%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP063^1 : TPTP v9.3.1. Released v7.5.0.
% 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 : n017.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 : Wed Sep 30 08:06:37 AM UTC 2026
% Result : Theorem 266.48s 71.55s
% Output : Refutation 263.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 340
% Syntax : Number of formulae : 1009 ( 586 unt; 0 typ; 2 def)
% Number of atoms : 2270 (1489 equ; 4 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 7186 ( 444 ~; 303 |; 55 &;6021 @)
% ( 0 <=>; 363 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 28 usr; 16 con; 0-4 aty)
% Number of variables : 1963 ( 74 ^;1873 !; 14 ?;1963 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(real_type,type,
real: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(genClo1161277105lle_PC_decl,type,
genClo1161277105lle_PC: nat > real > real ).
thf(genClo1278781456e_beta_decl,type,
genClo1278781456e_beta: real ).
thf(genClo872980712lle_mu_decl,type,
genClo872980712lle_mu: real ).
thf(genClo1144207539le_rho_decl,type,
genClo1144207539le_rho: real ).
thf(genClo1015804716orrect_decl,type,
genClo1015804716orrect: nat > real > $o ).
thf(genClo293725282kRead2_decl,type,
genClo293725282kRead2: ( nat > real ) > ( nat > real ) > real > ( nat > $o ) > $o ).
thf(genClo1650508560e_rmax_decl,type,
genClo1650508560e_rmax: real ).
thf(genClo1651033342e_rmin_decl,type,
genClo1651033342e_rmin: real ).
thf(genClo1163638703lle_te_decl,type,
genClo1163638703lle_te: nat > nat > real ).
thf(abs_abs_real_decl,type,
abs_abs_real: real > real ).
thf(minus_minus_nat_decl,type,
minus_minus_nat: nat > nat > nat ).
thf(minus_minus_real_decl,type,
minus_minus_real: real > real > real ).
thf(one_one_nat_decl,type,
one_one_nat: nat ).
thf(one_one_real_decl,type,
one_one_real: real ).
thf(plus_plus_nat_decl,type,
plus_plus_nat: nat > nat > nat ).
thf(plus_plus_real_decl,type,
plus_plus_real: real > real > real ).
thf(times_times_nat_decl,type,
times_times_nat: nat > nat > nat ).
thf(times_times_real_decl,type,
times_times_real: real > real > real ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(zero_zero_real_decl,type,
zero_zero_real: real ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ord_less_eq_real_decl,type,
ord_less_eq_real: real > real > $o ).
thf(i_decl,type,
i: nat ).
thf(l_decl,type,
l: nat ).
thf(p_decl,type,
p: nat ).
thf(q_decl,type,
q: nat ).
thf(sk1_decl,type,
sk1: real > real > real ).
thf(sk2_decl,type,
sk2: real > real > real ).
thf(sk1_def,definition,
( sk1
= ( @+[A: real > real > real] :
! [B: real,C: real] :
( ( A @ B @ ( plus_plus_real @ B @ C ) )
= C ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: real > real > real] :
! [B: real,C: real] :
( ( A @ C @ ( plus_plus_real @ B @ C ) )
= B ) ) ) ).
thf(229,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( plus_plus_nat @ B @ C ) )
=> ( ( plus_plus_nat @ D @ A )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_group__cancel_Oadd2) ).
thf(1036,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( plus_plus_nat @ B @ C ) )
=> ( ( plus_plus_nat @ D @ A )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(151,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_add__is__0) ).
thf(809,plain,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(89,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(629,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(11,axiom,
! [A: real,B: real] :
( ( A
= ( times_times_real @ B @ A ) )
= ( ( A = zero_zero_real )
| ( B = one_one_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_mult__cancel__right1) ).
thf(365,plain,
! [A: real,B: real] :
( ( A
= ( times_times_real @ B @ A ) )
= ( ( A = zero_zero_real )
| ( B = one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(235,axiom,
! [A: nat] :
( ( genClo1163638703lle_te @ A @ zero_zero_nat )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_synch0) ).
thf(1056,plain,
! [A: nat] :
( ( genClo1163638703lle_te @ A @ zero_zero_nat )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(1057,plain,
! [A: nat] :
( ( genClo1163638703lle_te @ A @ zero_zero_nat )
= zero_zero_real ),
inference(cnf,[status(esa)],[1056]) ).
thf(1058,plain,
! [A: nat] :
( ( genClo1163638703lle_te @ A @ zero_zero_nat )
= zero_zero_real ),
inference(lifteq,[status(thm)],[1057]) ).
thf(1,conjecture,
ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) @ genClo1278781456e_beta,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) @ genClo1278781456e_beta ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(340,plain,
~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) @ genClo1278781456e_beta ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(2194,plain,
! [A: nat] :
( ~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ zero_zero_real ) ) @ genClo1278781456e_beta )
| ( ( genClo1163638703lle_te @ A @ zero_zero_nat )
!= ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[1058,340]) ).
thf(2253,plain,
! [A: nat] :
( ~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ zero_zero_real ) ) @ genClo1278781456e_beta )
| ( A != q )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat ) ),
inference(simp,[status(thm)],[2194]) ).
thf(2272,plain,
( ~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ zero_zero_real ) ) @ genClo1278781456e_beta )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat ) ),
inference(simp,[status(thm)],[2253]) ).
thf(179,axiom,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_diff__zero) ).
thf(889,plain,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(890,plain,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
inference(cnf,[status(esa)],[889]) ).
thf(891,plain,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
inference(lifteq,[status(thm)],[890]) ).
thf(3399,plain,
( ~ ( ord_less_eq_real @ ( abs_abs_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) ) @ genClo1278781456e_beta )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat ) ),
inference(rewrite,[status(thm)],[2272,891]) ).
thf(5,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_distrib__left) ).
thf(347,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(163,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_add_Oleft__commute) ).
thf(846,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(227,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_le__add1) ).
thf(1031,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(180,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_add_Oleft__neutral) ).
thf(892,plain,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(893,plain,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(cnf,[status(esa)],[892]) ).
thf(894,plain,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(lifteq,[status(thm)],[893]) ).
thf(198,axiom,
ord_less_eq_real @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_ie) ).
thf(944,plain,
ord_less_eq_real @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(157,axiom,
~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_not__one__le__zero) ).
thf(830,plain,
~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(831,plain,
~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ),
inference(polarity_switch,[status(thm)],[830]) ).
thf(2629,plain,
( ~ $true
| ( ( ord_less_eq_real @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) )
!= ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ) ),
inference(paramod_ordered,[status(thm)],[944,831]) ).
thf(2630,plain,
( ( ord_less_eq_real @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) )
!= ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ),
inference(simp,[status(thm)],[2629]) ).
thf(2643,plain,
( ( ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real )
| ( ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) )
!= zero_zero_real ) ),
inference(simp,[status(thm)],[2630]) ).
thf(3481,plain,
! [A: nat] :
( ( ( genClo1163638703lle_te @ q @ A )
!= one_one_real )
| ( ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) )
!= zero_zero_real )
| ( ( plus_plus_nat @ zero_zero_nat @ A )
!= ( plus_plus_nat @ i @ one_one_nat ) ) ),
inference(paramod_ordered,[status(thm)],[894,2643]) ).
thf(3509,plain,
! [A: nat] :
( ( ( genClo1163638703lle_te @ q @ A )
!= one_one_real )
| ( ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) )
!= zero_zero_real )
| ( i != zero_zero_nat )
| ( A != one_one_nat ) ),
inference(simp,[status(thm)],[3481]) ).
thf(3561,plain,
( ( ( genClo1163638703lle_te @ q @ one_one_nat )
!= one_one_real )
| ( ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) )
!= zero_zero_real )
| ( i != zero_zero_nat ) ),
inference(simp,[status(thm)],[3509]) ).
thf(7785,plain,
! [A: nat] :
( ( ( genClo1163638703lle_te @ q @ one_one_nat )
!= one_one_real )
| ( ( genClo1163638703lle_te @ p @ A )
!= zero_zero_real )
| ( i != zero_zero_nat )
| ( ( plus_plus_nat @ zero_zero_nat @ A )
!= ( plus_plus_nat @ i @ one_one_nat ) ) ),
inference(paramod_ordered,[status(thm)],[894,3561]) ).
thf(7789,plain,
! [A: nat] :
( ( ( genClo1163638703lle_te @ q @ one_one_nat )
!= one_one_real )
| ( ( genClo1163638703lle_te @ p @ A )
!= zero_zero_real )
| ( i != zero_zero_nat )
| ( i != zero_zero_nat )
| ( A != one_one_nat ) ),
inference(simp,[status(thm)],[7785]) ).
thf(7798,plain,
( ( ( genClo1163638703lle_te @ q @ one_one_nat )
!= one_one_real )
| ( ( genClo1163638703lle_te @ p @ one_one_nat )
!= zero_zero_real )
| ( i != zero_zero_nat ) ),
inference(simp,[status(thm)],[7789]) ).
thf(246,axiom,
! [A: real,B: real] :
( ( abs_abs_real @ ( times_times_real @ A @ B ) )
= ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_abs__mult) ).
thf(1083,plain,
! [A: real,B: real] :
( ( abs_abs_real @ ( times_times_real @ A @ B ) )
= ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(197,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_add__decreasing) ).
thf(941,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(72,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ A @ B )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_diff__is__0__eq_H) ).
thf(555,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ A @ B )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(101,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_bot__nat__0_Oextremum) ).
thf(666,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(244,axiom,
ord_less_eq_real @ one_one_real @ one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_le__numeral__extra_I4_J) ).
thf(1079,plain,
ord_less_eq_real @ one_one_real @ one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(139,axiom,
( ( abs_abs_real @ one_one_real )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_abs__1) ).
thf(774,plain,
( ( abs_abs_real @ one_one_real )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(775,plain,
( ( abs_abs_real @ one_one_real )
= one_one_real ),
inference(lifteq,[status(thm)],[774]) ).
thf(1416,plain,
( ~ ( ord_less_eq_real @ one_one_real @ genClo1278781456e_beta )
| ( ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) )
!= ( abs_abs_real @ one_one_real ) ) ),
inference(paramod_ordered,[status(thm)],[775,340]) ).
thf(1417,plain,
( ~ ( ord_less_eq_real @ one_one_real @ genClo1278781456e_beta )
| ( ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) )
!= one_one_real ) ),
inference(simp,[status(thm)],[1416]) ).
thf(1543,plain,
( ~ $true
| ( ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) )
!= one_one_real )
| ( ( ord_less_eq_real @ one_one_real @ one_one_real )
!= ( ord_less_eq_real @ one_one_real @ genClo1278781456e_beta ) ) ),
inference(paramod_ordered,[status(thm)],[1079,1417]) ).
thf(1544,plain,
( ( ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) )
!= one_one_real )
| ( ( ord_less_eq_real @ one_one_real @ one_one_real )
!= ( ord_less_eq_real @ one_one_real @ genClo1278781456e_beta ) ) ),
inference(simp,[status(thm)],[1543]) ).
thf(1547,plain,
( ( ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) )
!= one_one_real )
| ( one_one_real != one_one_real )
| ( one_one_real != genClo1278781456e_beta ) ),
inference(simp,[status(thm)],[1544]) ).
thf(1549,plain,
( ( ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) )
!= one_one_real )
| ( one_one_real != genClo1278781456e_beta ) ),
inference(simp,[status(thm)],[1547]) ).
thf(255,axiom,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( minus_minus_real @ A @ B )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_eq__iff__diff__eq__0) ).
thf(1110,plain,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( minus_minus_real @ A @ B )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(47,axiom,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( B != zero_zero_nat )
=> ( ( times_times_nat @ A @ B )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_no__zero__divisors) ).
thf(478,plain,
! [A: nat,B: nat] :
( ( A != zero_zero_nat )
=> ( ( B != zero_zero_nat )
=> ( ( times_times_nat @ A @ B )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(479,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ! [B: nat] :
( ( B != zero_zero_nat )
=> ( ( times_times_nat @ A @ B )
!= zero_zero_nat ) ) ),
inference(miniscope,[status(thm)],[478]) ).
thf(480,plain,
! [B: nat,A: nat] :
( ( A = zero_zero_nat )
| ( B = zero_zero_nat )
| ( ( times_times_nat @ A @ B )
!= zero_zero_nat ) ),
inference(cnf,[status(esa)],[479]) ).
thf(481,plain,
! [B: nat,A: nat] :
( ( A = zero_zero_nat )
| ( B = zero_zero_nat )
| ( ( times_times_nat @ A @ B )
!= zero_zero_nat ) ),
inference(lifteq,[status(thm)],[480]) ).
thf(55,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_zero__le) ).
thf(505,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(506,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(cnf,[status(esa)],[505]) ).
thf(10,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_diff__le__mono) ).
thf(362,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(363,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ! [C: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ),
inference(miniscope,[status(thm)],[362]) ).
thf(364,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ),
inference(cnf,[status(esa)],[363]) ).
thf(2167,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ~ $true
| ( ord_less_eq_nat @ ( minus_minus_nat @ B @ D ) @ ( minus_minus_nat @ C @ D ) )
| ( ( ord_less_eq_nat @ zero_zero_nat @ A )
!= ( ord_less_eq_nat @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[506,364]) ).
thf(2168,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ D ) @ ( minus_minus_nat @ C @ D ) )
| ( ( ord_less_eq_nat @ zero_zero_nat @ A )
!= ( ord_less_eq_nat @ B @ C ) ) ),
inference(simp,[status(thm)],[2167]) ).
thf(2169,plain,
! [B: nat,A: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ zero_zero_nat @ B ) @ ( minus_minus_nat @ A @ B ) ),
inference(pattern_uni,[status(thm)],[2168:[bind(A,$thf( A )),bind(B,$thf( zero_zero_nat )),bind(C,$thf( A ))]]) ).
thf(2184,plain,
! [B: nat,A: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ zero_zero_nat @ B ) @ ( minus_minus_nat @ A @ B ) ),
inference(simp,[status(thm)],[2169]) ).
thf(46,axiom,
! [A: nat,B: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_diff__is__0__eq) ).
thf(475,plain,
! [A: nat,B: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(476,plain,
! [B: nat,A: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
= ( ord_less_eq_nat @ A @ B ) ),
inference(cnf,[status(esa)],[475]) ).
thf(477,plain,
! [B: nat,A: nat] :
( ( ord_less_eq_nat @ A @ B )
= ( ( minus_minus_nat @ A @ B )
= zero_zero_nat ) ),
inference(lifteq,[status(thm)],[476]) ).
thf(8606,plain,
! [B: nat,A: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ zero_zero_nat @ B ) @ ( minus_minus_nat @ A @ B ) )
= zero_zero_nat ),
inference(rewrite,[status(thm)],[2184,477]) ).
thf(8607,plain,
! [B: nat,A: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ zero_zero_nat @ B ) @ ( minus_minus_nat @ A @ B ) )
= zero_zero_nat ),
inference(lifteq,[status(thm)],[8606]) ).
thf(94,axiom,
( times_times_nat
= ( ^ [A: nat,B: nat] : ( times_times_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_mult_Ocommute) ).
thf(645,plain,
( times_times_nat
= ( ^ [A: nat,B: nat] : ( times_times_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(276,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
=> ( ord_less_eq_real @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_abs__le__D1) ).
thf(1168,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
=> ( ord_less_eq_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(178,axiom,
! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_abs__ge__self) ).
thf(887,plain,
! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(888,plain,
! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ),
inference(cnf,[status(esa)],[887]) ).
thf(2842,plain,
! [A: nat] :
( ~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ zero_zero_real @ zero_zero_real ) ) @ genClo1278781456e_beta )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( ( genClo1163638703lle_te @ A @ zero_zero_nat )
!= ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[1058,2272]) ).
thf(2859,plain,
! [A: nat] :
( ~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ zero_zero_real @ zero_zero_real ) ) @ genClo1278781456e_beta )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( A != p )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat ) ),
inference(simp,[status(thm)],[2842]) ).
thf(2865,plain,
( ~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ zero_zero_real @ zero_zero_real ) ) @ genClo1278781456e_beta )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat ) ),
inference(simp,[status(thm)],[2859]) ).
thf(3371,plain,
! [A: real] :
( ~ $true
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) )
!= ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ zero_zero_real @ zero_zero_real ) ) @ genClo1278781456e_beta ) ) ),
inference(paramod_ordered,[status(thm)],[888,2865]) ).
thf(3372,plain,
! [A: real] :
( ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) )
!= ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ zero_zero_real @ zero_zero_real ) ) @ genClo1278781456e_beta ) ) ),
inference(simp,[status(thm)],[3371]) ).
thf(3384,plain,
! [A: real] :
( ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( A
!= ( abs_abs_real @ ( minus_minus_real @ zero_zero_real @ zero_zero_real ) ) )
| ( ( abs_abs_real @ A )
!= genClo1278781456e_beta ) ),
inference(simp,[status(thm)],[3372]) ).
thf(3392,plain,
( ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( ( abs_abs_real @ ( abs_abs_real @ ( minus_minus_real @ zero_zero_real @ zero_zero_real ) ) )
!= genClo1278781456e_beta ) ),
inference(simp,[status(thm)],[3384]) ).
thf(111,axiom,
! [A: real] :
( ( abs_abs_real @ ( abs_abs_real @ A ) )
= ( abs_abs_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_abs__abs) ).
thf(696,plain,
! [A: real] :
( ( abs_abs_real @ ( abs_abs_real @ A ) )
= ( abs_abs_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(697,plain,
! [A: real] :
( ( abs_abs_real @ ( abs_abs_real @ A ) )
= ( abs_abs_real @ A ) ),
inference(cnf,[status(esa)],[696]) ).
thf(698,plain,
! [A: real] :
( ( abs_abs_real @ ( abs_abs_real @ A ) )
= ( abs_abs_real @ A ) ),
inference(lifteq,[status(thm)],[697]) ).
thf(4450,plain,
( ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( ( abs_abs_real @ ( minus_minus_real @ zero_zero_real @ zero_zero_real ) )
!= genClo1278781456e_beta ) ),
inference(rewrite,[status(thm)],[3392,698]) ).
thf(134,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_diff__diff__left) ).
thf(760,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(288,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_distrib__right) ).
thf(1200,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(210,axiom,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_add__diff__cancel__left_H) ).
thf(977,plain,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(107,axiom,
! [A: real,B: real] :
( ( ( plus_plus_real @ A @ B )
= A )
= ( B = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_add__cancel__left__right) ).
thf(683,plain,
! [A: real,B: real] :
( ( ( plus_plus_real @ A @ B )
= A )
= ( B = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(320,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ( ( plus_plus_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_add__nonpos__eq__0__iff) ).
thf(1290,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ( ( plus_plus_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(240,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
= ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2) ).
thf(1068,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
= ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(191,axiom,
( ( minus_minus_real @ one_one_real @ one_one_real )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_diff__numeral__special_I9_J) ).
thf(927,plain,
( ( minus_minus_real @ one_one_real @ one_one_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(928,plain,
( ( minus_minus_real @ one_one_real @ one_one_real )
= zero_zero_real ),
inference(lifteq,[status(thm)],[927]) ).
thf(189,axiom,
( ( abs_abs_real @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_abs__0) ).
thf(922,plain,
( ( abs_abs_real @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(923,plain,
( ( abs_abs_real @ zero_zero_real )
= zero_zero_real ),
inference(lifteq,[status(thm)],[922]) ).
thf(1420,plain,
( ~ ( ord_less_eq_real @ zero_zero_real @ genClo1278781456e_beta )
| ( ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) )
!= ( abs_abs_real @ zero_zero_real ) ) ),
inference(paramod_ordered,[status(thm)],[923,340]) ).
thf(1423,plain,
( ~ ( ord_less_eq_real @ zero_zero_real @ genClo1278781456e_beta )
| ( ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) )
!= zero_zero_real ) ),
inference(simp,[status(thm)],[1420]) ).
thf(1668,plain,
( ~ ( ord_less_eq_real @ zero_zero_real @ genClo1278781456e_beta )
| ( zero_zero_real != zero_zero_real )
| ( ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) )
!= ( minus_minus_real @ one_one_real @ one_one_real ) ) ),
inference(paramod_ordered,[status(thm)],[928,1423]) ).
thf(1669,plain,
( ~ ( ord_less_eq_real @ zero_zero_real @ genClo1278781456e_beta )
| ( ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) )
!= ( minus_minus_real @ one_one_real @ one_one_real ) ) ),
inference(simp,[status(thm)],[1668]) ).
thf(1673,plain,
( ~ ( ord_less_eq_real @ zero_zero_real @ genClo1278781456e_beta )
| ( ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real )
| ( ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real ) ),
inference(simp,[status(thm)],[1669]) ).
thf(2090,plain,
( ~ ( ord_less_eq_real @ zero_zero_real @ genClo1278781456e_beta )
| ( ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real )
| ( ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) )
!= ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) )
| ( one_one_real != one_one_real ) ),
inference(eqfactor_ordered,[status(thm)],[1673]) ).
thf(2095,plain,
( ~ ( ord_less_eq_real @ zero_zero_real @ genClo1278781456e_beta )
| ( ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real )
| ( q != p )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= ( plus_plus_nat @ i @ one_one_nat ) ) ),
inference(simp,[status(thm)],[2090]) ).
thf(2099,plain,
( ~ ( ord_less_eq_real @ zero_zero_real @ genClo1278781456e_beta )
| ( ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real )
| ( q != p ) ),
inference(simp,[status(thm)],[2095]) ).
thf(105,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_ring__class_Oring__distribs_I2_J) ).
thf(677,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(230,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right) ).
thf(1041,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(278,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ C @ D ) )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_add__mono__thms__linordered__semiring_I1_J) ).
thf(1173,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ C @ D ) )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(126,axiom,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
= ( minus_minus_real @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_add__diff__cancel__right) ).
thf(741,plain,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
= ( minus_minus_real @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(242,axiom,
! [A: real] :
( ( zero_zero_real
= ( abs_abs_real @ A ) )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_abs__0__eq) ).
thf(1073,plain,
! [A: real] :
( ( zero_zero_real
= ( abs_abs_real @ A ) )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(22,axiom,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_add_Oright__neutral) ).
thf(399,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(400,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(cnf,[status(esa)],[399]) ).
thf(401,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(lifteq,[status(thm)],[400]) ).
thf(29,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_add__left__imp__eq) ).
thf(419,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(420,plain,
! [C: real,B: real,A: real] :
( ( ( plus_plus_real @ A @ B )
!= ( plus_plus_real @ A @ C ) )
| ( B = C ) ),
inference(cnf,[status(esa)],[419]) ).
thf(421,plain,
! [C: real,B: real,A: real] :
( ( ( plus_plus_real @ A @ B )
!= ( plus_plus_real @ A @ C ) )
| ( B = C ) ),
inference(lifteq,[status(thm)],[420]) ).
thf(422,plain,
? [A: real > real > real] :
! [B: real,C: real] :
( ( A @ B @ ( plus_plus_real @ B @ C ) )
= C ),
inference(detectInverse,[status(thm)],[421]) ).
thf(423,plain,
! [B: real,A: real] :
( ( sk1 @ A @ ( plus_plus_real @ A @ B ) )
= B ),
inference(cnf,[status(esa)],[422]) ).
thf(4707,plain,
! [B: real,A: real] :
( ( sk1 @ A @ ( plus_plus_real @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[423]) ).
thf(4710,plain,
! [C: real,B: real,A: real] :
( ( ( sk1 @ B @ A )
= C )
| ( ( plus_plus_real @ A @ zero_zero_real )
!= ( plus_plus_real @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[401,4707]) ).
thf(4711,plain,
! [A: real] :
( ( sk1 @ A @ A )
= zero_zero_real ),
inference(pattern_uni,[status(thm)],[4710:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( zero_zero_real ))]]) ).
thf(37,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_nat__le__linear) ).
thf(449,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(15,axiom,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_comm__monoid__add__class_Oadd__0) ).
thf(377,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(378,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(cnf,[status(esa)],[377]) ).
thf(379,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(lifteq,[status(thm)],[378]) ).
thf(313,axiom,
( genClo293725282kRead2
= ( ^ [A: nat > real,B: nat > real,C: real,D: nat > $o] :
! [E: nat] :
( ( D @ E )
=> ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ E ) @ ( B @ E ) ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_okRead2__def) ).
thf(1269,plain,
( genClo293725282kRead2
= ( ^ [A: nat > real,B: nat > real,C: real,D: nat > $o] :
! [E: nat] :
( ( D @ E )
=> ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ E ) @ ( B @ E ) ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(175,axiom,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_mult_Oright__neutral) ).
thf(878,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(34,axiom,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ A @ B ) )
= ( B = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_add__cancel__right__right) ).
thf(438,plain,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ A @ B ) )
= ( B = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(439,plain,
! [B: real,A: real] :
( ( A
= ( plus_plus_real @ A @ B ) )
= ( B = zero_zero_real ) ),
inference(cnf,[status(esa)],[438]) ).
thf(440,plain,
! [B: real,A: real] :
( ( A
= ( plus_plus_real @ A @ B ) )
= ( B = zero_zero_real ) ),
inference(lifteq,[status(thm)],[439]) ).
thf(17,axiom,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_comm__monoid__mult__class_Omult__1) ).
thf(383,plain,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(384,plain,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(cnf,[status(esa)],[383]) ).
thf(385,plain,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(lifteq,[status(thm)],[384]) ).
thf(65,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_mult_Oassoc) ).
thf(533,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(118,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus_nat @ A @ C )
= ( plus_plus_nat @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_add__mono__thms__linordered__semiring_I4_J) ).
thf(715,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus_nat @ A @ C )
= ( plus_plus_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(45,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_add__right__imp__eq) ).
thf(470,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(471,plain,
! [C: real,B: real,A: real] :
( ( ( plus_plus_real @ A @ B )
!= ( plus_plus_real @ C @ B ) )
| ( A = C ) ),
inference(cnf,[status(esa)],[470]) ).
thf(472,plain,
! [C: real,B: real,A: real] :
( ( ( plus_plus_real @ A @ B )
!= ( plus_plus_real @ C @ B ) )
| ( A = C ) ),
inference(lifteq,[status(thm)],[471]) ).
thf(199,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_left__diff__distrib) ).
thf(945,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(4,axiom,
( times_times_real
= ( ^ [A: real,B: real] : ( times_times_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_mult_Ocommute) ).
thf(345,plain,
( times_times_real
= ( ^ [A: real,B: real] : ( times_times_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(346,plain,
( times_times_real
= ( ^ [A: real,B: real] : ( times_times_real @ B @ A ) ) ),
inference(lifteq,[status(thm)],[345]) ).
thf(1354,plain,
! [A: real] :
( ( times_times_real @ A )
= ( ^ [B: real] : ( times_times_real @ B @ A ) ) ),
inference(func_ext,[status(esa)],[346]) ).
thf(193,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( A = B )
& ( ord_less_eq_nat @ C @ D ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_add__mono__thms__linordered__semiring_I2_J) ).
thf(930,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( A = B )
& ( ord_less_eq_nat @ C @ D ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(24,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_comm__semiring__class_Odistrib) ).
thf(404,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(292,axiom,
! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_abs__ge__zero) ).
thf(1212,plain,
! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(1213,plain,
! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ),
inference(cnf,[status(esa)],[1212]) ).
thf(3402,plain,
( ~ ( ord_less_eq_real @ ( abs_abs_real @ zero_zero_real ) @ genClo1278781456e_beta )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat ) ),
inference(rewrite,[status(thm)],[2865,891]) ).
thf(3590,plain,
( ~ ( ord_less_eq_real @ zero_zero_real @ genClo1278781456e_beta )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat ) ),
inference(rewrite,[status(thm)],[3402,923]) ).
thf(3605,plain,
! [A: real] :
( ~ $true
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) )
!= ( ord_less_eq_real @ zero_zero_real @ genClo1278781456e_beta ) ) ),
inference(paramod_ordered,[status(thm)],[1213,3590]) ).
thf(3606,plain,
! [A: real] :
( ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) )
!= ( ord_less_eq_real @ zero_zero_real @ genClo1278781456e_beta ) ) ),
inference(simp,[status(thm)],[3605]) ).
thf(3615,plain,
! [A: real] :
( ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( zero_zero_real != zero_zero_real )
| ( ( abs_abs_real @ A )
!= genClo1278781456e_beta ) ),
inference(simp,[status(thm)],[3606]) ).
thf(3629,plain,
! [A: real] :
( ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( ( abs_abs_real @ A )
!= genClo1278781456e_beta ) ),
inference(simp,[status(thm)],[3615]) ).
thf(261,axiom,
( ( abs_abs_real @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_abs__zero) ).
thf(1127,plain,
( ( abs_abs_real @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(116,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_add__nonpos__nonpos) ).
thf(709,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ zero_zero_real )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(177,axiom,
! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_abs__triangle__ineq2__sym) ).
thf(885,plain,
! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(298,axiom,
! [A: real] :
( ( abs_abs_real @ ( abs_abs_real @ A ) )
= ( abs_abs_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_abs__idempotent) ).
thf(1228,plain,
! [A: real] :
( ( abs_abs_real @ ( abs_abs_real @ A ) )
= ( abs_abs_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(19,axiom,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_add_Oleft__neutral) ).
thf(389,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(323,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_add__left__cancel) ).
thf(1298,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(119,axiom,
( ord_less_eq_real
= ( ^ [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_le__iff__diff__le__0) ).
thf(719,plain,
( ord_less_eq_real
= ( ^ [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(54,axiom,
! [A: real,B: real,C: real] :
( ( A != zero_zero_real )
=> ( ( ( times_times_real @ B @ A )
= ( times_times_real @ C @ A ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_mult__right__cancel) ).
thf(501,plain,
! [A: real,B: real,C: real] :
( ( A != zero_zero_real )
=> ( ( ( times_times_real @ B @ A )
= ( times_times_real @ C @ A ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(502,plain,
! [A: real] :
( ( A != zero_zero_real )
=> ! [B: real,C: real] :
( ( ( times_times_real @ B @ A )
= ( times_times_real @ C @ A ) )
= ( B = C ) ) ),
inference(miniscope,[status(thm)],[501]) ).
thf(503,plain,
! [C: real,B: real,A: real] :
( ( A = zero_zero_real )
| ( ( ( times_times_real @ B @ A )
= ( times_times_real @ C @ A ) )
= ( B = C ) ) ),
inference(cnf,[status(esa)],[502]) ).
thf(504,plain,
! [C: real,B: real,A: real] :
( ( A = zero_zero_real )
| ( ( ( times_times_real @ B @ A )
= ( times_times_real @ C @ A ) )
= ( B = C ) ) ),
inference(lifteq,[status(thm)],[503]) ).
thf(194,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_diff__right__mono) ).
thf(934,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(332,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_diff__add__0) ).
thf(1328,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(1329,plain,
! [B: nat,A: nat] :
( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
= zero_zero_nat ),
inference(cnf,[status(esa)],[1328]) ).
thf(1330,plain,
! [B: nat,A: nat] :
( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
= zero_zero_nat ),
inference(lifteq,[status(thm)],[1329]) ).
thf(311,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
= ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_diff__ge__0__iff__ge) ).
thf(1264,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
= ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(81,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_bot__nat__0_Oextremum__unique) ).
thf(587,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(160,axiom,
! [A: nat,B: real,C: nat] :
( ( ( genClo1015804716orrect @ A @ B )
& ( ord_less_eq_real @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ C @ one_one_nat ) ) @ B ) )
=> ( ord_less_eq_real @ genClo1651033342e_rmin @ ( minus_minus_real @ B @ ( genClo1163638703lle_te @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_rts1) ).
thf(838,plain,
! [A: nat,B: real,C: nat] :
( ( ( genClo1015804716orrect @ A @ B )
& ( ord_less_eq_real @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ C @ one_one_nat ) ) @ B ) )
=> ( ord_less_eq_real @ genClo1651033342e_rmin @ ( minus_minus_real @ B @ ( genClo1163638703lle_te @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(113,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_Nat_Oadd__0__right) ).
thf(700,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(701,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(cnf,[status(esa)],[700]) ).
thf(702,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(lifteq,[status(thm)],[701]) ).
thf(129,axiom,
ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_posD) ).
thf(751,plain,
ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(148,axiom,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
= ( minus_minus_real @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_add__diff__cancel__left) ).
thf(802,plain,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
= ( minus_minus_real @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(3,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_mult__left__cancel) ).
thf(341,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(342,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ! [B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( B = C ) ) ),
inference(miniscope,[status(thm)],[341]) ).
thf(343,plain,
! [C: nat,B: nat,A: nat] :
( ( A = zero_zero_nat )
| ( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( B = C ) ) ),
inference(cnf,[status(esa)],[342]) ).
thf(344,plain,
! [C: nat,B: nat,A: nat] :
( ( A = zero_zero_nat )
| ( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( B = C ) ) ),
inference(lifteq,[status(thm)],[343]) ).
thf(236,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_add__diff__cancel__left_H) ).
thf(1059,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(263,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_diff__add__eq) ).
thf(1132,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(68,axiom,
! [A: real,B: real,C: real] :
( ( A != zero_zero_real )
=> ( ( ( times_times_real @ A @ B )
= ( times_times_real @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_mult__left__cancel) ).
thf(542,plain,
! [A: real,B: real,C: real] :
( ( A != zero_zero_real )
=> ( ( ( times_times_real @ A @ B )
= ( times_times_real @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(41,axiom,
! [A: real,B: real] :
( ( ( plus_plus_real @ A @ B )
= B )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_add__cancel__left__left) ).
thf(460,plain,
! [A: real,B: real] :
( ( ( plus_plus_real @ A @ B )
= B )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(1539,plain,
( ~ $true
| ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) @ genClo1278781456e_beta )
!= ( ord_less_eq_real @ one_one_real @ one_one_real ) ) ),
inference(paramod_ordered,[status(thm)],[1079,340]) ).
thf(1540,plain,
( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) @ genClo1278781456e_beta )
!= ( ord_less_eq_real @ one_one_real @ one_one_real ) ),
inference(simp,[status(thm)],[1539]) ).
thf(1545,plain,
( ( ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) )
!= one_one_real )
| ( one_one_real != genClo1278781456e_beta ) ),
inference(simp,[status(thm)],[1540]) ).
thf(183,axiom,
( ( abs_abs_real @ one_one_real )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_abs__one) ).
thf(902,plain,
( ( abs_abs_real @ one_one_real )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(269,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_add__right__imp__eq) ).
thf(1147,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(257,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_Nat_Ole__diff__conv2) ).
thf(1115,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(36,axiom,
! [A: real] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_mult__zero__right) ).
thf(446,plain,
! [A: real] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(447,plain,
! [A: real] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(cnf,[status(esa)],[446]) ).
thf(448,plain,
! [A: real] :
( ( times_times_real @ A @ zero_zero_real )
= zero_zero_real ),
inference(lifteq,[status(thm)],[447]) ).
thf(207,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
=> ( ord_less_eq_real @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_add__le__imp__le__right) ).
thf(969,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
=> ( ord_less_eq_real @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(338,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_diff__add__zero) ).
thf(1347,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(176,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( ord_less_eq_real @ A @ B )
& ( C = D ) )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_add__mono__thms__linordered__semiring_I3_J) ).
thf(881,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( ord_less_eq_real @ A @ B )
& ( C = D ) )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(28,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ C @ B ) )
= ( ( B = zero_zero_nat )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_mult__cancel__right) ).
thf(416,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ C @ B ) )
= ( ( B = zero_zero_nat )
| ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(14,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_mult__eq__0__iff) ).
thf(374,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(375,plain,
! [B: nat,A: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
inference(cnf,[status(esa)],[374]) ).
thf(376,plain,
! [B: nat,A: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
inference(lifteq,[status(thm)],[375]) ).
thf(49,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_bot__nat__0_Oextremum__uniqueI) ).
thf(485,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(195,axiom,
! [A: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
= ( ord_less_eq_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_double__add__le__zero__iff__single__add__le__zero) ).
thf(937,plain,
! [A: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
= ( ord_less_eq_real @ A @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(224,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_add__decreasing2) ).
thf(1020,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(3482,plain,
! [A: nat] :
( ( ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real )
| ( ( genClo1163638703lle_te @ p @ A )
!= zero_zero_real )
| ( ( plus_plus_nat @ zero_zero_nat @ A )
!= ( plus_plus_nat @ i @ one_one_nat ) ) ),
inference(paramod_ordered,[status(thm)],[894,2643]) ).
thf(3516,plain,
! [A: nat] :
( ( ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real )
| ( ( genClo1163638703lle_te @ p @ A )
!= zero_zero_real )
| ( i != zero_zero_nat )
| ( A != one_one_nat ) ),
inference(simp,[status(thm)],[3482]) ).
thf(3569,plain,
( ( ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real )
| ( ( genClo1163638703lle_te @ p @ one_one_nat )
!= zero_zero_real )
| ( i != zero_zero_nat ) ),
inference(simp,[status(thm)],[3516]) ).
thf(150,axiom,
! [A: real] :
( ( ( abs_abs_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_abs__eq__0) ).
thf(806,plain,
! [A: real] :
( ( ( abs_abs_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(190,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(924,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(334,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( minus_minus_nat @ B @ A )
= C )
= ( B
= ( plus_plus_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_Nat_Ole__imp__diff__is__add) ).
thf(1334,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( minus_minus_nat @ B @ A )
= C )
= ( B
= ( plus_plus_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(646,plain,
( times_times_nat
= ( ^ [A: nat,B: nat] : ( times_times_nat @ B @ A ) ) ),
inference(lifteq,[status(thm)],[645]) ).
thf(7,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_minus__nat_Odiff__0) ).
thf(353,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(206,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_add__nonneg__nonneg) ).
thf(966,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(136,axiom,
! [A: real] :
( ( ( abs_abs_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_abs__eq__0__iff) ).
thf(766,plain,
! [A: real] :
( ( ( abs_abs_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(124,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
= ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_Nat_Oadd__diff__assoc2) ).
thf(734,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
= ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(21,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_mult__mono) ).
thf(396,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ C )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(56,axiom,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ B @ A ) )
= ( B = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_add__cancel__right__left) ).
thf(507,plain,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ B @ A ) )
= ( B = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(174,axiom,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_mult_Ocomm__neutral) ).
thf(875,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(876,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(cnf,[status(esa)],[875]) ).
thf(877,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(lifteq,[status(thm)],[876]) ).
thf(110,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_eq__imp__le) ).
thf(692,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(241,axiom,
ord_less_eq_real @ genClo1278781456e_beta @ genClo1651033342e_rmin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_nonoverlap) ).
thf(1072,plain,
ord_less_eq_real @ genClo1278781456e_beta @ genClo1651033342e_rmin,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(38,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_add_Oleft__cancel) ).
thf(451,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(452,plain,
! [C: real,B: real,A: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
= ( B = C ) ),
inference(cnf,[status(esa)],[451]) ).
thf(453,plain,
! [C: real,B: real,A: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
= ( B = C ) ),
inference(lifteq,[status(thm)],[452]) ).
thf(258,axiom,
ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( genClo1161277105lle_PC @ l @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) ) @ ( genClo1161277105lle_PC @ l @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_posX) ).
thf(1119,plain,
ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( genClo1161277105lle_PC @ l @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) ) @ ( genClo1161277105lle_PC @ l @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(303,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ B @ ( plus_plus_real @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_add__increasing2) ).
thf(1242,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ B @ ( plus_plus_real @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(164,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_add__mono) ).
thf(849,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(196,axiom,
ord_less_eq_real @ zero_zero_real @ zero_zero_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_le__numeral__extra_I3_J) ).
thf(940,plain,
ord_less_eq_real @ zero_zero_real @ zero_zero_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(1592,plain,
( ~ $true
| ( ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) )
!= zero_zero_real )
| ( ( ord_less_eq_real @ zero_zero_real @ zero_zero_real )
!= ( ord_less_eq_real @ zero_zero_real @ genClo1278781456e_beta ) ) ),
inference(paramod_ordered,[status(thm)],[940,1423]) ).
thf(1593,plain,
( ( ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) )
!= zero_zero_real )
| ( ( ord_less_eq_real @ zero_zero_real @ zero_zero_real )
!= ( ord_less_eq_real @ zero_zero_real @ genClo1278781456e_beta ) ) ),
inference(simp,[status(thm)],[1592]) ).
thf(1597,plain,
( ( ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) )
!= zero_zero_real )
| ( zero_zero_real != zero_zero_real )
| ( zero_zero_real != genClo1278781456e_beta ) ),
inference(simp,[status(thm)],[1593]) ).
thf(1604,plain,
( ( ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) )
!= zero_zero_real )
| ( zero_zero_real != genClo1278781456e_beta ) ),
inference(simp,[status(thm)],[1597]) ).
thf(290,axiom,
! [A: real] :
( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
= ( ord_less_eq_real @ zero_zero_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_abs__le__self__iff) ).
thf(1206,plain,
! [A: real] :
( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
= ( ord_less_eq_real @ zero_zero_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(16,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_add__right__cancel) ).
thf(380,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(99,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_zero__neq__one) ).
thf(659,plain,
zero_zero_real != one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(660,plain,
zero_zero_real != one_one_real,
inference(polarity_switch,[status(thm)],[659]) ).
thf(661,plain,
zero_zero_real != one_one_real,
inference(lifteq,[status(thm)],[660]) ).
thf(335,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( minus_minus_nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_add__diff__cancel__right) ).
thf(1338,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( minus_minus_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(69,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_left__diff__distrib_H) ).
thf(546,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(145,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C )
=> ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_add__le__imp__le__diff) ).
thf(793,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C )
=> ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(327,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_add_Oright__neutral) ).
thf(1311,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(203,axiom,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_diff__self) ).
thf(957,plain,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(958,plain,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
inference(cnf,[status(esa)],[957]) ).
thf(959,plain,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
inference(lifteq,[status(thm)],[958]) ).
thf(112,axiom,
ord_less_eq_real @ zero_zero_real @ one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_zero__le__one) ).
thf(699,plain,
ord_less_eq_real @ zero_zero_real @ one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(1409,plain,
( ~ $true
| ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) @ genClo1278781456e_beta )
!= ( ord_less_eq_real @ zero_zero_real @ one_one_real ) ) ),
inference(paramod_ordered,[status(thm)],[699,340]) ).
thf(1410,plain,
( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) @ genClo1278781456e_beta )
!= ( ord_less_eq_real @ zero_zero_real @ one_one_real ) ),
inference(simp,[status(thm)],[1409]) ).
thf(1413,plain,
( ( ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) )
!= zero_zero_real )
| ( one_one_real != genClo1278781456e_beta ) ),
inference(simp,[status(thm)],[1410]) ).
thf(1450,plain,
( ( zero_zero_real != zero_zero_real )
| ( one_one_real != genClo1278781456e_beta )
| ( ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) )
!= ( abs_abs_real @ zero_zero_real ) ) ),
inference(paramod_ordered,[status(thm)],[923,1413]) ).
thf(1451,plain,
( ( one_one_real != genClo1278781456e_beta )
| ( ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) )
!= ( abs_abs_real @ zero_zero_real ) ) ),
inference(simp,[status(thm)],[1450]) ).
thf(1453,plain,
( ( one_one_real != genClo1278781456e_beta )
| ( ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) )
!= zero_zero_real ) ),
inference(simp,[status(thm)],[1451]) ).
thf(3754,plain,
! [A: real] :
( ( one_one_real != genClo1278781456e_beta )
| ( zero_zero_real != zero_zero_real )
| ( ( minus_minus_real @ A @ A )
!= ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[959,1453]) ).
thf(3755,plain,
! [A: real] :
( ( one_one_real != genClo1278781456e_beta )
| ( ( minus_minus_real @ A @ A )
!= ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) ),
inference(simp,[status(thm)],[3754]) ).
thf(3760,plain,
! [A: real] :
( ( one_one_real != genClo1278781456e_beta )
| ( A
!= ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) )
| ( A
!= ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ),
inference(simp,[status(thm)],[3755]) ).
thf(3767,plain,
( ( one_one_real != genClo1278781456e_beta )
| ( ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) )
!= ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ),
inference(simp,[status(thm)],[3760]) ).
thf(315,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_add_Oassoc) ).
thf(1274,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(294,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ C )
= ( ( ord_less_eq_real @ ( minus_minus_real @ B @ C ) @ A )
& ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_abs__diff__le__iff) ).
thf(1217,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ C )
= ( ( ord_less_eq_real @ ( minus_minus_real @ B @ C ) @ A )
& ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(74,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
!= zero_zero_nat )
=> ( ( A != zero_zero_nat )
& ( B != zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_mult__not__zero) ).
thf(561,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
!= zero_zero_nat )
=> ( ( A != zero_zero_nat )
& ( B != zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(20,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( ( minus_minus_nat @ B @ A )
= ( minus_minus_nat @ C @ A ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_eq__diff__iff) ).
thf(392,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( ( minus_minus_nat @ B @ A )
= ( minus_minus_nat @ C @ A ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(30,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_diff__le__mono2) ).
thf(424,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(153,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( plus_plus_nat @ B @ C ) )
=> ( ( plus_plus_nat @ A @ D )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_group__cancel_Oadd1) ).
thf(815,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A
= ( plus_plus_nat @ B @ C ) )
=> ( ( plus_plus_nat @ A @ D )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(296,axiom,
! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_abs__triangle__ineq) ).
thf(1223,plain,
! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(169,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_diff__add__inverse) ).
thf(862,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(348,plain,
! [C: real,B: real,A: real] :
( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
inference(cnf,[status(esa)],[347]) ).
thf(349,plain,
! [C: real,B: real,A: real] :
( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
inference(lifteq,[status(thm)],[348]) ).
thf(154,axiom,
! [A: nat,B: nat] :
( ( zero_zero_nat
= ( plus_plus_nat @ A @ B ) )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_zero__eq__add__iff__both__eq__0) ).
thf(820,plain,
! [A: nat,B: nat] :
( ( zero_zero_nat
= ( plus_plus_nat @ A @ B ) )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(1074,plain,
! [A: real] :
( ( zero_zero_real
= ( abs_abs_real @ A ) )
= ( A = zero_zero_real ) ),
inference(cnf,[status(esa)],[1073]) ).
thf(1075,plain,
! [A: real] :
( ( zero_zero_real
= ( abs_abs_real @ A ) )
= ( A = zero_zero_real ) ),
inference(lifteq,[status(thm)],[1074]) ).
thf(5814,plain,
! [A: real] :
( ( ( zero_zero_real = one_one_real )
= ( A = zero_zero_real ) )
| ( ( abs_abs_real @ one_one_real )
!= ( abs_abs_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[775,1075]) ).
thf(5815,plain,
( ( zero_zero_real = one_one_real )
= ( one_one_real = zero_zero_real ) ),
inference(pattern_uni,[status(thm)],[5814:[bind(A,$thf( one_one_real ))]]) ).
thf(25,axiom,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_zero__diff) ).
thf(407,plain,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(3858,plain,
! [B: real,A: real] :
( ( ord_less_eq_real @ B @ ( abs_abs_real @ A ) )
| ( ( abs_abs_real @ ( abs_abs_real @ A ) )
!= ( abs_abs_real @ B ) ) ),
inference(paramod_ordered,[status(thm)],[698,888]) ).
thf(3859,plain,
! [A: real] : ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) ),
inference(pattern_uni,[status(thm)],[3858:[bind(A,$thf( C )),bind(B,$thf( abs_abs_real @ C ))]]) ).
thf(3884,plain,
! [A: real] : ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) ),
inference(simp,[status(thm)],[3859]) ).
thf(48,axiom,
! [A: real] :
( ( one_one_real = A )
= ( A = one_one_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_one__reorient) ).
thf(482,plain,
! [A: real] :
( ( one_one_real = A )
= ( A = one_one_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(483,plain,
! [A: real] :
( ( one_one_real = A )
= ( A = one_one_real ) ),
inference(cnf,[status(esa)],[482]) ).
thf(484,plain,
! [A: real] :
( ( one_one_real = A )
= ( A = one_one_real ) ),
inference(lifteq,[status(thm)],[483]) ).
thf(86,axiom,
! [A: real,B: real] :
( ( ( times_times_real @ A @ B )
!= zero_zero_real )
=> ( ( A != zero_zero_real )
& ( B != zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_mult__not__zero) ).
thf(616,plain,
! [A: real,B: real] :
( ( ( times_times_real @ A @ B )
!= zero_zero_real )
=> ( ( A != zero_zero_real )
& ( B != zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(617,plain,
! [B: real,A: real] :
( ( ( ( times_times_real @ A @ B )
= zero_zero_real )
| ( A != zero_zero_real ) )
& ( ( ( times_times_real @ A @ B )
= zero_zero_real )
| ( B != zero_zero_real ) ) ),
inference(cnf,[status(esa)],[616]) ).
thf(618,plain,
! [B: real,A: real] :
( ( ( times_times_real @ A @ B )
= zero_zero_real )
| ( A != zero_zero_real ) ),
inference(cnfConj,[status(thm)],[617]) ).
thf(620,plain,
! [B: real,A: real] :
( ( ( times_times_real @ A @ B )
= zero_zero_real )
| ( A != zero_zero_real ) ),
inference(lifteq,[status(thm)],[618]) ).
thf(621,plain,
! [A: real] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
inference(simp,[status(thm)],[620]) ).
thf(2016,plain,
! [D: real,C: real,B: real,A: real] :
( ( ( plus_plus_real @ ( times_times_real @ B @ C ) @ ( times_times_real @ B @ D ) )
= zero_zero_real )
| ( ( times_times_real @ zero_zero_real @ A )
!= ( times_times_real @ B @ ( plus_plus_real @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[621,349]) ).
thf(2017,plain,
! [B: real,A: real] :
( ( plus_plus_real @ ( times_times_real @ zero_zero_real @ A ) @ ( times_times_real @ zero_zero_real @ B ) )
= zero_zero_real ),
inference(pattern_uni,[status(thm)],[2016:[bind(A,$thf( plus_plus_real @ E @ F )),bind(B,$thf( zero_zero_real )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(2023,plain,
! [B: real,A: real] :
( ( plus_plus_real @ ( times_times_real @ zero_zero_real @ A ) @ ( times_times_real @ zero_zero_real @ B ) )
= zero_zero_real ),
inference(simp,[status(thm)],[2017]) ).
thf(6852,plain,
( ( plus_plus_real @ zero_zero_real @ zero_zero_real )
= zero_zero_real ),
inference(rewrite,[status(thm)],[2023,621]) ).
thf(9,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_diff__self__eq__0) ).
thf(359,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(360,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
inference(cnf,[status(esa)],[359]) ).
thf(361,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
inference(lifteq,[status(thm)],[360]) ).
thf(252,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_le__add2) ).
thf(1101,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(1102,plain,
! [B: nat,A: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) ),
inference(cnf,[status(esa)],[1101]) ).
thf(7574,plain,
! [B: nat,A: nat] :
( ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ A ) )
= zero_zero_nat ),
inference(rewrite,[status(thm)],[1102,477]) ).
thf(7591,plain,
! [B: nat,A: nat] :
( ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ A ) )
= zero_zero_nat ),
inference(lifteq,[status(thm)],[7574]) ).
thf(286,axiom,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( plus_plus_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_nat__le__iff__add) ).
thf(1195,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( plus_plus_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(209,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_nat__add__left__cancel__le) ).
thf(974,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(254,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_Nat_Odiff__diff__right) ).
thf(1106,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(187,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_le__add__diff__inverse) ).
thf(916,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(44,axiom,
! [A: real] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_double__zero) ).
thf(467,plain,
! [A: real] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(165,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_diff__add__inverse2) ).
thf(852,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(33,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_is__num__normalize_I1_J) ).
thf(435,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(61,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_diff__commute) ).
thf(522,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(132,axiom,
( plus_plus_nat
= ( ^ [A: nat,B: nat] : ( plus_plus_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_add_Ocommute) ).
thf(757,plain,
( plus_plus_nat
= ( ^ [A: nat,B: nat] : ( plus_plus_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(366,plain,
! [B: real,A: real] :
( ( A
= ( times_times_real @ B @ A ) )
= ( ( A = zero_zero_real )
| ( B = one_one_real ) ) ),
inference(cnf,[status(esa)],[365]) ).
thf(367,plain,
! [B: real,A: real] :
( ( A
= ( times_times_real @ B @ A ) )
= ( ( A = zero_zero_real )
| ( B = one_one_real ) ) ),
inference(lifteq,[status(thm)],[366]) ).
thf(2344,plain,
! [C: real,B: real,A: real] :
( ( ( ( B = zero_zero_real )
| ( C = one_one_real ) )
= ( B = zero_zero_real ) )
| ( ( times_times_real @ zero_zero_real @ A )
!= ( times_times_real @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[621,367]) ).
thf(2345,plain,
! [A: real] :
( ( ( A = zero_zero_real )
| ( zero_zero_real = one_one_real ) )
= ( A = zero_zero_real ) ),
inference(pattern_uni,[status(thm)],[2344:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( zero_zero_real ))]]) ).
thf(223,axiom,
! [A: real] :
( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_abs__le__zero__iff) ).
thf(1017,plain,
! [A: real] :
( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(238,axiom,
ord_less_eq_real @ ( minus_minus_real @ ( genClo1161277105lle_PC @ l @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) ) @ ( genClo1161277105lle_PC @ l @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) @ ( times_times_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_bound1) ).
thf(1064,plain,
ord_less_eq_real @ ( minus_minus_real @ ( genClo1161277105lle_PC @ l @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) ) @ ( genClo1161277105lle_PC @ l @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) @ ( times_times_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(121,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
= ( ord_less_eq_real @ zero_zero_real @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_le__add__same__cancel2) ).
thf(725,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
= ( ord_less_eq_real @ zero_zero_real @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(211,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ~ ! [C: nat] :
( B
!= ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_less__eqE) ).
thf(980,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ~ ! [C: nat] :
( B
!= ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(18,axiom,
! [A: real,B: real,C: real] :
( ( ( times_times_real @ A @ B )
= ( times_times_real @ A @ C ) )
= ( ( A = zero_zero_real )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_mult__cancel__left) ).
thf(386,plain,
! [A: real,B: real,C: real] :
( ( ( times_times_real @ A @ B )
= ( times_times_real @ A @ C ) )
= ( ( A = zero_zero_real )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(387,plain,
! [C: real,B: real,A: real] :
( ( ( times_times_real @ A @ B )
= ( times_times_real @ A @ C ) )
= ( ( A = zero_zero_real )
| ( B = C ) ) ),
inference(cnf,[status(esa)],[386]) ).
thf(388,plain,
! [C: real,B: real,A: real] :
( ( ( times_times_real @ A @ B )
= ( times_times_real @ A @ C ) )
= ( ( A = zero_zero_real )
| ( B = C ) ) ),
inference(lifteq,[status(thm)],[387]) ).
thf(83,axiom,
! [A: real,B: real] :
( ( A
= ( times_times_real @ A @ B ) )
= ( ( A = zero_zero_real )
| ( B = one_one_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_mult__cancel__left1) ).
thf(593,plain,
! [A: real,B: real] :
( ( A
= ( times_times_real @ A @ B ) )
= ( ( A = zero_zero_real )
| ( B = one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(214,axiom,
zero_zero_nat != one_one_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_zero__neq__one) ).
thf(989,plain,
zero_zero_nat != one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(167,axiom,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
= ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_add__cancel__right__right) ).
thf(857,plain,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ A @ B ) )
= ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(758,plain,
( plus_plus_nat
= ( ^ [A: nat,B: nat] : ( plus_plus_nat @ B @ A ) ) ),
inference(lifteq,[status(thm)],[757]) ).
thf(1360,plain,
! [A: nat] :
( ( plus_plus_nat @ A )
= ( ^ [B: nat] : ( plus_plus_nat @ B @ A ) ) ),
inference(func_ext,[status(esa)],[758]) ).
thf(339,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= C )
=> ( A
= ( minus_minus_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_add__implies__diff) ).
thf(1350,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= C )
=> ( A
= ( minus_minus_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(60,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_mult_Oassoc) ).
thf(519,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(78,axiom,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_zero__reorient) ).
thf(578,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(248,axiom,
! [A: nat] :
( ( genClo1015804716orrect @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ zero_zero_real @ ( genClo1161277105lle_PC @ A @ zero_zero_real ) )
& ( ord_less_eq_real @ ( genClo1161277105lle_PC @ A @ zero_zero_real ) @ genClo872980712lle_mu ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_init) ).
thf(1089,plain,
! [A: nat] :
( ( genClo1015804716orrect @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ zero_zero_real @ ( genClo1161277105lle_PC @ A @ zero_zero_real ) )
& ( ord_less_eq_real @ ( genClo1161277105lle_PC @ A @ zero_zero_real ) @ genClo872980712lle_mu ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(300,axiom,
! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_abs__triangle__ineq4) ).
thf(1234,plain,
! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(173,axiom,
genClo1015804716orrect @ p @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_corr__p) ).
thf(874,plain,
genClo1015804716orrect @ p @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(267,axiom,
genClo1015804716orrect @ l @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_corr__l__tq) ).
thf(1143,plain,
genClo1015804716orrect @ l @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(1270,plain,
( genClo293725282kRead2
= ( ^ [A: nat > real,B: nat > real,C: real,D: nat > $o] :
! [E: nat] :
( ( D @ E )
=> ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ E ) @ ( B @ E ) ) ) @ C ) ) ) ),
inference(lifteq,[status(thm)],[1269]) ).
thf(309,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ C @ D ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_add__mono__thms__linordered__semiring_I1_J) ).
thf(1259,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ C @ D ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(96,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_add_Oleft__commute) ).
thf(650,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(200,axiom,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_diff__0__right) ).
thf(948,plain,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(5526,plain,
! [C: real,B: real,A: real] :
( ( ( B = zero_zero_real )
= ( C = one_one_real ) )
| ( ( A
= ( plus_plus_real @ A @ B ) )
!= ( one_one_real = C ) ) ),
inference(paramod_ordered,[status(thm)],[440,484]) ).
thf(5527,plain,
! [A: real] :
( ( ( plus_plus_real @ one_one_real @ A )
= one_one_real )
= ( A = zero_zero_real ) ),
inference(pattern_uni,[status(thm)],[5526:[bind(A,$thf( one_one_real )),bind(B,$thf( E )),bind(C,$thf( plus_plus_real @ one_one_real @ E ))]]) ).
thf(5615,plain,
! [A: real] :
( ( ( plus_plus_real @ one_one_real @ A )
= one_one_real )
= ( A = zero_zero_real ) ),
inference(simp,[status(thm)],[5527]) ).
thf(250,axiom,
! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_abs__triangle__ineq3) ).
thf(1096,plain,
! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(1663,plain,
( ( one_one_real != genClo1278781456e_beta )
| ( zero_zero_real != zero_zero_real )
| ( ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) )
!= ( minus_minus_real @ one_one_real @ one_one_real ) ) ),
inference(paramod_ordered,[status(thm)],[928,1453]) ).
thf(1664,plain,
( ( one_one_real != genClo1278781456e_beta )
| ( ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) )
!= ( minus_minus_real @ one_one_real @ one_one_real ) ) ),
inference(simp,[status(thm)],[1663]) ).
thf(1672,plain,
( ( one_one_real != genClo1278781456e_beta )
| ( ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real )
| ( ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real ) ),
inference(simp,[status(thm)],[1664]) ).
thf(265,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ ( minus_minus_real @ B @ C ) )
= ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_le__diff__eq) ).
thf(1138,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ ( minus_minus_real @ B @ C ) )
= ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(77,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_diff__le__self) ).
thf(576,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(577,plain,
! [B: nat,A: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
inference(cnf,[status(esa)],[576]) ).
thf(7572,plain,
! [B: nat,A: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ A )
= zero_zero_nat ),
inference(rewrite,[status(thm)],[577,477]) ).
thf(7593,plain,
! [B: nat,A: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ A )
= zero_zero_nat ),
inference(lifteq,[status(thm)],[7572]) ).
thf(8,axiom,
! [A: real,B: real] :
( ( ( times_times_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_mult__eq__0__iff) ).
thf(356,plain,
! [A: real,B: real] :
( ( ( times_times_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(273,axiom,
! [A: nat,B: real,C: nat] :
( ( ( genClo1015804716orrect @ A @ B )
& ( ord_less_eq_real @ B @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ C @ one_one_nat ) ) ) )
=> ( ord_less_eq_real @ ( minus_minus_real @ B @ ( genClo1163638703lle_te @ A @ C ) ) @ genClo1650508560e_rmax ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_rts0) ).
thf(1160,plain,
! [A: nat,B: real,C: nat] :
( ( ( genClo1015804716orrect @ A @ B )
& ( ord_less_eq_real @ B @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ C @ one_one_nat ) ) ) )
=> ( ord_less_eq_real @ ( minus_minus_real @ B @ ( genClo1163638703lle_te @ A @ C ) ) @ genClo1650508560e_rmax ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(50,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_distrib__right) ).
thf(488,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(720,plain,
( ( ^ [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) )
= ord_less_eq_real ),
inference(lifteq,[status(thm)],[719]) ).
thf(1659,plain,
! [A: real] :
( ( ^ [B: real] : ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ zero_zero_real ) )
= ( ord_less_eq_real @ A ) ),
inference(func_ext,[status(esa)],[720]) ).
thf(93,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_add__left__cancel) ).
thf(642,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(293,axiom,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_diff__diff__add) ).
thf(1214,plain,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(82,axiom,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_zero__reorient) ).
thf(590,plain,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(115,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_le__add__diff__inverse2) ).
thf(706,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(108,axiom,
! [A: nat,B: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
=> ( ( ( minus_minus_nat @ B @ A )
= zero_zero_nat )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_diffs0__imp__equal) ).
thf(686,plain,
! [A: nat,B: nat] :
( ( ( minus_minus_nat @ A @ B )
= zero_zero_nat )
=> ( ( ( minus_minus_nat @ B @ A )
= zero_zero_nat )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(256,axiom,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_one__reorient) ).
thf(1112,plain,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(1113,plain,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
inference(cnf,[status(esa)],[1112]) ).
thf(1114,plain,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
inference(lifteq,[status(thm)],[1113]) ).
thf(58,axiom,
! [A: real,B: real] :
( ( ( times_times_real @ A @ B )
= B )
= ( ( B = zero_zero_real )
| ( A = one_one_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_mult__cancel__right2) ).
thf(513,plain,
! [A: real,B: real] :
( ( ( times_times_real @ A @ B )
= B )
= ( ( B = zero_zero_real )
| ( A = one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(514,plain,
! [B: real,A: real] :
( ( ( times_times_real @ A @ B )
= B )
= ( ( B = zero_zero_real )
| ( A = one_one_real ) ) ),
inference(cnf,[status(esa)],[513]) ).
thf(515,plain,
! [B: real,A: real] :
( ( ( times_times_real @ A @ B )
= B )
= ( ( B = zero_zero_real )
| ( A = one_one_real ) ) ),
inference(lifteq,[status(thm)],[514]) ).
thf(322,axiom,
genClo1015804716orrect @ q @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_corr__q) ).
thf(1297,plain,
genClo1015804716orrect @ q @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(125,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( ord_less_eq_nat @ A @ ( plus_plus_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_le__diff__conv) ).
thf(738,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( ord_less_eq_nat @ A @ ( plus_plus_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(299,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_add__right__mono) ).
thf(1231,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(285,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
= ( ord_less_eq_nat @ zero_zero_nat @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_le__add__same__cancel1) ).
thf(1192,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
= ( ord_less_eq_nat @ zero_zero_nat @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(40,axiom,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_mult_Oright__neutral) ).
thf(457,plain,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1799,plain,
! [A: nat > real] :
( ( genClo293725282kRead2 @ A )
= ( ^ [B: nat > real,C: real,D: nat > $o] :
! [E: nat] :
( ( D @ E )
=> ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ E ) @ ( B @ E ) ) ) @ C ) ) ) ),
inference(func_ext,[status(esa)],[1270]) ).
thf(3611,plain,
( ~ $true
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( ( ord_less_eq_real @ zero_zero_real @ zero_zero_real )
!= ( ord_less_eq_real @ zero_zero_real @ genClo1278781456e_beta ) ) ),
inference(paramod_ordered,[status(thm)],[940,3590]) ).
thf(3612,plain,
( ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( ( ord_less_eq_real @ zero_zero_real @ zero_zero_real )
!= ( ord_less_eq_real @ zero_zero_real @ genClo1278781456e_beta ) ) ),
inference(simp,[status(thm)],[3611]) ).
thf(3613,plain,
( ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( zero_zero_real != zero_zero_real )
| ( zero_zero_real != genClo1278781456e_beta ) ),
inference(simp,[status(thm)],[3612]) ).
thf(3628,plain,
( ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( zero_zero_real != genClo1278781456e_beta ) ),
inference(simp,[status(thm)],[3613]) ).
thf(75,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ B )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ B @ C ) )
= ( ord_less_eq_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_le__diff__iff_H) ).
thf(569,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ B )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ B @ C ) )
= ( ord_less_eq_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(95,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(647,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(217,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_trans__le__add1) ).
thf(997,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(212,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_eq_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_add__leD2) ).
thf(984,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_eq_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(186,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ( ( minus_minus_nat @ B @ A )
= C )
= ( B
= ( plus_plus_nat @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add) ).
thf(911,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ( ( minus_minus_nat @ B @ A )
= C )
= ( B
= ( plus_plus_nat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(2291,plain,
! [A: real] :
( ~ $true
| ( ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real )
| ( q != p )
| ( ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) )
!= ( ord_less_eq_real @ zero_zero_real @ genClo1278781456e_beta ) ) ),
inference(paramod_ordered,[status(thm)],[1213,2099]) ).
thf(2292,plain,
! [A: real] :
( ( ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real )
| ( q != p )
| ( ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) )
!= ( ord_less_eq_real @ zero_zero_real @ genClo1278781456e_beta ) ) ),
inference(simp,[status(thm)],[2291]) ).
thf(2310,plain,
! [A: real] :
( ( ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real )
| ( q != p )
| ( zero_zero_real != zero_zero_real )
| ( ( abs_abs_real @ A )
!= genClo1278781456e_beta ) ),
inference(simp,[status(thm)],[2292]) ).
thf(2314,plain,
! [A: real] :
( ( ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real )
| ( q != p )
| ( ( abs_abs_real @ A )
!= genClo1278781456e_beta ) ),
inference(simp,[status(thm)],[2310]) ).
thf(3469,plain,
! [B: real,A: nat] :
( ( ( genClo1163638703lle_te @ p @ A )
!= one_one_real )
| ( q != p )
| ( ( abs_abs_real @ B )
!= genClo1278781456e_beta )
| ( ( plus_plus_nat @ zero_zero_nat @ A )
!= ( plus_plus_nat @ i @ one_one_nat ) ) ),
inference(paramod_ordered,[status(thm)],[894,2314]) ).
thf(3528,plain,
! [B: real,A: nat] :
( ( ( genClo1163638703lle_te @ p @ A )
!= one_one_real )
| ( q != p )
| ( ( abs_abs_real @ B )
!= genClo1278781456e_beta )
| ( i != zero_zero_nat )
| ( A != one_one_nat ) ),
inference(simp,[status(thm)],[3469]) ).
thf(3540,plain,
! [A: real] :
( ( ( genClo1163638703lle_te @ p @ one_one_nat )
!= one_one_real )
| ( q != p )
| ( ( abs_abs_real @ A )
!= genClo1278781456e_beta )
| ( i != zero_zero_nat ) ),
inference(simp,[status(thm)],[3528]) ).
thf(120,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc) ).
thf(721,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(329,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ A )
= ( ord_less_eq_real @ B @ zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_add__le__same__cancel1) ).
thf(1318,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ A )
= ( ord_less_eq_real @ B @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(247,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_add__left__mono) ).
thf(1086,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(149,axiom,
genClo1015804716orrect @ l @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_corr__l) ).
thf(805,plain,
genClo1015804716orrect @ l @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(7502,plain,
! [A: real] :
( ~ $true
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) )
!= ( ord_less_eq_real @ ( abs_abs_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) ) @ genClo1278781456e_beta ) ) ),
inference(paramod_ordered,[status(thm)],[888,3399]) ).
thf(7503,plain,
! [A: real] :
( ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) )
!= ( ord_less_eq_real @ ( abs_abs_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) ) @ genClo1278781456e_beta ) ) ),
inference(simp,[status(thm)],[7502]) ).
thf(7525,plain,
! [A: real] :
( ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( A
!= ( abs_abs_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) ) )
| ( ( abs_abs_real @ A )
!= genClo1278781456e_beta ) ),
inference(simp,[status(thm)],[7503]) ).
thf(7541,plain,
( ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( ( abs_abs_real @ ( abs_abs_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) ) )
!= genClo1278781456e_beta ) ),
inference(simp,[status(thm)],[7525]) ).
thf(9782,plain,
( ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( ( abs_abs_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) )
!= genClo1278781456e_beta ) ),
inference(rewrite,[status(thm)],[7541,698]) ).
thf(277,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse) ).
thf(1170,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(3065,plain,
! [A: nat] :
( ~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ zero_zero_real @ zero_zero_real ) ) @ genClo1278781456e_beta )
| ( A != zero_zero_nat )
| ( ( plus_plus_nat @ A @ zero_zero_nat )
!= ( plus_plus_nat @ i @ one_one_nat ) ) ),
inference(paramod_ordered,[status(thm)],[702,2865]) ).
thf(3087,plain,
( ~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ zero_zero_real @ zero_zero_real ) ) @ genClo1278781456e_beta )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= ( plus_plus_nat @ zero_zero_nat @ zero_zero_nat ) ) ),
inference(simp,[status(thm)],[3065]) ).
thf(6647,plain,
( ~ ( ord_less_eq_real @ ( abs_abs_real @ zero_zero_real ) @ genClo1278781456e_beta )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat ) ),
inference(rewrite,[status(thm)],[3087,894,959]) ).
thf(73,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_divisors__zero) ).
thf(558,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= zero_zero_nat )
=> ( ( A = zero_zero_nat )
| ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(226,axiom,
! [A: real,B: real,C: real,D: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ( ( minus_minus_real @ A @ D )
= ( plus_plus_real @ B @ ( minus_minus_real @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_group__cancel_Osub1) ).
thf(1026,plain,
! [A: real,B: real,C: real,D: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ( ( minus_minus_real @ A @ D )
= ( plus_plus_real @ B @ ( minus_minus_real @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(64,axiom,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_mult__zero__left) ).
thf(530,plain,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(202,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ( ord_less_eq_nat @ C @ ( plus_plus_nat @ D @ B ) )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ( ord_less_eq_nat @ C @ ( plus_plus_nat @ D @ B ) )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_add__le__add__imp__diff__le) ).
thf(953,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ( ord_less_eq_nat @ C @ ( plus_plus_nat @ D @ B ) )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ( ord_less_eq_nat @ C @ ( plus_plus_nat @ D @ B ) )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(283,axiom,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( plus_plus_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_le__iff__add) ).
thf(1187,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( plus_plus_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(104,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_ring__class_Oring__distribs_I1_J) ).
thf(674,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(100,axiom,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( times_times_nat @ B @ A )
= ( times_times_nat @ C @ A ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_mult__right__cancel) ).
thf(662,plain,
! [A: nat,B: nat,C: nat] :
( ( A != zero_zero_nat )
=> ( ( ( times_times_nat @ B @ A )
= ( times_times_nat @ C @ A ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(264,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_comm__semiring__class_Odistrib) ).
thf(1135,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(128,axiom,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_comm__monoid__mult__class_Omult__1) ).
thf(748,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(749,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(cnf,[status(esa)],[748]) ).
thf(750,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(lifteq,[status(thm)],[749]) ).
thf(253,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ord_less_eq_real @ ( minus_minus_real @ A @ D ) @ ( minus_minus_real @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_diff__mono) ).
thf(1103,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ord_less_eq_real @ ( minus_minus_real @ A @ D ) @ ( minus_minus_real @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(324,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
= ( ord_less_eq_real @ A @ zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_add__le__same__cancel2) ).
thf(1301,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
= ( ord_less_eq_real @ A @ zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(76,axiom,
! [A: real,B: real] :
( ( ( times_times_real @ A @ B )
= zero_zero_real )
=> ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_divisors__zero) ).
thf(573,plain,
! [A: real,B: real] :
( ( ( times_times_real @ A @ B )
= zero_zero_real )
=> ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(109,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( times_times_real @ B @ C ) )
= ( times_times_real @ B @ ( times_times_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_mult_Oleft__commute) ).
thf(689,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( times_times_real @ B @ C ) )
= ( times_times_real @ B @ ( times_times_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(51,axiom,
! [A: real,B: real,C: real,D: real] :
( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( plus_plus_real @ ( times_times_real @ C @ B ) @ D ) )
= ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ C ) @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_combine__common__factor) ).
thf(491,plain,
! [A: real,B: real,C: real,D: real] :
( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( plus_plus_real @ ( times_times_real @ C @ B ) @ D ) )
= ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ C ) @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(492,plain,
! [D: real,C: real,B: real,A: real] :
( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( plus_plus_real @ ( times_times_real @ C @ B ) @ D ) )
= ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ C ) @ B ) @ D ) ),
inference(cnf,[status(esa)],[491]) ).
thf(493,plain,
! [D: real,C: real,B: real,A: real] :
( ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ C ) @ B ) @ D )
= ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( plus_plus_real @ ( times_times_real @ C @ B ) @ D ) ) ),
inference(lifteq,[status(thm)],[492]) ).
thf(405,plain,
! [C: real,B: real,A: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
inference(cnf,[status(esa)],[404]) ).
thf(406,plain,
! [C: real,B: real,A: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
inference(lifteq,[status(thm)],[405]) ).
thf(7910,plain,
! [D: real,C: real,B: real,A: real] :
( ( plus_plus_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ B ) ) @ D )
= ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( plus_plus_real @ ( times_times_real @ C @ B ) @ D ) ) ),
inference(rewrite,[status(thm)],[493,406]) ).
thf(1188,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( plus_plus_nat @ A @ C ) ) ) ),
inference(lifteq,[status(thm)],[1187]) ).
thf(7567,plain,
( ( ^ [A: nat,B: nat] :
( ( minus_minus_nat @ A @ B )
= zero_zero_nat ) )
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( plus_plus_nat @ A @ C ) ) ) ),
inference(rewrite,[status(thm)],[1188,477]) ).
thf(184,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
= ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_Nat_Odiff__add__assoc2) ).
thf(904,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
= ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(220,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_le__add__diff__inverse) ).
thf(1007,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(23,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_le__refl) ).
thf(402,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(162,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
= ( ord_less_eq_nat @ zero_zero_nat @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_le__add__same__cancel2) ).
thf(843,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
= ( ord_less_eq_nat @ zero_zero_nat @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(486,plain,
! [A: nat] :
( ~ ( ord_less_eq_nat @ A @ zero_zero_nat )
| ( A = zero_zero_nat ) ),
inference(cnf,[status(esa)],[485]) ).
thf(487,plain,
! [A: nat] :
( ( A = zero_zero_nat )
| ~ ( ord_less_eq_nat @ A @ zero_zero_nat ) ),
inference(lifteq,[status(thm)],[486]) ).
thf(7703,plain,
! [A: nat] :
( ( A = zero_zero_nat )
| ( ( minus_minus_nat @ A @ zero_zero_nat )
!= zero_zero_nat ) ),
inference(rewrite,[status(thm)],[487,477]) ).
thf(7704,plain,
! [A: nat] :
( ( ( minus_minus_nat @ A @ zero_zero_nat )
!= zero_zero_nat )
| ( A = zero_zero_nat ) ),
inference(lifteq,[status(thm)],[7703]) ).
thf(1514,plain,
( ~ $true
| ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) @ genClo1278781456e_beta )
!= ( ord_less_eq_real @ zero_zero_real @ zero_zero_real ) ) ),
inference(paramod_ordered,[status(thm)],[940,340]) ).
thf(1515,plain,
( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) @ genClo1278781456e_beta )
!= ( ord_less_eq_real @ zero_zero_real @ zero_zero_real ) ),
inference(simp,[status(thm)],[1514]) ).
thf(1520,plain,
( ( ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) )
!= zero_zero_real )
| ( zero_zero_real != genClo1278781456e_beta ) ),
inference(simp,[status(thm)],[1515]) ).
thf(260,axiom,
! [A: real,B: real] :
( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
= ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_abs__add__abs) ).
thf(1124,plain,
! [A: real,B: real] :
( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
= ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(308,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_right__diff__distrib) ).
thf(1256,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(27,axiom,
! [A: real,B: real,C: real] :
( ( ( times_times_real @ A @ B )
= ( times_times_real @ C @ B ) )
= ( ( B = zero_zero_real )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_mult__cancel__right) ).
thf(413,plain,
! [A: real,B: real,C: real] :
( ( ( times_times_real @ A @ B )
= ( times_times_real @ C @ B ) )
= ( ( B = zero_zero_real )
| ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(80,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( A = zero_zero_nat )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_mult__cancel__left) ).
thf(584,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ A @ C ) )
= ( ( A = zero_zero_nat )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(271,axiom,
! [A: real,B: real,C: real] :
( ( A
= ( minus_minus_real @ B @ C ) )
= ( B
= ( plus_plus_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_eq__diff__eq_H) ).
thf(1154,plain,
! [A: real,B: real,C: real] :
( ( A
= ( minus_minus_real @ B @ C ) )
= ( B
= ( plus_plus_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(4708,plain,
! [C: real,B: real,A: real] :
( ( ( sk1 @ B @ A )
= C )
| ( ( plus_plus_real @ zero_zero_real @ A )
!= ( plus_plus_real @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[379,4707]) ).
thf(4709,plain,
! [A: real] :
( ( sk1 @ zero_zero_real @ A )
= A ),
inference(pattern_uni,[status(thm)],[4708:[bind(A,$thf( A )),bind(B,$thf( zero_zero_real )),bind(C,$thf( A ))]]) ).
thf(381,plain,
! [C: real,B: real,A: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
= ( A = C ) ),
inference(cnf,[status(esa)],[380]) ).
thf(382,plain,
! [C: real,B: real,A: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
= ( A = C ) ),
inference(lifteq,[status(thm)],[381]) ).
thf(314,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ? [C: nat] :
( B
= ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_le__Suc__ex) ).
thf(1271,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ? [C: nat] :
( B
= ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(143,axiom,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_add__diff__cancel__right_H) ).
thf(787,plain,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(302,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_add__increasing) ).
thf(1239,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(43,axiom,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_mult__zero__right) ).
thf(464,plain,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(465,plain,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(cnf,[status(esa)],[464]) ).
thf(466,plain,
! [A: nat] :
( ( times_times_nat @ A @ zero_zero_nat )
= zero_zero_nat ),
inference(lifteq,[status(thm)],[465]) ).
thf(188,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_left__diff__distrib_H) ).
thf(919,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(12,axiom,
( plus_plus_real
= ( ^ [A: real,B: real] : ( plus_plus_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_add_Ocommute) ).
thf(368,plain,
( plus_plus_real
= ( ^ [A: real,B: real] : ( plus_plus_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(369,plain,
( plus_plus_real
= ( ^ [A: real,B: real] : ( plus_plus_real @ B @ A ) ) ),
inference(lifteq,[status(thm)],[368]) ).
thf(1356,plain,
! [A: real] :
( ( plus_plus_real @ A )
= ( ^ [B: real] : ( plus_plus_real @ B @ A ) ) ),
inference(func_ext,[status(esa)],[369]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_le__trans) ).
thf(350,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(35,axiom,
! [A: real,B: real,C: real,D: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ( ( plus_plus_real @ D @ A )
= ( plus_plus_real @ B @ ( plus_plus_real @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_group__cancel_Oadd2) ).
thf(441,plain,
! [A: real,B: real,C: real,D: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ( ( plus_plus_real @ D @ A )
= ( plus_plus_real @ B @ ( plus_plus_real @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(442,plain,
! [A: real,B: real,C: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ! [D: real] :
( ( plus_plus_real @ D @ A )
= ( plus_plus_real @ B @ ( plus_plus_real @ D @ C ) ) ) ),
inference(miniscope,[status(thm)],[441]) ).
thf(443,plain,
! [D: real,C: real,B: real,A: real] :
( ( A
!= ( plus_plus_real @ B @ C ) )
| ( ( plus_plus_real @ D @ A )
= ( plus_plus_real @ B @ ( plus_plus_real @ D @ C ) ) ) ),
inference(cnf,[status(esa)],[442]) ).
thf(444,plain,
! [D: real,C: real,B: real,A: real] :
( ( A
!= ( plus_plus_real @ B @ C ) )
| ( ( plus_plus_real @ D @ A )
= ( plus_plus_real @ B @ ( plus_plus_real @ D @ C ) ) ) ),
inference(lifteq,[status(thm)],[443]) ).
thf(445,plain,
! [C: real,B: real,A: real] :
( ( plus_plus_real @ C @ ( plus_plus_real @ A @ B ) )
= ( plus_plus_real @ A @ ( plus_plus_real @ C @ B ) ) ),
inference(simp,[status(thm)],[444]) ).
thf(3743,plain,
! [A: real] :
( ( zero_zero_real != zero_zero_real )
| ( zero_zero_real != genClo1278781456e_beta )
| ( ( minus_minus_real @ A @ A )
!= ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[959,1604]) ).
thf(3744,plain,
! [A: real] :
( ( zero_zero_real != genClo1278781456e_beta )
| ( ( minus_minus_real @ A @ A )
!= ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) ),
inference(simp,[status(thm)],[3743]) ).
thf(3766,plain,
! [A: real] :
( ( zero_zero_real != genClo1278781456e_beta )
| ( A
!= ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) )
| ( A
!= ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ),
inference(simp,[status(thm)],[3744]) ).
thf(3773,plain,
( ( zero_zero_real != genClo1278781456e_beta )
| ( ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) )
!= ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ),
inference(simp,[status(thm)],[3766]) ).
thf(53,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= ( ord_less_eq_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_le__diff__iff) ).
thf(497,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= ( ord_less_eq_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(498,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ! [C: nat] :
( ( ord_less_eq_nat @ A @ C )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= ( ord_less_eq_nat @ B @ C ) ) ) ),
inference(miniscope,[status(thm)],[497]) ).
thf(499,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
| ~ ( ord_less_eq_nat @ A @ C )
| ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= ( ord_less_eq_nat @ B @ C ) ) ),
inference(cnf,[status(esa)],[498]) ).
thf(500,plain,
! [C: nat,B: nat,A: nat] :
( ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= ( ord_less_eq_nat @ B @ C ) )
| ~ ( ord_less_eq_nat @ A @ B )
| ~ ( ord_less_eq_nat @ A @ C ) ),
inference(lifteq,[status(thm)],[499]) ).
thf(8358,plain,
! [C: nat,B: nat,A: nat] :
( ( ( ( minus_minus_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= zero_zero_nat )
= ( ( minus_minus_nat @ B @ C )
= zero_zero_nat ) )
| ( ( minus_minus_nat @ A @ B )
!= zero_zero_nat )
| ( ( minus_minus_nat @ A @ C )
!= zero_zero_nat ) ),
inference(rewrite,[status(thm)],[500,477]) ).
thf(8359,plain,
! [C: nat,B: nat,A: nat] :
( ( ( minus_minus_nat @ A @ B )
!= zero_zero_nat )
| ( ( minus_minus_nat @ A @ C )
!= zero_zero_nat )
| ( ( ( minus_minus_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= zero_zero_nat )
= ( ( minus_minus_nat @ B @ C )
= zero_zero_nat ) ) ),
inference(lifteq,[status(thm)],[8358]) ).
thf(291,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
= ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_add__cancel__left__right) ).
thf(1209,plain,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
= ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(142,axiom,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_diff__right__commute) ).
thf(784,plain,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(473,plain,
? [A: real > real > real] :
! [B: real,C: real] :
( ( A @ C @ ( plus_plus_real @ B @ C ) )
= B ),
inference(detectInverse,[status(thm)],[472]) ).
thf(474,plain,
! [B: real,A: real] :
( ( sk2 @ B @ ( plus_plus_real @ A @ B ) )
= A ),
inference(cnf,[status(esa)],[473]) ).
thf(7280,plain,
! [B: real,A: real] :
( ( sk2 @ B @ ( plus_plus_real @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[474]) ).
thf(7281,plain,
! [C: real,B: real,A: real] :
( ( ( sk2 @ C @ A )
= B )
| ( ( plus_plus_real @ zero_zero_real @ A )
!= ( plus_plus_real @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[379,7280]) ).
thf(7282,plain,
! [A: real] :
( ( sk2 @ A @ A )
= zero_zero_real ),
inference(pattern_uni,[status(thm)],[7281:[bind(A,$thf( A )),bind(B,$thf( zero_zero_real )),bind(C,$thf( A ))]]) ).
thf(268,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
= ( ord_less_eq_real @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_add__le__cancel__left) ).
thf(1144,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
= ( ord_less_eq_real @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(279,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( genClo1015804716orrect @ A @ ( genClo1163638703lle_te @ A @ C ) )
& ( genClo1015804716orrect @ B @ ( genClo1163638703lle_te @ B @ C ) ) )
=> ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ A @ C ) @ ( genClo1163638703lle_te @ B @ C ) ) ) @ genClo1278781456e_beta ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_rts2b) ).
thf(1175,plain,
! [A: nat,B: nat,C: nat] :
( ( ( genClo1015804716orrect @ A @ ( genClo1163638703lle_te @ A @ C ) )
& ( genClo1015804716orrect @ B @ ( genClo1163638703lle_te @ B @ C ) ) )
=> ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ A @ C ) @ ( genClo1163638703lle_te @ B @ C ) ) ) @ genClo1278781456e_beta ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(508,plain,
! [B: real,A: real] :
( ( A
= ( plus_plus_real @ B @ A ) )
= ( B = zero_zero_real ) ),
inference(cnf,[status(esa)],[507]) ).
thf(509,plain,
! [B: real,A: real] :
( ( A
= ( plus_plus_real @ B @ A ) )
= ( B = zero_zero_real ) ),
inference(lifteq,[status(thm)],[508]) ).
thf(32,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_mult_Oleft__commute) ).
thf(432,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(433,plain,
! [C: nat,B: nat,A: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
inference(cnf,[status(esa)],[432]) ).
thf(434,plain,
! [C: nat,B: nat,A: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
inference(lifteq,[status(thm)],[433]) ).
thf(7291,plain,
! [C: real,B: real,A: real] :
( ( ( sk2 @ C @ A )
= B )
| ( ( plus_plus_real @ A @ zero_zero_real )
!= ( plus_plus_real @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[401,7280]) ).
thf(7292,plain,
! [A: real] :
( ( sk2 @ zero_zero_real @ A )
= A ),
inference(pattern_uni,[status(thm)],[7291:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( zero_zero_real ))]]) ).
thf(331,axiom,
! [A: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
= ( ord_less_eq_real @ zero_zero_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_zero__le__double__add__iff__zero__le__single__add) ).
thf(1325,plain,
! [A: real] :
( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
= ( ord_less_eq_real @ zero_zero_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(181,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_add__nonneg__eq__0__iff) ).
thf(895,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ zero_zero_nat @ B )
=> ( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(337,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ ( plus_plus_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_trans__le__add2) ).
thf(1344,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ ( plus_plus_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(137,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_eq_nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_add__leD1) ).
thf(769,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_eq_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(102,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
= ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_right__diff__distrib_H) ).
thf(668,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
= ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(280,axiom,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_diff__add__eq__diff__diff__swap) ).
thf(1177,plain,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
= ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(461,plain,
! [B: real,A: real] :
( ( ( plus_plus_real @ A @ B )
= B )
= ( A = zero_zero_real ) ),
inference(cnf,[status(esa)],[460]) ).
thf(462,plain,
! [B: real,A: real] :
( ( ( plus_plus_real @ A @ B )
= B )
= ( A = zero_zero_real ) ),
inference(lifteq,[status(thm)],[461]) ).
thf(52,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_diff__diff__cancel) ).
thf(494,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(245,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_add__increasing2) ).
thf(1080,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ zero_zero_nat @ A )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(71,axiom,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_mult_Ocomm__neutral) ).
thf(552,plain,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(147,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_add__le__mono) ).
thf(799,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(274,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_combine__common__factor) ).
thf(1162,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(304,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_comm__monoid__add__class_Oadd__0) ).
thf(1245,plain,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(171,axiom,
! [A: real,B: real,C: real] :
( ( A
= ( minus_minus_real @ B @ C ) )
= ( ( plus_plus_real @ A @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_eq__diff__eq) ).
thf(868,plain,
! [A: real,B: real,C: real] :
( ( A
= ( minus_minus_real @ B @ C ) )
= ( ( plus_plus_real @ A @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(141,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( A = B )
& ( ord_less_eq_real @ C @ D ) )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_add__mono__thms__linordered__semiring_I2_J) ).
thf(780,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( A = B )
& ( ord_less_eq_real @ C @ D ) )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(222,axiom,
! [A: nat,B: real,C: real] :
( ( ( genClo1015804716orrect @ A @ C )
& ( ord_less_eq_real @ B @ C ) )
=> ( ord_less_eq_real @ ( genClo1161277105lle_PC @ A @ B ) @ ( genClo1161277105lle_PC @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_PC__monotone) ).
thf(1015,plain,
! [A: nat,B: real,C: real] :
( ( ( genClo1015804716orrect @ A @ C )
& ( ord_less_eq_real @ B @ C ) )
=> ( ord_less_eq_real @ ( genClo1161277105lle_PC @ A @ B ) @ ( genClo1161277105lle_PC @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(213,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
= ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_diff__le__eq) ).
thf(986,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
= ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(2790,plain,
! [A: nat] :
( ( ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real )
| ( zero_zero_real != zero_zero_real )
| ( ( genClo1163638703lle_te @ A @ zero_zero_nat )
!= ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[1058,2643]) ).
thf(2791,plain,
! [A: nat] :
( ( ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real )
| ( ( genClo1163638703lle_te @ A @ zero_zero_nat )
!= ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ),
inference(simp,[status(thm)],[2790]) ).
thf(2792,plain,
! [A: nat] :
( ( ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real )
| ( A != p )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat ) ),
inference(simp,[status(thm)],[2791]) ).
thf(2797,plain,
( ( ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat ) ),
inference(simp,[status(thm)],[2792]) ).
thf(218,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
= ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc) ).
thf(1000,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
= ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(306,axiom,
! [A: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( abs_abs_real @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_abs__of__nonneg) ).
thf(1250,plain,
! [A: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( abs_abs_real @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(3365,plain,
! [A: real] :
( ~ $true
| ( ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) )
!= ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) @ genClo1278781456e_beta ) ) ),
inference(paramod_ordered,[status(thm)],[888,340]) ).
thf(3366,plain,
! [A: real] :
( ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) )
!= ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) @ genClo1278781456e_beta ) ),
inference(simp,[status(thm)],[3365]) ).
thf(3386,plain,
! [A: real] :
( ( A
!= ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) )
| ( ( abs_abs_real @ A )
!= genClo1278781456e_beta ) ),
inference(simp,[status(thm)],[3366]) ).
thf(3394,plain,
( ( abs_abs_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ) )
!= genClo1278781456e_beta ),
inference(simp,[status(thm)],[3386]) ).
thf(10031,plain,
( ( abs_abs_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) )
!= genClo1278781456e_beta ),
inference(rewrite,[status(thm)],[3394,698]) ).
thf(31,axiom,
! [A: real,B: real,C: real,D: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ( ( plus_plus_real @ A @ D )
= ( plus_plus_real @ B @ ( plus_plus_real @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_group__cancel_Oadd1) ).
thf(427,plain,
! [A: real,B: real,C: real,D: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ( ( plus_plus_real @ A @ D )
= ( plus_plus_real @ B @ ( plus_plus_real @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(428,plain,
! [A: real,B: real,C: real] :
( ( A
= ( plus_plus_real @ B @ C ) )
=> ! [D: real] :
( ( plus_plus_real @ A @ D )
= ( plus_plus_real @ B @ ( plus_plus_real @ C @ D ) ) ) ),
inference(miniscope,[status(thm)],[427]) ).
thf(429,plain,
! [D: real,C: real,B: real,A: real] :
( ( A
!= ( plus_plus_real @ B @ C ) )
| ( ( plus_plus_real @ A @ D )
= ( plus_plus_real @ B @ ( plus_plus_real @ C @ D ) ) ) ),
inference(cnf,[status(esa)],[428]) ).
thf(430,plain,
! [D: real,C: real,B: real,A: real] :
( ( A
!= ( plus_plus_real @ B @ C ) )
| ( ( plus_plus_real @ A @ D )
= ( plus_plus_real @ B @ ( plus_plus_real @ C @ D ) ) ) ),
inference(lifteq,[status(thm)],[429]) ).
thf(431,plain,
! [C: real,B: real,A: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
inference(simp,[status(thm)],[430]) ).
thf(97,axiom,
! [A: real] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_mult__zero__left) ).
thf(653,plain,
! [A: real] :
( ( times_times_real @ zero_zero_real @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(767,plain,
! [A: real] :
( ( ( abs_abs_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(cnf,[status(esa)],[766]) ).
thf(768,plain,
! [A: real] :
( ( ( abs_abs_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(lifteq,[status(thm)],[767]) ).
thf(156,axiom,
! [A: nat,B: real,C: real] :
( ( ( ord_less_eq_real @ B @ C )
& ( genClo1015804716orrect @ A @ C ) )
=> ( genClo1015804716orrect @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_correct__closed) ).
thf(827,plain,
! [A: nat,B: real,C: real] :
( ( ( ord_less_eq_real @ B @ C )
& ( genClo1015804716orrect @ A @ C ) )
=> ( genClo1015804716orrect @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(325,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
= ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2) ).
thf(1304,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
= ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(1680,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A )
= ( ^ [B: nat] :
? [C: nat] :
( B
= ( plus_plus_nat @ A @ C ) ) ) ),
inference(func_ext,[status(esa)],[1188]) ).
thf(7571,plain,
! [A: nat] :
( ( ^ [B: nat] :
( ( minus_minus_nat @ A @ B )
= zero_zero_nat ) )
= ( ^ [B: nat] :
? [C: nat] :
( B
= ( plus_plus_nat @ A @ C ) ) ) ),
inference(rewrite,[status(thm)],[1680,477]) ).
thf(316,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_add__right__cancel) ).
thf(1277,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(152,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ A )
= ( ord_less_eq_nat @ B @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_add__le__same__cancel1) ).
thf(812,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ A )
= ( ord_less_eq_nat @ B @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(59,axiom,
! [A: real] :
( ( zero_zero_real
= ( plus_plus_real @ A @ A ) )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_double__zero__sym) ).
thf(516,plain,
! [A: real] :
( ( zero_zero_real
= ( plus_plus_real @ A @ A ) )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(354,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
inference(cnf,[status(esa)],[353]) ).
thf(355,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
inference(lifteq,[status(thm)],[354]) ).
thf(155,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ord_less_eq_nat @ A @ B )
& ( C = D ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_add__mono__thms__linordered__semiring_I3_J) ).
thf(823,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ord_less_eq_nat @ A @ B )
& ( C = D ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(232,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_add__eq__0__iff__both__eq__0) ).
thf(1049,plain,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(243,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_diff__diff__add) ).
thf(1076,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(289,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= B )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_add__cancel__left__left) ).
thf(1203,plain,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= B )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(1207,plain,
! [A: real] :
( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
= ( ord_less_eq_real @ zero_zero_real @ A ) ),
inference(cnf,[status(esa)],[1206]) ).
thf(1208,plain,
! [A: real] :
( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
= ( ord_less_eq_real @ zero_zero_real @ A ) ),
inference(lifteq,[status(thm)],[1207]) ).
thf(146,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
= ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_Nat_Odiff__add__assoc) ).
thf(795,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
= ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(106,axiom,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_add_Ogroup__left__neutral) ).
thf(680,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(140,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2) ).
thf(776,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(62,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_diff__right__commute) ).
thf(525,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(117,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_add__eq__self__zero) ).
thf(712,plain,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
=> ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(7611,plain,
( ( one_one_real != genClo1278781456e_beta )
| ( q != p )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= ( plus_plus_nat @ i @ one_one_nat ) ) ),
inference(simp,[status(thm)],[3767]) ).
thf(7635,plain,
( ( one_one_real != genClo1278781456e_beta )
| ( q != p ) ),
inference(simp,[status(thm)],[7611]) ).
thf(297,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_add__right__mono) ).
thf(1225,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(208,axiom,
! [A: nat,B: nat,C: nat] :
( ( genClo1015804716orrect @ A @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) )
=> ( ( genClo1015804716orrect @ C @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) )
=> ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) @ ( genClo1163638703lle_te @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_beta__bound1) ).
thf(971,plain,
! [A: nat,B: nat,C: nat] :
( ( genClo1015804716orrect @ A @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) )
=> ( ( genClo1015804716orrect @ C @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) )
=> ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) @ ( genClo1163638703lle_te @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(312,axiom,
! [A: nat,B: nat] :
( ( genClo1015804716orrect @ A @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) )
=> ( ord_less_eq_real @ genClo1651033342e_rmin @ ( minus_minus_real @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) @ ( genClo1163638703lle_te @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_rts1d) ).
thf(1267,plain,
! [A: nat,B: nat] :
( ( genClo1015804716orrect @ A @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) )
=> ( ord_less_eq_real @ genClo1651033342e_rmin @ ( minus_minus_real @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) @ ( genClo1163638703lle_te @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(408,plain,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(cnf,[status(esa)],[407]) ).
thf(409,plain,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(lifteq,[status(thm)],[408]) ).
thf(251,axiom,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_mult_Oleft__neutral) ).
thf(1098,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(579,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(cnf,[status(esa)],[578]) ).
thf(580,plain,
! [A: nat] :
( ( zero_zero_nat = A )
= ( A = zero_zero_nat ) ),
inference(lifteq,[status(thm)],[579]) ).
thf(166,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
=> ( ord_less_eq_real @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_add__le__imp__le__left) ).
thf(855,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) )
=> ( ord_less_eq_real @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(234,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_add__le__cancel__left) ).
thf(1053,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(13,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= ( minus_minus_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_Nat_Odiff__diff__eq) ).
thf(370,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= ( minus_minus_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(161,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_add__le__cancel__right) ).
thf(840,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(42,axiom,
ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_le__numeral__extra_I3_J) ).
thf(463,plain,
ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(201,axiom,
! [A: nat,B: nat] :
( ( genClo1015804716orrect @ A @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) )
=> ( ord_less_eq_real @ ( genClo1163638703lle_te @ A @ B ) @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_rte) ).
thf(951,plain,
! [A: nat,B: nat] :
( ( genClo1015804716orrect @ A @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) )
=> ( ord_less_eq_real @ ( genClo1163638703lle_te @ A @ B ) @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(318,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( minus_minus_nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_diff__cancel2) ).
thf(1285,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( minus_minus_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(295,axiom,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_diff__diff__eq2) ).
thf(1220,plain,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(1358,plain,
! [A: nat] :
( ( times_times_nat @ A )
= ( ^ [B: nat] : ( times_times_nat @ B @ A ) ) ),
inference(func_ext,[status(esa)],[646]) ).
thf(127,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_add__leE) ).
thf(744,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(114,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_add__mono) ).
thf(703,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(266,axiom,
! [A: nat,B: nat] :
( ( genClo1015804716orrect @ A @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) )
=> ( ord_less_eq_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) @ ( genClo1163638703lle_te @ A @ B ) ) @ genClo1650508560e_rmax ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_rts0d) ).
thf(1141,plain,
! [A: nat,B: nat] :
( ( genClo1015804716orrect @ A @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) )
=> ( ord_less_eq_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) @ ( genClo1163638703lle_te @ A @ B ) ) @ genClo1650508560e_rmax ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(85,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_Nat_Oex__has__greatest__nat) ).
thf(600,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(233,axiom,
ord_less_eq_nat @ one_one_nat @ one_one_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_le__numeral__extra_I4_J) ).
thf(1052,plain,
ord_less_eq_nat @ one_one_nat @ one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(990,plain,
zero_zero_nat != one_one_nat,
inference(polarity_switch,[status(thm)],[989]) ).
thf(991,plain,
zero_zero_nat != one_one_nat,
inference(lifteq,[status(thm)],[990]) ).
thf(98,axiom,
! [A: real,B: real] :
( ( ( times_times_real @ A @ B )
= A )
= ( ( A = zero_zero_real )
| ( B = one_one_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_mult__cancel__left2) ).
thf(656,plain,
! [A: real,B: real] :
( ( ( times_times_real @ A @ B )
= A )
= ( ( A = zero_zero_real )
| ( B = one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(225,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_diff__eq__diff__eq) ).
thf(1023,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(4459,plain,
! [A: nat] :
( ( A != zero_zero_nat )
| ( ( abs_abs_real @ ( minus_minus_real @ zero_zero_real @ zero_zero_real ) )
!= genClo1278781456e_beta )
| ( ( plus_plus_nat @ zero_zero_nat @ A )
!= ( plus_plus_nat @ i @ one_one_nat ) ) ),
inference(paramod_ordered,[status(thm)],[894,4450]) ).
thf(4469,plain,
( ( ( abs_abs_real @ ( minus_minus_real @ zero_zero_real @ zero_zero_real ) )
!= genClo1278781456e_beta )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= ( plus_plus_nat @ zero_zero_nat @ zero_zero_nat ) ) ),
inference(simp,[status(thm)],[4459]) ).
thf(5873,plain,
( ( ( abs_abs_real @ zero_zero_real )
!= genClo1278781456e_beta )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat ) ),
inference(rewrite,[status(thm)],[4469,894,959]) ).
thf(88,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_le0) ).
thf(627,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(281,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C )
=> ( ( ord_less_eq_real @ C @ ( plus_plus_real @ D @ B ) )
=> ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C )
=> ( ( ord_less_eq_real @ C @ ( plus_plus_real @ D @ B ) )
=> ( ord_less_eq_real @ ( minus_minus_real @ C @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_add__le__add__imp__diff__le) ).
thf(1180,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C )
=> ( ( ord_less_eq_real @ C @ ( plus_plus_real @ D @ B ) )
=> ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C )
=> ( ( ord_less_eq_real @ C @ ( plus_plus_real @ D @ B ) )
=> ( ord_less_eq_real @ ( minus_minus_real @ C @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(67,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_le__antisym) ).
thf(539,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(103,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(671,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(79,axiom,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_mult_Oleft__neutral) ).
thf(581,plain,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(133,axiom,
genClo1015804716orrect @ q @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_corr__q__tq) ).
thf(759,plain,
genClo1015804716orrect @ q @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(284,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_add__left__mono) ).
thf(1189,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(138,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_add__increasing) ).
thf(771,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(3470,plain,
! [A: nat] :
( ( ( genClo1163638703lle_te @ q @ A )
!= one_one_real )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( ( plus_plus_nat @ zero_zero_nat @ A )
!= ( plus_plus_nat @ i @ one_one_nat ) ) ),
inference(paramod_ordered,[status(thm)],[894,2797]) ).
thf(3513,plain,
! [A: nat] :
( ( ( genClo1163638703lle_te @ q @ A )
!= one_one_real )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( i != zero_zero_nat )
| ( A != one_one_nat ) ),
inference(simp,[status(thm)],[3470]) ).
thf(3565,plain,
( ( ( genClo1163638703lle_te @ q @ one_one_nat )
!= one_one_real )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( i != zero_zero_nat ) ),
inference(simp,[status(thm)],[3513]) ).
thf(2221,plain,
! [A: nat] :
( ( one_one_real != genClo1278781456e_beta )
| ( ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ zero_zero_real )
!= zero_zero_real )
| ( ( genClo1163638703lle_te @ A @ zero_zero_nat )
!= ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[1058,1453]) ).
thf(2245,plain,
! [A: nat] :
( ( one_one_real != genClo1278781456e_beta )
| ( ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ zero_zero_real )
!= zero_zero_real )
| ( A != q )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat ) ),
inference(simp,[status(thm)],[2221]) ).
thf(2264,plain,
( ( one_one_real != genClo1278781456e_beta )
| ( ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ zero_zero_real )
!= zero_zero_real )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat ) ),
inference(simp,[status(thm)],[2245]) ).
thf(2592,plain,
! [A: nat] :
( ( one_one_real != genClo1278781456e_beta )
| ( ( minus_minus_real @ zero_zero_real @ zero_zero_real )
!= zero_zero_real )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( ( genClo1163638703lle_te @ A @ zero_zero_nat )
!= ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) ) ),
inference(paramod_ordered,[status(thm)],[1058,2264]) ).
thf(2595,plain,
! [A: nat] :
( ( one_one_real != genClo1278781456e_beta )
| ( ( minus_minus_real @ zero_zero_real @ zero_zero_real )
!= zero_zero_real )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( A != p )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat ) ),
inference(simp,[status(thm)],[2592]) ).
thf(2597,plain,
( ( one_one_real != genClo1278781456e_beta )
| ( ( minus_minus_real @ zero_zero_real @ zero_zero_real )
!= zero_zero_real )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat ) ),
inference(simp,[status(thm)],[2595]) ).
thf(3400,plain,
( ( one_one_real != genClo1278781456e_beta )
| ( zero_zero_real != zero_zero_real )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat ) ),
inference(rewrite,[status(thm)],[2597,891]) ).
thf(3401,plain,
( ( one_one_real != genClo1278781456e_beta )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat ) ),
inference(simp,[status(thm)],[3400]) ).
thf(272,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( minus_minus_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_add__diff__cancel__left) ).
thf(1157,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( minus_minus_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(330,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ( plus_plus_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_add__nonneg__eq__0__iff) ).
thf(1321,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ( plus_plus_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
& ( B = zero_zero_real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(221,axiom,
! [A: real,B: real,C: real,D: real] :
( ( A = B )
=> ( ( ord_less_eq_real @ ( abs_abs_real @ C ) @ D )
=> ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_sin__bound__lemma) ).
thf(1010,plain,
! [A: real,B: real,C: real,D: real] :
( ( A = B )
=> ( ( ord_less_eq_real @ ( abs_abs_real @ C ) @ D )
=> ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(495,plain,
! [B: nat,A: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
| ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
= A ) ),
inference(cnf,[status(esa)],[494]) ).
thf(496,plain,
! [B: nat,A: nat] :
( ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
= A )
| ~ ( ord_less_eq_nat @ A @ B ) ),
inference(lifteq,[status(thm)],[495]) ).
thf(8152,plain,
! [B: nat,A: nat] :
( ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
= A )
| ( ( minus_minus_nat @ A @ B )
!= zero_zero_nat ) ),
inference(rewrite,[status(thm)],[496,477]) ).
thf(8153,plain,
! [B: nat,A: nat] :
( ( ( minus_minus_nat @ A @ B )
!= zero_zero_nat )
| ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
= A ) ),
inference(lifteq,[status(thm)],[8152]) ).
thf(205,axiom,
! [A: real,B: real,C: real] :
( ( ( minus_minus_real @ A @ B )
= C )
= ( A
= ( plus_plus_real @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_diff__eq__eq) ).
thf(963,plain,
! [A: real,B: real,C: real] :
( ( ( minus_minus_real @ A @ B )
= C )
= ( A
= ( plus_plus_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1666,plain,
( ( zero_zero_real != zero_zero_real )
| ( zero_zero_real != genClo1278781456e_beta )
| ( ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) )
!= ( minus_minus_real @ one_one_real @ one_one_real ) ) ),
inference(paramod_ordered,[status(thm)],[928,1604]) ).
thf(1667,plain,
( ( zero_zero_real != genClo1278781456e_beta )
| ( ( minus_minus_real @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ) @ ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) ) )
!= ( minus_minus_real @ one_one_real @ one_one_real ) ) ),
inference(simp,[status(thm)],[1666]) ).
thf(1674,plain,
( ( zero_zero_real != genClo1278781456e_beta )
| ( ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real )
| ( ( genClo1163638703lle_te @ q @ ( plus_plus_nat @ i @ one_one_nat ) )
!= one_one_real ) ),
inference(simp,[status(thm)],[1667]) ).
thf(237,axiom,
! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_abs__diff__triangle__ineq) ).
thf(1062,plain,
! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(90,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_add_Oassoc) ).
thf(632,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(216,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
=> ( ord_less_eq_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_add__le__imp__le__left) ).
thf(995,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
=> ( ord_less_eq_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(307,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_mult__mono) ).
thf(1253,plain,
! [A: real,B: real,C: real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ( ord_less_eq_real @ zero_zero_real @ C )
=> ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(336,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_distrib__left) ).
thf(1341,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(123,axiom,
! [A: real] :
( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
= ( times_times_real @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_abs__mult__self__eq) ).
thf(731,plain,
! [A: real] :
( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
= ( times_times_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(417,plain,
! [C: nat,B: nat,A: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ C @ B ) )
= ( ( B = zero_zero_nat )
| ( A = C ) ) ),
inference(cnf,[status(esa)],[416]) ).
thf(418,plain,
! [C: nat,B: nat,A: nat] :
( ( ( times_times_nat @ A @ B )
= ( times_times_nat @ C @ B ) )
= ( ( B = zero_zero_nat )
| ( A = C ) ) ),
inference(lifteq,[status(thm)],[417]) ).
thf(57,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(510,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(321,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_diff__add) ).
thf(1294,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(192,axiom,
ord_less_eq_nat @ zero_zero_nat @ one_one_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_zero__le__one) ).
thf(929,plain,
ord_less_eq_nat @ zero_zero_nat @ one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(326,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_add__diff__cancel__right_H) ).
thf(1308,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(135,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( minus_minus_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_Nat_Odiff__cancel) ).
thf(763,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( minus_minus_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(182,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
= ( ord_less_eq_real @ zero_zero_real @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_le__add__same__cancel1) ).
thf(899,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
= ( ord_less_eq_real @ zero_zero_real @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(158,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_add_Ocomm__neutral) ).
thf(832,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(70,axiom,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_diff__zero) ).
thf(549,plain,
! [A: nat] :
( ( minus_minus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(66,axiom,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_add_Ocomm__neutral) ).
thf(536,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(231,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_add__nonpos__eq__0__iff) ).
thf(1045,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(130,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( plus_plus_real @ ( minus_minus_real @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_le__add__diff__inverse2) ).
thf(752,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( plus_plus_real @ ( minus_minus_real @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(317,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_add__left__imp__eq) ).
thf(1280,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(1111,plain,
( ( ^ [A: real,B: real] :
( ( minus_minus_real @ A @ B )
= zero_zero_real ) )
= ( (=) @ real ) ),
inference(lifteq,[status(thm)],[1110]) ).
thf(1678,plain,
! [A: real] :
( ( ^ [B: real] :
( ( minus_minus_real @ A @ B )
= zero_zero_real ) )
= ( (=) @ real @ A ) ),
inference(func_ext,[status(esa)],[1111]) ).
thf(26,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_add_Oright__cancel) ).
thf(410,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(159,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_add__decreasing) ).
thf(835,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(170,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_add__nonneg__nonneg) ).
thf(865,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( ord_less_eq_real @ zero_zero_real @ B )
=> ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(305,axiom,
~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_not__one__le__zero) ).
thf(1248,plain,
~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(144,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_add__le__mono1) ).
thf(790,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(328,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= C )
=> ( A
= ( minus_minus_real @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_add__implies__diff) ).
thf(1314,plain,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= C )
=> ( A
= ( minus_minus_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(357,plain,
! [B: real,A: real] :
( ( ( times_times_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) ),
inference(cnf,[status(esa)],[356]) ).
thf(358,plain,
! [B: real,A: real] :
( ( ( times_times_real @ A @ B )
= zero_zero_real )
= ( ( A = zero_zero_real )
| ( B = zero_zero_real ) ) ),
inference(lifteq,[status(thm)],[357]) ).
thf(275,axiom,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(1165,plain,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(414,plain,
! [C: real,B: real,A: real] :
( ( ( times_times_real @ A @ B )
= ( times_times_real @ C @ B ) )
= ( ( B = zero_zero_real )
| ( A = C ) ) ),
inference(cnf,[status(esa)],[413]) ).
thf(415,plain,
! [C: real,B: real,A: real] :
( ( ( times_times_real @ A @ B )
= ( times_times_real @ C @ B ) )
= ( ( B = zero_zero_real )
| ( A = C ) ) ),
inference(lifteq,[status(thm)],[414]) ).
thf(228,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( minus_minus_real @ C @ B ) @ ( minus_minus_real @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_diff__left__mono) ).
thf(1033,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ ( minus_minus_real @ C @ B ) @ ( minus_minus_real @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(319,axiom,
! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_abs__triangle__ineq2) ).
thf(1288,plain,
! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(287,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
= ( ord_less_eq_real @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_add__le__cancel__right) ).
thf(1197,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ B ) )
= ( ord_less_eq_real @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(204,axiom,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ B @ A ) )
= ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_add__cancel__right__left) ).
thf(960,plain,
! [A: nat,B: nat] :
( ( A
= ( plus_plus_nat @ B @ A ) )
= ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(91,axiom,
! [A: real,B: real] :
( ( A != zero_zero_real )
=> ( ( B != zero_zero_real )
=> ( ( times_times_real @ A @ B )
!= zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_no__zero__divisors) ).
thf(635,plain,
! [A: real,B: real] :
( ( A != zero_zero_real )
=> ( ( B != zero_zero_real )
=> ( ( times_times_real @ A @ B )
!= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(531,plain,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(cnf,[status(esa)],[530]) ).
thf(532,plain,
! [A: nat] :
( ( times_times_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(lifteq,[status(thm)],[531]) ).
thf(239,axiom,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_add__diff__cancel) ).
thf(1065,plain,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(122,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
= ( ord_less_eq_nat @ A @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_add__le__same__cancel2) ).
thf(728,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
= ( ord_less_eq_nat @ A @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(301,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_le__add__diff) ).
thf(1236,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(262,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_add__decreasing2) ).
thf(1129,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ zero_zero_real )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(310,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( ord_less_eq_real @ A @ B )
= ( ord_less_eq_real @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_diff__eq__diff__less__eq) ).
thf(1261,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( minus_minus_real @ A @ B )
= ( minus_minus_real @ C @ D ) )
=> ( ( ord_less_eq_real @ A @ B )
= ( ord_less_eq_real @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(3443,plain,
! [A: nat] :
( ~ ( ord_less_eq_real @ zero_zero_real @ genClo1278781456e_beta )
| ( ( genClo1163638703lle_te @ p @ A )
!= one_one_real )
| ( q != p )
| ( ( plus_plus_nat @ zero_zero_nat @ A )
!= ( plus_plus_nat @ i @ one_one_nat ) ) ),
inference(paramod_ordered,[status(thm)],[894,2099]) ).
thf(3531,plain,
! [A: nat] :
( ~ ( ord_less_eq_real @ zero_zero_real @ genClo1278781456e_beta )
| ( ( genClo1163638703lle_te @ p @ A )
!= one_one_real )
| ( q != p )
| ( i != zero_zero_nat )
| ( A != one_one_nat ) ),
inference(simp,[status(thm)],[3443]) ).
thf(3543,plain,
( ~ ( ord_less_eq_real @ zero_zero_real @ genClo1278781456e_beta )
| ( ( genClo1163638703lle_te @ p @ one_one_nat )
!= one_one_real )
| ( q != p )
| ( i != zero_zero_nat ) ),
inference(simp,[status(thm)],[3531]) ).
thf(168,axiom,
! [A: nat,B: nat,C: real,D: nat] :
( ( ( genClo1015804716orrect @ A @ C )
& ( genClo1015804716orrect @ B @ C )
& ( ord_less_eq_real @ ( plus_plus_real @ ( genClo1163638703lle_te @ B @ D ) @ genClo1278781456e_beta ) @ C ) )
=> ( ord_less_eq_real @ ( genClo1163638703lle_te @ A @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_rts2a) ).
thf(860,plain,
! [A: nat,B: nat,C: real,D: nat] :
( ( ( genClo1015804716orrect @ A @ C )
& ( genClo1015804716orrect @ B @ C )
& ( ord_less_eq_real @ ( plus_plus_real @ ( genClo1163638703lle_te @ B @ D ) @ genClo1278781456e_beta ) @ C ) )
=> ( ord_less_eq_real @ ( genClo1163638703lle_te @ A @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(1532,plain,
( ~ $true
| ( ( ord_less_eq_real @ one_one_real @ zero_zero_real )
!= ( ord_less_eq_real @ genClo1278781456e_beta @ genClo1651033342e_rmin ) ) ),
inference(paramod_ordered,[status(thm)],[1072,831]) ).
thf(1533,plain,
( ( ord_less_eq_real @ one_one_real @ zero_zero_real )
!= ( ord_less_eq_real @ genClo1278781456e_beta @ genClo1651033342e_rmin ) ),
inference(simp,[status(thm)],[1532]) ).
thf(1537,plain,
( ( one_one_real != genClo1278781456e_beta )
| ( zero_zero_real != genClo1651033342e_rmin ) ),
inference(simp,[status(thm)],[1533]) ).
thf(84,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus_real @ A @ C )
= ( plus_plus_real @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_add__mono__thms__linordered__semiring_I4_J) ).
thf(596,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus_real @ A @ C )
= ( plus_plus_real @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(1018,plain,
! [A: real] :
( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
= ( A = zero_zero_real ) ),
inference(cnf,[status(esa)],[1017]) ).
thf(1019,plain,
! [A: real] :
( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
= ( A = zero_zero_real ) ),
inference(lifteq,[status(thm)],[1018]) ).
thf(63,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_less__eq__nat_Osimps_I1_J) ).
thf(528,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(458,plain,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
inference(cnf,[status(esa)],[457]) ).
thf(459,plain,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
inference(lifteq,[status(thm)],[458]) ).
thf(219,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_right__diff__distrib_H) ).
thf(1004,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(7671,plain,
( ( zero_zero_real != genClo1278781456e_beta )
| ( q != p )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= ( plus_plus_nat @ i @ one_one_nat ) ) ),
inference(simp,[status(thm)],[3773]) ).
thf(7694,plain,
( ( zero_zero_real != genClo1278781456e_beta )
| ( q != p ) ),
inference(simp,[status(thm)],[7671]) ).
thf(172,axiom,
! [A: real,B: real] :
( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
= ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_abs__minus__commute) ).
thf(871,plain,
! [A: real,B: real] :
( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
= ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(259,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_Nat_Oadd__diff__assoc) ).
thf(1120,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(249,axiom,
! [A: nat,B: nat,C: nat] :
( ( genClo1015804716orrect @ A @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) )
=> ( ( genClo1015804716orrect @ C @ ( genClo1163638703lle_te @ C @ B ) )
=> ( ord_less_eq_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) @ ( genClo1163638703lle_te @ C @ B ) ) @ ( plus_plus_real @ genClo1650508560e_rmax @ genClo1278781456e_beta ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_beta__bound2) ).
thf(1093,plain,
! [A: nat,B: nat,C: nat] :
( ( genClo1015804716orrect @ A @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) )
=> ( ( genClo1015804716orrect @ C @ ( genClo1163638703lle_te @ C @ B ) )
=> ( ord_less_eq_real @ ( minus_minus_real @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ B @ one_one_nat ) ) @ ( genClo1163638703lle_te @ C @ B ) ) @ ( plus_plus_real @ genClo1650508560e_rmax @ genClo1278781456e_beta ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(87,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_le__zero__eq) ).
thf(624,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(7496,plain,
! [A: nat] :
( ~ ( ord_less_eq_real @ ( abs_abs_real @ ( genClo1163638703lle_te @ p @ A ) ) @ genClo1278781456e_beta )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( ( plus_plus_nat @ zero_zero_nat @ A )
!= ( plus_plus_nat @ i @ one_one_nat ) ) ),
inference(paramod_ordered,[status(thm)],[894,3399]) ).
thf(7518,plain,
! [A: nat] :
( ~ ( ord_less_eq_real @ ( abs_abs_real @ ( genClo1163638703lle_te @ p @ A ) ) @ genClo1278781456e_beta )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( i != zero_zero_nat )
| ( A != one_one_nat ) ),
inference(simp,[status(thm)],[7496]) ).
thf(7538,plain,
( ~ ( ord_less_eq_real @ ( abs_abs_real @ ( genClo1163638703lle_te @ p @ one_one_nat ) ) @ genClo1278781456e_beta )
| ( ( plus_plus_nat @ i @ one_one_nat )
!= zero_zero_nat )
| ( i != zero_zero_nat ) ),
inference(simp,[status(thm)],[7518]) ).
thf(270,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_add__le__imp__le__right) ).
thf(1152,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(185,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_add__nonpos__nonpos) ).
thf(908,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
=> ( ( ord_less_eq_nat @ B @ zero_zero_nat )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(215,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_diff__add__cancel) ).
thf(992,plain,
! [A: real,B: real] :
( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(333,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_add__diff__eq) ).
thf(1331,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(282,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_plus__nat_Oadd__0) ).
thf(1184,plain,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(92,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_le__0__eq) ).
thf(639,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(131,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_eq_nat @ A @ ( minus_minus_nat @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_add__le__imp__le__diff) ).
thf(755,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_eq_nat @ A @ ( minus_minus_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(591,plain,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
inference(cnf,[status(esa)],[590]) ).
thf(592,plain,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
inference(lifteq,[status(thm)],[591]) ).
thf(39,axiom,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_diff__0__eq__0) ).
thf(454,plain,
! [A: nat] :
( ( minus_minus_nat @ zero_zero_nat @ A )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(468,plain,
! [A: real] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(cnf,[status(esa)],[467]) ).
thf(469,plain,
! [A: real] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(lifteq,[status(thm)],[468]) ).
thf(126280,plain,
$false,
inference(e,[status(thm)],[1036,809,629,365,3399,347,846,1031,7798,1083,941,555,666,1549,1110,481,8607,645,892,1168,4450,760,1200,977,683,1290,1068,2099,677,1041,1173,741,1073,4711,449,379,1269,878,440,385,533,715,472,698,945,340,1354,930,404,3629,1127,709,885,1228,389,1298,719,504,934,1330,1264,587,838,702,751,802,344,1059,1132,542,460,1545,902,1147,421,1115,448,969,1347,881,416,376,485,937,1020,3569,806,475,924,1334,646,353,966,766,734,396,4707,507,877,692,1072,453,1119,774,1242,849,1604,1206,380,661,1338,546,793,1311,3767,1274,1217,561,392,424,815,957,1223,894,862,349,820,5815,407,3884,1423,484,6852,361,889,7591,1079,1195,974,1106,916,467,852,435,522,830,757,2345,1017,1064,725,980,388,593,989,857,1360,1350,519,578,1089,1234,874,1143,1270,1259,650,948,5615,1328,1096,1672,1138,7593,356,1160,488,1659,642,1214,590,706,686,1075,1114,515,1297,738,1231,1192,457,1799,3628,569,647,997,984,911,3540,721,1318,1086,805,9782,1170,6647,558,1026,530,953,1187,674,662,888,1135,750,513,1103,1301,573,689,7910,7567,904,1007,402,843,7704,3590,1520,1124,1256,413,584,1154,875,4709,382,1271,787,1239,466,919,1356,350,445,3773,8359,1058,1209,406,831,784,419,377,7282,1144,616,1175,362,451,509,434,477,758,2314,7292,621,700,1325,895,1344,769,668,1177,462,1112,494,1080,345,367,552,799,1162,399,959,1245,868,780,1015,986,2797,1000,1250,10031,431,653,922,1213,768,827,505,438,1304,944,7571,1277,812,516,355,823,1049,1413,1076,1203,1208,795,680,927,374,776,525,712,7635,1225,887,971,1267,409,1098,580,855,1053,441,370,840,463,951,359,1285,1220,470,576,1358,744,703,1141,600,1052,386,446,497,991,656,1023,5873,627,1180,539,482,671,581,759,891,1189,771,3565,3401,1157,1321,1010,8153,368,1453,2643,963,1674,1062,1101,632,401,3561,995,1253,699,1341,748,731,418,510,1294,929,1308,478,1212,763,383,899,832,346,549,536,1045,752,1280,1678,432,410,835,1673,865,1248,790,1314,341,358,1056,7280,696,1165,415,1033,1288,1197,960,635,532,1065,728,1236,1129,1261,3543,860,1537,596,1019,528,459,1004,7694,871,1120,501,369,1093,624,7538,464,1152,427,908,992,1331,923,1184,659,775,639,755,491,592,454,1417,469,940]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP063^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % 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
% 0.10/0.20 % Computer : n017.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 19:40:37 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.11/1.18 % [INFO] Parsing done (388ms).
% 2.44/1.20 % [INFO] Running in sequential loop mode.
% 3.17/1.59 % [INFO] eprover registered as external prover.
% 3.17/1.60 % [INFO] Scanning for conjecture ...
% 3.65/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 337 axioms. Running axiom selection ...
% 3.87/1.88 % [INFO] Axiom selection finished. Selected 337 axioms (removed 0 axioms).
% 4.66/2.12 % [INFO] Problem is higher-order (TPTP THF).
% 5.00/2.14 % [INFO] Type checking passed.
% 5.00/2.15 % [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 ...
% 266.48/71.54 % External prover 'e' found a proof!
% 266.48/71.54 % [INFO] Killing All external provers ...
% 266.48/71.54 % Time passed: 71191ms (effective reasoning time: 70336ms)
% 266.48/71.54 % 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)>
% 266.48/71.55 % Axioms used in derivation (337): fact_5_corr__l, fact_129_add__mono__thms__linordered__semiring_I4_J, fact_8_le__add__diff__inverse, fact_77_abs__of__nonneg, fact_118_add_Oleft__commute, fact_34_zero__eq__add__iff__both__eq__0, fact_29_le__zero__eq, fact_38_add__cancel__right__left, fact_322_left__diff__distrib_H, fact_210_le0, fact_179_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right, fact_171_diff__eq__eq, fact_79_zero__reorient, fact_233_diff__le__mono, fact_188_diff__add, fact_160_diff__left__mono, fact_30_add__le__cancel__right, fact_53_diff__zero, fact_85_comm__monoid__add__class_Oadd__0, fact_297_mult__right__cancel, fact_147_less__eqE, fact_4_corr__q, fact_277_mult__cancel__right, fact_99_add__increasing2, fact_161_diff__mono, fact_90_add__nonpos__eq__0__iff, fact_71_add__le__same__cancel1, fact_131_ab__semigroup__add__class_Oadd__ac_I1_J, fact_83_add_Ocomm__neutral, fact_158_diff__eq__diff__less__eq, fact_163_add__implies__diff, fact_92_add__nonneg__eq__0__iff, fact_241_bot__nat__0_Oextremum__unique, fact_173_abs__ge__self, fact_135_diff__right__commute, fact_93_add__nonneg__eq__0__iff, fact_46_add_Oright__neutral, fact_288_mult_Oleft__neutral, fact_52_diff__zero, fact_0_rts2b, fact_76_abs__le__self__iff, fact_102_add__increasing, fact_292_mult__cancel__left1, fact_1_corr__p, fact_157_add__mono__thms__linordered__semiring_I3_J, fact_193_abs__triangle__ineq, fact_105_add__decreasing, fact_336_mult__mono, fact_121_add_Oright__cancel, fact_269_eq__diff__eq_H, fact_7_corr__l__tq, fact_268_PC__monotone, fact_168_diff__diff__eq2, fact_186_add__le__add__imp__diff__le, fact_72_add__le__same__cancel1, fact_113_add__right__imp__eq, fact_272_nonoverlap, fact_95_add__nonpos__nonpos, fact_42_add__cancel__left__left, fact_50_cancel__comm__monoid__add__class_Odiff__cancel, fact_16_diff__add__cancel, fact_228_le__antisym, fact_222_Nat_Oadd__diff__assoc2, fact_110_le__iff__diff__le__0, fact_180_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2, fact_317_comm__monoid__mult__class_Omult__1, fact_301_no__zero__divisors, fact_258_nat__le__iff__add, fact_207_okRead2__def, fact_175_abs__one, fact_56_diff__self, fact_235_le__diff__iff_H, fact_127_group__cancel_Oadd1, fact_21_add__diff__cancel__right, fact_213_Nat_Oadd__0__right, fact_319_mult_Ocomm__neutral, fact_54_zero__diff, fact_201_diff__numeral__special_I9_J, fact_31_add__le__cancel__right, fact_55_diff__0__right, fact_58_add__diff__cancel__right_H, fact_298_mult__left__cancel, fact_149_add__left__mono, fact_253_le__Suc__ex, fact_172_group__cancel_Osub1, fact_282_mult__eq__0__iff, fact_116_add__left__imp__eq, fact_285_mult__zero__left, fact_27_abs__idempotent, fact_178_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse, fact_124_add_Oassoc, fact_198_abs__triangle__ineq4, fact_107_not__one__le__zero, fact_119_add_Ocommute, fact_315_combine__common__factor, fact_202_beta__bound2, fact_217_diff__is__0__eq, fact_214_diff__0__eq__0, fact_82_add_Ocomm__neutral, fact_312_distrib__right, fact_267_le__diff__conv, fact_284_mult__zero__right, fact_64_double__add__le__zero__iff__single__add__le__zero, fact_109_zero__le__one, fact_250_le__add2, fact_143_add__le__imp__le__left, fact_287_mult_Oleft__neutral, fact_309_comm__semiring__class_Odistrib, fact_249_le__add1, fact_278_mult__cancel__right, fact_15_add__diff__cancel, fact_112_rts2a, fact_145_add__right__mono, fact_181_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2, fact_318_mult_Ocomm__neutral, fact_332_mult_Oassoc, fact_270_le__numeral__extra_I3_J, fact_174_abs__le__D1, fact_329_mult_Ocommute, fact_104_add__decreasing, fact_40_add__cancel__left__right, fact_251_add__leD1, fact_257_trans__le__add2, fact_218_diff__is__0__eq_H, fact_43_add__cancel__left__left, fact_128_group__cancel_Oadd1, fact_293_mult__cancel__left2, fact_246_synch0, fact_216_nat__add__left__cancel__le, fact_176_abs__minus__commute, fact_11_le__add__diff__inverse2, fact_275_init, fact_49_add_Oleft__neutral, fact_20_add__diff__cancel__left_H, fact_144_le__iff__add, fact_190_add__le__imp__le__diff, fact_244_add__eq__self__zero, fact_230_le__diff__iff, fact_86_zero__neq__one, fact_152_add__mono__thms__linordered__semiring_I1_J, fact_106_not__one__le__zero, fact_162_add__implies__diff, fact_299_mult__left__cancel, fact_219_diff__diff__cancel, fact_326_abs__mult, fact_81_add_Ogroup__left__neutral, fact_185_le__add__diff, fact_177_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add, fact_134_one__reorient, fact_302_divisors__zero, fact_9_le__add__diff__inverse, fact_197_abs__diff__triangle__ineq, fact_290_mult_Oright__neutral, fact_289_mult_Oright__neutral, fact_227_eq__imp__le, fact_316_comm__monoid__mult__class_Omult__1, fact_63_zero__le__double__add__iff__zero__le__single__add, fact_286_mult__zero__left, fact_61_abs__0__eq, fact_280_mult__cancel__left, fact_205_rts0d, fact_13_abs__1, fact_303_divisors__zero, fact_335_mult__mono, fact_2_corr__q__tq, fact_324_right__diff__distrib_H, fact_265_Nat_Odiff__add__assoc, fact_115_add__left__imp__eq, fact_74_diff__add__zero, fact_155_add__mono__thms__linordered__semiring_I2_J, fact_240_Nat_Oex__has__greatest__nat, fact_266_Nat_Ole__diff__conv2, fact_111_abs__ge__zero, fact_33_add__le__cancel__left, fact_65_le__add__same__cancel2, fact_41_add__cancel__left__right, fact_69_add__le__same__cancel2, fact_245_diff__add__0, fact_223_less__eq__nat_Osimps_I1_J, fact_307_ring__class_Oring__distribs_I1_J, fact_237_nat__le__linear, fact_47_add_Oright__neutral, fact_291_abs__mult__self__eq, fact_57_add__diff__cancel__right_H, fact_150_add__mono, fact_32_add__le__cancel__left, fact_187_add__le__add__imp__diff__le, fact_331_mult_Oassoc, fact_120_add_Ocommute, fact_125_group__cancel_Oadd2, fact_24_add__right__cancel, fact_44_double__zero__sym, fact_238_diffs0__imp__equal, fact_22_add__diff__cancel__right, fact_262_diff__add__inverse2, fact_313_distrib__right, fact_325_right__diff__distrib_H, fact_308_comm__semiring__class_Odistrib, fact_305_mult__not__zero, fact_3_ie, fact_221_Nat_Odiff__diff__right, fact_18_add__diff__cancel__left, fact_123_add_Oassoc, fact_142_add__le__imp__le__left, fact_132_ab__semigroup__add__class_Oadd__ac_I1_J, fact_10_le__add__diff__inverse2, fact_75_abs__le__zero__iff, fact_39_add__cancel__right__left, fact_169_add__diff__eq, fact_247_is__num__normalize_I1_J, fact_311_distrib__left, fact_133_one__reorient, fact_148_add__left__mono, fact_87_zero__neq__one, fact_330_mult_Ocommute, fact_108_zero__le__one, fact_26_add__left__cancel, fact_156_add__mono__thms__linordered__semiring_I3_J, fact_159_diff__right__mono, fact_94_add__nonpos__nonpos, fact_73_diff__ge__0__iff__ge, fact_294_mult__cancel__right1, fact_51_cancel__comm__monoid__add__class_Odiff__cancel, fact_146_add__right__mono, fact_136_diff__right__commute, fact_328_mult_Oleft__commute, fact_274_le__numeral__extra_I4_J, fact_254_add__le__mono, fact_14_abs__add__abs, fact_153_add__mono__thms__linordered__semiring_I1_J, fact_334_ab__semigroup__mult__class_Omult__ac_I1_J, fact_88_eq__iff__diff__eq__0, fact_264_Nat_Odiff__add__assoc2, fact_19_add__diff__cancel__left_H, fact_283_mult__zero__right, fact_130_add__mono__thms__linordered__semiring_I4_J, fact_194_abs__triangle__ineq2__sym, fact_255_add__le__mono1, fact_60_abs__eq__0, fact_276_bound1, fact_226_le__trans, fact_84_comm__monoid__add__class_Oadd__0, fact_333_ab__semigroup__mult__class_Omult__ac_I1_J, fact_98_add__increasing2, fact_199_abs__diff__le__iff, fact_166_diff__add__eq__diff__diff__swap, fact_103_add__increasing, fact_243_plus__nat_Oadd__0, fact_314_combine__common__factor, fact_139_correct__closed, fact_215_diff__self__eq__0, fact_295_mult__cancel__right2, fact_242_bot__nat__0_Oextremum__uniqueI, fact_211_bot__nat__0_Oextremum, fact_296_mult__right__cancel, fact_259_Nat_Odiff__cancel, fact_37_add__cancel__right__right, fact_220_diff__diff__left, fact_232_Nat_Odiff__diff__eq, fact_263_Nat_Ole__imp__diff__is__add, fact_122_add_Oleft__cancel, fact_141_add__le__imp__le__right, fact_252_add__leD2, fact_256_trans__le__add1, fact_138_beta__bound1, fact_45_double__zero, fact_192_diff__le__eq, fact_170_eq__diff__eq, fact_114_add__right__imp__eq, fact_62_abs__0, fact_68_le__add__same__cancel1, fact_196_abs__triangle__ineq2, fact_189_add__le__imp__le__diff, fact_17_add__diff__cancel__left, fact_12_rte, fact_323_left__diff__distrib_H, fact_70_add__le__same__cancel2, fact_6_posD, fact_260_diff__cancel2, fact_191_le__diff__eq, fact_281_mult__eq__0__iff, fact_248_add__leE, fact_80_zero__le, fact_91_add__nonpos__eq__0__iff, fact_327_mult_Oleft__commute, fact_184_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2, fact_279_mult__cancel__left, fact_204_rts1, fact_97_add__nonneg__nonneg, fact_182_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc, fact_66_le__add__same__cancel2, fact_183_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc, fact_100_add__decreasing2, fact_310_distrib__left, fact_151_add__mono, fact_59_abs__zero, fact_206_rts0, fact_200_posX, fact_195_abs__triangle__ineq3, fact_137_diff__eq__diff__eq, fact_78_zero__reorient, fact_126_group__cancel_Oadd2, fact_165_diff__diff__add, fact_300_no__zero__divisors, fact_28_abs__abs, fact_164_diff__diff__add, fact_224_le__0__eq, fact_167_diff__add__eq, fact_140_add__le__imp__le__right, fact_239_minus__nat_Odiff__0, fact_101_add__decreasing2, fact_208_sin__bound__lemma, fact_273_le__numeral__extra_I4_J, fact_212_add__is__0, fact_203_rts1d, fact_271_le__numeral__extra_I3_J, fact_236_diff__le__mono2, fact_25_add__left__cancel, fact_96_add__nonneg__nonneg, fact_35_add__eq__0__iff__both__eq__0, fact_67_le__add__same__cancel1, fact_229_eq__diff__iff, fact_225_le__refl, fact_320_left__diff__distrib, fact_48_add_Oleft__neutral, fact_23_add__right__cancel, fact_234_diff__le__self, fact_154_add__mono__thms__linordered__semiring_I2_J, fact_304_mult__not__zero, fact_36_add__cancel__right__right, fact_261_diff__add__inverse, fact_306_ring__class_Oring__distribs_I2_J, fact_117_add_Oleft__commute, fact_89_abs__eq__0__iff, fact_209_Nat_Oadd__diff__assoc, fact_231_diff__commute, fact_321_right__diff__distrib
% 266.48/71.55 % No. of inferences in proof: 1007
% 266.48/71.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 71191 ms resp. 70336 ms w/o parsing
% 263.34/71.79 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 263.34/71.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------