%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM978_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 : n007.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 08:10:34 AM UTC 2026
% Result : Theorem 8.95s 3.62s
% Output : Refutation 9.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 140
% Syntax : Number of formulae : 282 ( 136 unt; 0 typ; 0 def)
% Number of atoms : 598 ( 188 equ; 0 cnn)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 2325 ( 54 ~; 9 |; 41 &;1963 @)
% ( 30 <=>; 228 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 43 usr; 9 con; 0-4 aty)
% Number of variables : 430 ( 0 ^; 428 !; 2 ?; 430 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(number_decl,type,
number:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[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(mult_zero_decl,type,
mult_zero:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(monoid_add_decl,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(semiring_char_0_decl,type,
semiring_char_0:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_decl,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_decl,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(linordered_semidom_decl,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(ring_n68954251visors_decl,type,
ring_n68954251visors:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(ordere216010020id_add_decl,type,
ordere216010020id_add:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_decl,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(ordere223160158up_add_decl,type,
ordere223160158up_add:
!>[TA: $tType] : $o ).
thf(semiri456707255roduct_decl,type,
semiri456707255roduct:
!>[TA: $tType] : $o ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(times_times_decl,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(bit0_decl,type,
bit0: int > int ).
thf(bit1_decl,type,
bit1: int > int ).
thf(pls_decl,type,
pls: int ).
thf(number_number_of_decl,type,
number_number_of:
!>[TA: $tType] : ( int > TA ) ).
thf(semiring_1_of_nat_decl,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(twoSqu1567020053sum2sq_decl,type,
twoSqu1567020053sum2sq: int > $o ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(pp_decl,type,
pp: bool > $o ).
thf(m_decl,type,
m: int ).
thf(n_decl,type,
n: nat ).
thf(t_decl,type,
t: int ).
thf(tn_decl,type,
tn: nat ).
thf(77,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_nat__add__right__cancel) ).
thf(365,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(43,axiom,
int @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(249,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(38,axiom,
! [A: int,B: int] :
( ( A @ ( B @ bit0 @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_mult__Bit0) ).
thf(234,plain,
! [A: int,B: int] :
( ( A @ ( B @ bit0 @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(131,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_less__zeroE) ).
thf(555,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(108,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_of__nat__add) ).
thf(481,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(18,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_mult__Pls) ).
thf(170,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(119,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: TA,C: TA] :
( ( C @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_pos__add__strict) ).
thf(523,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: TA,C: TA] :
( ( C @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(60,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_rel__simps_I17_J) ).
thf(308,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(102,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_neq0__conv) ).
thf(449,plain,
! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) )
& ( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(82,axiom,
nat @ one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(379,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(85,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_add__less__mono) ).
thf(385,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( D @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(1,conjecture,
n @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( n @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(142,plain,
~ ( n @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(125,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_less__irrefl__nat) ).
thf(538,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(8,axiom,
! [A: int] :
( ( A @ bit1 )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_rel__simps_I46_J) ).
thf(153,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(91,axiom,
! [A: nat,B: nat] :
( ( B != A )
<=> ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_nat__neq__iff) ).
thf(404,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(93,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_double__eq__0__iff) ).
thf(417,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(54,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_of__nat__less__iff) ).
thf(288,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(135,axiom,
nat @ semiring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
thf(565,plain,
nat @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(113,axiom,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_add__neg__neg) ).
thf(504,plain,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(73,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_less__imp__of__nat__less) ).
thf(357,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(9,axiom,
int @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
thf(157,plain,
int @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(133,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_add__less__cancel__right) ).
thf(559,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A @ ( C @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) )
& ( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_even__less__0__iff) ).
thf(284,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(34,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_95_right__distrib__number__of) ).
thf(228,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)],[34]) ).
thf(101,axiom,
nat @ linordered_semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(448,plain,
nat @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(40,axiom,
int @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(238,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(115,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_add_Ocomm__neutral) ).
thf(514,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(71,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ zero_zero @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_of__nat__0) ).
thf(348,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ zero_zero @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(137,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(574,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(89,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_nat__add__left__cancel__less) ).
thf(396,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( C @ ( nat @ plus_plus ) ) @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(121,axiom,
! [A: nat,B: nat] :
~ ( A @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_not__add__less2) ).
thf(527,plain,
! [A: nat,B: nat] :
~ ( A @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(55,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_gr__implies__not0) ).
thf(292,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(37,axiom,
int @ semiri456707255roduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(233,plain,
int @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(83,axiom,
nat @ semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(380,plain,
nat @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(48,axiom,
int @ semiring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).
thf(270,plain,
int @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(84,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_add__less__cancel__left) ).
thf(381,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(31,axiom,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_rel__simps_I49_J) ).
thf(220,plain,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(12,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_24_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(160,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)],[12]) ).
thf(56,axiom,
~ ( pls @ ( pls @ ( int @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_rel__simps_I2_J) ).
thf(297,plain,
~ ( pls @ ( pls @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(94,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ one_one @ ( TA @ semiring_1_of_nat ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_of__nat__1) ).
thf(424,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ one_one @ ( TA @ semiring_1_of_nat ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(22,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_add__Bit0__Bit0) ).
thf(192,plain,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(24,axiom,
int @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(197,plain,
int @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(75,axiom,
nat @ ordere236663937imp_le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(361,plain,
nat @ ordere236663937imp_le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(65,axiom,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_add__strict__right__mono) ).
thf(329,plain,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( A @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(141,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_less__not__refl2) ).
thf(583,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(105,axiom,
! [TA: $tType] :
( ( TA @ ring_n68954251visors )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) )
<=> ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_mult__eq__0__iff) ).
thf(461,plain,
! [TA: $tType] :
( ( TA @ ring_n68954251visors )
=> ! [A: TA,B: TA] :
( ( ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(63,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= B )
=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_add__eq__self__zero) ).
thf(324,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= B )
=> ( A
= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(32,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_26_add__imp__eq) ).
thf(224,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)],[32]) ).
thf(136,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_zero__reorient) ).
thf(566,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= A ) )
& ( ( ( TA @ zero_zero )
= A )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(109,axiom,
! [TA: $tType] :
( ( TA @ mult_zero )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_mult__zero__right) ).
thf(484,plain,
! [TA: $tType] :
( ( TA @ mult_zero )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(139,axiom,
nat @ semiri456707255roduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(578,plain,
nat @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(62,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_double__zero__sym) ).
thf(317,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) ) )
& ( ( ( TA @ zero_zero )
= ( A @ ( A @ ( TA @ plus_plus ) ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(17,axiom,
int @ ring_n68954251visors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__no__zero__divisors) ).
thf(169,plain,
int @ ring_n68954251visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(128,axiom,
nat @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(547,plain,
nat @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(64,axiom,
nat @ mult_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(328,plain,
nat @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(106,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_Nat_Oadd__0__right) ).
thf(471,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(87,axiom,
nat @ ordere216010020id_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__comm__monoid__add) ).
thf(393,plain,
nat @ ordere216010020id_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(103,axiom,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_p0) ).
thf(457,plain,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(19,axiom,
! [A: int] :
( ( pls
= ( A @ bit0 ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_rel__simps_I38_J) ).
thf(173,plain,
! [A: int] :
( ( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(39,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(237,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(126,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_add__0__right) ).
thf(541,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(132,axiom,
n @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_smaller_I1_J) ).
thf(558,plain,
n @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(122,axiom,
nat @ ordere223160158up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(530,plain,
nat @ ordere223160158up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(96,axiom,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_linorder__neqE__nat) ).
thf(430,plain,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(14,axiom,
int @ one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(166,plain,
int @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(51,axiom,
~ ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_nQ1) ).
thf(279,plain,
~ ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(6,axiom,
int @ number_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(149,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(79,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_add__less__imp__less__right) ).
thf(375,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(90,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( A @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_add__less__mono1) ).
thf(402,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( A @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(138,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(577,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(140,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_less__not__refl3) ).
thf(579,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(52,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less ) ) )
=> ( ( ( C @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( D @ ( nat @ plus_plus ) ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_less__add__eq__less) ).
thf(281,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( C @ ( D @ ( nat @ ord_less ) ) )
=> ( ( ( C @ ( B @ ( nat @ plus_plus ) ) )
= ( A @ ( D @ ( nat @ plus_plus ) ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(4,axiom,
int @ linordered_semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
thf(144,plain,
int @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,axiom,
int @ monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
thf(181,plain,
int @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(11,axiom,
int @ ordere223160158up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(159,plain,
int @ ordere223160158up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(30,axiom,
int @ semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(219,plain,
int @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(80,axiom,
nat @ comm_semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(377,plain,
nat @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(76,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(362,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(98,axiom,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_add__0__left) ).
thf(434,plain,
! [TA: $tType] :
( ( TA @ monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(58,axiom,
nat @ comm_monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(303,plain,
nat @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(49,axiom,
! [TA: $tType] :
( ( TA @ semiring_char_0 )
=> ! [A: nat,B: nat] :
( ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_of__nat__eq__iff) ).
thf(271,plain,
! [TA: $tType] :
( ( TA @ semiring_char_0 )
=> ! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) ) )
& ( ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(28,axiom,
int @ comm_monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__add) ).
thf(208,plain,
int @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(86,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_rel__simps_I14_J) ).
thf(387,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(124,axiom,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_add__0) ).
thf(535,plain,
! [TA: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(117,axiom,
tn @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tn0) ).
thf(520,plain,
tn @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(25,axiom,
( ( pls @ bit0 )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_Bit0__Pls) ).
thf(198,plain,
( ( pls @ bit0 )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(118,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_of__nat__less__imp__less) ).
thf(521,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(50,axiom,
t @ ( int @ one_one @ ( int @ ord_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_t1) ).
thf(278,plain,
t @ ( int @ one_one @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(88,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_trans__less__add1) ).
thf(394,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(134,axiom,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_add__strict__mono) ).
thf(563,plain,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( D @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(57,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_of__nat__0__less__iff) ).
thf(299,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(15,axiom,
int @ ordere236663937imp_le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(167,plain,
int @ ordere236663937imp_le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(111,axiom,
! [A: bool @ ( nat @ fun ) @ ( nat @ fun ),B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C @ ( B @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_nat__less__cases) ).
thf(490,plain,
! [A: bool @ ( nat @ fun ) @ ( nat @ fun ),B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C @ ( B @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(123,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_double__add__less__zero__iff__single__add__less__zero) ).
thf(531,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(129,axiom,
~ ( ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) )
=> ~ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_smaller_I2_J) ).
thf(548,plain,
~ ( ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) )
=> ~ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(46,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_15_add__right__cancel) ).
thf(255,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)],[46]) ).
thf(130,axiom,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_add__pos__pos) ).
thf(553,plain,
! [TA: $tType] :
( ( TA @ ordere216010020id_add )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(104,axiom,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_plus__nat_Oadd__0) ).
thf(458,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(5,axiom,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_rel__simps_I50_J) ).
thf(145,plain,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(29,axiom,
! [A: int,B: int] :
( ( ( B @ bit0 )
= ( A @ bit0 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_rel__simps_I48_J) ).
thf(209,plain,
! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ bit0 )
= ( A @ bit0 ) ) )
& ( ( ( B @ bit0 )
= ( A @ bit0 ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(110,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_gr0I) ).
thf(487,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(120,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_add__lessD1) ).
thf(525,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(7,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_27_add__right__imp__eq) ).
thf(150,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)],[7]) ).
thf(21,axiom,
! [A: int,B: int] :
( ( ( B @ bit1 )
= ( A @ bit1 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_rel__simps_I51_J) ).
thf(182,plain,
! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ bit1 )
= ( A @ bit1 ) ) )
& ( ( ( B @ bit1 )
= ( A @ bit1 ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(66,axiom,
nat @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(331,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(69,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_nat__add__left__cancel) ).
thf(338,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = A )
=> ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ plus_plus ) ) )
= ( A @ ( C @ ( nat @ plus_plus ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(74,axiom,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( C @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_add__strict__left__mono) ).
thf(359,plain,
! [TA: $tType] :
( ( TA @ ordere223160158up_add )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ plus_plus ) ) @ ( C @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(127,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_less__not__refl) ).
thf(544,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(61,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_less__nat__zero__code) ).
thf(314,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(3,axiom,
int @ linord219039673up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(143,plain,
int @ linord219039673up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(44,axiom,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_rel__simps_I39_J) ).
thf(250,plain,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(35,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(231,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(116,axiom,
! [TA: $tType] :
( ( TA @ mult_zero )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_mult__zero__left) ).
thf(517,plain,
! [TA: $tType] :
( ( TA @ mult_zero )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(59,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_zero__less__double__add__iff__zero__less__single__add) ).
thf(304,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(10,axiom,
int @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(158,plain,
int @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(72,axiom,
! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_zero__less__int__conv) ).
thf(351,plain,
! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
& ( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(81,axiom,
nat @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(378,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(97,axiom,
nat @ monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(433,plain,
nat @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(27,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(207,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(70,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_trans__less__add2) ).
thf(346,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ plus_plus ) ) @ ( C @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(100,axiom,
nat @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(447,plain,
nat @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(78,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
~ ( TA @ zero_zero @ ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_of__nat__less__0__iff) ).
thf(373,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
~ ( TA @ zero_zero @ ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(16,axiom,
int @ comm_semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(168,plain,
int @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(47,axiom,
! [A: int] :
( ( ( A @ bit0 )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_rel__simps_I44_J) ).
thf(262,plain,
! [A: int] :
( ( ( A = pls )
=> ( ( A @ bit0 )
= pls ) )
& ( ( ( A @ bit0 )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(114,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
<=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_add__gr__0) ).
thf(506,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
=> ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(23,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(195,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(99,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) )
<=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_add__is__0) ).
thf(437,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) )
=> ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( nat @ plus_plus ) ) )
= ( nat @ zero_zero ) )
=> ( ( A
= ( nat @ zero_zero ) )
& ( B
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(107,axiom,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA] :
( ( B
= ( A @ ( B @ ( TA @ plus_plus ) ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_add__0__iff) ).
thf(474,plain,
! [TA: $tType] :
( ( TA @ semiri456707255roduct )
=> ! [A: TA,B: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( B
= ( A @ ( B @ ( TA @ plus_plus ) ) ) ) )
& ( ( B
= ( A @ ( B @ ( TA @ plus_plus ) ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_add__less__imp__less__left) ).
thf(415,plain,
! [TA: $tType] :
( ( TA @ ordere236663937imp_le )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( C @ ( TA @ plus_plus ) ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(41,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_25_add__left__imp__eq) ).
thf(239,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)],[41]) ).
thf(42,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_14_add__left__cancel) ).
thf(242,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)],[42]) ).
thf(67,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ? [C: nat] :
( ( ( C @ ( B @ ( nat @ plus_plus ) ) )
= A )
& ( C @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_less__imp__add__positive) ).
thf(332,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ? [C: nat] :
( ( ( C @ ( B @ ( nat @ plus_plus ) ) )
= A )
& ( C @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(95,axiom,
! [A: nat,B: nat] :
~ ( B @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_not__add__less1) ).
thf(427,plain,
! [A: nat,B: nat] :
~ ( B @ ( A @ ( B @ ( nat @ plus_plus ) ) @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(112,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_not__less0) ).
thf(501,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(13,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_94_left__distrib__number__of) ).
thf(163,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)],[13]) ).
thf(26,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_70_eq__number__of) ).
thf(200,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)],[26]) ).
thf(68,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(337,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(36,axiom,
int @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(232,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(45,axiom,
int @ ordere216010020id_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__comm__monoid__add) ).
thf(254,plain,
int @ ordere216010020id_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(33,axiom,
int @ mult_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
thf(227,plain,
int @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(587,plain,
$false,
inference(e,[status(thm)],[365,249,234,555,481,170,523,308,449,379,385,142,538,153,404,417,288,565,504,357,157,559,284,228,448,238,514,348,574,396,527,292,233,380,270,381,220,160,297,424,192,197,361,329,583,461,324,224,566,484,578,317,169,547,328,471,393,457,173,237,541,558,530,430,166,279,149,375,402,577,579,281,144,181,159,219,377,362,434,303,271,208,387,535,520,198,521,278,394,563,299,167,490,531,548,255,553,458,145,209,487,525,150,182,331,338,359,544,314,143,250,231,517,304,158,351,378,433,207,346,447,373,168,262,506,195,437,474,415,239,242,332,427,501,163,200,337,232,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM978_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
% 0.14/0.40 % Computer : n007.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 04:22:09 UTC 2026
% 0.18/0.40 % CPUTime :
% 0.18/0.40 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
% 0.84/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.40/1.25 % [INFO] Parsing done (275ms).
% 1.40/1.26 % [INFO] Running in sequential loop mode.
% 2.42/1.66 % [INFO] eprover registered as external prover.
% 2.42/1.67 % [INFO] Scanning for conjecture ...
% 2.81/1.81 % [INFO] Found a conjecture (or negated_conjecture) and 139 axioms. Running axiom selection ...
% 3.00/1.94 % [INFO] Axiom selection finished. Selected 139 axioms (removed 0 axioms).
% 3.40/2.12 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.65/2.14 % [INFO] Type checking passed.
% 3.65/2.14 % [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 ...
% 8.95/3.62 % External prover 'e' found a proof!
% 8.95/3.62 % [INFO] Killing All external provers ...
% 8.95/3.62 % Time passed: 3081ms (effective reasoning time: 2353ms)
% 8.95/3.62 % 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)>
% 8.95/3.62 % Axioms used in derivation (139): fact_19_double__zero__sym, fact_18_of__nat__eq__iff, fact_76_mult__zero__left, arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add, arity_Int_Oint___Groups_Oordered__comm__monoid__add, fact_37_not__add__less2, arity_Int_Oint___Groups_Oone, fact_95_right__distrib__number__of, fact_30_plus__nat_Oadd__0, fact_33_add__less__mono, fact_24_ab__semigroup__add__class_Oadd__ac_I1_J, arity_Int_Oint___Rings_Olinordered__idom, fact_42_add__0__left, arity_Nat_Onat___Rings_Osemiring__1, arity_Int_Oint___Int_Oring__char__0, fact_43_add__less__imp__less__left, fact_65_less__imp__add__positive, fact_88_rel__simps_I14_J, fact_63_pos__add__strict, arity_Int_Oint___Groups_Ocomm__monoid__add, arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_28_add__eq__self__zero, fact_55_less__not__refl3, fact_17_nat__add__left__cancel__less, fact_72_rel__simps_I48_J, fact_12_of__nat__0, fact_81_rel__simps_I50_J, fact_67_add__0__iff, fact_94_left__distrib__number__of, arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_3_less__nat__zero__code, fact_45_add__strict__mono, fact_13_t1, fact_2_neq0__conv, fact_80_rel__simps_I39_J, fact_83_rel__simps_I44_J, fact_4_less__zeroE, arity_Int_Oint___Groups_Ocancel__ab__semigroup__add, fact_7_gr__implies__not0, fact_26_add__imp__eq, arity_Int_Oint___Int_Onumber__ring, fact_41_add__0, arity_Int_Oint___Rings_Osemiring__1, fact_35_trans__less__add2, arity_Nat_Onat___Groups_Ocomm__monoid__add, arity_Nat_Onat___Rings_Omult__zero, fact_74_nat__add__right__cancel, fact_89_of__nat__1, fact_50_of__nat__less__imp__less, fact_6_not__less0, fact_47_add__strict__right__mono, fact_20_add__less__cancel__left, fact_16_add__is__0, fact_23_of__nat__add, fact_1_smaller_I1_J, fact_29_Nat_Oadd__0__right, fact_11_of__nat__less__iff, fact_25_add__left__imp__eq, fact_59_nat__neq__iff, fact_73_nat__add__left__cancel, fact_27_add__right__imp__eq, arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_10_double__add__less__zero__iff__single__add__less__zero, fact_90_mult__Pls, fact_51_less__imp__of__nat__less, arity_Int_Oint___Rings_Oring__no__zero__divisors, fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_75_nQ1, fact_52_add__neg__neg, fact_40_add__0__right, fact_49_of__nat__less__0__iff, arity_Nat_Onat___Rings_Olinordered__semidom, fact_66_zero__less__int__conv, arity_Int_Oint___Rings_Osemiring, fact_8_gr0I, arity_Nat_Onat___Rings_Ocomm__semiring__1, arity_Int_Oint___Groups_Omonoid__add, arity_Nat_Onat___Groups_Ozero, arity_Nat_Onat___Groups_Oordered__comm__monoid__add, fact_78_mult__eq__0__iff, fact_62_smaller_I2_J, fact_87_rel__simps_I2_J, fact_53_add__pos__pos, fact_79_rel__simps_I46_J, fact_9_zero__less__double__add__iff__zero__less__single__add, fact_82_rel__simps_I49_J, fact_31_add__lessD1, fact_84_rel__simps_I38_J, fact_71_rel__simps_I51_J, fact_86_rel__simps_I17_J, arity_Int_Oint___Groups_Ocancel__semigroup__add, fact_93_p0, fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_77_mult__zero__right, arity_Int_Oint___Rings_Ocomm__semiring__1, fact_21_add__less__cancel__right, arity_Nat_Onat___Int_Onumber, arity_Nat_Onat___Nat_Osemiring__char__0, arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le, fact_60_less__not__refl, fact_92_add__Bit0__Bit0, fact_44_add__less__imp__less__right, arity_Nat_Onat___Groups_Oone, fact_91_mult__Bit0, fact_48_zero__reorient, arity_Int_Oint___Groups_Oab__semigroup__add, fact_38_not__add__less1, fact_39_add_Ocomm__neutral, arity_Nat_Onat___Rings_Osemiring, fact_54_nat__less__cases, fact_32_less__add__eq__less, fact_64_even__less__0__iff, fact_36_trans__less__add1, help_pp_1_1_U, fact_14_add__left__cancel, fact_56_less__not__refl2, arity_Nat_Onat___Groups_Omonoid__add, fact_5_of__nat__0__less__iff, fact_15_add__right__cancel, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Groups_Olinordered__ab__group__add, arity_Nat_Onat___Groups_Oab__semigroup__add, arity_Int_Oint___Groups_Ozero, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, arity_Int_Oint___Rings_Omult__zero, fact_34_add__less__mono1, fact_58_linorder__neqE__nat, fact_46_add__strict__left__mono, fact_22_add__gr__0, arity_Int_Oint___Nat_Osemiring__char__0, help_pp_2_1_U, fact_0_tn0, arity_Int_Oint___Rings_Olinordered__semidom, fact_61_double__eq__0__iff, fact_85_Bit0__Pls, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_70_eq__number__of, fact_57_less__irrefl__nat
% 8.95/3.62 % No. of inferences in proof: 282
% 8.95/3.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3081 ms resp. 2353 ms w/o parsing
% 9.34/3.80 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.62/3.80 % [INFO] Killing All external provers ...
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