TSTP Solution File: NUM992_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM992_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:43:58 EDT 2023
% Result : Theorem 26.21s 5.69s
% Output : Refutation 26.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 137
% Syntax : Number of formulae : 282 ( 104 unt; 26 typ; 0 def)
% Number of atoms : 597 ( 160 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 3150 ( 63 ~; 24 |; 88 &;2756 @)
% ( 51 <=>; 168 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 6 con; 0-3 aty)
% Number of variables : 376 ( 0 ^; 355 !; 4 ?; 376 :)
% ( 17 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(number_type,type,
number:
!>[TA: $tType] : $o ).
thf(ring_type,type,
ring:
!>[TA: $tType] : $o ).
thf(semiring_type,type,
semiring:
!>[TA: $tType] : $o ).
thf(number_ring_type,type,
number_ring:
!>[TA: $tType] : $o ).
thf(ring_char_0_type,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(minus_minus_type,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(times_times_type,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(bit0_type,type,
bit0: int > int ).
thf(bit1_type,type,
bit1: int > int ).
thf(pls_type,type,
pls: int ).
thf(number_number_of_type,type,
number_number_of:
!>[TA: $tType] : ( int > TA ) ).
thf(semiring_1_of_nat_type,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(m1_type,type,
m1: int ).
thf(n_type,type,
n: nat ).
thf(t_type,type,
t: int ).
thf(25,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( zero_zero @ TA ) )
<=> ( ord_less @ int @ A @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_less__special_I3_J) ).
thf(177,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( zero_zero @ TA ) )
=> ( ord_less @ int @ A @ pls ) )
& ( ( ord_less @ int @ A @ pls )
=> ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(72,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( plus_plus @ int @ B @ ( one_one @ int ) ) @ A )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_add1__zle__eq) ).
thf(336,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( plus_plus @ int @ B @ ( one_one @ int ) ) @ A )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ B @ ( one_one @ int ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(71,axiom,
! [A: int] :
( ( times_times @ int @ pls @ A )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_mult__Pls) ).
thf(333,plain,
! [A: int] :
( ( times_times @ int @ pls @ A )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(104,axiom,
! [A: nat] :
( ( ( semiring_1_of_nat @ int @ A )
= ( zero_zero @ int ) )
<=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_int__eq__0__conv) ).
thf(468,plain,
! [A: nat] :
( ( ( ( semiring_1_of_nat @ int @ A )
= ( zero_zero @ int ) )
=> ( A
= ( zero_zero @ nat ) ) )
& ( ( A
= ( zero_zero @ nat ) )
=> ( ( semiring_1_of_nat @ int @ A )
= ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(88,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_rel__simps_I14_J) ).
thf(408,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(4,axiom,
number @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(115,plain,
number @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(54,axiom,
! [A: int,B: int] :
( ( minus_minus @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
= ( bit0 @ ( minus_minus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_diff__bin__simps_I10_J) ).
thf(276,plain,
! [A: int,B: int] :
( ( minus_minus @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
= ( bit0 @ ( minus_minus @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(98,axiom,
! [TA: $tType] :
( ( ( number @ TA )
& ( ring @ TA ) )
=> ! [A: int,B: TA,C: TA] :
( ( times_times @ TA @ ( minus_minus @ TA @ C @ B ) @ ( number_number_of @ TA @ A ) )
= ( minus_minus @ TA @ ( times_times @ TA @ C @ ( number_number_of @ TA @ A ) ) @ ( times_times @ TA @ B @ ( number_number_of @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_left__diff__distrib__number__of) ).
thf(449,plain,
! [TA: $tType] :
( ( ( number @ TA )
& ( ring @ TA ) )
=> ! [A: int,B: TA,C: TA] :
( ( times_times @ TA @ ( minus_minus @ TA @ C @ B ) @ ( number_number_of @ TA @ A ) )
= ( minus_minus @ TA @ ( times_times @ TA @ C @ ( number_number_of @ TA @ A ) ) @ ( times_times @ TA @ B @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(80,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) )
<=> ( ord_less @ int @ A @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_less__special_I4_J) ).
thf(379,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) )
=> ( ord_less @ int @ A @ ( bit1 @ pls ) ) )
& ( ( ord_less @ int @ A @ ( bit1 @ pls ) )
=> ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(96,axiom,
! [A: nat] :
( ( ord_less @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) )
<=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_zero__less__int__conv) ).
thf(440,plain,
! [A: nat] :
( ( ( ord_less @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
& ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(52,axiom,
! [A: int,B: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_rel__simps_I49_J) ).
thf(269,plain,
! [A: int,B: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(9,axiom,
ord_less_eq @ int @ ( minus_minus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ m1 ) @ ( zero_zero @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39__0961_A_L_Aint_An_A_N_Am1_A_060_061_A0_096) ).
thf(120,plain,
ord_less_eq @ int @ ( minus_minus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ m1 ) @ ( zero_zero @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(44,axiom,
~ ( ord_less @ int @ pls @ pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_rel__simps_I2_J) ).
thf(246,plain,
~ ( ord_less @ int @ pls @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(247,plain,
~ ( ord_less @ int @ pls @ pls ),
inference(polarity_switch,[status(thm)],[246]) ).
thf(16,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_less__eq__int__code_I16_J) ).
thf(142,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(18,axiom,
! [A: nat,B: int,C: int] :
( ( ord_less @ int @ C @ B )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ int @ ( times_times @ int @ ( semiring_1_of_nat @ int @ A ) @ C ) @ ( times_times @ int @ ( semiring_1_of_nat @ int @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_zmult__zless__mono2__lemma) ).
thf(153,plain,
! [A: nat,B: int,C: int] :
( ( ord_less @ int @ C @ B )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ int @ ( times_times @ int @ ( semiring_1_of_nat @ int @ A ) @ C ) @ ( times_times @ int @ ( semiring_1_of_nat @ int @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(24,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) )
<=> ( ord_less_eq @ int @ A @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_le__special_I4_J) ).
thf(174,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less_eq @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) )
=> ( ord_less_eq @ int @ A @ ( bit1 @ pls ) ) )
& ( ( ord_less_eq @ int @ A @ ( bit1 @ pls ) )
=> ( ord_less_eq @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(58,axiom,
! [A: int,B: int] :
( ( minus_minus @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
= ( bit1 @ ( minus_minus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_diff__bin__simps_I9_J) ).
thf(288,plain,
! [A: int,B: int] :
( ( minus_minus @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
= ( bit1 @ ( minus_minus @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(62,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) )
= ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_zadd__int) ).
thf(301,plain,
! [A: nat,B: nat] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) )
= ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(67,axiom,
! [A: int] :
( ( ord_less @ int @ ( bit1 @ A ) @ pls )
<=> ( ord_less @ int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_rel__simps_I12_J) ).
thf(320,plain,
! [A: int] :
( ( ( ord_less @ int @ ( bit1 @ A ) @ pls )
=> ( ord_less @ int @ A @ pls ) )
& ( ( ord_less @ int @ A @ pls )
=> ( ord_less @ int @ ( bit1 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(82,axiom,
ord_less_eq @ int @ ( minus_minus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) ) @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m1 ) ) @ ( zero_zero @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__0964_A_K_A_I1_A_L_Aint_An_J_A_N_A4_A_K_Am1_A_060_061_A0_096) ).
thf(389,plain,
ord_less_eq @ int @ ( minus_minus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) ) @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m1 ) ) @ ( zero_zero @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(12,axiom,
! [A: int] :
( ( ord_less @ int @ pls @ ( bit0 @ A ) )
<=> ( ord_less @ int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_rel__simps_I4_J) ).
thf(125,plain,
! [A: int] :
( ( ( ord_less @ int @ pls @ ( bit0 @ A ) )
=> ( ord_less @ int @ pls @ A ) )
& ( ( ord_less @ int @ pls @ A )
=> ( ord_less @ int @ pls @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(30,axiom,
ord_less_eq @ int @ ( one_one @ int ) @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_tpos) ).
thf(196,plain,
ord_less_eq @ int @ ( one_one @ int ) @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(29,axiom,
! [A: int] :
( ( ( bit0 @ A )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_rel__simps_I44_J) ).
thf(189,plain,
! [A: int] :
( ( ( ( bit0 @ A )
= pls )
=> ( A = pls ) )
& ( ( A = pls )
=> ( ( bit0 @ A )
= pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(56,axiom,
ord_less @ nat @ ( zero_zero @ nat ) @ n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_n0) ).
thf(284,plain,
ord_less @ nat @ ( zero_zero @ nat ) @ n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(68,axiom,
( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_int__0) ).
thf(325,plain,
( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(97,axiom,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_rel__simps_I39_J) ).
thf(445,plain,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(446,plain,
~ ? [A: int] :
( pls
= ( bit1 @ A ) ),
inference(miniscope,[status(thm)],[445]) ).
thf(447,plain,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
inference(cnf,[status(esa)],[446]) ).
thf(448,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(lifteq,[status(thm)],[447]) ).
thf(105,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(475,plain,
ring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(22,axiom,
! [A: int] :
( ( ord_less_eq @ int @ pls @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_rel__simps_I22_J) ).
thf(164,plain,
! [A: int] :
( ( ( ord_less_eq @ int @ pls @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ pls @ A ) )
& ( ( ord_less_eq @ int @ pls @ A )
=> ( ord_less_eq @ int @ pls @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(79,axiom,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
= ( bit1 @ ( plus_plus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_add__Bit0__Bit1) ).
thf(376,plain,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
= ( bit1 @ ( plus_plus @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(10,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int,B: int] :
( ( ord_less @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
<=> ( ord_less @ int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_less__number__of) ).
thf(121,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int,B: int] :
( ( ( ord_less @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(17,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_double__eq__0__iff) ).
thf(147,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(14,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_rel__simps_I17_J) ).
thf(132,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(65,axiom,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
= ( bit1 @ ( plus_plus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_add__Bit1__Bit0) ).
thf(312,plain,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
= ( bit1 @ ( plus_plus @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(5,axiom,
semiring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(116,plain,
semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(42,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_le__imp__0__less) ).
thf(243,plain,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(45,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_add__number__of__eq) ).
thf(248,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(6,axiom,
linorder @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(117,plain,
linorder @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(39,axiom,
ord_less @ int @ ( one_one @ int ) @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_t1) ).
thf(236,plain,
ord_less @ int @ ( one_one @ int ) @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(100,axiom,
~ ( ord_less @ int @ m1 @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096_126_Am1_A_060_A1_A_L_Aint_An_096) ).
thf(455,plain,
~ ( ord_less @ int @ m1 @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(456,plain,
~ ( ord_less @ int @ m1 @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) ),
inference(polarity_switch,[status(thm)],[455]) ).
thf(531,plain,
( ( ord_less @ int @ ( one_one @ int ) @ t )
!= ( ord_less @ int @ m1 @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) ) ),
inference(paramod_ordered,[status(thm)],[236,456]) ).
thf(534,plain,
( ( m1
!= ( one_one @ int ) )
| ( t
!= ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) ) ),
inference(simp,[status(thm)],[531]) ).
thf(38,axiom,
! [A: int] :
( ( number_number_of @ int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_number__of__is__id) ).
thf(233,plain,
! [A: int] :
( ( number_number_of @ int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(99,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) )
<=> ( ord_less @ int @ pls @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_less__special_I1_J) ).
thf(452,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) )
=> ( ord_less @ int @ pls @ A ) )
& ( ( ord_less @ int @ pls @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(75,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ B @ A )
<=> ? [C: nat] :
( A
= ( plus_plus @ int @ B @ ( semiring_1_of_nat @ int @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_zle__iff__zadd) ).
thf(349,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ B @ A )
=> ? [C: nat] :
( A
= ( plus_plus @ int @ B @ ( semiring_1_of_nat @ int @ C ) ) ) )
& ( ? [C: nat] :
( A
= ( plus_plus @ int @ B @ ( semiring_1_of_nat @ int @ C ) ) )
=> ( ord_less_eq @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(20,axiom,
number_ring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(160,plain,
number_ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(92,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_less__eq__number__of__int__code) ).
thf(424,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(93,axiom,
! [A: int,B: int] :
( ( minus_minus @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
= ( bit0 @ ( minus_minus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_diff__bin__simps_I7_J) ).
thf(429,plain,
! [A: int,B: int] :
( ( minus_minus @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
= ( bit0 @ ( minus_minus @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(15,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( one_one @ int ) @ A )
<=> ( ord_less @ int @ ( zero_zero @ int ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_int__one__le__iff__zero__less) ).
thf(137,plain,
! [A: int] :
( ( ( ord_less_eq @ int @ ( one_one @ int ) @ A )
=> ( ord_less @ int @ ( zero_zero @ int ) @ A ) )
& ( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less_eq @ int @ ( one_one @ int ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(108,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( bit0 @ A ) @ pls )
<=> ( ord_less_eq @ int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_rel__simps_I27_J) ).
thf(484,plain,
! [A: int] :
( ( ( ord_less_eq @ int @ ( bit0 @ A ) @ pls )
=> ( ord_less_eq @ int @ A @ pls ) )
& ( ( ord_less_eq @ int @ A @ pls )
=> ( ord_less_eq @ int @ ( bit0 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(31,axiom,
! [A: int,B: int] :
( ( ( bit1 @ B )
= ( bit1 @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_rel__simps_I51_J) ).
thf(197,plain,
! [A: int,B: int] :
( ( ( ( bit1 @ B )
= ( bit1 @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( bit1 @ B )
= ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(95,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_less__eq__int__code_I14_J) ).
thf(435,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(190,plain,
( ! [A: int] :
( ( ( bit0 @ A )
= pls )
=> ( A = pls ) )
& ! [A: int] :
( ( A = pls )
=> ( ( bit0 @ A )
= pls ) ) ),
inference(miniscope,[status(thm)],[189]) ).
thf(191,plain,
! [A: int] :
( ( A != pls )
| ( ( bit0 @ A )
= pls ) ),
inference(cnf,[status(esa)],[190]) ).
thf(193,plain,
! [A: int] :
( ( A != pls )
| ( ( bit0 @ A )
= pls ) ),
inference(lifteq,[status(thm)],[191]) ).
thf(194,plain,
( ( bit0 @ pls )
= pls ),
inference(simp,[status(thm)],[193]) ).
thf(1,conjecture,
ord_less @ int @ ( times_times @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( minus_minus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) ) @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m1 ) ) ) @ ( times_times @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less @ int @ ( times_times @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( minus_minus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) ) @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m1 ) ) ) @ ( times_times @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( zero_zero @ int ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(113,plain,
~ ( ord_less @ int @ ( times_times @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( minus_minus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) ) @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m1 ) ) ) @ ( times_times @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(514,plain,
( ~ ( ord_less @ int @ ( times_times @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( minus_minus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) ) @ ( times_times @ int @ ( number_number_of @ int @ pls ) @ m1 ) ) ) @ ( times_times @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( zero_zero @ int ) ) )
| ( ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) )
!= ( bit0 @ pls ) ) ),
inference(paramod_ordered,[status(thm)],[194,113]) ).
thf(522,plain,
( ~ ( ord_less @ int @ ( times_times @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( minus_minus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) ) @ ( times_times @ int @ ( number_number_of @ int @ pls ) @ m1 ) ) ) @ ( times_times @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( zero_zero @ int ) ) )
| ( ( bit0 @ ( bit1 @ pls ) )
!= pls ) ),
inference(simp,[status(thm)],[514]) ).
thf(110,axiom,
! [A: int] :
( ( minus_minus @ int @ pls @ ( bit0 @ A ) )
= ( bit0 @ ( minus_minus @ int @ pls @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_diff__bin__simps_I3_J) ).
thf(493,plain,
! [A: int] :
( ( minus_minus @ int @ pls @ ( bit0 @ A ) )
= ( bit0 @ ( minus_minus @ int @ pls @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(57,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA,B: int,C: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ C ) @ ( times_times @ TA @ ( number_number_of @ TA @ B ) @ A ) )
= ( times_times @ TA @ ( number_number_of @ TA @ ( times_times @ int @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_mult__number__of__left) ).
thf(285,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA,B: int,C: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ C ) @ ( times_times @ TA @ ( number_number_of @ TA @ B ) @ A ) )
= ( times_times @ TA @ ( number_number_of @ TA @ ( times_times @ int @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(87,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_rel__simps_I16_J) ).
thf(403,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( bit1 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(76,axiom,
! [A: int,B: int] :
( ( ( bit0 @ B )
= ( bit0 @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_rel__simps_I48_J) ).
thf(356,plain,
! [A: int,B: int] :
( ( ( ( bit0 @ B )
= ( bit0 @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( bit0 @ B )
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(23,axiom,
! [A: int] :
( ( ord_less @ int @ ( bit0 @ A ) @ pls )
<=> ( ord_less @ int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_rel__simps_I10_J) ).
thf(169,plain,
! [A: int] :
( ( ( ord_less @ int @ ( bit0 @ A ) @ pls )
=> ( ord_less @ int @ A @ pls ) )
& ( ( ord_less @ int @ A @ pls )
=> ( ord_less @ int @ ( bit0 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(90,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ ( bit1 @ pls ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_numeral__1__eq__1) ).
thf(420,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ ( bit1 @ pls ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(112,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( ring_char_0 @ TA ) )
=> ! [A: int,B: int] :
( ( ( number_number_of @ TA @ B )
= ( number_number_of @ TA @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_eq__number__of) ).
thf(499,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( ring_char_0 @ TA ) )
=> ! [A: int,B: int] :
( ( ( ( number_number_of @ TA @ B )
= ( number_number_of @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( number_number_of @ TA @ B )
= ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(70,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_rel__simps_I34_J) ).
thf(328,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(11,axiom,
number @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(124,plain,
number @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(106,axiom,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_int__int__eq) ).
thf(476,plain,
! [A: nat,B: nat] :
( ( ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(109,axiom,
! [A: int] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_rel__simps_I46_J) ).
thf(489,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(84,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_rel__simps_I31_J) ).
thf(393,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(101,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( bit1 @ A ) @ pls )
<=> ( ord_less @ int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_rel__simps_I29_J) ).
thf(457,plain,
! [A: int] :
( ( ( ord_less_eq @ int @ ( bit1 @ A ) @ pls )
=> ( ord_less @ int @ A @ pls ) )
& ( ( ord_less @ int @ A @ pls )
=> ( ord_less_eq @ int @ ( bit1 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(78,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_rel__simps_I32_J) ).
thf(371,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(40,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA,B: int,C: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ C ) @ ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ A ) )
= ( plus_plus @ TA @ ( number_number_of @ TA @ ( plus_plus @ int @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_add__number__of__left) ).
thf(237,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA,B: int,C: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ C ) @ ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ A ) )
= ( plus_plus @ TA @ ( number_number_of @ TA @ ( plus_plus @ int @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(32,axiom,
! [A: int] :
( ( ord_less @ int @ pls @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_rel__simps_I5_J) ).
thf(205,plain,
! [A: int] :
( ( ( ord_less @ int @ pls @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ pls @ A ) )
& ( ( ord_less_eq @ int @ pls @ A )
=> ( ord_less @ int @ pls @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(85,axiom,
! [A: nat] : ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_zero__zle__int) ).
thf(398,plain,
! [A: nat] : ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(51,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ B @ ( plus_plus @ int @ A @ ( one_one @ int ) ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_zle__add1__eq__le) ).
thf(264,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ B @ ( plus_plus @ int @ A @ ( one_one @ int ) ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less @ int @ B @ ( plus_plus @ int @ A @ ( one_one @ int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(21,axiom,
! [TA: $tType] :
( ( ( number @ TA )
& ( semiring @ TA ) )
=> ! [A: int,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ C @ B ) @ ( number_number_of @ TA @ A ) )
= ( plus_plus @ TA @ ( times_times @ TA @ C @ ( number_number_of @ TA @ A ) ) @ ( times_times @ TA @ B @ ( number_number_of @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_left__distrib__number__of) ).
thf(161,plain,
! [TA: $tType] :
( ( ( number @ TA )
& ( semiring @ TA ) )
=> ! [A: int,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ C @ B ) @ ( number_number_of @ TA @ A ) )
= ( plus_plus @ TA @ ( times_times @ TA @ C @ ( number_number_of @ TA @ A ) ) @ ( times_times @ TA @ B @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(55,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_less__eq__int__code_I13_J) ).
thf(279,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(26,axiom,
! [TA: $tType] :
( ( ( number @ TA )
& ( semiring @ TA ) )
=> ! [A: TA,B: TA,C: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ C ) @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( times_times @ TA @ ( number_number_of @ TA @ C ) @ B ) @ ( times_times @ TA @ ( number_number_of @ TA @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_right__distrib__number__of) ).
thf(180,plain,
! [TA: $tType] :
( ( ( number @ TA )
& ( semiring @ TA ) )
=> ! [A: TA,B: TA,C: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ C ) @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( times_times @ TA @ ( number_number_of @ TA @ C ) @ B ) @ ( times_times @ TA @ ( number_number_of @ TA @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(61,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_rel__simps_I15_J) ).
thf(296,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less @ int @ ( bit0 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(91,axiom,
semiring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(423,plain,
semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(59,axiom,
! [TA: $tType] :
( ( ( number @ TA )
& ( linorder @ TA ) )
=> ! [A: int,B: int] :
( ( ord_less_eq @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
<=> ~ ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( number_number_of @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_le__number__of__eq__not__less) ).
thf(291,plain,
! [TA: $tType] :
( ( ( number @ TA )
& ( linorder @ TA ) )
=> ! [A: int,B: int] :
( ( ( ord_less_eq @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
=> ~ ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( number_number_of @ TA @ B ) ) )
& ( ~ ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( number_number_of @ TA @ B ) )
=> ( ord_less_eq @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(7,axiom,
ord_less @ int @ ( minus_minus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) ) @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m1 ) ) @ ( zero_zero @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__0962_A_K_A_I1_A_L_Aint_An_J_A_N_A4_A_K_Am1_A_060_A0_096) ).
thf(118,plain,
ord_less @ int @ ( minus_minus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) ) @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m1 ) ) @ ( zero_zero @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(50,axiom,
! [A: int] :
( ( ord_less_eq @ int @ pls @ ( bit0 @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_rel__simps_I21_J) ).
thf(259,plain,
! [A: int] :
( ( ( ord_less_eq @ int @ pls @ ( bit0 @ A ) )
=> ( ord_less_eq @ int @ pls @ A ) )
& ( ( ord_less_eq @ int @ pls @ A )
=> ( ord_less_eq @ int @ pls @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(89,axiom,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_rel__simps_I38_J) ).
thf(413,plain,
! [A: int] :
( ( ( pls
= ( bit0 @ A ) )
=> ( pls = A ) )
& ( ( pls = A )
=> ( pls
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(81,axiom,
! [A: nat] :
( ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ A ) @ ( zero_zero @ int ) )
<=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_int__le__0__conv) ).
thf(382,plain,
! [A: nat] :
( ( ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ A ) @ ( zero_zero @ int ) )
=> ( A
= ( zero_zero @ nat ) ) )
& ( ( A
= ( zero_zero @ nat ) )
=> ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ A ) @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(43,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(245,plain,
linordered_idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(506,plain,
( ( ord_less @ int @ ( times_times @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( minus_minus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) ) @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m1 ) ) ) @ ( times_times @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( zero_zero @ int ) ) )
!= ( ord_less @ int @ ( minus_minus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) ) @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m1 ) ) @ ( zero_zero @ int ) ) ),
inference(paramod_ordered,[status(thm)],[118,113]) ).
thf(509,plain,
( ( ( times_times @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( minus_minus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) ) @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m1 ) ) )
!= ( minus_minus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) ) @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m1 ) ) )
| ( ( times_times @ int @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ) @ ( zero_zero @ int ) )
!= ( zero_zero @ int ) ) ),
inference(simp,[status(thm)],[506]) ).
thf(122,plain,
! [TA: $tType,B: int,A: int] :
( ~ ( number_ring @ TA )
| ~ ( linordered_idom @ TA )
| ~ ( ord_less @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
| ( ord_less @ int @ B @ A ) ),
inference(cnf,[status(esa)],[121]) ).
thf(548,plain,
! [TA: $tType,B: int,A: int] :
( ~ ( number_ring @ TA )
| ~ ( linordered_idom @ TA )
| ~ ( ord_less @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
| ( ( ord_less @ int @ B @ A )
!= ( ord_less @ int @ pls @ pls ) ) ),
inference(paramod_ordered,[status(thm)],[122,247]) ).
thf(549,plain,
! [TA: $tType] :
( ~ ( number_ring @ TA )
| ~ ( linordered_idom @ TA )
| ~ ( ord_less @ TA @ ( number_number_of @ TA @ pls ) @ ( number_number_of @ TA @ pls ) ) ),
inference(pattern_uni,[status(thm)],[548:[bind(A,$thf( pls )),bind(B,$thf( pls ))]]) ).
thf(621,plain,
! [TA: $tType] :
( ~ ( linordered_idom @ TA )
| ~ ( ord_less @ TA @ ( number_number_of @ TA @ pls ) @ ( number_number_of @ TA @ pls ) )
| ( ( number_ring @ int )
!= ( number_ring @ TA ) ) ),
inference(paramod_ordered,[status(thm)],[160,549]) ).
thf(622,plain,
( ~ ( linordered_idom @ int )
| ~ ( ord_less @ int @ ( number_number_of @ int @ pls ) @ ( number_number_of @ int @ pls ) ) ),
inference(pattern_uni,[status(thm)],[621:[bind_type(TA,$thf( int ))]]) ).
thf(630,plain,
( ~ $true
| ~ ( ord_less @ int @ ( number_number_of @ int @ pls ) @ ( number_number_of @ int @ pls ) ) ),
inference(rewrite,[status(thm)],[622,245]) ).
thf(631,plain,
~ ( ord_less @ int @ ( number_number_of @ int @ pls ) @ ( number_number_of @ int @ pls ) ),
inference(simp,[status(thm)],[630]) ).
thf(532,plain,
( ( ord_less @ int @ ( one_one @ int ) @ t )
!= ( ord_less @ int @ pls @ pls ) ),
inference(paramod_ordered,[status(thm)],[236,247]) ).
thf(535,plain,
( ( pls
!= ( one_one @ int ) )
| ( t != pls ) ),
inference(simp,[status(thm)],[532]) ).
thf(107,axiom,
ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
thf(483,plain,
ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ ( semiring_1_of_nat @ int @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(19,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ B @ ( minus_minus @ int @ A @ ( one_one @ int ) ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_zle__diff1__eq) ).
thf(155,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ B @ ( minus_minus @ int @ A @ ( one_one @ int ) ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less_eq @ int @ B @ ( minus_minus @ int @ A @ ( one_one @ int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(102,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( number_number_of @ TA @ A ) @ ( zero_zero @ TA ) )
<=> ( ord_less_eq @ int @ A @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_le__special_I3_J) ).
thf(462,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less_eq @ TA @ ( number_number_of @ TA @ A ) @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ int @ A @ pls ) )
& ( ( ord_less_eq @ int @ A @ pls )
=> ( ord_less_eq @ TA @ ( number_number_of @ TA @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(41,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_number__of__Pls) ).
thf(240,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(46,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int,B: int] :
( ( ord_less_eq @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_le__number__of) ).
thf(251,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int,B: int] :
( ( ( ord_less_eq @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(13,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ B @ A )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ B @ ( one_one @ int ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_zless__imp__add1__zle) ).
thf(130,plain,
! [A: int,B: int] :
( ( ord_less @ int @ B @ A )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ B @ ( one_one @ int ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(48,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( times_times @ int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_arith__simps_I32_J) ).
thf(255,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( times_times @ int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(123,plain,
! [TA: $tType,B: int,A: int] :
( ~ ( number_ring @ TA )
| ~ ( linordered_idom @ TA )
| ~ ( ord_less @ int @ B @ A )
| ( ord_less @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ),
inference(cnf,[status(esa)],[121]) ).
thf(60,axiom,
( ( semiring_1_of_nat @ int @ ( one_one @ nat ) )
= ( one_one @ int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_int__1) ).
thf(294,plain,
( ( semiring_1_of_nat @ int @ ( one_one @ nat ) )
= ( one_one @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(295,plain,
( ( semiring_1_of_nat @ int @ ( one_one @ nat ) )
= ( one_one @ int ) ),
inference(lifteq,[status(thm)],[294]) ).
thf(69,axiom,
ring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(327,plain,
ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(35,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ B @ A )
<=> ( ( ord_less_eq @ int @ B @ A )
& ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_less__int__def) ).
thf(218,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ B @ A )
=> ( ( ord_less_eq @ int @ B @ A )
& ( B != A ) ) )
& ( ( ( ord_less_eq @ int @ B @ A )
& ( B != A ) )
=> ( ord_less @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(103,axiom,
! [A: int,B: int] :
( ( times_times @ int @ ( bit0 @ B ) @ A )
= ( bit0 @ ( times_times @ int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_mult__Bit0) ).
thf(465,plain,
! [A: int,B: int] :
( ( times_times @ int @ ( bit0 @ B ) @ A )
= ( bit0 @ ( times_times @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(37,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_Bit0__Pls) ).
thf(231,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(63,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_less__eq__int__code_I15_J) ).
thf(304,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(49,axiom,
ord_less_eq @ int @ pls @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_rel__simps_I19_J) ).
thf(258,plain,
ord_less_eq @ int @ pls @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(83,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
<=> ( ord_less_eq @ int @ ( bit1 @ pls ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_le__special_I2_J) ).
thf(390,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
=> ( ord_less_eq @ int @ ( bit1 @ pls ) @ A ) )
& ( ( ord_less_eq @ int @ ( bit1 @ pls ) @ A )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(28,axiom,
! [TA: $tType] :
( ( ( number @ TA )
& ( ring @ TA ) )
=> ! [A: TA,B: TA,C: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ C ) @ ( minus_minus @ TA @ B @ A ) )
= ( minus_minus @ TA @ ( times_times @ TA @ ( number_number_of @ TA @ C ) @ B ) @ ( times_times @ TA @ ( number_number_of @ TA @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_right__diff__distrib__number__of) ).
thf(186,plain,
! [TA: $tType] :
( ( ( number @ TA )
& ( ring @ TA ) )
=> ! [A: TA,B: TA,C: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ C ) @ ( minus_minus @ TA @ B @ A ) )
= ( minus_minus @ TA @ ( times_times @ TA @ ( number_number_of @ TA @ C ) @ B ) @ ( times_times @ TA @ ( number_number_of @ TA @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(3,axiom,
linorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(114,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(119,plain,
linord219039673up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(383,plain,
( ! [A: nat] :
( ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ A ) @ ( zero_zero @ int ) )
=> ( A
= ( zero_zero @ nat ) ) )
& ! [A: nat] :
( ( A
= ( zero_zero @ nat ) )
=> ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ A ) @ ( zero_zero @ int ) ) ) ),
inference(miniscope,[status(thm)],[382]) ).
thf(384,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
| ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ A ) @ ( zero_zero @ int ) ) ),
inference(cnf,[status(esa)],[383]) ).
thf(386,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
| ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ A ) @ ( zero_zero @ int ) ) ),
inference(lifteq,[status(thm)],[384]) ).
thf(387,plain,
ord_less_eq @ int @ ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) ) @ ( zero_zero @ int ),
inference(simp,[status(thm)],[386]) ).
thf(326,plain,
( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
= ( zero_zero @ int ) ),
inference(lifteq,[status(thm)],[325]) ).
thf(667,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ),
inference(rewrite,[status(thm)],[387,326]) ).
thf(74,axiom,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
= ( bit0 @ ( plus_plus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_add__Bit0__Bit0) ).
thf(346,plain,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
= ( bit0 @ ( plus_plus @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(66,axiom,
! [A: nat,B: nat] :
( ( ord_less @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) )
<=> ( ord_less @ nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_zless__int) ).
thf(315,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) )
=> ( ord_less @ nat @ B @ A ) )
& ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ int @ ( semiring_1_of_nat @ int @ B ) @ ( semiring_1_of_nat @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(94,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_le__special_I1_J) ).
thf(432,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) )
=> ( ord_less_eq @ int @ pls @ A ) )
& ( ( ord_less_eq @ int @ pls @ A )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(27,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( plus_plus @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ ( bit1 @ pls ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_add__special_I2_J) ).
thf(183,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( plus_plus @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ ( bit1 @ pls ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(53,axiom,
! [A: int,B: nat,C: nat] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ C ) @ ( plus_plus @ int @ ( semiring_1_of_nat @ int @ B ) @ A ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ C @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_zadd__int__left) ).
thf(273,plain,
! [A: int,B: nat,C: nat] :
( ( plus_plus @ int @ ( semiring_1_of_nat @ int @ C ) @ ( plus_plus @ int @ ( semiring_1_of_nat @ int @ B ) @ A ) )
= ( plus_plus @ int @ ( semiring_1_of_nat @ int @ ( plus_plus @ nat @ C @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(33,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_less__int__code_I14_J) ).
thf(210,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less @ int @ ( bit0 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(73,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_rel__simps_I33_J) ).
thf(341,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(86,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_one__add__one__is__two) ).
thf(400,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(64,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
<=> ( ord_less @ int @ ( bit1 @ pls ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_less__special_I2_J) ).
thf(309,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
=> ( ord_less @ int @ ( bit1 @ pls ) @ A ) )
& ( ( ord_less @ int @ ( bit1 @ pls ) @ A )
=> ( ord_less @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(34,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ A @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_add__special_I3_J) ).
thf(215,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ A @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(111,axiom,
! [A: int,B: int] :
( ( times_times @ int @ ( bit1 @ B ) @ A )
= ( plus_plus @ int @ ( bit0 @ ( times_times @ int @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_mult__Bit1) ).
thf(496,plain,
! [A: int,B: int] :
( ( times_times @ int @ ( bit1 @ B ) @ A )
= ( plus_plus @ int @ ( bit0 @ ( times_times @ int @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(77,axiom,
! [TA: $tType] :
( ( number @ TA )
=> ! [A: TA,B: int] :
( ( ( number_number_of @ TA @ B )
= A )
<=> ( A
= ( number_number_of @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_number__of__reorient) ).
thf(364,plain,
! [TA: $tType] :
( ( number @ TA )
=> ! [A: TA,B: int] :
( ( ( ( number_number_of @ TA @ B )
= A )
=> ( A
= ( number_number_of @ TA @ B ) ) )
& ( ( A
= ( number_number_of @ TA @ B ) )
=> ( ( number_number_of @ TA @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(47,axiom,
linorder @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(254,plain,
linorder @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(36,axiom,
! [A: int,B: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_rel__simps_I50_J) ).
thf(227,plain,
! [A: int,B: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(3941,plain,
$false,
inference(e,[status(thm)],[177,336,333,468,408,115,276,449,379,440,269,120,247,142,153,174,288,301,320,389,125,196,189,284,325,448,475,164,376,121,147,132,312,116,243,248,117,534,233,452,349,160,424,429,137,484,197,435,522,493,456,285,403,356,169,420,499,328,124,476,489,393,457,371,237,205,398,264,161,279,180,296,423,291,118,259,413,445,382,236,113,245,509,631,535,483,155,462,240,251,130,455,255,123,194,295,327,218,465,231,304,258,390,186,114,119,246,667,346,549,315,432,183,273,210,326,294,341,400,122,309,215,496,364,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM992_5 : TPTP v8.1.2. Released v6.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n023.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 17:06:15 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.85/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.30/1.00 % [INFO] Parsing done (177ms).
% 1.30/1.01 % [INFO] Running in sequential loop mode.
% 1.95/1.20 % [INFO] eprover registered as external prover.
% 1.95/1.20 % [INFO] cvc4 registered as external prover.
% 1.95/1.20 % [INFO] Scanning for conjecture ...
% 2.03/1.29 % [INFO] Found a conjecture and 112 axioms. Running axiom selection ...
% 2.21/1.36 % [INFO] Axiom selection finished. Selected 110 axioms (removed 2 axioms).
% 2.48/1.46 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.79/1.47 % [INFO] Type checking passed.
% 2.79/1.48 % [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 ...
% 26.21/5.68 % External prover 'e' found a proof!
% 26.21/5.68 % [INFO] Killing All external provers ...
% 26.21/5.68 % Time passed: 5179ms (effective reasoning time: 4671ms)
% 26.21/5.68 % 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)>
% 26.21/5.69 % Axioms used in derivation (110): fact_37_add__Bit0__Bit0, fact_86_int__1, fact_17_tpos, fact_79_le__number__of__eq__not__less, fact_82_zadd__int__left, fact_36_mult__Bit0, fact_13_numeral__1__eq__1, fact_9_less__special_I1_J, fact_35_mult__Pls, fact_39__0961_A_L_Aint_An_A_N_Am1_A_060_061_A0_096, arity_Int_Oint___Rings_Olinordered__idom, arity_Int_Oint___Int_Oring__char__0, fact_28_Bit0__Pls, fact_5_add__special_I3_J, fact_43_left__diff__distrib__number__of, fact_20_rel__simps_I48_J, fact_41_right__distrib__number__of, fact_63_rel__simps_I5_J, fact_97_int__int__eq, fact_76_int__le__0__conv, fact_93_add1__zle__eq, fact_65_rel__simps_I15_J, fact_14_diff__bin__simps_I3_J, fact_64_rel__simps_I33_J, fact_46_le__number__of, fact_34_rel__simps_I31_J, fact_92_zless__imp__add1__zle, fact_70_le__special_I4_J, arity_Int_Oint___Rings_Oring, fact_42_number__of__Pls, fact_2__096_126_Am1_A_060_A1_A_L_Aint_An_096, fact_55_rel__simps_I22_J, fact_6_less__special_I2_J, fact_57_rel__simps_I27_J, fact_80_less__eq__int__code_I14_J, arity_Int_Oint___Int_Onumber__ring, fact_11__0964_A_K_A_I1_A_L_Aint_An_J_A_N_A4_A_K_Am1_A_060_061_A0_096, fact_30_rel__simps_I2_J, fact_16_n0, arity_HOL_Obool___Orderings_Olinorder, fact_33_rel__simps_I19_J, fact_77_zero__less__int__conv, fact_96_number__of__is__id, fact_74_less__int__def, fact_91_int__one__le__iff__zero__less, fact_60_add__Bit0__Bit1, fact_18_eq__number__of, fact_78_zmult__zless__mono2__lemma, fact_54_rel__simps_I4_J, fact_1_t1, fact_44_right__diff__distrib__number__of, fact_25_rel__simps_I49_J, fact_27_rel__simps_I38_J, fact_75_less__eq__number__of__int__code, arity_Nat_Onat___Orderings_Olinorder, fact_4_add__special_I2_J, fact_85_zle__iff__zadd, fact_87_int__eq__0__conv, fact_49_add__number__of__left, fact_84_zless__int, fact_19_rel__simps_I51_J, fact_66_zle__add1__eq__le, fact_52_rel__simps_I16_J, fact_23_rel__simps_I39_J, fact_32_rel__simps_I34_J, arity_Int_Oint___Orderings_Olinorder, fact_72_less__eq__int__code_I16_J, fact_61_diff__bin__simps_I10_J, fact_73_less__eq__int__code_I13_J, fact_88_int__0, fact_94_le__imp__0__less, fact_68_le__special_I3_J, arity_Int_Oint___Rings_Osemiring, fact_71_le__special_I2_J, fact_58_rel__simps_I21_J, fact_51_rel__simps_I12_J, fact_56_rel__simps_I32_J, fact_45_less__number__of, fact_81_zero__zle__int, fact_29_rel__simps_I17_J, fact_8_one__add__one__is__two, fact_95_number__of__reorient, arity_Nat_Onat___Int_Onumber, fact_31_rel__simps_I14_J, fact_47_mult__number__of__left, fact_50_add__number__of__eq, fact_7_less__special_I4_J, fact_59_add__Bit1__Bit0, arity_Nat_Onat___Rings_Osemiring, fact_22_rel__simps_I46_J, fact_62_rel__simps_I29_J, fact_48_arith__simps_I32_J, fact_12_mult__Bit1, fact_83_zadd__int, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Groups_Olinordered__ab__group__add, fact_3__0962_A_K_A_I1_A_L_Aint_An_J_A_N_A4_A_K_Am1_A_060_A0_096, fact_90_less__int__code_I14_J, fact_0_n1pos, fact_38_diff__bin__simps_I7_J, fact_24_rel__simps_I50_J, fact_53_rel__simps_I10_J, fact_21_double__eq__0__iff, fact_26_rel__simps_I44_J, fact_89_less__eq__int__code_I15_J, fact_67_zle__diff1__eq, fact_10_less__special_I3_J, fact_15_diff__bin__simps_I9_J, fact_40_left__distrib__number__of, fact_69_le__special_I1_J
% 26.21/5.69 % No. of inferences in proof: 256
% 26.21/5.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5179 ms resp. 4671 ms w/o parsing
% 26.21/5.75 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 26.21/5.75 % [INFO] Killing All external provers ...
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