%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM925+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n002.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 08:10:24 AM UTC 2026
% Result : Theorem 7.05s 2.33s
% Output : Refutation 7.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 153
% Syntax : Number of formulae : 308 ( 148 unt; 0 typ; 0 def)
% Number of atoms : 660 ( 271 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 2959 ( 43 ~; 10 |; 104 &;2564 @)
% ( 38 <=>; 200 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 6 con; 0-3 aty)
% Number of variables : 420 ( 0 ^; 420 !; 0 ?; 420 :)
% Comments :
%------------------------------------------------------------------------------
thf(power_power_decl,type,
power_power: $i > $i > $i > $i ).
thf(int_decl,type,
int: $i ).
thf(plus_plus_decl,type,
plus_plus: $i > $i > $i > $i ).
thf(one_one_decl,type,
one_one: $i > $i ).
thf(semiring_1_of_nat_decl,type,
semiring_1_of_nat: $i > $i > $i ).
thf(n_decl,type,
n: $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(zero_zero_decl,type,
zero_zero: $i > $i ).
thf(linordered_idom_decl,type,
linordered_idom: $i > $o ).
thf(ord_less_decl,type,
ord_less: $i > $i > $i > $o ).
thf(ti_decl,type,
ti: $i > $i > $i ).
thf(undefined_decl,type,
undefined: $i > $i ).
thf(number_ring_decl,type,
number_ring: $i > $o ).
thf(number_semiring_decl,type,
number_semiring: $i > $o ).
thf(ring_char_0_decl,type,
ring_char_0: $i > $o ).
thf(power_decl,type,
power: $i > $o ).
thf(mult_zero_decl,type,
mult_zero: $i > $o ).
thf(no_zero_divisors_decl,type,
no_zero_divisors: $i > $o ).
thf(zero_neq_one_decl,type,
zero_neq_one: $i > $o ).
thf(number_decl,type,
number: $i > $o ).
thf(semiring_1_decl,type,
semiring_1: $i > $o ).
thf(t_decl,type,
t: $i ).
thf(ring_11004092258visors_decl,type,
ring_11004092258visors: $i > $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add: $i > $o ).
thf(semiring_0_decl,type,
semiring_0: $i > $o ).
thf(98,axiom,
nat @ no_zero_divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(515,plain,
nat @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(87,axiom,
int @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
thf(482,plain,
int @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(130,axiom,
! [A: $i] :
~ ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_int__less__0__conv) ).
thf(629,plain,
! [A: $i] :
~ ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( B @ ( int @ semiring_1_of_nat ) @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zadd__int) ).
thf(479,plain,
! [A: $i,B: $i] :
( ( B @ ( int @ semiring_1_of_nat ) @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( C @ ( B @ ( A @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_zadd__int__left) ).
thf(555,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( C @ ( B @ ( A @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( int @ ord_less ) ) )
| ( A = B )
| ( B @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_zless__linear) ).
thf(666,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)],[140]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( B @ ( pls @ ( A @ number_number_of ) @ ( A @ plus_plus ) ) )
= ( B @ ( A @ ti ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_add__numeral__0) ).
thf(352,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( B @ ( pls @ ( A @ number_number_of ) @ ( A @ plus_plus ) ) )
= ( B @ ( A @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(102,axiom,
( ( pls @ bit0 )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_Bit0__Pls) ).
thf(523,plain,
( ( pls @ bit0 )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(31,axiom,
int @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(276,plain,
int @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(57,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 ) ) )
<=> ( C @ ( B @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_less__number__of) ).
thf(379,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i,C: $i] :
( ( ( C @ ( B @ ( int @ ord_less ) ) )
=> ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less ) ) ) )
& ( ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less ) ) )
=> ( C @ ( B @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(136,axiom,
! [A: $i] :
( ( A @ linord219039673up_add )
=> ! [B: $i] :
( ( ( B @ ( B @ ( A @ plus_plus ) ) )
= ( A @ zero_zero ) )
<=> ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_double__eq__0__iff) ).
thf(655,plain,
! [A: $i] :
( ( A @ linord219039673up_add )
=> ! [B: $i] :
( ( ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) )
=> ( ( B @ ( B @ ( A @ plus_plus ) ) )
= ( A @ zero_zero ) ) )
& ( ( ( B @ ( B @ ( A @ plus_plus ) ) )
= ( A @ zero_zero ) )
=> ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( C @ ( int @ plus_plus ) ) @ ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_zadd__strict__right__mono) ).
thf(677,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( C @ ( int @ plus_plus ) ) @ ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(121,axiom,
! [A: $i] :
( ( A @ bit1 )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_rel__simps_I46_J) ).
thf(597,plain,
! [A: $i] :
( ( A @ bit1 )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(58,axiom,
int @ one_one @ ( int @ zero_zero @ ( int @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_int__0__less__1) ).
thf(385,plain,
int @ one_one @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(106,axiom,
nat @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(533,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i] :
( ( A @ zero_zero @ ( B @ ( B @ ( A @ plus_plus ) ) @ ( A @ ord_less ) ) )
<=> ( A @ zero_zero @ ( B @ ( A @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_even__less__0__iff) ).
thf(174,plain,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i] :
( ( ( A @ zero_zero @ ( B @ ( A @ ord_less ) ) )
=> ( A @ zero_zero @ ( B @ ( B @ ( A @ plus_plus ) ) @ ( A @ ord_less ) ) ) )
& ( ( A @ zero_zero @ ( B @ ( B @ ( A @ plus_plus ) ) @ ( A @ ord_less ) ) )
=> ( A @ zero_zero @ ( B @ ( A @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ number_semiring )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ plus_plus ) ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_arg1) ).
thf(301,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ number_semiring )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ plus_plus ) ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(43,axiom,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( A @ one_one @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less ) ) )
<=> ( pls @ bit1 @ ( B @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_less__special_I4_J) ).
thf(320,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( ( pls @ bit1 @ ( B @ ( int @ ord_less ) ) )
=> ( A @ one_one @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less ) ) ) )
& ( ( A @ one_one @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less ) ) )
=> ( pls @ bit1 @ ( B @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ bit0 @ ( A @ bit0 @ ( int @ plus_plus ) ) )
= ( B @ ( A @ ( int @ plus_plus ) ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_add__Bit0__Bit0) ).
thf(257,plain,
! [A: $i,B: $i] :
( ( B @ bit0 @ ( A @ bit0 @ ( int @ plus_plus ) ) )
= ( B @ ( A @ ( int @ plus_plus ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(116,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/sandbox/benchmark/theBenchmark.p',fact_7_add__special_I3_J) ).
thf(570,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)],[116]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ linord219039673up_add )
=> ( ( A @ zero_zero @ ( A @ ti ) )
= ( A @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_1_res) ).
thf(460,plain,
! [A: $i] :
( ( A @ linord219039673up_add )
=> ( ( A @ zero_zero @ ( A @ ti ) )
= ( A @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(67,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( int @ plus_plus ) ) @ ( A @ number_number_of ) )
= ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_number__of__add) ).
thf(421,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( int @ plus_plus ) ) @ ( A @ number_number_of ) )
= ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ bit0 )
= ( A @ ( A @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Bit0__def) ).
thf(448,plain,
! [A: $i] :
( ( A @ bit0 )
= ( A @ ( A @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ bit0 @ ( A @ bit1 @ ( int @ ord_less ) ) )
<=> ( B @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_less__int__code_I15_J) ).
thf(216,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less ) ) )
=> ( B @ bit0 @ ( A @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( B @ bit0 @ ( A @ bit1 @ ( int @ ord_less ) ) )
=> ( B @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(84,axiom,
nat @ mult_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(475,plain,
nat @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(91,axiom,
( ( pls @ ( int @ ti ) )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OPls_res) ).
thf(492,plain,
( ( pls @ ( int @ ti ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ( ( A @ one_one @ ( A @ one_one @ ( A @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( A @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_one__add__one__is__two) ).
thf(376,plain,
! [A: $i] :
( ( A @ number_ring )
=> ( ( A @ one_one @ ( A @ one_one @ ( A @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( A @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(17,axiom,
( ( n @ ( nat @ ti ) )
= n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_n_____res) ).
thf(211,plain,
( ( n @ ( nat @ ti ) )
= n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ plus_plus ) ) )
= ( C @ ( B @ ( int @ plus_plus ) ) @ ( A @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_add__number__of__eq) ).
thf(238,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ plus_plus ) ) )
= ( C @ ( B @ ( int @ plus_plus ) ) @ ( A @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(118,axiom,
! [A: $i] :
( ( int @ zero_zero @ ( A @ bit0 @ ( int @ ord_less ) ) )
<=> ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_bin__less__0__simps_I3_J) ).
thf(574,plain,
! [A: $i] :
( ( ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) )
=> ( int @ zero_zero @ ( A @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( int @ zero_zero @ ( A @ bit0 @ ( int @ ord_less ) ) )
=> ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',fact_96_power2__less__0) ).
thf(280,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)],[33]) ).
thf(40,axiom,
! [A: $i] :
( ( ( A @ zero_neq_one )
& ( A @ no_zero_divisors )
& ( A @ mult_zero )
& ( A @ power ) )
=> ( ( A @ zero_zero @ ( A @ ti ) )
= ( A @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_0_res) ).
thf(312,plain,
! [A: $i] :
( ( ( A @ zero_neq_one )
& ( A @ no_zero_divisors )
& ( A @ mult_zero )
& ( A @ power ) )
=> ( ( A @ zero_zero @ ( A @ ti ) )
= ( A @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(61,axiom,
! [A: $i] :
( ( ( A @ bit0 )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_rel__simps_I44_J) ).
thf(397,plain,
! [A: $i] :
( ( ( A = pls )
=> ( ( A @ bit0 )
= pls ) )
& ( ( ( A @ bit0 )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(148,axiom,
! [A: $i] :
( ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) )
<=> ( pls @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_rel__simps_I10_J) ).
thf(687,plain,
! [A: $i] :
( ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ zero_neq_one )
& ( C @ no_zero_divisors )
& ( C @ mult_zero )
& ( C @ power ) )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ power_power ) ) )
= ( B @ ( A @ ( C @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_0_arg1) ).
thf(512,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ zero_neq_one )
& ( C @ no_zero_divisors )
& ( C @ mult_zero )
& ( C @ power ) )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ power_power ) ) )
= ( B @ ( A @ ( C @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ number )
=> ( ( A @ ( B @ number_number_of ) @ ( B @ ti ) )
= ( A @ ( B @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_res) ).
thf(270,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)],[29]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ( B @ bit1 @ ( A @ bit1 @ ( int @ ord_less ) ) )
<=> ( B @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_rel__simps_I17_J) ).
thf(534,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less ) ) )
=> ( B @ bit1 @ ( A @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( B @ bit1 @ ( A @ bit1 @ ( int @ ord_less ) ) )
=> ( B @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',fact_95_zero__less__power2) ).
thf(334,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)],[46]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( A @ ( int @ ord_less ) ) )
<=> ( ( A = B )
| ( B @ ( A @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_zless__add1__eq) ).
thf(260,plain,
! [A: $i,B: $i] :
( ( ( ( A = B )
| ( B @ ( A @ ( int @ ord_less ) ) ) )
=> ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( A @ ( int @ ord_less ) ) ) )
& ( ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( A @ ( int @ ord_less ) ) )
=> ( ( A = B )
| ( B @ ( A @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ( ( pls @ ( A @ number_number_of ) )
= ( A @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_number__of__Pls) ).
thf(424,plain,
! [A: $i] :
( ( A @ number_ring )
=> ( ( pls @ ( A @ number_number_of ) )
= ( A @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(5,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/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_0_arg1) ).
thf(165,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)],[5]) ).
thf(63,axiom,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_nat__numeral__1__eq__1) ).
thf(407,plain,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(149,axiom,
int @ semiring_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__0) ).
thf(693,plain,
int @ semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',fact_46_zadd__left__commute) ).
thf(197,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)],[14]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( B @ bit0 @ ( A @ bit0 @ ( int @ ord_less ) ) )
<=> ( B @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_less__int__code_I13_J) ).
thf(361,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less ) ) )
=> ( B @ bit0 @ ( A @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( B @ bit0 @ ( A @ bit0 @ ( int @ ord_less ) ) )
=> ( B @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(139,axiom,
nat @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(665,plain,
nat @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(100,axiom,
int @ number_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(519,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(151,axiom,
! [A: $i,B: $i] :
( ( B @ bit1 @ ( A @ bit0 @ ( int @ plus_plus ) ) )
= ( B @ ( A @ ( int @ plus_plus ) ) @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_add__Bit0__Bit1) ).
thf(697,plain,
! [A: $i,B: $i] :
( ( B @ bit1 @ ( A @ bit0 @ ( int @ plus_plus ) ) )
= ( B @ ( A @ ( int @ plus_plus ) ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ zero_neq_one )
& ( C @ no_zero_divisors )
& ( C @ mult_zero )
& ( C @ power ) )
=> ( ( B @ ( nat @ ti ) @ ( A @ ( C @ power_power ) ) )
= ( B @ ( A @ ( C @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_0_arg2) ).
thf(615,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ zero_neq_one )
& ( C @ no_zero_divisors )
& ( C @ mult_zero )
& ( C @ power ) )
=> ( ( B @ ( nat @ ti ) @ ( A @ ( C @ power_power ) ) )
= ( B @ ( A @ ( C @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ undefined @ ( A @ ti ) )
= ( A @ undefined ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
thf(169,plain,
! [A: $i] :
( ( A @ undefined @ ( A @ ti ) )
= ( A @ undefined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21,axiom,
! [A: $i] :
( ( ( A @ zero_neq_one )
& ( A @ no_zero_divisors )
& ( A @ mult_zero )
& ( A @ power ) )
=> ! [B: $i,C: $i] :
( ( ( C @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) ) )
= ( A @ zero_zero ) )
<=> ( ( ( C @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_power__eq__0__iff__number__of) ).
thf(225,plain,
! [A: $i] :
( ( ( A @ zero_neq_one )
& ( A @ no_zero_divisors )
& ( A @ mult_zero )
& ( A @ power ) )
=> ! [B: $i,C: $i] :
( ( ( ( ( C @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) )
=> ( ( C @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) ) )
= ( A @ zero_zero ) ) )
& ( ( ( C @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) ) )
= ( A @ zero_zero ) )
=> ( ( ( C @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(141,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ( ( A @ one_one )
= ( pls @ bit1 @ ( A @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_semiring__norm_I110_J) ).
thf(669,plain,
! [A: $i] :
( ( A @ number_ring )
=> ( ( A @ one_one )
= ( pls @ bit1 @ ( A @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(85,axiom,
! [A: $i] :
( ( A @ ( pls @ ( int @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_add__Pls) ).
thf(476,plain,
! [A: $i] :
( ( A @ ( pls @ ( int @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(90,axiom,
! [A: $i] :
( ( A @ ( int @ zero_zero @ ( int @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_zadd__0) ).
thf(489,plain,
! [A: $i] :
( ( A @ ( int @ zero_zero @ ( int @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(145,axiom,
( ( nat @ one_one @ ( nat @ one_one @ ( nat @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_nat__1__add__1) ).
thf(679,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)],[145]) ).
thf(153,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(706,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ti ) @ ( nat @ ord_less ) ) )
<=> ( B @ ( A @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_1_arg1) ).
thf(328,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ti ) @ ( nat @ ord_less ) ) ) )
& ( ( B @ ( A @ ( nat @ ti ) @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(83,axiom,
! [A: $i] :
( pls
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_rel__simps_I39_J) ).
thf(471,plain,
! [A: $i] :
( pls
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(113,axiom,
! [A: $i] :
( ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) )
<=> ( A @ ( pls @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_rel__simps_I4_J) ).
thf(558,plain,
! [A: $i] :
( ( ( A @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) ) )
& ( ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ ( pls @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(120,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/sandbox/benchmark/theBenchmark.p',fact_97_sum__power2__gt__zero__iff) ).
thf(586,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)],[120]) ).
thf(128,axiom,
! [A: $i] :
( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_int__eq__0__conv) ).
thf(618,plain,
! [A: $i] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ) )
& ( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(117,axiom,
nat @ semiring_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__0) ).
thf(573,plain,
nat @ semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(9,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/sandbox/benchmark/theBenchmark.p',fact_17_plus__numeral__code_I9_J) ).
thf(180,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)],[9]) ).
thf(73,axiom,
int @ mult_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
thf(444,plain,
int @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ semiring_0 )
& ( C @ power ) )
=> ( ( B @ ( nat @ ti ) @ ( A @ ( C @ power_power ) ) )
= ( B @ ( A @ ( C @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_1_arg2) ).
thf(601,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ semiring_0 )
& ( C @ power ) )
=> ( ( B @ ( nat @ ti ) @ ( A @ ( C @ power_power ) ) )
= ( B @ ( A @ ( C @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(150,axiom,
! [A: $i] :
( ( int @ zero_zero @ ( A @ ( int @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_zadd__0__right) ).
thf(694,plain,
! [A: $i] :
( ( int @ zero_zero @ ( A @ ( int @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',fact_6_add__special_I2_J) ).
thf(191,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)],[11]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ( A @ bit0 )
= ( B @ bit0 ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_rel__simps_I48_J) ).
thf(291,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)],[35]) ).
thf(65,axiom,
! [A: $i] :
( ( int @ zero_zero @ ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) )
<=> ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_odd__less__0) ).
thf(413,plain,
! [A: $i] :
( ( ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) )
=> ( int @ zero_zero @ ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) ) )
& ( ( int @ zero_zero @ ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) )
=> ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(133,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/sandbox/benchmark/theBenchmark.p',fact_40_eq__number__of) ).
thf(641,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)],[133]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ number_semiring )
=> ( ( B @ ( A @ ( C @ plus_plus ) ) @ ( C @ ti ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_res) ).
thf(445,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ number_semiring )
=> ( ( B @ ( A @ ( C @ plus_plus ) ) @ ( C @ ti ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(94,axiom,
! [A: $i] :
( ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) )
!= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_odd__nonzero) ).
thf(498,plain,
! [A: $i] :
( ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) )
!= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(80,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/sandbox/benchmark/theBenchmark.p',fact_3_one__power2) ).
thf(466,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)],[80]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( B @ number_semiring )
=> ( ( A @ ( B @ semiring_1_of_nat ) @ ( B @ ti ) )
= ( A @ ( B @ semiring_1_of_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Nat_Osemiring__1__class_Oof__nat_res) ).
thf(540,plain,
! [A: $i,B: $i] :
( ( B @ number_semiring )
=> ( ( A @ ( B @ semiring_1_of_nat ) @ ( B @ ti ) )
= ( A @ ( B @ semiring_1_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(142,axiom,
! [A: $i] :
( ( ( A @ semiring_0 )
& ( A @ power ) )
=> ( ( A @ zero_zero @ ( A @ ti ) )
= ( A @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_2_res) ).
thf(672,plain,
! [A: $i] :
( ( ( A @ semiring_0 )
& ( A @ power ) )
=> ( ( A @ zero_zero @ ( A @ ti ) )
= ( A @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ semiring_0 )
& ( C @ power ) )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ power_power ) ) )
= ( B @ ( A @ ( C @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_1_arg1) ).
thf(604,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ semiring_0 )
& ( C @ power ) )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ power_power ) ) )
= ( B @ ( A @ ( C @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(7,axiom,
~ ( int @ zero_zero @ ( pls @ ( int @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_bin__less__0__simps_I1_J) ).
thf(172,plain,
~ ( int @ zero_zero @ ( pls @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(146,axiom,
! [A: $i] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( int @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_quartic__square__square) ).
thf(681,plain,
! [A: $i] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( int @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(66,axiom,
( ( int @ zero_zero )
= ( pls @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_zero__is__num__zero) ).
thf(419,plain,
( ( int @ zero_zero )
= ( pls @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(134,axiom,
! [A: $i] :
( ( ( A @ semiring_0 )
& ( A @ power ) )
=> ( ( A @ one_one @ ( A @ ti ) )
= ( A @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oone__class_Oone_res) ).
thf(649,plain,
! [A: $i] :
( ( ( A @ semiring_0 )
& ( A @ power ) )
=> ( ( A @ one_one @ ( A @ ti ) )
= ( A @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( pls @ ( A @ number_number_of ) @ ( B @ ( A @ plus_plus ) ) )
= ( B @ ( A @ ti ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_add__numeral__0__right) ).
thf(451,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( pls @ ( A @ number_number_of ) @ ( B @ ( A @ plus_plus ) ) )
= ( B @ ( A @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ linord219039673up_add )
=> ( ( B @ ( A @ ( C @ plus_plus ) ) @ ( C @ ti ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_res) ).
thf(567,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ linord219039673up_add )
=> ( ( B @ ( A @ ( C @ plus_plus ) ) @ ( C @ ti ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ linord219039673up_add )
=> ( ( B @ ( C @ ti ) @ ( A @ ( C @ plus_plus ) ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_arg2) ).
thf(494,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ linord219039673up_add )
=> ( ( B @ ( C @ ti ) @ ( A @ ( C @ plus_plus ) ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(126,axiom,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( B @ ( A @ number_number_of ) @ ( A @ zero_zero @ ( A @ ord_less ) ) )
<=> ( B @ ( pls @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_less__special_I1_J) ).
thf(609,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( ( B @ ( pls @ ( int @ ord_less ) ) )
=> ( B @ ( A @ number_number_of ) @ ( A @ zero_zero @ ( A @ ord_less ) ) ) )
& ( ( B @ ( A @ number_number_of ) @ ( A @ zero_zero @ ( A @ ord_less ) ) )
=> ( B @ ( pls @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(18,axiom,
( ( int @ zero_zero )
!= ( int @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_int__0__neq__1) ).
thf(213,plain,
( ( int @ zero_zero )
!= ( int @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ linord219039673up_add )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ plus_plus ) ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_arg1) ).
thf(483,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ linord219039673up_add )
=> ( ( B @ ( A @ ( C @ ti ) @ ( C @ plus_plus ) ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ power_power ) ) )
= ( B @ ( A @ ( nat @ power_power ) ) @ ( int @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_zpower__int) ).
thf(251,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ power_power ) ) )
= ( B @ ( A @ ( nat @ power_power ) ) @ ( int @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( B @ number )
=> ( ( A @ ( int @ ti ) @ ( B @ number_number_of ) )
= ( A @ ( B @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_arg1) ).
thf(626,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)],[129]) ).
thf(1,conjecture,
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ power_power ) ) )
!= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ power_power ) ) )
!= ( int @ zero_zero ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(155,plain,
~ ( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ power_power ) ) )
!= ( int @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(48,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(345,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(53,axiom,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_int__0) ).
thf(367,plain,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ semiring_0 )
& ( C @ power ) )
=> ( ( B @ ( A @ ( C @ power_power ) ) @ ( C @ ti ) )
= ( B @ ( A @ ( C @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_1_res) ).
thf(552,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ semiring_0 )
& ( C @ power ) )
=> ( ( B @ ( A @ ( C @ power_power ) ) @ ( C @ ti ) )
= ( B @ ( A @ ( C @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(152,axiom,
! [A: $i,B: $i] :
( ( B @ bit0 @ ( A @ bit1 @ ( int @ ord_less ) ) )
<=> ( B @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_rel__simps_I16_J) ).
thf(700,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less ) ) )
=> ( B @ bit0 @ ( A @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( B @ bit0 @ ( A @ bit1 @ ( int @ ord_less ) ) )
=> ( B @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(101,axiom,
! [A: $i] :
( ( A @ number_semiring )
=> ( ( pls @ ( A @ number_number_of ) )
= ( A @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_semiring__numeral__0__eq__0) ).
thf(520,plain,
! [A: $i] :
( ( A @ number_semiring )
=> ( ( pls @ ( A @ number_number_of ) )
= ( A @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(125,axiom,
nat @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(608,plain,
nat @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(24,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/sandbox/benchmark/theBenchmark.p',fact_2_sum__power2__eq__zero__iff) ).
thf(241,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)],[24]) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',fact_4_zero__power2) ).
thf(394,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)],[60]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ bit1 )
= ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Bit1__def) ).
thf(306,plain,
! [A: $i] :
( ( A @ bit1 )
= ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(143,axiom,
( ( nat @ one_one )
= ( pls @ bit1 @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_Numeral1__eq1__nat) ).
thf(675,plain,
( ( nat @ one_one )
= ( pls @ bit1 @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(137,axiom,
int @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(663,plain,
int @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ zero_neq_one )
& ( C @ no_zero_divisors )
& ( C @ mult_zero )
& ( C @ power ) )
=> ( ( B @ ( A @ ( C @ power_power ) ) @ ( C @ ti ) )
= ( B @ ( A @ ( C @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_0_res) ).
thf(516,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ zero_neq_one )
& ( C @ no_zero_divisors )
& ( C @ mult_zero )
& ( C @ power ) )
=> ( ( B @ ( A @ ( C @ power_power ) ) @ ( C @ ti ) )
= ( B @ ( A @ ( C @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ number_semiring )
=> ! [B: $i] :
( ( B @ ( int @ semiring_1_of_nat ) @ ( A @ number_number_of ) )
= ( B @ ( A @ semiring_1_of_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_number__of__int) ).
thf(342,plain,
! [A: $i] :
( ( A @ number_semiring )
=> ! [B: $i] :
( ( B @ ( int @ semiring_1_of_nat ) @ ( A @ number_number_of ) )
= ( B @ ( A @ semiring_1_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(51,axiom,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ ord_less ) ) )
<=> ( B @ ( pls @ bit1 @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_less__special_I2_J) ).
thf(355,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( ( B @ ( pls @ bit1 @ ( int @ ord_less ) ) )
=> ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ ord_less ) ) ) )
& ( ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ ord_less ) ) )
=> ( B @ ( pls @ bit1 @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(12,axiom,
nat @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(194,plain,
nat @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ti ) @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_ti_idem) ).
thf(162,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ti ) @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(105,axiom,
( pls
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Pls__def) ).
thf(531,plain,
( pls
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(103,axiom,
! [A: $i] :
( ( A @ ( int @ ti ) @ bit1 )
= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OBit1_arg1) ).
thf(525,plain,
! [A: $i] :
( ( A @ ( int @ ti ) @ bit1 )
= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(119,axiom,
! [A: $i] :
( ( int @ zero_zero @ ( A @ bit1 @ ( int @ ord_less ) ) )
<=> ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_bin__less__0__simps_I4_J) ).
thf(580,plain,
! [A: $i] :
( ( ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) )
=> ( int @ zero_zero @ ( A @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( int @ zero_zero @ ( A @ bit1 @ ( int @ ord_less ) ) )
=> ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(154,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/sandbox/benchmark/theBenchmark.p',fact_36_add__nat__number__of) ).
thf(707,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)],[154]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( A @ bit0 )
!= ( B @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_rel__simps_I49_J) ).
thf(409,plain,
! [A: $i,B: $i] :
( ( A @ bit0 )
!= ( B @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(71,axiom,
int @ linord219039673up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(441,plain,
int @ linord219039673up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(55,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/sandbox/benchmark/theBenchmark.p',fact_16_less__number__of__int__code) ).
thf(370,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)],[55]) ).
thf(95,axiom,
! [A: $i] :
( ( ( A @ semiring_0 )
& ( A @ power ) )
=> ! [B: $i] :
( ( ( ( B @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
=> ( ( B @ ( nat @ number_number_of ) @ ( A @ zero_zero @ ( A @ power_power ) ) )
= ( A @ zero_zero ) ) )
& ( ( ( B @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) )
=> ( ( B @ ( nat @ number_number_of ) @ ( A @ zero_zero @ ( A @ power_power ) ) )
= ( A @ one_one ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_power__0__left__number__of) ).
thf(502,plain,
! [A: $i] :
( ( ( A @ semiring_0 )
& ( A @ power ) )
=> ! [B: $i] :
( ( ( ( B @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
=> ( ( B @ ( nat @ number_number_of ) @ ( A @ zero_zero @ ( A @ power_power ) ) )
= ( A @ zero_zero ) ) )
& ( ( ( B @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) )
=> ( ( B @ ( nat @ number_number_of ) @ ( A @ zero_zero @ ( A @ power_power ) ) )
= ( A @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( B @ bit0 @ ( A @ bit1 @ ( int @ plus_plus ) ) )
= ( B @ ( A @ ( int @ plus_plus ) ) @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_add__Bit1__Bit0) ).
thf(463,plain,
! [A: $i,B: $i] :
( ( B @ bit0 @ ( A @ bit1 @ ( int @ plus_plus ) ) )
= ( B @ ( A @ ( int @ plus_plus ) ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(82,axiom,
int @ no_zero_divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
thf(470,plain,
int @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( B @ ( int @ semiring_1_of_nat ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_int__int__eq) ).
thf(386,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( A @ ( int @ semiring_1_of_nat ) )
= ( B @ ( int @ semiring_1_of_nat ) ) ) )
& ( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( B @ ( int @ semiring_1_of_nat ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(93,axiom,
int @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(497,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(42,axiom,
int @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(319,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(37,axiom,
( ( nat @ zero_zero )
= ( pls @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_semiring__norm_I113_J) ).
thf(304,plain,
( ( nat @ zero_zero )
= ( pls @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_zadd__commute) ).
thf(632,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(3,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/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_0_arg2) ).
thf(158,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)],[3]) ).
thf(135,axiom,
! [A: $i] :
( ( A @ number_semiring )
=> ( ( A @ one_one @ ( A @ one_one @ ( A @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( A @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_semiring__one__add__one__is__two) ).
thf(652,plain,
! [A: $i] :
( ( A @ number_semiring )
=> ( ( A @ one_one @ ( A @ one_one @ ( A @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( A @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(22,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/sandbox/benchmark/theBenchmark.p',fact_45_zadd__assoc) ).
thf(235,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)],[22]) ).
thf(147,axiom,
! [A: $i,B: $i] :
( ( B @ number_semiring )
=> ( ( A @ ( nat @ ti ) @ ( B @ semiring_1_of_nat ) )
= ( A @ ( B @ semiring_1_of_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Nat_Osemiring__1__class_Oof__nat_arg1) ).
thf(684,plain,
! [A: $i,B: $i] :
( ( B @ number_semiring )
=> ( ( A @ ( nat @ ti ) @ ( B @ semiring_1_of_nat ) )
= ( A @ ( B @ semiring_1_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( B @ bit1 @ ( A @ bit1 @ ( int @ ord_less ) ) )
<=> ( B @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_less__int__code_I16_J) ).
thf(346,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less ) ) )
=> ( B @ bit1 @ ( A @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( B @ bit1 @ ( A @ bit1 @ ( int @ ord_less ) ) )
=> ( B @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(110,axiom,
! [A: $i] :
( ( A @ ( int @ ti ) @ bit0 )
= ( A @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OBit0_arg1) ).
thf(549,plain,
! [A: $i] :
( ( A @ ( int @ ti ) @ bit0 )
= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',fact_5_zero__eq__power2) ).
thf(433,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)],[70]) ).
thf(96,axiom,
( ( pls @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_nat__number__of__Pls) ).
thf(510,plain,
( ( pls @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( A @ bit1 )
!= ( B @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_rel__simps_I50_J) ).
thf(315,plain,
! [A: $i,B: $i] :
( ( A @ bit1 )
!= ( B @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(62,axiom,
( ( t @ ( int @ ti ) )
= t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_t_____res) ).
thf(405,plain,
( ( t @ ( int @ ti ) )
= t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(10,axiom,
! [A: $i] :
( ( pls
= ( A @ bit0 ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_rel__simps_I38_J) ).
thf(183,plain,
! [A: $i] :
( ( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ bit1 @ ( int @ ti ) )
= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OBit1_res) ).
thf(273,plain,
! [A: $i] :
( ( A @ bit1 @ ( int @ ti ) )
= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(114,axiom,
! [A: $i] :
( ( pls @ ( A @ ( int @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_add__Pls__right) ).
thf(564,plain,
! [A: $i] :
( ( pls @ ( A @ ( int @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(16,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(210,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(44,axiom,
( ( nat @ one_one @ ( int @ semiring_1_of_nat ) )
= ( int @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_int__1) ).
thf(326,plain,
( ( nat @ one_one @ ( int @ semiring_1_of_nat ) )
= ( int @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(13,axiom,
( ( int @ one_one )
= ( pls @ bit1 @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_one__is__num__one) ).
thf(195,plain,
( ( int @ one_one )
= ( pls @ bit1 @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(138,axiom,
int @ ring_11004092258visors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
thf(664,plain,
int @ ring_11004092258visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ( B @ ( nat @ ti ) @ ( A @ ( nat @ ord_less ) ) )
<=> ( B @ ( A @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_1_arg2) ).
thf(635,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( nat @ ord_less ) ) )
=> ( B @ ( nat @ ti ) @ ( A @ ( nat @ ord_less ) ) ) )
& ( ( B @ ( nat @ ti ) @ ( A @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',fact_41_number__of__reorient) ).
thf(283,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)],[34]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( B @ bit0 @ ( A @ bit0 @ ( int @ ord_less ) ) )
<=> ( B @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_rel__simps_I14_J) ).
thf(427,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less ) ) )
=> ( B @ bit0 @ ( A @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( B @ bit0 @ ( A @ bit0 @ ( int @ ord_less ) ) )
=> ( B @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ power_power ) ) @ ( int @ semiring_1_of_nat ) )
= ( B @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ power_power ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_int__power) ).
thf(528,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ power_power ) ) @ ( int @ semiring_1_of_nat ) )
= ( B @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ power_power ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( A @ bit1 )
= ( B @ bit1 ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_rel__simps_I51_J) ).
thf(200,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)],[15]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ number_number_of ) @ ( A @ plus_plus ) ) @ ( B @ ( A @ number_number_of ) @ ( A @ plus_plus ) ) )
= ( D @ ( C @ ( B @ ( int @ plus_plus ) ) @ ( A @ number_number_of ) @ ( A @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_add__number__of__left) ).
thf(277,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ number_number_of ) @ ( A @ plus_plus ) ) @ ( B @ ( A @ number_number_of ) @ ( A @ plus_plus ) ) )
= ( D @ ( C @ ( B @ ( int @ plus_plus ) ) @ ( A @ number_number_of ) @ ( A @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(72,axiom,
~ ( pls @ ( pls @ ( int @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_rel__simps_I2_J) ).
thf(442,plain,
~ ( pls @ ( pls @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(54,axiom,
n @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_n0) ).
thf(369,plain,
n @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(124,axiom,
t @ ( int @ one_one @ ( int @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_t1) ).
thf(607,plain,
t @ ( int @ one_one @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ bit0 @ ( int @ ti ) )
= ( A @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OBit0_res) ).
thf(254,plain,
! [A: $i] :
( ( A @ bit0 @ ( int @ ti ) )
= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(89,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ( ( pls @ bit1 @ ( A @ number_number_of ) )
= ( A @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_numeral__1__eq__1) ).
thf(486,plain,
! [A: $i] :
( ( A @ number_ring )
=> ( ( pls @ bit1 @ ( A @ number_number_of ) )
= ( A @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(81,axiom,
n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
thf(469,plain,
n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ( ( A @ zero_zero )
= ( pls @ ( A @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_semiring__norm_I112_J) ).
thf(309,plain,
! [A: $i] :
( ( A @ number_ring )
=> ( ( A @ zero_zero )
= ( pls @ ( A @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(109,axiom,
! [A: $i] :
( ( pls @ ( A @ bit1 @ ( int @ ord_less ) ) )
<=> ( pls @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_rel__simps_I12_J) ).
thf(543,plain,
! [A: $i] :
( ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( pls @ ( A @ bit1 @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ number_semiring )
=> ( ( B @ ( C @ ti ) @ ( A @ ( C @ plus_plus ) ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_arg2) ).
thf(222,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ number_semiring )
=> ( ( B @ ( C @ ti ) @ ( A @ ( C @ plus_plus ) ) )
= ( B @ ( A @ ( C @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(77,axiom,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( A @ zero_zero @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less ) ) )
<=> ( pls @ ( B @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_less__special_I3_J) ).
thf(454,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( ( pls @ ( B @ ( int @ ord_less ) ) )
=> ( A @ zero_zero @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less ) ) ) )
& ( ( A @ zero_zero @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less ) ) )
=> ( pls @ ( B @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(733,plain,
$false,
inference(e,[status(thm)],[515,482,629,479,555,666,352,523,276,379,655,677,597,385,533,174,301,320,257,570,460,421,448,216,475,492,376,211,238,574,280,312,397,687,512,270,534,334,260,424,165,407,693,197,361,665,519,697,615,169,225,669,476,489,679,706,328,471,558,586,618,573,180,444,601,694,191,291,413,641,445,498,466,540,672,604,172,681,419,649,451,567,494,609,213,483,251,626,155,345,367,552,700,520,608,241,394,306,675,663,516,342,355,194,162,531,525,580,707,409,441,370,502,463,470,386,497,319,304,632,158,652,235,684,346,549,433,510,315,405,183,273,564,210,326,195,664,635,283,427,528,200,277,442,369,607,254,486,469,309,543,222,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM925+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40 % Computer : n002.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
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.70/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.94/0.88 % [INFO] Parsing done (166ms).
% 0.94/0.88 % [INFO] Running in sequential loop mode.
% 1.86/1.08 % [INFO] eprover registered as external prover.
% 1.86/1.09 % [INFO] Scanning for conjecture ...
% 2.14/1.16 % [INFO] Found a conjecture (or negated_conjecture) and 152 axioms. Running axiom selection ...
% 2.36/1.23 % [INFO] Axiom selection finished. Selected 152 axioms (removed 0 axioms).
% 2.75/1.32 % [INFO] Problem is first-order (TPTP FOF).
% 2.75/1.33 % [INFO] Type checking passed.
% 2.75/1.34 % [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 ...
% 7.05/2.32 % External prover 'e' found a proof!
% 7.05/2.32 % [INFO] Killing All external provers ...
% 7.05/2.32 % Time passed: 1820ms (effective reasoning time: 1437ms)
% 7.05/2.32 % 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)>
% 7.05/2.33 % Axioms used in derivation (152): fact_73_Pls__def, fact_46_zadd__left__commute, fact_70_rel__simps_I44_J, fact_2_sum__power2__eq__zero__iff, fact_77_add__Bit0__Bit0, fact_36_add__nat__number__of, fact_61_int__less__0__conv, tsy_c_Groups_Oplus__class_Oplus_0_arg2, fact_50_less__special_I1_J, fact_13_numeral__1__eq__1, fact_29_nat__1__add__1, arity_Int_Oint___Rings_Olinordered__idom, arity_Nat_Onat___Rings_Osemiring__1, fact_9_semiring__one__add__one__is__two, tsy_c_Groups_Oplus__class_Oplus_1_arg2, fact_12_semiring__norm_I110_J, fact_4_zero__power2, arity_Int_Oint___Int_Oring__char__0, tsy_c_Int_OPls_res, fact_20_zpower__int, fact_44_even__less__0__iff, fact_68_rel__simps_I50_J, fact_31_rel__simps_I17_J, tsy_c_Groups_Oplus__class_Oplus_0_res, tsy_c_Orderings_Oord__class_Oless_1_arg2, tsy_c_Power_Opower__class_Opower_0_arg1, fact_91_add__Bit0__Bit1, fact_88_add__number__of__eq, fact_22_zadd__int__left, arity_Nat_Onat___Int_Onumber__semiring, fact_56_bin__less__0__simps_I4_J, fact_7_add__special_I3_J, fact_97_sum__power2__gt__zero__iff, arity_Nat_Onat___Power_Opower, fact_26_semiring__norm_I113_J, fact_75_add__Pls__right, arity_Int_Oint___Rings_Oring__1__no__zero__divisors, arity_Int_Oint___Rings_Ono__zero__divisors, tsy_c_Int_Onumber__class_Onumber__of_res, fact_33_less__int__code_I13_J, tsy_c_Groups_Oplus__class_Oplus_1_res, fact_5_zero__eq__power2, fact_60_zless__add1__eq, fact_40_eq__number__of, fact_48_int__int__eq, tsy_c_Groups_Oplus__class_Oplus_1_arg1, fact_47_zadd__commute, arity_Int_Oint___Int_Onumber__semiring, tsy_c_Groups_Ozero__class_Ozero_1_res, arity_Int_Oint___Int_Onumber__ring, tsy_c_Groups_Ozero__class_Ozero_0_res, arity_Int_Oint___Rings_Osemiring__1, arity_Nat_Onat___Rings_Omult__zero, fact_66_rel__simps_I46_J, fact_52_less__int__code_I15_J, tsy_c_Power_Opower__class_Opower_1_arg1, fact_21_int__power, fact_6_add__special_I2_J, fact_80_zadd__0, fact_1_t1, fact_57_bin__less__0__simps_I1_J, fact_59_int__0__less__1, fact_96_power2__less__0, fact_64_odd__less__0, tsy_c_Power_Opower__class_Opower_0_arg2, fact_93_odd__nonzero, fact_95_zero__less__power2, fact_83_semiring__norm_I112_J, fact_34_rel__simps_I14_J, tsy_c_Orderings_Oord__class_Oless_0_arg2, tsy_c_Groups_Oplus__class_Oplus_0_arg1, fact_67_rel__simps_I39_J, fact_87_add__number__of__left, arity_Nat_Onat___Rings_Osemiring__0, tsy_c_Int_OBit1_res, fact_25_nat__number__of__Pls, tsy_c_Orderings_Oord__class_Oless_1_arg1, tsy_c_Power_Opower__class_Opower_1_arg2, fact_54_rel__simps_I10_J, fact_79_zadd__0__right, tsy_c_HOL_Oundefined_res, fact_78_Bit0__def, fact_49_less__special_I3_J, help_ti_idem, fact_86_power__eq__0__iff__number__of, fact_39_Numeral1__eq1__nat, fact_51_rel__simps_I12_J, fact_82_number__of__Pls, fact_45_zadd__assoc, fact_10_quartic__square__square, fact_41_number__of__reorient, arity_Int_Oint___Power_Opower, fact_62_less__special_I4_J, fact_85_add__numeral__0__right, arity_Int_Oint___Rings_Osemiring__0, fact_55_rel__simps_I4_J, fact_69_rel__simps_I49_J, fact_18_less__number__of, fact_8_one__add__one__is__two, fact_72_Bit0__Pls, fact_42_rel__simps_I51_J, fact_11_power__0__left__number__of, arity_Nat_Onat___Int_Onumber, fact_23_zadd__int, fact_14_n0, tsy_c_Groups_Ozero__class_Ozero_2_res, arity_Int_Oint___Rings_Ozero__neq__one, fact_90_add__Bit1__Bit0, fact_28_int__0, tsy_c_Int_Onumber__class_Onumber__of_arg1, tsy_c_Nat_Osemiring__1__class_Oof__nat_res, fact_24_int__1, tsy_c_Int_OBit0_res, fact_43_rel__simps_I48_J, fact_32_rel__simps_I2_J, tsy_c_Power_Opower__class_Opower_1_res, tsy_c_Groups_Oone__class_Oone_res, fact_94_number__of__int, fact_15_zless__linear, fact_30_less__int__code_I16_J, tsy_c_Power_Opower__class_Opower_0_res, fact_81_semiring__numeral__0__eq__0, fact_76_add__Pls, tsy_c_Orderings_Oord__class_Oless_0_arg1, fact_65_double__eq__0__iff, fact_16_less__number__of__int__code, arity_Nat_Onat___Rings_Ono__zero__divisors, tsy_v_t_____res, fact_37_one__is__num__one, fact_92_Bit1__def, fact_63_less__special_I2_J, fact_58_bin__less__0__simps_I3_J, tsy_c_Int_OBit0_arg1, fact_89_number__of__add, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Groups_Olinordered__ab__group__add, fact_35_zadd__strict__right__mono, tsy_v_n_____res, tsy_c_Int_OBit1_arg1, arity_Int_Oint___Rings_Omult__zero, fact_0_n1pos, fact_74_int__0__neq__1, fact_27_int__eq__0__conv, fact_53_rel__simps_I16_J, arity_Nat_Onat___Rings_Ozero__neq__one, fact_38_nat__numeral__1__eq__1, fact_84_add__numeral__0, fact_71_rel__simps_I38_J, fact_3_one__power2, tsy_c_Nat_Osemiring__1__class_Oof__nat_arg1, fact_17_plus__numeral__code_I9_J, fact_19_zero__is__num__zero
% 7.05/2.33 % No. of inferences in proof: 308
% 7.05/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1820 ms resp. 1437 ms w/o parsing
% 7.70/2.42 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.70/2.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------