_less__irrefl__nat, fact_74_mem__def, fact_84_nat__less__cases, fact_82_atom_Osize_I5_J, fact_26__096a_A_061_ADvd_A_Izlcms_A_Imap_Ahd__coeff_Aas_J_J_A0_A_0911_093_A_124_IEX_Ab_058set_Aas_O_Aa_A_061_Ahd__coeff1_A_Izlcms_A_Imap_Ahd__coeff_Aas_J_J_Ab_J_096, fact_44_asubst_Osimps_I5_J, fact_43_hd__coeff1_Osimps_I5_J, fact_48_zero__less__one, fact_60_sgn__pos, fact_24_map__cong, arity_Int_Oint___Rings_Osemiring__1, fact_11_Z_Oanormal__decr, fact_10__096_B_Bthesis_O_A_I_B_Bb_O_A_091_124_Ab_A_058_Aset_Aas_059_Aa_A_061_Ahd__coeff1_A_Izlcms_A_Imap_Ahd__coeff_Aas_J_J_Ab_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_69_atom_Osize_I2_J, fact_57_list_Osimps_I2_J, fact_42_zlcms_Osimps_I1_J, fact_62_zero__neq__one, fact_0_div0, arity_Int_Oint___Rings_Oring__1, fact_85_less__not__refl3, fact_37_map_Osimps_I1_J, fact_13_Nats__0, fact_31_List_Omember__def, fact_58_one__reorient, fact_79_gr0I, fact_73_ext, fact_86_less__not__refl2, fact_17_map__eq__conv, fact_67_member__set, fact_66_divisor_Osimps_I2_J, fact_51_member__rec_I1_J, fact_80_gr__implies__not0, fact_33_list_Oinject, fact_52_member__rec_I2_J, fact_4__096a_A_061_Ahd__coeff1_A_Izlcms_A_Imap_Ahd__coeff_Aas_J_J_Ab_096, arity_Nat_Onat___Rings_Olinordered__semidom, fact_71_Cons__eq__map__conv, fact_70_map__eq__Cons__conv, fact_1_a, fact_68_zlcms__pos, fact_27_sgn__less, fact_88_linorder__neqE__nat, arity_Nat_Onat___Groups_Ozero, fact_96_map__ident, fact_83_insert__Nil, fact_28_sgn__greater, fact_22_map__ext, fact_32_list__ex1__iff, fact_8_of__int__0__eq__iff, fact_49_insert, fact_23_map__idI, fact_46_of__int__0__less__iff, fact_77_less__nat__zero__code, fact_20_divisor__asubst, fact_30_ListMem__iff, fact_15_iszero__def, fact_75_neq__Nil__conv, fact_47_not__one__less__zero, fact_36_Nil__is__map__conv, fact_18_sgn__sgn, arity_Nat_Onat___Groups_Oone, fact_95_hd__coeffs1__def, fact_64_not__iszero__1, fact_39_of__int__less__iff, fact_59_sgn__1__pos, fact_72_list_Oexhaust, fact_65_Nats__1, arity_Int_Oint___Groups_Osgn__if, fact_25_zlcms0__iff, fact_61_one__neq__zero, fact_2_hd0, help_pp_1_1_U, fact_6_zero__reorient, fact_34_atom_Osimps_I2_J, fact_90_less__not__refl, fact_50_linorder__neqE__linordered__idom, fact_40_list__ex1__simps_I1_J, arity_Int_Oint___Groups_Ozero, fact_35_map_Osimps_I2_J, help_pp_2_1_U, arity_Int_Oint___Rings_Olinordered__semidom, fact_56_not__Cons__self, fact_55_list_Osimps_I3_J, fact_21_ex__map__conv, arity_Nat_Onat___Rings_Ozero__neq__one, fact_16_of__int__eq__iff, fact_41_of__int__1, fact_7_of__int__0
% 23.55/10.36 % No. of inferences in proof: 234
% 23.55/10.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9864 ms resp. 9313 ms w/o parsing
% 24.03/10.42 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.03/10.42 % [INFO] Killing All external provers ...
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