TSTP Solution File: SWW488_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW488_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:24:52 EDT 2023
% Result : Theorem 9.13s 3.27s
% Output : Refutation 9.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 189
% Syntax : Number of formulae : 335 ( 62 unt; 45 typ; 0 def)
% Number of atoms : 801 ( 236 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 2916 ( 40 ~; 6 |; 39 &;2479 @)
% ( 28 <=>; 324 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 44 usr; 7 con; 0-5 aty)
% Number of variables : 620 ( 0 ^; 581 !; 0 ?; 620 :)
% ( 39 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(comm_ring_1_type,type,
comm_ring_1:
!>[TA: $tType] : $o ).
thf(cancel1352612707id_add_type,type,
cancel1352612707id_add:
!>[TA: $tType] : $o ).
thf(one_type,type,
one:
!>[TA: $tType] : $o ).
thf(idom_type,type,
idom:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(ring_1_type,type,
ring_1:
!>[TA: $tType] : $o ).
thf(ring_char_0_type,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(monoid_add_type,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(zero_neq_one_type,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(comm_semiring_0_type,type,
comm_semiring_0:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_type,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_type,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_type,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(linordered_semidom_type,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_type,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(ordere216010020id_add_type,type,
ordere216010020id_add:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_type,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(ordere223160158up_add_type,type,
ordere223160158up_add:
!>[TA: $tType] : $o ).
thf(semiri456707255roduct_type,type,
semiri456707255roduct:
!>[TA: $tType] : $o ).
thf(fundam296178794t_poly_type,type,
fundam296178794t_poly:
!>[TA: $tType] : ( ( poly1 @ TA ) > TA > ( poly1 @ TA ) ) ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(ring_1_Ints_type,type,
ring_1_Ints:
!>[TA: $tType] : ( fun @ TA @ bool ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(coeff_type,type,
coeff:
!>[TA: $tType] : ( ( poly1 @ TA ) > ( fun @ nat @ TA ) ) ).
thf(monom_type,type,
monom:
!>[TA: $tType] : ( TA > nat > ( poly1 @ TA ) ) ).
thf(order_type,type,
order:
!>[TA: $tType] : ( TA > ( poly1 @ TA ) > nat ) ).
thf(pcompose_type,type,
pcompose:
!>[TA: $tType] : ( ( poly1 @ TA ) > ( poly1 @ TA ) > ( poly1 @ TA ) ) ).
thf(poly_type,type,
poly:
!>[TA: $tType] : ( ( poly1 @ TA ) > ( fun @ TA @ TA ) ) ).
thf(poly_rec_type,type,
poly_rec:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ ( fun @ ( poly1 @ TA ) @ ( fun @ TB @ TB ) ) ) > ( poly1 @ TA ) > TB ) ).
thf(synthetic_div_type,type,
synthetic_div:
!>[TA: $tType] : ( ( poly1 @ TA ) > TA > ( poly1 @ TA ) ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(h_type,type,
h: a ).
thf(x_type,type,
x: a ).
thf(106,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(440,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(94,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_add__right__cancel) ).
thf(403,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(89,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ( cancel1352612707id_add @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ocancel__comm__monoid__add) ).
thf(387,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ( cancel1352612707id_add @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(120,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(479,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(39,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ A @ B ) )
=> ( ord_less @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_add__less__imp__less__right) ).
thf(234,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ A @ B ) )
=> ( ord_less @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(74,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( zero @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ozero) ).
thf(352,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( zero @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(88,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( member @ TA @ B @ ( ring_1_Ints @ TA ) )
=> ( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( member @ TA @ ( plus_plus @ TA @ B @ A ) @ ( ring_1_Ints @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_Ints__add) ).
thf(385,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( member @ TA @ B @ ( ring_1_Ints @ TA ) )
=> ( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( member @ TA @ ( plus_plus @ TA @ B @ A ) @ ( ring_1_Ints @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(141,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: TA] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_Ints__double__eq__0__iff) ).
thf(550,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: TA] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( ( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(117,axiom,
comm_semiring_0 @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
thf(472,plain,
comm_semiring_0 @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(71,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(340,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(98,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( one @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Oone) ).
thf(417,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( one @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(45,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( ( ( plus_plus @ nat @ B @ C )
= ( plus_plus @ nat @ D @ A ) )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_less__add__eq__less) ).
thf(257,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( ( ( plus_plus @ nat @ B @ C )
= ( plus_plus @ nat @ D @ A ) )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(90,axiom,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA] :
( ( B
= ( plus_plus @ TA @ B @ A ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_add__0__iff) ).
thf(389,plain,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA] :
( ( ( B
= ( plus_plus @ TA @ B @ A ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( B
= ( plus_plus @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(24,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly1 @ TA,B: poly1 @ TA] :
( ( ( coeff @ TA @ B )
= ( coeff @ TA @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_coeff__inject) ).
thf(184,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly1 @ TA,B: poly1 @ TA] :
( ( ( ( coeff @ TA @ B )
= ( coeff @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( coeff @ TA @ B )
= ( coeff @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(128,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: nat,B: poly1 @ TA,C: poly1 @ TA] :
( ( aa @ nat @ TA @ ( coeff @ TA @ ( plus_plus @ ( poly1 @ TA ) @ C @ B ) ) @ A )
= ( plus_plus @ TA @ ( aa @ nat @ TA @ ( coeff @ TA @ C ) @ A ) @ ( aa @ nat @ TA @ ( coeff @ TA @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_coeff__add) ).
thf(504,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: nat,B: poly1 @ TA,C: poly1 @ TA] :
( ( aa @ nat @ TA @ ( coeff @ TA @ ( plus_plus @ ( poly1 @ TA ) @ C @ B ) ) @ A )
= ( plus_plus @ TA @ ( aa @ nat @ TA @ ( coeff @ TA @ C ) @ A ) @ ( aa @ nat @ TA @ ( coeff @ TA @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(76,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ nat @ ( plus_plus @ nat @ C @ A ) @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_add__less__mono1) ).
thf(357,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ nat @ ( plus_plus @ nat @ C @ A ) @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(29,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_linorder__neqE__linordered__idom) ).
thf(196,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(52,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: nat,C: TA] :
( ( plus_plus @ ( poly1 @ TA ) @ ( monom @ TA @ C @ B ) @ ( monom @ TA @ A @ B ) )
= ( monom @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_add__monom) ).
thf(284,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: nat,C: TA] :
( ( plus_plus @ ( poly1 @ TA ) @ ( monom @ TA @ C @ B ) @ ( monom @ TA @ A @ B ) )
= ( monom @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(7,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
<=> ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_one__reorient) ).
thf(152,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( ( one_one @ TA )
= A )
=> ( A
= ( one_one @ TA ) ) )
& ( ( A
= ( one_one @ TA ) )
=> ( ( one_one @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(34,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA,B: nat,C: nat] :
( ( ( C = B )
=> ( ( aa @ nat @ TA @ ( coeff @ TA @ ( monom @ TA @ A @ C ) ) @ B )
= A ) )
& ( ( C != B )
=> ( ( aa @ nat @ TA @ ( coeff @ TA @ ( monom @ TA @ A @ C ) ) @ B )
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_coeff__monom) ).
thf(216,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA,B: nat,C: nat] :
( ( ( C = B )
=> ( ( aa @ nat @ TA @ ( coeff @ TA @ ( monom @ TA @ A @ C ) ) @ B )
= A ) )
& ( ( C != B )
=> ( ( aa @ nat @ TA @ ( coeff @ TA @ ( monom @ TA @ A @ C ) ) @ B )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(21,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( monoid_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clar_Rings_Ocomm__semiring__0__Groups_Omonoid__add) ).
thf(179,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( monoid_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(107,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_nat__add__left__commute) ).
thf(443,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(84,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_idom @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Olinordered__idom) ).
thf(376,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_idom @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(32,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
<=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_zero__less__double__add__iff__zero__less__single__add) ).
thf(211,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
& ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(41,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_nat__add__right__cancel) ).
thf(238,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(55,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere216010020id_add @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Oordered__comm__monoid__add) ).
thf(293,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere216010020id_add @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(103,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ B @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_not__add__less2) ).
thf(428,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ B @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(129,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly1 @ TA,B: poly1 @ TA] :
( ( B = A )
<=> ! [C: nat] :
( ( aa @ nat @ TA @ ( coeff @ TA @ B ) @ C )
= ( aa @ nat @ TA @ ( coeff @ TA @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_expand__poly__eq) ).
thf(507,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly1 @ TA,B: poly1 @ TA] :
( ( ( B = A )
=> ! [C: nat] :
( ( aa @ nat @ TA @ ( coeff @ TA @ B ) @ C )
= ( aa @ nat @ TA @ ( coeff @ TA @ A ) @ C ) ) )
& ( ! [C: nat] :
( ( aa @ nat @ TA @ ( coeff @ TA @ B ) @ C )
= ( aa @ nat @ TA @ ( coeff @ TA @ A ) @ C ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(134,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_add__0__left) ).
thf(527,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(109,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ B @ A )
= ( plus_plus @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(452,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ B @ A )
= ( plus_plus @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(86,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
<=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_double__add__less__zero__iff__single__add__less__zero) ).
thf(380,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) )
& ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(139,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ( monoid_add @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Omonoid__add) ).
thf(546,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ( monoid_add @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(80,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( ( ord_less @ TA @ ( plus_plus @ TA @ ( plus_plus @ TA @ ( one_one @ TA ) @ A ) @ A ) @ ( zero_zero @ TA ) )
<=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Ints__odd__less__0) ).
thf(366,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( ( ( ord_less @ TA @ ( plus_plus @ TA @ ( plus_plus @ TA @ ( one_one @ TA ) @ A ) @ A ) @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) )
& ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ ( plus_plus @ TA @ ( one_one @ TA ) @ A ) @ A ) @ ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(9,axiom,
comm_semiring_0 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__0) ).
thf(160,plain,
comm_semiring_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(57,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_zero__less__one) ).
thf(297,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(101,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_trans__less__add1) ).
thf(424,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(26,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( ab_semigroup_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clar_Rings_Ocomm__semiring__0__Groups_Oab__semigroup__add) ).
thf(192,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( ab_semigroup_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(13,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA,B: nat,C: TA] :
( ( ( monom @ TA @ C @ B )
= ( monom @ TA @ A @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_monom__eq__iff) ).
thf(165,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA,B: nat,C: TA] :
( ( ( ( monom @ TA @ C @ B )
= ( monom @ TA @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( monom @ TA @ C @ B )
= ( monom @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(46,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_double__eq__0__iff) ).
thf(260,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(73,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_less__nat__zero__code) ).
thf(349,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(43,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ( cancel146912293up_add @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ocancel__ab__semigroup__add) ).
thf(252,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ( cancel146912293up_add @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(68,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( member @ TA @ ( zero_zero @ TA ) @ ( ring_1_Ints @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_Ints__0) ).
thf(329,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( member @ TA @ ( zero_zero @ TA ) @ ( ring_1_Ints @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(132,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ring_char_0 @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Int_Oring__char__0) ).
thf(522,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ring_char_0 @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(113,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: TA] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( ( plus_plus @ TA @ ( plus_plus @ TA @ ( one_one @ TA ) @ A ) @ A )
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_Ints__odd__nonzero) ).
thf(461,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: TA] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( ( plus_plus @ TA @ ( plus_plus @ TA @ ( one_one @ TA ) @ A ) @ A )
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(125,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_gr__implies__not0) ).
thf(493,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(66,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere223160158up_add @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(324,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere223160158up_add @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(37,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_add__imp__eq) ).
thf(229,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(144,axiom,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Nat_Oadd__0__right) ).
thf(566,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(122,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(484,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(36,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ B @ A )
= B )
=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_add__eq__self__zero) ).
thf(225,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ B @ A )
= B )
=> ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(136,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: poly1 @ TA] :
( ( plus_plus @ ( poly1 @ TA ) @ ( zero_zero @ ( poly1 @ TA ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_add__poly__code_I1_J) ).
thf(537,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: poly1 @ TA] :
( ( plus_plus @ ( poly1 @ TA ) @ ( zero_zero @ ( poly1 @ TA ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(119,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ A @ B ) )
<=> ( ord_less @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_add__less__cancel__right) ).
thf(476,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ A @ B ) )
=> ( ord_less @ TA @ C @ A ) )
& ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(111,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ( ab_semigroup_add @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Oab__semigroup__add) ).
thf(457,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ( ab_semigroup_add @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(16,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( comm_monoid_add @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clar_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add) ).
thf(173,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( comm_monoid_add @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(145,axiom,
! [TA: $tType] :
( ( idom @ TA )
=> ! [A: TA,B: poly1 @ TA] :
( ( ( aa @ TA @ TA @ ( poly @ TA @ B ) @ A )
= ( zero_zero @ TA ) )
<=> ( ( B
= ( zero_zero @ ( poly1 @ TA ) ) )
| ( ( order @ TA @ A @ B )
!= ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_order__root) ).
thf(569,plain,
! [TA: $tType] :
( ( idom @ TA )
=> ! [A: TA,B: poly1 @ TA] :
( ( ( ( aa @ TA @ TA @ ( poly @ TA @ B ) @ A )
= ( zero_zero @ TA ) )
=> ( ( B
= ( zero_zero @ ( poly1 @ TA ) ) )
| ( ( order @ TA @ A @ B )
!= ( zero_zero @ nat ) ) ) )
& ( ( ( B
= ( zero_zero @ ( poly1 @ TA ) ) )
| ( ( order @ TA @ A @ B )
!= ( zero_zero @ nat ) ) )
=> ( ( aa @ TA @ TA @ ( poly @ TA @ B ) @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(82,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: poly1 @ TA] :
( ( pcompose @ TA @ ( zero_zero @ ( poly1 @ TA ) ) @ A )
= ( zero_zero @ ( poly1 @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_pcompose__0) ).
thf(371,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: poly1 @ TA] :
( ( pcompose @ TA @ ( zero_zero @ ( poly1 @ TA ) ) @ A )
= ( zero_zero @ ( poly1 @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(72,axiom,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( idom @ TA ) )
=> ! [A: poly1 @ TA] :
( ( ( poly @ TA @ A )
= ( poly @ TA @ ( zero_zero @ ( poly1 @ TA ) ) ) )
<=> ( A
= ( zero_zero @ ( poly1 @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_poly__zero) ).
thf(343,plain,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( idom @ TA ) )
=> ! [A: poly1 @ TA] :
( ( ( ( poly @ TA @ A )
= ( poly @ TA @ ( zero_zero @ ( poly1 @ TA ) ) ) )
=> ( A
= ( zero_zero @ ( poly1 @ TA ) ) ) )
& ( ( A
= ( zero_zero @ ( poly1 @ TA ) ) )
=> ( ( poly @ TA @ A )
= ( poly @ TA @ ( zero_zero @ ( poly1 @ TA ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(47,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord219039673up_add @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Olinordered__ab__group__add) ).
thf(266,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linord219039673up_add @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(62,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( zero_neq_one @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ozero__neq__one) ).
thf(311,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( zero_neq_one @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(92,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
=> ( ord_less @ nat @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_add__lessD1) ).
thf(398,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
=> ( ord_less @ nat @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(135,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_nat__add__left__cancel) ).
thf(530,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(96,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere236663937imp_le @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(412,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere236663937imp_le @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(130,axiom,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_plus__nat_Oadd__0) ).
thf(513,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(3,axiom,
comm_semiring_1 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(148,plain,
comm_semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(161,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(149,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(18,axiom,
zero_neq_one @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(176,plain,
zero_neq_one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(51,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA] :
( ( synthetic_div @ TA @ ( zero_zero @ ( poly1 @ TA ) ) @ A )
= ( zero_zero @ ( poly1 @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_synthetic__div__0) ).
thf(281,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA] :
( ( synthetic_div @ TA @ ( zero_zero @ ( poly1 @ TA ) ) @ A )
= ( zero_zero @ ( poly1 @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(63,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_double__zero__sym) ).
thf(313,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(126,axiom,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( zero_zero @ TA )
!= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_zero__neq__one) ).
thf(498,plain,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( zero_zero @ TA )
!= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(115,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_add__left__imp__eq) ).
thf(466,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(40,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_add__strict__right__mono) ).
thf(236,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(22,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(181,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(137,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ A )
= ( plus_plus @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_nat__add__commute) ).
thf(540,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ A )
= ( plus_plus @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(8,axiom,
semiri456707255roduct @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(159,plain,
semiri456707255roduct @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(172,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(50,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_zero__reorient) ).
thf(274,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= A )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(99,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ B @ A ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_not__add__less1) ).
thf(419,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(78,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( comm_semiring_0 @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ocomm__semiring__0) ).
thf(362,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( comm_semiring_0 @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(42,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( plus_plus @ nat @ B @ A ) )
<=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_add__gr__0) ).
thf(245,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( plus_plus @ nat @ B @ A ) )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) )
& ( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( plus_plus @ nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(105,axiom,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( idom @ TA ) )
=> ! [A: poly1 @ TA,B: poly1 @ TA] :
( ( ( poly @ TA @ B )
= ( poly @ TA @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_poly__eq__iff) ).
thf(434,plain,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( idom @ TA ) )
=> ! [A: poly1 @ TA,B: poly1 @ TA] :
( ( ( ( poly @ TA @ B )
= ( poly @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( poly @ TA @ B )
= ( poly @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(49,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_add__0__right) ).
thf(271,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(31,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_gr0I) ).
thf(208,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(110,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_semidom @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Olinordered__semidom) ).
thf(455,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_semidom @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(60,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat] :
( ( monom @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ ( poly1 @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_monom__eq__0) ).
thf(306,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat] :
( ( monom @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ ( poly1 @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(143,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA] :
( ( fundam296178794t_poly @ TA @ ( zero_zero @ ( poly1 @ TA ) ) @ A )
= ( zero_zero @ ( poly1 @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_offset__poly__0) ).
thf(563,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA] :
( ( fundam296178794t_poly @ TA @ ( zero_zero @ ( poly1 @ TA ) ) @ A )
= ( zero_zero @ ( poly1 @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(58,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ C @ B ) @ ( plus_plus @ nat @ C @ A ) )
<=> ( ord_less @ nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_nat__add__left__cancel__less) ).
thf(299,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ord_less @ nat @ ( plus_plus @ nat @ C @ B ) @ ( plus_plus @ nat @ C @ A ) )
=> ( ord_less @ nat @ B @ A ) )
& ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ ( plus_plus @ nat @ C @ B ) @ ( plus_plus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(104,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_ext) ).
thf(431,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(118,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_less__zeroE) ).
thf(473,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(124,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(490,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(102,axiom,
! [TA: $tType] :
( ( idom @ TA )
=> ( idom @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Oidom) ).
thf(426,plain,
! [TA: $tType] :
( ( idom @ TA )
=> ( idom @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(11,axiom,
ordere223160158up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(162,plain,
ordere223160158up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(140,axiom,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( comm_ring_1 @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ocomm__ring__1) ).
thf(548,plain,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( comm_ring_1 @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(83,axiom,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( ring_1 @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Oring__1) ).
thf(374,plain,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( ring_1 @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(123,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(487,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(131,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat,B: TA] :
( ( ( monom @ TA @ B @ A )
= ( zero_zero @ ( poly1 @ TA ) ) )
<=> ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_monom__eq__0__iff) ).
thf(516,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat,B: TA] :
( ( ( ( monom @ TA @ B @ A )
= ( zero_zero @ ( poly1 @ TA ) ) )
=> ( B
= ( zero_zero @ TA ) ) )
& ( ( B
= ( zero_zero @ TA ) )
=> ( ( monom @ TA @ B @ A )
= ( zero_zero @ ( poly1 @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(27,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(194,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(56,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA] : ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_less__add__one) ).
thf(295,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA] : ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(5,axiom,
ab_semigroup_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(150,plain,
ab_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(97,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(414,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(95,axiom,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( one_one @ TA )
!= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_one__neq__zero) ).
thf(409,plain,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( one_one @ TA )
!= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(30,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) )
<=> ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_add__is__0) ).
thf(199,plain,
! [A: nat,B: nat] :
( ( ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) )
=> ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) ) )
& ( ( ( B
= ( zero_zero @ nat ) )
& ( A
= ( zero_zero @ nat ) ) )
=> ( ( plus_plus @ nat @ B @ A )
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(69,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_add__left__cancel) ).
thf(331,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(77,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
<=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_even__less__0__iff) ).
thf(359,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) )
& ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(19,axiom,
ordere216010020id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__comm__monoid__add) ).
thf(177,plain,
ordere216010020id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(23,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(182,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(17,axiom,
ordere236663937imp_le @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(175,plain,
ordere236663937imp_le @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(108,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: nat] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( aa @ nat @ TA @ ( coeff @ TA @ ( one_one @ ( poly1 @ TA ) ) ) @ A )
= ( one_one @ TA ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( aa @ nat @ TA @ ( coeff @ TA @ ( one_one @ ( poly1 @ TA ) ) ) @ A )
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_coeff__1) ).
thf(446,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: nat] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( aa @ nat @ TA @ ( coeff @ TA @ ( one_one @ ( poly1 @ TA ) ) ) @ A )
= ( one_one @ TA ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( aa @ nat @ TA @ ( coeff @ TA @ ( one_one @ ( poly1 @ TA ) ) ) @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(142,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
<=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_neq0__conv) ).
thf(556,plain,
! [A: nat] :
( ( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
& ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( A
!= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(121,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ nat @ C @ ( plus_plus @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_trans__less__add2) ).
thf(482,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ C @ B )
=> ( ord_less @ nat @ C @ ( plus_plus @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(133,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( poly @ TA @ ( one_one @ ( poly1 @ TA ) ) ) @ A )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_poly__1) ).
thf(524,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( poly @ TA @ ( one_one @ ( poly1 @ TA ) ) ) @ A )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(64,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat] :
( ( aa @ nat @ TA @ ( coeff @ TA @ ( zero_zero @ ( poly1 @ TA ) ) ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_coeff__0) ).
thf(319,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat] :
( ( aa @ nat @ TA @ ( coeff @ TA @ ( zero_zero @ ( poly1 @ TA ) ) ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(59,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_not__one__less__zero) ).
thf(304,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(14,axiom,
comm_monoid_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(171,plain,
comm_monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(87,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ( cancel_semigroup_add @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ocancel__semigroup__add) ).
thf(383,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ( cancel_semigroup_add @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(54,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_not__less0) ).
thf(290,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(85,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_zero__less__two) ).
thf(378,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(33,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( comm_semiring_1 @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Rings_Ocomm__semiring__1) ).
thf(214,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( comm_semiring_1 @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(53,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA,B: poly1 @ TA,C: poly1 @ TA] :
( ( aa @ TA @ TA @ ( poly @ TA @ ( plus_plus @ ( poly1 @ TA ) @ C @ B ) ) @ A )
= ( plus_plus @ TA @ ( aa @ TA @ TA @ ( poly @ TA @ C ) @ A ) @ ( aa @ TA @ TA @ ( poly @ TA @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_poly__add) ).
thf(287,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA,B: poly1 @ TA,C: poly1 @ TA] :
( ( aa @ TA @ TA @ ( poly @ TA @ ( plus_plus @ ( poly1 @ TA ) @ C @ B ) ) @ A )
= ( plus_plus @ TA @ ( aa @ TA @ TA @ ( poly @ TA @ C ) @ A ) @ ( aa @ TA @ TA @ ( poly @ TA @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(6,axiom,
linordered_semidom @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(151,plain,
linordered_semidom @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
( ( aa @ a @ a @ ( poly @ a @ ( fundam296178794t_poly @ a @ ( zero_zero @ ( poly1 @ a ) ) @ h ) ) @ x )
= ( aa @ a @ a @ ( poly @ a @ ( zero_zero @ ( poly1 @ a ) ) ) @ ( plus_plus @ a @ h @ x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( aa @ a @ a @ ( poly @ a @ ( fundam296178794t_poly @ a @ ( zero_zero @ ( poly1 @ a ) ) @ h ) ) @ x )
!= ( aa @ a @ a @ ( poly @ a @ ( zero_zero @ ( poly1 @ a ) ) ) @ ( plus_plus @ a @ h @ x ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(146,plain,
( ( aa @ a @ a @ ( poly @ a @ ( fundam296178794t_poly @ a @ ( zero_zero @ ( poly1 @ a ) ) @ h ) ) @ x )
!= ( aa @ a @ a @ ( poly @ a @ ( zero_zero @ ( poly1 @ a ) ) ) @ ( plus_plus @ a @ h @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(25,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( zero @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clar_Rings_Ocomm__semiring__0__Groups_Ozero) ).
thf(190,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( zero @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(100,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ D @ C )
=> ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_add__strict__mono) ).
thf(422,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ D @ C )
=> ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(67,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ D @ C ) @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(326,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ D @ C ) @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(48,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_add_Ocomm__neutral) ).
thf(268,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(28,axiom,
cancel1352612707id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__comm__monoid__add) ).
thf(195,plain,
cancel1352612707id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(93,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ C @ A ) )
<=> ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_add__less__cancel__left) ).
thf(400,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ C @ A ) )
=> ( ord_less @ TA @ B @ A ) )
& ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(91,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ A )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_mem__def) ).
thf(395,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( member @ TA @ B @ A )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(114,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_pos__add__strict) ).
thf(464,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(112,axiom,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_add__pos__pos) ).
thf(459,plain,
! [TA: $tType] :
( ( ordere216010020id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(12,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( member @ TA @ ( one_one @ TA ) @ ( ring_1_Ints @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_Ints__1) ).
thf(163,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( member @ TA @ ( one_one @ TA ) @ ( ring_1_Ints @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(20,axiom,
monoid_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(178,plain,
monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(127,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_add__right__imp__eq) ).
thf(501,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(81,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_add__strict__left__mono) ).
thf(369,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(44,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: poly1 @ TA] :
( ( plus_plus @ ( poly1 @ TA ) @ A @ ( zero_zero @ ( poly1 @ TA ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_add__poly__code_I2_J) ).
thf(254,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: poly1 @ TA] :
( ( plus_plus @ ( poly1 @ TA ) @ A @ ( zero_zero @ ( poly1 @ TA ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(65,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ( comm_monoid_add @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Groups_Ocomm__monoid__add) ).
thf(322,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ( comm_monoid_add @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(70,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
= ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_nat__add__assoc) ).
thf(337,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
= ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(116,axiom,
! [TA: $tType,TB: $tType] :
( ( zero @ TB )
=> ! [A: TA,B: fun @ TB @ ( fun @ ( poly1 @ TB ) @ ( fun @ TA @ TA ) )] :
( ( ( aa @ TA @ TA @ ( aa @ ( poly1 @ TB ) @ ( fun @ TA @ TA ) @ ( aa @ TB @ ( fun @ ( poly1 @ TB ) @ ( fun @ TA @ TA ) ) @ B @ ( zero_zero @ TB ) ) @ ( zero_zero @ ( poly1 @ TB ) ) ) @ A )
= A )
=> ( ( poly_rec @ TA @ TB @ A @ B @ ( zero_zero @ ( poly1 @ TB ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_poly__rec__0) ).
thf(469,plain,
! [TA: $tType,TB: $tType] :
( ( zero @ TB )
=> ! [A: TA,B: fun @ TB @ ( fun @ ( poly1 @ TB ) @ ( fun @ TA @ TA ) )] :
( ( ( aa @ TA @ TA @ ( aa @ ( poly1 @ TB ) @ ( fun @ TA @ TA ) @ ( aa @ TB @ ( fun @ ( poly1 @ TB ) @ ( fun @ TA @ TA ) ) @ B @ ( zero_zero @ TB ) ) @ ( zero_zero @ ( poly1 @ TB ) ) ) @ A )
= A )
=> ( ( poly_rec @ TA @ TB @ A @ B @ ( zero_zero @ ( poly1 @ TB ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(75,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( poly @ TA @ ( zero_zero @ ( poly1 @ TA ) ) ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_poly__0) ).
thf(354,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA] :
( ( aa @ TA @ TA @ ( poly @ TA @ ( zero_zero @ ( poly1 @ TA ) ) ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(61,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ C @ A ) )
=> ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_add__less__imp__less__left) ).
thf(309,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ C @ B ) @ ( plus_plus @ TA @ C @ A ) )
=> ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(138,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_add__0) ).
thf(543,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(35,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA,B: poly1 @ TA,C: poly1 @ TA] :
( ( aa @ TA @ TA @ ( poly @ TA @ ( pcompose @ TA @ C @ B ) ) @ A )
= ( aa @ TA @ TA @ ( poly @ TA @ C ) @ ( aa @ TA @ TA @ ( poly @ TA @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_poly__pcompose) ).
thf(222,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA,B: poly1 @ TA,C: poly1 @ TA] :
( ( aa @ TA @ TA @ ( poly @ TA @ ( pcompose @ TA @ C @ B ) ) @ A )
= ( aa @ TA @ TA @ ( poly @ TA @ C ) @ ( aa @ TA @ TA @ ( poly @ TA @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(79,axiom,
! [TA: $tType] :
( ( idom @ TA )
=> ( semiri456707255roduct @ ( poly1 @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial_Opoly___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(364,plain,
! [TA: $tType] :
( ( idom @ TA )
=> ( semiri456707255roduct @ ( poly1 @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(38,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ ( plus_plus @ nat @ D @ B ) @ ( plus_plus @ nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_add__less__mono) ).
thf(232,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ ( plus_plus @ nat @ D @ B ) @ ( plus_plus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(577,plain,
$false,
inference(e,[status(thm)],[440,403,387,479,234,352,385,550,472,340,417,257,389,184,504,357,196,284,152,216,179,443,376,211,238,293,428,507,527,452,380,546,366,160,297,424,192,165,260,349,252,329,522,461,493,324,229,566,484,225,537,476,457,173,569,371,343,266,311,398,530,412,513,148,161,149,176,281,313,498,466,236,181,540,159,172,274,419,362,245,434,271,208,455,306,563,299,431,473,490,426,162,548,374,487,516,194,295,150,414,409,199,331,359,177,182,175,446,556,482,524,319,304,171,383,290,378,214,287,151,146,190,422,326,268,195,400,395,464,459,163,178,501,369,254,322,337,469,354,309,543,222,364,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW488_5 : TPTP v8.1.2. Released v6.0.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n021.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 22:20:58 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.95/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.65/1.09 % [INFO] Parsing done (205ms).
% 1.65/1.10 % [INFO] Running in sequential loop mode.
% 2.11/1.30 % [INFO] eprover registered as external prover.
% 2.11/1.31 % [INFO] cvc4 registered as external prover.
% 2.11/1.31 % [INFO] Scanning for conjecture ...
% 2.48/1.40 % [INFO] Found a conjecture and 143 axioms. Running axiom selection ...
% 2.79/1.48 % [INFO] Axiom selection finished. Selected 143 axioms (removed 0 axioms).
% 3.05/1.60 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.05/1.62 % [INFO] Type checking passed.
% 3.05/1.62 % [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 ...
% 9.13/3.26 % External prover 'e' found a proof!
% 9.13/3.26 % [INFO] Killing All external provers ...
% 9.13/3.27 % Time passed: 2733ms (effective reasoning time: 2162ms)
% 9.13/3.27 % 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)>
% 9.13/3.27 % Axioms used in derivation (143): fact_42_plus__nat_Oadd__0, arity_Nat_Onat___Rings_Olinordered__semidom, arity_Polynomial_Opoly___Rings_Ocomm__ring__1, fact_35_poly__pcompose, fact_32_monom__eq__0__iff, fact_88_less__add__one, tfree_0, arity_Polynomial_Opoly___Groups_Oordered__cancel__ab__semigroup__add, fact_15_add__right__imp__eq, fact_57_coeff__1, fact_95_zero__less__two, fact_93_coeff__inject, fact_17_add__left__imp__eq, fact_2_poly__add, fact_45_Ints__odd__nonzero, fact_14_zero__reorient, fact_8_add__0__left, fact_46_nat__add__right__cancel, fact_48_poly__1, arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, arity_Polynomial_Opoly___Groups_Oordered__comm__monoid__add, fact_37_Ints__double__eq__0__iff, fact_11_add__0__right, fact_74_mem__def, fact_50_nat__add__left__commute, fact_0_offset__poly__0, fact_31_poly__rec__0, arity_Polynomial_Opoly___Groups_Olinordered__ab__group__add, fact_25_poly__eq__iff, arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_18_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_36_add__monom, arity_Polynomial_Opoly___Groups_Omonoid__add, arity_Polynomial_Opoly___Groups_Oone, fact_82_add__lessD1, fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, arity_Nat_Onat___Groups_Ocomm__monoid__add, fact_86_trans__less__add2, fact_3_double__zero__sym, fact_27_add_Ocomm__neutral, arity_Nat_Onat___Groups_Ocancel__comm__monoid__add, fact_39_Ints__0, arity_Polynomial_Opoly___Groups_Ocancel__semigroup__add, arity_Polynomial_Opoly___Rings_Oring__1, arity_Polynomial_Opoly___Rings_Oidom, fact_79_add__strict__mono, arity_Polynomial_Opoly___Rings_Ozero__neq__one, arity_Polynomial_Opoly___Groups_Ozero, fact_64_add__gr__0, clar_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add, arity_Polynomial_Opoly___Int_Oring__char__0, arity_Polynomial_Opoly___Rings_Olinordered__semidom, fact_34_synthetic__div__0, fact_47_nat__add__left__cancel, fact_7_poly__zero, arity_Polynomial_Opoly___Groups_Oordered__ab__semigroup__add__imp__le, fact_49_nat__add__assoc, fact_81_add__less__imp__less__left, fact_68_coeff__add, arity_Polynomial_Opoly___Groups_Ocancel__ab__semigroup__add, fact_51_nat__add__commute, arity_Polynomial_Opoly___Rings_Ocomm__semiring__1, clar_Rings_Ocomm__semiring__0__Groups_Oab__semigroup__add, fact_73_ext, fact_96_even__less__0__iff, clar_Rings_Ocomm__semiring__0__Groups_Omonoid__add, fact_61_nat__add__left__cancel__less, arity_Polynomial_Opoly___Rings_Olinordered__idom, fact_13_add__poly__code_I1_J, fact_80_add__less__imp__less__right, clar_Rings_Ocomm__semiring__0__Groups_Ozero, arity_Polynomial_Opoly___Groups_Ocomm__monoid__add, fact_62_add__less__cancel__right, arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_55_one__neq__zero, fact_60_neq0__conv, arity_Nat_Onat___Groups_Ozero, arity_Polynomial_Opoly___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, arity_Nat_Onat___Groups_Oordered__comm__monoid__add, fact_54_zero__neq__one, fact_90_not__add__less1, fact_12_add__poly__code_I2_J, fact_30_pcompose__0, fact_70_not__one__less__zero, fact_28_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_76_gr0I, fact_22_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, arity_Nat_Onat___Rings_Ocomm__semiring__0, fact_40_Ints__add, fact_38_monom__eq__iff, fact_94_linorder__neqE__linordered__idom, arity_Polynomial_Opoly___Groups_Ocancel__comm__monoid__add, fact_85_add__less__mono1, fact_71_not__less0, fact_43_Nat_Oadd__0__right, fact_16_add__imp__eq, fact_44_add__eq__self__zero, fact_20_ab__semigroup__add__class_Oadd__ac_I1_J, fact_5_add__left__cancel, arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_33_monom__eq__0, fact_67_coeff__0, fact_84_add__less__mono, fact_75_gr__implies__not0, fact_56_Ints__odd__less__0, arity_Nat_Onat___Groups_Oone, fact_29_order__root, fact_72_zero__less__one, fact_53_Ints__1, fact_6_add__right__cancel, fact_83_less__add__eq__less, fact_69_coeff__monom, fact_92_expand__poly__eq, fact_9_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_24_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_97_add__pos__pos, fact_10_add__0, help_pp_1_1_U, fact_23_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_58_less__zeroE, fact_52_one__reorient, fact_87_trans__less__add1, fact_77_add__strict__right__mono, arity_Polynomial_Opoly___Groups_Oab__semigroup__add, arity_Nat_Onat___Groups_Omonoid__add, fact_91_pos__add__strict, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_41_add__is__0, fact_66_double__add__less__zero__iff__single__add__less__zero, fact_65_zero__less__double__add__iff__zero__less__single__add, help_pp_2_1_U, fact_63_add__less__cancel__left, fact_4_double__eq__0__iff, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_59_less__nat__zero__code, arity_Nat_Onat___Rings_Ozero__neq__one, arity_Polynomial_Opoly___Rings_Ocomm__semiring__0, fact_89_not__add__less2, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_26_add__0__iff, fact_1_poly__0, fact_78_add__strict__left__mono
% 9.13/3.27 % No. of inferences in proof: 290
% 9.13/3.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2733 ms resp. 2162 ms w/o parsing
% 9.13/3.34 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.13/3.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------