TSTP Solution File: ITP064^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP064^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:22:33 EDT 2024
% Result : Theorem 13.99s 4.22s
% Output : Refutation 14.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 224
% Syntax : Number of formulae : 422 ( 239 unt; 28 typ; 0 def)
% Number of atoms : 887 ( 400 equ; 8 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 2973 ( 24 ~; 5 |; 38 &;2646 @)
% ( 0 <=>; 260 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 26 usr; 15 con; 0-4 aty)
% Number of variables : 937 ( 62 ^ 875 !; 0 ?; 937 :)
% Comments :
%------------------------------------------------------------------------------
thf(real_type,type,
real: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(genClo1160817912lle_IC_type,type,
genClo1160817912lle_IC: nat > nat > real > real ).
thf(genClo721845095Lambda_type,type,
genClo721845095Lambda: real ).
thf(genClo1278781456e_beta_type,type,
genClo1278781456e_beta: real ).
thf(genClo1400225944_theta_type,type,
genClo1400225944_theta: nat > nat > nat > real ).
thf(genClo1015804716orrect_type,type,
genClo1015804716orrect: nat > real > $o ).
thf(genClo293725281kRead1_type,type,
genClo293725281kRead1: ( nat > real ) > real > ( nat > $o ) > $o ).
thf(genClo293725282kRead2_type,type,
genClo293725282kRead2: ( nat > real ) > ( nat > real ) > real > ( nat > $o ) > $o ).
thf(genClo208577157axsync_type,type,
genClo208577157axsync: nat > real > $o ).
thf(genClo1650508560e_rmax_type,type,
genClo1650508560e_rmax: real ).
thf(genClo1651033342e_rmin_type,type,
genClo1651033342e_rmin: real ).
thf(genClo1163638703lle_te_type,type,
genClo1163638703lle_te: nat > nat > real ).
thf(abs_abs_real_type,type,
abs_abs_real: real > real ).
thf(minus_minus_real_type,type,
minus_minus_real: real > real > real ).
thf(one_one_nat_type,type,
one_one_nat: nat ).
thf(one_one_real_type,type,
one_one_real: real ).
thf(plus_plus_nat_type,type,
plus_plus_nat: nat > nat > nat ).
thf(plus_plus_real_type,type,
plus_plus_real: real > real > real ).
thf(zero_zero_real_type,type,
zero_zero_real: real ).
thf(if_real_type,type,
if_real: $o > real > real > real ).
thf(ord_less_eq_real_type,type,
ord_less_eq_real: real > real > $o ).
thf(ord_max_real_type,type,
ord_max_real: real > real > real ).
thf(delta_S_type,type,
delta_S: real ).
thf(i_type,type,
i: nat ).
thf(l_type,type,
l: nat ).
thf(m_type,type,
m: nat ).
thf(p_type,type,
p: nat ).
thf(193,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_0_correct__closed) ).
thf(760,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)],[193]) ).
thf(15,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_127_add__diff__cancel__right) ).
thf(234,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)],[15]) ).
thf(116,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_195_eq__diff__eq) ).
thf(555,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)],[116]) ).
thf(66,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_222_diff__le__eq) ).
thf(408,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)],[66]) ).
thf(124,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_177_add__mono__thms__linordered__semiring_I1_J) ).
thf(582,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)],[124]) ).
thf(9,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_316_add__le__same__cancel2) ).
thf(217,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)],[9]) ).
thf(19,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_201_abs__minus__commute) ).
thf(247,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)],[19]) ).
thf(77,axiom,
( ( abs_abs_real @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_abs__zero) ).
thf(440,plain,
( ( abs_abs_real @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(25,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_186_diff__mono) ).
thf(269,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)],[25]) ).
thf(157,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_233_rts0d) ).
thf(677,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)],[157]) ).
thf(58,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_221_le__diff__eq) ).
thf(384,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)],[58]) ).
thf(98,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_235_sin__bound__lemma) ).
thf(500,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)],[98]) ).
thf(188,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ A @ ( ord_max_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_max_OcoboundedI1) ).
thf(747,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ A @ ( ord_max_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(110,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_120_abs__add__abs) ).
thf(538,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)],[110]) ).
thf(65,axiom,
! [A: real,B: real,C: real > real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_order__subst2) ).
thf(404,plain,
! [A: real,B: real,C: real > real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(172,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ B )
=> ( ord_less_eq_real @ ( ord_max_real @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_max_OboundedI) ).
thf(709,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ B )
=> ( ord_less_eq_real @ ( ord_max_real @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(120,axiom,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_add_Oleft__neutral) ).
thf(570,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(54,axiom,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_zero__reorient) ).
thf(372,plain,
! [A: real] :
( ( zero_zero_real = A )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(169,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_max_real @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_max__absorb1) ).
thf(702,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_max_real @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(49,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_351_add__nonpos__nonpos) ).
thf(357,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)],[49]) ).
thf(69,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_181_add__mono__thms__linordered__semiring_I3_J) ).
thf(416,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)],[69]) ).
thf(13,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_327_abs__le__self__iff) ).
thf(228,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)],[13]) ).
thf(80,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_144_add__left__imp__eq) ).
thf(448,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)],[80]) ).
thf(29,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_192_diff__add__eq) ).
thf(284,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)],[29]) ).
thf(197,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( ord_max_real @ B @ C ) )
= ( ord_max_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_max__add__distrib__right) ).
thf(770,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ A @ ( ord_max_real @ B @ C ) )
= ( ord_max_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(88,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_123_add__diff__cancel__left) ).
thf(475,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)],[88]) ).
thf(40,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_227_abs__diff__triangle__ineq) ).
thf(321,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)],[40]) ).
thf(92,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ A )
=> ( ord_less_eq_real @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_dual__order_Otrans) ).
thf(485,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ C @ A )
=> ( ord_less_eq_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(46,axiom,
! [A: real,B: real] :
( ( if_real @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Real__Oreal_T) ).
thf(348,plain,
! [A: real,B: real] :
( ( if_real @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(90,axiom,
( genClo293725281kRead1
= ( ^ [A: nat > real,B: real,C: nat > $o] :
! [D: nat,E: nat] :
( ( ( C @ D )
& ( C @ E ) )
=> ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ D ) @ ( A @ E ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_okRead1__def) ).
thf(480,plain,
( genClo293725281kRead1
= ( ^ [A: nat > real,B: real,C: nat > $o] :
! [D: nat,E: nat] :
( ( ( C @ D )
& ( C @ E ) )
=> ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ D ) @ ( A @ E ) ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(161,axiom,
genClo1015804716orrect @ l @ ( ord_max_real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_corr__l__tml) ).
thf(687,plain,
genClo1015804716orrect @ l @ ( ord_max_real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(28,axiom,
! [A: real,B: real] :
( ( A = B )
=> ( ord_less_eq_real @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_eq__refl) ).
thf(280,plain,
! [A: real,B: real] :
( ( A = B )
=> ( ord_less_eq_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(164,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_238_rts2b) ).
thf(692,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)],[164]) ).
thf(32,axiom,
! [A: real,B: real] :
( ( ( plus_plus_real @ A @ B )
= B )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_add__cancel__left__left) ).
thf(293,plain,
! [A: real,B: real] :
( ( ( plus_plus_real @ A @ B )
= B )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(62,axiom,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_add__diff__cancel__left_H) ).
thf(396,plain,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(67,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_199_abs__le__D1) ).
thf(411,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)],[67]) ).
thf(18,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_158_add__mono__thms__linordered__semiring_I4_J) ).
thf(243,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)],[18]) ).
thf(73,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_343_add__increasing) ).
thf(428,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)],[73]) ).
thf(6,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_diff__add__cancel) ).
thf(206,plain,
! [A: real,B: real] :
( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(132,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_229_abs__diff__le__iff) ).
thf(602,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)],[132]) ).
thf(195,axiom,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ ( ord_max_real @ A @ B ) @ C )
= ( ord_max_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_max__diff__distrib__left) ).
thf(766,plain,
! [A: real,B: real,C: real] :
( ( minus_minus_real @ ( ord_max_real @ A @ B ) @ C )
= ( ord_max_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(37,axiom,
! [A: real,B: real,C: real > real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_ord__le__eq__subst) ).
thf(307,plain,
! [A: real,B: real,C: real > real,D: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(81,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_146_add_Oleft__commute) ).
thf(452,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)],[81]) ).
thf(107,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_185_diff__left__mono) ).
thf(529,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)],[107]) ).
thf(150,axiom,
genClo1015804716orrect @ m @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_corr__m) ).
thf(661,plain,
genClo1015804716orrect @ m @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(57,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_order__trans) ).
thf(381,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(174,axiom,
( ord_max_real
= ( ^ [A: real,B: real] : ( if_real @ ( ord_less_eq_real @ A @ B ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_max__def) ).
thf(714,plain,
( ord_max_real
= ( ^ [A: real,B: real] : ( if_real @ ( ord_less_eq_real @ A @ B ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(10,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_167_add__le__imp__le__left) ).
thf(220,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)],[10]) ).
thf(52,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_189_diff__diff__add) ).
thf(366,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)],[52]) ).
thf(45,axiom,
! [A: real,B: real,C: real] :
( ( ( ord_less_eq_real @ A @ B )
=> ~ ( ord_less_eq_real @ B @ C ) )
=> ( ( ( ord_less_eq_real @ B @ A )
=> ~ ( ord_less_eq_real @ A @ C ) )
=> ( ( ( ord_less_eq_real @ A @ C )
=> ~ ( ord_less_eq_real @ C @ B ) )
=> ( ( ( ord_less_eq_real @ C @ B )
=> ~ ( ord_less_eq_real @ B @ A ) )
=> ( ( ( ord_less_eq_real @ B @ C )
=> ~ ( ord_less_eq_real @ C @ A ) )
=> ~ ( ( ord_less_eq_real @ C @ A )
=> ~ ( ord_less_eq_real @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_le__cases3) ).
thf(334,plain,
! [A: real,B: real,C: real] :
( ( ( ord_less_eq_real @ A @ B )
=> ~ ( ord_less_eq_real @ B @ C ) )
=> ( ( ( ord_less_eq_real @ B @ A )
=> ~ ( ord_less_eq_real @ A @ C ) )
=> ( ( ( ord_less_eq_real @ A @ C )
=> ~ ( ord_less_eq_real @ C @ B ) )
=> ( ( ( ord_less_eq_real @ C @ B )
=> ~ ( ord_less_eq_real @ B @ A ) )
=> ( ( ( ord_less_eq_real @ B @ C )
=> ~ ( ord_less_eq_real @ C @ A ) )
=> ~ ( ( ord_less_eq_real @ C @ A )
=> ~ ( ord_less_eq_real @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(35,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_322_double__add__le__zero__iff__single__add__le__zero) ).
thf(302,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)],[35]) ).
thf(61,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_157_add__mono__thms__linordered__semiring_I4_J) ).
thf(392,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)],[61]) ).
thf(140,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_dual__order_Oantisym) ).
thf(630,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(181,axiom,
! [A: real,B: real] :
( ( A
= ( ord_max_real @ A @ B ) )
=> ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_max_OorderI) ).
thf(729,plain,
! [A: real,B: real] :
( ( A
= ( ord_max_real @ A @ B ) )
=> ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(21,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_347_add__increasing2) ).
thf(252,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)],[21]) ).
thf(43,axiom,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_eq__iff) ).
thf(329,plain,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(152,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_232_rts0) ).
thf(665,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)],[152]) ).
thf(95,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_226_abs__triangle__ineq2) ).
thf(493,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)],[95]) ).
thf(159,axiom,
! [A: real] :
( ( ord_max_real @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_max_Oidem) ).
thf(682,plain,
! [A: real] :
( ( ord_max_real @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(115,axiom,
! [A: real,B: real > real,C: real,D: real] :
( ( ord_less_eq_real @ A @ ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_order__subst1) ).
thf(551,plain,
! [A: real,B: real > real,C: real,D: real] :
( ( ord_less_eq_real @ A @ ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(146,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_162_diff__right__commute) ).
thf(650,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)],[146]) ).
thf(135,axiom,
! [A: real,B: real] :
( ( if_real @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Real__Oreal_T) ).
thf(615,plain,
! [A: real,B: real] :
( ( if_real @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(134,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_153_group__cancel_Oadd2) ).
thf(610,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)],[134]) ).
thf(70,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_314_add__le__same__cancel1) ).
thf(420,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)],[70]) ).
thf(103,axiom,
! [A: real] : ( ord_less_eq_real @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_dual__order_Orefl) ).
thf(519,plain,
! [A: real] : ( ord_less_eq_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(186,axiom,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( ( ord_max_real @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_max_Oabsorb__iff2) ).
thf(742,plain,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( ( ord_max_real @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(93,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_137_add__le__cancel__left) ).
thf(488,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)],[93]) ).
thf(12,axiom,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ B @ A ) )
= ( B = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_add__cancel__right__left) ).
thf(225,plain,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ B @ A ) )
= ( B = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(190,axiom,
! [A: real,B: real] : ( ord_less_eq_real @ A @ ( ord_max_real @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_max_Ocobounded1) ).
thf(753,plain,
! [A: real,B: real] : ( ord_less_eq_real @ A @ ( ord_max_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(154,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ ( ord_max_real @ B @ C ) )
= ( ( ord_less_eq_real @ A @ B )
| ( ord_less_eq_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_le__max__iff__disj) ).
thf(669,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ ( ord_max_real @ B @ C ) )
= ( ( ord_less_eq_real @ A @ B )
| ( ord_less_eq_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(144,axiom,
! [A: real,B: real,C: real] :
( ( A = B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_ord__eq__le__trans) ).
thf(642,plain,
! [A: real,B: real,C: real] :
( ( A = B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(106,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_115_le__add__diff__inverse) ).
thf(526,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)],[106]) ).
thf(158,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_max_real @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_max_Oabsorb1) ).
thf(679,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_max_real @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(113,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_228_abs__triangle__ineq4) ).
thf(547,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)],[113]) ).
thf(8,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_154_group__cancel_Oadd2) ).
thf(212,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)],[8]) ).
thf(145,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_236_eq__diff__eq_H) ).
thf(647,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)],[145]) ).
thf(178,axiom,
( genClo208577157axsync
= ( ^ [A: nat,B: real] :
! [C: nat,D: nat] :
( ( ( genClo1015804716orrect @ C @ ( ord_max_real @ ( genClo1163638703lle_te @ C @ A ) @ ( genClo1163638703lle_te @ D @ A ) ) )
& ( genClo1015804716orrect @ D @ ( ord_max_real @ ( genClo1163638703lle_te @ C @ A ) @ ( genClo1163638703lle_te @ D @ A ) ) ) )
=> ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1160817912lle_IC @ C @ A @ ( ord_max_real @ ( genClo1163638703lle_te @ C @ A ) @ ( genClo1163638703lle_te @ D @ A ) ) ) @ ( genClo1160817912lle_IC @ D @ A @ ( ord_max_real @ ( genClo1163638703lle_te @ C @ A ) @ ( genClo1163638703lle_te @ D @ A ) ) ) ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_okmaxsync__def) ).
thf(721,plain,
( genClo208577157axsync
= ( ^ [A: nat,B: real] :
! [C: nat,D: nat] :
( ( ( genClo1015804716orrect @ C @ ( ord_max_real @ ( genClo1163638703lle_te @ C @ A ) @ ( genClo1163638703lle_te @ D @ A ) ) )
& ( genClo1015804716orrect @ D @ ( ord_max_real @ ( genClo1163638703lle_te @ C @ A ) @ ( genClo1163638703lle_te @ D @ A ) ) ) )
=> ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1160817912lle_IC @ C @ A @ ( ord_max_real @ ( genClo1163638703lle_te @ C @ A ) @ ( genClo1163638703lle_te @ D @ A ) ) ) @ ( genClo1160817912lle_IC @ D @ A @ ( ord_max_real @ ( genClo1163638703lle_te @ C @ A ) @ ( genClo1163638703lle_te @ D @ A ) ) ) ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(133,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_197_group__cancel_Osub1) ).
thf(605,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)],[133]) ).
thf(16,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_150_add_Oleft__cancel) ).
thf(237,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)],[16]) ).
thf(24,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_152_add_Oassoc) ).
thf(266,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)],[24]) ).
thf(111,axiom,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_add_Ocomm__neutral) ).
thf(541,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(117,axiom,
! [A: real > real > $o,B: real,C: real] :
( ! [D: real,E: real] :
( ( ord_less_eq_real @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: real,E: real] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_linorder__wlog) ).
thf(558,plain,
! [A: real > real > $o,B: real,C: real] :
( ! [D: real,E: real] :
( ( ord_less_eq_real @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: real,E: real] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(126,axiom,
! [A: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( abs_abs_real @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_abs__of__nonneg) ).
thf(586,plain,
! [A: real] :
( ( ord_less_eq_real @ zero_zero_real @ A )
=> ( ( abs_abs_real @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(151,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_285_beta__bound1) ).
thf(662,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)],[151]) ).
thf(141,axiom,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_add__diff__cancel) ).
thf(633,plain,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(50,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_349_add__nonneg__nonneg) ).
thf(360,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)],[50]) ).
thf(34,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_187_add__implies__diff) ).
thf(298,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)],[34]) ).
thf(189,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 @ ( ord_max_real @ A @ C ) @ ( ord_max_real @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_max_Omono) ).
thf(750,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 @ ( ord_max_real @ A @ C ) @ ( ord_max_real @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(136,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_antisym__conv) ).
thf(618,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(72,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_324_diff__ge__0__iff__ge) ).
thf(425,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)],[72]) ).
thf(101,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_216_add__le__add__imp__diff__le) ).
thf(513,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)],[101]) ).
thf(121,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_159_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(573,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)],[121]) ).
thf(33,axiom,
( ( abs_abs_real @ one_one_real )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_abs__1) ).
thf(296,plain,
( ( abs_abs_real @ one_one_real )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(55,axiom,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_one__reorient) ).
thf(375,plain,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(125,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_224_abs__triangle__ineq2__sym) ).
thf(584,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)],[125]) ).
thf(71,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_234_okRead2__def) ).
thf(423,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)],[71]) ).
thf(165,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_231_rts1d) ).
thf(694,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)],[165]) ).
thf(182,axiom,
! [A: real,B: real] :
( ( ord_max_real @ ( ord_max_real @ A @ B ) @ B )
= ( ord_max_real @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_max_Oright__idem) ).
thf(732,plain,
! [A: real,B: real] :
( ( ord_max_real @ ( ord_max_real @ A @ B ) @ B )
= ( ord_max_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(68,axiom,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_add_Ogroup__left__neutral) ).
thf(413,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(123,axiom,
! [A: real] :
( ( abs_abs_real @ ( abs_abs_real @ A ) )
= ( abs_abs_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_abs__idempotent) ).
thf(579,plain,
! [A: real] :
( ( abs_abs_real @ ( abs_abs_real @ A ) )
= ( abs_abs_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(31,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_225_abs__triangle__ineq3) ).
thf(291,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)],[31]) ).
thf(60,axiom,
ord_less_eq_real @ genClo1278781456e_beta @ genClo1651033342e_rmin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_nonoverlap) ).
thf(391,plain,
ord_less_eq_real @ genClo1278781456e_beta @ genClo1651033342e_rmin,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(85,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_179_add__mono__thms__linordered__semiring_I2_J) ).
thf(466,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)],[85]) ).
thf(155,axiom,
! [A: real,B: real] :
( ( ord_max_real @ A @ ( ord_max_real @ A @ B ) )
= ( ord_max_real @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_max_Oleft__idem) ).
thf(672,plain,
! [A: real,B: real] :
( ( ord_max_real @ A @ ( ord_max_real @ A @ B ) )
= ( ord_max_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(119,axiom,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_diff__0__right) ).
thf(567,plain,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(75,axiom,
zero_zero_real != one_one_real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_zero__neq__one) ).
thf(434,plain,
zero_zero_real != one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(131,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_194_add__diff__eq) ).
thf(599,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)],[131]) ).
thf(184,axiom,
! [A: real,B: real,C: real] :
( ( ord_max_real @ A @ ( ord_max_real @ B @ C ) )
= ( ord_max_real @ B @ ( ord_max_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_max_Oleft__commute) ).
thf(737,plain,
! [A: real,B: real,C: real] :
( ( ord_max_real @ A @ ( ord_max_real @ B @ C ) )
= ( ord_max_real @ B @ ( ord_max_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(39,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_149_add_Oright__cancel) ).
thf(318,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)],[39]) ).
thf(59,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_141_add__right__imp__eq) ).
thf(387,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)],[59]) ).
thf(192,axiom,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( ( ord_max_real @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_max_Oabsorb__iff1) ).
thf(758,plain,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( ( ord_max_real @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(109,axiom,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_comm__monoid__add__class_Oadd__0) ).
thf(535,plain,
! [A: real] :
( ( plus_plus_real @ zero_zero_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(41,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_196_diff__eq__eq) ).
thf(323,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)],[41]) ).
thf(129,axiom,
! [A: real] : ( ord_less_eq_real @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_order__refl) ).
thf(594,plain,
! [A: real] : ( ord_less_eq_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(180,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_max_real @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_max_Oabsorb2) ).
thf(726,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_max_real @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(137,axiom,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_diff__zero) ).
thf(621,plain,
! [A: real] :
( ( minus_minus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(168,axiom,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( B
= ( ord_max_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_max_Oorder__iff) ).
thf(700,plain,
( ord_less_eq_real
= ( ^ [A: real,B: real] :
( B
= ( ord_max_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(17,axiom,
! [A: real,B: real] :
( ( ( plus_plus_real @ A @ B )
= A )
= ( B = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_add__cancel__left__right) ).
thf(240,plain,
! [A: real,B: real] :
( ( ( plus_plus_real @ A @ B )
= A )
= ( B = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(196,axiom,
ord_less_eq_real @ ( ord_max_real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_tml__le__tp) ).
thf(769,plain,
ord_less_eq_real @ ( ord_max_real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(1,conjecture,
genClo1015804716orrect @ m @ ( ord_max_real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( genClo1015804716orrect @ m @ ( ord_max_real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(198,plain,
~ ( genClo1015804716orrect @ m @ ( ord_max_real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(63,axiom,
( plus_plus_nat
= ( ^ [A: nat,B: nat] : ( plus_plus_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_add_Ocommute) ).
thf(399,plain,
( plus_plus_nat
= ( ^ [A: nat,B: nat] : ( plus_plus_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(142,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_132_add__left__cancel) ).
thf(636,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)],[142]) ).
thf(82,axiom,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(455,plain,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(99,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_156_group__cancel_Oadd1) ).
thf(505,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)],[99]) ).
thf(74,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_184_diff__right__mono) ).
thf(431,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)],[74]) ).
thf(147,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_129_add__right__cancel) ).
thf(653,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)],[147]) ).
thf(149,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_341_add__decreasing) ).
thf(658,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)],[149]) ).
thf(160,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_21_rte) ).
thf(685,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)],[160]) ).
thf(104,axiom,
! [A: real] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_double__zero) ).
thf(521,plain,
! [A: real] :
( ( ( plus_plus_real @ A @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(87,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
| ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_linear) ).
thf(473,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
| ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(156,axiom,
( ord_max_real
= ( ^ [A: real,B: real] : ( ord_max_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_max_Ocommute) ).
thf(675,plain,
( ord_max_real
= ( ^ [A: real,B: real] : ( ord_max_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(127,axiom,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_add_Oright__neutral) ).
thf(589,plain,
! [A: real] :
( ( plus_plus_real @ A @ zero_zero_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(22,axiom,
! [A: real] :
( ( ( abs_abs_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_abs__eq__0__iff) ).
thf(255,plain,
! [A: real] :
( ( ( abs_abs_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(7,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_183_diff__eq__diff__less__eq) ).
thf(209,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)],[7]) ).
thf(83,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_155_group__cancel_Oadd1) ).
thf(458,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)],[83]) ).
thf(173,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_282_rts2a) ).
thf(712,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)],[173]) ).
thf(170,axiom,
! [A: real,B: real,C: real] :
( ( ord_max_real @ ( ord_max_real @ A @ B ) @ C )
= ( ord_max_real @ A @ ( ord_max_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_max_Oassoc) ).
thf(705,plain,
! [A: real,B: real,C: real] :
( ( ord_max_real @ ( ord_max_real @ A @ B ) @ C )
= ( ord_max_real @ A @ ( ord_max_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(3,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001t__Real__Oreal_T) ).
thf(199,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(44,axiom,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ A @ B ) )
= ( B = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_add__cancel__right__right) ).
thf(331,plain,
! [A: real,B: real] :
( ( A
= ( plus_plus_real @ A @ B ) )
= ( B = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(176,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_237_beta__bound2) ).
thf(717,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)],[176]) ).
thf(84,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_323_zero__le__double__add__iff__zero__le__single__add) ).
thf(463,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)],[84]) ).
thf(112,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_130_add__right__cancel) ).
thf(544,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)],[112]) ).
thf(86,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_135_add__le__cancel__right) ).
thf(470,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)],[86]) ).
thf(122,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_345_add__decreasing2) ).
thf(576,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)],[122]) ).
thf(187,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( ord_max_real @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_real @ A @ C )
=> ~ ( ord_less_eq_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_max_OboundedE) ).
thf(744,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( ord_max_real @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_real @ A @ C )
=> ~ ( ord_less_eq_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(148,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_223_abs__triangle__ineq) ).
thf(656,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)],[148]) ).
thf(79,axiom,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( minus_minus_real @ A @ B )
= zero_zero_real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_eq__iff__diff__eq__0) ).
thf(446,plain,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( minus_minus_real @ A @ B )
= zero_zero_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(97,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_318_le__add__same__cancel1) ).
thf(497,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)],[97]) ).
thf(139,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_193_diff__diff__eq2) ).
thf(627,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)],[139]) ).
thf(51,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_173_add__left__mono) ).
thf(363,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)],[51]) ).
thf(162,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( ord_max_real @ A @ B ) @ C )
= ( ( ord_less_eq_real @ A @ C )
& ( ord_less_eq_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_max_Obounded__iff) ).
thf(688,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ ( ord_max_real @ A @ B ) @ C )
= ( ( ord_less_eq_real @ A @ C )
& ( ord_less_eq_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(105,axiom,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_order__class_Oorder_Oeq__iff) ).
thf(524,plain,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(96,axiom,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ B @ A )
& ( ord_less_eq_real @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_dual__order_Oeq__iff) ).
thf(495,plain,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ B @ A )
& ( ord_less_eq_real @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(20,axiom,
( plus_plus_real
= ( ^ [A: real,B: real] : ( plus_plus_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_add_Ocommute) ).
thf(250,plain,
( plus_plus_real
= ( ^ [A: real,B: real] : ( plus_plus_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(14,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_320_le__add__same__cancel2) ).
thf(231,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)],[14]) ).
thf(91,axiom,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_diff__self) ).
thf(482,plain,
! [A: real] :
( ( minus_minus_real @ A @ A )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(5,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_145_add_Oleft__commute) ).
thf(203,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)],[5]) ).
thf(167,axiom,
genClo1015804716orrect @ l @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_corr__l) ).
thf(699,plain,
genClo1015804716orrect @ l @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(102,axiom,
( ( abs_abs_real @ one_one_real )
= one_one_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_abs__one) ).
thf(517,plain,
( ( abs_abs_real @ one_one_real )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(23,axiom,
! [A: real,B: real > real,C: real,D: real] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_ord__eq__le__subst) ).
thf(258,plain,
! [A: real,B: real > real,C: real,D: real] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(47,axiom,
! [A: real] :
( ( abs_abs_real @ ( abs_abs_real @ A ) )
= ( abs_abs_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_abs__abs) ).
thf(351,plain,
! [A: real] :
( ( abs_abs_real @ ( abs_abs_real @ A ) )
= ( abs_abs_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(64,axiom,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_add__diff__cancel__right_H) ).
thf(401,plain,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(56,axiom,
! [A: real] :
( ( zero_zero_real
= ( abs_abs_real @ A ) )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_abs__0__eq) ).
thf(378,plain,
! [A: real] :
( ( zero_zero_real
= ( abs_abs_real @ A ) )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(100,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_117_le__add__diff__inverse2) ).
thf(510,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)],[100]) ).
thf(153,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_230_rts1) ).
thf(667,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)],[153]) ).
thf(89,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_219_add__le__imp__le__diff) ).
thf(478,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)],[89]) ).
thf(114,axiom,
! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_abs__ge__self) ).
thf(549,plain,
! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(194,axiom,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( ord_max_real @ A @ B ) @ C )
= ( ord_max_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_max__add__distrib__left) ).
thf(763,plain,
! [A: real,B: real,C: real] :
( ( plus_plus_real @ ( ord_max_real @ A @ B ) @ C )
= ( ord_max_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(26,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_ord__le__eq__trans) ).
thf(272,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(175,axiom,
ord_less_eq_real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_tli__le__tp) ).
thf(716,plain,
ord_less_eq_real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(30,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_143_add__left__imp__eq) ).
thf(287,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)],[30]) ).
thf(38,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_131_add__left__cancel) ).
thf(315,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)],[38]) ).
thf(183,axiom,
! [A: real,B: real] : ( ord_less_eq_real @ A @ ( ord_max_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_max_Ocobounded2) ).
thf(735,plain,
! [A: real,B: real] : ( ord_less_eq_real @ A @ ( ord_max_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(118,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_160_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(564,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)],[118]) ).
thf(36,axiom,
( ( abs_abs_real @ zero_zero_real )
= zero_zero_real ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_abs__0) ).
thf(305,plain,
( ( abs_abs_real @ zero_zero_real )
= zero_zero_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(42,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_175_add__mono) ).
thf(326,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)],[42]) ).
thf(76,axiom,
! [A: real] :
( ( ( abs_abs_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_abs__eq__0) ).
thf(437,plain,
! [A: real] :
( ( ( abs_abs_real @ A )
= zero_zero_real )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(108,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_antisym) ).
thf(532,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(166,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_max_real @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_max__absorb2) ).
thf(696,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_max_real @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(177,axiom,
genClo1015804716orrect @ p @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_corr__p) ).
thf(720,plain,
genClo1015804716orrect @ p @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(138,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_151_add_Oassoc) ).
thf(624,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)],[138]) ).
thf(185,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( genClo1015804716orrect @ A @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ C @ one_one_nat ) ) )
& ( genClo1015804716orrect @ B @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ C @ one_one_nat ) ) ) )
=> ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1400225944_theta @ A @ ( plus_plus_nat @ C @ one_one_nat ) @ B ) @ ( genClo1160817912lle_IC @ B @ C @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ C @ one_one_nat ) ) ) ) ) @ genClo721845095Lambda ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_readerror) ).
thf(740,plain,
! [A: nat,B: nat,C: nat] :
( ( ( genClo1015804716orrect @ A @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ C @ one_one_nat ) ) )
& ( genClo1015804716orrect @ B @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ C @ one_one_nat ) ) ) )
=> ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1400225944_theta @ A @ ( plus_plus_nat @ C @ one_one_nat ) @ B ) @ ( genClo1160817912lle_IC @ B @ C @ ( genClo1163638703lle_te @ A @ ( plus_plus_nat @ C @ one_one_nat ) ) ) ) ) @ genClo721845095Lambda ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(130,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_328_abs__le__zero__iff) ).
thf(596,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)],[130]) ).
thf(179,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ A @ ( ord_max_real @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_max_OcoboundedI2) ).
thf(723,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ A @ ( ord_max_real @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(4,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_170_add__right__mono) ).
thf(200,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)],[4]) ).
thf(78,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_142_add__right__imp__eq) ).
thf(442,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)],[78]) ).
thf(53,axiom,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_order_Otrans) ).
thf(369,plain,
! [A: real,B: real,C: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ C )
=> ( ord_less_eq_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(27,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_164_diff__eq__diff__eq) ).
thf(277,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)],[27]) ).
thf(163,axiom,
ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1160817912lle_IC @ l @ i @ ( ord_max_real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) ) @ ( genClo1160817912lle_IC @ m @ i @ ( ord_max_real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) ) ) ) @ delta_S,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_IC__bound) ).
thf(691,plain,
ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( genClo1160817912lle_IC @ l @ i @ ( ord_max_real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) ) @ ( genClo1160817912lle_IC @ m @ i @ ( ord_max_real @ ( genClo1163638703lle_te @ l @ i ) @ ( genClo1163638703lle_te @ m @ i ) ) ) ) ) @ delta_S,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(48,axiom,
! [A: real] :
( ( zero_zero_real
= ( plus_plus_real @ A @ A ) )
= ( A = zero_zero_real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_double__zero__sym) ).
thf(354,plain,
! [A: real] :
( ( zero_zero_real
= ( plus_plus_real @ A @ A ) )
= ( A = zero_zero_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(143,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_order__class_Oorder_Oantisym) ).
thf(639,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(191,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( B
= ( ord_max_real @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_max_OorderE) ).
thf(755,plain,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( B
= ( ord_max_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(94,axiom,
! [A: real,B: real] :
( ~ ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_le__cases) ).
thf(491,plain,
! [A: real,B: real] :
( ~ ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(11,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_191_diff__add__eq__diff__diff__swap) ).
thf(222,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)],[11]) ).
thf(128,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_165_add__le__imp__le__right) ).
thf(592,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)],[128]) ).
thf(171,axiom,
ord_less_eq_real @ ( genClo1163638703lle_te @ m @ i ) @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_tmi__le__tp) ).
thf(708,plain,
ord_less_eq_real @ ( genClo1163638703lle_te @ m @ i ) @ ( genClo1163638703lle_te @ p @ ( plus_plus_nat @ i @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(892,plain,
$false,
inference(cvc4,[status(thm)],[760,234,555,408,582,217,247,440,269,677,384,500,747,538,404,709,570,372,702,357,416,228,448,284,770,475,321,485,348,480,687,280,692,293,396,411,243,428,206,602,766,307,452,529,661,381,714,220,366,334,302,392,630,729,252,329,665,493,682,551,650,615,610,420,519,742,488,225,753,669,642,526,679,547,212,647,721,605,237,266,541,558,586,662,633,360,298,750,618,425,513,573,296,375,584,423,694,732,413,579,291,391,466,672,567,434,599,737,318,387,758,535,323,594,726,621,700,240,769,198,399,636,455,505,431,653,658,685,521,473,675,589,255,209,458,712,705,199,331,717,463,544,470,576,744,656,446,497,627,363,688,524,495,250,231,482,203,699,517,258,351,401,378,510,667,478,549,763,272,716,287,315,735,564,305,326,437,532,696,720,624,740,596,723,200,442,369,277,691,354,639,755,491,222,592,708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP064^1 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n027.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sat May 18 18:33:08 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.94/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.89/1.19 % [INFO] Parsing done (266ms).
% 1.89/1.20 % [INFO] Running in sequential loop mode.
% 2.62/1.42 % [INFO] eprover registered as external prover.
% 2.62/1.42 % [INFO] cvc4 registered as external prover.
% 2.62/1.43 % [INFO] Scanning for conjecture ...
% 2.93/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 358 axioms. Running axiom selection ...
% 3.20/1.59 % [INFO] Axiom selection finished. Selected 195 axioms (removed 163 axioms).
% 3.63/1.72 % [INFO] Problem is higher-order (TPTP THF).
% 3.63/1.74 % [INFO] Type checking passed.
% 3.63/1.74 % [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 ...
% 13.99/4.22 % External prover 'cvc4' found a proof!
% 13.99/4.22 % [INFO] Killing All external provers ...
% 13.99/4.22 % Time passed: 3687ms (effective reasoning time: 3020ms)
% 13.99/4.22 % 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)>
% 13.99/4.22 % Axioms used in derivation (195): fact_332_abs__eq__0__iff, fact_100_max_Oabsorb2, fact_60_order__class_Oorder_Oeq__iff, fact_161_one__reorient, fact_316_add__le__same__cancel2, fact_1_corr__m, fact_104_max_OorderI, fact_139_add__diff__cancel__right_H, fact_310_abs__zero, fact_281_nonoverlap, fact_345_add__decreasing2, fact_130_add__right__cancel, fact_230_rts1, fact_320_le__add__same__cancel2, fact_151_add_Oassoc, fact_119_abs__1, fact_122_diff__add__cancel, fact_324_diff__ge__0__iff__ge, fact_86_max_Oabsorb__iff1, fact_78_dual__order_Oantisym, fact_296_add__cancel__left__left, fact_198_abs__ge__self, fact_142_add__right__imp__eq, fact_62_ord__eq__le__trans, fact_298_double__zero, fact_192_diff__add__eq, fact_200_abs__one, fact_50_eq__refl, fact_222_diff__le__eq, fact_141_add__right__imp__eq, fact_227_abs__diff__triangle__ineq, fact_26_order__refl, fact_110_max__def, fact_133_abs__idempotent, fact_46_antisym, fact_8_max_Oidem, fact_5_corr__l__tml, fact_338_add_Ocomm__neutral, fact_313_abs__0, fact_323_zero__le__double__add__iff__zero__le__single__add, fact_72_linorder__wlog, fact_117_le__add__diff__inverse2, fact_3_tml__le__tp, fact_300_add_Oright__neutral, fact_309_diff__self, fact_24_max__absorb1, fact_135_add__le__cancel__right, fact_225_abs__triangle__ineq3, fact_336_add_Ogroup__left__neutral, fact_347_add__increasing2, fact_66_order__class_Oorder_Oantisym, fact_70_dual__order_Orefl, fact_204_max__add__distrib__right, fact_206_max__diff__distrib__left, fact_341_add__decreasing, fact_0_correct__closed, fact_235_sin__bound__lemma, fact_58_antisym__conv, fact_290_add__cancel__right__right, fact_194_add__diff__eq, fact_237_beta__bound2, fact_197_group__cancel_Osub1, fact_40_ord__le__eq__subst, fact_159_ab__semigroup__add__class_Oadd__ac_I1_J, fact_158_add__mono__thms__linordered__semiring_I4_J, fact_224_abs__triangle__ineq2__sym, fact_179_add__mono__thms__linordered__semiring_I2_J, fact_292_add__cancel__right__left, fact_302_add_Oleft__neutral, fact_147_add_Ocommute, fact_196_diff__eq__eq, fact_201_abs__minus__commute, fact_15_max_Oassoc, fact_145_add_Oleft__commute, fact_98_max_OboundedE, fact_175_add__mono, fact_233_rts0d, fact_308_diff__0__right, fact_152_add_Oassoc, fact_167_add__le__imp__le__left, fact_343_add__increasing, fact_19_max_Oleft__commute, fact_52_le__cases, fact_326_abs__of__nonneg, fact_32_order__subst2, fact_48_linear, fact_120_abs__add__abs, fact_195_eq__diff__eq, fact_6_tmi__le__tp, fact_123_add__diff__cancel__left, fact_223_abs__triangle__ineq, fact_297_double__zero__sym, fact_82_max_OcoboundedI1, fact_56_le__cases3, fact_112_max__absorb2, fact_328_abs__le__zero__iff, help_If_2_1_If_001t__Real__Oreal_T, fact_331_zero__reorient, fact_115_le__add__diff__inverse, fact_236_eq__diff__eq_H, fact_108_max_Omono, fact_146_add_Oleft__commute, fact_226_abs__triangle__ineq2, fact_305_diff__zero, fact_193_diff__diff__eq2, fact_84_max_Oabsorb__iff2, fact_219_add__le__imp__le__diff, fact_231_rts1d, fact_143_add__left__imp__eq, fact_125_add__diff__cancel__left_H, fact_17_max_Ocommute, fact_322_double__add__le__zero__iff__single__add__le__zero, fact_28_order__subst1, fact_177_add__mono__thms__linordered__semiring_I1_J, fact_2_corr__p, fact_150_add_Oleft__cancel, fact_184_diff__right__mono, fact_153_group__cancel_Oadd2, fact_154_group__cancel_Oadd2, fact_183_diff__eq__diff__less__eq, fact_202_max__add__distrib__left, fact_36_ord__eq__le__subst, fact_311_abs__eq__0, fact_132_add__left__cancel, fact_285_beta__bound1, fact_340_comm__monoid__add__class_Oadd__0, fact_318_le__add__same__cancel1, fact_284_okRead1__def, fact_149_add_Oright__cancel, fact_129_add__right__cancel, fact_137_add__le__cancel__left, fact_283_readerror, fact_127_add__diff__cancel__right, fact_114_okmaxsync__def, fact_221_le__diff__eq, fact_4_corr__l, fact_94_max_Oorder__iff, fact_102_max_Oabsorb1, fact_21_rte, fact_312_abs__0__eq, fact_164_diff__eq__diff__eq, fact_80_max_OcoboundedI2, fact_157_add__mono__thms__linordered__semiring_I4_J, fact_106_max_OorderE, fact_165_add__le__imp__le__right, fact_76_dual__order_Oeq__iff, fact_131_add__left__cancel, fact_14_IC__bound, fact_22_max_Obounded__iff, fact_349_add__nonneg__nonneg, fact_186_diff__mono, fact_90_max_Ocobounded2, fact_185_diff__left__mono, fact_181_add__mono__thms__linordered__semiring_I3_J, fact_234_okRead2__def, fact_160_ab__semigroup__add__class_Oadd__ac_I1_J, fact_68_order__trans, fact_148_add_Ocommute, fact_54_order_Otrans, fact_170_add__right__mono, fact_88_le__max__iff__disj, fact_156_group__cancel_Oadd1, fact_155_group__cancel_Oadd1, fact_187_add__implies__diff, fact_189_diff__diff__add, help_If_3_1_If_001t__Real__Oreal_T, fact_74_dual__order_Otrans, fact_303_cancel__comm__monoid__add__class_Odiff__cancel, fact_327_abs__le__self__iff, help_If_1_1_If_001t__Real__Oreal_T, fact_96_max_OboundedI, fact_144_add__left__imp__eq, fact_162_diff__right__commute, fact_12_max_Oright__idem, fact_351_add__nonpos__nonpos, fact_173_add__left__mono, fact_228_abs__triangle__ineq4, fact_92_max_Ocobounded1, fact_121_add__diff__cancel, fact_314_add__le__same__cancel1, fact_191_diff__add__eq__diff__diff__swap, fact_229_abs__diff__le__iff, fact_134_abs__abs, fact_7_tli__le__tp, fact_282_rts2a, fact_232_rts0, fact_44_eq__iff, fact_294_add__cancel__left__right, fact_238_rts2b, fact_333_eq__iff__diff__eq__0, fact_10_max_Oleft__idem, fact_335_zero__neq__one, fact_216_add__le__add__imp__diff__le, fact_64_ord__le__eq__trans, fact_199_abs__le__D1
% 13.99/4.22 % No. of inferences in proof: 394
% 13.99/4.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3687 ms resp. 3020 ms w/o parsing
% 14.42/4.32 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.42/4.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------