%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM040_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n020.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 06:57:56 AM UTC 2026
% Result : Theorem 118.68s 41.42s
% Output : Refutation 119.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 131
% Syntax : Number of formulae : 479 ( 198 unt; 0 typ; 9 def)
% Number of atoms : 1506 ( 717 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 9787 ( 328 ~; 179 |; 68 &;9006 @)
% ( 12 <=>; 194 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 57 usr; 13 con; 0-5 aty)
% Number of variables : 1547 ( 0 ^;1519 !; 19 ?;1547 :)
% ( 0 !>; 0 ?*; 0 @-; 9 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(atom_type,type,
atom: $tType ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(ring_decl,type,
ring:
!>[TA: $tType] : $o ).
thf(cl_Groups_Oplus_decl,type,
cl_Groups_Oplus:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(cl_Groups_Ominus_decl,type,
cl_Groups_Ominus:
!>[TA: $tType] : $o ).
thf(semiring_decl,type,
semiring:
!>[TA: $tType] : $o ).
thf(comm_ring_decl,type,
comm_ring:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(monoid_mult_decl,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(comm_semiring_decl,type,
comm_semiring:
!>[TA: $tType] : $o ).
thf(semiring_div_decl,type,
semiring_div:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_decl,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(comm_monoid_mult_decl,type,
comm_monoid_mult:
!>[TA: $tType] : $o ).
thf(ab_semigroup_mult_decl,type,
ab_semigroup_mult:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(ab_sem1668676832m_mult_decl,type,
ab_sem1668676832m_mult:
!>[TA: $tType] : $o ).
thf(semiri456707255roduct_decl,type,
semiri456707255roduct:
!>[TA: $tType] : $o ).
thf(div_mod_decl,type,
div_mod:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(times_times_decl,type,
times_times:
!>[TA: $tType] : ( TA > ( TA @ ( TA @ fun ) ) ) ).
thf(iprod_decl,type,
iprod:
!>[TA: $tType] : ( ( TA @ list ) > ( TA @ list ) > TA ) ).
thf(zipwith0_decl,type,
zipwith0:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TA @ list @ ( TB @ list @ fun ) @ ( TC @ list @ fun ) ) ) ).
thf(cons_decl,type,
cons:
!>[TA: $tType] : ( TA > ( TA @ list ) > ( TA @ list ) ) ).
thf(map_decl,type,
map:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > ( TB @ list ) > ( TA @ list ) ) ).
thf(i_Z_decl,type,
i_Z: atom > ( int @ list ) > $o ).
thf(asubst_decl,type,
asubst: int > ( int @ list ) > atom > atom ).
thf(dvd_decl,type,
dvd: int > int > ( int @ list ) > atom ).
thf(c_PresArith_Oatom_OLe_decl,type,
c_PresArith_Oatom_OLe: int > ( int @ list ) > atom ).
thf(nDvd_decl,type,
nDvd: int > int > ( int @ list ) > atom ).
thf(atom_case_decl,type,
atom_case:
!>[TA: $tType] : ( ( TA @ ( int @ list @ fun ) @ ( int @ fun ) ) > ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ) ) > ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ) ) > atom > TA ) ).
thf(atom_rec_decl,type,
atom_rec:
!>[TA: $tType] : ( ( TA @ ( int @ list @ fun ) @ ( int @ fun ) ) > ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ) ) > ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ) ) > atom > TA ) ).
thf(divisor_decl,type,
divisor: atom > int ).
thf(hd_coeff_decl,type,
hd_coeff: atom > int ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(a_decl,type,
a: atom ).
thf(d_decl,type,
d: int ).
thf(e_decl,type,
e: int @ list ).
thf(i_decl,type,
i: int ).
thf(j_decl,type,
j: int ).
thf(ks_decl,type,
ks: int @ list ).
thf(ks1_decl,type,
ks1: int @ list ).
thf(l_decl,type,
l: int ).
thf(sk1_decl,type,
sk1: int > ( int @ list ) > atom > int ).
thf(sk2_decl,type,
sk2: int > ( int @ list ) > atom > int ).
thf(sk3_decl,type,
sk3: int > int > atom > ( int @ list ) ).
thf(sk4_decl,type,
sk4: ( int @ list ) > atom > int ).
thf(sk5_decl,type,
sk5: int > atom > ( int @ list ) ).
thf(sk6_decl,type,
sk6: int > ( int @ list ) > atom > int ).
thf(sk7_decl,type,
sk7: int > ( int @ list ) > atom > int ).
thf(sk8_decl,type,
sk8: int > int > atom > ( int @ list ) ).
thf(sk9_decl,type,
sk9: int @ list ).
thf(sk1_def,definition,
( sk1
= ( @+[A: int > ( int @ list ) > atom > int] :
! [B: int,C: int,D: int @ list] :
( ( D @ ( C @ ( B @ dvd ) ) @ ( D @ ( C @ A ) ) )
= B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: int > ( int @ list ) > atom > int] :
! [B: int,C: int,D: int @ list] :
( ( D @ ( C @ ( B @ dvd ) ) @ ( D @ ( B @ A ) ) )
= C ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: int > int > atom > ( int @ list )] :
! [B: int,C: int,D: int @ list] :
( ( D @ ( C @ ( B @ dvd ) ) @ ( C @ ( B @ A ) ) )
= D ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: ( int @ list ) > atom > int] :
! [B: int,C: int @ list] :
( ( C @ ( B @ c_PresArith_Oatom_OLe ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: int > atom > ( int @ list )] :
! [B: int,C: int @ list] :
( ( C @ ( B @ c_PresArith_Oatom_OLe ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: int > ( int @ list ) > atom > int] :
! [B: int,C: int,D: int @ list] :
( ( D @ ( C @ ( B @ nDvd ) ) @ ( D @ ( C @ A ) ) )
= B ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: int > ( int @ list ) > atom > int] :
! [B: int,C: int,D: int @ list] :
( ( D @ ( C @ ( B @ nDvd ) ) @ ( D @ ( B @ A ) ) )
= C ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: int > int > atom > ( int @ list )] :
! [B: int,C: int,D: int @ list] :
( ( D @ ( C @ ( B @ nDvd ) ) @ ( C @ ( B @ A ) ) )
= D ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: int @ list] :
( ks1
= ( A @ ( int @ one_one @ ( int @ cons ) ) ) ) ) ) ).
thf(29,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(249,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(105,axiom,
int @ semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(468,plain,
int @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
thf(481,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)],[110]) ).
thf(69,axiom,
! [A: int @ list,B: int,C: int,D: int,E: int @ list,F: int] :
( ( A @ ( B @ ( int @ cons ) ) @ ( C @ ( D @ dvd ) ) @ ( E @ ( F @ asubst ) ) )
= ( A @ ( E @ ( B @ ( int @ times_times ) @ ( int @ ( int @ map ) ) ) @ ( int @ list @ plus_plus @ ( int @ list @ ( int @ list @ fun ) @ ( int @ list @ aa ) ) ) @ ( int @ list @ ( int @ list @ aa ) ) ) @ ( F @ ( B @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( C @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( D @ dvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_asubst_Osimps_I2_J) ).
thf(365,plain,
! [A: int @ list,B: int,C: int,D: int,E: int @ list,F: int] :
( ( A @ ( B @ ( int @ cons ) ) @ ( C @ ( D @ dvd ) ) @ ( E @ ( F @ asubst ) ) )
= ( A @ ( E @ ( B @ ( int @ times_times ) @ ( int @ ( int @ map ) ) ) @ ( int @ list @ plus_plus @ ( int @ list @ ( int @ list @ fun ) @ ( int @ list @ aa ) ) ) @ ( int @ list @ ( int @ list @ aa ) ) ) @ ( F @ ( B @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( C @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( D @ dvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(5,axiom,
! [A: int @ list,B: int,C: int @ list,D: int,E: int] :
( ( C @ ( D @ ( E @ nDvd ) ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_atom_Osimps_I7_J) ).
thf(138,plain,
! [A: int @ list,B: int,C: int @ list,D: int,E: int] :
( ( C @ ( D @ ( E @ nDvd ) ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,axiom,
! [A: int @ list,B: int,C: int,D: int @ list,E: int,F: int] :
( ( ( D @ ( E @ ( F @ nDvd ) ) )
= ( A @ ( B @ ( C @ nDvd ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_atom_Osimps_I3_J) ).
thf(206,plain,
! [A: int @ list,B: int,C: int,D: int @ list,E: int,F: int] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ nDvd ) ) )
= ( A @ ( B @ ( C @ nDvd ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ nDvd ) ) )
= ( A @ ( B @ ( C @ nDvd ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(207,plain,
( ! [A: int @ list,B: int,C: int,D: int @ list,E: int,F: int] :
( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ nDvd ) ) )
= ( A @ ( B @ ( C @ nDvd ) ) ) ) )
& ! [A: int @ list,B: int,C: int,D: int @ list,E: int,F: int] :
( ( ( D @ ( E @ ( F @ nDvd ) ) )
= ( A @ ( B @ ( C @ nDvd ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(miniscope,[status(thm)],[206]) ).
thf(208,plain,
! [L: int,K: int,J: int @ list,I: int,H: int,G: int @ list,F: int,E: int,D: int @ list,C: int,B: int,A: int @ list] :
( ( ( ( J @ ( K @ ( L @ nDvd ) ) )
= ( G @ ( H @ ( I @ nDvd ) ) ) )
| ( J != G )
| ( K != H )
| ( L != I ) )
& ( ( D = A )
| ( ( D @ ( E @ ( F @ nDvd ) ) )
!= ( A @ ( B @ ( C @ nDvd ) ) ) ) )
& ( ( E = B )
| ( ( D @ ( E @ ( F @ nDvd ) ) )
!= ( A @ ( B @ ( C @ nDvd ) ) ) ) )
& ( ( F = C )
| ( ( D @ ( E @ ( F @ nDvd ) ) )
!= ( A @ ( B @ ( C @ nDvd ) ) ) ) ) ),
inference(cnf,[status(esa)],[207]) ).
thf(211,plain,
! [F: int,E: int,D: int @ list,C: int,B: int,A: int @ list] :
( ( D = A )
| ( ( D @ ( E @ ( F @ nDvd ) ) )
!= ( A @ ( B @ ( C @ nDvd ) ) ) ) ),
inference(cnfConj,[status(thm)],[208]) ).
thf(219,plain,
! [F: int,E: int,D: int @ list,C: int,B: int,A: int @ list] :
( ( D = A )
| ( ( D @ ( E @ ( F @ nDvd ) ) )
!= ( A @ ( B @ ( C @ nDvd ) ) ) ) ),
inference(lifteq,[status(thm)],[211]) ).
thf(220,plain,
? [A: int > int > atom > ( int @ list )] :
! [B: int,C: int,D: int @ list] :
( ( D @ ( C @ ( B @ nDvd ) ) @ ( C @ ( B @ A ) ) )
= D ),
inference(detectInverse,[status(thm)],[219]) ).
thf(221,plain,
! [C: int @ list,B: int,A: int] :
( ( C @ ( B @ ( A @ nDvd ) ) @ ( B @ ( A @ sk8 ) ) )
= C ),
inference(cnf,[status(esa)],[220]) ).
thf(3449,plain,
! [C: int @ list,B: int,A: int] :
( ( C @ ( B @ ( A @ nDvd ) ) @ ( B @ ( A @ sk8 ) ) )
= C ),
inference(lifteq,[status(thm)],[221]) ).
thf(23,axiom,
int @ cl_Groups_Oplus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oplus) ).
thf(234,plain,
int @ cl_Groups_Oplus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(86,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( C @ ( D @ ( E @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( D @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
<=> ( C
= ( A @ ( D @ ( E @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_eq__add__iff2) ).
thf(408,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( C
= ( A @ ( D @ ( E @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( ( C @ ( D @ ( E @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( D @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( D @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( C
= ( A @ ( D @ ( E @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(102,axiom,
int @ monoid_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(461,plain,
int @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(14,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA @ list] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) @ ( TA @ ( TA @ map ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_scale1) ).
thf(189,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA @ list] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) @ ( TA @ ( TA @ map ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(190,plain,
! [TA: $tType,A: TA @ list] :
( ( ( A @ ( TA @ one_one @ ( TA @ times_times ) @ ( TA @ ( TA @ map ) ) ) )
= A )
| ~ ( TA @ monoid_mult ) ),
inference(cnf,[status(esa)],[189]) ).
thf(191,plain,
! [TA: $tType,A: TA @ list] :
( ~ ( TA @ monoid_mult )
| ( ( A @ ( TA @ one_one @ ( TA @ times_times ) @ ( TA @ ( TA @ map ) ) ) )
= A ) ),
inference(lifteq,[status(thm)],[190]) ).
thf(5382,plain,
! [TA: $tType,A: TA @ list] :
( ( ( int @ monoid_mult )
!= ( TA @ monoid_mult ) )
| ~ $true
| ( ( A @ ( TA @ one_one @ ( TA @ times_times ) @ ( TA @ ( TA @ map ) ) ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[461,191]) ).
thf(5383,plain,
! [TA: $tType,A: TA @ list] :
( ( ( int @ monoid_mult )
!= ( TA @ monoid_mult ) )
| ( ( A @ ( TA @ one_one @ ( TA @ times_times ) @ ( TA @ ( TA @ map ) ) ) )
= A ) ),
inference(simp,[status(thm)],[5382]) ).
thf(5384,plain,
! [A: int @ list] :
( ( A @ ( int @ one_one @ ( int @ times_times ) @ ( int @ ( int @ map ) ) ) )
= A ),
inference(pattern_uni,[status(thm)],[5383:[bind_type(TA,$thf( int ))]]) ).
thf(100,axiom,
~ ! [A: int @ list] :
( ks1
!= ( A @ ( int @ one_one @ ( int @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28__096_B_Bthesis_O_A_I_B_Bks_H_O_Aks_A_061_A1_A_D_Aks_H_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(453,plain,
~ ! [A: int @ list] :
( ks1
!= ( A @ ( int @ one_one @ ( int @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(454,plain,
~ ! [A: int @ list] :
( ks1
!= ( A @ ( int @ one_one @ ( int @ cons ) ) ) ),
inference(polarity_switch,[status(thm)],[453]) ).
thf(455,plain,
~ ~ ? [A: int @ list] :
( ks1
= ( A @ ( int @ one_one @ ( int @ cons ) ) ) ),
inference(miniscope,[status(thm)],[454]) ).
thf(456,plain,
( ks1
= ( sk9 @ ( int @ one_one @ ( int @ cons ) ) ) ),
inference(cnf,[status(esa)],[455]) ).
thf(457,plain,
( ks1
= ( sk9 @ ( int @ one_one @ ( int @ cons ) ) ) ),
inference(lifteq,[status(thm)],[456]) ).
thf(96,axiom,
( ks1
= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20__096ks_A_061_A1_A_D_Aks_H_096) ).
thf(442,plain,
( ks1
= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(443,plain,
( ks1
= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) ),
inference(lifteq,[status(thm)],[442]) ).
thf(1375,plain,
( ( sk9 @ ( int @ one_one @ ( int @ cons ) ) )
= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) ),
inference(rewrite,[status(thm)],[457,443]) ).
thf(108,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/sandbox2/benchmark/theBenchmark.p',fact_87_map_Osimps_I2_J) ).
thf(475,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)],[108]) ).
thf(476,plain,
! [TA: $tType,TB: $tType,C: TA @ ( TB @ fun ),B: TB,A: TB @ list] :
( ( A @ ( B @ ( TB @ cons ) ) @ ( C @ ( TA @ ( TB @ map ) ) ) )
= ( A @ ( C @ ( TA @ ( TB @ map ) ) ) @ ( B @ ( C @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ cons ) ) ) ),
inference(cnf,[status(esa)],[475]) ).
thf(477,plain,
! [TA: $tType,TB: $tType,C: TA @ ( TB @ fun ),B: TB,A: TB @ list] :
( ( A @ ( B @ ( TB @ cons ) ) @ ( C @ ( TA @ ( TB @ map ) ) ) )
= ( A @ ( C @ ( TA @ ( TB @ map ) ) ) @ ( B @ ( C @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ cons ) ) ) ),
inference(lifteq,[status(thm)],[476]) ).
thf(3811,plain,
! [TA: $tType,C: TA @ ( int @ fun ),B: int,A: int @ list] :
( ( ( sk9 @ ( int @ one_one @ ( int @ cons ) ) )
!= ( A @ ( B @ ( int @ cons ) ) ) )
| ( ( ks @ ( int @ one_one @ ( int @ cons ) ) @ ( C @ ( TA @ ( int @ map ) ) ) )
= ( A @ ( C @ ( TA @ ( int @ map ) ) ) @ ( B @ ( C @ ( TA @ ( int @ aa ) ) ) @ ( TA @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1375,477]) ).
thf(3812,plain,
! [TA: $tType,A: TA @ ( int @ fun )] :
( ( ks @ ( int @ one_one @ ( int @ cons ) ) @ ( A @ ( TA @ ( int @ map ) ) ) )
= ( sk9 @ ( A @ ( TA @ ( int @ map ) ) ) @ ( int @ one_one @ ( A @ ( TA @ ( int @ aa ) ) ) @ ( TA @ cons ) ) ) ),
inference(pattern_uni,[status(thm)],[3811:[bind(A,$thf( sk9 )),bind(B,$thf( int @ one_one ))]]) ).
thf(4160,plain,
! [TA: $tType,A: TA @ ( int @ fun )] :
( ( ks @ ( int @ one_one @ ( int @ cons ) ) @ ( A @ ( TA @ ( int @ map ) ) ) )
= ( sk9 @ ( A @ ( TA @ ( int @ map ) ) ) @ ( int @ one_one @ ( A @ ( TA @ ( int @ aa ) ) ) @ ( TA @ cons ) ) ) ),
inference(simp,[status(thm)],[3812]) ).
thf(5446,plain,
! [B: int @ ( int @ fun ),A: int @ list] :
( ( ( A @ ( int @ one_one @ ( int @ times_times ) @ ( int @ ( int @ map ) ) ) )
!= ( ks @ ( int @ one_one @ ( int @ cons ) ) @ ( B @ ( int @ ( int @ map ) ) ) ) )
| ( A
= ( sk9 @ ( B @ ( int @ ( int @ map ) ) ) @ ( int @ one_one @ ( B @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5384,4160]) ).
thf(5447,plain,
( ( ks @ ( int @ one_one @ ( int @ cons ) ) )
= ( sk9 @ ( int @ one_one @ ( int @ times_times ) @ ( int @ ( int @ map ) ) ) @ ( int @ one_one @ ( int @ one_one @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) ) ),
inference(pattern_uni,[status(thm)],[5446:[bind(A,$thf( ks @ ( int @ one_one @ ( int @ cons ) ) )),bind(B,$thf( int @ one_one @ ( int @ times_times ) ))]]) ).
thf(5495,plain,
( ( ks @ ( int @ one_one @ ( int @ cons ) ) )
= ( sk9 @ ( int @ one_one @ ( int @ one_one @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) ) ),
inference(rewrite,[status(thm)],[5447,5384]) ).
thf(70,axiom,
( a
= ( ks1 @ ( l @ ( d @ nDvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_NDvd) ).
thf(368,plain,
( a
= ( ks1 @ ( l @ ( d @ nDvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(369,plain,
( ( ks1 @ ( l @ ( d @ nDvd ) ) )
= a ),
inference(lifteq,[status(thm)],[368]) ).
thf(1521,plain,
( ( ks @ ( int @ one_one @ ( int @ cons ) ) @ ( l @ ( d @ nDvd ) ) )
= a ),
inference(rewrite,[status(thm)],[369,443]) ).
thf(209,plain,
! [F: int,E: int,D: int @ list,C: int,B: int,A: int @ list] :
( ( F = C )
| ( ( D @ ( E @ ( F @ nDvd ) ) )
!= ( A @ ( B @ ( C @ nDvd ) ) ) ) ),
inference(cnfConj,[status(thm)],[208]) ).
thf(213,plain,
! [F: int,E: int,D: int @ list,C: int,B: int,A: int @ list] :
( ( F = C )
| ( ( D @ ( E @ ( F @ nDvd ) ) )
!= ( A @ ( B @ ( C @ nDvd ) ) ) ) ),
inference(lifteq,[status(thm)],[209]) ).
thf(214,plain,
? [A: int > ( int @ list ) > atom > int] :
! [B: int,C: int,D: int @ list] :
( ( D @ ( C @ ( B @ nDvd ) ) @ ( D @ ( C @ A ) ) )
= B ),
inference(detectInverse,[status(thm)],[213]) ).
thf(215,plain,
! [C: int @ list,B: int,A: int] :
( ( C @ ( B @ ( A @ nDvd ) ) @ ( C @ ( B @ sk6 ) ) )
= A ),
inference(cnf,[status(esa)],[214]) ).
thf(2582,plain,
! [C: int @ list,B: int,A: int] :
( ( C @ ( B @ ( A @ nDvd ) ) @ ( C @ ( B @ sk6 ) ) )
= A ),
inference(lifteq,[status(thm)],[215]) ).
thf(2583,plain,
! [C: int @ list,B: int,A: int] :
( ( ( ks @ ( int @ one_one @ ( int @ cons ) ) @ ( l @ ( d @ nDvd ) ) )
!= ( C @ ( B @ ( A @ nDvd ) ) ) )
| ( ( a @ ( C @ ( B @ sk6 ) ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[1521,2582]) ).
thf(2584,plain,
( ( a @ ( ks @ ( int @ one_one @ ( int @ cons ) ) @ ( l @ sk6 ) ) )
= d ),
inference(pattern_uni,[status(thm)],[2583:[bind(A,$thf( d )),bind(B,$thf( l )),bind(C,$thf( ks @ ( int @ one_one @ ( int @ cons ) ) ))]]) ).
thf(5643,plain,
( ( ( ks @ ( int @ one_one @ ( int @ cons ) ) )
!= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) )
| ( ( a @ ( sk9 @ ( int @ one_one @ ( int @ one_one @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( l @ sk6 ) ) )
= d ) ),
inference(paramod_ordered,[status(thm)],[5495,2584]) ).
thf(5644,plain,
( ( a @ ( sk9 @ ( int @ one_one @ ( int @ one_one @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( l @ sk6 ) ) )
= d ),
inference(pattern_uni,[status(thm)],[5643:[]]) ).
thf(4,axiom,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_not__Cons__self2) ).
thf(135,plain,
! [TA: $tType,A: TA @ list,B: TA] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(136,plain,
! [TA: $tType,B: TA,A: TA @ list] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
inference(cnf,[status(esa)],[135]) ).
thf(137,plain,
! [TA: $tType,B: TA,A: TA @ list] :
( ( A @ ( B @ ( TA @ cons ) ) )
!= A ),
inference(lifteq,[status(thm)],[136]) ).
thf(1400,plain,
! [B: int,A: int @ list] :
( ( ( sk9 @ ( int @ one_one @ ( int @ cons ) ) )
!= ( A @ ( B @ ( int @ cons ) ) ) )
| ( ( ks @ ( int @ one_one @ ( int @ cons ) ) )
!= A ) ),
inference(paramod_ordered,[status(thm)],[1375,137]) ).
thf(1401,plain,
( sk9
!= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) ),
inference(pattern_uni,[status(thm)],[1400:[bind(A,$thf( sk9 )),bind(B,$thf( int @ one_one ))]]) ).
thf(74,axiom,
int @ ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(379,plain,
int @ ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(210,plain,
! [F: int,E: int,D: int @ list,C: int,B: int,A: int @ list] :
( ( E = B )
| ( ( D @ ( E @ ( F @ nDvd ) ) )
!= ( A @ ( B @ ( C @ nDvd ) ) ) ) ),
inference(cnfConj,[status(thm)],[208]) ).
thf(216,plain,
! [F: int,E: int,D: int @ list,C: int,B: int,A: int @ list] :
( ( E = B )
| ( ( D @ ( E @ ( F @ nDvd ) ) )
!= ( A @ ( B @ ( C @ nDvd ) ) ) ) ),
inference(lifteq,[status(thm)],[210]) ).
thf(217,plain,
? [A: int > ( int @ list ) > atom > int] :
! [B: int,C: int,D: int @ list] :
( ( D @ ( C @ ( B @ nDvd ) ) @ ( D @ ( B @ A ) ) )
= C ),
inference(detectInverse,[status(thm)],[216]) ).
thf(218,plain,
! [C: int @ list,B: int,A: int] :
( ( C @ ( B @ ( A @ nDvd ) ) @ ( C @ ( A @ sk7 ) ) )
= B ),
inference(cnf,[status(esa)],[217]) ).
thf(2723,plain,
! [C: int @ list,B: int,A: int] :
( ( C @ ( B @ ( A @ nDvd ) ) @ ( C @ ( A @ sk7 ) ) )
= B ),
inference(lifteq,[status(thm)],[218]) ).
thf(2724,plain,
! [C: int @ list,B: int,A: int] :
( ( ( ks @ ( int @ one_one @ ( int @ cons ) ) @ ( l @ ( d @ nDvd ) ) )
!= ( C @ ( B @ ( A @ nDvd ) ) ) )
| ( ( a @ ( C @ ( A @ sk7 ) ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1521,2723]) ).
thf(2725,plain,
( ( a @ ( ks @ ( int @ one_one @ ( int @ cons ) ) @ ( d @ sk7 ) ) )
= l ),
inference(pattern_uni,[status(thm)],[2724:[bind(A,$thf( d )),bind(B,$thf( l )),bind(C,$thf( ks @ ( int @ one_one @ ( int @ cons ) ) ))]]) ).
thf(5613,plain,
( ( ( ks @ ( int @ one_one @ ( int @ cons ) ) )
!= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) )
| ( ( a @ ( sk9 @ ( int @ one_one @ ( int @ one_one @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( d @ sk7 ) ) )
= l ) ),
inference(paramod_ordered,[status(thm)],[5495,2725]) ).
thf(5614,plain,
( ( a @ ( sk9 @ ( int @ one_one @ ( int @ one_one @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( d @ sk7 ) ) )
= l ),
inference(pattern_uni,[status(thm)],[5613:[]]) ).
thf(6,axiom,
! [TA: $tType] :
( ( ( TA @ cl_Groups_Ominus )
& ( TA @ zero ) )
=> ( TA @ list @ cl_Groups_Ominus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_List_Olist___Groups_Ominus) ).
thf(142,plain,
! [TA: $tType] :
( ( ( TA @ cl_Groups_Ominus )
& ( TA @ zero ) )
=> ( TA @ list @ cl_Groups_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(115,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( TA @ div_mod ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_mod__mult__mult1) ).
thf(500,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( TA @ div_mod ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(3,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/sandbox2/benchmark/theBenchmark.p',fact_34_list_Oinject) ).
thf(126,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)],[3]) ).
thf(127,plain,
! [TA: $tType,D: TA,C: TA @ list,B: TA,A: TA @ list] :
( ( ( ( C @ ( D @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) ) )
| ( C != A )
| ( D != B ) )
& ( ( C = A )
| ( ( C @ ( D @ ( TA @ cons ) ) )
!= ( A @ ( B @ ( TA @ cons ) ) ) ) )
& ( ( D = B )
| ( ( C @ ( D @ ( TA @ cons ) ) )
!= ( A @ ( B @ ( TA @ cons ) ) ) ) ) ),
inference(cnf,[status(esa)],[126]) ).
thf(128,plain,
! [TA: $tType,D: TA,C: TA @ list,B: TA,A: TA @ list] :
( ( D = B )
| ( ( C @ ( D @ ( TA @ cons ) ) )
!= ( A @ ( B @ ( TA @ cons ) ) ) ) ),
inference(cnfConj,[status(thm)],[127]) ).
thf(131,plain,
! [TA: $tType,D: TA,C: TA @ list,B: TA,A: TA @ list] :
( ( D = B )
| ( ( C @ ( D @ ( TA @ cons ) ) )
!= ( A @ ( B @ ( TA @ cons ) ) ) ) ),
inference(lifteq,[status(thm)],[128]) ).
thf(1503,plain,
! [D: int @ list,C: int @ list @ list,B: int @ list,A: int @ list @ list] :
( ( D != sk9 )
| ( B
!= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) )
| ( ( C @ ( D @ ( int @ list @ cons ) ) )
!= ( A @ ( B @ ( int @ list @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[131,1401]) ).
thf(1504,plain,
! [C: int @ list @ list,B: int @ list,A: int @ list @ list] :
( ( B
!= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) )
| ( ( C @ ( sk9 @ ( int @ list @ cons ) ) )
!= ( A @ ( B @ ( int @ list @ cons ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1503:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( sk9 ))]]) ).
thf(1507,plain,
! [B: int @ list @ list,A: int @ list @ list] :
( ( B @ ( sk9 @ ( int @ list @ cons ) ) )
!= ( A @ ( ks @ ( int @ one_one @ ( int @ cons ) ) @ ( int @ list @ cons ) ) ) ),
inference(simp,[status(thm)],[1504]) ).
thf(1,conjecture,
( ( d @ ( e @ ( ks @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( l @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) )
= ( d @ ( e @ ( ks @ ( int @ iprod ) ) @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( l @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( d @ ( e @ ( ks @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( l @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) )
!= ( d @ ( e @ ( ks @ ( int @ iprod ) ) @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( l @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(124,plain,
( ( d @ ( e @ ( ks @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( l @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) )
!= ( d @ ( e @ ( ks @ ( int @ iprod ) ) @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( l @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(125,plain,
( ( d @ ( e @ ( ks @ ( int @ iprod ) ) @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( l @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) )
!= ( d @ ( e @ ( ks @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( l @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) ) ),
inference(lifteq,[status(thm)],[124]) ).
thf(533,plain,
( ( d != d )
| ( ( e @ ( ks @ ( int @ iprod ) ) @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( l @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) )
!= ( e @ ( ks @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( l @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) ) ) ),
inference(simp,[status(thm)],[125]) ).
thf(534,plain,
( ( e @ ( ks @ ( int @ iprod ) ) @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( l @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) )
!= ( e @ ( ks @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( l @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) ) ),
inference(simp,[status(thm)],[533]) ).
thf(535,plain,
( ( ( e @ ( ks @ ( int @ iprod ) ) @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) )
!= ( e @ ( ks @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) ) )
| ( ( l @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) )
!= ( l @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) ) ) ),
inference(simp,[status(thm)],[534]) ).
thf(536,plain,
( ( e @ ( ks @ ( int @ iprod ) ) @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) )
!= ( e @ ( ks @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) ) ),
inference(simp,[status(thm)],[535]) ).
thf(730,plain,
( ( ( e @ ( ks @ ( int @ iprod ) ) )
!= ( e @ ( ks @ ( int @ iprod ) ) ) )
| ( ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) )
!= ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) ) ) ),
inference(simp,[status(thm)],[536]) ).
thf(767,plain,
( ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) )
!= ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) ) ),
inference(simp,[status(thm)],[730]) ).
thf(768,plain,
( ( j != i )
| ( ( int @ plus_plus )
!= ( int @ plus_plus ) ) ),
inference(simp,[status(thm)],[767]) ).
thf(781,plain,
j != i,
inference(simp,[status(thm)],[768]) ).
thf(791,plain,
! [D: int,C: int @ list,B: int,A: int @ list] :
( ( D != j )
| ( B != i )
| ( ( C @ ( D @ ( int @ cons ) ) )
!= ( A @ ( B @ ( int @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[131,781]) ).
thf(792,plain,
! [C: int @ list,B: int,A: int @ list] :
( ( B != i )
| ( ( C @ ( j @ ( int @ cons ) ) )
!= ( A @ ( B @ ( int @ cons ) ) ) ) ),
inference(pattern_uni,[status(thm)],[791:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( j ))]]) ).
thf(795,plain,
! [B: int @ list,A: int @ list] :
( ( B @ ( j @ ( int @ cons ) ) )
!= ( A @ ( i @ ( int @ cons ) ) ) ),
inference(simp,[status(thm)],[792]) ).
thf(1407,plain,
! [B: int @ list,A: int @ list] :
( ( ( sk9 @ ( int @ one_one @ ( int @ cons ) ) )
!= ( A @ ( i @ ( int @ cons ) ) ) )
| ( ( ks @ ( int @ one_one @ ( int @ cons ) ) )
!= ( B @ ( j @ ( int @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1375,795]) ).
thf(1420,plain,
! [B: int @ list,A: int @ list] :
( ( ( sk9 @ ( int @ one_one @ ( int @ cons ) ) )
!= ( A @ ( i @ ( int @ cons ) ) ) )
| ( ks != B )
| ( j
!= ( int @ one_one ) ) ),
inference(simp,[status(thm)],[1407]) ).
thf(1462,plain,
! [A: int @ list] :
( ( ( sk9 @ ( int @ one_one @ ( int @ cons ) ) )
!= ( A @ ( i @ ( int @ cons ) ) ) )
| ( j
!= ( int @ one_one ) ) ),
inference(simp,[status(thm)],[1420]) ).
thf(1872,plain,
! [A: int @ list] :
( ( ( ks @ ( int @ one_one @ ( int @ cons ) ) )
!= ( A @ ( i @ ( int @ cons ) ) ) )
| ( j
!= ( int @ one_one ) ) ),
inference(rewrite,[status(thm)],[1462,1375]) ).
thf(107,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
thf(472,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(13,axiom,
! [A: int @ list,B: int,C: int,D: int @ list,E: int] :
( ( D @ ( E @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ ( C @ nDvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_atom_Osimps_I6_J) ).
thf(185,plain,
! [A: int @ list,B: int,C: int,D: int @ list,E: int] :
( ( D @ ( E @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ ( C @ nDvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(769,plain,
! [D: int @ ( int @ fun ),C: int @ ( int @ fun ) @ list,B: int @ ( int @ fun ),A: int @ ( int @ fun ) @ list] :
( ( D
!= ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) ) )
| ( B
!= ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) ) )
| ( ( C @ ( D @ ( int @ ( int @ fun ) @ cons ) ) )
!= ( A @ ( B @ ( int @ ( int @ fun ) @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[131,767]) ).
thf(770,plain,
! [C: int @ ( int @ fun ) @ list,B: int @ ( int @ fun ),A: int @ ( int @ fun ) @ list] :
( ( B
!= ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) ) )
| ( ( C @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ fun ) @ cons ) ) )
!= ( A @ ( B @ ( int @ ( int @ fun ) @ cons ) ) ) ) ),
inference(pattern_uni,[status(thm)],[769:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) ))]]) ).
thf(782,plain,
! [B: int @ ( int @ fun ) @ list,A: int @ ( int @ fun ) @ list] :
( ( B @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ fun ) @ cons ) ) )
!= ( A @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ fun ) @ cons ) ) ) ),
inference(simp,[status(thm)],[770]) ).
thf(139,plain,
~ ? [A: int @ list,B: int,C: int @ list,D: int,E: int] :
( ( C @ ( D @ ( E @ nDvd ) ) )
= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ),
inference(miniscope,[status(thm)],[138]) ).
thf(140,plain,
! [E: int,D: int,C: int @ list,B: int,A: int @ list] :
( ( C @ ( D @ ( E @ nDvd ) ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ),
inference(cnf,[status(esa)],[139]) ).
thf(141,plain,
! [E: int,D: int,C: int @ list,B: int,A: int @ list] :
( ( C @ ( D @ ( E @ nDvd ) ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ),
inference(lifteq,[status(thm)],[140]) ).
thf(1547,plain,
! [E: int,D: int,C: int @ list,B: int,A: int @ list] :
( ( ( ks @ ( int @ one_one @ ( int @ cons ) ) @ ( l @ ( d @ nDvd ) ) )
!= ( C @ ( D @ ( E @ nDvd ) ) ) )
| ( ( A @ ( B @ c_PresArith_Oatom_OLe ) )
!= a ) ),
inference(paramod_ordered,[status(thm)],[1521,141]) ).
thf(1548,plain,
! [B: int,A: int @ list] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) )
!= a ),
inference(pattern_uni,[status(thm)],[1547:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ks @ ( int @ one_one @ ( int @ cons ) ) )),bind(D,$thf( l )),bind(E,$thf( d ))]]) ).
thf(1598,plain,
! [F: int,E: int @ list,D: atom,C: atom @ list,B: atom,A: atom @ list] :
( ( B
!= ( E @ ( F @ c_PresArith_Oatom_OLe ) ) )
| ( D != a )
| ( ( C @ ( D @ ( atom @ cons ) ) )
!= ( A @ ( B @ ( atom @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[131,1548]) ).
thf(1599,plain,
! [E: int @ list,D: int,C: atom,B: atom @ list,A: atom @ list] :
( ( C != a )
| ( ( B @ ( C @ ( atom @ cons ) ) )
!= ( A @ ( E @ ( D @ c_PresArith_Oatom_OLe ) @ ( atom @ cons ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1598:[bind(A,$thf( A )),bind(B,$thf( H @ ( G @ c_PresArith_Oatom_OLe ) )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( H )),bind(F,$thf( G ))]]) ).
thf(1601,plain,
! [D: int @ list,C: int,B: atom @ list,A: atom @ list] :
( ( B @ ( a @ ( atom @ cons ) ) )
!= ( A @ ( D @ ( C @ c_PresArith_Oatom_OLe ) @ ( atom @ cons ) ) ) ),
inference(simp,[status(thm)],[1599]) ).
thf(49,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_add__left__imp__eq) ).
thf(301,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(1422,plain,
! [B: int @ list,A: int @ list] :
( ( sk9 != A )
| ( i
!= ( int @ one_one ) )
| ( ks != B )
| ( j
!= ( int @ one_one ) ) ),
inference(simp,[status(thm)],[1407]) ).
thf(1464,plain,
( ( i
!= ( int @ one_one ) )
| ( j
!= ( int @ one_one ) ) ),
inference(simp,[status(thm)],[1422]) ).
thf(1511,plain,
! [D: int,C: int @ list,B: int,A: int @ list] :
( ( D != i )
| ( B
!= ( int @ one_one ) )
| ( j
!= ( int @ one_one ) )
| ( ( C @ ( D @ ( int @ cons ) ) )
!= ( A @ ( B @ ( int @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[131,1464]) ).
thf(1512,plain,
! [C: int @ list,B: int,A: int @ list] :
( ( B
!= ( int @ one_one ) )
| ( j
!= ( int @ one_one ) )
| ( ( C @ ( i @ ( int @ cons ) ) )
!= ( A @ ( B @ ( int @ cons ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1511:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( i ))]]) ).
thf(1518,plain,
! [B: int @ list,A: int @ list] :
( ( j
!= ( int @ one_one ) )
| ( ( B @ ( i @ ( int @ cons ) ) )
!= ( A @ ( int @ one_one @ ( int @ cons ) ) ) ) ),
inference(simp,[status(thm)],[1512]) ).
thf(3786,plain,
! [TB: $tType,E: int @ ( int @ fun ) @ list,D: int @ ( int @ fun ) @ list,C: int @ ( int @ fun ) @ ( TB @ fun ),B: TB,A: TB @ list] :
( ( ( A @ ( C @ ( int @ ( int @ fun ) @ ( TB @ map ) ) ) @ ( B @ ( C @ ( int @ ( int @ fun ) @ ( TB @ aa ) ) ) @ ( int @ ( int @ fun ) @ cons ) ) )
!= ( D @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ fun ) @ cons ) ) ) )
| ( ( A @ ( B @ ( TB @ cons ) ) @ ( C @ ( int @ ( int @ fun ) @ ( TB @ map ) ) ) )
!= ( E @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ fun ) @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,782]) ).
thf(3787,plain,
! [B: int @ list,A: int @ ( int @ fun ) @ list] :
( ( B @ ( i @ ( int @ cons ) ) @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ map ) ) ) )
!= ( A @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ fun ) @ cons ) ) ) ),
inference(pattern_uni,[status(thm)],[3786:[bind(A,$thf( G )),bind(B,$thf( i )),bind(C,$thf( int @ plus_plus )),bind(D,$thf( G @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ map ) ) ) )),bind(E,$thf( E )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( int ))]]) ).
thf(4156,plain,
! [B: int @ list,A: int @ ( int @ fun ) @ list] :
( ( B @ ( i @ ( int @ cons ) ) @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ map ) ) ) )
!= ( A @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ fun ) @ cons ) ) ) ),
inference(simp,[status(thm)],[3787]) ).
thf(94,axiom,
! [TA: $tType] :
( ( TA @ comm_ring )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) @ ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_square__diff__square__factored) ).
thf(436,plain,
! [TA: $tType] :
( ( TA @ comm_ring )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) @ ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(78,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( B @ ( C @ ( TA @ div_mod ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_zmod__simps_I4_J) ).
thf(389,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( B @ ( C @ ( TA @ div_mod ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(12,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 ) ) )
= ( A @ ( C @ ( TA @ list @ minus_minus ) ) @ ( B @ ( D @ ( TA @ minus_minus ) ) @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_list__diff__Cons__Cons) ).
thf(182,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 ) ) )
= ( A @ ( C @ ( TA @ list @ minus_minus ) ) @ ( B @ ( D @ ( TA @ minus_minus ) ) @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(183,plain,
! [TA: $tType,D: TA,C: TA @ list,B: TA,A: TA @ list] :
( ( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ list @ minus_minus ) ) )
= ( A @ ( C @ ( TA @ list @ minus_minus ) ) @ ( B @ ( D @ ( TA @ minus_minus ) ) @ ( TA @ cons ) ) ) )
| ~ ( TA @ zero )
| ~ ( TA @ cl_Groups_Ominus ) ),
inference(cnf,[status(esa)],[182]) ).
thf(184,plain,
! [TA: $tType,D: TA,C: TA @ list,B: TA,A: TA @ list] :
( ~ ( TA @ zero )
| ~ ( TA @ cl_Groups_Ominus )
| ( ( A @ ( C @ ( TA @ list @ minus_minus ) ) @ ( B @ ( D @ ( TA @ minus_minus ) ) @ ( TA @ cons ) ) )
= ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ list @ minus_minus ) ) ) ) ),
inference(lifteq,[status(thm)],[183]) ).
thf(10,axiom,
! [A: int @ list,B: int,C: int @ list,D: int] :
( ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_atom_Osimps_I1_J) ).
thf(166,plain,
! [A: int @ list,B: int,C: int @ list,D: int] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ) )
& ( ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(167,plain,
( ! [A: int @ list,B: int,C: int @ list,D: int] :
( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ) )
& ! [A: int @ list,B: int,C: int @ list,D: int] :
( ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(miniscope,[status(thm)],[166]) ).
thf(168,plain,
! [H: int,G: int @ list,F: int,E: int @ list,D: int,C: int @ list,B: int,A: int @ list] :
( ( ( ( G @ ( H @ c_PresArith_Oatom_OLe ) )
= ( E @ ( F @ c_PresArith_Oatom_OLe ) ) )
| ( G != E )
| ( H != F ) )
& ( ( C = A )
| ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ) )
& ( ( D = B )
| ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ) ) ),
inference(cnf,[status(esa)],[167]) ).
thf(170,plain,
! [D: int,C: int @ list,B: int,A: int @ list] :
( ( C = A )
| ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ) ),
inference(cnfConj,[status(thm)],[168]) ).
thf(175,plain,
! [D: int,C: int @ list,B: int,A: int @ list] :
( ( C = A )
| ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ) ),
inference(lifteq,[status(thm)],[170]) ).
thf(2782,plain,
! [D: int,C: int @ list,B: int,A: int @ list] :
( ( A != sk9 )
| ( C
!= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) )
| ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ) ),
inference(paramod_ordered,[status(thm)],[175,1401]) ).
thf(2783,plain,
! [C: int,B: int @ list,A: int] :
( ( B
!= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) )
| ( ( B @ ( C @ c_PresArith_Oatom_OLe ) )
!= ( sk9 @ ( A @ c_PresArith_Oatom_OLe ) ) ) ),
inference(pattern_uni,[status(thm)],[2782:[bind(A,$thf( sk9 ))]]) ).
thf(3131,plain,
! [B: int,A: int] :
( ( ks @ ( int @ one_one @ ( int @ cons ) ) @ ( B @ c_PresArith_Oatom_OLe ) )
!= ( sk9 @ ( A @ c_PresArith_Oatom_OLe ) ) ),
inference(simp,[status(thm)],[2783]) ).
thf(64,axiom,
int @ ab_semigroup_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__mult) ).
thf(357,plain,
int @ ab_semigroup_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(89,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(421,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(21,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_list__add__assoc) ).
thf(228,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( B @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(43,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(289,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(9,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/sandbox2/benchmark/theBenchmark.p',fact_94_atom_Osimps_I2_J) ).
thf(148,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)],[9]) ).
thf(149,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 ) ) ) ) )
& ! [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 ) ) ) ),
inference(miniscope,[status(thm)],[148]) ).
thf(150,plain,
! [L: int,K: int,J: int @ list,I: int,H: int,G: int @ list,F: int,E: int,D: int @ list,C: int,B: int,A: int @ list] :
( ( ( ( J @ ( K @ ( L @ dvd ) ) )
= ( G @ ( H @ ( I @ dvd ) ) ) )
| ( J != G )
| ( K != H )
| ( L != I ) )
& ( ( D = A )
| ( ( D @ ( E @ ( F @ dvd ) ) )
!= ( A @ ( B @ ( C @ dvd ) ) ) ) )
& ( ( E = B )
| ( ( D @ ( E @ ( F @ dvd ) ) )
!= ( A @ ( B @ ( C @ dvd ) ) ) ) )
& ( ( F = C )
| ( ( D @ ( E @ ( F @ dvd ) ) )
!= ( A @ ( B @ ( C @ dvd ) ) ) ) ) ),
inference(cnf,[status(esa)],[149]) ).
thf(151,plain,
! [F: int,E: int,D: int @ list,C: int,B: int,A: int @ list] :
( ( F = C )
| ( ( D @ ( E @ ( F @ dvd ) ) )
!= ( A @ ( B @ ( C @ dvd ) ) ) ) ),
inference(cnfConj,[status(thm)],[150]) ).
thf(155,plain,
! [F: int,E: int,D: int @ list,C: int,B: int,A: int @ list] :
( ( F = C )
| ( ( D @ ( E @ ( F @ dvd ) ) )
!= ( A @ ( B @ ( C @ dvd ) ) ) ) ),
inference(lifteq,[status(thm)],[151]) ).
thf(156,plain,
? [A: int > ( int @ list ) > atom > int] :
! [B: int,C: int,D: int @ list] :
( ( D @ ( C @ ( B @ dvd ) ) @ ( D @ ( C @ A ) ) )
= B ),
inference(detectInverse,[status(thm)],[155]) ).
thf(157,plain,
! [C: int @ list,B: int,A: int] :
( ( C @ ( B @ ( A @ dvd ) ) @ ( C @ ( B @ sk1 ) ) )
= A ),
inference(cnf,[status(esa)],[156]) ).
thf(1922,plain,
! [C: int @ list,B: int,A: int] :
( ( C @ ( B @ ( A @ dvd ) ) @ ( C @ ( B @ sk1 ) ) )
= A ),
inference(lifteq,[status(thm)],[157]) ).
thf(806,plain,
! [F: int @ list,E: int @ list,D: int @ list,C: int @ list @ list,B: int @ list,A: int @ list @ list] :
( ( B
!= ( F @ ( j @ ( int @ cons ) ) ) )
| ( D
!= ( E @ ( i @ ( int @ cons ) ) ) )
| ( ( C @ ( D @ ( int @ list @ cons ) ) )
!= ( A @ ( B @ ( int @ list @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[131,795]) ).
thf(807,plain,
! [E: int @ list,D: int @ list,C: int @ list,B: int @ list @ list,A: int @ list @ list] :
( ( C
!= ( D @ ( i @ ( int @ cons ) ) ) )
| ( ( B @ ( C @ ( int @ list @ cons ) ) )
!= ( A @ ( E @ ( j @ ( int @ cons ) ) @ ( int @ list @ cons ) ) ) ) ),
inference(pattern_uni,[status(thm)],[806:[bind(A,$thf( A )),bind(B,$thf( H @ ( j @ ( int @ cons ) ) )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( H ))]]) ).
thf(817,plain,
! [D: int @ list,C: int @ list,B: int @ list @ list,A: int @ list @ list] :
( ( B @ ( C @ ( i @ ( int @ cons ) ) @ ( int @ list @ cons ) ) )
!= ( A @ ( D @ ( j @ ( int @ cons ) ) @ ( int @ list @ cons ) ) ) ),
inference(simp,[status(thm)],[807]) ).
thf(73,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_mod__add__right__eq) ).
thf(376,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(61,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(348,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(8,axiom,
! [A: atom,B: int @ list,C: int] :
( ( A @ ( B @ ( C @ asubst ) ) @ divisor )
= ( A @ divisor ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_divisor__asubst) ).
thf(145,plain,
! [A: atom,B: int @ list,C: int] :
( ( A @ ( B @ ( C @ asubst ) ) @ divisor )
= ( A @ divisor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(146,plain,
! [C: int,B: int @ list,A: atom] :
( ( A @ ( B @ ( C @ asubst ) ) @ divisor )
= ( A @ divisor ) ),
inference(cnf,[status(esa)],[145]) ).
thf(147,plain,
! [C: int,B: int @ list,A: atom] :
( ( A @ ( B @ ( C @ asubst ) ) @ divisor )
= ( A @ divisor ) ),
inference(lifteq,[status(thm)],[146]) ).
thf(82,axiom,
( ( a @ hd_coeff )
= ( int @ one_one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_assms_I2_J) ).
thf(397,plain,
( ( a @ hd_coeff )
= ( int @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(40,axiom,
! [TA: $tType,A: int @ list,B: int,C: int,D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),F: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ ( C @ nDvd ) ) @ ( D @ ( E @ ( F @ ( TA @ atom_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_atom_Orecs_I3_J) ).
thf(280,plain,
! [TA: $tType,A: int @ list,B: int,C: int,D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),F: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ ( C @ nDvd ) ) @ ( D @ ( E @ ( F @ ( TA @ atom_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(129,plain,
! [TA: $tType,D: TA,C: TA @ list,B: TA,A: TA @ list] :
( ( C = A )
| ( ( C @ ( D @ ( TA @ cons ) ) )
!= ( A @ ( B @ ( TA @ cons ) ) ) ) ),
inference(cnfConj,[status(thm)],[127]) ).
thf(132,plain,
! [TA: $tType,D: TA,C: TA @ list,B: TA,A: TA @ list] :
( ( C = A )
| ( ( C @ ( D @ ( TA @ cons ) ) )
!= ( A @ ( B @ ( TA @ cons ) ) ) ) ),
inference(lifteq,[status(thm)],[129]) ).
thf(81,axiom,
int @ comm_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__ring) ).
thf(396,plain,
int @ comm_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(1596,plain,
! [F: int,E: int @ list,D: atom,C: atom @ list,B: atom,A: atom @ list] :
( ( D
!= ( E @ ( F @ c_PresArith_Oatom_OLe ) ) )
| ( B != a )
| ( ( C @ ( D @ ( atom @ cons ) ) )
!= ( A @ ( B @ ( atom @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[131,1548]) ).
thf(1597,plain,
! [E: int @ list,D: int,C: atom @ list,B: atom,A: atom @ list] :
( ( B != a )
| ( ( C @ ( E @ ( D @ c_PresArith_Oatom_OLe ) @ ( atom @ cons ) ) )
!= ( A @ ( B @ ( atom @ cons ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1596:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ c_PresArith_Oatom_OLe ) )),bind(E,$thf( H )),bind(F,$thf( G ))]]) ).
thf(1600,plain,
! [D: int @ list,C: int,B: atom @ list,A: atom @ list] :
( ( B @ ( D @ ( C @ c_PresArith_Oatom_OLe ) @ ( atom @ cons ) ) )
!= ( A @ ( a @ ( atom @ cons ) ) ) ),
inference(simp,[status(thm)],[1597]) ).
thf(35,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_mod__add__left__eq) ).
thf(265,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(44,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_mod__mod__trivial) ).
thf(292,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(75,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(380,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(95,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
thf(439,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(5544,plain,
! [B: int,A: int @ list] :
( ( ( ks @ ( int @ one_one @ ( int @ cons ) ) )
!= ( A @ ( B @ ( int @ cons ) ) ) )
| ( ( sk9 @ ( int @ one_one @ ( int @ one_one @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) )
!= A ) ),
inference(paramod_ordered,[status(thm)],[5495,137]) ).
thf(5545,plain,
( ( sk9 @ ( int @ one_one @ ( int @ one_one @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) )
!= ks ),
inference(pattern_uni,[status(thm)],[5544:[bind(A,$thf( ks )),bind(B,$thf( int @ one_one ))]]) ).
thf(6182,plain,
( ( ( sk9 @ ( int @ one_one @ ( int @ one_one @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) )
!= ( sk9 @ ( int @ one_one @ ( int @ one_one @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) ) )
| ( ( ks @ ( int @ one_one @ ( int @ cons ) ) )
!= ks ) ),
inference(paramod_ordered,[status(thm)],[5495,5545]) ).
thf(6183,plain,
( ( ks @ ( int @ one_one @ ( int @ cons ) ) )
!= ks ),
inference(pattern_uni,[status(thm)],[6182:[]]) ).
thf(2900,plain,
! [F: int @ list,E: int @ list,D: int,C: int @ list,B: int,A: int @ list] :
( ( C
!= ( F @ ( j @ ( int @ cons ) ) ) )
| ( A
!= ( E @ ( i @ ( int @ cons ) ) ) )
| ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ) ),
inference(paramod_ordered,[status(thm)],[175,795]) ).
thf(2901,plain,
! [E: int @ list,D: int @ list,C: int,B: int,A: int @ list] :
( ( A
!= ( D @ ( i @ ( int @ cons ) ) ) )
| ( ( E @ ( j @ ( int @ cons ) ) @ ( C @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ) ),
inference(pattern_uni,[status(thm)],[2900:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( H @ ( j @ ( int @ cons ) ) )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( H ))]]) ).
thf(3054,plain,
! [D: int @ list,C: int @ list,B: int,A: int] :
( ( D @ ( j @ ( int @ cons ) ) @ ( B @ c_PresArith_Oatom_OLe ) )
!= ( C @ ( i @ ( int @ cons ) ) @ ( A @ c_PresArith_Oatom_OLe ) ) ),
inference(simp,[status(thm)],[2901]) ).
thf(56,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ cl_Groups_Ominus )
=> ( TA @ ( TB @ fun ) @ cl_Groups_Ominus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Groups_Ominus) ).
thf(334,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ cl_Groups_Ominus )
=> ( TA @ ( TB @ fun ) @ cl_Groups_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(79,axiom,
int @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(392,plain,
int @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(47,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( TA @ one_one @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
thf(297,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( TA @ one_one @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(90,axiom,
! [A: int @ list,B: int] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ divisor )
= ( int @ one_one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_divisor_Osimps_I1_J) ).
thf(424,plain,
! [A: int @ list,B: int] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ divisor )
= ( int @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(15,axiom,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_not__Cons__self) ).
thf(192,plain,
! [TA: $tType,A: TA,B: TA @ list] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(802,plain,
! [F: int @ list,E: int @ list,D: int @ list,C: int @ list @ list,B: int @ list,A: int @ list @ list] :
( ( D
!= ( E @ ( i @ ( int @ cons ) ) ) )
| ( B
!= ( F @ ( j @ ( int @ cons ) ) ) )
| ( ( C @ ( D @ ( int @ list @ cons ) ) )
!= ( A @ ( B @ ( int @ list @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[131,795]) ).
thf(803,plain,
! [E: int @ list,D: int @ list,C: int @ list @ list,B: int @ list,A: int @ list @ list] :
( ( B
!= ( D @ ( j @ ( int @ cons ) ) ) )
| ( ( C @ ( E @ ( i @ ( int @ cons ) ) @ ( int @ list @ cons ) ) )
!= ( A @ ( B @ ( int @ list @ cons ) ) ) ) ),
inference(pattern_uni,[status(thm)],[802:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( H @ ( i @ ( int @ cons ) ) )),bind(E,$thf( H )),bind(F,$thf( F ))]]) ).
thf(815,plain,
! [D: int @ list,C: int @ list,B: int @ list @ list,A: int @ list @ list] :
( ( B @ ( D @ ( i @ ( int @ cons ) ) @ ( int @ list @ cons ) ) )
!= ( A @ ( C @ ( j @ ( int @ cons ) ) @ ( int @ list @ cons ) ) ) ),
inference(simp,[status(thm)],[803]) ).
thf(111,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( C @ ( D @ ( E @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( D @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
<=> ( ( C @ ( D @ ( B @ ( E @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_eq__add__iff1) ).
thf(484,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( ( C @ ( D @ ( B @ ( E @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A )
=> ( ( C @ ( D @ ( E @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( D @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( D @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( ( C @ ( D @ ( B @ ( E @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(30,axiom,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(252,plain,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(16,axiom,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ nDvd ) ) @ divisor )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_divisor_Osimps_I3_J) ).
thf(195,plain,
! [A: int @ list,B: int,C: int] :
( ( A @ ( B @ ( C @ nDvd ) ) @ divisor )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(196,plain,
! [C: int,B: int,A: int @ list] :
( ( A @ ( B @ ( C @ nDvd ) ) @ divisor )
= C ),
inference(cnf,[status(esa)],[195]) ).
thf(197,plain,
! [C: int,B: int,A: int @ list] :
( ( A @ ( B @ ( C @ nDvd ) ) @ divisor )
= C ),
inference(lifteq,[status(thm)],[196]) ).
thf(3784,plain,
! [TB: $tType,E: int @ ( int @ fun ) @ list,D: int @ ( int @ fun ) @ list,C: int @ ( int @ fun ) @ ( TB @ fun ),B: TB,A: TB @ list] :
( ( ( A @ ( C @ ( int @ ( int @ fun ) @ ( TB @ map ) ) ) @ ( B @ ( C @ ( int @ ( int @ fun ) @ ( TB @ aa ) ) ) @ ( int @ ( int @ fun ) @ cons ) ) )
!= ( E @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ fun ) @ cons ) ) ) )
| ( ( A @ ( B @ ( TB @ cons ) ) @ ( C @ ( int @ ( int @ fun ) @ ( TB @ map ) ) ) )
!= ( D @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ fun ) @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[477,782]) ).
thf(3785,plain,
! [B: int @ list,A: int @ ( int @ fun ) @ list] :
( ( B @ ( j @ ( int @ cons ) ) @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ map ) ) ) )
!= ( A @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ fun ) @ cons ) ) ) ),
inference(pattern_uni,[status(thm)],[3784:[bind(A,$thf( G )),bind(B,$thf( j )),bind(C,$thf( int @ plus_plus )),bind(D,$thf( D )),bind(E,$thf( G @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ map ) ) ) )),bind_type(TA,$thf( TA )),bind_type(TB,$thf( int ))]]) ).
thf(4155,plain,
! [B: int @ list,A: int @ ( int @ fun ) @ list] :
( ( B @ ( j @ ( int @ cons ) ) @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ map ) ) ) )
!= ( A @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ fun ) @ cons ) ) ) ),
inference(simp,[status(thm)],[3785]) ).
thf(121,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(522,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(19,axiom,
! [TA: $tType] :
( ( ( TA @ zero )
& ( TA @ cl_Groups_Oplus ) )
=> ! [A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ cons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_list__add__Cons) ).
thf(224,plain,
! [TA: $tType] :
( ( ( TA @ zero )
& ( TA @ cl_Groups_Oplus ) )
=> ! [A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(120,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( D @ ( E @ ( TA @ div_mod ) ) )
= ( D @ ( C @ ( TA @ div_mod ) ) ) )
=> ( ( ( D @ ( B @ ( TA @ div_mod ) ) )
= ( D @ ( A @ ( TA @ div_mod ) ) ) )
=> ( ( D @ ( B @ ( E @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( D @ ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_mod__add__cong) ).
thf(519,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( D @ ( E @ ( TA @ div_mod ) ) )
= ( D @ ( C @ ( TA @ div_mod ) ) ) )
=> ( ( ( D @ ( B @ ( TA @ div_mod ) ) )
= ( D @ ( A @ ( TA @ div_mod ) ) ) )
=> ( ( D @ ( B @ ( E @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( D @ ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(52,axiom,
int @ monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
thf(317,plain,
int @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(186,plain,
~ ? [A: int @ list,B: int,C: int,D: int @ list,E: int] :
( ( D @ ( E @ c_PresArith_Oatom_OLe ) )
= ( A @ ( B @ ( C @ nDvd ) ) ) ),
inference(miniscope,[status(thm)],[185]) ).
thf(187,plain,
! [E: int,D: int @ list,C: int,B: int,A: int @ list] :
( ( D @ ( E @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ ( C @ nDvd ) ) ) ),
inference(cnf,[status(esa)],[186]) ).
thf(188,plain,
! [E: int,D: int @ list,C: int,B: int,A: int @ list] :
( ( D @ ( E @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ ( C @ nDvd ) ) ) ),
inference(lifteq,[status(thm)],[187]) ).
thf(775,plain,
! [D: int @ ( int @ fun ),C: int @ ( int @ fun ) @ list,B: int @ ( int @ fun ),A: int @ ( int @ fun ) @ list] :
( ( B
!= ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) ) )
| ( D
!= ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) ) )
| ( ( C @ ( D @ ( int @ ( int @ fun ) @ cons ) ) )
!= ( A @ ( B @ ( int @ ( int @ fun ) @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[131,767]) ).
thf(776,plain,
! [C: int @ ( int @ fun ),B: int @ ( int @ fun ) @ list,A: int @ ( int @ fun ) @ list] :
( ( C
!= ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) ) )
| ( ( B @ ( C @ ( int @ ( int @ fun ) @ cons ) ) )
!= ( A @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ fun ) @ cons ) ) ) ) ),
inference(pattern_uni,[status(thm)],[775:[bind(A,$thf( A )),bind(B,$thf( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(783,plain,
! [B: int @ ( int @ fun ) @ list,A: int @ ( int @ fun ) @ list] :
( ( B @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ fun ) @ cons ) ) )
!= ( A @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ fun ) @ cons ) ) ) ),
inference(simp,[status(thm)],[776]) ).
thf(54,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( C @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_mod__mult__self1) ).
thf(328,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( C @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(58,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_mod__mult__mult2) ).
thf(339,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(810,plain,
! [F: int @ list,E: int @ list,D: int @ list,C: int @ list @ list,B: int @ list,A: int @ list @ list] :
( ( B
!= ( E @ ( i @ ( int @ cons ) ) ) )
| ( D
!= ( F @ ( j @ ( int @ cons ) ) ) )
| ( ( C @ ( D @ ( int @ list @ cons ) ) )
!= ( A @ ( B @ ( int @ list @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[131,795]) ).
thf(811,plain,
! [E: int @ list,D: int @ list,C: int @ list,B: int @ list @ list,A: int @ list @ list] :
( ( C
!= ( D @ ( j @ ( int @ cons ) ) ) )
| ( ( B @ ( C @ ( int @ list @ cons ) ) )
!= ( A @ ( E @ ( i @ ( int @ cons ) ) @ ( int @ list @ cons ) ) ) ) ),
inference(pattern_uni,[status(thm)],[810:[bind(A,$thf( A )),bind(B,$thf( H @ ( i @ ( int @ cons ) ) )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( H )),bind(F,$thf( F ))]]) ).
thf(819,plain,
! [D: int @ list,C: int @ list,B: int @ list @ list,A: int @ list @ list] :
( ( B @ ( C @ ( j @ ( int @ cons ) ) @ ( int @ list @ cons ) ) )
!= ( A @ ( D @ ( i @ ( int @ cons ) ) @ ( int @ list @ cons ) ) ) ),
inference(simp,[status(thm)],[811]) ).
thf(1379,plain,
! [D: int @ list,C: int @ list,B: int @ list @ list,A: int @ list @ list] :
( ( ( sk9 @ ( int @ one_one @ ( int @ cons ) ) )
!= ( D @ ( i @ ( int @ cons ) ) ) )
| ( ( A @ ( ks @ ( int @ one_one @ ( int @ cons ) ) @ ( int @ list @ cons ) ) )
!= ( B @ ( C @ ( j @ ( int @ cons ) ) @ ( int @ list @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1375,819]) ).
thf(1419,plain,
! [D: int @ list,C: int @ list,B: int @ list @ list,A: int @ list @ list] :
( ( sk9 != D )
| ( i
!= ( int @ one_one ) )
| ( A != B )
| ( ( ks @ ( int @ one_one @ ( int @ cons ) ) )
!= ( C @ ( j @ ( int @ cons ) ) ) ) ),
inference(simp,[status(thm)],[1379]) ).
thf(1461,plain,
! [A: int @ list] :
( ( i
!= ( int @ one_one ) )
| ( ( ks @ ( int @ one_one @ ( int @ cons ) ) )
!= ( A @ ( j @ ( int @ cons ) ) ) ) ),
inference(simp,[status(thm)],[1419]) ).
thf(123,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_add__left__cancel) ).
thf(526,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(80,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(393,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(116,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
thf(503,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(66,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_mod__mult__left__eq) ).
thf(360,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(755,plain,
! [D: int,C: int @ list,B: int,A: int @ list] :
( ( B
!= ( e @ ( ks @ ( int @ iprod ) ) @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) ) )
| ( D
!= ( e @ ( ks @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) ) )
| ( ( C @ ( D @ ( int @ cons ) ) )
!= ( A @ ( B @ ( int @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[131,536]) ).
thf(756,plain,
! [C: int,B: int @ list,A: int @ list] :
( ( C
!= ( e @ ( ks @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) ) )
| ( ( B @ ( C @ ( int @ cons ) ) )
!= ( A @ ( e @ ( ks @ ( int @ iprod ) ) @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) ) ) ),
inference(pattern_uni,[status(thm)],[755:[bind(A,$thf( A )),bind(B,$thf( e @ ( ks @ ( int @ iprod ) ) @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(765,plain,
! [B: int @ list,A: int @ list] :
( ( B @ ( e @ ( ks @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) )
!= ( A @ ( e @ ( ks @ ( int @ iprod ) ) @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) ) ),
inference(simp,[status(thm)],[756]) ).
thf(398,plain,
( ( a @ hd_coeff )
= ( int @ one_one ) ),
inference(lifteq,[status(thm)],[397]) ).
thf(2780,plain,
! [D: int,C: int @ list,B: int,A: int @ list] :
( ( C != sk9 )
| ( A
!= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) )
| ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ) ),
inference(paramod_ordered,[status(thm)],[175,1401]) ).
thf(2781,plain,
! [C: int,B: int,A: int @ list] :
( ( A
!= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) )
| ( ( sk9 @ ( C @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ) ),
inference(pattern_uni,[status(thm)],[2780:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk9 ))]]) ).
thf(3130,plain,
! [B: int,A: int] :
( ( sk9 @ ( B @ c_PresArith_Oatom_OLe ) )
!= ( ks @ ( int @ one_one @ ( int @ cons ) ) @ ( A @ c_PresArith_Oatom_OLe ) ) ),
inference(simp,[status(thm)],[2781]) ).
thf(1935,plain,
! [D: int @ list,C: int,B: atom @ list,A: atom @ list] :
( ( B != A )
| ( ( D @ ( C @ c_PresArith_Oatom_OLe ) )
!= a ) ),
inference(simp,[status(thm)],[1600]) ).
thf(1959,plain,
! [B: int @ list,A: int] :
( ( B @ ( A @ c_PresArith_Oatom_OLe ) )
!= a ),
inference(simp,[status(thm)],[1935]) ).
thf(153,plain,
! [F: int,E: int,D: int @ list,C: int,B: int,A: int @ list] :
( ( D = A )
| ( ( D @ ( E @ ( F @ dvd ) ) )
!= ( A @ ( B @ ( C @ dvd ) ) ) ) ),
inference(cnfConj,[status(thm)],[150]) ).
thf(161,plain,
! [F: int,E: int,D: int @ list,C: int,B: int,A: int @ list] :
( ( D = A )
| ( ( D @ ( E @ ( F @ dvd ) ) )
!= ( A @ ( B @ ( C @ dvd ) ) ) ) ),
inference(lifteq,[status(thm)],[153]) ).
thf(97,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/sandbox2/benchmark/theBenchmark.p',fact_29_zipwith0_Osimps_I2_J) ).
thf(444,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( ( TC @ zero )
& ( TA @ zero ) )
=> ! [A: TA @ list,B: TA,C: TC @ list,D: TC,E: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TC @ cons ) ) @ ( E @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) )
= ( A @ ( C @ ( E @ ( TB @ ( TA @ ( TC @ zipwith0 ) ) ) @ ( TB @ list @ ( TA @ list @ fun ) @ ( TC @ list @ aa ) ) ) @ ( TB @ list @ ( TA @ list @ aa ) ) ) @ ( B @ ( D @ ( E @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ cons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(65,axiom,
( ( a @ divisor @ ( i @ ( int @ div_mod ) ) )
= ( a @ divisor @ ( j @ ( int @ div_mod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I3_J) ).
thf(358,plain,
( ( a @ divisor @ ( i @ ( int @ div_mod ) ) )
= ( a @ divisor @ ( j @ ( int @ div_mod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(359,plain,
( ( a @ divisor @ ( j @ ( int @ div_mod ) ) )
= ( a @ divisor @ ( i @ ( int @ div_mod ) ) ) ),
inference(lifteq,[status(thm)],[358]) ).
thf(1678,plain,
! [C: int,B: int,A: int @ list] :
( ( ( ks @ ( int @ one_one @ ( int @ cons ) ) @ ( l @ ( d @ nDvd ) ) )
!= ( A @ ( B @ ( C @ nDvd ) ) ) )
| ( ( a @ divisor )
= C ) ),
inference(paramod_ordered,[status(thm)],[1521,197]) ).
thf(1679,plain,
( ( a @ divisor )
= d ),
inference(pattern_uni,[status(thm)],[1678:[bind(A,$thf( ks @ ( int @ one_one @ ( int @ cons ) ) )),bind(B,$thf( l )),bind(C,$thf( d ))]]) ).
thf(1754,plain,
( ( d @ ( j @ ( int @ div_mod ) ) )
= ( d @ ( i @ ( int @ div_mod ) ) ) ),
inference(rewrite,[status(thm)],[359,1679]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_mod__add__self1) ).
thf(430,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(11,axiom,
! [TA: $tType] :
( ( ( TA @ cl_Groups_Oplus )
& ( TA @ zero ) )
=> ( TA @ list @ cl_Groups_Oplus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_List_Olist___Groups_Oplus) ).
thf(180,plain,
! [TA: $tType] :
( ( ( TA @ cl_Groups_Oplus )
& ( TA @ zero ) )
=> ( TA @ list @ cl_Groups_Oplus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(46,axiom,
int @ comm_semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(296,plain,
int @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(42,axiom,
! [TA: $tType,A: int @ list,B: int,C: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ ( C @ ( D @ ( E @ ( TA @ atom_case ) ) ) ) )
= ( A @ ( B @ ( E @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_atom_Osimps_I10_J) ).
thf(286,plain,
! [TA: $tType,A: int @ list,B: int,C: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ ( C @ ( D @ ( E @ ( TA @ atom_case ) ) ) ) )
= ( A @ ( B @ ( E @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(33,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(259,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(84,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(402,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(7,axiom,
bool @ cl_Groups_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ominus) ).
thf(144,plain,
bool @ cl_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(152,plain,
! [F: int,E: int,D: int @ list,C: int,B: int,A: int @ list] :
( ( E = B )
| ( ( D @ ( E @ ( F @ dvd ) ) )
!= ( A @ ( B @ ( C @ dvd ) ) ) ) ),
inference(cnfConj,[status(thm)],[150]) ).
thf(158,plain,
! [F: int,E: int,D: int @ list,C: int,B: int,A: int @ list] :
( ( E = B )
| ( ( D @ ( E @ ( F @ dvd ) ) )
!= ( A @ ( B @ ( C @ dvd ) ) ) ) ),
inference(lifteq,[status(thm)],[152]) ).
thf(159,plain,
? [A: int > ( int @ list ) > atom > int] :
! [B: int,C: int,D: int @ list] :
( ( D @ ( C @ ( B @ dvd ) ) @ ( D @ ( B @ A ) ) )
= C ),
inference(detectInverse,[status(thm)],[158]) ).
thf(160,plain,
! [C: int @ list,B: int,A: int] :
( ( C @ ( B @ ( A @ dvd ) ) @ ( C @ ( A @ sk2 ) ) )
= B ),
inference(cnf,[status(esa)],[159]) ).
thf(1997,plain,
! [C: int @ list,B: int,A: int] :
( ( C @ ( B @ ( A @ dvd ) ) @ ( C @ ( A @ sk2 ) ) )
= B ),
inference(lifteq,[status(thm)],[160]) ).
thf(181,plain,
! [TA: $tType] :
( ( TA @ list @ cl_Groups_Oplus )
| ~ ( TA @ cl_Groups_Oplus )
| ~ ( TA @ zero ) ),
inference(cnf,[status(esa)],[180]) ).
thf(641,plain,
! [TB: $tType,F: TB,E: TB @ list,D: TB @ list,C: TB @ list @ list,B: TB @ list,A: TB @ list @ list] :
( ( B
!= ( E @ ( F @ ( TB @ cons ) ) ) )
| ( D != E )
| ( ( C @ ( D @ ( TB @ list @ cons ) ) )
!= ( A @ ( B @ ( TB @ list @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[131,137]) ).
thf(642,plain,
! [TB: $tType,E: TB @ list,D: TB,C: TB @ list,B: TB @ list @ list,A: TB @ list @ list] :
( ( C != E )
| ( ( B @ ( C @ ( TB @ list @ cons ) ) )
!= ( A @ ( E @ ( D @ ( TB @ cons ) ) @ ( TB @ list @ cons ) ) ) ) ),
inference(pattern_uni,[status(thm)],[641:[bind(A,$thf( A )),bind(B,$thf( H @ ( G @ ( TB @ cons ) ) )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( H )),bind(F,$thf( G ))]]) ).
thf(672,plain,
! [TA: $tType,D: TA @ list,C: TA,B: TA @ list @ list,A: TA @ list @ list] :
( ( B @ ( D @ ( TA @ list @ cons ) ) )
!= ( A @ ( D @ ( C @ ( TA @ cons ) ) @ ( TA @ list @ cons ) ) ) ),
inference(simp,[status(thm)],[642]) ).
thf(169,plain,
! [D: int,C: int @ list,B: int,A: int @ list] :
( ( D = B )
| ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ) ),
inference(cnfConj,[status(thm)],[168]) ).
thf(172,plain,
! [D: int,C: int @ list,B: int,A: int @ list] :
( ( D = B )
| ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ) ),
inference(lifteq,[status(thm)],[169]) ).
thf(38,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_mod__add__eq) ).
thf(274,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(27,axiom,
int @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
thf(245,plain,
int @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( C @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
<=> ( ( C = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_crossproduct__eq) ).
thf(318,plain,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ( C = A )
| ( D = B ) )
=> ( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( C @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) )
& ( ( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( C @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( ( C = A )
| ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(118,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_add__right__cancel) ).
thf(509,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(2148,plain,
! [F: int,E: int,D: int @ list,C: int,B: int,A: int @ list] :
( ( D != sk9 )
| ( A
!= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) )
| ( ( D @ ( E @ ( F @ dvd ) ) )
!= ( A @ ( B @ ( C @ dvd ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[161,1401]) ).
thf(2149,plain,
! [E: int,D: int,C: int,B: int,A: int @ list] :
( ( A
!= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) )
| ( ( sk9 @ ( D @ ( E @ dvd ) ) )
!= ( A @ ( B @ ( C @ dvd ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2148:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( sk9 ))]]) ).
thf(2378,plain,
! [D: int,C: int,B: int,A: int] :
( ( sk9 @ ( C @ ( D @ dvd ) ) )
!= ( ks @ ( int @ one_one @ ( int @ cons ) ) @ ( A @ ( B @ dvd ) ) ) ),
inference(simp,[status(thm)],[2149]) ).
thf(37,axiom,
! [TA: $tType] :
( ( TA @ ab_semigroup_mult )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(271,plain,
! [TA: $tType] :
( ( TA @ ab_semigroup_mult )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(113,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( C @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_mod__mult__self2) ).
thf(494,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( C @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(3450,plain,
! [C: int @ list,B: int,A: int] :
( ( ( ks @ ( int @ one_one @ ( int @ cons ) ) @ ( l @ ( d @ nDvd ) ) )
!= ( C @ ( B @ ( A @ nDvd ) ) ) )
| ( ( a @ ( B @ ( A @ sk8 ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[1521,3449]) ).
thf(3451,plain,
( ( a @ ( l @ ( d @ sk8 ) ) )
= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) ),
inference(pattern_uni,[status(thm)],[3450:[bind(A,$thf( d )),bind(B,$thf( l )),bind(C,$thf( ks @ ( int @ one_one @ ( int @ cons ) ) ))]]) ).
thf(17,axiom,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( TA @ one_one )
= A )
<=> ( A
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_one__reorient) ).
thf(198,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)],[17]) ).
thf(103,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_mod__add__self2) ).
thf(462,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(60,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(345,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(2902,plain,
! [F: int @ list,E: int @ list,D: int,C: int @ list,B: int,A: int @ list] :
( ( C
!= ( E @ ( i @ ( int @ cons ) ) ) )
| ( A
!= ( F @ ( j @ ( int @ cons ) ) ) )
| ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ) ),
inference(paramod_ordered,[status(thm)],[175,795]) ).
thf(2903,plain,
! [E: int @ list,D: int @ list,C: int,B: int,A: int @ list] :
( ( A
!= ( D @ ( j @ ( int @ cons ) ) ) )
| ( ( E @ ( i @ ( int @ cons ) ) @ ( C @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ) ),
inference(pattern_uni,[status(thm)],[2902:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( H @ ( i @ ( int @ cons ) ) )),bind(D,$thf( D )),bind(E,$thf( H )),bind(F,$thf( F ))]]) ).
thf(3055,plain,
! [D: int @ list,C: int @ list,B: int,A: int] :
( ( D @ ( i @ ( int @ cons ) ) @ ( B @ c_PresArith_Oatom_OLe ) )
!= ( C @ ( j @ ( int @ cons ) ) @ ( A @ c_PresArith_Oatom_OLe ) ) ),
inference(simp,[status(thm)],[2903]) ).
thf(83,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(399,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(25,axiom,
int @ semiri456707255roduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(241,plain,
int @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(5537,plain,
( ( ( ks @ ( int @ one_one @ ( int @ cons ) ) )
!= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) )
| ( ( sk9 @ ( int @ one_one @ ( int @ one_one @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( l @ ( d @ nDvd ) ) )
= a ) ),
inference(paramod_ordered,[status(thm)],[5495,1521]) ).
thf(5538,plain,
( ( sk9 @ ( int @ one_one @ ( int @ one_one @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( l @ ( d @ nDvd ) ) )
= a ),
inference(pattern_uni,[status(thm)],[5537:[]]) ).
thf(425,plain,
! [B: int,A: int @ list] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ divisor )
= ( int @ one_one ) ),
inference(cnf,[status(esa)],[424]) ).
thf(426,plain,
! [B: int,A: int @ list] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ divisor )
= ( int @ one_one ) ),
inference(lifteq,[status(thm)],[425]) ).
thf(31,axiom,
! [TA: $tType,A: int @ list,B: int,C: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ ( C @ ( D @ ( E @ ( TA @ atom_rec ) ) ) ) )
= ( A @ ( B @ ( E @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_atom_Orecs_I1_J) ).
thf(255,plain,
! [TA: $tType,A: int @ list,B: int,C: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ c_PresArith_Oatom_OLe ) @ ( C @ ( D @ ( E @ ( TA @ atom_rec ) ) ) ) )
= ( A @ ( B @ ( E @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(119,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_zmod__simps_I2_J) ).
thf(516,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(59,axiom,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_mult__left__idem) ).
thf(342,plain,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(101,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_mult__1__right) ).
thf(458,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(193,plain,
! [TA: $tType,B: TA @ list,A: TA] :
( B
!= ( B @ ( A @ ( TA @ cons ) ) ) ),
inference(cnf,[status(esa)],[192]) ).
thf(194,plain,
! [TA: $tType,B: TA @ list,A: TA] :
( ( B @ ( A @ ( TA @ cons ) ) )
!= B ),
inference(lifteq,[status(thm)],[193]) ).
thf(122,axiom,
int @ comm_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring) ).
thf(525,plain,
int @ comm_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(45,axiom,
int @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(295,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(162,plain,
? [A: int > int > atom > ( int @ list )] :
! [B: int,C: int,D: int @ list] :
( ( D @ ( C @ ( B @ dvd ) ) @ ( C @ ( B @ A ) ) )
= D ),
inference(detectInverse,[status(thm)],[161]) ).
thf(163,plain,
! [C: int @ list,B: int,A: int] :
( ( C @ ( B @ ( A @ dvd ) ) @ ( B @ ( A @ sk3 ) ) )
= C ),
inference(cnf,[status(esa)],[162]) ).
thf(2092,plain,
! [C: int @ list,B: int,A: int] :
( ( C @ ( B @ ( A @ dvd ) ) @ ( B @ ( A @ sk3 ) ) )
= C ),
inference(lifteq,[status(thm)],[163]) ).
thf(55,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(331,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(71,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_mod__mult__eq) ).
thf(370,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( A @ ( C @ ( TA @ div_mod ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(57,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( A @ ( B @ ( int @ div_mod ) ) @ ( C @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) )
= ( A @ ( B @ ( C @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_zmod__simps_I3_J) ).
thf(336,plain,
! [A: int,B: int,C: int] :
( ( A @ ( A @ ( B @ ( int @ div_mod ) ) @ ( C @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) )
= ( A @ ( B @ ( C @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(2150,plain,
! [F: int,E: int,D: int @ list,C: int,B: int,A: int @ list] :
( ( A != sk9 )
| ( D
!= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) )
| ( ( D @ ( E @ ( F @ dvd ) ) )
!= ( A @ ( B @ ( C @ dvd ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[161,1401]) ).
thf(2151,plain,
! [E: int,D: int,C: int @ list,B: int,A: int] :
( ( C
!= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) )
| ( ( C @ ( D @ ( E @ dvd ) ) )
!= ( sk9 @ ( A @ ( B @ dvd ) ) ) ) ),
inference(pattern_uni,[status(thm)],[2150:[bind(A,$thf( sk9 ))]]) ).
thf(2379,plain,
! [D: int,C: int,B: int,A: int] :
( ( ks @ ( int @ one_one @ ( int @ cons ) ) @ ( C @ ( D @ dvd ) ) )
!= ( sk9 @ ( A @ ( B @ dvd ) ) ) ),
inference(simp,[status(thm)],[2151]) ).
thf(51,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(314,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(77,axiom,
! [TA: $tType,A: int @ list,B: int,C: int,D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),F: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ ( C @ nDvd ) ) @ ( D @ ( E @ ( F @ ( TA @ atom_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_atom_Osimps_I12_J) ).
thf(386,plain,
! [TA: $tType,A: int @ list,B: int,C: int,D: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),E: TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ fun ),F: TA @ ( int @ list @ fun ) @ ( int @ fun )] :
( ( A @ ( B @ ( C @ nDvd ) ) @ ( D @ ( E @ ( F @ ( TA @ atom_case ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TA @ ( int @ list @ fun ) @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ fun ) @ ( int @ aa ) ) ) @ ( TA @ ( int @ list @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(143,plain,
! [TA: $tType] :
( ( TA @ list @ cl_Groups_Ominus )
| ~ ( TA @ cl_Groups_Ominus )
| ~ ( TA @ zero ) ),
inference(cnf,[status(esa)],[142]) ).
thf(114,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(497,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(99,axiom,
! [TA: $tType] :
( ( ( TA @ zero )
& ( TA @ cl_Groups_Oplus ) )
=> ( ( TA @ list @ plus_plus )
= ( TA @ plus_plus @ ( TA @ ( TA @ ( TA @ zipwith0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_list__add__def) ).
thf(450,plain,
! [TA: $tType] :
( ( ( TA @ zero )
& ( TA @ cl_Groups_Oplus ) )
=> ( ( TA @ list @ plus_plus )
= ( TA @ plus_plus @ ( TA @ ( TA @ ( TA @ zipwith0 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(67,axiom,
int @ semiring_div,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Divides_Osemiring__div) ).
thf(363,plain,
int @ semiring_div,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(639,plain,
! [TB: $tType,F: TB,E: TB @ list,D: TB @ list,C: TB @ list @ list,B: TB @ list,A: TB @ list @ list] :
( ( D
!= ( E @ ( F @ ( TB @ cons ) ) ) )
| ( B != E )
| ( ( C @ ( D @ ( TB @ list @ cons ) ) )
!= ( A @ ( B @ ( TB @ list @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[131,137]) ).
thf(640,plain,
! [TB: $tType,E: TB @ list,D: TB,C: TB @ list @ list,B: TB @ list,A: TB @ list @ list] :
( ( B != E )
| ( ( C @ ( E @ ( D @ ( TB @ cons ) ) @ ( TB @ list @ cons ) ) )
!= ( A @ ( B @ ( TB @ list @ cons ) ) ) ) ),
inference(pattern_uni,[status(thm)],[639:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ ( TB @ cons ) ) )),bind(E,$thf( H )),bind(F,$thf( G ))]]) ).
thf(671,plain,
! [TA: $tType,D: TA @ list,C: TA,B: TA @ list @ list,A: TA @ list @ list] :
( ( B @ ( D @ ( C @ ( TA @ cons ) ) @ ( TA @ list @ cons ) ) )
!= ( A @ ( D @ ( TA @ list @ cons ) ) ) ),
inference(simp,[status(thm)],[640]) ).
thf(173,plain,
? [A: ( int @ list ) > atom > int] :
! [B: int,C: int @ list] :
( ( C @ ( B @ c_PresArith_Oatom_OLe ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[172]) ).
thf(174,plain,
! [B: int @ list,A: int] :
( ( B @ ( A @ c_PresArith_Oatom_OLe ) @ ( B @ sk4 ) )
= A ),
inference(cnf,[status(esa)],[173]) ).
thf(1844,plain,
! [B: int @ list,A: int] :
( ( B @ ( A @ c_PresArith_Oatom_OLe ) @ ( B @ sk4 ) )
= A ),
inference(lifteq,[status(thm)],[174]) ).
thf(1509,plain,
! [D: int,C: int @ list,B: int,A: int @ list] :
( ( D != j )
| ( i
!= ( int @ one_one ) )
| ( B
!= ( int @ one_one ) )
| ( ( C @ ( D @ ( int @ cons ) ) )
!= ( A @ ( B @ ( int @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[131,1464]) ).
thf(1510,plain,
! [C: int @ list,B: int,A: int @ list] :
( ( i
!= ( int @ one_one ) )
| ( B
!= ( int @ one_one ) )
| ( ( C @ ( j @ ( int @ cons ) ) )
!= ( A @ ( B @ ( int @ cons ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1509:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( j ))]]) ).
thf(1517,plain,
! [B: int @ list,A: int @ list] :
( ( i
!= ( int @ one_one ) )
| ( ( B @ ( j @ ( int @ cons ) ) )
!= ( A @ ( int @ one_one @ ( int @ cons ) ) ) ) ),
inference(simp,[status(thm)],[1510]) ).
thf(741,plain,
! [D: int,C: int @ list,B: int,A: int @ list] :
( ( D
!= ( e @ ( ks @ ( int @ iprod ) ) @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) ) )
| ( B
!= ( e @ ( ks @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) ) )
| ( ( C @ ( D @ ( int @ cons ) ) )
!= ( A @ ( B @ ( int @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[131,536]) ).
thf(742,plain,
! [C: int @ list,B: int,A: int @ list] :
( ( B
!= ( e @ ( ks @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) ) )
| ( ( C @ ( e @ ( ks @ ( int @ iprod ) ) @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) )
!= ( A @ ( B @ ( int @ cons ) ) ) ) ),
inference(pattern_uni,[status(thm)],[741:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( e @ ( ks @ ( int @ iprod ) ) @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) ))]]) ).
thf(759,plain,
! [B: int @ list,A: int @ list] :
( ( B @ ( e @ ( ks @ ( int @ iprod ) ) @ ( j @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) )
!= ( A @ ( e @ ( ks @ ( int @ iprod ) ) @ ( i @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) ) ),
inference(simp,[status(thm)],[742]) ).
thf(104,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_comm__semiring__class_Odistrib) ).
thf(465,plain,
! [TA: $tType] :
( ( TA @ comm_semiring )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(22,axiom,
! [A: int @ list,B: int,C: int,D: int,E: int @ list,F: int] :
( ( A @ ( B @ ( int @ cons ) ) @ ( C @ ( D @ nDvd ) ) @ ( E @ ( F @ asubst ) ) )
= ( A @ ( E @ ( B @ ( int @ times_times ) @ ( int @ ( int @ map ) ) ) @ ( int @ list @ plus_plus @ ( int @ list @ ( int @ list @ fun ) @ ( int @ list @ aa ) ) ) @ ( int @ list @ ( int @ list @ aa ) ) ) @ ( F @ ( B @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( C @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( D @ nDvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_asubst_Osimps_I3_J) ).
thf(231,plain,
! [A: int @ list,B: int,C: int,D: int,E: int @ list,F: int] :
( ( A @ ( B @ ( int @ cons ) ) @ ( C @ ( D @ nDvd ) ) @ ( E @ ( F @ asubst ) ) )
= ( A @ ( E @ ( B @ ( int @ times_times ) @ ( int @ ( int @ map ) ) ) @ ( int @ list @ plus_plus @ ( int @ list @ ( int @ list @ fun ) @ ( int @ list @ aa ) ) ) @ ( int @ list @ ( int @ list @ aa ) ) ) @ ( F @ ( B @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( C @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( D @ nDvd ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(2904,plain,
! [F: int @ list,E: int @ list,D: int,C: int @ list,B: int,A: int @ list] :
( ( A
!= ( F @ ( j @ ( int @ cons ) ) ) )
| ( C
!= ( E @ ( i @ ( int @ cons ) ) ) )
| ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ) ),
inference(paramod_ordered,[status(thm)],[175,795]) ).
thf(2905,plain,
! [E: int @ list,D: int @ list,C: int,B: int @ list,A: int] :
( ( B
!= ( D @ ( i @ ( int @ cons ) ) ) )
| ( ( B @ ( C @ c_PresArith_Oatom_OLe ) )
!= ( E @ ( j @ ( int @ cons ) ) @ ( A @ c_PresArith_Oatom_OLe ) ) ) ),
inference(pattern_uni,[status(thm)],[2904:[bind(A,$thf( H @ ( j @ ( int @ cons ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( H ))]]) ).
thf(3056,plain,
! [D: int @ list,C: int @ list,B: int,A: int] :
( ( C @ ( i @ ( int @ cons ) ) @ ( B @ c_PresArith_Oatom_OLe ) )
!= ( D @ ( j @ ( int @ cons ) ) @ ( A @ c_PresArith_Oatom_OLe ) ) ),
inference(simp,[status(thm)],[2905]) ).
thf(50,axiom,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( B != A )
& ( D != C ) )
<=> ( ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
!= ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_crossproduct__noteq) ).
thf(304,plain,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
!= ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( ( B != A )
& ( D != C ) ) )
& ( ( ( B != A )
& ( D != C ) )
=> ( ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
!= ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(1505,plain,
! [D: int @ list,C: int @ list @ list,B: int @ list,A: int @ list @ list] :
( ( B != sk9 )
| ( D
!= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) )
| ( ( C @ ( D @ ( int @ list @ cons ) ) )
!= ( A @ ( B @ ( int @ list @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[131,1401]) ).
thf(1506,plain,
! [C: int @ list,B: int @ list @ list,A: int @ list @ list] :
( ( C
!= ( ks @ ( int @ one_one @ ( int @ cons ) ) ) )
| ( ( B @ ( C @ ( int @ list @ cons ) ) )
!= ( A @ ( sk9 @ ( int @ list @ cons ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1505:[bind(A,$thf( A )),bind(B,$thf( sk9 ))]]) ).
thf(1508,plain,
! [B: int @ list @ list,A: int @ list @ list] :
( ( B @ ( ks @ ( int @ one_one @ ( int @ cons ) ) @ ( int @ list @ cons ) ) )
!= ( A @ ( sk9 @ ( int @ list @ cons ) ) ) ),
inference(simp,[status(thm)],[1506]) ).
thf(32,axiom,
int @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(258,plain,
int @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(88,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_mod__mult__right__eq) ).
thf(418,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( TA @ div_mod ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(62,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( B @ ( C @ ( TA @ div_mod ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_zmod__simps_I1_J) ).
thf(351,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( B @ ( C @ ( TA @ div_mod ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(93,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_add__right__imp__eq) ).
thf(433,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(109,axiom,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( D @ ( E @ ( TA @ div_mod ) ) )
= ( D @ ( C @ ( TA @ div_mod ) ) ) )
=> ( ( ( D @ ( B @ ( TA @ div_mod ) ) )
= ( D @ ( A @ ( TA @ div_mod ) ) ) )
=> ( ( D @ ( B @ ( E @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( D @ ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_mod__mult__cong) ).
thf(478,plain,
! [TA: $tType] :
( ( TA @ semiring_div )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( D @ ( E @ ( TA @ div_mod ) ) )
= ( D @ ( C @ ( TA @ div_mod ) ) ) )
=> ( ( ( D @ ( B @ ( TA @ div_mod ) ) )
= ( D @ ( A @ ( TA @ div_mod ) ) ) )
=> ( ( D @ ( B @ ( E @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) )
= ( D @ ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ div_mod ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(76,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ map ) ) ) @ ( TA @ iprod ) ) )
= ( A @ ( B @ ( TA @ iprod ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_iprod__assoc) ).
thf(383,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ map ) ) ) @ ( TA @ iprod ) ) )
= ( A @ ( B @ ( TA @ iprod ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(24,axiom,
! [A: int @ list,B: atom,C: int @ list,D: int] :
( ( A @ ( B @ ( C @ ( D @ asubst ) ) @ i_Z ) )
<=> ( A @ ( A @ ( C @ ( int @ iprod ) ) @ ( D @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( B @ i_Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_IZ__asubst) ).
thf(235,plain,
! [A: int @ list,B: atom,C: int @ list,D: int] :
( ( ( A @ ( A @ ( C @ ( int @ iprod ) ) @ ( D @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( B @ i_Z ) )
=> ( A @ ( B @ ( C @ ( D @ asubst ) ) @ i_Z ) ) )
& ( ( A @ ( B @ ( C @ ( D @ asubst ) ) @ i_Z ) )
=> ( A @ ( A @ ( C @ ( int @ iprod ) ) @ ( D @ ( int @ plus_plus @ ( int @ ( int @ fun ) @ ( int @ aa ) ) ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) @ ( B @ i_Z ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(28,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_mult )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_mult__1) ).
thf(246,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_mult )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(48,axiom,
int @ one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(300,plain,
int @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(98,axiom,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_add__imp__eq) ).
thf(447,plain,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(793,plain,
! [D: int,C: int @ list,B: int,A: int @ list] :
( ( B != j )
| ( D != i )
| ( ( C @ ( D @ ( int @ cons ) ) )
!= ( A @ ( B @ ( int @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[131,781]) ).
thf(794,plain,
! [C: int,B: int @ list,A: int @ list] :
( ( C != i )
| ( ( B @ ( C @ ( int @ cons ) ) )
!= ( A @ ( j @ ( int @ cons ) ) ) ) ),
inference(pattern_uni,[status(thm)],[793:[bind(A,$thf( A )),bind(B,$thf( j ))]]) ).
thf(796,plain,
! [B: int @ list,A: int @ list] :
( ( B @ ( i @ ( int @ cons ) ) )
!= ( A @ ( j @ ( int @ cons ) ) ) ),
inference(simp,[status(thm)],[794]) ).
thf(5669,plain,
! [B: int @ list,A: int @ list] :
( ( ( sk9 @ ( int @ one_one @ ( int @ one_one @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ cons ) ) )
!= ( A @ ( j @ ( int @ cons ) ) ) )
| ( ( ks @ ( int @ one_one @ ( int @ cons ) ) )
!= ( B @ ( i @ ( int @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[5495,796]) ).
thf(5737,plain,
! [B: int @ list,A: int @ list] :
( ( sk9 != A )
| ( j
!= ( int @ one_one @ ( int @ one_one @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) ) )
| ( ks != B )
| ( i
!= ( int @ one_one ) ) ),
inference(simp,[status(thm)],[5669]) ).
thf(5971,plain,
( ( j
!= ( int @ one_one @ ( int @ one_one @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) ) )
| ( i
!= ( int @ one_one ) ) ),
inference(simp,[status(thm)],[5737]) ).
thf(34,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(262,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(85,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_mult )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_mult_Ocomm__neutral) ).
thf(405,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_mult )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(72,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ iprod ) ) )
= ( A @ ( B @ ( TA @ iprod ) ) @ ( A @ ( C @ ( TA @ iprod ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_iprod__left__add__distrib) ).
thf(373,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA @ list,C: TA @ list] :
( ( A @ ( B @ ( C @ ( TA @ list @ plus_plus @ ( TA @ list @ ( TA @ list @ fun ) @ ( TA @ list @ aa ) ) ) @ ( TA @ list @ ( TA @ list @ aa ) ) ) @ ( TA @ iprod ) ) )
= ( A @ ( B @ ( TA @ iprod ) ) @ ( A @ ( C @ ( TA @ iprod ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(176,plain,
? [A: int > atom > ( int @ list )] :
! [B: int,C: int @ list] :
( ( C @ ( B @ c_PresArith_Oatom_OLe ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[175]) ).
thf(177,plain,
! [B: int @ list,A: int] :
( ( B @ ( A @ c_PresArith_Oatom_OLe ) @ ( A @ sk5 ) )
= B ),
inference(cnf,[status(esa)],[176]) ).
thf(1859,plain,
! [B: int @ list,A: int] :
( ( B @ ( A @ c_PresArith_Oatom_OLe ) @ ( A @ sk5 ) )
= B ),
inference(lifteq,[status(thm)],[177]) ).
thf(26,axiom,
! [A: int @ list,B: int,C: int,D: int @ list,E: int] :
( ( A @ ( B @ ( int @ cons ) ) @ ( C @ c_PresArith_Oatom_OLe ) @ ( D @ ( E @ asubst ) ) )
= ( A @ ( D @ ( B @ ( int @ times_times ) @ ( int @ ( int @ map ) ) ) @ ( int @ list @ plus_plus @ ( int @ list @ ( int @ list @ fun ) @ ( int @ list @ aa ) ) ) @ ( int @ list @ ( int @ list @ aa ) ) ) @ ( E @ ( B @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( C @ ( int @ minus_minus ) ) @ c_PresArith_Oatom_OLe ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_asubst_Osimps_I1_J) ).
thf(242,plain,
! [A: int @ list,B: int,C: int,D: int @ list,E: int] :
( ( A @ ( B @ ( int @ cons ) ) @ ( C @ c_PresArith_Oatom_OLe ) @ ( D @ ( E @ asubst ) ) )
= ( A @ ( D @ ( B @ ( int @ times_times ) @ ( int @ ( int @ map ) ) ) @ ( int @ list @ plus_plus @ ( int @ list @ ( int @ list @ fun ) @ ( int @ list @ aa ) ) ) @ ( int @ list @ ( int @ list @ aa ) ) ) @ ( E @ ( B @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( C @ ( int @ minus_minus ) ) @ c_PresArith_Oatom_OLe ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(87,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( C @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( int @ div_mod ) ) @ ( C @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_zmod__zmult1__eq) ).
thf(415,plain,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( C @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) )
= ( A @ ( A @ ( B @ ( int @ div_mod ) ) @ ( C @ ( int @ times_times ) @ ( int @ ( int @ aa ) ) ) @ ( int @ div_mod ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(117,axiom,
! [TA: $tType] :
( ( TA @ semiring )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( C @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( B @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_combine__common__factor) ).
thf(506,plain,
! [TA: $tType] :
( ( TA @ semiring )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( C @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( B @ ( D @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(36,axiom,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_times_Oidem) ).
thf(268,plain,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(41,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ iprod ) ) )
= ( A @ ( C @ ( TA @ iprod ) ) @ ( B @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_iprod__Cons) ).
thf(283,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA @ list,B: TA,C: TA @ list,D: TA] :
( ( A @ ( B @ ( TA @ cons ) ) @ ( C @ ( D @ ( TA @ cons ) ) @ ( TA @ iprod ) ) )
= ( A @ ( C @ ( TA @ iprod ) ) @ ( B @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(91,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( TA @ one_one @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
thf(427,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( TA @ one_one @ ( B @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(2906,plain,
! [F: int @ list,E: int @ list,D: int,C: int @ list,B: int,A: int @ list] :
( ( A
!= ( E @ ( i @ ( int @ cons ) ) ) )
| ( C
!= ( F @ ( j @ ( int @ cons ) ) ) )
| ( ( C @ ( D @ c_PresArith_Oatom_OLe ) )
!= ( A @ ( B @ c_PresArith_Oatom_OLe ) ) ) ),
inference(paramod_ordered,[status(thm)],[175,795]) ).
thf(2907,plain,
! [E: int @ list,D: int @ list,C: int,B: int @ list,A: int] :
( ( B
!= ( D @ ( j @ ( int @ cons ) ) ) )
| ( ( B @ ( C @ c_PresArith_Oatom_OLe ) )
!= ( E @ ( i @ ( int @ cons ) ) @ ( A @ c_PresArith_Oatom_OLe ) ) ) ),
inference(pattern_uni,[status(thm)],[2906:[bind(A,$thf( H @ ( i @ ( int @ cons ) ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( H )),bind(F,$thf( F ))]]) ).
thf(3057,plain,
! [D: int @ list,C: int @ list,B: int,A: int] :
( ( C @ ( j @ ( int @ cons ) ) @ ( B @ c_PresArith_Oatom_OLe ) )
!= ( D @ ( i @ ( int @ cons ) ) @ ( A @ c_PresArith_Oatom_OLe ) ) ),
inference(simp,[status(thm)],[2907]) ).
thf(798,plain,
! [F: int @ list,E: int @ list,D: int @ list,C: int @ list @ list,B: int @ list,A: int @ list @ list] :
( ( D
!= ( F @ ( j @ ( int @ cons ) ) ) )
| ( B
!= ( E @ ( i @ ( int @ cons ) ) ) )
| ( ( C @ ( D @ ( int @ list @ cons ) ) )
!= ( A @ ( B @ ( int @ list @ cons ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[131,795]) ).
thf(799,plain,
! [E: int @ list,D: int @ list,C: int @ list @ list,B: int @ list,A: int @ list @ list] :
( ( B
!= ( D @ ( i @ ( int @ cons ) ) ) )
| ( ( C @ ( E @ ( j @ ( int @ cons ) ) @ ( int @ list @ cons ) ) )
!= ( A @ ( B @ ( int @ list @ cons ) ) ) ) ),
inference(pattern_uni,[status(thm)],[798:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( H @ ( j @ ( int @ cons ) ) )),bind(E,$thf( E )),bind(F,$thf( H ))]]) ).
thf(822,plain,
! [D: int @ list,C: int @ list,B: int @ list @ list,A: int @ list @ list] :
( ( B @ ( D @ ( j @ ( int @ cons ) ) @ ( int @ list @ cons ) ) )
!= ( A @ ( C @ ( i @ ( int @ cons ) ) @ ( int @ list @ cons ) ) ) ),
inference(simp,[status(thm)],[799]) ).
thf(39,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(277,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ plus_plus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(20,axiom,
int @ cl_Groups_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ominus) ).
thf(227,plain,
int @ cl_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(106,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_mult__1__left) ).
thf(469,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( A @ ( TA @ one_one @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(63,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(354,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) @ ( D @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(112,axiom,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_mult__idem) ).
thf(491,plain,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ times_times ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(68,axiom,
int @ comm_monoid_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).
thf(364,plain,
int @ comm_monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(13241,plain,
$false,
inference(e,[status(thm)],[249,468,481,365,138,3449,234,408,5644,1401,379,5614,142,500,1507,1872,472,185,2723,782,1601,301,1518,4156,436,389,184,3131,125,357,189,421,228,289,1922,817,475,443,376,348,147,397,280,5384,453,132,396,1600,265,1521,206,292,380,439,6183,5545,534,3054,334,392,297,424,192,137,815,4160,484,252,197,4155,522,461,224,519,317,1375,188,141,783,328,124,339,1461,526,393,503,360,765,398,3130,1959,166,148,1548,161,444,1754,430,180,296,819,286,259,191,402,144,1997,181,1464,672,172,274,245,318,509,2378,271,477,494,213,3451,155,198,462,345,3055,399,2725,135,5495,241,5538,426,795,255,516,342,458,2582,194,145,525,295,2092,182,331,370,1679,336,2379,314,2584,175,386,143,497,450,363,671,1844,1517,759,465,231,368,3056,304,1508,258,418,781,158,351,433,478,383,536,235,246,300,447,5971,262,405,373,1859,242,126,358,195,767,415,506,268,796,283,427,3057,822,131,277,442,227,469,354,491,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM040_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.40 % Computer : n020.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 23:25:19 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.83/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.38/1.28 % [INFO] Parsing done (280ms).
% 1.38/1.30 % [INFO] Running in sequential loop mode.
% 2.98/1.71 % [INFO] eprover registered as external prover.
% 2.98/1.72 % [INFO] Scanning for conjecture ...
% 3.24/1.89 % [INFO] Found a conjecture (or negated_conjecture) and 123 axioms. Running axiom selection ...
% 3.50/2.01 % [INFO] Axiom selection finished. Selected 121 axioms (removed 2 axioms).
% 4.49/2.17 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.49/2.19 % [INFO] Type checking passed.
% 4.49/2.19 % [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 ...
% 118.68/41.41 % External prover 'e' found a proof!
% 118.68/41.41 % [INFO] Killing All external provers ...
% 118.68/41.41 % Time passed: 40860ms (effective reasoning time: 40110ms)
% 118.68/41.41 % 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)>
% 118.68/41.42 % Axioms used in derivation (121): fact_94_atom_Osimps_I2_J, fact_93_asubst_Osimps_I1_J, fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_81_not__Cons__self2, arity_Int_Oint___Groups_Oone, fact_16_ab__semigroup__add__class_Oadd__ac_I1_J, arity_Int_Oint___Rings_Ocomm__ring, arity_Int_Oint___Groups_Ominus, fact_2_mod__add__self1, fact_52_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_72_zmod__simps_I3_J, fact_22_list__add__def, fact_37_iprod__Cons, fact_23_assms_I2_J, fact_89_scale1, arity_HOL_Obool___Groups_Ominus, fact_0_assms_I3_J, arity_Int_Oint___Rings_Oring, fact_11_zmod__simps_I2_J, fact_83_comm__semiring__class_Odistrib, fact_30_list__add__Cons, fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, arity_Int_Oint___Rings_Ocomm__semiring, arity_Int_Oint___Groups_Ocancel__ab__semigroup__add, fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_75_atom_Osimps_I6_J, fact_59_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact_53_ab__semigroup__mult__class_Omult__ac_I1_J, fact_39_divisor__asubst, fact_67_mod__mult__mult2, fact_50_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_12_list__add__assoc, fact_95_list__diff__Cons__Cons, fact_13_add__right__imp__eq, fact_80_not__Cons__self, arity_Int_Oint___Groups_Oplus, fact_74_ext, fact_69_mod__mult__eq, fact_92_asubst_Osimps_I2_J, fact_76_atom_Osimps_I7_J, fact_82_mult__left__idem, fact_43_atom_Osimps_I10_J, arity_List_Olist___Groups_Ominus, fact_90_mult__idem, fact_3_NDvd, fact_1_mod__add__self2, fact_87_map_Osimps_I2_J, fact_28__096_B_Bthesis_O_A_I_B_Bks_H_O_Aks_A_061_A1_A_D_Aks_H_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_44_atom_Orecs_I1_J, arity_List_Olist___Groups_Oplus, fact_66_zmod__simps_I4_J, fact_24_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_64_mult__1__left, fact_60_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_18_zmod__simps_I1_J, fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, arity_Int_Oint___Groups_Omonoid__mult, fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_91_times_Oidem, fact_98_square__diff__square__factored, fact_15_add__left__imp__eq, fact_36_atom_Orecs_I3_J, fact_14_add__imp__eq, fact_63_mult__1, fact_41_mod__mult__self1, fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_51_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_71_mod__mult__right__eq, fact_9_mod__add__left__eq, fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_73_zmod__zmult1__eq, fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_4_mod__mod__trivial, fact_40_atom_Osimps_I1_J, arity_Int_Oint___Rings_Osemiring, fact_70_mod__mult__left__eq, arity_Int_Oint___Groups_Omonoid__add, fact_7_iprod__left__add__distrib, fact_85_IZ__asubst, arity_Int_Oint___Groups_Ocancel__semigroup__add, fact_31_one__reorient, arity_Int_Oint___Rings_Ocomm__semiring__1, fact_65_mod__mult__cong, fact_5_add__left__cancel, fact_62_mult__1__right, fact_97_eq__add__iff2, fact_19_atom_Osimps_I3_J, fact_47_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_6_add__right__cancel, fact_10_mod__add__eq, fact_86_asubst_Osimps_I3_J, arity_Int_Oint___Groups_Oab__semigroup__add, fact_20__096ks_A_061_A1_A_D_Aks_H_096, fact_42_mod__mult__self2, fact_54_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_68_mod__mult__mult1, fact_58_crossproduct__eq, fact_29_zipwith0_Osimps_I2_J, arity_Int_Oint___Groups_Oab__semigroup__mult, fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_35_atom_Osimps_I12_J, fact_61_mult_Ocomm__neutral, fact_55_crossproduct__noteq, fact_96_eq__add__iff1, fact_21_divisor_Osimps_I3_J, arity_Int_Oint___Divides_Osemiring__div, fact_88_iprod__assoc, fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_38_divisor_Osimps_I1_J, arity_Int_Oint___Groups_Ozero, fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_84_combine__common__factor, fact_49_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, arity_Int_Oint___Groups_Ocomm__monoid__mult, fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_34_list_Oinject, arity_fun___Groups_Ominus, fact_8_mod__add__right__eq, fact_17_mod__add__cong, fact_48_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J
% 118.68/41.42 % No. of inferences in proof: 470
% 118.68/41.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 40860 ms resp. 40110 ms w/o parsing
% 119.57/41.63 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 119.57/41.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------