%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM928_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 08:10:28 AM UTC 2026
% Result : Theorem 71.50s 16.03s
% Output : Refutation 72.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 117
% Syntax : Number of formulae : 261 ( 84 unt; 0 typ; 1 def)
% Number of atoms : 580 ( 299 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 3404 ( 60 ~; 37 |; 31 &;3066 @)
% ( 14 <=>; 196 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 38 usr; 7 con; 0-5 aty)
% Number of variables : 745 ( 4 ^; 734 !; 6 ?; 745 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(number_decl,type,
number:
!>[TA: $tType] : $o ).
thf(ring_decl,type,
ring:
!>[TA: $tType] : $o ).
thf(cl_Groups_Ominus_decl,type,
cl_Groups_Ominus:
!>[TA: $tType] : $o ).
thf(ring_1_decl,type,
ring_1:
!>[TA: $tType] : $o ).
thf(semiring_decl,type,
semiring:
!>[TA: $tType] : $o ).
thf(number_ring_decl,type,
number_ring:
!>[TA: $tType] : $o ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(comm_ring_decl,type,
comm_ring:
!>[TA: $tType] : $o ).
thf(group_add_decl,type,
group_add:
!>[TA: $tType] : $o ).
thf(ab_group_add_decl,type,
ab_group_add:
!>[TA: $tType] : $o ).
thf(comm_semiring_decl,type,
comm_semiring:
!>[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(ab_semigroup_mult_decl,type,
ab_semigroup_mult:
!>[TA: $tType] : $o ).
thf(boolean_algebra_decl,type,
boolean_algebra:
!>[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(comm_monoid_decl,type,
comm_monoid:
!>[TA: $tType] : ( ( TA @ ( TA @ fun ) @ ( TA @ fun ) ) > TA > $o ) ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(semigroup_decl,type,
semigroup:
!>[TA: $tType] : ( ( TA @ ( TA @ fun ) @ ( TA @ fun ) ) > $o ) ).
thf(times_times_decl,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(uminus_uminus_decl,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(min_decl,type,
min: int ).
thf(number_number_of_decl,type,
number_number_of:
!>[TA: $tType] : ( int > TA ) ).
thf(ring_1_of_int_decl,type,
ring_1_of_int:
!>[TA: $tType] : ( int > TA ) ).
thf(product_Pair_decl,type,
product_Pair:
!>[TA: $tType,TB: $tType] : ( TB > TA > ( TA @ ( TB @ product_prod ) ) ) ).
thf(product_prod_rec_decl,type,
product_prod_rec:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ product_prod ) ) > TA ) ).
thf(twoSqu1567020053sum2sq_decl,type,
twoSqu1567020053sum2sq: int > $o ).
thf(twoSqu196287499sum2sq_decl,type,
twoSqu196287499sum2sq: ( int @ ( int @ product_prod ) ) > int ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(x_decl,type,
x: int ).
thf(y_decl,type,
y: int ).
thf(sk1_decl,type,
sk1:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > ( TA @ ( TB @ fun ) ) > TB ) ).
thf(sk1_def,definition,
( sk1
= ( ^ [TA: $tType,TB: $tType,A: TA @ ( TB @ fun ),B: TA @ ( TB @ fun )] :
@+[C: TB] :
( ( C @ ( A @ ( TA @ ( TB @ aa ) ) ) )
!= ( C @ ( B @ ( TA @ ( TB @ aa ) ) ) ) ) ) ) ).
thf(67,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( C @ ( D @ ( E @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( D @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) )
<=> ( ( C @ ( D @ ( B @ ( E @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_eq__add__iff1) ).
thf(340,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 @ plus_plus ) ) )
= A )
=> ( ( C @ ( D @ ( E @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( D @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( D @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) )
=> ( ( C @ ( D @ ( B @ ( E @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(107,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) )
= ( B @ ( A @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(457,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) )
= ( B @ ( A @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(68,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA,B: TA] :
( ( A @ ( TA @ uminus_uminus ) @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_minus__mult__minus) ).
thf(347,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA,B: TA] :
( ( A @ ( TA @ uminus_uminus ) @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(114,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(481,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(18,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_add__left__cancel) ).
thf(170,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(55,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(308,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(35,axiom,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(247,plain,
! [TA: $tType] :
( ( TA @ ab_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_Pair__eq) ).
thf(217,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(44,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( int @ minus_minus ) ) @ ( C @ ( int @ times_times ) ) )
= ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( C @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_int__distrib_I4_J) ).
thf(276,plain,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( int @ minus_minus ) ) @ ( C @ ( int @ times_times ) ) )
= ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( C @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(50,axiom,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( B != A )
& ( D != C ) )
<=> ( ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
!= ( B @ ( C @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_crossproduct__noteq) ).
thf(288,plain,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
!= ( B @ ( C @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) )
=> ( ( B != A )
& ( D != C ) ) )
& ( ( ( B != A )
& ( D != C ) )
=> ( ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
!= ( B @ ( C @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(52,axiom,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_right__distrib__number__of) ).
thf(301,plain,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(59,axiom,
int @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
thf(320,plain,
int @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(83,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( A @ ( C @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_int__distrib_I1_J) ).
thf(389,plain,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( A @ ( C @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(20,axiom,
! [TA: $tType] :
( ( ( TA @ ring_char_0 )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_eq__number__of) ).
thf(180,plain,
! [TA: $tType] :
( ( ( TA @ ring_char_0 )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) ) )
& ( ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(181,plain,
! [TA: $tType,B: int,A: int] :
( ( ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) )
| ( B != A )
| ~ ( TA @ ring_char_0 )
| ~ ( TA @ number_ring ) )
& ( ( B = A )
| ( ( B @ ( TA @ number_number_of ) )
!= ( A @ ( TA @ number_number_of ) ) )
| ~ ( TA @ ring_char_0 )
| ~ ( TA @ number_ring ) ) ),
inference(cnf,[status(esa)],[180]) ).
thf(182,plain,
! [TA: $tType,B: int,A: int] :
( ( B = A )
| ( ( B @ ( TA @ number_number_of ) )
!= ( A @ ( TA @ number_number_of ) ) )
| ~ ( TA @ ring_char_0 )
| ~ ( TA @ number_ring ) ),
inference(cnfConj,[status(thm)],[181]) ).
thf(184,plain,
! [TA: $tType,B: int,A: int] :
( ~ ( TA @ ring_char_0 )
| ~ ( TA @ number_ring )
| ( B = A )
| ( ( B @ ( TA @ number_number_of ) )
!= ( A @ ( TA @ number_number_of ) ) ) ),
inference(lifteq,[status(thm)],[182]) ).
thf(1,conjecture,
y @ ( x @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(2,negated_conjecture,
~ ( y @ ( x @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(118,plain,
~ ( y @ ( x @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(503,plain,
! [TA: $tType,B: int,A: int] :
( ( B != x )
| ~ ( y @ ( A @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq )
| ~ ( TA @ ring_char_0 )
| ~ ( TA @ number_ring )
| ( ( B @ ( TA @ number_number_of ) )
!= ( A @ ( TA @ number_number_of ) ) ) ),
inference(paramod_ordered,[status(thm)],[184,118]) ).
thf(504,plain,
! [TA: $tType,A: int] :
( ~ ( y @ ( A @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq )
| ~ ( TA @ ring_char_0 )
| ~ ( TA @ number_ring )
| ( ( x @ ( TA @ number_number_of ) )
!= ( A @ ( TA @ number_number_of ) ) ) ),
inference(pattern_uni,[status(thm)],[503:[bind(A,$thf( A )),bind(B,$thf( x ))]]) ).
thf(5,axiom,
! [TA: $tType,A: TA,B: TA,C: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( B @ ( C @ ( TA @ comm_monoid ) ) )
=> ( ( B @ ( A @ ( C @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_comm__monoid_Ocomm__neutral) ).
thf(125,plain,
! [TA: $tType,A: TA,B: TA,C: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( B @ ( C @ ( TA @ comm_monoid ) ) )
=> ( ( B @ ( A @ ( C @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(72,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_number__of__add) ).
thf(357,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(108,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(460,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(14,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_add__right__cancel) ).
thf(157,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( C = A )
=> ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(43,axiom,
y @ twoSqu1567020053sum2sq,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(275,plain,
y @ twoSqu1567020053sum2sq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(765,plain,
( ( ( y @ ( x @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq )
!= ( y @ twoSqu1567020053sum2sq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[275,118]) ).
thf(766,plain,
( ( y @ ( x @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq )
!= ( y @ twoSqu1567020053sum2sq ) ),
inference(simp,[status(thm)],[765]) ).
thf(770,plain,
( ( y @ ( x @ ( int @ times_times ) ) )
!= y ),
inference(simp,[status(thm)],[766]) ).
thf(94,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ minus_minus ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_number__of__diff) ).
thf(416,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ minus_minus ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(62,axiom,
! [TA: $tType] :
( ( TA @ semiring )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( C @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_combine__common__factor) ).
thf(325,plain,
! [TA: $tType] :
( ( TA @ semiring )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( C @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(104,axiom,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_mult__idem) ).
thf(448,plain,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ times_times ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(38,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ uminus_uminus ) )
= ( B @ ( A @ ( TA @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_minus__diff__eq) ).
thf(261,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ uminus_uminus ) )
= ( B @ ( A @ ( TA @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(15,axiom,
bool @ cl_Groups_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ominus) ).
thf(164,plain,
bool @ cl_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(60,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(321,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(32,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(238,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_prod_Orecs) ).
thf(119,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TC,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( TA @ ( TC @ product_Pair ) ) ) @ ( C @ ( TB @ ( TA @ ( TC @ product_prod_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(120,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TB @ ( TC @ fun ) @ ( TA @ fun ),B: TA,A: TC] :
( ( A @ ( B @ ( TC @ ( TA @ product_Pair ) ) ) @ ( C @ ( TB @ ( TC @ ( TA @ product_prod_rec ) ) ) ) )
= ( A @ ( B @ ( C @ ( TB @ ( TC @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TC @ aa ) ) ) ) ),
inference(cnf,[status(esa)],[119]) ).
thf(121,plain,
! [TA: $tType,TB: $tType,TC: $tType,C: TB @ ( TC @ fun ) @ ( TA @ fun ),B: TA,A: TC] :
( ( A @ ( B @ ( C @ ( TB @ ( TC @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( A @ ( B @ ( TC @ ( TA @ product_Pair ) ) ) @ ( C @ ( TB @ ( TC @ ( TA @ product_prod_rec ) ) ) ) ) ),
inference(lifteq,[status(thm)],[120]) ).
thf(70,axiom,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_mult__left__idem) ).
thf(353,plain,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( B @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(87,axiom,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_times_Oidem) ).
thf(397,plain,
! [TA: $tType] :
( ( TA @ ab_sem1668676832m_mult )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ times_times ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(46,axiom,
int @ number_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(280,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(116,axiom,
x @ twoSqu1567020053sum2sq,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(487,plain,
x @ twoSqu1567020053sum2sq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(951,plain,
( ( ( y @ ( x @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq )
!= ( x @ twoSqu1567020053sum2sq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[487,118]) ).
thf(952,plain,
( ( y @ ( x @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq )
!= ( x @ twoSqu1567020053sum2sq ) ),
inference(simp,[status(thm)],[951]) ).
thf(956,plain,
( ( y @ ( x @ ( int @ times_times ) ) )
!= x ),
inference(simp,[status(thm)],[952]) ).
thf(105,axiom,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_number__of__is__id) ).
thf(451,plain,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(452,plain,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
inference(cnf,[status(esa)],[451]) ).
thf(453,plain,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
inference(lifteq,[status(thm)],[452]) ).
thf(86,axiom,
int @ ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(396,plain,
int @ ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(8,axiom,
bool @ boolean_algebra,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Lattices_Oboolean__algebra) ).
thf(133,plain,
bool @ boolean_algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(54,axiom,
int @ semiri456707255roduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(307,plain,
int @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(101,axiom,
! [A: int,B: int] :
( ( A @ ( int @ uminus_uminus ) @ ( B @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_diff__int__def__symmetric) ).
thf(439,plain,
! [A: int,B: int] :
( ( A @ ( int @ uminus_uminus ) @ ( B @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(24,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_Pair__inject) ).
thf(201,plain,
! [TA: $tType,TB: $tType,A: TA,B: TB,C: TA,D: TB] :
( ( ( C @ ( D @ ( TA @ ( TB @ product_Pair ) ) ) )
= ( A @ ( B @ ( TA @ ( TB @ product_Pair ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(82,axiom,
! [A: int] :
( ( A @ twoSqu1567020053sum2sq )
<=> ? [B: int,C: int] :
( ( C @ ( B @ ( int @ ( int @ product_Pair ) ) ) @ twoSqu196287499sum2sq )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_is__sum2sq__def) ).
thf(381,plain,
! [A: int] :
( ( ? [B: int,C: int] :
( ( C @ ( B @ ( int @ ( int @ product_Pair ) ) ) @ twoSqu196287499sum2sq )
= A )
=> ( A @ twoSqu1567020053sum2sq ) )
& ( ( A @ twoSqu1567020053sum2sq )
=> ? [B: int,C: int] :
( ( C @ ( B @ ( int @ ( int @ product_Pair ) ) ) @ twoSqu196287499sum2sq )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(65,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_arith__simps_I32_J) ).
thf(334,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(84,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( int @ times_times ) ) @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_mult__number__of__left) ).
thf(392,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( int @ times_times ) ) @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(91,axiom,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ! [A: int] :
( ( A @ ( int @ uminus_uminus ) @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ ring_1_of_int ) @ ( TA @ uminus_uminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_of__int__minus) ).
thf(407,plain,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ! [A: int] :
( ( A @ ( int @ uminus_uminus ) @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ ring_1_of_int ) @ ( TA @ uminus_uminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(99,axiom,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ minus_minus ) ) @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ ring_1_of_int ) @ ( B @ ( TA @ ring_1_of_int ) @ ( TA @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_of__int__diff) ).
thf(429,plain,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ minus_minus ) ) @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ ring_1_of_int ) @ ( B @ ( TA @ ring_1_of_int ) @ ( TA @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(16,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(165,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ cl_Groups_Ominus )
=> ( TA @ ( TB @ fun ) @ cl_Groups_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(111,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( B @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(467,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( B @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(109,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(461,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ times_times ) ) @ ( B @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(61,axiom,
int @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(324,plain,
int @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(49,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ minus_minus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_add__number__of__diff1) ).
thf(285,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ minus_minus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(29,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(229,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(115,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(484,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(58,axiom,
! [A: int,B: int,C: int,D: int,E: int,F: int,G: int] :
( ( A @ ( B @ ( F @ ( int @ times_times ) ) @ ( C @ ( int @ minus_minus ) ) @ ( int @ times_times ) ) @ ( D @ ( E @ ( F @ ( int @ times_times ) ) @ ( G @ ( int @ minus_minus ) ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( D @ ( E @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( F @ ( int @ times_times ) ) @ ( A @ ( C @ ( int @ times_times ) ) @ ( D @ ( G @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ minus_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_xzgcda__linear__aux1) ).
thf(317,plain,
! [A: int,B: int,C: int,D: int,E: int,F: int,G: int] :
( ( A @ ( B @ ( F @ ( int @ times_times ) ) @ ( C @ ( int @ minus_minus ) ) @ ( int @ times_times ) ) @ ( D @ ( E @ ( F @ ( int @ times_times ) ) @ ( G @ ( int @ minus_minus ) ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( D @ ( E @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( F @ ( int @ times_times ) ) @ ( A @ ( C @ ( int @ times_times ) ) @ ( D @ ( G @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ minus_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(89,axiom,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= ( A @ ( int @ ring_1_of_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_int__number__of__def) ).
thf(403,plain,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= ( A @ ( int @ ring_1_of_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(71,axiom,
int @ comm_semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(356,plain,
int @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(10,axiom,
! [TA: $tType] :
( ( TA @ boolean_algebra )
=> ! [A: TA,B: TA] :
( ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_compl__eq__compl__iff) ).
thf(141,plain,
! [TA: $tType] :
( ( TA @ boolean_algebra )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) ) )
& ( ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(117,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: TA,C: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ minus_minus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( int @ uminus_uminus ) @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_add__number__of__diff2) ).
thf(488,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: TA,C: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ minus_minus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( int @ uminus_uminus ) @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( D @ ( TA @ semigroup ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_semigroup_Oassoc) ).
thf(122,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( D @ ( TA @ semigroup ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(123,plain,
! [TA: $tType,D: TA @ ( TA @ fun ) @ ( TA @ fun ),C: TA,B: TA,A: TA] :
( ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
| ~ ( D @ ( TA @ semigroup ) ) ),
inference(cnf,[status(esa)],[122]) ).
thf(124,plain,
! [TA: $tType,D: TA @ ( TA @ fun ) @ ( TA @ fun ),C: TA,B: TA,A: TA] :
( ~ ( D @ ( TA @ semigroup ) )
| ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(lifteq,[status(thm)],[123]) ).
thf(63,axiom,
! [TA: $tType] :
( ( TA @ ab_semigroup_mult )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(328,plain,
! [TA: $tType] :
( ( TA @ ab_semigroup_mult )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(113,axiom,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( C @ ( B @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) )
<=> ( ( C = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_crossproduct__eq) ).
thf(471,plain,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ( C = A )
| ( D = B ) )
=> ( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( C @ ( B @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( C @ ( B @ ( TA @ times_times ) ) @ ( A @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) )
=> ( ( C = A )
| ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(9,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_neg__equal__iff__equal) ).
thf(134,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) ) )
& ( ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,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_73_ext) ).
thf(128,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)],[6]) ).
thf(34,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(244,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(73,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( min @ ( int @ number_number_of ) @ ( TA @ ring_1_of_int ) )
= ( min @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_of__int__m1) ).
thf(360,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( min @ ( int @ number_number_of ) @ ( TA @ ring_1_of_int ) )
= ( min @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(56,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_add__number__of__left) ).
thf(311,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(51,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( D @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) ) @ ( A @ ( C @ ( TA @ minus_minus ) ) @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_mult__diff__mult) ).
thf(298,plain,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( D @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) ) @ ( A @ ( C @ ( TA @ minus_minus ) ) @ ( D @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(97,axiom,
int @ semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(425,plain,
int @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(11,axiom,
! [TA: $tType] :
( ( TA @ ab_group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ minus_minus ) ) )
= ( A @ ( C @ ( TA @ minus_minus ) ) @ ( B @ ( D @ ( TA @ minus_minus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_add__diff__add) ).
thf(148,plain,
! [TA: $tType] :
( ( TA @ ab_group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ minus_minus ) ) )
= ( A @ ( C @ ( TA @ minus_minus ) ) @ ( B @ ( D @ ( TA @ minus_minus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(39,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_add__left__imp__eq) ).
thf(264,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(45,axiom,
int @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(279,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(80,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ ( C @ ( int @ times_times ) ) )
= ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( C @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_int__distrib_I2_J) ).
thf(375,plain,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ ( C @ ( int @ times_times ) ) )
= ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( C @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(47,axiom,
int @ comm_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring) ).
thf(281,plain,
int @ comm_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(93,axiom,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_plus__numeral__code_I9_J) ).
thf(413,plain,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(103,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(445,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(69,axiom,
! [TA: $tType] :
( ( ( TA @ ring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ minus_minus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_right__diff__distrib__number__of) ).
thf(350,plain,
! [TA: $tType] :
( ( ( TA @ ring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ minus_minus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(21,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ cl_Groups_Ominus )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TA] :
( ( C @ ( A @ ( B @ ( TB @ ( TA @ fun ) @ minus_minus ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_fun__diff__def) ).
thf(187,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ cl_Groups_Ominus )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TA] :
( ( C @ ( A @ ( B @ ( TB @ ( TA @ fun ) @ minus_minus ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(90,axiom,
int @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(406,plain,
int @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(95,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_comm__semiring__class_Odistrib) ).
thf(419,plain,
! [TA: $tType] :
( ( TA @ comm_semiring )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(76,axiom,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_left__distrib__number__of) ).
thf(367,plain,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(23,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( TA @ uminus_uminus ) @ ( B @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_diff__minus__eq__add) ).
thf(198,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( TA @ uminus_uminus ) @ ( B @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(129,plain,
! [TA: $tType,TB: $tType,B: TA @ ( TB @ fun ),A: TA @ ( TB @ fun )] :
( ( B = A )
| ( ( A @ ( B @ ( TA @ ( TB @ sk1 ) ) ) @ ( B @ ( TA @ ( TB @ aa ) ) ) )
!= ( A @ ( B @ ( TA @ ( TB @ sk1 ) ) ) @ ( A @ ( TA @ ( TB @ aa ) ) ) ) ) ),
inference(cnf,[status(esa)],[128]) ).
thf(130,plain,
! [TA: $tType,TB: $tType,B: TA @ ( TB @ fun ),A: TA @ ( TB @ fun )] :
( ( B = A )
| ( ( A @ ( B @ ( TA @ ( TB @ sk1 ) ) ) @ ( B @ ( TA @ ( TB @ aa ) ) ) )
!= ( A @ ( B @ ( TA @ ( TB @ sk1 ) ) ) @ ( A @ ( TA @ ( TB @ aa ) ) ) ) ) ),
inference(lifteq,[status(thm)],[129]) ).
thf(28,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(226,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(40,axiom,
int @ cl_Groups_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ominus) ).
thf(267,plain,
int @ cl_Groups_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(33,axiom,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_add__imp__eq) ).
thf(241,plain,
! [TA: $tType] :
( ( TA @ cancel146912293up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( A @ ( C @ ( TA @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(17,axiom,
! [TA: $tType] :
( ( TA @ ab_group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_minus__add__distrib) ).
thf(167,plain,
! [TA: $tType] :
( ( TA @ ab_group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) @ ( B @ ( TA @ uminus_uminus ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(98,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ uminus_uminus ) )
= ( A @ ( int @ uminus_uminus ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_arith__simps_I30_J) ).
thf(426,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ uminus_uminus ) )
= ( A @ ( int @ uminus_uminus ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(79,axiom,
int @ group_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ogroup__add) ).
thf(374,plain,
int @ group_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(404,plain,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= ( A @ ( int @ ring_1_of_int ) ) ),
inference(cnf,[status(esa)],[403]) ).
thf(405,plain,
! [A: int] :
( ( A @ ( int @ ring_1_of_int ) )
= ( A @ ( int @ number_number_of ) ) ),
inference(lifteq,[status(thm)],[404]) ).
thf(1003,plain,
! [A: int] :
( ( A @ ( int @ ring_1_of_int ) )
= A ),
inference(rewrite,[status(thm)],[405,453]) ).
thf(48,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_add__number__of__eq) ).
thf(282,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(19,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) )
= ( A @ ( TA @ ring_1_of_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_number__of__eq) ).
thf(177,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) )
= ( A @ ( TA @ ring_1_of_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(64,axiom,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_times__numeral__code_I5_J) ).
thf(331,plain,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(77,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_number__of__mult) ).
thf(370,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(501,plain,
! [TA: $tType,B: int,A: int] :
( ( B
!= ( y @ ( x @ ( int @ times_times ) ) ) )
| ~ ( A @ twoSqu1567020053sum2sq )
| ~ ( TA @ ring_char_0 )
| ~ ( TA @ number_ring )
| ( ( B @ ( TA @ number_number_of ) )
!= ( A @ ( TA @ number_number_of ) ) ) ),
inference(paramod_ordered,[status(thm)],[184,118]) ).
thf(502,plain,
! [TA: $tType,A: int] :
( ~ ( A @ twoSqu1567020053sum2sq )
| ~ ( TA @ ring_char_0 )
| ~ ( TA @ number_ring )
| ( ( y @ ( x @ ( int @ times_times ) ) @ ( TA @ number_number_of ) )
!= ( A @ ( TA @ number_number_of ) ) ) ),
inference(pattern_uni,[status(thm)],[501:[bind(A,$thf( A )),bind(B,$thf( y @ ( x @ ( int @ times_times ) ) ))]]) ).
thf(126,plain,
! [TA: $tType,C: TA @ ( TA @ fun ) @ ( TA @ fun ),B: TA,A: TA] :
( ( ( B @ ( A @ ( C @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A )
| ~ ( B @ ( C @ ( TA @ comm_monoid ) ) ) ),
inference(cnf,[status(esa)],[125]) ).
thf(127,plain,
! [TA: $tType,C: TA @ ( TA @ fun ) @ ( TA @ fun ),B: TA,A: TA] :
( ~ ( B @ ( C @ ( TA @ comm_monoid ) ) )
| ( ( B @ ( A @ ( C @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(lifteq,[status(thm)],[126]) ).
thf(112,axiom,
int @ comm_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__ring) ).
thf(470,plain,
int @ comm_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(13,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(154,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(57,axiom,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ ring_1_of_int ) @ ( B @ ( TA @ ring_1_of_int ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_of__int__mult) ).
thf(314,plain,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ ring_1_of_int ) @ ( B @ ( TA @ ring_1_of_int ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(36,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) ) )
=> ( ( D = C )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_diff__eq__diff__eq) ).
thf(250,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) ) )
=> ( ( ( B = A )
=> ( D = C ) )
& ( ( D = C )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(74,axiom,
int @ ab_group_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__group__add) ).
thf(363,plain,
int @ ab_group_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ ring_1_of_int ) @ ( B @ ( TA @ ring_1_of_int ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_of__int__add) ).
thf(304,plain,
! [TA: $tType] :
( ( TA @ ring_1 )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ ring_1_of_int ) @ ( B @ ( TA @ ring_1_of_int ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(37,axiom,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_add__right__imp__eq) ).
thf(258,plain,
! [TA: $tType] :
( ( TA @ cancel_semigroup_add )
=> ! [A: TA,B: TA,C: TA] :
( ( ( B @ ( C @ ( TA @ plus_plus ) ) )
= ( B @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(31,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ minus_minus ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_add__diff__cancel) ).
thf(235,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ minus_minus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(25,axiom,
! [TA: $tType] :
( ( TA @ ring_char_0 )
=> ! [A: int,B: int] :
( ( ( B @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ ring_1_of_int ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_of__int__eq__iff) ).
thf(207,plain,
! [TA: $tType] :
( ( TA @ ring_char_0 )
=> ! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ ring_1_of_int ) ) ) )
& ( ( ( B @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ ring_1_of_int ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(42,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( int @ number_number_of ) @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_of__int__number__of__eq) ).
thf(272,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( int @ number_number_of ) @ ( TA @ ring_1_of_int ) )
= ( A @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(26,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ plus_plus ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_diff__add__cancel) ).
thf(214,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ plus_plus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(81,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( C @ ( int @ minus_minus ) ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( A @ ( C @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_int__distrib_I3_J) ).
thf(378,plain,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( C @ ( int @ minus_minus ) ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( A @ ( C @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ cl_Groups_Ominus )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ minus_minus ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_minus__apply) ).
thf(151,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ cl_Groups_Ominus )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ fun ) @ minus_minus ) ) @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(100,axiom,
! [TA: $tType] :
( ( TA @ ring )
=> ! [A: TA,B: TA,C: TA,D: TA,E: TA] :
( ( ( C @ ( D @ ( E @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( D @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) )
<=> ( C
= ( A @ ( D @ ( E @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_eq__add__iff2) ).
thf(432,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 @ plus_plus ) ) ) )
=> ( ( C @ ( D @ ( E @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( D @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( D @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) )
=> ( C
= ( A @ ( D @ ( E @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(410,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(22,axiom,
! [TA: $tType] :
( ( TA @ number )
=> ! [A: TA,B: int] :
( ( ( B @ ( TA @ number_number_of ) )
= A )
<=> ( A
= ( B @ ( TA @ number_number_of ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_number__of__reorient) ).
thf(190,plain,
! [TA: $tType] :
( ( TA @ number )
=> ! [A: TA,B: int] :
( ( ( A
= ( B @ ( TA @ number_number_of ) ) )
=> ( ( B @ ( TA @ number_number_of ) )
= A ) )
& ( ( ( B @ ( TA @ number_number_of ) )
= A )
=> ( A
= ( B @ ( TA @ number_number_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(96,axiom,
! [A: int,B: int,C: int,D: int] :
( ( A @ ( B @ ( int @ ( int @ product_Pair ) ) ) @ twoSqu196287499sum2sq @ ( C @ ( D @ ( int @ ( int @ product_Pair ) ) ) @ twoSqu196287499sum2sq @ ( int @ times_times ) ) )
= ( B @ ( C @ ( int @ times_times ) ) @ ( A @ ( D @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( D @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ ( int @ product_Pair ) ) ) @ twoSqu196287499sum2sq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_mult__sum2sq) ).
thf(422,plain,
! [A: int,B: int,C: int,D: int] :
( ( A @ ( B @ ( int @ ( int @ product_Pair ) ) ) @ twoSqu196287499sum2sq @ ( C @ ( D @ ( int @ ( int @ product_Pair ) ) ) @ twoSqu196287499sum2sq @ ( int @ times_times ) ) )
= ( B @ ( C @ ( int @ times_times ) ) @ ( A @ ( D @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( D @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ ( int @ product_Pair ) ) ) @ twoSqu196287499sum2sq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(78,axiom,
int @ ab_semigroup_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__mult) ).
thf(373,plain,
int @ ab_semigroup_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(41,axiom,
! [A: int,B: int,C: int] :
( ( ( B @ ( C @ ( int @ minus_minus ) ) )
= A )
=> ( C
= ( B @ ( A @ ( int @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_Int2_Oaux1) ).
thf(268,plain,
! [A: int,B: int,C: int] :
( ( ( B @ ( C @ ( int @ minus_minus ) ) )
= A )
=> ( C
= ( B @ ( A @ ( int @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(88,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) @ ( D @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(400,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( D @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( C @ ( TA @ times_times ) ) @ ( D @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(85,axiom,
int @ ring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1) ).
thf(395,plain,
int @ ring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(110,axiom,
! [A: int] :
( ( A @ ( min @ ( int @ times_times ) ) )
= ( A @ ( int @ uminus_uminus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_mult__Min) ).
thf(464,plain,
! [A: int] :
( ( A @ ( min @ ( int @ times_times ) ) )
= ( A @ ( int @ uminus_uminus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ boolean_algebra )
=> ( TA @ ( TB @ fun ) @ boolean_algebra ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Lattices_Oboolean__algebra) ).
thf(131,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ boolean_algebra )
=> ( TA @ ( TB @ fun ) @ boolean_algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(102,axiom,
! [TA: $tType] :
( ( TA @ comm_ring )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( TA @ times_times ) ) @ ( B @ ( B @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_square__diff__square__factored) ).
thf(442,plain,
! [TA: $tType] :
( ( TA @ comm_ring )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( TA @ times_times ) ) @ ( B @ ( B @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(106,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( min @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) )
= ( A @ ( TA @ uminus_uminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_mult__minus1__right) ).
thf(454,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( min @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) )
= ( A @ ( TA @ uminus_uminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(75,axiom,
! [TA: $tType] :
( ( ( TA @ ring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_left__diff__distrib__number__of) ).
thf(364,plain,
! [TA: $tType] :
( ( ( TA @ ring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(30,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(232,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(66,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(337,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ times_times ) ) @ ( A @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(12433,plain,
$false,
inference(e,[status(thm)],[340,457,347,481,170,308,247,217,276,288,301,320,389,184,504,125,357,460,157,770,416,325,448,261,164,321,238,121,353,397,280,956,453,396,133,307,439,201,381,334,392,407,429,275,165,467,461,324,285,229,484,317,403,356,141,488,124,328,471,134,128,244,360,311,298,425,148,264,279,180,375,118,281,413,445,350,187,406,419,451,367,198,130,226,267,241,167,426,374,487,1003,282,177,331,370,502,127,470,154,314,250,363,304,258,235,207,272,214,119,378,151,432,410,190,422,373,268,400,395,464,131,442,454,364,232,337,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM928_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % 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
% 0.13/0.40 % Computer : n020.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 04:22:34 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.85/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.89/1.31 % [INFO] Parsing done (307ms).
% 1.89/1.33 % [INFO] Running in sequential loop mode.
% 2.77/1.72 % [INFO] eprover registered as external prover.
% 2.77/1.73 % [INFO] Scanning for conjecture ...
% 2.96/1.87 % [INFO] Found a conjecture (or negated_conjecture) and 123 axioms. Running axiom selection ...
% 3.14/1.99 % [INFO] Axiom selection finished. Selected 115 axioms (removed 8 axioms).
% 4.22/2.22 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.22/2.25 % [INFO] Type checking passed.
% 4.22/2.25 % [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 ...
% 71.50/16.02 % External prover 'e' found a proof!
% 71.50/16.02 % [INFO] Killing All external provers ...
% 71.50/16.02 % Time passed: 15466ms (effective reasoning time: 14691ms)
% 71.50/16.02 % 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)>
% 71.50/16.03 % Axioms used in derivation (115): arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_17_of__int__mult, fact_69_int__distrib_I3_J, fact_7_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_15_mult__number__of__left, arity_Int_Oint___Rings_Ocomm__ring, fact_88_compl__eq__compl__iff, arity_Int_Oint___Int_Oring__char__0, fact_91_minus__diff__eq, arity_Int_Oint___Groups_Ominus, fact_56_ab__semigroup__add__class_Oadd__ac_I1_J, fact_18_number__of__mult, fact_54_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_66_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_76_eq__add__iff1, fact_83_xzgcda__linear__aux1, fact_32_of__int__m1, arity_HOL_Obool___Groups_Ominus, fact_35_right__diff__distrib__number__of, fact_85_Int2_Oaux1, fact_9_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_45_number__of__diff, fact_33_right__distrib__number__of, arity_Int_Oint___Rings_Oring, arity_HOL_Obool___Lattices_Oboolean__algebra, fact_60_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_38_add__number__of__left, fact_40_of__int__add, arity_Int_Oint___Groups_Oab__group__add, fact_74_mult__sum2sq, arity_Int_Oint___Groups_Ocancel__ab__semigroup__add, fact_70_int__distrib_I4_J, arity_Int_Oint___Int_Onumber__ring, fact_42_left__diff__distrib__number__of, arity_Int_Oint___Rings_Ocomm__semiring, fact_67_crossproduct__noteq, fact_82_add__diff__add, fact_0_mult__left__idem, fact_47_int__number__of__def, fact_10_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_46_number__of__add, fact_87_neg__equal__iff__equal, fact_48_number__of__is__id, fact_49_diff__eq__diff__eq, fact_64_crossproduct__eq, fact_6_ab__semigroup__mult__class_Omult__ac_I1_J, fact_51_add__imp__eq, fact_43_add__number__of__diff1, arity_Int_Oint___Rings_Oring__1, fact_94_diff__int__def__symmetric, fact_58_add__diff__cancel, fact_4_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_79_square__diff__square__factored, fact_22_of__int__eq__iff, fact_73_ext, fact_24_number__of__reorient, fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_1_times_Oidem, fact_44_plus__numeral__code_I9_J, fact_86_add__number__of__diff2, fact_23_of__int__number__of__eq, fact_97_mult__minus1__right, fact_5_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_11_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_36_add__right__cancel, fact_77_eq__add__iff2, fact_13_comm__monoid_Ocomm__neutral, fact_53_minus__apply, fact_80_combine__common__factor, fact_52_add__left__imp__eq, fact_34_left__distrib__number__of, arity_Int_Oint___Rings_Osemiring, fact_2_mult__idem, fact_25_number__of__eq, fact_61_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_3_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_26_times__numeral__code_I5_J, fact_37_add__left__cancel, fact_63_fun__diff__def, fact_72_int__distrib_I2_J, fact_31_Pair__inject, fact_84_prod_Orecs, arity_fun___Lattices_Oboolean__algebra, arity_Int_Oint___Groups_Ogroup__add, arity_Int_Oint___Groups_Ocancel__semigroup__add, fact_78_mult__diff__mult, fact_90_minus__add__distrib, arity_Int_Oint___Rings_Ocomm__semiring__1, fact_16_arith__simps_I32_J, conj_1, fact_50_add__right__imp__eq, fact_12_semigroup_Oassoc, fact_55_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_95_mult__Min, fact_14_is__sum2sq__def, fact_59_diff__add__cancel, fact_62_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_21_eq__number__of, fact_8_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, arity_Int_Oint___Groups_Oab__semigroup__add, fact_39_add__number__of__eq, fact_71_int__distrib_I1_J, fact_96_of__int__minus, arity_Int_Oint___Groups_Oab__semigroup__mult, fact_81_comm__semiring__class_Odistrib, arity_Int_Oint___Int_Onumber, conj_0, fact_89_minus__mult__minus, fact_41_of__int__diff, fact_93_arith__simps_I30_J, fact_29_Pair__eq, arity_fun___Groups_Ominus, fact_65_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_92_diff__minus__eq__add
% 71.50/16.03 % No. of inferences in proof: 260
% 71.50/16.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 15466 ms resp. 14691 ms w/o parsing
% 72.66/16.16 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 72.66/16.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------