%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM924+5 : TPTP v9.3.1. Released v5.3.0.
% 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 : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:10:22 AM UTC 2026
% Result : Theorem 8.29s 3.68s
% Output : Refutation 9.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 155
% Syntax : Number of formulae : 312 ( 122 unt; 0 typ; 0 def)
% Number of atoms : 733 ( 214 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 3768 ( 31 ~; 9 |; 108 &;3316 @)
% ( 51 <=>; 253 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 31 usr; 7 con; 0-3 aty)
% Number of variables : 518 ( 0 ^; 518 !; 0 ?; 518 :)
% Comments :
%------------------------------------------------------------------------------
thf(ord_less_decl,type,
ord_less: $i > $i > $i > $o ).
thf(int_decl,type,
int: $i ).
thf(plus_plus_decl,type,
plus_plus: $i > $i > $i > $i ).
thf(power_power_decl,type,
power_power: $i > $i > $i > $i ).
thf(s_decl,type,
s: $i ).
thf(number_number_of_decl,type,
number_number_of: $i > $i > $i ).
thf(nat_decl,type,
nat: $i ).
thf(bit0_decl,type,
bit0: $i > $i ).
thf(bit1_decl,type,
bit1: $i > $i ).
thf(pls_decl,type,
pls: $i ).
thf(one_one_decl,type,
one_one: $i > $i ).
thf(zero_zero_decl,type,
zero_zero: $i > $i ).
thf(number_decl,type,
number: $i > $o ).
thf(linorder_decl,type,
linorder: $i > $o ).
thf(ord_less_eq_decl,type,
ord_less_eq: $i > $i > $i > $o ).
thf(ti_decl,type,
ti: $i > $i > $i ).
thf(semiring_decl,type,
semiring: $i > $o ).
thf(times_times_decl,type,
times_times: $i > $i > $i > $i ).
thf(linordered_ring_decl,type,
linordered_ring: $i > $o ).
thf(undefined_decl,type,
undefined: $i > $i ).
thf(number_semiring_decl,type,
number_semiring: $i > $o ).
thf(m_decl,type,
m: $i ).
thf(semiring_1_decl,type,
semiring_1: $i > $o ).
thf(twoSqu33214720sum2sq_decl,type,
twoSqu33214720sum2sq: $i > $o ).
thf(ring_char_0_decl,type,
ring_char_0: $i > $o ).
thf(linord581940658strict_decl,type,
linord581940658strict: $i > $o ).
thf(linordered_idom_decl,type,
linordered_idom: $i > $o ).
thf(number_ring_decl,type,
number_ring: $i > $o ).
thf(t_decl,type,
t: $i ).
thf(zprime_decl,type,
zprime: $i > $o ).
thf(ring_11004092258visors_decl,type,
ring_11004092258visors: $i > $o ).
thf(67,axiom,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_nat__numeral__1__eq__1) ).
thf(384,plain,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(135,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( A @ one_one @ ( B @ ( A @ number_number_of ) @ ( A @ plus_plus ) ) )
= ( pls @ bit1 @ ( B @ ( int @ plus_plus ) ) @ ( A @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_add__special_I3_J) ).
thf(645,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( A @ one_one @ ( B @ ( A @ number_number_of ) @ ( A @ plus_plus ) ) )
= ( pls @ bit1 @ ( B @ ( int @ plus_plus ) ) @ ( A @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(133,axiom,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( A @ zero_zero @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq ) ) )
<=> ( pls @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_le__special_I3_J) ).
thf(629,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( ( pls @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ zero_zero @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq ) ) ) )
& ( ( A @ zero_zero @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq ) ) )
=> ( pls @ ( B @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(94,axiom,
! [A: $i] :
( ( A @ number )
=> ! [B: $i,C: $i] :
( ( ( B @ ( A @ number_number_of ) )
= ( C @ ( A @ ti ) ) )
<=> ( ( C @ ( A @ ti ) )
= ( B @ ( A @ number_number_of ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_number__of__reorient) ).
thf(468,plain,
! [A: $i] :
( ( A @ number )
=> ! [B: $i,C: $i] :
( ( ( ( C @ ( A @ ti ) )
= ( B @ ( A @ number_number_of ) ) )
=> ( ( B @ ( A @ number_number_of ) )
= ( C @ ( A @ ti ) ) ) )
& ( ( ( B @ ( A @ number_number_of ) )
= ( C @ ( A @ ti ) ) )
=> ( ( C @ ( A @ ti ) )
= ( B @ ( A @ number_number_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ plus_plus ) ) @ ( A @ ( int @ power_power ) ) )
= ( C @ ( A @ ( int @ power_power ) ) @ ( B @ ( A @ ( int @ power_power ) ) @ ( int @ times_times ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_zpower__zadd__distrib) ).
thf(234,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ plus_plus ) ) @ ( A @ ( int @ power_power ) ) )
= ( C @ ( A @ ( int @ power_power ) ) @ ( B @ ( A @ ( int @ power_power ) ) @ ( int @ times_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(77,axiom,
int @ semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(408,plain,
int @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(110,axiom,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) ) @ ( A @ zero_zero @ ( A @ ord_less ) ) )
<=> ( ( B @ ( A @ ti ) )
!= ( A @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_zero__less__power2) ).
thf(523,plain,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i] :
( ( ( ( B @ ( A @ ti ) )
!= ( A @ zero_zero ) )
=> ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) ) @ ( A @ zero_zero @ ( A @ ord_less ) ) ) )
& ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) ) @ ( A @ zero_zero @ ( A @ ord_less ) ) )
=> ( ( B @ ( A @ ti ) )
!= ( A @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(139,axiom,
int @ ring_11004092258visors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
thf(655,plain,
int @ ring_11004092258visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ semiring )
& ( C @ number ) )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ times_times ) ) )
= ( B @ ( A @ ( C @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_arg1) ).
thf(185,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ semiring )
& ( C @ number ) )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ times_times ) ) )
= ( B @ ( A @ ( C @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( B @ bit1 @ ( A @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_less__eq__int__code_I16_J) ).
thf(288,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less_eq ) ) )
=> ( B @ bit1 @ ( A @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( B @ bit1 @ ( A @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( B @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(137,axiom,
int @ one_one @ ( t @ ( int @ ord_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_calculation_I1_J) ).
thf(651,plain,
int @ one_one @ ( t @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ bit0 @ ( int @ ti ) )
= ( A @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit0_res) ).
thf(257,plain,
! [A: $i] :
( ( A @ bit0 @ ( int @ ti ) )
= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(62,axiom,
! [A: $i] :
( ( ( A @ semiring )
& ( A @ number ) )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ plus_plus ) ) @ ( B @ ( A @ number_number_of ) @ ( A @ times_times ) ) )
= ( D @ ( B @ ( A @ number_number_of ) @ ( A @ times_times ) ) @ ( C @ ( B @ ( A @ number_number_of ) @ ( A @ times_times ) ) @ ( A @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_right__distrib__number__of) ).
thf(372,plain,
! [A: $i] :
( ( ( A @ semiring )
& ( A @ number ) )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ plus_plus ) ) @ ( B @ ( A @ number_number_of ) @ ( A @ times_times ) ) )
= ( D @ ( B @ ( A @ number_number_of ) @ ( A @ times_times ) ) @ ( C @ ( B @ ( A @ number_number_of ) @ ( A @ times_times ) ) @ ( A @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ semiring_1 )
=> ( ( A @ one_one @ ( A @ ti ) )
= ( A @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oone__class_Oone_res) ).
thf(357,plain,
! [A: $i] :
( ( A @ semiring_1 )
=> ( ( A @ one_one @ ( A @ ti ) )
= ( A @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(1,conjecture,
int @ zero_zero @ ( int @ one_one @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( int @ zero_zero @ ( int @ one_one @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(157,plain,
~ ( int @ zero_zero @ ( int @ one_one @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(82,axiom,
int @ zero_zero @ ( t @ ( int @ ord_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096t_A_060_A0_096) ).
thf(421,plain,
int @ zero_zero @ ( t @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( ~ ( pls @ ( B @ ( int @ ord_less ) ) )
=> ( ( ~ ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( nat @ number_number_of ) ) ) )
& ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) )
= ( B @ ( nat @ number_number_of ) ) ) ) ) )
& ( ( pls @ ( B @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) )
= ( A @ ( nat @ number_number_of ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add__nat__number__of) ).
thf(606,plain,
! [A: $i,B: $i] :
( ( ~ ( pls @ ( B @ ( int @ ord_less ) ) )
=> ( ( ~ ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( nat @ number_number_of ) ) ) )
& ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) )
= ( B @ ( nat @ number_number_of ) ) ) ) ) )
& ( ( pls @ ( B @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) )
= ( A @ ( nat @ number_number_of ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( B @ bit1 @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_less__eq__int__code_I14_J) ).
thf(316,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less_eq ) ) )
=> ( B @ bit1 @ ( A @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( B @ bit1 @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( B @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ ( int @ number_number_of ) @ ( A @ ( int @ number_number_of ) @ ( int @ ord_less ) ) )
<=> ( B @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_less__number__of__int__code) ).
thf(216,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less ) ) )
=> ( B @ ( int @ number_number_of ) @ ( A @ ( int @ number_number_of ) @ ( int @ ord_less ) ) ) )
& ( ( B @ ( int @ number_number_of ) @ ( A @ ( int @ number_number_of ) @ ( int @ ord_less ) ) )
=> ( B @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ linorder )
& ( C @ number ) )
=> ( ( B @ ( C @ ti ) @ ( A @ ( C @ ord_less ) ) )
<=> ( B @ ( A @ ( C @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_0_arg2) ).
thf(492,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ linorder )
& ( C @ number ) )
=> ( ( ( B @ ( A @ ( C @ ord_less ) ) )
=> ( B @ ( C @ ti ) @ ( A @ ( C @ ord_less ) ) ) )
& ( ( B @ ( C @ ti ) @ ( A @ ( C @ ord_less ) ) )
=> ( B @ ( A @ ( C @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ti ) @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_ti_idem) ).
thf(179,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ti ) @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(125,axiom,
! [A: $i,B: $i] :
( ( B @ number )
=> ( ( A @ ( int @ ti ) @ ( B @ number_number_of ) )
= ( A @ ( B @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_arg1) ).
thf(591,plain,
! [A: $i,B: $i] :
( ( B @ number )
=> ( ( A @ ( int @ ti ) @ ( B @ number_number_of ) )
= ( A @ ( B @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ( B @ bit0 @ ( A @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_rel__simps_I33_J) ).
thf(623,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less ) ) )
=> ( B @ bit0 @ ( A @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( B @ bit0 @ ( A @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( B @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ times_times ) ) )
= ( C @ ( B @ ( int @ times_times ) ) @ ( A @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_arith__simps_I32_J) ).
thf(480,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ times_times ) ) )
= ( C @ ( B @ ( int @ times_times ) ) @ ( A @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(73,axiom,
( ( m @ ( int @ ti ) )
= m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_m_res) ).
thf(397,plain,
( ( m @ ( int @ ti ) )
= m ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(90,axiom,
! [A: $i] :
( ( A @ number_semiring )
=> ! [B: $i,C: $i] :
( ( C @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( ( B @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( ( B @ ( A @ number_number_of ) @ ( C @ ( A @ number_number_of ) @ ( A @ times_times ) ) )
= ( B @ ( C @ ( int @ times_times ) ) @ ( A @ number_number_of ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_semiring__mult__number__of) ).
thf(453,plain,
! [A: $i] :
( ( A @ number_semiring )
=> ! [B: $i,C: $i] :
( ( C @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( ( B @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( ( B @ ( A @ number_number_of ) @ ( C @ ( A @ number_number_of ) @ ( A @ times_times ) ) )
= ( B @ ( C @ ( int @ times_times ) ) @ ( A @ number_number_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ bit0 @ ( int @ times_times ) ) )
= ( B @ ( A @ ( int @ times_times ) ) @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_mult__Bit0) ).
thf(411,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ bit0 @ ( int @ times_times ) ) )
= ( B @ ( A @ ( int @ times_times ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(86,axiom,
! [A: $i] :
( ( A @ bit1 @ ( pls @ ( int @ ord_less ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_rel__simps_I5_J) ).
thf(428,plain,
! [A: $i] :
( ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( pls @ ( int @ ord_less ) ) ) )
& ( ( A @ bit1 @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ ord_less_eq ) ) )
=> ( C @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( A @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_zadd__left__mono) ).
thf(206,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ ord_less_eq ) ) )
=> ( C @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( A @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(27,axiom,
int @ linord581940658strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring__strict) ).
thf(233,plain,
int @ linord581940658strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(105,axiom,
int @ number_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(512,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( ( A @ bit1 )
= ( B @ bit1 ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_rel__simps_I51_J) ).
thf(546,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( A @ bit1 )
= ( B @ bit1 ) ) )
& ( ( ( A @ bit1 )
= ( B @ bit1 ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( int @ times_times ) ) @ ( int @ times_times ) ) )
= ( C @ ( B @ ( int @ times_times ) ) @ ( A @ ( int @ times_times ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_zmult__assoc) ).
thf(381,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( int @ times_times ) ) @ ( int @ times_times ) ) )
= ( C @ ( B @ ( int @ times_times ) ) @ ( A @ ( int @ times_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( B @ bit1 @ ( A @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_rel__simps_I34_J) ).
thf(366,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less_eq ) ) )
=> ( B @ bit1 @ ( A @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( B @ bit1 @ ( A @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( B @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ linordered_idom )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ ord_less ) ) )
<=> ( B @ ( A @ ( C @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_1_arg1) ).
thf(275,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ linordered_idom )
=> ( ( ( B @ ( A @ ( C @ ord_less ) ) )
=> ( B @ ( A @ ( C @ ti ) @ ( C @ ord_less ) ) ) )
& ( ( B @ ( A @ ( C @ ti ) @ ( C @ ord_less ) ) )
=> ( B @ ( A @ ( C @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B @ number )
=> ( ( A @ ( B @ number_number_of ) @ ( B @ ti ) )
= ( A @ ( B @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_res) ).
thf(260,plain,
! [A: $i,B: $i] :
( ( B @ number )
=> ( ( A @ ( B @ number_number_of ) @ ( B @ ti ) )
= ( A @ ( B @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( int @ ord_less ) ) )
=> ( ( B @ ( A @ ( int @ ord_less_eq ) ) )
=> ( B @ ( D @ ( int @ plus_plus ) ) @ ( A @ ( C @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_zadd__zless__mono) ).
thf(349,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( int @ ord_less ) ) )
=> ( ( B @ ( A @ ( int @ ord_less_eq ) ) )
=> ( B @ ( D @ ( int @ plus_plus ) ) @ ( A @ ( C @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ semiring )
& ( C @ number ) )
=> ( ( B @ ( C @ ti ) @ ( A @ ( C @ plus_plus ) ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_arg2) ).
thf(566,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ semiring )
& ( C @ number ) )
=> ( ( B @ ( C @ ti ) @ ( A @ ( C @ plus_plus ) ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(32,axiom,
~ ! [A: $i] :
( ( int @ one_one @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) )
!= ( A @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_) ).
thf(252,plain,
~ ! [A: $i] :
( ( int @ one_one @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) )
!= ( A @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(142,axiom,
! [A: $i] :
( ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_rel__simps_I21_J) ).
thf(665,plain,
! [A: $i] :
( ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(124,axiom,
! [A: $i] :
( ( ( A @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) )
<=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_eq__number__of__0) ).
thf(583,plain,
! [A: $i] :
( ( ( pls @ ( A @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) )
=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_zmult__commute) ).
thf(456,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(42,axiom,
t @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ twoSqu33214720sum2sq,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_qf1pt) ).
thf(285,plain,
t @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ twoSqu33214720sum2sq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(108,axiom,
nat @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(519,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ linordered_ring )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ plus_plus ) ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_arg1) ).
thf(403,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ linordered_ring )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ plus_plus ) ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ undefined @ ( A @ ti ) )
= ( A @ undefined ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
thf(188,plain,
! [A: $i] :
( ( A @ undefined @ ( A @ ti ) )
= ( A @ undefined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ linordered_ring )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( C @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_1_arg1) ).
thf(169,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ linordered_ring )
=> ( ( ( B @ ( A @ ( C @ ord_less_eq ) ) )
=> ( B @ ( A @ ( C @ ti ) @ ( C @ ord_less_eq ) ) ) )
& ( ( B @ ( A @ ( C @ ti ) @ ( C @ ord_less_eq ) ) )
=> ( B @ ( A @ ( C @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(52,axiom,
! [A: $i] :
( ( ( A @ semiring )
& ( A @ number ) )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ number_number_of ) @ ( C @ ( B @ ( A @ plus_plus ) ) @ ( A @ times_times ) ) )
= ( D @ ( A @ number_number_of ) @ ( C @ ( A @ times_times ) ) @ ( D @ ( A @ number_number_of ) @ ( B @ ( A @ times_times ) ) @ ( A @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_left__distrib__number__of) ).
thf(328,plain,
! [A: $i] :
( ( ( A @ semiring )
& ( A @ number ) )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ number_number_of ) @ ( C @ ( B @ ( A @ plus_plus ) ) @ ( A @ times_times ) ) )
= ( D @ ( A @ number_number_of ) @ ( C @ ( A @ times_times ) ) @ ( D @ ( A @ number_number_of ) @ ( B @ ( A @ times_times ) ) @ ( A @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_int__one__le__iff__zero__less) ).
thf(225,plain,
! [A: $i] :
( ( ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
=> ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(112,axiom,
! [A: $i] :
( ( A @ ( int @ ti ) @ bit0 )
= ( A @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit0_arg1) ).
thf(537,plain,
! [A: $i] :
( ( A @ ( int @ ti ) @ bit0 )
= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(101,axiom,
! [A: $i] :
( ( A @ number_semiring )
=> ! [B: $i,C: $i] :
( ( C @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( ( B @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( ( B @ ( A @ number_number_of ) @ ( C @ ( A @ number_number_of ) @ ( A @ plus_plus ) ) )
= ( B @ ( C @ ( int @ plus_plus ) ) @ ( A @ number_number_of ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_semiring__add__number__of) ).
thf(489,plain,
! [A: $i] :
( ( A @ number_semiring )
=> ! [B: $i,C: $i] :
( ( C @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( ( B @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( ( B @ ( A @ number_number_of ) @ ( C @ ( A @ number_number_of ) @ ( A @ plus_plus ) ) )
= ( B @ ( C @ ( int @ plus_plus ) ) @ ( A @ number_number_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(150,axiom,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ ord_less_eq ) ) )
<=> ( B @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_le__special_I2_J) ).
thf(706,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( ( B @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ ord_less_eq ) ) ) )
& ( ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ ord_less_eq ) ) )
=> ( B @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(146,axiom,
! [A: $i] :
( ( ( nat @ zero_zero )
= ( A @ ( nat @ number_number_of ) ) )
<=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_eq__0__number__of) ).
thf(686,plain,
! [A: $i] :
( ( ( pls @ ( A @ ( int @ ord_less_eq ) ) )
=> ( ( nat @ zero_zero )
= ( A @ ( nat @ number_number_of ) ) ) )
& ( ( ( nat @ zero_zero )
= ( A @ ( nat @ number_number_of ) ) )
=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(95,axiom,
( ( pls @ ( int @ ti ) )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OPls_res) ).
thf(476,plain,
( ( pls @ ( int @ ti ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(70,axiom,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( t @ ( int @ ord_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_t__l__p) ).
thf(393,plain,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( t @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ linordered_ring )
=> ( ( B @ ( C @ ti ) @ ( A @ ( C @ times_times ) ) )
= ( B @ ( A @ ( C @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_arg2) ).
thf(173,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ linordered_ring )
=> ( ( B @ ( C @ ti ) @ ( A @ ( C @ times_times ) ) )
= ( B @ ( A @ ( C @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ( B @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_zle__linear) ).
thf(721,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ( B @ ( A @ ( int @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(120,axiom,
( ( nat @ zero_zero )
= ( pls @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_semiring__norm_I113_J) ).
thf(569,plain,
( ( nat @ zero_zero )
= ( pls @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(29,axiom,
( ( s @ ( int @ ti ) )
= s ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_s_____res) ).
thf(237,plain,
( ( s @ ( int @ ti ) )
= s ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(36,axiom,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( B @ ( A @ number_number_of ) @ ( A @ zero_zero @ ( A @ ord_less_eq ) ) )
<=> ( B @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_le__special_I1_J) ).
thf(266,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( ( B @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( B @ ( A @ number_number_of ) @ ( A @ zero_zero @ ( A @ ord_less_eq ) ) ) )
& ( ( B @ ( A @ number_number_of ) @ ( A @ zero_zero @ ( A @ ord_less_eq ) ) )
=> ( B @ ( pls @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_rel__simps_I22_J) ).
thf(360,plain,
! [A: $i] :
( ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(144,axiom,
! [A: $i] :
( ( pls @ ( A @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( pls @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_rel__simps_I29_J) ).
thf(674,plain,
! [A: $i] :
( ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( pls @ ( A @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_zadd__commute) ).
thf(425,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(106,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ number_number_of ) @ ( A @ times_times ) ) @ ( B @ ( A @ number_number_of ) @ ( A @ times_times ) ) )
= ( D @ ( C @ ( B @ ( int @ times_times ) ) @ ( A @ number_number_of ) @ ( A @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_mult__number__of__left) ).
thf(513,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ number_number_of ) @ ( A @ times_times ) ) @ ( B @ ( A @ number_number_of ) @ ( A @ times_times ) ) )
= ( D @ ( C @ ( B @ ( int @ times_times ) ) @ ( A @ number_number_of ) @ ( A @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ semiring )
& ( C @ number ) )
=> ( ( B @ ( C @ ti ) @ ( A @ ( C @ times_times ) ) )
= ( B @ ( A @ ( C @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_arg2) ).
thf(166,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ semiring )
& ( C @ number ) )
=> ( ( B @ ( C @ ti ) @ ( A @ ( C @ times_times ) ) )
= ( B @ ( A @ ( C @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ bit1 @ ( int @ ti ) )
= ( A @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit1_res) ).
thf(279,plain,
! [A: $i] :
( ( A @ bit1 @ ( int @ ti ) )
= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(63,axiom,
( ( t @ ( int @ ti ) )
= t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_t_____res) ).
thf(375,plain,
( ( t @ ( int @ ti ) )
= t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(154,axiom,
! [A: $i] :
( ( A @ ( int @ one_one @ ( int @ times_times ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_zmult__1) ).
thf(733,plain,
! [A: $i] :
( ( A @ ( int @ one_one @ ( int @ times_times ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(117,axiom,
( ( pls @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_nat__number__of__Pls) ).
thf(562,plain,
( ( pls @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ linordered_ring )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ times_times ) ) )
= ( B @ ( A @ ( C @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_arg1) ).
thf(176,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ linordered_ring )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ times_times ) ) )
= ( B @ ( A @ ( C @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(84,axiom,
( ( nat @ one_one @ ( nat @ one_one @ ( nat @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_nat__1__add__1) ).
thf(423,plain,
( ( nat @ one_one @ ( nat @ one_one @ ( nat @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(147,axiom,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ zprime,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_p) ).
thf(694,plain,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ zprime,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ semiring )
& ( C @ number ) )
=> ( ( B @ ( A @ ( C @ times_times ) ) @ ( C @ ti ) )
= ( B @ ( A @ ( C @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_0_res) ).
thf(191,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ semiring )
& ( C @ number ) )
=> ( ( B @ ( A @ ( C @ times_times ) ) @ ( C @ ti ) )
= ( B @ ( A @ ( C @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( C @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_zle__trans) ).
thf(286,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( C @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ semiring_1 )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ power_power ) ) )
= ( B @ ( A @ ( C @ power_power ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_arg1) ).
thf(577,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ semiring_1 )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ power_power ) ) )
= ( B @ ( A @ ( C @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i,C: $i] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) ) @ ( A @ plus_plus ) ) @ ( A @ zero_zero @ ( A @ ord_less ) ) )
<=> ( ( ( C @ ( A @ ti ) )
!= ( A @ zero_zero ) )
| ( ( B @ ( A @ ti ) )
!= ( A @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_sum__power2__gt__zero__iff) ).
thf(335,plain,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i,C: $i] :
( ( ( ( ( C @ ( A @ ti ) )
!= ( A @ zero_zero ) )
| ( ( B @ ( A @ ti ) )
!= ( A @ zero_zero ) ) )
=> ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) ) @ ( A @ plus_plus ) ) @ ( A @ zero_zero @ ( A @ ord_less ) ) ) )
& ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) ) @ ( A @ plus_plus ) ) @ ( A @ zero_zero @ ( A @ ord_less ) ) )
=> ( ( ( C @ ( A @ ti ) )
!= ( A @ zero_zero ) )
| ( ( B @ ( A @ ti ) )
!= ( A @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(113,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ plus_plus ) ) )
= ( B @ ( pls @ bit1 @ ( int @ plus_plus ) ) @ ( A @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_add__special_I2_J) ).
thf(540,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ plus_plus ) ) )
= ( B @ ( pls @ bit1 @ ( int @ plus_plus ) ) @ ( A @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(76,axiom,
( ( nat @ one_one )
= ( pls @ bit1 @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Numeral1__eq1__nat) ).
thf(406,plain,
( ( nat @ one_one )
= ( pls @ bit1 @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ linordered_ring )
=> ( ( B @ ( A @ ( C @ plus_plus ) ) @ ( C @ ti ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_res) ).
thf(736,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ linordered_ring )
=> ( ( B @ ( A @ ( C @ plus_plus ) ) @ ( C @ ti ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(64,axiom,
nat @ linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(377,plain,
nat @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( B @ ( int @ number_number_of ) @ ( A @ ( int @ number_number_of ) @ ( int @ plus_plus ) ) )
= ( B @ ( A @ ( int @ plus_plus ) ) @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_plus__numeral__code_I9_J) ).
thf(434,plain,
! [A: $i,B: $i] :
( ( B @ ( int @ number_number_of ) @ ( A @ ( int @ number_number_of ) @ ( int @ plus_plus ) ) )
= ( B @ ( A @ ( int @ plus_plus ) ) @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(47,axiom,
int @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(303,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ ( int @ ti ) @ twoSqu33214720sum2sq )
<=> ( A @ twoSqu33214720sum2sq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_TwoSquares__Mirabelle__vsgmegnqdl_Ois__sum2sq_arg1) ).
thf(208,plain,
! [A: $i] :
( ( ( A @ twoSqu33214720sum2sq )
=> ( A @ ( int @ ti ) @ twoSqu33214720sum2sq ) )
& ( ( A @ ( int @ ti ) @ twoSqu33214720sum2sq )
=> ( A @ twoSqu33214720sum2sq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ ( int @ ti ) @ zprime )
<=> ( A @ zprime ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_IntPrimes_Ozprime_arg1) ).
thf(387,plain,
! [A: $i] :
( ( ( A @ zprime )
=> ( A @ ( int @ ti ) @ zprime ) )
& ( ( A @ ( int @ ti ) @ zprime )
=> ( A @ zprime ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(126,axiom,
! [A: $i,B: $i] :
( ( B @ ( int @ number_number_of ) @ ( A @ ( int @ number_number_of ) @ ( int @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_less__eq__number__of__int__code) ).
thf(594,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less_eq ) ) )
=> ( B @ ( int @ number_number_of ) @ ( A @ ( int @ number_number_of ) @ ( int @ ord_less_eq ) ) ) )
& ( ( B @ ( int @ number_number_of ) @ ( A @ ( int @ number_number_of ) @ ( int @ ord_less_eq ) ) )
=> ( B @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(98,axiom,
! [A: $i] :
( ( int @ one_one @ ( A @ ( int @ times_times ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_zmult__1__right) ).
thf(483,plain,
! [A: $i] :
( ( int @ one_one @ ( A @ ( int @ times_times ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(109,axiom,
! [A: $i] :
( ( A @ linordered_ring )
=> ( ( A @ zero_zero @ ( A @ ti ) )
= ( A @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_0_res) ).
thf(520,plain,
! [A: $i] :
( ( A @ linordered_ring )
=> ( ( A @ zero_zero @ ( A @ ti ) )
= ( A @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(15,axiom,
nat @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(198,plain,
nat @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ linorder )
& ( C @ number ) )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ ord_less ) ) )
<=> ( B @ ( A @ ( C @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_0_arg1) ).
thf(399,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ linorder )
& ( C @ number ) )
=> ( ( ( B @ ( A @ ( C @ ord_less ) ) )
=> ( B @ ( A @ ( C @ ti ) @ ( C @ ord_less ) ) ) )
& ( ( B @ ( A @ ( C @ ti ) @ ( C @ ord_less ) ) )
=> ( B @ ( A @ ( C @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(148,axiom,
! [A: $i] :
( ( ( A @ ring_char_0 )
& ( A @ number_ring ) )
=> ! [B: $i,C: $i] :
( ( ( B @ ( A @ number_number_of ) )
= ( C @ ( A @ number_number_of ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_eq__number__of) ).
thf(695,plain,
! [A: $i] :
( ( ( A @ ring_char_0 )
& ( A @ number_ring ) )
=> ! [B: $i,C: $i] :
( ( ( B = C )
=> ( ( B @ ( A @ number_number_of ) )
= ( C @ ( A @ number_number_of ) ) ) )
& ( ( ( B @ ( A @ number_number_of ) )
= ( C @ ( A @ number_number_of ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(71,axiom,
pls @ ( pls @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_rel__simps_I19_J) ).
thf(394,plain,
pls @ ( pls @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ( B @ ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_add1__zle__eq) ).
thf(680,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less ) ) )
=> ( B @ ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) )
& ( ( B @ ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
=> ( B @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ linordered_ring )
=> ( ( B @ ( C @ ti ) @ ( A @ ( C @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( C @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_1_arg2) ).
thf(194,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ linordered_ring )
=> ( ( ( B @ ( A @ ( C @ ord_less_eq ) ) )
=> ( B @ ( C @ ti ) @ ( A @ ( C @ ord_less_eq ) ) ) )
& ( ( B @ ( C @ ti ) @ ( A @ ( C @ ord_less_eq ) ) )
=> ( B @ ( A @ ( C @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ linorder )
& ( C @ number ) )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( C @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_0_arg1) ).
thf(162,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ linorder )
& ( C @ number ) )
=> ( ( ( B @ ( A @ ( C @ ord_less_eq ) ) )
=> ( B @ ( A @ ( C @ ti ) @ ( C @ ord_less_eq ) ) ) )
& ( ( B @ ( A @ ( C @ ti ) @ ( C @ ord_less_eq ) ) )
=> ( B @ ( A @ ( C @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(111,axiom,
! [A: $i,B: $i] :
( ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( A @ ( int @ ord_less ) ) )
<=> ( B @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_zle__add1__eq__le) ).
thf(531,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less_eq ) ) )
=> ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( A @ ( int @ ord_less ) ) ) )
& ( ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( A @ ( int @ ord_less ) ) )
=> ( B @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(136,axiom,
! [A: $i] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_mult__Pls) ).
thf(648,plain,
! [A: $i] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(100,axiom,
! [A: $i] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_le__imp__0__less) ).
thf(487,plain,
! [A: $i] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ plus_plus ) ) @ ( A @ ( int @ times_times ) ) )
= ( C @ ( A @ ( int @ times_times ) ) @ ( B @ ( A @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_zadd__zmult__distrib2) ).
thf(617,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ plus_plus ) ) @ ( A @ ( int @ times_times ) ) )
= ( C @ ( A @ ( int @ times_times ) ) @ ( B @ ( A @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(107,axiom,
! [A: $i] :
( ( A @ ( int @ ti ) @ bit1 )
= ( A @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit1_arg1) ).
thf(516,plain,
! [A: $i] :
( ( A @ ( int @ ti ) @ bit1 )
= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( B @ ( nat @ number_number_of ) @ ( A @ ( nat @ number_number_of ) @ ( nat @ ord_less ) ) )
<=> ( ( B @ ( A @ ( int @ ord_less ) ) )
& ( ( B @ ( A @ ( int @ ord_less ) ) )
=> ( B @ ( pls @ ( int @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_less__nat__number__of) ).
thf(712,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ ( int @ ord_less ) ) )
& ( ( B @ ( A @ ( int @ ord_less ) ) )
=> ( B @ ( pls @ ( int @ ord_less ) ) ) ) )
=> ( B @ ( nat @ number_number_of ) @ ( A @ ( nat @ number_number_of ) @ ( nat @ ord_less ) ) ) )
& ( ( B @ ( nat @ number_number_of ) @ ( A @ ( nat @ number_number_of ) @ ( nat @ ord_less ) ) )
=> ( ( B @ ( A @ ( int @ ord_less ) ) )
& ( ( B @ ( A @ ( int @ ord_less ) ) )
=> ( B @ ( pls @ ( int @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ semiring_1 )
=> ( ( B @ ( A @ ( C @ power_power ) ) @ ( C @ ti ) )
= ( B @ ( A @ ( C @ power_power ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_res) ).
thf(580,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ semiring_1 )
=> ( ( B @ ( A @ ( C @ power_power ) ) @ ( C @ ti ) )
= ( B @ ( A @ ( C @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i,C: $i] :
~ ( A @ zero_zero @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) ) @ ( A @ plus_plus ) ) @ ( A @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_not__sum__power2__lt__zero) ).
thf(282,plain,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i,C: $i] :
~ ( A @ zero_zero @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) ) @ ( A @ plus_plus ) ) @ ( A @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(80,axiom,
int @ linordered_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring) ).
thf(414,plain,
int @ linordered_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ linordered_idom )
=> ( ( B @ ( C @ ti ) @ ( A @ ( C @ ord_less ) ) )
<=> ( B @ ( A @ ( C @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_1_arg2) ).
thf(739,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ linordered_idom )
=> ( ( ( B @ ( A @ ( C @ ord_less ) ) )
=> ( B @ ( C @ ti ) @ ( A @ ( C @ ord_less ) ) ) )
& ( ( B @ ( C @ ti ) @ ( A @ ( C @ ord_less ) ) )
=> ( B @ ( A @ ( C @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(78,axiom,
( ( int @ one_one @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) )
= ( t @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
thf(409,plain,
( ( int @ one_one @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) )
= ( t @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i] :
~ ( A @ zero_zero @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) ) @ ( A @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_power2__less__0) ).
thf(263,plain,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i] :
~ ( A @ zero_zero @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) ) @ ( A @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( B @ bit0 @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_less__eq__int__code_I13_J) ).
thf(310,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less_eq ) ) )
=> ( B @ bit0 @ ( A @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( B @ bit0 @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( B @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(16,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_6_p0) ).
thf(199,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)],[16]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ linordered_ring )
=> ( ( B @ ( A @ ( C @ times_times ) ) @ ( C @ ti ) )
= ( B @ ( A @ ( C @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_1_res) ).
thf(182,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ linordered_ring )
=> ( ( B @ ( A @ ( C @ times_times ) ) @ ( C @ ti ) )
= ( B @ ( A @ ( C @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(53,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(331,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(104,axiom,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i,C: $i] :
( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) ) @ ( A @ plus_plus ) ) )
= ( A @ zero_zero ) )
<=> ( ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_sum__power2__eq__zero__iff) ).
thf(502,plain,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i,C: $i] :
( ( ( ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) ) @ ( A @ plus_plus ) ) )
= ( A @ zero_zero ) ) )
& ( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) ) @ ( A @ plus_plus ) ) )
= ( A @ zero_zero ) )
=> ( ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(149,axiom,
! [A: $i] :
( ( A @ ( int @ number_number_of ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_number__of__is__id) ).
thf(703,plain,
! [A: $i] :
( ( A @ ( int @ number_number_of ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(140,axiom,
! [A: $i] :
( ( A @ ring_11004092258visors )
=> ! [B: $i] :
( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) ) )
= ( A @ zero_zero ) )
<=> ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_zero__eq__power2) ).
thf(656,plain,
! [A: $i] :
( ( A @ ring_11004092258visors )
=> ! [B: $i] :
( ( ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) ) )
= ( A @ zero_zero ) ) )
& ( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) ) )
= ( A @ zero_zero ) )
=> ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ semiring_1 )
=> ( ( B @ ( nat @ ti ) @ ( A @ ( C @ power_power ) ) )
= ( B @ ( A @ ( C @ power_power ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_arg2) ).
thf(600,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ semiring_1 )
=> ( ( B @ ( nat @ ti ) @ ( A @ ( C @ power_power ) ) )
= ( B @ ( A @ ( C @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(68,axiom,
int @ zero_zero @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( t @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( int @ ord_less ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
thf(386,plain,
int @ zero_zero @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( t @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( B @ bit1 @ ( A @ bit0 @ ( int @ ord_less ) ) )
<=> ( B @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_rel__simps_I15_J) ).
thf(571,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less_eq ) ) )
=> ( B @ bit1 @ ( A @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( B @ bit1 @ ( A @ bit0 @ ( int @ ord_less ) ) )
=> ( B @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(116,axiom,
! [A: $i] :
( ( A @ ( nat @ number_number_of ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
<=> ( A @ ( pls @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_less__0__number__of) ).
thf(556,plain,
! [A: $i] :
( ( ( A @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ ( nat @ number_number_of ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( nat @ number_number_of ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( pls @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ semiring_1 )
=> ( ( A @ zero_zero @ ( A @ ti ) )
= ( A @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_1_res) ).
thf(203,plain,
! [A: $i] :
( ( A @ semiring_1 )
=> ( ( A @ zero_zero @ ( A @ ti ) )
= ( A @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(143,axiom,
( ( t
= ( int @ zero_zero ) )
=> ( ( int @ one_one @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) )
= ( int @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_calculation_I2_J) ).
thf(671,plain,
( ( t
= ( int @ zero_zero ) )
=> ( ( int @ one_one @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) )
= ( int @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( B @ ( int @ number_number_of ) @ ( A @ ( int @ number_number_of ) @ ( int @ times_times ) ) )
= ( B @ ( A @ ( int @ times_times ) ) @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_times__numeral__code_I5_J) ).
thf(465,plain,
! [A: $i,B: $i] :
( ( B @ ( int @ number_number_of ) @ ( A @ ( int @ number_number_of ) @ ( int @ times_times ) ) )
= ( B @ ( A @ ( int @ times_times ) ) @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ ord_less ) ) )
=> ( B @ ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_zless__imp__add1__zle) ).
thf(231,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ ord_less ) ) )
=> ( B @ ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(48,axiom,
! [A: $i] :
( ( pls @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_rel__simps_I27_J) ).
thf(304,plain,
! [A: $i] :
( ( ( pls @ ( A @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( A @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( pls @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ linorder )
& ( C @ number ) )
=> ( ( B @ ( C @ ti ) @ ( A @ ( C @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( C @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_0_arg2) ).
thf(158,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ linorder )
& ( C @ number ) )
=> ( ( ( B @ ( A @ ( C @ ord_less_eq ) ) )
=> ( B @ ( C @ ti ) @ ( A @ ( C @ ord_less_eq ) ) ) )
& ( ( B @ ( C @ ti ) @ ( A @ ( C @ ord_less_eq ) ) )
=> ( B @ ( A @ ( C @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ semiring )
& ( C @ number ) )
=> ( ( B @ ( A @ ( C @ plus_plus ) ) @ ( C @ ti ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_res) ).
thf(652,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ semiring )
& ( C @ number ) )
=> ( ( B @ ( A @ ( C @ plus_plus ) ) @ ( C @ ti ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( B @ bit0 @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_rel__simps_I31_J) ).
thf(351,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less_eq ) ) )
=> ( B @ bit0 @ ( A @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( B @ bit0 @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( B @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ semiring_1 )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ zero_zero @ ( A @ power_power ) ) )
= ( A @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_zero__power2) ).
thf(378,plain,
! [A: $i] :
( ( A @ semiring_1 )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ zero_zero @ ( A @ power_power ) ) )
= ( A @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(96,axiom,
! [A: $i] : ( A @ ( A @ ( int @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_zle__refl) ).
thf(478,plain,
! [A: $i] : ( A @ ( A @ ( int @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(37,axiom,
int @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(272,plain,
int @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) )
= ( C @ ( B @ ( int @ times_times ) ) @ ( C @ ( A @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_zadd__zmult__distrib) ).
thf(346,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) )
= ( C @ ( B @ ( int @ times_times ) ) @ ( C @ ( A @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(21,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(214,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) )
= ( C @ ( B @ ( int @ plus_plus ) ) @ ( A @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_zadd__assoc) ).
thf(300,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) )
= ( C @ ( B @ ( int @ plus_plus ) ) @ ( A @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(131,axiom,
! [A: $i] :
( ( A @ semiring_1 )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ one_one @ ( A @ power_power ) ) )
= ( A @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_one__power2) ).
thf(620,plain,
! [A: $i] :
( ( A @ semiring_1 )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ one_one @ ( A @ power_power ) ) )
= ( A @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( B @ bit1 @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_rel__simps_I32_J) ).
thf(447,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less_eq ) ) )
=> ( B @ bit1 @ ( A @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( B @ bit1 @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( B @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(83,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(422,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(38,axiom,
( ( int @ zero_zero )
= ( pls @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_zero__is__num__zero) ).
thf(273,plain,
( ( int @ zero_zero )
= ( pls @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ semiring )
& ( C @ number ) )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ plus_plus ) ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_arg1) ).
thf(603,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ semiring )
& ( C @ number ) )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ plus_plus ) ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(118,axiom,
! [A: $i] :
( ( A @ linordered_ring )
=> ! [B: $i,C: $i] : ( C @ ( C @ ( A @ times_times ) ) @ ( B @ ( B @ ( A @ times_times ) ) @ ( A @ plus_plus ) ) @ ( A @ zero_zero @ ( A @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_sum__squares__ge__zero) ).
thf(564,plain,
! [A: $i] :
( ( A @ linordered_ring )
=> ! [B: $i,C: $i] : ( C @ ( C @ ( A @ times_times ) ) @ ( B @ ( B @ ( A @ times_times ) ) @ ( A @ plus_plus ) ) @ ( A @ zero_zero @ ( A @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(45,axiom,
! [A: $i] :
( ( ( A @ linorder )
& ( A @ number ) )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq ) ) )
<=> ~ ( B @ ( A @ number_number_of ) @ ( C @ ( A @ number_number_of ) @ ( A @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_le__number__of__eq__not__less) ).
thf(294,plain,
! [A: $i] :
( ( ( A @ linorder )
& ( A @ number ) )
=> ! [B: $i,C: $i] :
( ( ~ ( B @ ( A @ number_number_of ) @ ( C @ ( A @ number_number_of ) @ ( A @ ord_less ) ) )
=> ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq ) ) ) )
& ( ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq ) ) )
=> ~ ( B @ ( A @ number_number_of ) @ ( C @ ( A @ number_number_of ) @ ( A @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(88,axiom,
! [A: $i] :
( ( A @ linord581940658strict )
=> ! [B: $i,C: $i] :
( ( ( C @ ( C @ ( A @ times_times ) ) @ ( B @ ( B @ ( A @ times_times ) ) @ ( A @ plus_plus ) ) )
= ( A @ zero_zero ) )
<=> ( ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_sum__squares__eq__zero__iff) ).
thf(437,plain,
! [A: $i] :
( ( A @ linord581940658strict )
=> ! [B: $i,C: $i] :
( ( ( ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) )
=> ( ( C @ ( C @ ( A @ times_times ) ) @ ( B @ ( B @ ( A @ times_times ) ) @ ( A @ plus_plus ) ) )
= ( A @ zero_zero ) ) )
& ( ( ( C @ ( C @ ( A @ times_times ) ) @ ( B @ ( B @ ( A @ times_times ) ) @ ( A @ plus_plus ) ) )
= ( A @ zero_zero ) )
=> ( ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(141,axiom,
nat @ semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(664,plain,
nat @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(134,axiom,
! [A: $i] :
( ( A @ linord581940658strict )
=> ! [B: $i,C: $i] :
( ( A @ zero_zero @ ( C @ ( C @ ( A @ times_times ) ) @ ( B @ ( B @ ( A @ times_times ) ) @ ( A @ plus_plus ) ) @ ( A @ ord_less_eq ) ) )
<=> ( ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_sum__squares__le__zero__iff) ).
thf(635,plain,
! [A: $i] :
( ( A @ linord581940658strict )
=> ! [B: $i,C: $i] :
( ( ( ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) )
=> ( A @ zero_zero @ ( C @ ( C @ ( A @ times_times ) ) @ ( B @ ( B @ ( A @ times_times ) ) @ ( A @ plus_plus ) ) @ ( A @ ord_less_eq ) ) ) )
& ( ( A @ zero_zero @ ( C @ ( C @ ( A @ times_times ) ) @ ( B @ ( B @ ( A @ times_times ) ) @ ( A @ plus_plus ) ) @ ( A @ ord_less_eq ) ) )
=> ( ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(81,axiom,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq ) ) )
<=> ( C @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_le__number__of) ).
thf(415,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i,C: $i] :
( ( ( C @ ( B @ ( int @ ord_less_eq ) ) )
=> ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq ) ) ) )
& ( ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq ) ) )
=> ( C @ ( B @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ plus_plus ) ) @ ( A @ ( int @ plus_plus ) ) )
= ( C @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_zadd__left__commute) ).
thf(239,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ plus_plus ) ) @ ( A @ ( int @ plus_plus ) ) )
= ( C @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ ord_less ) ) )
<=> ( ( A != B )
& ( B @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_zless__le) ).
thf(242,plain,
! [A: $i,B: $i] :
( ( ( ( A != B )
& ( B @ ( A @ ( int @ ord_less_eq ) ) ) )
=> ( B @ ( A @ ( int @ ord_less ) ) ) )
& ( ( B @ ( A @ ( int @ ord_less ) ) )
=> ( ( A != B )
& ( B @ ( A @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(72,axiom,
~ ( t @ ( int @ one_one @ ( int @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__096_126_A1_A_060_061_At_096) ).
thf(395,plain,
~ ( t @ ( int @ one_one @ ( int @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( int @ times_times ) ) @ ( A @ number_number_of ) )
= ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_number__of__mult) ).
thf(332,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( int @ times_times ) ) @ ( A @ number_number_of ) )
= ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( B @ bit1 @ ( A @ bit0 @ ( int @ ord_less ) ) )
<=> ( B @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_less__int__code_I14_J) ).
thf(459,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less_eq ) ) )
=> ( B @ bit1 @ ( A @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( B @ bit1 @ ( A @ bit0 @ ( int @ ord_less ) ) )
=> ( B @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(153,axiom,
! [A: $i,B: $i] :
( ( ( A @ bit0 )
= ( B @ bit0 ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_rel__simps_I48_J) ).
thf(723,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( A @ bit0 )
= ( B @ bit0 ) ) )
& ( ( ( A @ bit0 )
= ( B @ bit0 ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ linordered_ring )
=> ( ( B @ ( C @ ti ) @ ( A @ ( C @ plus_plus ) ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_arg2) ).
thf(200,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ linordered_ring )
=> ( ( B @ ( C @ ti ) @ ( A @ ( C @ plus_plus ) ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( B @ bit0 @ ( A @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( B @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_less__eq__int__code_I15_J) ).
thf(322,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less ) ) )
=> ( B @ bit0 @ ( A @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( B @ bit0 @ ( A @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( B @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(99,axiom,
int @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(486,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_zle__antisym) ).
thf(543,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(22,axiom,
int @ linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(215,plain,
int @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( int @ ord_less ) ) )
| ( A = B )
| ( B @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_zless__linear) ).
thf(222,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( int @ ord_less ) ) )
| ( A = B )
| ( B @ ( A @ ( int @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(103,axiom,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( A @ one_one @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq ) ) )
<=> ( pls @ bit1 @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_le__special_I4_J) ).
thf(496,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( ( pls @ bit1 @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ one_one @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq ) ) ) )
& ( ( A @ one_one @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq ) ) )
=> ( pls @ bit1 @ ( B @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(743,plain,
$false,
inference(e,[status(thm)],[384,645,629,468,234,408,523,655,185,288,651,257,372,357,157,421,606,316,216,492,179,591,623,480,397,453,411,428,206,233,512,546,381,366,275,260,349,566,252,665,583,456,285,519,403,188,169,328,225,537,489,706,686,476,393,173,721,569,237,266,360,674,425,513,166,279,375,733,562,176,423,694,191,286,577,335,540,406,736,377,434,303,208,387,594,483,520,198,399,695,394,680,194,162,531,648,487,617,516,712,580,282,414,739,409,263,310,199,182,331,502,703,656,600,386,571,556,203,671,465,231,304,158,652,351,378,478,272,346,214,300,620,447,422,273,603,564,294,437,664,635,415,239,242,395,332,459,723,200,322,486,543,215,222,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924+5 : TPTP v9.3.1. Released v5.3.0.
% 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
% 0.12/0.53 % Computer : n011.cluster.edu
% 0.12/0.53 % Model : x86_64 x86_64
% 0.12/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.53 % Memory : 8046.5625MB
% 0.12/0.53 % OS : Linux 6.8.0-71-generic
% 0.12/0.53 % CPULimit : 300
% 0.12/0.53 % WCLimit : 300
% 0.12/0.53 % DateTime : Sat Sep 26 04:18:45 UTC 2026
% 0.12/0.53 % CPUTime :
% 0.12/0.53 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
% 0.87/1.12 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.74/1.41 % [INFO] Parsing done (290ms).
% 1.74/1.43 % [INFO] Running in sequential loop mode.
% 2.58/1.82 % [INFO] eprover registered as external prover.
% 2.58/1.83 % [INFO] Scanning for conjecture ...
% 2.77/1.97 % [INFO] Found a conjecture (or negated_conjecture) and 154 axioms. Running axiom selection ...
% 3.06/2.09 % [INFO] Axiom selection finished. Selected 154 axioms (removed 0 axioms).
% 3.54/2.25 % [INFO] Problem is first-order (TPTP FOF).
% 3.54/2.26 % [INFO] Type checking passed.
% 3.54/2.27 % [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 ...
% 8.29/3.67 % External prover 'e' found a proof!
% 8.29/3.67 % [INFO] Killing All external provers ...
% 8.29/3.67 % Time passed: 2997ms (effective reasoning time: 2237ms)
% 8.29/3.67 % 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)>
% 8.29/3.68 % Axioms used in derivation (154): fact_43_arith__simps_I32_J, fact_78_nat__numeral__1__eq__1, fact_17_t__l__p, fact_54_rel__simps_I27_J, tsy_c_Groups_Oplus__class_Oplus_0_arg2, arity_Int_Oint___Rings_Olinordered__ring__strict, fact_42_mult__number__of__left, arity_Nat_Onat___Rings_Osemiring__1, fact_31_zpower__zadd__distrib, tsy_v_s_____res, tsy_c_Int_OPls_res, fact_35_less__eq__int__code_I13_J, arity_Int_Oint___Rings_Olinordered__idom, fact_50_le__number__of__eq__not__less, fact_25_times__numeral__code_I5_J, tsy_c_Groups_Oplus__class_Oplus_1_arg2, fact_59_le__special_I4_J, fact_13_zero__power2, arity_Int_Oint___Int_Oring__char__0, fact_58_semiring__norm_I113_J, fact_85_le__imp__0__less, fact_69_zadd__zmult__distrib2, fact_81_add1__zle__eq, arity_Int_Oint___Rings_Olinordered__ring, tsy_c_Groups_Oplus__class_Oplus_0_res, tsy_c_Orderings_Oord__class_Oless_1_arg2, tsy_c_Groups_Otimes__class_Otimes_0_res, fact_63_mult__Bit0, fact_33_rel__simps_I34_J, arity_Nat_Onat___Int_Onumber__semiring, fact_28_zmult__assoc, tsy_c_Groups_Otimes__class_Otimes_0_arg2, fact_11_zero__less__power2, fact_39_eq__number__of__0, arity_Int_Oint___Rings_Oring__1__no__zero__divisors, fact_37_zless__le, tsy_c_Int_Onumber__class_Onumber__of_res, tsy_c_Groups_Oplus__class_Oplus_1_res, fact_74_less__int__code_I14_J, fact_61_nat__1__add__1, tsy_c_Groups_Oplus__class_Oplus_1_arg1, arity_Int_Oint___Int_Onumber__semiring, fact_83_semiring__add__number__of, tsy_c_Groups_Ozero__class_Ozero_1_res, fact_21_zle__refl, arity_Int_Oint___Int_Onumber__ring, fact_72_less__eq__int__code_I15_J, fact_0__096t_A_060_A0_096, fact_73_rel__simps_I33_J, fact_14_zero__eq__power2, arity_Int_Oint___Rings_Osemiring__1, fact_51_rel__simps_I22_J, fact_4_calculation_I2_J, tsy_c_Groups_Ozero__class_Ozero_0_res, fact_89_rel__simps_I48_J, fact_76_less__nat__number__of, fact_47_le__special_I3_J, fact_82_zle__add1__eq__le, fact_52_less__eq__int__code_I14_J, tsy_c_Orderings_Oord__class_Oless__eq_1_arg1, fact_18__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_, tsy_c_Groups_Otimes__class_Otimes_1_res, fact_19_p, fact_49_less__0__number__of, tsy_c_Orderings_Oord__class_Oless__eq_0_arg2, fact_91_sum__squares__eq__zero__iff, fact_34_rel__simps_I19_J, fact_77_int__one__le__iff__zero__less, fact_64_less__number__of__int__code, tsy_c_Orderings_Oord__class_Oless__eq_0_arg1, fact_38_zadd__left__mono, fact_92_left__distrib__number__of, fact_40_eq__0__number__of, tsy_c_Groups_Otimes__class_Otimes_0_arg1, arity_Nat_Onat___Orderings_Olinorder, tsy_c_Orderings_Oord__class_Oless_0_arg2, tsy_c_Groups_Oplus__class_Oplus_0_arg1, fact_87_number__of__reorient, fact_75_rel__simps_I15_J, fact_3_t, fact_10_power2__less__0, fact_56_zadd__zless__mono, tsy_v_m_res, tsy_c_Groups_Otimes__class_Otimes_1_arg1, tsy_c_Int_OBit1_res, fact_5__096_126_A1_A_060_061_At_096, tsy_c_Orderings_Oord__class_Oless_1_arg1, tsy_c_Orderings_Oord__class_Oless__eq_1_arg2, tsy_c_HOL_Oundefined_res, arity_Int_Oint___Orderings_Olinorder, fact_7_not__sum__power2__lt__zero, fact_67_plus__numeral__code_I9_J, help_ti_idem, fact_48_le__special_I1_J, fact_79_Numeral1__eq1__nat, fact_90_zless__linear, tsy_c_IntPrimes_Ozprime_arg1, fact_27_le__number__of, arity_Int_Oint___Rings_Osemiring, fact_80_zless__imp__add1__zle, fact_6_p0, fact_20_qf1pt, fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096, fact_71_rel__simps_I5_J, fact_68_zadd__zmult__distrib, fact_70_rel__simps_I29_J, tsy_c_Power_Opower__class_Opower_arg1, fact_29_zle__trans, tsy_c_Power_Opower__class_Opower_res, fact_9_sum__power2__eq__zero__iff, fact_8_sum__power2__gt__zero__iff, fact_30_zle__antisym, fact_41_semiring__mult__number__of, fact_94_zadd__assoc, fact_93_right__distrib__number__of, fact_86_eq__number__of, fact_32_less__eq__int__code_I16_J, fact_84_add__nat__number__of, arity_Nat_Onat___Int_Onumber, fact_12_one__power2, fact_88_rel__simps_I51_J, fact_26_less__eq__number__of__int__code, fact_1_calculation_I1_J, fact_36_rel__simps_I31_J, fact_60_le__special_I2_J, tsy_c_TwoSquares__Mirabelle__vsgmegnqdl_Ois__sum2sq_arg1, fact_96_zadd__commute, fact_46_sum__squares__ge__zero, fact_22_number__of__is__id, tsy_c_Int_Onumber__class_Onumber__of_arg1, fact_65_zmult__1__right, tsy_c_Int_OBit0_res, fact_23_zmult__commute, tsy_c_Groups_Otimes__class_Otimes_1_arg2, fact_44_number__of__mult, tsy_c_Orderings_Oord__class_Oless_0_arg1, arity_Nat_Onat___Rings_Osemiring, tsy_c_Groups_Oone__class_Oone_res, tsy_c_Power_Opower__class_Opower_arg2, fact_57_nat__number__of__Pls, fact_62_mult__Pls, tsy_v_t_____res, fact_15_add__special_I2_J, fact_55_rel__simps_I21_J, fact_97_zero__is__num__zero, tsy_c_Int_OBit0_arg1, fact_24_zle__linear, arity_Int_Oint___Int_Onumber, tsy_c_Int_OBit1_arg1, fact_45_sum__squares__le__zero__iff, fact_66_zmult__1, fact_95_zadd__left__commute, fact_16_add__special_I3_J, fact_53_rel__simps_I32_J
% 8.29/3.68 % No. of inferences in proof: 312
% 8.29/3.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2997 ms resp. 2237 ms w/o parsing
% 9.08/3.83 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.08/3.83 % [INFO] Killing All external provers ...
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