%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP062^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:36 AM UTC 2026
% Result : Theorem 95.57s 23.01s
% Output : Refutation 96.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 353
% Syntax : Number of formulae : 815 ( 483 unt; 0 typ; 0 def)
% Number of atoms : 1839 ( 820 equ; 9 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 7884 ( 176 ~; 72 |; 50 &;6961 @)
% ( 0 <=>; 625 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 99 ( 99 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 34 usr; 11 con; 0-4 aty)
% Number of variables : 2049 ( 80 ^;1956 !; 13 ?;2049 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_real_type,type,
set_real: $tType ).
thf(real_type,type,
real: $tType ).
thf(num_type,type,
num: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(genClo1161277105lle_PC_decl,type,
genClo1161277105lle_PC: nat > real > real ).
thf(genClo1144207539le_rho_decl,type,
genClo1144207539le_rho: real ).
thf(genClo1015804716orrect_decl,type,
genClo1015804716orrect: nat > real > $o ).
thf(genClo293725281kRead1_decl,type,
genClo293725281kRead1: ( nat > real ) > real > ( nat > $o ) > $o ).
thf(genClo293725282kRead2_decl,type,
genClo293725282kRead2: ( nat > real ) > ( nat > real ) > real > ( nat > $o ) > $o ).
thf(genClo2108747022bound1_decl,type,
genClo2108747022bound1: ( nat > real > real ) > $o ).
thf(genClo2108747023bound2_decl,type,
genClo2108747023bound2: ( nat > real > real ) > $o ).
thf(abs_abs_real_decl,type,
abs_abs_real: real > real ).
thf(minus_minus_nat_decl,type,
minus_minus_nat: nat > nat > nat ).
thf(minus_minus_real_decl,type,
minus_minus_real: real > real > real ).
thf(one_one_nat_decl,type,
one_one_nat: nat ).
thf(one_one_real_decl,type,
one_one_real: real ).
thf(plus_plus_nat_decl,type,
plus_plus_nat: nat > nat > nat ).
thf(plus_plus_num_decl,type,
plus_plus_num: num > num > num ).
thf(plus_plus_real_decl,type,
plus_plus_real: real > real > real ).
thf(times_times_nat_decl,type,
times_times_nat: nat > nat > nat ).
thf(times_times_num_decl,type,
times_times_num: num > num > num ).
thf(times_times_real_decl,type,
times_times_real: real > real > real ).
thf(neg_numeral_dbl_real_decl,type,
neg_numeral_dbl_real: real > real ).
thf(bit0_decl,type,
bit0: num > num ).
thf(one_decl,type,
one: num ).
thf(numeral_numeral_nat_decl,type,
numeral_numeral_nat: num > nat ).
thf(numeral_numeral_real_decl,type,
numeral_numeral_real: num > real ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ord_less_eq_num_decl,type,
ord_less_eq_num: num > num > $o ).
thf(ord_less_eq_real_decl,type,
ord_less_eq_real: real > real > $o ).
thf(collect_real_decl,type,
collect_real: ( real > $o ) > set_real ).
thf(member_real_decl,type,
member_real: real > set_real > $o ).
thf(c_decl,type,
c: nat > real > real ).
thf(d_decl,type,
d: nat > real > real ).
thf(p_decl,type,
p: nat ).
thf(q_decl,type,
q: nat ).
thf(s_decl,type,
s: real ).
thf(t_decl,type,
t: real ).
thf(77,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_le__add__diff) ).
thf(645,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(354,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( plus_plus_real @ ( minus_minus_real @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_le__add__diff__inverse2) ).
thf(1586,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)],[354]) ).
thf(280,axiom,
! [A: num] :
( ( plus_plus_nat @ ( numeral_numeral_nat @ A ) @ one_one_nat )
= ( numeral_numeral_nat @ ( plus_plus_num @ A @ one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_numeral__plus__one) ).
thf(1337,plain,
! [A: num] :
( ( plus_plus_nat @ ( numeral_numeral_nat @ A ) @ one_one_nat )
= ( numeral_numeral_nat @ ( plus_plus_num @ A @ one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(298,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
= ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ D ) @ B ) @ C ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_ordered__ring__class_Ole__add__iff1) ).
thf(1411,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
= ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ D ) @ B ) @ C ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(71,axiom,
! [A: num,B: num] :
( ( ord_less_eq_num @ A @ B )
| ( ord_less_eq_num @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_linear) ).
thf(629,plain,
! [A: num,B: num] :
( ( ord_less_eq_num @ A @ B )
| ( ord_less_eq_num @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(316,axiom,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_comm__monoid__mult__class_Omult__1) ).
thf(1469,plain,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(111,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( A = B )
& ( ord_less_eq_nat @ C @ D ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_add__mono__thms__linordered__semiring_I2_J) ).
thf(760,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( A = B )
& ( ord_less_eq_nat @ C @ D ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(311,axiom,
! [A: num,B: real,C: real] :
( ( times_times_real @ ( numeral_numeral_real @ A ) @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ A ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_right__diff__distrib__numeral) ).
thf(1454,plain,
! [A: num,B: real,C: real] :
( ( times_times_real @ ( numeral_numeral_real @ A ) @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ A ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(188,axiom,
! [A: nat,B: nat,C: nat > real,D: real] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_ord__le__eq__subst) ).
thf(1031,plain,
! [A: nat,B: nat,C: nat > real,D: real] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ 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)],[188]) ).
thf(222,axiom,
! [A: real,B: real] :
( ( A = B )
=> ( ord_less_eq_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_eq__refl) ).
thf(1153,plain,
! [A: real,B: real] :
( ( A = B )
=> ( ord_less_eq_real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(1154,plain,
! [B: real,A: real] :
( ( A != B )
| ( ord_less_eq_real @ A @ B ) ),
inference(cnf,[status(esa)],[1153]) ).
thf(1155,plain,
! [B: real,A: real] :
( ( A != B )
| ( ord_less_eq_real @ A @ B ) ),
inference(lifteq,[status(thm)],[1154]) ).
thf(1156,plain,
! [A: real] : ( ord_less_eq_real @ A @ A ),
inference(simp,[status(thm)],[1155]) ).
thf(1,conjecture,
ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(355,plain,
~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(197,axiom,
( ( neg_numeral_dbl_real @ one_one_real )
= ( numeral_numeral_real @ ( bit0 @ one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_dbl__simps_I3_J) ).
thf(1064,plain,
( ( neg_numeral_dbl_real @ one_one_real )
= ( numeral_numeral_real @ ( bit0 @ one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(1065,plain,
( ( numeral_numeral_real @ ( bit0 @ one ) )
= ( neg_numeral_dbl_real @ one_one_real ) ),
inference(lifteq,[status(thm)],[1064]) ).
thf(1708,plain,
~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
inference(rewrite,[status(thm)],[355,1065]) ).
thf(1894,plain,
! [A: real] :
( ~ $true
| ( ( ord_less_eq_real @ A @ A )
!= ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1156,1708]) ).
thf(1895,plain,
! [A: real] :
( ( ord_less_eq_real @ A @ A )
!= ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ) ),
inference(simp,[status(thm)],[1894]) ).
thf(1897,plain,
! [A: real] :
( ( A
!= ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) )
| ( A
!= ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ) ),
inference(simp,[status(thm)],[1895]) ).
thf(1899,plain,
( ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
!= ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
inference(simp,[status(thm)],[1897]) ).
thf(147,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ~ ! [C: nat] :
( B
!= ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_less__eqE) ).
thf(893,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ~ ! [C: nat] :
( B
!= ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(164,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ D ) @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ E ) )
= ( ord_less_eq_nat @ D @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_nat__le__add__iff2) ).
thf(962,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ D ) @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ E ) )
= ( ord_less_eq_nat @ D @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(231,axiom,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( numeral_numeral_real @ ( bit0 @ one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_one__add__one) ).
thf(1179,plain,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( numeral_numeral_real @ ( bit0 @ one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(342,axiom,
! [A: num] :
( ( ord_less_eq_real @ ( numeral_numeral_real @ A ) @ one_one_real )
= ( ord_less_eq_num @ A @ one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_numeral__le__one__iff) ).
thf(1554,plain,
! [A: num] :
( ( ord_less_eq_real @ ( numeral_numeral_real @ A ) @ one_one_real )
= ( ord_less_eq_num @ A @ one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(39,axiom,
! [A: num,B: num,C: num] :
( ( ( ord_less_eq_num @ A @ B )
=> ~ ( ord_less_eq_num @ B @ C ) )
=> ( ( ( ord_less_eq_num @ B @ A )
=> ~ ( ord_less_eq_num @ A @ C ) )
=> ( ( ( ord_less_eq_num @ A @ C )
=> ~ ( ord_less_eq_num @ C @ B ) )
=> ( ( ( ord_less_eq_num @ C @ B )
=> ~ ( ord_less_eq_num @ B @ A ) )
=> ( ( ( ord_less_eq_num @ B @ C )
=> ~ ( ord_less_eq_num @ C @ A ) )
=> ~ ( ( ord_less_eq_num @ C @ A )
=> ~ ( ord_less_eq_num @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_le__cases3) ).
thf(481,plain,
! [A: num,B: num,C: num] :
( ( ( ord_less_eq_num @ A @ B )
=> ~ ( ord_less_eq_num @ B @ C ) )
=> ( ( ( ord_less_eq_num @ B @ A )
=> ~ ( ord_less_eq_num @ A @ C ) )
=> ( ( ( ord_less_eq_num @ A @ C )
=> ~ ( ord_less_eq_num @ C @ B ) )
=> ( ( ( ord_less_eq_num @ C @ B )
=> ~ ( ord_less_eq_num @ B @ A ) )
=> ( ( ( ord_less_eq_num @ B @ C )
=> ~ ( ord_less_eq_num @ C @ A ) )
=> ~ ( ( ord_less_eq_num @ C @ A )
=> ~ ( ord_less_eq_num @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_diff__le__mono2) ).
thf(365,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(236,axiom,
! [A: num] :
( ( one_one_nat
= ( numeral_numeral_nat @ A ) )
= ( one = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_one__eq__numeral__iff) ).
thf(1190,plain,
! [A: num] :
( ( one_one_nat
= ( numeral_numeral_nat @ A ) )
= ( one = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(239,axiom,
( genClo2108747023bound2
= ( ^ [A: nat > real > real] :
! [B: nat,C: real,D: real] :
( ( ( genClo1015804716orrect @ B @ D )
& ( ord_less_eq_real @ C @ D ) )
=> ( ord_less_eq_real @ ( times_times_real @ ( minus_minus_real @ D @ C ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( A @ B @ D ) @ ( A @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_rho__bound2__def) ).
thf(1200,plain,
( genClo2108747023bound2
= ( ^ [A: nat > real > real] :
! [B: nat,C: real,D: real] :
( ( ( genClo1015804716orrect @ B @ D )
& ( ord_less_eq_real @ C @ D ) )
=> ( ord_less_eq_real @ ( times_times_real @ ( minus_minus_real @ D @ C ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( A @ B @ D ) @ ( A @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(170,axiom,
ord_less_eq_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Eq2) ).
thf(977,plain,
ord_less_eq_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(180,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
= ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ D ) @ B ) @ C )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_eq__add__iff1) ).
thf(1005,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
= ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ D ) @ B ) @ C )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(199,axiom,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_add__diff__cancel__right_H) ).
thf(1068,plain,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(347,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/sandbox2/benchmark/theBenchmark.p',fact_237_okRead1__def) ).
thf(1569,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)],[347]) ).
thf(201,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/sandbox2/benchmark/theBenchmark.p',fact_206_diff__eq__diff__less__eq) ).
thf(1073,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)],[201]) ).
thf(338,axiom,
( ( numeral_numeral_nat @ one )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_numerals_I1_J) ).
thf(1543,plain,
( ( numeral_numeral_nat @ one )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(1544,plain,
( ( numeral_numeral_nat @ one )
= one_one_nat ),
inference(lifteq,[status(thm)],[1543]) ).
thf(241,axiom,
! [A: real,B: num > real,C: num,D: num] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_num @ C @ D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_ord__eq__le__subst) ).
thf(1205,plain,
! [A: real,B: num > real,C: num,D: num] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_num @ C @ D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ 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)],[241]) ).
thf(10,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
= ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_diff__mult__distrib2) ).
thf(377,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
= ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(378,plain,
! [C: nat,B: nat,A: nat] :
( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
= ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
inference(cnf,[status(esa)],[377]) ).
thf(379,plain,
! [C: nat,B: nat,A: nat] :
( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
= ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
inference(lifteq,[status(thm)],[378]) ).
thf(270,axiom,
( ( plus_plus_num @ one @ one )
= ( bit0 @ one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_semiring__norm_I2_J) ).
thf(1305,plain,
( ( plus_plus_num @ one @ one )
= ( bit0 @ one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(322,axiom,
! [A: real,B: real,C: real] :
( ( A
= ( minus_minus_real @ B @ C ) )
= ( B
= ( plus_plus_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_eq__diff__eq_H) ).
thf(1486,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)],[322]) ).
thf(46,axiom,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_mult_Ocomm__neutral) ).
thf(521,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(522,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(cnf,[status(esa)],[521]) ).
thf(523,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(lifteq,[status(thm)],[522]) ).
thf(61,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/sandbox2/benchmark/theBenchmark.p',fact_90_is__num__normalize_I1_J) ).
thf(582,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)],[61]) ).
thf(102,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/sandbox2/benchmark/theBenchmark.p',fact_98_group__cancel_Oadd2) ).
thf(730,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)],[102]) ).
thf(267,axiom,
! [A: nat,B: real > nat,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_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_ord__eq__le__subst) ).
thf(1290,plain,
! [A: nat,B: real > nat,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_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(142,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_add__right__mono) ).
thf(878,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(30,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ ( times_times_nat @ A @ ( times_times_nat @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_le__cube) ).
thf(440,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ ( times_times_nat @ A @ ( times_times_nat @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(43,axiom,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= one_one_nat )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_nat__mult__eq__1__iff) ).
thf(511,plain,
! [A: nat,B: nat] :
( ( ( times_times_nat @ A @ B )
= one_one_nat )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(218,axiom,
! [A: num] :
( ( bit0 @ A )
!= one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_semiring__norm_I85_J) ).
thf(1134,plain,
! [A: num] :
( ( bit0 @ A )
!= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(1135,plain,
~ ? [A: num] :
( ( bit0 @ A )
= one ),
inference(miniscope,[status(thm)],[1134]) ).
thf(1136,plain,
! [A: num] :
( ( bit0 @ A )
!= one ),
inference(cnf,[status(esa)],[1135]) ).
thf(1137,plain,
! [A: num] :
( ( bit0 @ A )
!= one ),
inference(lifteq,[status(thm)],[1136]) ).
thf(192,axiom,
! [A: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_one__le__numeral) ).
thf(1049,plain,
! [A: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(1050,plain,
! [A: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ A ) ),
inference(cnf,[status(esa)],[1049]) ).
thf(233,axiom,
( ( abs_abs_real @ one_one_real )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_abs__1) ).
thf(1182,plain,
( ( abs_abs_real @ one_one_real )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(1183,plain,
( ( abs_abs_real @ one_one_real )
= one_one_real ),
inference(lifteq,[status(thm)],[1182]) ).
thf(1613,plain,
( ~ ( ord_less_eq_real @ one_one_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) )
| ( ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
!= ( abs_abs_real @ one_one_real ) ) ),
inference(paramod_ordered,[status(thm)],[1183,355]) ).
thf(1614,plain,
( ~ ( ord_less_eq_real @ one_one_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) )
| ( ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) )
!= one_one_real ) ),
inference(simp,[status(thm)],[1613]) ).
thf(1709,plain,
( ~ ( ord_less_eq_real @ one_one_real @ ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) )
| ( ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) )
!= one_one_real ) ),
inference(rewrite,[status(thm)],[1614,1065]) ).
thf(1859,plain,
! [A: num] :
( ~ $true
| ( ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) )
!= one_one_real )
| ( ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ A ) )
!= ( ord_less_eq_real @ one_one_real @ ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1050,1709]) ).
thf(1860,plain,
! [A: num] :
( ( ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) )
!= one_one_real )
| ( ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ A ) )
!= ( ord_less_eq_real @ one_one_real @ ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ) ) ),
inference(simp,[status(thm)],[1859]) ).
thf(1865,plain,
! [A: num] :
( ( ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) )
!= one_one_real )
| ( one_one_real != one_one_real )
| ( ( numeral_numeral_real @ A )
!= ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ) ),
inference(simp,[status(thm)],[1860]) ).
thf(1867,plain,
! [A: num] :
( ( ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) )
!= one_one_real )
| ( ( numeral_numeral_real @ A )
!= ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ) ),
inference(simp,[status(thm)],[1865]) ).
thf(225,axiom,
! [A: real] : ( ord_less_eq_real @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_order__refl) ).
thf(1164,plain,
! [A: real] : ( ord_less_eq_real @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(277,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/sandbox2/benchmark/theBenchmark.p',fact_57_abs__add__abs) ).
thf(1327,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)],[277]) ).
thf(256,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/sandbox2/benchmark/theBenchmark.p',fact_129_add__mono__thms__linordered__semiring_I2_J) ).
thf(1260,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)],[256]) ).
thf(107,axiom,
( times_times_nat
= ( ^ [A: nat,B: nat] : ( times_times_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_mult_Ocommute) ).
thf(746,plain,
( times_times_nat
= ( ^ [A: nat,B: nat] : ( times_times_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(747,plain,
( times_times_nat
= ( ^ [A: nat,B: nat] : ( times_times_nat @ B @ A ) ) ),
inference(lifteq,[status(thm)],[746]) ).
thf(159,axiom,
! [A: nat,B: nat,C: num] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ C ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_distrib__right__numeral) ).
thf(945,plain,
! [A: nat,B: nat,C: num] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ C ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(313,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/sandbox2/benchmark/theBenchmark.p',fact_231_sin__bound__lemma) ).
thf(1458,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)],[313]) ).
thf(203,axiom,
! [A: set_real] :
( ? [B: real] : ( member_real @ B @ A )
=> ( ? [B: real] :
! [C: real] :
( ( member_real @ C @ A )
=> ( ord_less_eq_real @ C @ B ) )
=> ? [B: real] :
( ! [C: real] :
( ( member_real @ C @ A )
=> ( ord_less_eq_real @ C @ B ) )
& ! [C: real] :
( ! [D: real] :
( ( member_real @ D @ A )
=> ( ord_less_eq_real @ D @ C ) )
=> ( ord_less_eq_real @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_complete__real) ).
thf(1078,plain,
! [A: set_real] :
( ? [B: real] : ( member_real @ B @ A )
=> ( ? [B: real] :
! [C: real] :
( ( member_real @ C @ A )
=> ( ord_less_eq_real @ C @ B ) )
=> ? [B: real] :
( ! [C: real] :
( ( member_real @ C @ A )
=> ( ord_less_eq_real @ C @ B ) )
& ! [C: real] :
( ! [D: real] :
( ( member_real @ D @ A )
=> ( ord_less_eq_real @ D @ C ) )
=> ( ord_less_eq_real @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(304,axiom,
( times_times_real
= ( ^ [A: real,B: real] : ( times_times_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_mult_Ocommute) ).
thf(1426,plain,
( times_times_real
= ( ^ [A: real,B: real] : ( times_times_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(272,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/sandbox2/benchmark/theBenchmark.p',fact_53_add__diff__cancel__left) ).
thf(1310,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)],[272]) ).
thf(49,axiom,
! [A: num,B: num,C: num > nat,D: nat] :
( ( ord_less_eq_num @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_ord__le__eq__subst) ).
thf(533,plain,
! [A: num,B: num,C: num > nat,D: nat] :
( ( ord_less_eq_num @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(325,axiom,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_add__diff__cancel) ).
thf(1507,plain,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(245,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/sandbox2/benchmark/theBenchmark.p',fact_258_order__subst2) ).
thf(1222,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)],[245]) ).
thf(156,axiom,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_comm__monoid__mult__class_Omult__1) ).
thf(930,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(238,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/sandbox2/benchmark/theBenchmark.p',fact_131_add__mono__thms__linordered__semiring_I3_J) ).
thf(1196,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)],[238]) ).
thf(350,axiom,
! [A: num] :
( ( plus_plus_real @ ( numeral_numeral_real @ A ) @ one_one_real )
= ( numeral_numeral_real @ ( plus_plus_num @ A @ one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_numeral__plus__one) ).
thf(1576,plain,
! [A: num] :
( ( plus_plus_real @ ( numeral_numeral_real @ A ) @ one_one_real )
= ( numeral_numeral_real @ ( plus_plus_num @ A @ one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(116,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ ( times_times_nat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_le__square) ).
thf(782,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ ( times_times_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(318,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/sandbox2/benchmark/theBenchmark.p',fact_49_add__diff__cancel__right) ).
thf(1475,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)],[318]) ).
thf(332,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
| ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_linear) ).
thf(1529,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)],[332]) ).
thf(329,axiom,
genClo1015804716orrect @ p @ t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_corr__p) ).
thf(1518,plain,
genClo1015804716orrect @ p @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(79,axiom,
! [A: num,B: num > num,C: num,D: num] :
( ( ord_less_eq_num @ A @ ( B @ C ) )
=> ( ( ord_less_eq_num @ C @ D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ E @ F )
=> ( ord_less_eq_num @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_order__subst1) ).
thf(651,plain,
! [A: num,B: num > num,C: num,D: num] :
( ( ord_less_eq_num @ A @ ( B @ C ) )
=> ( ( ord_less_eq_num @ C @ D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ E @ F )
=> ( ord_less_eq_num @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(250,axiom,
( ( numeral_numeral_real @ one )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_numeral__One) ).
thf(1243,plain,
( ( numeral_numeral_real @ one )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(215,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( numeral_numeral_nat @ ( bit0 @ one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_one__add__one) ).
thf(1126,plain,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( numeral_numeral_nat @ ( bit0 @ one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(1127,plain,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( numeral_numeral_nat @ ( bit0 @ one ) ) ),
inference(lifteq,[status(thm)],[1126]) ).
thf(168,axiom,
genClo2108747022bound1 @ c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_rb1) ).
thf(973,plain,
genClo2108747022bound1 @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(191,axiom,
! [A: real] :
( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_mult__2) ).
thf(1046,plain,
! [A: real] :
( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A )
= ( plus_plus_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(194,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/sandbox2/benchmark/theBenchmark.p',fact_123_add__left__mono) ).
thf(1055,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)],[194]) ).
thf(266,axiom,
! [A: num] :
( ( times_times_num @ A @ one )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_semiring__norm_I11_J) ).
thf(1287,plain,
! [A: num] :
( ( times_times_num @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(8,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( minus_minus_nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_add__diff__cancel__right) ).
thf(370,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( minus_minus_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(371,plain,
! [C: nat,B: nat,A: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( minus_minus_nat @ A @ C ) ),
inference(cnf,[status(esa)],[370]) ).
thf(372,plain,
! [C: nat,B: nat,A: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( minus_minus_nat @ A @ C ) ),
inference(lifteq,[status(thm)],[371]) ).
thf(93,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(702,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(273,axiom,
! [A: real,B: real,C: num] :
( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ C ) )
= ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ C ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_left__diff__distrib__numeral) ).
thf(1313,plain,
! [A: real,B: real,C: num] :
( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ C ) )
= ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ C ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(50,axiom,
! [A: num,B: num,C: nat] :
( ( times_times_nat @ ( numeral_numeral_nat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ B ) @ C ) )
= ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_mult__numeral__left__semiring__numeral) ).
thf(542,plain,
! [A: num,B: num,C: nat] :
( ( times_times_nat @ ( numeral_numeral_nat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ B ) @ C ) )
= ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(278,axiom,
! [A: num] : ( ord_less_eq_num @ one @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_semiring__norm_I68_J) ).
thf(1330,plain,
! [A: num] : ( ord_less_eq_num @ one @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(257,axiom,
! [A: num,B: num] :
( ( times_times_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) )
= ( numeral_numeral_real @ ( times_times_num @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_numeral__times__numeral) ).
thf(1264,plain,
! [A: num,B: num] :
( ( times_times_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) )
= ( numeral_numeral_real @ ( times_times_num @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(68,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_add__mono) ).
thf(619,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(131,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/sandbox2/benchmark/theBenchmark.p',fact_97_group__cancel_Oadd2) ).
thf(838,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)],[131]) ).
thf(339,axiom,
! [A: num,B: real,C: real] :
( ( times_times_real @ ( numeral_numeral_real @ A ) @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ A ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_distrib__left__numeral) ).
thf(1545,plain,
! [A: num,B: real,C: real] :
( ( times_times_real @ ( numeral_numeral_real @ A ) @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ A ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(149,axiom,
! [A: set_real] :
( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_Collect__mem__eq) ).
thf(900,plain,
! [A: set_real] :
( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(901,plain,
! [A: set_real] :
( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
= A ),
inference(cnf,[status(esa)],[900]) ).
thf(902,plain,
! [A: set_real] :
( ( collect_real
@ ^ [B: real] : ( member_real @ B @ A ) )
= A ),
inference(lifteq,[status(thm)],[901]) ).
thf(74,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_le__add__diff__inverse2) ).
thf(638,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(252,axiom,
! [A: nat] :
( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_mult__2) ).
thf(1247,plain,
! [A: nat] :
( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(275,axiom,
! [A: num,B: real > num,C: real,D: real] :
( ( ord_less_eq_num @ A @ ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_num @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_order__subst1) ).
thf(1319,plain,
! [A: num,B: real > num,C: real,D: real] :
( ( ord_less_eq_num @ A @ ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_num @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(283,axiom,
! [A: nat,B: real,C: real] :
( ( ( ord_less_eq_real @ B @ C )
& ( genClo1015804716orrect @ A @ C ) )
=> ( genClo1015804716orrect @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_correct__closed) ).
thf(1347,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)],[283]) ).
thf(114,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_add_Oright__cancel) ).
thf(770,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)],[114]) ).
thf(288,axiom,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_verit__eq__simplify_I8_J) ).
thf(1362,plain,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(247,axiom,
! [A: num] :
( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ A ) )
= ( numeral_numeral_real @ ( bit0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_dbl__simps_I5_J) ).
thf(1232,plain,
! [A: num] :
( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ A ) )
= ( numeral_numeral_real @ ( bit0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(143,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_mult__le__mono) ).
thf(881,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(22,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_diff__le__mono) ).
thf(416,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(323,axiom,
! [A: real,B: real,C: real > num,D: num] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_ord__le__eq__subst) ).
thf(1489,plain,
! [A: real,B: real,C: real > num,D: num] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(269,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/sandbox2/benchmark/theBenchmark.p',fact_37_add__le__cancel__left) ).
thf(1302,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)],[269]) ).
thf(1470,plain,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(cnf,[status(esa)],[1469]) ).
thf(1471,plain,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(lifteq,[status(thm)],[1470]) ).
thf(2038,plain,
! [A: real] :
( ( A
!= ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) )
| ( ( times_times_real @ one_one_real @ A )
!= ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ) ),
inference(paramod_ordered,[status(thm)],[1471,1899]) ).
thf(2090,plain,
( ( ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho )
!= one_one_real )
| ( ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
!= ( minus_minus_real @ t @ s ) ) ),
inference(simp,[status(thm)],[2038]) ).
thf(291,axiom,
( genClo2108747022bound1
= ( ^ [A: nat > real > real] :
! [B: nat,C: real,D: real] :
( ( ( genClo1015804716orrect @ B @ D )
& ( ord_less_eq_real @ C @ D ) )
=> ( ord_less_eq_real @ ( minus_minus_real @ ( A @ B @ D ) @ ( A @ B @ C ) ) @ ( times_times_real @ ( minus_minus_real @ D @ C ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_rho__bound1__def) ).
thf(1373,plain,
( genClo2108747022bound1
= ( ^ [A: nat > real > real] :
! [B: nat,C: real,D: real] :
( ( ( genClo1015804716orrect @ B @ D )
& ( ord_less_eq_real @ C @ D ) )
=> ( ord_less_eq_real @ ( minus_minus_real @ ( A @ B @ D ) @ ( A @ B @ C ) ) @ ( times_times_real @ ( minus_minus_real @ D @ C ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(189,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_distrib__left) ).
thf(1040,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1863,plain,
! [A: num] :
( ( ord_less_eq_real @ one_one_real @ ( neg_numeral_dbl_real @ one_one_real ) )
| ( ( numeral_numeral_real @ ( bit0 @ one ) )
!= ( numeral_numeral_real @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1065,1050]) ).
thf(1864,plain,
ord_less_eq_real @ one_one_real @ ( neg_numeral_dbl_real @ one_one_real ),
inference(pattern_uni,[status(thm)],[1863:[bind(A,$thf( bit0 @ one ))]]) ).
thf(44,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_le__antisym) ).
thf(514,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(185,axiom,
! [A: real,B: num > real,C: num,D: num] :
( ( ord_less_eq_real @ A @ ( B @ C ) )
=> ( ( ord_less_eq_num @ C @ D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_order__subst1) ).
thf(1020,plain,
! [A: real,B: num > real,C: num,D: num] :
( ( ord_less_eq_real @ A @ ( B @ C ) )
=> ( ( ord_less_eq_num @ C @ D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ 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)],[185]) ).
thf(193,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/sandbox2/benchmark/theBenchmark.p',fact_184_add__le__add__imp__diff__le) ).
thf(1051,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)],[193]) ).
thf(352,axiom,
( ( abs_abs_real @ one_one_real )
= one_one_real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_abs__one) ).
thf(1581,plain,
( ( abs_abs_real @ one_one_real )
= one_one_real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(165,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/sandbox2/benchmark/theBenchmark.p',fact_230_abs__triangle__ineq2__sym) ).
thf(966,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)],[165]) ).
thf(264,axiom,
ord_less_eq_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__092_060open_062_It_A_N_As_J_A_K_A_I1_A_N_A_092_060rho_062_J_A_092_060le_062_AD_Aq_At_A_N_AD_Aq_As_092_060close_062) ).
thf(1283,plain,
ord_less_eq_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(172,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_diff__add__cancel) ).
thf(981,plain,
! [A: real,B: real] :
( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(227,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/sandbox2/benchmark/theBenchmark.p',fact_203_abs__diff__triangle__ineq) ).
thf(1169,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)],[227]) ).
thf(242,axiom,
( ( (=) @ real )
= ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_eq__iff) ).
thf(1214,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)],[242]) ).
thf(1215,plain,
( ( ^ [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
& ( ord_less_eq_real @ B @ A ) ) )
= ( (=) @ real ) ),
inference(lifteq,[status(thm)],[1214]) ).
thf(90,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_eq__imp__le) ).
thf(692,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(200,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/sandbox2/benchmark/theBenchmark.p',fact_23_okRead2__def) ).
thf(1071,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)],[200]) ).
thf(1072,plain,
( genClo293725282kRead2
= ( ^ [A: nat > real,B: nat > real,C: real,D: nat > $o] :
! [E: nat] :
( ( D @ E )
=> ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ E ) @ ( B @ E ) ) ) @ C ) ) ) ),
inference(lifteq,[status(thm)],[1071]) ).
thf(16,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_left__diff__distrib_H) ).
thf(396,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(234,axiom,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_mult_Oright__neutral) ).
thf(1184,plain,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(1185,plain,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
inference(cnf,[status(esa)],[1184]) ).
thf(1186,plain,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
inference(lifteq,[status(thm)],[1185]) ).
thf(1966,plain,
! [A: real] :
( ( A
!= ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) )
| ( ( times_times_real @ A @ one_one_real )
!= ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ) ),
inference(paramod_ordered,[status(thm)],[1186,1899]) ).
thf(2002,plain,
( ( ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
!= ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) )
| ( ( minus_minus_real @ t @ s )
!= one_one_real ) ),
inference(simp,[status(thm)],[1966]) ).
thf(175,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/sandbox2/benchmark/theBenchmark.p',fact_205_abs__diff__le__iff) ).
thf(988,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)],[175]) ).
thf(26,axiom,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( plus_plus_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_le__iff__add) ).
thf(428,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( plus_plus_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(210,axiom,
! [A: num] :
( ( ord_less_eq_nat @ ( numeral_numeral_nat @ A ) @ one_one_nat )
= ( ord_less_eq_num @ A @ one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_numeral__le__one__iff) ).
thf(1104,plain,
! [A: num] :
( ( ord_less_eq_nat @ ( numeral_numeral_nat @ A ) @ one_one_nat )
= ( ord_less_eq_num @ A @ one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(11,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_diff__right__commute) ).
thf(380,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(158,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_add__right__cancel) ).
thf(942,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)],[158]) ).
thf(86,axiom,
! [A: num,B: num] :
( ( plus_plus_nat @ ( numeral_numeral_nat @ A ) @ ( numeral_numeral_nat @ B ) )
= ( numeral_numeral_nat @ ( plus_plus_num @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_numeral__plus__numeral) ).
thf(678,plain,
! [A: num,B: num] :
( ( plus_plus_nat @ ( numeral_numeral_nat @ A ) @ ( numeral_numeral_nat @ B ) )
= ( numeral_numeral_nat @ ( plus_plus_num @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(81,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_distrib__left) ).
thf(661,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(118,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
=> ( ord_less_eq_nat @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_add__le__imp__le__left) ).
thf(793,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
=> ( ord_less_eq_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1306,plain,
( ( plus_plus_num @ one @ one )
= ( bit0 @ one ) ),
inference(lifteq,[status(thm)],[1305]) ).
thf(120,axiom,
! [A: num,B: num] :
( ( ord_less_eq_num @ A @ B )
=> ( ( ord_less_eq_num @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_antisym__conv) ).
thf(798,plain,
! [A: num,B: num] :
( ( ord_less_eq_num @ A @ B )
=> ( ( ord_less_eq_num @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(282,axiom,
! [A: num] :
( one
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_verit__eq__simplify_I10_J) ).
thf(1343,plain,
! [A: num] :
( one
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(330,axiom,
ord_less_eq_real @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_PC__ie) ).
thf(1519,plain,
ord_less_eq_real @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(254,axiom,
! [A: nat,B: real,C: real] :
( ( ( genClo1015804716orrect @ A @ C )
& ( ord_less_eq_real @ B @ C ) )
=> ( ord_less_eq_real @ ( minus_minus_real @ ( genClo1161277105lle_PC @ A @ C ) @ ( genClo1161277105lle_PC @ A @ B ) ) @ ( times_times_real @ ( minus_minus_real @ C @ B ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_rate__1) ).
thf(1255,plain,
! [A: nat,B: real,C: real] :
( ( ( genClo1015804716orrect @ A @ C )
& ( ord_less_eq_real @ B @ C ) )
=> ( ord_less_eq_real @ ( minus_minus_real @ ( genClo1161277105lle_PC @ A @ C ) @ ( genClo1161277105lle_PC @ A @ B ) ) @ ( times_times_real @ ( minus_minus_real @ C @ B ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(429,plain,
( ord_less_eq_nat
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( plus_plus_nat @ A @ C ) ) ) ),
inference(lifteq,[status(thm)],[428]) ).
thf(125,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
= ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc) ).
thf(815,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
= ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(249,axiom,
! [A: real,B: real,C: real > nat,D: nat] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_order__subst2) ).
thf(1238,plain,
! [A: real,B: real,C: real > nat,D: nat] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(344,axiom,
! [A: num] :
( ( times_times_num @ one @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_semiring__norm_I12_J) ).
thf(1560,plain,
! [A: num] :
( ( times_times_num @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(205,axiom,
( ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) )
= ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_Eq4) ).
thf(1091,plain,
( ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) )
= ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(214,axiom,
! [A: real,B: real,C: real,D: real] :
( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( plus_plus_real @ ( times_times_real @ C @ B ) @ D ) )
= ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ C ) @ B ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_combine__common__factor) ).
thf(1123,plain,
! [A: real,B: real,C: real,D: real] :
( ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( plus_plus_real @ ( times_times_real @ C @ B ) @ D ) )
= ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ C ) @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(137,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/sandbox2/benchmark/theBenchmark.p',fact_89_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(862,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)],[137]) ).
thf(1570,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(lifteq,[status(thm)],[1569]) ).
thf(229,axiom,
! [A: real,B: real] :
( ~ ( ord_less_eq_real @ A @ B )
=> ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_le__cases) ).
thf(1174,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)],[229]) ).
thf(153,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_order__refl) ).
thf(916,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(57,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/sandbox2/benchmark/theBenchmark.p',fact_95_group__cancel_Oadd1) ).
thf(566,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)],[57]) ).
thf(312,axiom,
ord_less_eq_real @ s @ t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_ie) ).
thf(1457,plain,
ord_less_eq_real @ s @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(33,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_mult__le__mono1) ).
thf(461,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(263,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( numeral_numeral_nat @ ( bit0 @ one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_nat__1__add__1) ).
thf(1281,plain,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( numeral_numeral_nat @ ( bit0 @ one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(96,axiom,
! [A: real] :
( ( one_one_real = A )
= ( A = one_one_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_one__reorient) ).
thf(710,plain,
! [A: real] :
( ( one_one_real = A )
= ( A = one_one_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(169,axiom,
! [A: nat] :
( ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_mult__2__right) ).
thf(974,plain,
! [A: nat] :
( ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(4,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_diff__mult__distrib) ).
thf(359,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(360,plain,
! [C: nat,B: nat,A: nat] :
( ( times_times_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(cnf,[status(esa)],[359]) ).
thf(361,plain,
! [C: nat,B: nat,A: nat] :
( ( times_times_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(lifteq,[status(thm)],[360]) ).
thf(289,axiom,
! [A: num] :
~ ( ord_less_eq_num @ ( bit0 @ A ) @ one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_semiring__norm_I69_J) ).
thf(1365,plain,
! [A: num] :
~ ( ord_less_eq_num @ ( bit0 @ A ) @ one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(134,axiom,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_mult_Oright__neutral) ).
thf(852,plain,
! [A: nat] :
( ( times_times_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(29,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_add__left__imp__eq) ).
thf(435,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)],[29]) ).
thf(53,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_add__left__cancel) ).
thf(551,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)],[53]) ).
thf(216,axiom,
! [A: real,B: real,C: num] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ C ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_distrib__right__numeral) ).
thf(1128,plain,
! [A: real,B: real,C: num] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ C ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(284,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(1350,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(141,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/sandbox2/benchmark/theBenchmark.p',fact_91_add__mono__thms__linordered__semiring_I4_J) ).
thf(874,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)],[141]) ).
thf(259,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( times_times_real @ B @ C ) )
= ( times_times_real @ B @ ( times_times_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_mult_Oleft__commute) ).
thf(1270,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( times_times_real @ B @ C ) )
= ( times_times_real @ B @ ( times_times_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(292,axiom,
! [A: real,B: real,C: real] :
( ( A
= ( minus_minus_real @ B @ C ) )
= ( ( plus_plus_real @ A @ C )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_eq__diff__eq) ).
thf(1375,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)],[292]) ).
thf(246,axiom,
! [A: num,B: num,C: num > real,D: real] :
( ( ord_less_eq_num @ A @ B )
=> ( ( ord_less_eq_real @ ( C @ B ) @ D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_order__subst2) ).
thf(1227,plain,
! [A: num,B: num,C: num > real,D: real] :
( ( ord_less_eq_num @ A @ B )
=> ( ( ord_less_eq_real @ ( C @ B ) @ D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ 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)],[246]) ).
thf(324,axiom,
! [A: num,B: num,C: num > real,D: real] :
( ( ord_less_eq_num @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_ord__le__eq__subst) ).
thf(1498,plain,
! [A: num,B: num,C: num > real,D: real] :
( ( ord_less_eq_num @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ 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)],[324]) ).
thf(207,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_ring__class_Oring__distribs_I1_J) ).
thf(1096,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
= ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(337,axiom,
! [A: real,B: real,C: real] :
( ( ( minus_minus_real @ A @ B )
= C )
= ( A
= ( plus_plus_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_diff__eq__eq) ).
thf(1540,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)],[337]) ).
thf(41,axiom,
! [A: nat,B: num > nat,C: num,D: num] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_num @ C @ D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_ord__eq__le__subst) ).
thf(499,plain,
! [A: nat,B: num > nat,C: num,D: num] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_num @ C @ D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(78,axiom,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_mult_Oleft__neutral) ).
thf(648,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(649,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(cnf,[status(esa)],[648]) ).
thf(650,plain,
! [A: nat] :
( ( times_times_nat @ one_one_nat @ A )
= A ),
inference(lifteq,[status(thm)],[649]) ).
thf(160,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse) ).
thf(948,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(334,axiom,
genClo2108747023bound2 @ d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_rb2) ).
thf(1534,plain,
genClo2108747023bound2 @ d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(184,axiom,
! [A: real,B: real,C: real,D: real] :
( ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( plus_plus_real @ ( times_times_real @ A @ ( minus_minus_real @ B @ D ) ) @ ( times_times_real @ ( minus_minus_real @ A @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_mult__diff__mult) ).
thf(1017,plain,
! [A: real,B: real,C: real,D: real] :
( ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ C @ D ) )
= ( plus_plus_real @ ( times_times_real @ A @ ( minus_minus_real @ B @ D ) ) @ ( times_times_real @ ( minus_minus_real @ A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(219,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/sandbox2/benchmark/theBenchmark.p',fact_120_add__right__mono) ).
thf(1138,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)],[219]) ).
thf(3,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_diff__commute) ).
thf(356,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(144,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_antisym) ).
thf(884,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(287,axiom,
genClo1015804716orrect @ q @ t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_corr__q) ).
thf(1361,plain,
genClo1015804716orrect @ q @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(157,axiom,
! [A: num,B: num,C: num > num,D: num] :
( ( ord_less_eq_num @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ E @ F )
=> ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_ord__le__eq__subst) ).
thf(933,plain,
! [A: num,B: num,C: num > num,D: num] :
( ( ord_less_eq_num @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ E @ F )
=> ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(54,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_distrib__right) ).
thf(554,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(88,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_add__right__imp__eq) ).
thf(686,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)],[88]) ).
thf(303,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/sandbox2/benchmark/theBenchmark.p',fact_24_abs__triangle__ineq2) ).
thf(1424,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)],[303]) ).
thf(75,axiom,
! [A: num] : ( ord_less_eq_num @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_order__refl) ).
thf(641,plain,
! [A: num] : ( ord_less_eq_num @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(642,plain,
! [A: num] : ( ord_less_eq_num @ A @ A ),
inference(cnf,[status(esa)],[641]) ).
thf(299,axiom,
! [A: num,B: num] :
( ( times_times_num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( bit0 @ ( times_times_num @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_semiring__norm_I13_J) ).
thf(1414,plain,
! [A: num,B: num] :
( ( times_times_num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( bit0 @ ( times_times_num @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(167,axiom,
! [A: num] :
( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ A ) )
= ( plus_plus_real @ ( numeral_numeral_real @ A ) @ one_one_real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_one__plus__numeral__commute) ).
thf(970,plain,
! [A: num] :
( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ A ) )
= ( plus_plus_real @ ( numeral_numeral_real @ A ) @ one_one_real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(94,axiom,
( neg_numeral_dbl_real
= ( ^ [A: real] : ( plus_plus_real @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_dbl__def) ).
thf(705,plain,
( neg_numeral_dbl_real
= ( ^ [A: real] : ( plus_plus_real @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(706,plain,
( ( ^ [A: real] : ( plus_plus_real @ A @ A ) )
= neg_numeral_dbl_real ),
inference(lifteq,[status(thm)],[705]) ).
thf(301,axiom,
( ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
= ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_Eq1) ).
thf(1419,plain,
( ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
= ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(187,axiom,
! [A: real] :
( ( minus_minus_real @ ( times_times_real @ A @ A ) @ one_one_real )
= ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( minus_minus_real @ A @ one_one_real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_square__diff__one__factored) ).
thf(1028,plain,
! [A: real] :
( ( minus_minus_real @ ( times_times_real @ A @ A ) @ one_one_real )
= ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( minus_minus_real @ A @ one_one_real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(1965,plain,
! [A: real] :
( ( ( times_times_real @ A @ ( minus_minus_real @ t @ s ) )
!= ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) )
| ( ( times_times_real @ A @ one_one_real )
!= ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) ) ),
inference(paramod_ordered,[status(thm)],[1186,1899]) ).
thf(1996,plain,
! [A: real] :
( ( ( times_times_real @ A @ ( minus_minus_real @ t @ s ) )
!= ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) )
| ( A
!= ( neg_numeral_dbl_real @ one_one_real ) )
| ( one_one_real != genClo1144207539le_rho ) ),
inference(simp,[status(thm)],[1965]) ).
thf(2023,plain,
( ( ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ ( minus_minus_real @ t @ s ) )
!= ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) )
| ( one_one_real != genClo1144207539le_rho ) ),
inference(simp,[status(thm)],[1996]) ).
thf(69,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ D ) @ ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ E ) )
= ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_nat__diff__add__eq1) ).
thf(622,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ D ) @ ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ E ) )
= ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(310,axiom,
! [A: real,B: real] :
( ( A = B )
| ~ ( ord_less_eq_real @ A @ B )
| ~ ( ord_less_eq_real @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_verit__la__disequality) ).
thf(1451,plain,
! [A: real,B: real] :
( ( A = B )
| ~ ( ord_less_eq_real @ A @ B )
| ~ ( ord_less_eq_real @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(217,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
= ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ D @ A ) @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_ordered__ring__class_Ole__add__iff2) ).
thf(1131,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ B ) @ C ) @ ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
= ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ D @ A ) @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(99,axiom,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_eq__iff) ).
thf(720,plain,
( ( (=) @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(721,plain,
( ( ^ [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) )
= ( (=) @ nat ) ),
inference(lifteq,[status(thm)],[720]) ).
thf(179,axiom,
! [A: num] :
( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ A ) )
= ( numeral_numeral_real @ ( plus_plus_num @ one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_one__plus__numeral) ).
thf(1002,plain,
! [A: num] :
( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ A ) )
= ( numeral_numeral_real @ ( plus_plus_num @ one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(1868,plain,
( ~ $true
| ( ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) )
!= one_one_real )
| ( ( ord_less_eq_real @ one_one_real @ ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) )
!= ( ord_less_eq_real @ one_one_real @ ( neg_numeral_dbl_real @ one_one_real ) ) ) ),
inference(paramod_ordered,[status(thm)],[1864,1709]) ).
thf(1869,plain,
( ( ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) )
!= one_one_real )
| ( ( ord_less_eq_real @ one_one_real @ ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) )
!= ( ord_less_eq_real @ one_one_real @ ( neg_numeral_dbl_real @ one_one_real ) ) ) ),
inference(simp,[status(thm)],[1868]) ).
thf(1872,plain,
( ( ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) )
!= one_one_real )
| ( one_one_real != one_one_real )
| ( ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) )
!= ( neg_numeral_dbl_real @ one_one_real ) ) ),
inference(simp,[status(thm)],[1869]) ).
thf(1874,plain,
( ( ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) )
!= one_one_real )
| ( ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) )
!= ( neg_numeral_dbl_real @ one_one_real ) ) ),
inference(simp,[status(thm)],[1872]) ).
thf(65,axiom,
! [A: nat,B: nat] :
( ( one_one_nat
= ( times_times_nat @ A @ B ) )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_nat__1__eq__mult__iff) ).
thf(605,plain,
! [A: nat,B: nat] :
( ( one_one_nat
= ( times_times_nat @ A @ B ) )
= ( ( A = one_one_nat )
& ( B = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(276,axiom,
! [A: real] :
( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
= ( times_times_real @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_abs__mult__self__eq) ).
thf(1324,plain,
! [A: real] :
( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
= ( times_times_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(15,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_add__diff__cancel__left_H) ).
thf(393,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(208,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/sandbox2/benchmark/theBenchmark.p',fact_190_diff__le__eq) ).
thf(1099,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)],[208]) ).
thf(174,axiom,
! [A: num,B: num,C: real] :
( ( plus_plus_real @ ( numeral_numeral_real @ A ) @ ( plus_plus_real @ ( numeral_numeral_real @ B ) @ C ) )
= ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_add__numeral__left) ).
thf(985,plain,
! [A: num,B: num,C: real] :
( ( plus_plus_real @ ( numeral_numeral_real @ A ) @ ( plus_plus_real @ ( numeral_numeral_real @ B ) @ C ) )
= ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(221,axiom,
! [A: num] :
( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ A ) )
= ( numeral_numeral_nat @ ( plus_plus_num @ one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_one__plus__numeral) ).
thf(1150,plain,
! [A: num] :
( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ A ) )
= ( numeral_numeral_nat @ ( plus_plus_num @ one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(319,axiom,
! [A: num] :
( ( numeral_numeral_real @ ( bit0 @ A ) )
= ( plus_plus_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_numeral__Bit0) ).
thf(1478,plain,
! [A: num] :
( ( numeral_numeral_real @ ( bit0 @ A ) )
= ( plus_plus_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(32,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
= ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2) ).
thf(457,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
= ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(173,axiom,
ord_less_eq_real @ one_one_real @ one_one_real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_le__numeral__extra_I4_J) ).
thf(984,plain,
ord_less_eq_real @ one_one_real @ one_one_real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(152,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/sandbox2/benchmark/theBenchmark.p',fact_96_group__cancel_Oadd1) ).
thf(911,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)],[152]) ).
thf(240,axiom,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_semiring__norm_I87_J) ).
thf(1202,plain,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(122,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_diff__add) ).
thf(805,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(42,axiom,
! [A: num,B: num] :
( ( ord_less_eq_nat @ ( numeral_numeral_nat @ A ) @ ( numeral_numeral_nat @ B ) )
= ( ord_less_eq_num @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_numeral__le__iff) ).
thf(508,plain,
! [A: num,B: num] :
( ( ord_less_eq_nat @ ( numeral_numeral_nat @ A ) @ ( numeral_numeral_nat @ B ) )
= ( ord_less_eq_num @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(345,axiom,
! [A: real] :
( ( abs_abs_real @ ( abs_abs_real @ A ) )
= ( abs_abs_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_abs__idempotent) ).
thf(1563,plain,
! [A: real] :
( ( abs_abs_real @ ( abs_abs_real @ A ) )
= ( abs_abs_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(1610,plain,
( ~ $true
| ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) )
!= ( ord_less_eq_real @ one_one_real @ one_one_real ) ) ),
inference(paramod_ordered,[status(thm)],[984,355]) ).
thf(1611,plain,
( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) )
!= ( ord_less_eq_real @ one_one_real @ one_one_real ) ),
inference(simp,[status(thm)],[1610]) ).
thf(1612,plain,
( ( ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
!= one_one_real )
| ( ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) )
!= one_one_real ) ),
inference(simp,[status(thm)],[1611]) ).
thf(1712,plain,
( ( ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
!= one_one_real )
| ( ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) )
!= one_one_real ) ),
inference(rewrite,[status(thm)],[1612,1065]) ).
thf(235,axiom,
! [A: num] :
( ( one_one_real
= ( numeral_numeral_real @ A ) )
= ( one = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_one__eq__numeral__iff) ).
thf(1187,plain,
! [A: num] :
( ( one_one_real
= ( numeral_numeral_real @ A ) )
= ( one = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(115,axiom,
! [A: num,B: nat > num,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_num @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_ord__eq__le__subst) ).
thf(773,plain,
! [A: num,B: nat > num,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_num @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(315,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
= ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_left__add__twice) ).
thf(1466,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
= ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(151,axiom,
! [A: num,B: nat > num,C: nat,D: nat] :
( ( ord_less_eq_num @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_num @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_order__subst1) ).
thf(906,plain,
! [A: num,B: nat > num,C: nat,D: nat] :
( ( ord_less_eq_num @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_num @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(262,axiom,
! [A: num] :
( ( ord_less_eq_num @ A @ one )
= ( A = one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_le__num__One__iff) ).
thf(1278,plain,
! [A: num] :
( ( ord_less_eq_num @ A @ one )
= ( A = one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(326,axiom,
! [A: num,B: num] :
( ( ord_less_eq_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) )
= ( ord_less_eq_num @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_numeral__le__iff) ).
thf(1510,plain,
! [A: num,B: num] :
( ( ord_less_eq_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) )
= ( ord_less_eq_num @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(27,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_le__refl) ).
thf(430,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(321,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/sandbox2/benchmark/theBenchmark.p',fact_209_diff__mono) ).
thf(1483,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)],[321]) ).
thf(260,axiom,
! [A: real] :
( ( abs_abs_real @ ( abs_abs_real @ A ) )
= ( abs_abs_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_abs__abs) ).
thf(1273,plain,
! [A: real] :
( ( abs_abs_real @ ( abs_abs_real @ A ) )
= ( abs_abs_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(340,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_le__add__diff__inverse) ).
thf(1548,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)],[340]) ).
thf(63,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_le__cases) ).
thf(601,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(244,axiom,
! [A: real,B: real] :
( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
= ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_abs__minus__commute) ).
thf(1219,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)],[244]) ).
thf(128,axiom,
! [A: num,B: num] :
( ( ord_less_eq_num @ A @ B )
=> ( ( ord_less_eq_num @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_antisym) ).
thf(824,plain,
! [A: num,B: num] :
( ( ord_less_eq_num @ A @ B )
=> ( ( ord_less_eq_num @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(126,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/sandbox2/benchmark/theBenchmark.p',fact_100_add_Oassoc) ).
thf(819,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)],[126]) ).
thf(56,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_Nat_Odiff__diff__right) ).
thf(562,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(24,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_diff__diff__left) ).
thf(423,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(18,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_diff__diff__add) ).
thf(402,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(132,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ( ( minus_minus_nat @ B @ A )
= C )
= ( B
= ( plus_plus_nat @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add) ).
thf(843,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ( ( minus_minus_nat @ B @ A )
= C )
= ( B
= ( plus_plus_nat @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(106,axiom,
! [A: real,B: real > $o] :
( ( member_real @ A @ ( collect_real @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_mem__Collect__eq) ).
thf(743,plain,
! [A: real,B: real > $o] :
( ( member_real @ A @ ( collect_real @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(60,axiom,
! [A: num,B: num,C: num > nat,D: nat] :
( ( ord_less_eq_num @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_order__subst2) ).
thf(577,plain,
! [A: num,B: num,C: num > nat,D: nat] :
( ( ord_less_eq_num @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(335,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_real @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_antisym) ).
thf(1535,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)],[335]) ).
thf(163,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2) ).
thf(958,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(331,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/sandbox2/benchmark/theBenchmark.p',fact_279_ord__le__eq__subst) ).
thf(1520,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)],[331]) ).
thf(51,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/sandbox2/benchmark/theBenchmark.p',fact_106_add_Oleft__commute) ).
thf(545,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)],[51]) ).
thf(21,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_diff__add__inverse2) ).
thf(413,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1617,plain,
( ( one_one_real != one_one_real )
| ( ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) )
!= one_one_real )
| ( ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
!= ( abs_abs_real @ one_one_real ) ) ),
inference(paramod_ordered,[status(thm)],[1183,1612]) ).
thf(1618,plain,
( ( ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) )
!= one_one_real )
| ( ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
!= ( abs_abs_real @ one_one_real ) ) ),
inference(simp,[status(thm)],[1617]) ).
thf(1620,plain,
( ( ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) )
!= one_one_real )
| ( ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) )
!= one_one_real ) ),
inference(simp,[status(thm)],[1618]) ).
thf(1707,plain,
( ( ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) )
!= one_one_real )
| ( ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) )
!= one_one_real ) ),
inference(rewrite,[status(thm)],[1620,1065]) ).
thf(97,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc) ).
thf(713,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(279,axiom,
! [A: nat,B: real > nat,C: real,D: real] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_order__subst1) ).
thf(1332,plain,
! [A: nat,B: real > nat,C: real,D: real] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_real @ C @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(35,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ord_less_eq_nat @ A @ B )
& ( C = D ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_add__mono__thms__linordered__semiring_I3_J) ).
thf(466,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ord_less_eq_nat @ A @ B )
& ( C = D ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(305,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/sandbox2/benchmark/theBenchmark.p',fact_151_diff__diff__eq2) ).
thf(1428,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)],[305]) ).
thf(195,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/sandbox2/benchmark/theBenchmark.p',fact_208_diff__left__mono) ).
thf(1058,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)],[195]) ).
thf(211,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/sandbox2/benchmark/theBenchmark.p',fact_270_ord__eq__le__subst) ).
thf(1107,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)],[211]) ).
thf(112,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_order_Otrans) ).
thf(764,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(117,axiom,
! [A: num,B: num > num,C: num,D: num] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_num @ C @ D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ E @ F )
=> ( ord_less_eq_num @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_ord__eq__le__subst) ).
thf(784,plain,
! [A: num,B: num > num,C: num,D: num] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_num @ C @ D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ E @ F )
=> ( ord_less_eq_num @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(103,axiom,
( plus_plus_real
= ( ^ [A: real,B: real] : ( plus_plus_real @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_add_Ocommute) ).
thf(735,plain,
( plus_plus_real
= ( ^ [A: real,B: real] : ( plus_plus_real @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(736,plain,
( plus_plus_real
= ( ^ [A: real,B: real] : ( plus_plus_real @ B @ A ) ) ),
inference(lifteq,[status(thm)],[735]) ).
thf(5,axiom,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_add__diff__cancel__right_H) ).
thf(362,plain,
! [A: nat,B: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(104,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/sandbox2/benchmark/theBenchmark.p',fact_99_add_Oassoc) ).
thf(737,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)],[104]) ).
thf(190,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_ring__class_Oring__distribs_I2_J) ).
thf(1043,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(271,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/sandbox2/benchmark/theBenchmark.p',fact_152_add__diff__eq) ).
thf(1307,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)],[271]) ).
thf(87,axiom,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_order__subst2) ).
thf(681,plain,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(297,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/sandbox2/benchmark/theBenchmark.p',fact_171_diff__right__commute) ).
thf(1408,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)],[297]) ).
thf(349,axiom,
( ( numeral_numeral_nat @ one )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_numeral__One) ).
thf(1574,plain,
( ( numeral_numeral_nat @ one )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(182,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/sandbox2/benchmark/theBenchmark.p',fact_189_le__diff__eq) ).
thf(1011,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)],[182]) ).
thf(23,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= ( ord_less_eq_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_le__diff__iff) ).
thf(419,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= ( ord_less_eq_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(177,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/sandbox2/benchmark/theBenchmark.p',fact_147_diff__diff__add) ).
thf(996,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)],[177]) ).
thf(348,axiom,
! [A: num] :
( ( abs_abs_real @ ( numeral_numeral_real @ A ) )
= ( numeral_numeral_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_abs__numeral) ).
thf(1571,plain,
! [A: num] :
( ( abs_abs_real @ ( numeral_numeral_real @ A ) )
= ( numeral_numeral_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(308,axiom,
! [A: real,B: real,C: real > nat,D: nat] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_ord__le__eq__subst) ).
thf(1439,plain,
! [A: real,B: real,C: real > nat,D: nat] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(146,axiom,
! [A: num,B: num,C: nat] :
( ( plus_plus_nat @ ( numeral_numeral_nat @ A ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ B ) @ C ) )
= ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_add__numeral__left) ).
thf(890,plain,
! [A: num,B: num,C: nat] :
( ( plus_plus_nat @ ( numeral_numeral_nat @ A ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ B ) @ C ) )
= ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(124,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
= ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_Nat_Oadd__diff__assoc2) ).
thf(811,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
= ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(72,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_order__subst1) ).
thf(631,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(101,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ D )
= ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ E ) )
= ( D
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_nat__eq__add__iff2) ).
thf(726,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ D )
= ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ E ) )
= ( D
= ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(133,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ D ) @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ E ) )
= ( minus_minus_nat @ D @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_nat__diff__add__eq2) ).
thf(848,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ D ) @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ E ) )
= ( minus_minus_nat @ D @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(70,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_comm__semiring__class_Odistrib) ).
thf(626,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(294,axiom,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_mult_Ocomm__neutral) ).
thf(1381,plain,
! [A: real] :
( ( times_times_real @ A @ one_one_real )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(196,axiom,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_add__diff__cancel__left_H) ).
thf(1061,plain,
! [A: real,B: real] :
( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(366,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ! [C: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ C @ A ) ) ),
inference(miniscope,[status(thm)],[365]) ).
thf(367,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ ( minus_minus_nat @ C @ A ) ) ),
inference(cnf,[status(esa)],[366]) ).
thf(343,axiom,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
= ( C
= ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ D @ A ) @ B ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_eq__add__iff2) ).
thf(1557,plain,
! [A: real,B: real,C: real,D: real,E: real] :
( ( ( plus_plus_real @ ( times_times_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ D @ B ) @ E ) )
= ( C
= ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ D @ A ) @ B ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(17,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_diff__diff__cancel) ).
thf(399,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ B @ ( minus_minus_nat @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(129,axiom,
! [A: nat,B: nat,C: nat > num,D: num] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_ord__le__eq__subst) ).
thf(827,plain,
! [A: nat,B: nat,C: nat > num,D: num] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(253,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/sandbox2/benchmark/theBenchmark.p',fact_249_order__subst1) ).
thf(1250,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)],[253]) ).
thf(209,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/sandbox2/benchmark/theBenchmark.p',fact_127_add__mono__thms__linordered__semiring_I1_J) ).
thf(1102,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)],[209]) ).
thf(431,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(cnf,[status(esa)],[430]) ).
thf(228,axiom,
! [A: num,B: num] :
( ( plus_plus_num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus_num @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_semiring__norm_I6_J) ).
thf(1171,plain,
! [A: num,B: num] :
( ( plus_plus_num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus_num @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(73,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_eq_nat @ A @ ( minus_minus_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_add__le__imp__le__diff) ).
thf(636,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_eq_nat @ A @ ( minus_minus_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(251,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/sandbox2/benchmark/theBenchmark.p',fact_187_add__le__imp__le__diff) ).
thf(1245,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)],[251]) ).
thf(198,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/sandbox2/benchmark/theBenchmark.p',fact_204_abs__triangle__ineq4) ).
thf(1066,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)],[198]) ).
thf(139,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/sandbox2/benchmark/theBenchmark.p',fact_105_add_Oleft__commute) ).
thf(868,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)],[139]) ).
thf(230,axiom,
! [A: real] :
( ( times_times_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
= ( plus_plus_real @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_mult__2__right) ).
thf(1176,plain,
! [A: real] :
( ( times_times_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
= ( plus_plus_real @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(66,axiom,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_ord__le__eq__subst) ).
thf(608,plain,
! [A: nat,B: nat,C: nat > nat,D: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_nat @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(100,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( minus_minus_nat @ B @ A )
= C )
= ( B
= ( plus_plus_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_Nat_Ole__imp__diff__is__add) ).
thf(722,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( minus_minus_nat @ B @ A )
= C )
= ( B
= ( plus_plus_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(1870,plain,
( ~ $true
| ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) )
!= ( ord_less_eq_real @ one_one_real @ ( neg_numeral_dbl_real @ one_one_real ) ) ) ),
inference(paramod_ordered,[status(thm)],[1864,1708]) ).
thf(1871,plain,
( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) )
!= ( ord_less_eq_real @ one_one_real @ ( neg_numeral_dbl_real @ one_one_real ) ) ),
inference(simp,[status(thm)],[1870]) ).
thf(1873,plain,
( ( ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
!= one_one_real )
| ( ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) )
!= ( neg_numeral_dbl_real @ one_one_real ) ) ),
inference(simp,[status(thm)],[1871]) ).
thf(119,axiom,
! [A: nat,B: nat] :
( ( A = B )
| ~ ( ord_less_eq_nat @ A @ B )
| ~ ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_verit__la__disequality) ).
thf(795,plain,
! [A: nat,B: nat] :
( ( A = B )
| ~ ( ord_less_eq_nat @ A @ B )
| ~ ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(52,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_le__add__diff__inverse) ).
thf(548,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(155,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_add__left__cancel) ).
thf(927,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)],[155]) ).
thf(67,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_nat__le__linear) ).
thf(617,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(281,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/sandbox2/benchmark/theBenchmark.p',fact_173_diff__eq__diff__eq) ).
thf(1340,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)],[281]) ).
thf(317,axiom,
! [A: num] :
( ( ( numeral_numeral_nat @ A )
= one_one_nat )
= ( A = one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_numeral__eq__one__iff) ).
thf(1472,plain,
! [A: num] :
( ( ( numeral_numeral_nat @ A )
= one_one_nat )
= ( A = one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(37,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_add__right__imp__eq) ).
thf(473,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)],[37]) ).
thf(202,axiom,
! [A: real,B: real] :
( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
=> ( ord_less_eq_real @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_abs__le__D1) ).
thf(1076,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)],[202]) ).
thf(85,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_combine__common__factor) ).
thf(675,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(353,axiom,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_mult_Oleft__neutral) ).
thf(1583,plain,
! [A: real] :
( ( times_times_real @ one_one_real @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(25,axiom,
( ( (=) @ num )
= ( ^ [A: num,B: num] :
( ( ord_less_eq_num @ A @ B )
& ( ord_less_eq_num @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_eq__iff) ).
thf(426,plain,
( ( (=) @ num )
= ( ^ [A: num,B: num] :
( ( ord_less_eq_num @ A @ B )
& ( ord_less_eq_num @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(226,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/sandbox2/benchmark/theBenchmark.p',fact_303_order_Otrans) ).
thf(1166,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)],[226]) ).
thf(166,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/sandbox2/benchmark/theBenchmark.p',fact_198_abs__triangle__ineq) ).
thf(968,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)],[166]) ).
thf(232,axiom,
ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_Eq3) ).
thf(1181,plain,
ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(130,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_linear) ).
thf(836,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(341,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_left__diff__distrib) ).
thf(1551,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(55,axiom,
! [A: nat,B: num > nat,C: num,D: num] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_num @ C @ D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_order__subst1) ).
thf(557,plain,
! [A: nat,B: num > nat,C: num,D: num] :
( ( ord_less_eq_nat @ A @ ( B @ C ) )
=> ( ( ord_less_eq_num @ C @ D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(135,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_eq__refl) ).
thf(855,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(328,axiom,
! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_abs__ge__self) ).
thf(1516,plain,
! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(186,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_distrib__right) ).
thf(1025,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(95,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_le__trans) ).
thf(707,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(145,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_add__le__cancel__left) ).
thf(887,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(346,axiom,
! [A: num] :
( ( ( numeral_numeral_real @ A )
= one_one_real )
= ( A = one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_numeral__eq__one__iff) ).
thf(1566,plain,
! [A: num] :
( ( ( numeral_numeral_real @ A )
= one_one_real )
= ( A = one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(290,axiom,
! [A: real,B: nat > real,C: nat,D: nat] :
( ( ord_less_eq_real @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_order__subst1) ).
thf(1368,plain,
! [A: real,B: nat > real,C: nat,D: nat] :
( ( ord_less_eq_real @ A @ ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ 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)],[290]) ).
thf(258,axiom,
! [A: real] :
( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_mult__numeral__1) ).
thf(1267,plain,
! [A: real] :
( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(333,axiom,
! [A: nat] :
( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_mult__numeral__1__right) ).
thf(1531,plain,
! [A: nat] :
( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(20,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ B )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ B @ C ) )
= ( ord_less_eq_nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_le__diff__iff_H) ).
thf(409,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ C @ B )
=> ( ( ord_less_eq_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ B @ C ) )
= ( ord_less_eq_nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1630,plain,
( ~ $true
| ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) )
!= ( ord_less_eq_real @ s @ t ) ) ),
inference(paramod_ordered,[status(thm)],[1457,355]) ).
thf(1631,plain,
( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) )
!= ( ord_less_eq_real @ s @ t ) ),
inference(simp,[status(thm)],[1630]) ).
thf(1632,plain,
( ( ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
!= s )
| ( ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) )
!= t ) ),
inference(simp,[status(thm)],[1631]) ).
thf(1711,plain,
( ( ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
!= s )
| ( ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) )
!= t ) ),
inference(rewrite,[status(thm)],[1632,1065]) ).
thf(98,axiom,
! [A: num,B: num] :
( ( times_times_nat @ ( numeral_numeral_nat @ A ) @ ( numeral_numeral_nat @ B ) )
= ( numeral_numeral_nat @ ( times_times_num @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_numeral__times__numeral) ).
thf(717,plain,
! [A: num,B: num] :
( ( times_times_nat @ ( numeral_numeral_nat @ A ) @ ( numeral_numeral_nat @ B ) )
= ( numeral_numeral_nat @ ( times_times_num @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(248,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_right__diff__distrib_H) ).
thf(1235,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(351,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/sandbox2/benchmark/theBenchmark.p',fact_117_add__le__imp__le__left) ).
thf(1579,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)],[351]) ).
thf(76,axiom,
! [A: num,B: num] :
( ~ ( ord_less_eq_num @ A @ B )
=> ( ord_less_eq_num @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_le__cases) ).
thf(643,plain,
! [A: num,B: num] :
( ~ ( ord_less_eq_num @ A @ B )
=> ( ord_less_eq_num @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(62,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_Nat_Oex__has__greatest__nat) ).
thf(585,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq_nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq_nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(36,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_left__add__mult__distrib) ).
thf(470,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ D ) )
= ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ C ) @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(59,axiom,
( plus_plus_nat
= ( ^ [A: nat,B: nat] : ( plus_plus_nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_add_Ocommute) ).
thf(575,plain,
( plus_plus_nat
= ( ^ [A: nat,B: nat] : ( plus_plus_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(576,plain,
( plus_plus_nat
= ( ^ [A: nat,B: nat] : ( plus_plus_nat @ B @ A ) ) ),
inference(lifteq,[status(thm)],[575]) ).
thf(336,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/sandbox2/benchmark/theBenchmark.p',fact_115_add__le__imp__le__right) ).
thf(1538,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)],[336]) ).
thf(161,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ D ) @ ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ E ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_nat__le__add__iff1) ).
thf(951,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ D ) @ ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ E ) )
= ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(123,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_mult_Oassoc) ).
thf(808,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(286,axiom,
! [A: num,B: num] :
( ( ( numeral_numeral_real @ A )
= ( numeral_numeral_real @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_numeral__eq__iff) ).
thf(1358,plain,
! [A: num,B: num] :
( ( ( numeral_numeral_real @ A )
= ( numeral_numeral_real @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(255,axiom,
! [A: num] :
( ( numeral_numeral_nat @ ( bit0 @ A ) )
= ( plus_plus_nat @ ( numeral_numeral_nat @ A ) @ ( numeral_numeral_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_numeral__Bit0) ).
thf(1257,plain,
! [A: num] :
( ( numeral_numeral_nat @ ( bit0 @ A ) )
= ( plus_plus_nat @ ( numeral_numeral_nat @ A ) @ ( numeral_numeral_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(220,axiom,
! [A: real,B: nat > real,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_real @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_real @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_ord__eq__le__subst) ).
thf(1141,plain,
! [A: real,B: nat > real,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ 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)],[220]) ).
thf(80,axiom,
! [A: nat,B: nat,C: nat > num,D: num] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_num @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_order__subst2) ).
thf(656,plain,
! [A: nat,B: nat,C: nat > num,D: num] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_num @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(265,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/sandbox2/benchmark/theBenchmark.p',fact_149_diff__add__eq__diff__diff__swap) ).
thf(1284,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)],[265]) ).
thf(285,axiom,
! [A: real,B: real,C: real > num,D: num] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_num @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_order__subst2) ).
thf(1353,plain,
! [A: real,B: real,C: real > num,D: num] :
( ( ord_less_eq_real @ A @ B )
=> ( ( ord_less_eq_num @ ( C @ B ) @ D )
=> ( ! [E: real,F: real] :
( ( ord_less_eq_real @ E @ F )
=> ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(1427,plain,
( times_times_real
= ( ^ [A: real,B: real] : ( times_times_real @ B @ A ) ) ),
inference(lifteq,[status(thm)],[1426]) ).
thf(181,axiom,
! [A: num,B: num,C: real] :
( ( times_times_real @ ( numeral_numeral_real @ A ) @ ( times_times_real @ ( numeral_numeral_real @ B ) @ C ) )
= ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_mult__numeral__left__semiring__numeral) ).
thf(1008,plain,
! [A: num,B: num,C: real] :
( ( times_times_real @ ( numeral_numeral_real @ A ) @ ( times_times_real @ ( numeral_numeral_real @ B ) @ C ) )
= ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(58,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ( ord_less_eq_nat @ C @ ( plus_plus_nat @ D @ B ) )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ( ord_less_eq_nat @ C @ ( plus_plus_nat @ D @ B ) )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_add__le__add__imp__diff__le) ).
thf(571,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ( ord_less_eq_nat @ C @ ( plus_plus_nat @ D @ B ) )
=> ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ( ord_less_eq_nat @ C @ ( plus_plus_nat @ D @ B ) )
=> ( ord_less_eq_nat @ ( minus_minus_nat @ C @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(136,axiom,
! [A: num,B: num,C: num] :
( ( ord_less_eq_num @ A @ B )
=> ( ( ord_less_eq_num @ B @ C )
=> ( ord_less_eq_num @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_order_Otrans) ).
thf(859,plain,
! [A: num,B: num,C: num] :
( ( ord_less_eq_num @ A @ B )
=> ( ( ord_less_eq_num @ B @ C )
=> ( ord_less_eq_num @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(176,axiom,
! [A: nat,B: nat,C: nat > real,D: real] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_real @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_real @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_real @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_order__subst2) ).
thf(991,plain,
! [A: nat,B: nat,C: nat > real,D: real] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_real @ ( C @ B ) @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ 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)],[176]) ).
thf(171,axiom,
! [A: num] :
( ( times_times_num @ ( bit0 @ one ) @ A )
= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_num__double) ).
thf(978,plain,
! [A: num] :
( ( times_times_num @ ( bit0 @ one ) @ A )
= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(13,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= ( minus_minus_nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_Nat_Odiff__diff__eq) ).
thf(386,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( minus_minus_nat @ ( minus_minus_nat @ B @ A ) @ ( minus_minus_nat @ C @ A ) )
= ( minus_minus_nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(274,axiom,
! [A: num] :
( ( plus_plus_num @ one @ A )
= ( plus_plus_num @ A @ one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_add__One__commute) ).
thf(1316,plain,
! [A: num] :
( ( plus_plus_num @ one @ A )
= ( plus_plus_num @ A @ one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(84,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ D )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ E ) )
= ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ D )
= E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_nat__eq__add__iff1) ).
thf(671,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ D )
= ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ E ) )
= ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ B @ A ) @ C ) @ D )
= E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(223,axiom,
! [A: num] :
( one
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_semiring__norm_I83_J) ).
thf(1157,plain,
! [A: num] :
( one
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(150,axiom,
! [A: num,B: nat,C: nat] :
( ( times_times_nat @ ( numeral_numeral_nat @ A ) @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ A ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_distrib__left__numeral) ).
thf(903,plain,
! [A: num,B: nat,C: nat] :
( ( times_times_nat @ ( numeral_numeral_nat @ A ) @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ A ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(47,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right) ).
thf(524,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1517,plain,
! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ),
inference(cnf,[status(esa)],[1516]) ).
thf(243,axiom,
! [A: real] :
( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_mult__numeral__1__right) ).
thf(1216,plain,
! [A: real] :
( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(309,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_mult_Oassoc) ).
thf(1448,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
= ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(1861,plain,
! [A: num] :
( ~ $true
| ( ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ A ) )
!= ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1050,1708]) ).
thf(1862,plain,
! [A: num] :
( ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ A ) )
!= ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ) ),
inference(simp,[status(thm)],[1861]) ).
thf(1866,plain,
! [A: num] :
( ( ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
!= one_one_real )
| ( ( numeral_numeral_real @ A )
!= ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ) ),
inference(simp,[status(thm)],[1862]) ).
thf(363,plain,
! [B: nat,A: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
inference(cnf,[status(esa)],[362]) ).
thf(364,plain,
! [B: nat,A: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
= A ),
inference(lifteq,[status(thm)],[363]) ).
thf(1733,plain,
! [B: nat,A: nat] :
( ( ( minus_minus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
= A )
| ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
!= ( plus_plus_nat @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1127,364]) ).
thf(1734,plain,
( ( minus_minus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat )
= one_one_nat ),
inference(pattern_uni,[status(thm)],[1733:[bind(A,$thf( one_one_nat )),bind(B,$thf( one_one_nat ))]]) ).
thf(302,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/sandbox2/benchmark/theBenchmark.p',fact_150_diff__add__eq) ).
thf(1421,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)],[302]) ).
thf(34,axiom,
! [A: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_one__le__numeral) ).
thf(464,plain,
! [A: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(465,plain,
! [A: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ A ) ),
inference(cnf,[status(esa)],[464]) ).
thf(1288,plain,
! [A: num] :
( ( times_times_num @ A @ one )
= A ),
inference(cnf,[status(esa)],[1287]) ).
thf(1289,plain,
! [A: num] :
( ( times_times_num @ A @ one )
= A ),
inference(lifteq,[status(thm)],[1288]) ).
thf(7,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_diff__le__self) ).
thf(368,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(261,axiom,
! [A: nat,B: real,C: real] :
( ( ( genClo1015804716orrect @ A @ C )
& ( ord_less_eq_real @ B @ C ) )
=> ( ord_less_eq_real @ ( genClo1161277105lle_PC @ A @ B ) @ ( genClo1161277105lle_PC @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_PC__monotone) ).
thf(1276,plain,
! [A: nat,B: real,C: real] :
( ( ( genClo1015804716orrect @ A @ C )
& ( ord_less_eq_real @ B @ C ) )
=> ( ord_less_eq_real @ ( genClo1161277105lle_PC @ A @ B ) @ ( genClo1161277105lle_PC @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(92,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_mult__le__mono2) ).
thf(699,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(45,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_Nat_Oadd__diff__assoc) ).
thf(517,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
= ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(108,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/sandbox2/benchmark/theBenchmark.p',fact_92_add__mono__thms__linordered__semiring_I4_J) ).
thf(748,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)],[108]) ).
thf(320,axiom,
! [A: nat,B: real,C: real] :
( ( ( genClo1015804716orrect @ A @ C )
& ( ord_less_eq_real @ B @ C ) )
=> ( ord_less_eq_real @ ( times_times_real @ ( minus_minus_real @ C @ B ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( genClo1161277105lle_PC @ A @ C ) @ ( genClo1161277105lle_PC @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_rate__2) ).
thf(1481,plain,
! [A: nat,B: real,C: real] :
( ( ( genClo1015804716orrect @ A @ C )
& ( ord_less_eq_real @ B @ C ) )
=> ( ord_less_eq_real @ ( times_times_real @ ( minus_minus_real @ C @ B ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( genClo1161277105lle_PC @ A @ C ) @ ( genClo1161277105lle_PC @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(14,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( minus_minus_nat @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_add__diff__cancel__left) ).
thf(390,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( minus_minus_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1244,plain,
( ( numeral_numeral_real @ one )
= one_one_real ),
inference(lifteq,[status(thm)],[1243]) ).
thf(83,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
= ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2) ).
thf(667,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
= ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(237,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/sandbox2/benchmark/theBenchmark.p',fact_207_diff__right__mono) ).
thf(1193,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)],[237]) ).
thf(38,axiom,
! [A: num] :
( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ A ) )
= ( plus_plus_nat @ ( numeral_numeral_nat @ A ) @ one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_one__plus__numeral__commute) ).
thf(478,plain,
! [A: num] :
( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ A ) )
= ( plus_plus_nat @ ( numeral_numeral_nat @ A ) @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(224,axiom,
! [A: real,B: real] :
( ( minus_minus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
= ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( minus_minus_real @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_square__diff__square__factored) ).
thf(1161,plain,
! [A: real,B: real] :
( ( minus_minus_real @ ( times_times_real @ A @ A ) @ ( times_times_real @ B @ B ) )
= ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( minus_minus_real @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(12,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
= ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_right__diff__distrib_H) ).
thf(383,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
= ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(327,axiom,
! [A: num,B: num] :
( ( ord_less_eq_num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_eq_num @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_semiring__norm_I71_J) ).
thf(1513,plain,
! [A: num,B: num] :
( ( ord_less_eq_num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_eq_num @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(212,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= C )
=> ( A
= ( minus_minus_real @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_add__implies__diff) ).
thf(1116,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)],[212]) ).
thf(178,axiom,
! [A: nat] :
( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_mult__numeral__1) ).
thf(999,plain,
! [A: nat] :
( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(109,axiom,
! [A: num,B: num] :
( ( A = B )
| ~ ( ord_less_eq_num @ A @ B )
| ~ ( ord_less_eq_num @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_verit__la__disequality) ).
thf(752,plain,
! [A: num,B: num] :
( ( A = B )
| ~ ( ord_less_eq_num @ A @ B )
| ~ ( ord_less_eq_num @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(28,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_mult_Oleft__commute) ).
thf(432,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(19,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( ( minus_minus_nat @ B @ A )
= ( minus_minus_nat @ C @ A ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_eq__diff__iff) ).
thf(405,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ( ( minus_minus_nat @ B @ A )
= ( minus_minus_nat @ C @ A ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1180,plain,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( numeral_numeral_real @ ( bit0 @ one ) ) ),
inference(lifteq,[status(thm)],[1179]) ).
thf(1757,plain,
( ( plus_plus_real @ one_one_real @ one_one_real )
= ( neg_numeral_dbl_real @ one_one_real ) ),
inference(rewrite,[status(thm)],[1180,1065]) ).
thf(138,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_add__le__cancel__right) ).
thf(865,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(9,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= C )
=> ( A
= ( minus_minus_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_add__implies__diff) ).
thf(373,plain,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= C )
=> ( A
= ( minus_minus_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(64,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_add__le__imp__le__right) ).
thf(603,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(307,axiom,
! [A: real,B: real] :
( ( abs_abs_real @ ( times_times_real @ A @ B ) )
= ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_abs__mult) ).
thf(1436,plain,
! [A: real,B: real] :
( ( abs_abs_real @ ( times_times_real @ A @ B ) )
= ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(357,plain,
! [C: nat,B: nat,A: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
inference(cnf,[status(esa)],[356]) ).
thf(358,plain,
! [C: nat,B: nat,A: nat] :
( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
= ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B ) ),
inference(lifteq,[status(thm)],[357]) ).
thf(82,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_nat__add__left__cancel__le) ).
thf(664,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(1636,plain,
( ~ $true
| ( ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) )
!= one_one_real )
| ( ( ord_less_eq_real @ s @ t )
!= ( ord_less_eq_real @ one_one_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1457,1614]) ).
thf(1637,plain,
( ( ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) )
!= one_one_real )
| ( ( ord_less_eq_real @ s @ t )
!= ( ord_less_eq_real @ one_one_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ) ) ),
inference(simp,[status(thm)],[1636]) ).
thf(1640,plain,
( ( ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) )
!= one_one_real )
| ( s != one_one_real )
| ( ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) )
!= t ) ),
inference(simp,[status(thm)],[1637]) ).
thf(1710,plain,
( ( ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) )
!= one_one_real )
| ( s != one_one_real )
| ( ( times_times_real @ ( times_times_real @ ( neg_numeral_dbl_real @ one_one_real ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) )
!= t ) ),
inference(rewrite,[status(thm)],[1640,1065]) ).
thf(91,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_add__right__cancel) ).
thf(696,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)],[91]) ).
thf(162,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_add_Oleft__cancel) ).
thf(955,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)],[162]) ).
thf(154,axiom,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_ord__eq__le__subst) ).
thf(918,plain,
! [A: nat,B: nat > nat,C: nat,D: nat] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq_nat @ C @ D )
=> ( ! [E: nat,F: nat] :
( ( ord_less_eq_nat @ E @ F )
=> ( ord_less_eq_nat @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_nat @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(121,axiom,
! [A: num,B: num] :
( ( A = B )
=> ( ord_less_eq_num @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_eq__refl) ).
thf(801,plain,
! [A: num,B: num] :
( ( A = B )
=> ( ord_less_eq_num @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(148,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_add__left__mono) ).
thf(897,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(113,axiom,
! [A: num,B: num] :
( ( ( numeral_numeral_nat @ A )
= ( numeral_numeral_nat @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_numeral__eq__iff) ).
thf(767,plain,
! [A: num,B: num] :
( ( ( numeral_numeral_nat @ A )
= ( numeral_numeral_nat @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(206,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/sandbox2/benchmark/theBenchmark.p',fact_35_add__le__cancel__right) ).
thf(1093,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)],[206]) ).
thf(105,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/sandbox2/benchmark/theBenchmark.p',fact_88_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(740,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)],[105]) ).
thf(427,plain,
( ( ^ [A: num,B: num] :
( ( ord_less_eq_num @ A @ B )
& ( ord_less_eq_num @ B @ A ) ) )
= ( (=) @ num ) ),
inference(lifteq,[status(thm)],[426]) ).
thf(295,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/sandbox2/benchmark/theBenchmark.p',fact_306_le__cases3) ).
thf(1384,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)],[295]) ).
thf(293,axiom,
! [A: real,B: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
= ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_left__add__twice) ).
thf(1378,plain,
! [A: real,B: real] :
( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
= ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(48,axiom,
! [A: real,B: real,C: real] :
( ( ( plus_plus_real @ A @ B )
= ( plus_plus_real @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_add__left__imp__eq) ).
thf(528,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)],[48]) ).
thf(127,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ C @ D ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_add__mono__thms__linordered__semiring_I1_J) ).
thf(822,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ C @ D ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(306,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/sandbox2/benchmark/theBenchmark.p',fact_155_group__cancel_Osub1) ).
thf(1431,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)],[306]) ).
thf(268,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_left__diff__distrib_H) ).
thf(1299,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
= ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(89,axiom,
ord_less_eq_nat @ one_one_nat @ one_one_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_le__numeral__extra_I4_J) ).
thf(691,plain,
ord_less_eq_nat @ one_one_nat @ one_one_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(31,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( ord_less_eq_nat @ A @ B )
=> ~ ( ord_less_eq_nat @ B @ C ) )
=> ( ( ( ord_less_eq_nat @ B @ A )
=> ~ ( ord_less_eq_nat @ A @ C ) )
=> ( ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ C @ B ) )
=> ( ( ( ord_less_eq_nat @ C @ B )
=> ~ ( ord_less_eq_nat @ B @ A ) )
=> ( ( ( ord_less_eq_nat @ B @ C )
=> ~ ( ord_less_eq_nat @ C @ A ) )
=> ~ ( ( ord_less_eq_nat @ C @ A )
=> ~ ( ord_less_eq_nat @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_le__cases3) ).
thf(442,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ord_less_eq_nat @ A @ B )
=> ~ ( ord_less_eq_nat @ B @ C ) )
=> ( ( ( ord_less_eq_nat @ B @ A )
=> ~ ( ord_less_eq_nat @ A @ C ) )
=> ( ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ C @ B ) )
=> ( ( ( ord_less_eq_nat @ C @ B )
=> ~ ( ord_less_eq_nat @ B @ A ) )
=> ( ( ( ord_less_eq_nat @ B @ C )
=> ~ ( ord_less_eq_nat @ C @ A ) )
=> ~ ( ( ord_less_eq_nat @ C @ A )
=> ~ ( ord_less_eq_nat @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(140,axiom,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_one__reorient) ).
thf(871,plain,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(296,axiom,
! [A: num,B: real > num,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_num @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_ord__eq__le__subst) ).
thf(1399,plain,
! [A: num,B: real > num,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_num @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq_num @ A @ ( B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(213,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/sandbox2/benchmark/theBenchmark.p',fact_125_add__mono) ).
thf(1120,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)],[213]) ).
thf(369,plain,
! [B: nat,A: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ A @ B ) @ A ),
inference(cnf,[status(esa)],[368]) ).
thf(1331,plain,
! [A: num] : ( ord_less_eq_num @ one @ A ),
inference(cnf,[status(esa)],[1330]) ).
thf(1366,plain,
~ ? [A: num] : ( ord_less_eq_num @ ( bit0 @ A ) @ one ),
inference(miniscope,[status(thm)],[1365]) ).
thf(1367,plain,
! [A: num] :
~ ( ord_less_eq_num @ ( bit0 @ A ) @ one ),
inference(cnf,[status(esa)],[1366]) ).
thf(314,axiom,
! [A: num,B: num] :
( ( plus_plus_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) )
= ( numeral_numeral_real @ ( plus_plus_num @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_numeral__plus__numeral) ).
thf(1463,plain,
! [A: num,B: num] :
( ( plus_plus_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) )
= ( numeral_numeral_real @ ( plus_plus_num @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(110,axiom,
! [A: num,B: num,C: num > num,D: num] :
( ( ord_less_eq_num @ A @ B )
=> ( ( ord_less_eq_num @ ( C @ B ) @ D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ E @ F )
=> ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_order__subst2) ).
thf(755,plain,
! [A: num,B: num,C: num > num,D: num] :
( ( ord_less_eq_num @ A @ B )
=> ( ( ord_less_eq_num @ ( C @ B ) @ D )
=> ( ! [E: num,F: num] :
( ( ord_less_eq_num @ E @ F )
=> ( ord_less_eq_num @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq_num @ ( C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(204,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_comm__semiring__class_Odistrib) ).
thf(1088,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
= ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(40,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_antisym__conv) ).
thf(496,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(183,axiom,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_right__diff__distrib) ).
thf(1014,plain,
! [A: real,B: real,C: real] :
( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
= ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(300,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/sandbox2/benchmark/theBenchmark.p',fact_25_abs__triangle__ineq3) ).
thf(1417,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)],[300]) ).
thf(43405,plain,
$false,
inference(e,[status(thm)],[645,1586,1337,1411,629,1469,760,1454,1031,1899,893,962,1179,1554,481,365,1190,1200,977,1005,1068,1569,1073,1544,1205,379,1305,1486,523,582,730,1290,878,440,511,1137,1867,1164,1327,1260,747,945,1458,1078,1426,1310,533,1507,1222,930,1196,1576,782,1475,1529,1518,651,1243,1127,973,1046,1055,1287,1709,372,702,1313,542,1330,1264,619,838,1545,902,638,1247,1319,1347,770,1362,1232,881,416,1489,1302,2090,1373,1040,1864,514,1020,1051,1581,966,1183,1283,981,1169,1215,692,1072,396,2002,988,428,1104,380,942,678,661,793,1306,1153,1708,798,1343,1519,1255,429,815,1238,1560,746,1091,1123,862,1570,1174,916,566,1457,461,1281,710,974,361,1365,852,435,551,1128,1350,874,1270,1375,1064,1227,1498,1096,1540,499,650,948,1534,1017,1138,356,884,1361,933,554,1182,686,1424,642,1414,1214,970,706,1419,1028,2023,622,1451,1131,721,1002,1874,605,1324,393,1099,985,1150,1478,1050,457,984,911,1202,805,508,1563,1712,1187,773,1466,1071,906,1278,1510,430,1483,1273,1548,601,1219,824,819,562,423,402,843,743,577,1535,958,1520,545,413,1707,713,1332,466,641,1428,1058,1107,764,900,784,736,362,737,1043,1307,681,1408,1574,1011,419,377,996,1571,1439,890,811,1471,631,726,848,626,1381,1061,367,1557,399,827,1250,1102,431,521,1171,636,1245,1066,868,1176,608,722,1873,795,548,927,617,1340,1472,355,1049,473,1076,675,1583,426,1166,1134,648,968,1181,836,1551,557,855,1516,1025,707,887,1566,1368,1267,1531,409,705,1156,1711,1186,717,1235,359,1579,643,585,370,470,576,1538,951,808,1358,1543,1257,1141,656,1284,1353,1427,1008,571,859,991,978,386,1316,671,1157,903,524,1517,1216,1126,1448,1866,1734,1421,465,1289,368,1276,699,517,748,1481,390,1244,667,1193,478,1161,383,1513,1116,999,752,432,405,1757,865,735,373,603,1436,358,664,1710,1065,696,720,955,918,801,897,767,1093,740,464,575,427,1384,1378,528,822,1431,1299,691,442,871,1399,1120,369,1331,1367,1184,1463,755,1088,496,364,1014,1417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP062^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.06/0.12 % Computer : n012.cluster.edu
% 0.06/0.12 % Model : x86_64 x86_64
% 0.06/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.12 % Memory : 8046.5625MB
% 0.06/0.12 % OS : Linux 6.8.0-71-generic
% 0.06/0.12 % CPULimit : 300
% 0.06/0.12 % WCLimit : 300
% 0.06/0.12 % DateTime : Tue Sep 29 19:45:33 UTC 2026
% 0.06/0.12 % CPUTime :
% 0.06/0.12 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.39/0.42 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.69 % [INFO] Parsing done (273ms).
% 1.55/0.71 % [INFO] Running in sequential loop mode.
% 2.13/0.97 % [INFO] eprover registered as external prover.
% 2.13/0.97 % [INFO] Scanning for conjecture ...
% 2.51/1.06 % [INFO] Found a conjecture (or negated_conjecture) and 352 axioms. Running axiom selection ...
% 2.82/1.16 % [INFO] Axiom selection finished. Selected 352 axioms (removed 0 axioms).
% 3.42/1.38 % [INFO] Problem is higher-order (TPTP THF).
% 3.82/1.40 % [INFO] Type checking passed.
% 3.82/1.40 % [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 ...
% 95.57/23.00 % External prover 'e' found a proof!
% 95.57/23.00 % [INFO] Killing All external provers ...
% 95.57/23.01 % Time passed: 22816ms (effective reasoning time: 22295ms)
% 95.57/23.01 % 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)>
% 95.57/23.01 % Axioms used in derivation (352): fact_67_le__add__diff__inverse2, fact_34_abs__abs, fact_299_eq__refl, fact_320_left__add__mult__distrib, fact_178_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2, fact_213_left__diff__distrib_H, fact_41_mult_Oleft__neutral, fact_9_Eq2, fact_196_one__le__numeral, fact_27_numeral__eq__iff, fact_252_order__subst1, fact_301_le__cases, fact_316_nat__le__add__iff1, fact_210_right__diff__distrib_H, fact_93_one__reorient, fact_126_add__mono, fact_65_semiring__norm_I68_J, fact_106_add_Oleft__commute, fact_245_nat__1__add__1, fact_154_diff__eq__eq, fact_193_eq__add__iff1, fact_1_rb1, fact_175_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add, fact_161_square__diff__one__factored, fact_42_mult_Oleft__neutral, fact_335_diff__le__mono2, fact_62_semiring__norm_I11_J, fact_292_antisym, fact_4_Eq4, fact_223_mult__2__right, fact_109_add__right__imp__eq, fact_311_complete__real, fact_240_order__refl, fact_302_le__cases, fact_287_ord__le__eq__subst, fact_242_semiring__norm_I6_J, fact_347_diff__mult__distrib2, fact_338_mult__le__mono2, fact_231_sin__bound__lemma, fact_189_le__diff__eq, fact_110_add__right__imp__eq, fact_334_le__diff__iff_H, fact_194_numeral__Bit0, fact_100_add_Oassoc, fact_253_order__subst1, fact_308_le__cases3, fact_235_mult__diff__mult, fact_163_mult_Oleft__commute, fact_119_le__iff__add, fact_184_add__le__add__imp__diff__le, fact_201_ordered__ring__class_Ole__add__iff2, fact_350_Nat_Ole__imp__diff__is__add, fact_206_diff__eq__diff__less__eq, fact_198_abs__triangle__ineq, fact_328_Nat_Oadd__diff__assoc, fact_349_diff__commute, fact_243_semiring__norm_I2_J, fact_150_diff__add__eq, fact_183_le__add__diff, fact_22_numeral__le__iff, fact_176_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse, fact_227_mult__numeral__1__right, fact_38_add__le__cancel__left, fact_122_less__eqE, fact_17_mult__numeral__left__semiring__numeral, fact_218_abs__mult, fact_89_ab__semigroup__add__class_Oadd__ac_I1_J, fact_8_corr__p, fact_113_one__plus__numeral__commute, fact_111_le__num__One__iff, fact_120_add__right__mono, fact_33_abs__idempotent, fact_55_diff__add__cancel, fact_271_ord__eq__le__subst, fact_78_num__double, fact_182_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2, fact_214_right__diff__distrib, fact_281_ord__le__eq__subst, fact_76_numeral__eq__one__iff, fact_155_group__cancel_Osub1, fact_283_ord__le__eq__subst, fact_112_one__plus__numeral__commute, fact_69_le__add__diff__inverse, fact_244_dbl__simps_I5_J, fact_160_abs__one, fact_179_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2, fact_291_antisym, fact_32_semiring__norm_I87_J, fact_247_numerals_I1_J, fact_262_order__subst2, fact_229_mult__numeral__1, fact_294_linear, fact_132_add__mono__thms__linordered__semiring_I3_J, fact_323_nat__add__left__cancel__le, fact_307_le__cases3, fact_135_distrib__right, fact_344_le__trans, fact_40_mult_Oright__neutral, fact_59_mem__Collect__eq, fact_268_verit__la__disequality, fact_195_numeral__Bit0, fact_212_left__diff__distrib_H, fact_43_numeral__plus__numeral, fact_174_rho__bound2__def, fact_149_diff__add__eq__diff__diff__swap, fact_16_semiring__norm_I83_J, fact_60_Collect__mem__eq, fact_204_abs__triangle__ineq4, fact_233_rate__2, fact_286_ord__le__eq__subst, fact_277_ord__eq__le__subst, fact_107_add__left__imp__eq, fact_300_le__cases, fact_141_ring__class_Oring__distribs_I1_J, fact_251_order__subst1, fact_5_Eq3, fact_18_mult__numeral__left__semiring__numeral, fact_104_add_Ocommute, fact_191_square__diff__square__factored, fact_288_eq__iff, fact_125_add__mono, fact_73_distrib__left__numeral, fact_158_comm__monoid__mult__class_Omult__1, fact_146_add__implies__diff, fact_332_diff__le__mono, fact_68_le__add__diff__inverse, fact_312_PC__monotone, fact_257_order__subst1, fact_58_abs__1, fact_310_antisym__conv, fact_203_abs__diff__triangle__ineq, fact_180_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc, fact_254_order__subst1, fact_133_combine__common__factor, fact_232_rate__1, fact_256_order__subst1, fact_219_abs__minus__commute, fact_305_order_Otrans, fact_152_add__diff__eq, fact_57_abs__add__abs, fact_10__092_060open_062_It_A_N_As_J_A_K_A_I1_A_N_A_092_060rho_062_J_A_092_060le_062_AD_Aq_At_A_N_AD_Aq_As_092_060close_062, fact_86_numeral__le__one__iff, fact_147_diff__diff__add, fact_84_one__add__one, fact_282_ord__le__eq__subst, fact_134_combine__common__factor, fact_88_ab__semigroup__add__class_Oadd__ac_I1_J, fact_138_distrib__left, fact_315_nat__eq__add__iff2, fact_64_semiring__norm_I71_J, fact_230_abs__triangle__ineq2__sym, fact_280_ord__le__eq__subst, fact_37_add__le__cancel__left, fact_148_diff__diff__add, fact_317_nat__le__add__iff2, fact_72_distrib__left__numeral, fact_156_mult_Ocomm__neutral, fact_340_mult__le__mono, fact_216_abs__ge__self, fact_313_verit__eq__simplify_I10_J, fact_82_numeral__plus__one, fact_101_add_Oleft__cancel, fact_269_verit__la__disequality, fact_25_abs__triangle__ineq3, fact_75_one__eq__numeral__iff, fact_0_rb2, fact_153_eq__diff__eq, fact_85_one__add__one, fact_49_add__diff__cancel__right, fact_190_diff__le__eq, fact_172_diff__right__commute, fact_177_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right, fact_348_diff__mult__distrib, fact_205_abs__diff__le__iff, fact_202_ordered__ring__class_Ole__add__iff1, fact_11_left__diff__distrib__numeral, fact_322_nat__mult__eq__1__iff, fact_143_le__numeral__extra_I4_J, fact_258_order__subst2, fact_24_abs__triangle__ineq2, fact_215_left__diff__distrib, fact_327_Nat_Oadd__diff__assoc2, fact_26_numeral__eq__iff, fact_209_diff__mono, fact_274_ord__eq__le__subst, fact_165_mult_Ocommute, fact_289_eq__iff, fact_87_numeral__le__one__iff, fact_246_add__One__commute, fact_115_add__le__imp__le__right, fact_168_mult_Oassoc, fact_309_antisym__conv, fact_234_dbl__simps_I3_J, fact_159_comm__monoid__mult__class_Omult__1, fact_6_corr__q, fact_171_diff__right__commute, fact_61_semiring__norm_I13_J, fact_98_group__cancel_Oadd2, fact_285_ord__le__eq__subst, fact_114_correct__closed, fact_255_order__subst1, fact_295_linear, fact_35_add__le__cancel__right, fact_20_numeral__times__numeral, fact_241_eq__diff__eq_H, fact_318_nat__diff__add__eq1, fact_186_diff__add, fact_63_semiring__norm_I12_J, fact_144_le__numeral__extra_I4_J, fact_326_Nat_Odiff__diff__right, fact_173_diff__eq__diff__eq, fact_331_Nat_Odiff__diff__eq, fact_44_numeral__plus__numeral, fact_30_add__right__cancel, fact_53_add__diff__cancel__left, fact_324_diff__diff__cancel, fact_102_add_Oright__cancel, fact_217_abs__le__D1, fact_129_add__mono__thms__linordered__semiring_I2_J, fact_239_order__refl, fact_336_Nat_Oex__has__greatest__nat, fact_97_group__cancel_Oadd2, fact_71_distrib__right__numeral, fact_50_add__diff__cancel__right, fact_226_mult__numeral__1__right, fact_15_semiring__norm_I85_J, fact_341_le__antisym, fact_279_ord__le__eq__subst, fact_237_okRead1__def, fact_140_comm__semiring__class_Odistrib, fact_80_one__plus__numeral, fact_105_add_Oleft__commute, fact_21_numeral__le__iff, fact_121_add__right__mono, fact_54_add__diff__cancel__left, fact_337_nat__le__linear, fact_108_add__left__imp__eq, fact_66_le__add__diff__inverse2, fact_304_order_Otrans, fact_23_okRead2__def, fact_52_add__diff__cancel__left_H, fact_225_mult__2, fact_275_ord__eq__le__subst, fact_199_numeral__One, fact_192_eq__add__iff2, fact_128_add__mono__thms__linordered__semiring_I1_J, fact_170_ab__semigroup__mult__class_Omult__ac_I1_J, fact_303_order_Otrans, fact_181_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc, fact_197_one__le__numeral, fact_130_add__mono__thms__linordered__semiring_I2_J, fact_3_Eq1, fact_123_add__left__mono, fact_200_numeral__One, fact_272_ord__eq__le__subst, fact_259_order__subst2, fact_103_add_Ocommute, fact_325_diff__diff__left, fact_345_le__refl, fact_261_order__subst2, fact_263_order__subst2, fact_314_nat__eq__add__iff1, fact_187_add__le__imp__le__diff, fact_330_le__diff__iff, fact_260_order__subst2, fact_164_mult_Oleft__commute, fact_95_group__cancel_Oadd1, fact_139_comm__semiring__class_Odistrib, fact_124_add__left__mono, fact_45_add__numeral__left, fact_248_dbl__def, fact_28_add__left__cancel, fact_7_PC__ie, fact_14_abs__mult__self__eq, fact_116_add__le__imp__le__right, fact_136_distrib__right, fact_151_diff__diff__eq2, fact_346_le__cube, fact_296_linear, fact_298_eq__refl, fact_51_add__diff__cancel__left_H, fact_249_order__subst1, fact_290_eq__iff, fact_238_order__refl, fact_70_distrib__right__numeral, fact_31_add__right__cancel, fact_92_add__mono__thms__linordered__semiring_I4_J, fact_166_mult_Ocommute, fact_264_order__subst2, fact_145_add__implies__diff, fact_81_one__plus__numeral, fact_266_order__subst2, fact_236_verit__eq__simplify_I8_J, fact_12_right__diff__distrib__numeral, fact_118_add__le__imp__le__left, fact_29_add__left__cancel, fact_351_diff__add__inverse2, fact_157_mult_Ocomm__neutral, fact_339_mult__le__mono1, fact_270_ord__eq__le__subst, fact_96_group__cancel_Oadd1, fact_56_add__diff__cancel, fact_39_mult_Oright__neutral, fact_220_left__add__twice, fact_46_add__numeral__left, fact_321_nat__1__eq__mult__iff, fact_83_numeral__plus__one, fact_142_ring__class_Oring__distribs_I2_J, fact_342_le__square, fact_137_distrib__left, fact_273_ord__eq__le__subst, fact_188_add__le__imp__le__diff, fact_319_nat__diff__add__eq2, fact_306_le__cases3, fact_224_mult__2, fact_297_eq__refl, fact_265_order__subst2, fact_13_abs__numeral, fact_222_mult__2__right, fact_221_left__add__twice, fact_167_mult_Oassoc, fact_79_semiring__norm_I69_J, fact_207_diff__right__mono, fact_91_add__mono__thms__linordered__semiring_I4_J, fact_90_is__num__normalize_I1_J, fact_162_rho__bound1__def, fact_2_ie, fact_267_verit__la__disequality, fact_211_right__diff__distrib_H, fact_117_add__le__imp__le__left, fact_36_add__le__cancel__right, fact_48_add__diff__cancel__right_H, fact_99_add_Oassoc, fact_293_antisym, fact_208_diff__left__mono, fact_276_ord__eq__le__subst, fact_343_eq__imp__le, fact_329_eq__diff__iff, fact_333_diff__le__self, fact_185_add__le__add__imp__diff__le, fact_250_order__subst1, fact_19_numeral__times__numeral, fact_127_add__mono__thms__linordered__semiring_I1_J, fact_169_ab__semigroup__mult__class_Omult__ac_I1_J, fact_94_one__reorient, fact_278_ord__eq__le__subst, fact_228_mult__numeral__1, fact_47_add__diff__cancel__right_H, fact_77_numeral__eq__one__iff, fact_74_one__eq__numeral__iff, fact_131_add__mono__thms__linordered__semiring_I3_J, fact_284_ord__le__eq__subst
% 95.57/23.01 % No. of inferences in proof: 815
% 95.57/23.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 22816 ms resp. 22295 ms w/o parsing
% 96.43/23.18 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 96.43/23.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------