TSTP Solution File: SCT171^2 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SCT171^2 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 14:16:03 EDT 2024
% Result : Theorem 17.67s 5.25s
% Output : Refutation 18.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 388
% Syntax : Number of formulae : 778 ( 243 unt; 0 typ; 0 def)
% Number of atoms : 2828 ( 656 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 6741 ( 382 ~; 40 |; 74 &;5309 @)
% ( 0 <=>; 936 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 1440 (1440 >; 0 *; 0 +; 0 <<)
% Number of symbols : 111 ( 109 usr; 9 con; 0-4 aty)
% Number of variables : 1994 ( 82 ^1884 !; 28 ?;1994 :)
% Comments :
%------------------------------------------------------------------------------
thf(arrow_475358991le_alt_type,type,
arrow_475358991le_alt: $tType ).
thf(arrow_1429601828e_indi_type,type,
arrow_1429601828e_indi: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(product_unit_type,type,
product_unit: $tType ).
thf(produc1501160679le_alt_type,type,
produc1501160679le_alt: $tType ).
thf(all_type,type,
all: ( produc1501160679le_alt > $o ) > $o ).
thf(arrow_797024463le_IIA_type,type,
arrow_797024463le_IIA: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ).
thf(arrow_823908191le_Lin_type,type,
arrow_823908191le_Lin: ( produc1501160679le_alt > $o ) > $o ).
thf(arrow_734252939e_Prof_type,type,
arrow_734252939e_Prof: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ).
thf(arrow_789600939_above_type,type,
arrow_789600939_above: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > arrow_475358991le_alt > produc1501160679le_alt > $o ).
thf(arrow_2098199487_below_type,type,
arrow_2098199487_below: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > arrow_475358991le_alt > produc1501160679le_alt > $o ).
thf(arrow_1212662430ctator_type,type,
arrow_1212662430ctator: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o ).
thf(arrow_2054445623_mkbot_type,type,
arrow_2054445623_mkbot: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > produc1501160679le_alt > $o ).
thf(arrow_55669061_mktop_type,type,
arrow_55669061_mktop: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > produc1501160679le_alt > $o ).
thf(arrow_1706409458nimity_type,type,
arrow_1706409458nimity: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ).
thf(finite_card_o_type,type,
finite_card_o: ( $o > $o ) > nat ).
thf(finite97476818e_indi_type,type,
finite97476818e_indi: ( arrow_1429601828e_indi > $o ) > nat ).
thf(finite537683861le_alt_type,type,
finite537683861le_alt: ( produc1501160679le_alt > $o ) > nat ).
thf(finite_finite_o_type,type,
finite_finite_o: ( $o > $o ) > $o ).
thf(finite664979089e_indi_type,type,
finite664979089e_indi: ( arrow_1429601828e_indi > $o ) > $o ).
thf(finite449174868le_alt_type,type,
finite449174868le_alt: ( produc1501160679le_alt > $o ) > $o ).
thf(in_rel1252994498le_alt_type,type,
in_rel1252994498le_alt: ( produc1501160679le_alt > $o ) > arrow_475358991le_alt > arrow_475358991le_alt > $o ).
thf(inj_on867909093le_alt_type,type,
inj_on867909093le_alt: ( $o > produc1501160679le_alt ) > ( $o > $o ) > $o ).
thf(inj_on978774663di_nat_type,type,
inj_on978774663di_nat: ( arrow_1429601828e_indi > nat ) > ( arrow_1429601828e_indi > $o ) > $o ).
thf(inj_on1911943593_alt_o_type,type,
inj_on1911943593_alt_o: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o ).
thf(pi_Arr195212324lt_o_o_type,type,
pi_Arr195212324lt_o_o: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(pi_Arr338314351e_indi_type,type,
pi_Arr338314351e_indi: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > $o ).
thf(pi_Arr830584606t_unit_type,type,
pi_Arr830584606t_unit: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > product_unit > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > product_unit ) > $o ).
thf(pi_Arr1304755663_alt_o_type,type,
pi_Arr1304755663_alt_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ).
thf(pi_Arr952516694lt_o_o_type,type,
pi_Arr952516694lt_o_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(pi_Arr1232280765e_indi_type,type,
pi_Arr1232280765e_indi: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > $o ).
thf(pi_Arr1963174508t_unit_type,type,
pi_Arr1963174508t_unit: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > product_unit > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > product_unit ) > $o ).
thf(pi_Pro422690258lt_o_o_type,type,
pi_Pro422690258lt_o_o: ( ( produc1501160679le_alt > $o ) > $o ) > ( ( produc1501160679le_alt > $o ) > $o > $o ) > ( ( produc1501160679le_alt > $o ) > $o ) > $o ).
thf(pi_Pro468373057e_indi_type,type,
pi_Pro468373057e_indi: ( ( produc1501160679le_alt > $o ) > $o ) > ( ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o ) > ( ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > $o ).
thf(pi_Pro1306850800t_unit_type,type,
pi_Pro1306850800t_unit: ( ( produc1501160679le_alt > $o ) > $o ) > ( ( produc1501160679le_alt > $o ) > product_unit > $o ) > ( ( produc1501160679le_alt > $o ) > product_unit ) > $o ).
thf(pi_o_A1186128886_alt_o_type,type,
pi_o_A1186128886_alt_o: ( $o > $o ) > ( $o > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ).
thf(pi_o_A1182933120_alt_o_type,type,
pi_o_A1182933120_alt_o: ( $o > $o ) > ( $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( $o > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ).
thf(pi_o_P553196292_alt_o_type,type,
pi_o_P553196292_alt_o: ( $o > $o ) > ( $o > ( produc1501160679le_alt > $o ) > $o ) > ( $o > produc1501160679le_alt > $o ) > $o ).
thf(pi_o_P657324555le_alt_type,type,
pi_o_P657324555le_alt: ( $o > $o ) > ( $o > produc1501160679le_alt > $o ) > ( $o > produc1501160679le_alt ) > $o ).
thf(pi_Arr1564509167_alt_o_type,type,
pi_Arr1564509167_alt_o: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ).
thf(pi_Arr1060328391_alt_o_type,type,
pi_Arr1060328391_alt_o: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( arrow_1429601828e_indi > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ).
thf(pi_Arr1929480907_alt_o_type,type,
pi_Arr1929480907_alt_o: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o ) > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ).
thf(pi_Arr329216900le_alt_type,type,
pi_Arr329216900le_alt: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( arrow_1429601828e_indi > produc1501160679le_alt ) > $o ).
thf(pi_Pro1782982558_alt_o_type,type,
pi_Pro1782982558_alt_o: ( product_unit > $o ) > ( product_unit > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( product_unit > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ).
thf(pi_Pro1662176984_alt_o_type,type,
pi_Pro1662176984_alt_o: ( product_unit > $o ) > ( product_unit > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( product_unit > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ).
thf(pi_Pro1312660828_alt_o_type,type,
pi_Pro1312660828_alt_o: ( product_unit > $o ) > ( product_unit > ( produc1501160679le_alt > $o ) > $o ) > ( product_unit > produc1501160679le_alt > $o ) > $o ).
thf(pi_Pro701847987le_alt_type,type,
pi_Pro701847987le_alt: ( product_unit > $o ) > ( product_unit > produc1501160679le_alt > $o ) > ( product_unit > produc1501160679le_alt ) > $o ).
thf(pi_Pro1701359055_alt_o_type,type,
pi_Pro1701359055_alt_o: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o > $o ) > ( produc1501160679le_alt > $o ) > $o ).
thf(pi_Pro1767455108e_indi_type,type,
pi_Pro1767455108e_indi: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > arrow_1429601828e_indi > $o ) > ( produc1501160679le_alt > arrow_1429601828e_indi ) > $o ).
thf(pi_Pro1475896499t_unit_type,type,
pi_Pro1475896499t_unit: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > product_unit > $o ) > ( produc1501160679le_alt > product_unit ) > $o ).
thf(one_one_nat_type,type,
one_one_nat: nat ).
thf(plus_plus_nat_type,type,
plus_plus_nat: nat > nat > nat ).
thf(zero_zero_nat_type,type,
zero_zero_nat: nat ).
thf(hilber598459244di_nat_type,type,
hilber598459244di_nat: ( arrow_1429601828e_indi > $o ) > ( arrow_1429601828e_indi > nat ) > nat > arrow_1429601828e_indi ).
thf(if_Pro1561232536_alt_o_type,type,
if_Pro1561232536_alt_o: $o > ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ).
thf(suc_type,type,
suc: nat > nat ).
thf(ord_le1859604819lt_o_o_type,type,
ord_le1859604819lt_o_o: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(ord_le157835011lt_o_o_type,type,
ord_le157835011lt_o_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(ord_le910298367lt_o_o_type,type,
ord_le910298367lt_o_o: ( ( produc1501160679le_alt > $o ) > $o ) > ( ( produc1501160679le_alt > $o ) > $o ) > $o ).
thf(ord_less_o_o_type,type,
ord_less_o_o: ( $o > $o ) > ( $o > $o ) > $o ).
thf(ord_le988258430_alt_o_type,type,
ord_le988258430_alt_o: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o ).
thf(ord_less_nat_type,type,
ord_less_nat: nat > nat > $o ).
thf(ord_le134800455lt_o_o_type,type,
ord_le134800455lt_o_o: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(ord_le1063113995lt_o_o_type,type,
ord_le1063113995lt_o_o: ( ( produc1501160679le_alt > $o ) > $o ) > ( ( produc1501160679le_alt > $o ) > $o ) > $o ).
thf(ord_less_eq_o_o_type,type,
ord_less_eq_o_o: ( $o > $o ) > ( $o > $o ) > $o ).
thf(ord_le2080035663_alt_o_type,type,
ord_le2080035663_alt_o: ( arrow_475358991le_alt > arrow_475358991le_alt > $o ) > ( arrow_475358991le_alt > arrow_475358991le_alt > $o ) > $o ).
thf(ord_le97612146_alt_o_type,type,
ord_le97612146_alt_o: ( produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o ).
thf(ord_less_eq_nat_type,type,
ord_less_eq_nat: nat > nat > $o ).
thf(top_top_o_o_type,type,
top_top_o_o: $o > $o ).
thf(top_to988227749indi_o_type,type,
top_to988227749indi_o: arrow_1429601828e_indi > $o ).
thf(top_to1841428258_alt_o_type,type,
top_to1841428258_alt_o: produc1501160679le_alt > $o ).
thf(produc1347929815le_alt_type,type,
produc1347929815le_alt: arrow_475358991le_alt > arrow_475358991le_alt > produc1501160679le_alt ).
thf(ord_at4362885an_nat_type,type,
ord_at4362885an_nat: nat > nat > nat > $o ).
thf(image_484224243di_nat_type,type,
image_484224243di_nat: ( arrow_1429601828e_indi > nat ) > ( arrow_1429601828e_indi > $o ) > nat > $o ).
thf(member1823529808lt_o_o_type,type,
member1823529808lt_o_o: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > ( ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o ) > $o ).
thf(member1452482393e_indi_type,type,
member1452482393e_indi: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > ( ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > $o ) > $o ).
thf(member1924666376t_unit_type,type,
member1924666376t_unit: ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > product_unit ) > ( ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > product_unit ) > $o ) > $o ).
thf(member616898751_alt_o_type,type,
member616898751_alt_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(member939334982lt_o_o_type,type,
member939334982lt_o_o: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ) > $o ).
thf(member44294883e_indi_type,type,
member44294883e_indi: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > $o ) > $o ).
thf(member843528338t_unit_type,type,
member843528338t_unit: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > product_unit ) > ( ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > product_unit ) > $o ) > $o ).
thf(member1961363906lt_o_o_type,type,
member1961363906lt_o_o: ( ( produc1501160679le_alt > $o ) > $o ) > ( ( ( produc1501160679le_alt > $o ) > $o ) > $o ) > $o ).
thf(member304866663e_indi_type,type,
member304866663e_indi: ( ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > ( ( ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi ) > $o ) > $o ).
thf(member221730070t_unit_type,type,
member221730070t_unit: ( ( produc1501160679le_alt > $o ) > product_unit ) > ( ( ( produc1501160679le_alt > $o ) > product_unit ) > $o ) > $o ).
thf(member1957863580_alt_o_type,type,
member1957863580_alt_o: ( $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > ( ( $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(member1394214384_alt_o_type,type,
member1394214384_alt_o: ( $o > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( ( $o > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(member1862122484_alt_o_type,type,
member1862122484_alt_o: ( $o > produc1501160679le_alt > $o ) > ( ( $o > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(member492167345le_alt_type,type,
member492167345le_alt: ( $o > produc1501160679le_alt ) > ( ( $o > produc1501160679le_alt ) > $o ) > $o ).
thf(member811956313_alt_o_type,type,
member811956313_alt_o: ( arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > ( ( arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(member1234151027_alt_o_type,type,
member1234151027_alt_o: ( arrow_1429601828e_indi > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( ( arrow_1429601828e_indi > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(member526088951_alt_o_type,type,
member526088951_alt_o: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(member351225838le_alt_type,type,
member351225838le_alt: ( arrow_1429601828e_indi > produc1501160679le_alt ) > ( ( arrow_1429601828e_indi > produc1501160679le_alt ) > $o ) > $o ).
thf(member1536989448_alt_o_type,type,
member1536989448_alt_o: ( product_unit > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > ( ( product_unit > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(member283501700_alt_o_type,type,
member283501700_alt_o: ( product_unit > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( ( product_unit > arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(member1661784200_alt_o_type,type,
member1661784200_alt_o: ( product_unit > produc1501160679le_alt > $o ) > ( ( product_unit > produc1501160679le_alt > $o ) > $o ) > $o ).
thf(member495332125le_alt_type,type,
member495332125le_alt: ( product_unit > produc1501160679le_alt ) > ( ( product_unit > produc1501160679le_alt ) > $o ) > $o ).
thf(member377231867_alt_o_type,type,
member377231867_alt_o: ( produc1501160679le_alt > $o ) > ( ( produc1501160679le_alt > $o ) > $o ) > $o ).
thf(member1640632174e_indi_type,type,
member1640632174e_indi: ( produc1501160679le_alt > arrow_1429601828e_indi ) > ( ( produc1501160679le_alt > arrow_1429601828e_indi ) > $o ) > $o ).
thf(member593902749t_unit_type,type,
member593902749t_unit: ( produc1501160679le_alt > product_unit ) > ( ( produc1501160679le_alt > product_unit ) > $o ) > $o ).
thf(member_o_type,type,
member_o: $o > ( $o > $o ) > $o ).
thf(member2052026769e_indi_type,type,
member2052026769e_indi: arrow_1429601828e_indi > ( arrow_1429601828e_indi > $o ) > $o ).
thf(member_Product_unit_type,type,
member_Product_unit: product_unit > ( product_unit > $o ) > $o ).
thf(member214075476le_alt_type,type,
member214075476le_alt: produc1501160679le_alt > ( produc1501160679le_alt > $o ) > $o ).
thf(f_type,type,
f: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ).
thf(lab_type,type,
lab: produc1501160679le_alt > $o ).
thf(lba_type,type,
lba: produc1501160679le_alt > $o ).
thf(p_type,type,
p: arrow_1429601828e_indi > produc1501160679le_alt > $o ).
thf(a_type,type,
a: arrow_475358991le_alt ).
thf(b_type,type,
b: arrow_475358991le_alt ).
thf(c_type,type,
c: arrow_475358991le_alt ).
thf(d_type,type,
d: arrow_475358991le_alt ).
thf(e_type,type,
e: arrow_475358991le_alt ).
thf(h_type,type,
h: arrow_1429601828e_indi > nat ).
thf(n_type,type,
n: nat ).
thf(319,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_xt1_I7_J) ).
thf(1718,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(262,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_order__less__imp__not__less) ).
thf(1411,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(229,axiom,
! [A: produc1501160679le_alt > $o,B: produc1501160679le_alt > $o] :
( ( if_Pro1561232536_alt_o @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_) ).
thf(1237,plain,
! [A: produc1501160679le_alt > $o,B: produc1501160679le_alt > $o] :
( ( if_Pro1561232536_alt_o @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(367,axiom,
! [A: arrow_1429601828e_indi] :
( ( ( ( ord_less_nat @ ( h @ A ) @ n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ e @ d ) @ ( arrow_55669061_mktop @ ( p @ A ) @ e ) ) )
& ( ~ ( ord_less_nat @ ( h @ A ) @ n )
=> ( ( ( ( h @ A )
= n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ e @ d ) @ ( arrow_789600939_above @ ( p @ A ) @ c @ e ) ) )
& ( ( ( h @ A )
!= n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ e @ d ) @ ( arrow_2054445623_mkbot @ ( p @ A ) @ e ) ) ) ) ) )
= ( ( ( ord_less_nat @ ( h @ A ) @ n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a ) @ lab ) )
& ( ~ ( ord_less_nat @ ( h @ A ) @ n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a ) @ lba ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).
thf(1840,plain,
! [A: arrow_1429601828e_indi] :
( ( ( ( ord_less_nat @ ( h @ A ) @ n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ e @ d ) @ ( arrow_55669061_mktop @ ( p @ A ) @ e ) ) )
& ( ~ ( ord_less_nat @ ( h @ A ) @ n )
=> ( ( ( ( h @ A )
= n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ e @ d ) @ ( arrow_789600939_above @ ( p @ A ) @ c @ e ) ) )
& ( ( ( h @ A )
!= n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ e @ d ) @ ( arrow_2054445623_mkbot @ ( p @ A ) @ e ) ) ) ) ) )
= ( ( ( ord_less_nat @ ( h @ A ) @ n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a ) @ lab ) )
& ( ~ ( ord_less_nat @ ( h @ A ) @ n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a ) @ lba ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(204,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_add__left__mono) ).
thf(1179,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(113,axiom,
! [A: produc1501160679le_alt > $o] :
( ( ord_le97612146_alt_o @ top_to1841428258_alt_o @ A )
= ( A = top_to1841428258_alt_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_top__unique) ).
thf(777,plain,
! [A: produc1501160679le_alt > $o] :
( ( ord_le97612146_alt_o @ top_to1841428258_alt_o @ A )
= ( A = top_to1841428258_alt_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(357,axiom,
! [A: arrow_475358991le_alt,B: arrow_475358991le_alt] :
( ( A != B )
=> ? [C: produc1501160679le_alt > $o] :
( ( member377231867_alt_o @ C @ arrow_823908191le_Lin )
& ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_complete__Lin) ).
thf(1818,plain,
! [A: arrow_475358991le_alt,B: arrow_475358991le_alt] :
( ( A != B )
=> ? [C: produc1501160679le_alt > $o] :
( ( member377231867_alt_o @ C @ arrow_823908191le_Lin )
& ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(288,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
=> ( ord_less_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_add__less__imp__less__left) ).
thf(1549,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
=> ( ord_less_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(299,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_order__less__imp__not__eq2) ).
thf(1586,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(270,axiom,
! [A: produc1501160679le_alt > $o,B: arrow_475358991le_alt,C: arrow_475358991le_alt] :
( ( B != C )
=> ( ( member377231867_alt_o @ A @ arrow_823908191le_Lin )
=> ( member377231867_alt_o @ ( arrow_2098199487_below @ A @ B @ C ) @ arrow_823908191le_Lin ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_below__Lin) ).
thf(1501,plain,
! [A: produc1501160679le_alt > $o,B: arrow_475358991le_alt,C: arrow_475358991le_alt] :
( ( B != C )
=> ( ( member377231867_alt_o @ A @ arrow_823908191le_Lin )
=> ( member377231867_alt_o @ ( arrow_2098199487_below @ A @ B @ C ) @ arrow_823908191le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(358,axiom,
( member214075476le_alt @ ( produc1347929815le_alt @ e @ d )
@ ( f
@ ^ [A: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ A ) @ n ) @ ( arrow_55669061_mktop @ ( p @ A ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ A )
= n )
@ ( arrow_789600939_above @ ( p @ A ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ A ) @ e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
thf(1823,plain,
( member214075476le_alt @ ( produc1347929815le_alt @ e @ d )
@ ( f
@ ^ [A: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ A ) @ n ) @ ( arrow_55669061_mktop @ ( p @ A ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ A )
= n )
@ ( arrow_789600939_above @ ( p @ A ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ A ) @ e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(208,axiom,
! [A: arrow_1429601828e_indi] : ( top_to988227749indi_o @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_top1I) ).
thf(1190,plain,
! [A: arrow_1429601828e_indi] : ( top_to988227749indi_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(199,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ ( suc @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_Suc__leI) ).
thf(1168,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ ( suc @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(106,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_order__less__asym) ).
thf(760,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(290,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_termination__basic__simps_I2_J) ).
thf(1554,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(180,axiom,
! [A: $o,B: $o > produc1501160679le_alt > $o,C: $o > $o,D: $o > ( produc1501160679le_alt > $o ) > $o] :
( ( member1862122484_alt_o @ B @ ( pi_o_P553196292_alt_o @ C @ D ) )
=> ( ~ ( member377231867_alt_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_PiE) ).
thf(1110,plain,
! [A: $o,B: $o > produc1501160679le_alt > $o,C: $o > $o,D: $o > ( produc1501160679le_alt > $o ) > $o] :
( ( member1862122484_alt_o @ B @ ( pi_o_P553196292_alt_o @ C @ D ) )
=> ( ~ ( member377231867_alt_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(371,axiom,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: arrow_1429601828e_indi > produc1501160679le_alt > $o,C: arrow_475358991le_alt,D: arrow_475358991le_alt,E: arrow_475358991le_alt,F: arrow_475358991le_alt] :
( ( E != F )
=> ( ( C != D )
=> ( ( E != D )
=> ( ( F != C )
=> ( ( member526088951_alt_o @ B @ arrow_734252939e_Prof )
=> ( ( member526088951_alt_o @ A @ arrow_734252939e_Prof )
=> ( ! [G: arrow_1429601828e_indi] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ E @ F ) @ ( B @ G ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ ( A @ G ) ) )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ E @ F ) @ ( f @ B ) )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ ( f @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__C1_C) ).
thf(1855,plain,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: arrow_1429601828e_indi > produc1501160679le_alt > $o,C: arrow_475358991le_alt,D: arrow_475358991le_alt,E: arrow_475358991le_alt,F: arrow_475358991le_alt] :
( ( E != F )
=> ( ( C != D )
=> ( ( E != D )
=> ( ( F != C )
=> ( ( member526088951_alt_o @ B @ arrow_734252939e_Prof )
=> ( ( member526088951_alt_o @ A @ arrow_734252939e_Prof )
=> ( ! [G: arrow_1429601828e_indi] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ E @ F ) @ ( B @ G ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ ( A @ G ) ) )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ E @ F ) @ ( f @ B ) )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ ( f @ A ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(9,axiom,
! [A: arrow_1429601828e_indi > nat,B: arrow_1429601828e_indi > $o] :
( ( inj_on978774663di_nat @ A @ B )
= ( ! [C: arrow_1429601828e_indi] :
( ( member2052026769e_indi @ C @ B )
=> ! [D: arrow_1429601828e_indi] :
( ( member2052026769e_indi @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_inj__on__def) ).
thf(408,plain,
! [A: arrow_1429601828e_indi > nat,B: arrow_1429601828e_indi > $o] :
( ( inj_on978774663di_nat @ A @ B )
= ( ! [C: arrow_1429601828e_indi] :
( ( member2052026769e_indi @ C @ B )
=> ! [D: arrow_1429601828e_indi] :
( ( member2052026769e_indi @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(258,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ord_less_eq_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_xt1_I3_J) ).
thf(1401,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( ord_less_eq_nat @ A @ C )
=> ( ord_less_eq_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(215,axiom,
! [A: produc1501160679le_alt > $o] : ( ord_le97612146_alt_o @ A @ top_to1841428258_alt_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_subset__UNIV) ).
thf(1205,plain,
! [A: produc1501160679le_alt > $o] : ( ord_le97612146_alt_o @ A @ top_to1841428258_alt_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(152,axiom,
! [A: $o > $o,B: $o > $o] :
( ( ord_less_eq_o_o
@ ^ [C: $o] : ( member_o @ C @ A )
@ ^ [C: $o] : ( member_o @ C @ B ) )
= ( ord_less_eq_o_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_pred__subset__eq) ).
thf(878,plain,
! [A: $o > $o,B: $o > $o] :
( ( ord_less_eq_o_o
@ ^ [C: $o] : ( member_o @ C @ A )
@ ^ [C: $o] : ( member_o @ C @ B ) )
= ( ord_less_eq_o_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(349,axiom,
! [A: arrow_475358991le_alt,B: arrow_475358991le_alt,C: arrow_475358991le_alt,D: arrow_475358991le_alt] :
( ( ( produc1347929815le_alt @ A @ B )
= ( produc1347929815le_alt @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Pair__inject) ).
thf(1793,plain,
! [A: arrow_475358991le_alt,B: arrow_475358991le_alt,C: arrow_475358991le_alt,D: arrow_475358991le_alt] :
( ( ( produc1347929815le_alt @ A @ B )
= ( produc1347929815le_alt @ C @ D ) )
=> ~ ( ( A = C )
=> ( B != D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(195,axiom,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
( ! [D: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member526088951_alt_o @ D @ C )
=> ( ord_le1063113995lt_o_o @ ( A @ D ) @ ( B @ D ) ) )
=> ( ord_le134800455lt_o_o @ ( pi_Arr1304755663_alt_o @ C @ A ) @ ( pi_Arr1304755663_alt_o @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_Pi__mono) ).
thf(1158,plain,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
( ! [D: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member526088951_alt_o @ D @ C )
=> ( ord_le1063113995lt_o_o @ ( A @ D ) @ ( B @ D ) ) )
=> ( ord_le134800455lt_o_o @ ( pi_Arr1304755663_alt_o @ C @ A ) @ ( pi_Arr1304755663_alt_o @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(107,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_552_add__less__mono) ).
thf(762,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(71,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_gr0I) ).
thf(614,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(313,axiom,
! [A: nat] :
( ( ord_less_nat @ A )
= ( ord_less_eq_nat @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_679_less__eq__Suc__le__raw) ).
thf(1692,plain,
! [A: nat] :
( ( ord_less_nat @ A )
= ( ord_less_eq_nat @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(335,axiom,
! [A: produc1501160679le_alt,B: produc1501160679le_alt > $o,C: produc1501160679le_alt > $o,D: $o > $o] :
( ( member377231867_alt_o @ B
@ ( pi_Pro1701359055_alt_o @ C
@ ^ [E: produc1501160679le_alt] : D ) )
=> ( ( member214075476le_alt @ A @ C )
=> ( member_o @ ( B @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_funcset__mem) ).
thf(1756,plain,
! [A: produc1501160679le_alt,B: produc1501160679le_alt > $o,C: produc1501160679le_alt > $o,D: $o > $o] :
( ( member377231867_alt_o @ B
@ ( pi_Pro1701359055_alt_o @ C
@ ^ [E: produc1501160679le_alt] : D ) )
=> ( ( member214075476le_alt @ A @ C )
=> ( member_o @ ( B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(51,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( A = zero_zero_nat )
| ? [C: nat] :
( ( A
= ( suc @ C ) )
& ( ord_less_nat @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_671_less__Suc__eq__0__disj) ).
thf(550,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( A = zero_zero_nat )
| ? [C: nat] :
( ( A
= ( suc @ C ) )
& ( ord_less_nat @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(326,axiom,
! [A: produc1501160679le_alt > $o,B: produc1501160679le_alt > $o] :
( ! [C: produc1501160679le_alt] :
( ( member214075476le_alt @ C @ B )
=> ( member214075476le_alt @ C @ A ) )
=> ( ord_le97612146_alt_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_511_subsetI) ).
thf(1735,plain,
! [A: produc1501160679le_alt > $o,B: produc1501160679le_alt > $o] :
( ! [C: produc1501160679le_alt] :
( ( member214075476le_alt @ C @ B )
=> ( member214075476le_alt @ C @ A ) )
=> ( ord_le97612146_alt_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(121,axiom,
! [A: nat,B: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_547_not__add__less2) ).
thf(797,plain,
! [A: nat,B: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(379,axiom,
( ( member214075476le_alt @ ( produc1347929815le_alt @ e @ d )
@ ( f
@ ^ [A: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ A ) @ n ) @ ( arrow_55669061_mktop @ ( p @ A ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ A )
= n )
@ ( arrow_789600939_above @ ( p @ A ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ A ) @ e ) ) ) ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a )
@ ( f
@ ^ [A: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ A ) @ n ) @ lab @ lba ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk) ).
thf(1872,plain,
( ( member214075476le_alt @ ( produc1347929815le_alt @ e @ d )
@ ( f
@ ^ [A: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ A ) @ n ) @ ( arrow_55669061_mktop @ ( p @ A ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ A )
= n )
@ ( arrow_789600939_above @ ( p @ A ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ A ) @ e ) ) ) ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a )
@ ( f
@ ^ [A: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ A ) @ n ) @ lab @ lba ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(227,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_order__less__le__trans) ).
thf(1233,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(127,axiom,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,D: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o] :
( ( member44294883e_indi @ B @ ( pi_Arr1232280765e_indi @ C @ D ) )
=> ( ~ ( member2052026769e_indi @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member526088951_alt_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_PiE) ).
thf(814,plain,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,D: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o] :
( ( member44294883e_indi @ B @ ( pi_Arr1232280765e_indi @ C @ D ) )
=> ( ~ ( member2052026769e_indi @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member526088951_alt_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(165,axiom,
! [A: $o,B: $o > $o,C: $o > $o] :
( ( ord_less_eq_o_o @ B @ C )
=> ( ( member_o @ A @ B )
=> ( member_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_subsetD) ).
thf(945,plain,
! [A: $o,B: $o > $o,C: $o > $o] :
( ( ord_less_eq_o_o @ B @ C )
=> ( ( member_o @ A @ B )
=> ( member_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(47,axiom,
! [A: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ! [C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
( ( member616898751_alt_o @ C @ B )
=> ( member616898751_alt_o @ C @ A ) )
=> ( ord_le134800455lt_o_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_subsetI) ).
thf(538,plain,
! [A: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ! [C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
( ( member616898751_alt_o @ C @ B )
=> ( member616898751_alt_o @ C @ A ) )
=> ( ord_le134800455lt_o_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(222,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_xt1_I9_J) ).
thf(1222,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(376,axiom,
member214075476le_alt @ ( produc1347929815le_alt @ b @ a ) @ lba,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).
thf(1867,plain,
member214075476le_alt @ ( produc1347929815le_alt @ b @ a ) @ lba,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(37,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ ( suc @ A ) @ B )
= ( plus_plus_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_642_add__Suc__shift) ).
thf(500,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ ( suc @ A ) @ B )
= ( plus_plus_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(101,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_542_le__trans) ).
thf(747,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(154,axiom,
! [A: nat] :
( ( suc @ A )
= ( plus_plus_nat @ A @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_688_Suc__eq__plus1) ).
thf(913,plain,
! [A: nat] :
( ( suc @ A )
= ( plus_plus_nat @ A @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(174,axiom,
! [A: nat,B: nat] :
( ( A = B )
= ( ( ord_less_eq_nat @ A @ B )
& ( ord_less_eq_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_order__eq__iff) ).
thf(1095,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)],[174]) ).
thf(211,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_662_less__Suc__eq__le) ).
thf(1196,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(365,axiom,
! [A: produc1501160679le_alt,B: produc1501160679le_alt > arrow_1429601828e_indi,C: produc1501160679le_alt > $o,D: produc1501160679le_alt > arrow_1429601828e_indi > $o] :
( ( member1640632174e_indi @ B @ ( pi_Pro1767455108e_indi @ C @ D ) )
=> ( ~ ( member2052026769e_indi @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member214075476le_alt @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_PiE) ).
thf(1835,plain,
! [A: produc1501160679le_alt,B: produc1501160679le_alt > arrow_1429601828e_indi,C: produc1501160679le_alt > $o,D: produc1501160679le_alt > arrow_1429601828e_indi > $o] :
( ( member1640632174e_indi @ B @ ( pi_Pro1767455108e_indi @ C @ D ) )
=> ( ~ ( member2052026769e_indi @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member214075476le_alt @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(295,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ C @ A )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_order__less__trans) ).
thf(1576,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ C @ A )
=> ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(12,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_Suc__mono) ).
thf(417,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(245,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_add__strict__left__mono) ).
thf(1366,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(280,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_564_trans__le__add1) ).
thf(1529,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(19,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_648_not__less__less__Suc__eq) ).
thf(436,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(317,axiom,
! [A: nat,B: nat > $o] :
( ~ ( B @ zero_zero_nat )
=> ( ( B @ A )
=> ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ! [D: nat] :
( ( ord_less_eq_nat @ D @ C )
=> ~ ( B @ D ) )
& ( B @ ( plus_plus_nat @ C @ one_one_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_ex__least__nat__less) ).
thf(1703,plain,
! [A: nat,B: nat > $o] :
( ~ ( B @ zero_zero_nat )
=> ( ( B @ A )
=> ? [C: nat] :
( ( ord_less_nat @ C @ A )
& ! [D: nat] :
( ( ord_less_eq_nat @ D @ C )
=> ~ ( B @ D ) )
& ( B @ ( plus_plus_nat @ C @ one_one_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(225,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_linorder__neqE) ).
thf(1228,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(236,axiom,
! [A: arrow_475358991le_alt,B: produc1501160679le_alt > $o] :
( ( member377231867_alt_o @ B @ arrow_823908191le_Lin )
=> ( member377231867_alt_o @ ( arrow_2054445623_mkbot @ B @ A ) @ arrow_823908191le_Lin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_mkbot__Lin) ).
thf(1254,plain,
! [A: arrow_475358991le_alt,B: produc1501160679le_alt > $o] :
( ( member377231867_alt_o @ B @ arrow_823908191le_Lin )
=> ( member377231867_alt_o @ ( arrow_2054445623_mkbot @ B @ A ) @ arrow_823908191le_Lin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(337,axiom,
~ ! [A: nat] :
( ( ord_less_nat @ A @ ( finite97476818e_indi @ top_to988227749indi_o ) )
=> ( ! [B: nat] :
( ( ord_less_eq_nat @ B @ A )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a )
@ ( f
@ ^ [C: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ C ) @ B ) @ lab @ lba ) ) ) )
=> ~ ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b )
@ ( f
@ ^ [B: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ B ) @ ( plus_plus_nat @ A @ one_one_nat ) ) @ lab @ lba ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_) ).
thf(1760,plain,
~ ! [A: nat] :
( ( ord_less_nat @ A @ ( finite97476818e_indi @ top_to988227749indi_o ) )
=> ( ! [B: nat] :
( ( ord_less_eq_nat @ B @ A )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a )
@ ( f
@ ^ [C: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ C ) @ B ) @ lab @ lba ) ) ) )
=> ~ ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b )
@ ( f
@ ^ [B: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ B ) @ ( plus_plus_nat @ A @ one_one_nat ) ) @ lab @ lba ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(116,axiom,
! [A: ( produc1501160679le_alt > $o ) > $o,B: produc1501160679le_alt > $o,C: ( produc1501160679le_alt > $o ) > $o] :
( ( member377231867_alt_o @ B @ C )
=> ( ( ord_le1063113995lt_o_o @ C @ A )
=> ( member377231867_alt_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_475_set__rev__mp) ).
thf(785,plain,
! [A: ( produc1501160679le_alt > $o ) > $o,B: produc1501160679le_alt > $o,C: ( produc1501160679le_alt > $o ) > $o] :
( ( member377231867_alt_o @ B @ C )
=> ( ( ord_le1063113995lt_o_o @ C @ A )
=> ( member377231867_alt_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(274,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532_less__not__refl3) ).
thf(1511,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(360,axiom,
member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ lab,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).
thf(1826,plain,
member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ lab,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(62,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_le0) ).
thf(587,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(239,axiom,
! [A: $o,B: $o > $o] :
( ( member_o @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_mem__def) ).
thf(1323,plain,
! [A: $o,B: $o > $o] :
( ( member_o @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(73,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_677_nat_Osimps_I2_J) ).
thf(619,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(286,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ ( plus_plus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_551_add__less__mono1) ).
thf(1545,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ ( plus_plus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(350,axiom,
! [A: $o,B: $o > produc1501160679le_alt,C: $o > $o,D: $o > produc1501160679le_alt > $o] :
( ( member492167345le_alt @ B @ ( pi_o_P657324555le_alt @ C @ D ) )
=> ( ~ ( member214075476le_alt @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_PiE) ).
thf(1800,plain,
! [A: $o,B: $o > produc1501160679le_alt,C: $o > $o,D: $o > produc1501160679le_alt > $o] :
( ( member492167345le_alt @ B @ ( pi_o_P657324555le_alt @ C @ D ) )
=> ( ~ ( member214075476le_alt @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(171,axiom,
! [A: nat,B: nat,C: nat > nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( ord_less_nat @ ( C @ D ) @ ( C @ E ) ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ ( C @ A ) @ B ) @ ( C @ ( plus_plus_nat @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568_mono__nat__linear__lb) ).
thf(1087,plain,
! [A: nat,B: nat,C: nat > nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( ord_less_nat @ ( C @ D ) @ ( C @ E ) ) )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ ( C @ A ) @ B ) @ ( C @ ( plus_plus_nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(191,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_less__irrefl__nat) ).
thf(1147,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(233,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
= ( ( ord_less_eq_nat @ A @ B )
& ~ ( ord_less_eq_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_less__le__not__le) ).
thf(1247,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
= ( ( ord_less_eq_nat @ A @ B )
& ~ ( ord_less_eq_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(167,axiom,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
( ( ord_le157835011lt_o_o @ B @ C )
=> ( ( member526088951_alt_o @ A @ B )
=> ( member526088951_alt_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_518_psubsetD) ).
thf(1013,plain,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
( ( ord_le157835011lt_o_o @ B @ C )
=> ( ( member526088951_alt_o @ A @ B )
=> ( member526088951_alt_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(329,axiom,
! [A: produc1501160679le_alt > $o,B: produc1501160679le_alt > $o] :
( ( ! [C: arrow_475358991le_alt,D: arrow_475358991le_alt] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ B )
= ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ A ) ) )
= ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_pred__equals__eq2) ).
thf(1741,plain,
! [A: produc1501160679le_alt > $o,B: produc1501160679le_alt > $o] :
( ( ! [C: arrow_475358991le_alt,D: arrow_475358991le_alt] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ B )
= ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ A ) ) )
= ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(181,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_538_nat__add__right__cancel) ).
thf(1115,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)],[181]) ).
thf(342,axiom,
! [A: produc1501160679le_alt > $o,B: arrow_475358991le_alt,C: arrow_475358991le_alt] :
( ( in_rel1252994498le_alt @ A @ B @ C )
= ( member214075476le_alt @ ( produc1347929815le_alt @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_575_in__rel__def) ).
thf(1773,plain,
! [A: produc1501160679le_alt > $o,B: arrow_475358991le_alt,C: arrow_475358991le_alt] :
( ( in_rel1252994498le_alt @ A @ B @ C )
= ( member214075476le_alt @ ( produc1347929815le_alt @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(23,axiom,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,C: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ( ord_le134800455lt_o_o @ B @ C )
=> ( ( member616898751_alt_o @ A @ B )
=> ( member616898751_alt_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_485_in__mono) ).
thf(448,plain,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,C: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ( ord_le134800455lt_o_o @ B @ C )
=> ( ( member616898751_alt_o @ A @ B )
=> ( member616898751_alt_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(344,axiom,
! [A: produc1501160679le_alt,B: produc1501160679le_alt > $o,C: produc1501160679le_alt > $o] :
( ( ord_le97612146_alt_o @ B @ C )
=> ( ( member214075476le_alt @ A @ B )
=> ( member214075476le_alt @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_487_in__mono) ).
thf(1778,plain,
! [A: produc1501160679le_alt,B: produc1501160679le_alt > $o,C: produc1501160679le_alt > $o] :
( ( ord_le97612146_alt_o @ B @ C )
=> ( ( member214075476le_alt @ A @ B )
=> ( member214075476le_alt @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(69,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_617_not__less0) ).
thf(606,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(242,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_541_eq__imp__le) ).
thf(1347,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(304,axiom,
! [A: $o,B: $o > arrow_1429601828e_indi > produc1501160679le_alt > $o,C: $o > $o,D: $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
( ( member1394214384_alt_o @ B @ ( pi_o_A1182933120_alt_o @ C @ D ) )
=> ( ~ ( member526088951_alt_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_PiE) ).
thf(1664,plain,
! [A: $o,B: $o > arrow_1429601828e_indi > produc1501160679le_alt > $o,C: $o > $o,D: $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
( ( member1394214384_alt_o @ B @ ( pi_o_A1182933120_alt_o @ C @ D ) )
=> ( ~ ( member526088951_alt_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(118,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
| ( ord_less_nat @ zero_zero_nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_624_add__gr__0) ).
thf(789,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) )
= ( ( ord_less_nat @ zero_zero_nat @ A )
| ( ord_less_nat @ zero_zero_nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(354,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a )
@ ( f
@ ^ [B: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ B ) @ A ) @ lab @ lba ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_n_I2_J) ).
thf(1811,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a )
@ ( f
@ ^ [B: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ B ) @ A ) @ lab @ lba ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(248,axiom,
finite664979089e_indi @ top_to988227749indi_o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_finite__indi) ).
thf(1373,plain,
finite664979089e_indi @ top_to988227749indi_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(179,axiom,
ord_less_nat @ n @ ( finite97476818e_indi @ top_to988227749indi_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_n_I1_J) ).
thf(1109,plain,
ord_less_nat @ n @ ( finite97476818e_indi @ top_to988227749indi_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(372,axiom,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
( ( arrow_1706409458nimity @ A )
= ( ! [B: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member526088951_alt_o @ B @ arrow_734252939e_Prof )
=> ! [C: arrow_475358991le_alt,D: arrow_475358991le_alt] :
( ! [E: arrow_1429601828e_indi] : ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ ( B @ E ) )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ ( A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_unanimity__def) ).
thf(1858,plain,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
( ( arrow_1706409458nimity @ A )
= ( ! [B: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member526088951_alt_o @ B @ arrow_734252939e_Prof )
=> ! [C: arrow_475358991le_alt,D: arrow_475358991le_alt] :
( ! [E: arrow_1429601828e_indi] : ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ ( B @ E ) )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ ( A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(42,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_not0__implies__Suc) ).
thf(514,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(124,axiom,
! [A: produc1501160679le_alt > $o] :
( ( member377231867_alt_o @ A @ arrow_823908191le_Lin )
=> ( member526088951_alt_o
@ ^ [B: arrow_1429601828e_indi] : A
@ arrow_734252939e_Prof ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_const__Lin__Prof) ).
thf(806,plain,
! [A: produc1501160679le_alt > $o] :
( ( member377231867_alt_o @ A @ arrow_823908191le_Lin )
=> ( member526088951_alt_o
@ ^ [B: arrow_1429601828e_indi] : A
@ arrow_734252939e_Prof ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(297,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ( plus_plus_nat @ A @ D )
= ( plus_plus_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_553_less__add__eq__less) ).
thf(1581,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ( plus_plus_nat @ A @ D )
= ( plus_plus_nat @ C @ B ) )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(265,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_le__neq__implies__less) ).
thf(1418,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(74,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_674_Zero__neq__Suc) ).
thf(623,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(187,axiom,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi > produc1501160679le_alt > $o,C: arrow_1429601828e_indi > $o,D: ( produc1501160679le_alt > $o ) > $o] :
( ( member526088951_alt_o @ B
@ ( pi_Arr1929480907_alt_o @ C
@ ^ [E: arrow_1429601828e_indi] : D ) )
=> ( ( member2052026769e_indi @ A @ C )
=> ( member377231867_alt_o @ ( B @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_funcset__mem) ).
thf(1136,plain,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi > produc1501160679le_alt > $o,C: arrow_1429601828e_indi > $o,D: ( produc1501160679le_alt > $o ) > $o] :
( ( member526088951_alt_o @ B
@ ( pi_Arr1929480907_alt_o @ C
@ ^ [E: arrow_1429601828e_indi] : D ) )
=> ( ( member2052026769e_indi @ A @ C )
=> ( member377231867_alt_o @ ( B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(134,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_not__leE) ).
thf(834,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(368,axiom,
! [A: arrow_1429601828e_indi,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
( ( member616898751_alt_o @ B
@ ( pi_Arr1304755663_alt_o @ arrow_734252939e_Prof
@ ^ [C: arrow_1429601828e_indi > produc1501160679le_alt > $o] : arrow_823908191le_Lin ) )
=> ( ! [C: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member526088951_alt_o @ C @ arrow_734252939e_Prof )
=> ! [D: arrow_475358991le_alt,E: arrow_475358991le_alt] :
( ( D != E )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ D @ E ) @ ( C @ A ) )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ D @ E ) @ ( B @ C ) ) ) ) )
=> ( arrow_1212662430ctator @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_dictatorI) ).
thf(1843,plain,
! [A: arrow_1429601828e_indi,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
( ( member616898751_alt_o @ B
@ ( pi_Arr1304755663_alt_o @ arrow_734252939e_Prof
@ ^ [C: arrow_1429601828e_indi > produc1501160679le_alt > $o] : arrow_823908191le_Lin ) )
=> ( ! [C: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member526088951_alt_o @ C @ arrow_734252939e_Prof )
=> ! [D: arrow_475358991le_alt,E: arrow_475358991le_alt] :
( ( D != E )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ D @ E ) @ ( C @ A ) )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ D @ E ) @ ( B @ C ) ) ) ) )
=> ( arrow_1212662430ctator @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(5,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_616_neq0__conv) ).
thf(397,plain,
! [A: nat] :
( ( A != zero_zero_nat )
= ( ord_less_nat @ zero_zero_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(96,axiom,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ( member616898751_alt_o @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_mem__def) ).
thf(734,plain,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ( member616898751_alt_o @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(25,axiom,
! [A: arrow_1429601828e_indi > nat,B: arrow_1429601828e_indi > $o] :
( ! [C: arrow_1429601828e_indi,D: arrow_1429601828e_indi] :
( ( member2052026769e_indi @ C @ B )
=> ( ( member2052026769e_indi @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on978774663di_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_inj__onI) ).
thf(453,plain,
! [A: arrow_1429601828e_indi > nat,B: arrow_1429601828e_indi > $o] :
( ! [C: arrow_1429601828e_indi,D: arrow_1429601828e_indi] :
( ( member2052026769e_indi @ C @ B )
=> ( ( member2052026769e_indi @ D @ B )
=> ( ( ( A @ C )
= ( A @ D ) )
=> ( C = D ) ) ) )
=> ( inj_on978774663di_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(112,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ? [C: nat] :
( B
= ( suc @ ( plus_plus_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_685_less__imp__Suc__add) ).
thf(774,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ? [C: nat] :
( B
= ( suc @ ( plus_plus_nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(256,axiom,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi > $o] :
( ( member2052026769e_indi @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_mem__def) ).
thf(1394,plain,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi > $o] :
( ( member2052026769e_indi @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(279,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_order__le__imp__less__or__eq) ).
thf(1526,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(243,axiom,
! [A: nat,B: nat > $o] :
( ~ ( B @ zero_zero_nat )
=> ( ( B @ A )
=> ? [C: nat] :
( ( ord_less_eq_nat @ C @ A )
& ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ~ ( B @ D ) )
& ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_626_ex__least__nat__le) ).
thf(1351,plain,
! [A: nat,B: nat > $o] :
( ~ ( B @ zero_zero_nat )
=> ( ( B @ A )
=> ? [C: nat] :
( ( ord_less_eq_nat @ C @ A )
& ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ~ ( B @ D ) )
& ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(10,axiom,
! [A: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,C: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ( member616898751_alt_o @ B @ C )
=> ( ( ord_le134800455lt_o_o @ C @ A )
=> ( member616898751_alt_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_476_set__rev__mp) ).
thf(411,plain,
! [A: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,C: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ( member616898751_alt_o @ B @ C )
=> ( ( ord_le134800455lt_o_o @ C @ A )
=> ( member616898751_alt_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(259,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_order__antisym__conv) ).
thf(1405,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)],[259]) ).
thf(213,axiom,
( ( image_484224243di_nat @ h @ top_to988227749indi_o )
= ( ord_at4362885an_nat @ zero_zero_nat @ ( finite97476818e_indi @ top_to988227749indi_o ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_696_surjh) ).
thf(1201,plain,
( ( image_484224243di_nat @ h @ top_to988227749indi_o )
= ( ord_at4362885an_nat @ zero_zero_nat @ ( finite97476818e_indi @ top_to988227749indi_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(231,axiom,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o,C: arrow_1429601828e_indi > $o] :
( ! [D: arrow_1429601828e_indi] :
( ( member2052026769e_indi @ D @ C )
=> ( member377231867_alt_o @ ( A @ D ) @ ( B @ D ) ) )
=> ( member526088951_alt_o @ A @ ( pi_Arr1929480907_alt_o @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_584_Pi__I_H) ).
thf(1242,plain,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o,C: arrow_1429601828e_indi > $o] :
( ! [D: arrow_1429601828e_indi] :
( ( member2052026769e_indi @ D @ C )
=> ( member377231867_alt_o @ ( A @ D ) @ ( B @ D ) ) )
=> ( member526088951_alt_o @ A @ ( pi_Arr1929480907_alt_o @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(219,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_557_less__imp__le__nat) ).
thf(1215,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(77,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_gr0__implies__Suc) ).
thf(634,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
=> ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(86,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
= ( ? [C: nat] :
( B
= ( plus_plus_nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_562_le__iff__add) ).
thf(661,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)],[86]) ).
thf(212,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_424_add__mono) ).
thf(1199,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(346,axiom,
~ ! [A: produc1501160679le_alt > $o] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a ) @ A )
=> ~ ( member377231867_alt_o @ A @ arrow_823908191le_Lin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_) ).
thf(1783,plain,
~ ! [A: produc1501160679le_alt > $o] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a ) @ A )
=> ~ ( member377231867_alt_o @ A @ arrow_823908191le_Lin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(41,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_637_Suc__leD) ).
thf(512,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(164,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_527_less__not__refl) ).
thf(942,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(20,axiom,
! [A: nat,B: nat] :
( ( ( suc @ zero_zero_nat )
= ( plus_plus_nat @ A @ B ) )
= ( ( ( A
= ( suc @ zero_zero_nat ) )
& ( B = zero_zero_nat ) )
| ( ( A = zero_zero_nat )
& ( B
= ( suc @ zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_one__is__add) ).
thf(439,plain,
! [A: nat,B: nat] :
( ( ( suc @ zero_zero_nat )
= ( plus_plus_nat @ A @ B ) )
= ( ( ( A
= ( suc @ zero_zero_nat ) )
& ( B = zero_zero_nat ) )
| ( ( A = zero_zero_nat )
& ( B
= ( suc @ zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(339,axiom,
arrow_1706409458nimity @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_u) ).
thf(1768,plain,
arrow_1706409458nimity @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(377,axiom,
member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( p @ ( hilber598459244di_nat @ top_to988227749indi_o @ h @ n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0) ).
thf(1868,plain,
member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( p @ ( hilber598459244di_nat @ top_to988227749indi_o @ h @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(324,axiom,
! [A: produc1501160679le_alt > $o,B: $o > $o,C: produc1501160679le_alt > $o] :
( ! [D: produc1501160679le_alt] :
( ( member214075476le_alt @ D @ C )
=> ( member_o @ ( A @ D ) @ B ) )
=> ( member377231867_alt_o @ A
@ ( pi_Pro1701359055_alt_o @ C
@ ^ [D: produc1501160679le_alt] : B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_576_funcsetI) ).
thf(1730,plain,
! [A: produc1501160679le_alt > $o,B: $o > $o,C: produc1501160679le_alt > $o] :
( ! [D: produc1501160679le_alt] :
( ( member214075476le_alt @ D @ C )
=> ( member_o @ ( A @ D ) @ B ) )
=> ( member377231867_alt_o @ A
@ ( pi_Pro1701359055_alt_o @ C
@ ^ [D: produc1501160679le_alt] : B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(197,axiom,
! [A: $o > produc1501160679le_alt,B: produc1501160679le_alt > $o,C: produc1501160679le_alt > $o,D: $o > $o] :
( ( member377231867_alt_o @ B
@ ( pi_Pro1701359055_alt_o @ C
@ ^ [E: produc1501160679le_alt] : D ) )
=> ( ( inj_on1911943593_alt_o @ B @ C )
=> ( ( member492167345le_alt @ A
@ ( pi_o_P657324555le_alt @ D
@ ^ [E: $o] : C ) )
=> ( ( inj_on867909093le_alt @ A @ D )
=> ( ( finite449174868le_alt @ C )
=> ( ( finite_finite_o @ D )
=> ( ( finite537683861le_alt @ C )
= ( finite_card_o @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_card__bij) ).
thf(1163,plain,
! [A: $o > produc1501160679le_alt,B: produc1501160679le_alt > $o,C: produc1501160679le_alt > $o,D: $o > $o] :
( ( member377231867_alt_o @ B
@ ( pi_Pro1701359055_alt_o @ C
@ ^ [E: produc1501160679le_alt] : D ) )
=> ( ( inj_on1911943593_alt_o @ B @ C )
=> ( ( member492167345le_alt @ A
@ ( pi_o_P657324555le_alt @ D
@ ^ [E: $o] : C ) )
=> ( ( inj_on867909093le_alt @ A @ D )
=> ( ( finite449174868le_alt @ C )
=> ( ( finite_finite_o @ D )
=> ( ( finite537683861le_alt @ C )
= ( finite_card_o @ D ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(321,axiom,
! [A: produc1501160679le_alt > $o > $o,B: produc1501160679le_alt > $o > $o,C: produc1501160679le_alt > $o] :
( ! [D: produc1501160679le_alt] :
( ( member214075476le_alt @ D @ C )
=> ( ord_less_eq_o_o @ ( A @ D ) @ ( B @ D ) ) )
=> ( ord_le1063113995lt_o_o @ ( pi_Pro1701359055_alt_o @ C @ A ) @ ( pi_Pro1701359055_alt_o @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_501_Pi__mono) ).
thf(1723,plain,
! [A: produc1501160679le_alt > $o > $o,B: produc1501160679le_alt > $o > $o,C: produc1501160679le_alt > $o] :
( ! [D: produc1501160679le_alt] :
( ( member214075476le_alt @ D @ C )
=> ( ord_less_eq_o_o @ ( A @ D ) @ ( B @ D ) ) )
=> ( ord_le1063113995lt_o_o @ ( pi_Pro1701359055_alt_o @ C @ A ) @ ( pi_Pro1701359055_alt_o @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(145,axiom,
! [A: produc1501160679le_alt > $o > $o,B: produc1501160679le_alt > $o,C: produc1501160679le_alt > $o] :
( ( ord_le97612146_alt_o @ B @ C )
=> ( ord_le1063113995lt_o_o @ ( pi_Pro1701359055_alt_o @ C @ A ) @ ( pi_Pro1701359055_alt_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_Pi__anti__mono) ).
thf(862,plain,
! [A: produc1501160679le_alt > $o > $o,B: produc1501160679le_alt > $o,C: produc1501160679le_alt > $o] :
( ( ord_le97612146_alt_o @ B @ C )
=> ( ord_le1063113995lt_o_o @ ( pi_Pro1701359055_alt_o @ C @ A ) @ ( pi_Pro1701359055_alt_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(202,axiom,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_one__reorient) ).
thf(1174,plain,
! [A: nat] :
( ( one_one_nat = A )
= ( A = one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(333,axiom,
! [A: arrow_475358991le_alt,B: arrow_475358991le_alt,C: produc1501160679le_alt > $o,D: arrow_475358991le_alt] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ ( arrow_2054445623_mkbot @ C @ D ) )
= ( ( B != D )
& ( ( A = D )
=> ( A != B ) )
& ( ( A != D )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_in__mkbot) ).
thf(1751,plain,
! [A: arrow_475358991le_alt,B: arrow_475358991le_alt,C: produc1501160679le_alt > $o,D: arrow_475358991le_alt] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ ( arrow_2054445623_mkbot @ C @ D ) )
= ( ( B != D )
& ( ( A = D )
=> ( A != B ) )
& ( ( A != D )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(382,axiom,
( ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( f @ p ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d )
@ ( f
@ ^ [A: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ A ) @ n ) @ ( arrow_55669061_mktop @ ( p @ A ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ A )
= n )
@ ( arrow_789600939_above @ ( p @ A ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ A ) @ e ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_PW) ).
thf(1883,plain,
( ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( f @ p ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d )
@ ( f
@ ^ [A: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ A ) @ n ) @ ( arrow_55669061_mktop @ ( p @ A ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ A )
= n )
@ ( arrow_789600939_above @ ( p @ A ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ A ) @ e ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(131,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_order__trans) ).
thf(825,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(241,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_less__imp__neq) ).
thf(1343,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(220,axiom,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi > produc1501160679le_alt > $o,C: arrow_1429601828e_indi > $o,D: arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o] :
( ( member526088951_alt_o @ B @ ( pi_Arr1929480907_alt_o @ C @ D ) )
=> ( ( member2052026769e_indi @ A @ C )
=> ( member377231867_alt_o @ ( B @ A ) @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_Pi__mem) ).
thf(1217,plain,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi > produc1501160679le_alt > $o,C: arrow_1429601828e_indi > $o,D: arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o] :
( ( member526088951_alt_o @ B @ ( pi_Arr1929480907_alt_o @ C @ D ) )
=> ( ( member2052026769e_indi @ A @ C )
=> ( member377231867_alt_o @ ( B @ A ) @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(66,axiom,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,C: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ( ord_le134800455lt_o_o @ B @ C )
=> ( ( member616898751_alt_o @ A @ B )
=> ( member616898751_alt_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_subsetD) ).
thf(598,plain,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,C: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ( ord_le134800455lt_o_o @ B @ C )
=> ( ( member616898751_alt_o @ A @ B )
=> ( member616898751_alt_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(359,axiom,
( ( member214075476le_alt @ ( produc1347929815le_alt @ c @ e )
@ ( f
@ ^ [A: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ A ) @ n ) @ ( arrow_55669061_mktop @ ( p @ A ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ A )
= n )
@ ( arrow_789600939_above @ ( p @ A ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ A ) @ e ) ) ) ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b )
@ ( f
@ ^ [A: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ A ) @ ( plus_plus_nat @ n @ one_one_nat ) ) @ lab @ lba ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am) ).
thf(1824,plain,
( ( member214075476le_alt @ ( produc1347929815le_alt @ c @ e )
@ ( f
@ ^ [A: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ A ) @ n ) @ ( arrow_55669061_mktop @ ( p @ A ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ A )
= n )
@ ( arrow_789600939_above @ ( p @ A ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ A ) @ e ) ) ) ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b )
@ ( f
@ ^ [A: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ A ) @ ( plus_plus_nat @ n @ one_one_nat ) ) @ lab @ lba ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(247,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_eq_nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_add__le__cancel__right) ).
thf(1370,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)],[247]) ).
thf(366,axiom,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: arrow_1429601828e_indi > produc1501160679le_alt > $o,C: arrow_475358991le_alt,D: arrow_475358991le_alt,E: arrow_475358991le_alt,F: arrow_475358991le_alt] :
( ( E != F )
=> ( ( C != D )
=> ( ( member526088951_alt_o @ B @ arrow_734252939e_Prof )
=> ( ( member526088951_alt_o @ A @ arrow_734252939e_Prof )
=> ( ! [G: arrow_1429601828e_indi] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ E @ F ) @ ( B @ G ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ ( A @ G ) ) )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ E @ F ) @ ( f @ B ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ ( f @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_pairwise__neutrality) ).
thf(1837,plain,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: arrow_1429601828e_indi > produc1501160679le_alt > $o,C: arrow_475358991le_alt,D: arrow_475358991le_alt,E: arrow_475358991le_alt,F: arrow_475358991le_alt] :
( ( E != F )
=> ( ( C != D )
=> ( ( member526088951_alt_o @ B @ arrow_734252939e_Prof )
=> ( ( member526088951_alt_o @ A @ arrow_734252939e_Prof )
=> ( ! [G: arrow_1429601828e_indi] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ E @ F ) @ ( B @ G ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ ( A @ G ) ) )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ E @ F ) @ ( f @ B ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ ( f @ A ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(141,axiom,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,D: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o] :
( ( member616898751_alt_o @ B @ ( pi_Arr1304755663_alt_o @ C @ D ) )
=> ( ~ ( member377231867_alt_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member526088951_alt_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_PiE) ).
thf(852,plain,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,D: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o] :
( ( member616898751_alt_o @ B @ ( pi_Arr1304755663_alt_o @ C @ D ) )
=> ( ~ ( member377231867_alt_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member526088951_alt_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(384,axiom,
! [A: produc1501160679le_alt > $o,B: produc1501160679le_alt > $o] :
( ( ord_le2080035663_alt_o
@ ^ [C: arrow_475358991le_alt,D: arrow_475358991le_alt] : ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ A )
@ ^ [C: arrow_475358991le_alt,D: arrow_475358991le_alt] : ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ B ) )
= ( ord_le97612146_alt_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_pred__subset__eq2) ).
thf(1888,plain,
! [A: produc1501160679le_alt > $o,B: produc1501160679le_alt > $o] :
( ( ord_le2080035663_alt_o
@ ^ [C: arrow_475358991le_alt,D: arrow_475358991le_alt] : ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ A )
@ ^ [C: arrow_475358991le_alt,D: arrow_475358991le_alt] : ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ B ) )
= ( ord_le97612146_alt_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(311,axiom,
! [A: produc1501160679le_alt > $o,B: ( produc1501160679le_alt > $o ) > $o,C: ( produc1501160679le_alt > $o ) > $o] :
( ( ord_le1063113995lt_o_o @ B @ C )
=> ( ( member377231867_alt_o @ A @ B )
=> ( member377231867_alt_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_484_in__mono) ).
thf(1687,plain,
! [A: produc1501160679le_alt > $o,B: ( produc1501160679le_alt > $o ) > $o,C: ( produc1501160679le_alt > $o ) > $o] :
( ( ord_le1063113995lt_o_o @ B @ C )
=> ( ( member377231867_alt_o @ A @ B )
=> ( member377231867_alt_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(26,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_less__antisym) ).
thf(461,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(347,axiom,
! [A: produc1501160679le_alt > $o,B: produc1501160679le_alt > $o > $o,C: produc1501160679le_alt > $o] :
( ! [D: produc1501160679le_alt] :
( ( member214075476le_alt @ D @ C )
=> ( member_o @ ( A @ D ) @ ( B @ D ) ) )
=> ( member377231867_alt_o @ A @ ( pi_Pro1701359055_alt_o @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_Pi__I) ).
thf(1787,plain,
! [A: produc1501160679le_alt > $o,B: produc1501160679le_alt > $o > $o,C: produc1501160679le_alt > $o] :
( ! [D: produc1501160679le_alt] :
( ( member214075476le_alt @ D @ C )
=> ( member_o @ ( A @ D ) @ ( B @ D ) ) )
=> ( member377231867_alt_o @ A @ ( pi_Pro1701359055_alt_o @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(35,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_673_Suc__neq__Zero) ).
thf(493,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(185,axiom,
! [A: produc1501160679le_alt > $o,B: ( produc1501160679le_alt > $o ) > $o] :
( ( member377231867_alt_o @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_mem__def) ).
thf(1128,plain,
! [A: produc1501160679le_alt > $o,B: ( produc1501160679le_alt > $o ) > $o] :
( ( member377231867_alt_o @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(255,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_termination__basic__simps_I4_J) ).
thf(1392,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(178,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_xt1_I12_J) ).
thf(1106,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(155,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_xt1_I6_J) ).
thf(916,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(28,axiom,
! [A: nat,B: nat > $o] :
( ( B @ zero_zero_nat )
=> ( ! [C: nat] :
( ( B @ C )
=> ( B @ ( suc @ C ) ) )
=> ( B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_nat__induct) ).
thf(467,plain,
! [A: nat,B: nat > $o] :
( ( B @ zero_zero_nat )
=> ( ! [C: nat] :
( ( B @ C )
=> ( B @ ( suc @ C ) ) )
=> ( B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(56,axiom,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_619_Nat_Oadd__0__right) ).
thf(566,plain,
! [A: nat] :
( ( plus_plus_nat @ A @ zero_zero_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(32,axiom,
! [A: nat] : ( ord_less_nat @ A @ ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_628_lessI) ).
thf(484,plain,
! [A: nat] : ( ord_less_nat @ A @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(150,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_549_trans__less__add1) ).
thf(874,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(94,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
= ( ord_less_eq_nat @ ( suc @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_663_less__eq__Suc__le) ).
thf(725,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
= ( ord_less_eq_nat @ ( suc @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(7,axiom,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi,C: arrow_1429601828e_indi > nat] :
( ( inj_on978774663di_nat @ C @ top_to988227749indi_o )
=> ( ( ( C @ A )
= ( C @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_injD) ).
thf(403,plain,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi,C: arrow_1429601828e_indi > nat] :
( ( inj_on978774663di_nat @ C @ top_to988227749indi_o )
=> ( ( ( C @ A )
= ( C @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(306,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_nat__add__left__cancel__less) ).
thf(1672,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(284,axiom,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,C: arrow_1429601828e_indi > $o,D: arrow_1429601828e_indi > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ( member811956313_alt_o @ B @ ( pi_Arr1564509167_alt_o @ C @ D ) )
=> ( ~ ( member616898751_alt_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member2052026769e_indi @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_PiE) ).
thf(1540,plain,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,C: arrow_1429601828e_indi > $o,D: arrow_1429601828e_indi > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ( member811956313_alt_o @ B @ ( pi_Arr1564509167_alt_o @ C @ D ) )
=> ( ~ ( member616898751_alt_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member2052026769e_indi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(381,axiom,
! [A: produc1501160679le_alt > $o > $o,B: produc1501160679le_alt > $o,C: produc1501160679le_alt > $o,D: produc1501160679le_alt > $o] :
( ! [E: produc1501160679le_alt] :
( ( member214075476le_alt @ E @ D )
=> ( ( C @ E )
= ( B @ E ) ) )
=> ( ( member377231867_alt_o @ C @ ( pi_Pro1701359055_alt_o @ D @ A ) )
= ( member377231867_alt_o @ B @ ( pi_Pro1701359055_alt_o @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_Pi__cong) ).
thf(1878,plain,
! [A: produc1501160679le_alt > $o > $o,B: produc1501160679le_alt > $o,C: produc1501160679le_alt > $o,D: produc1501160679le_alt > $o] :
( ! [E: produc1501160679le_alt] :
( ( member214075476le_alt @ E @ D )
=> ( ( C @ E )
= ( B @ E ) ) )
=> ( ( member377231867_alt_o @ C @ ( pi_Pro1701359055_alt_o @ D @ A ) )
= ( member377231867_alt_o @ B @ ( pi_Pro1701359055_alt_o @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(188,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_le__eq__less__or__eq) ).
thf(1138,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(64,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_635_le__SucI) ).
thf(593,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(148,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_linorder__le__cases) ).
thf(869,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)],[148]) ).
thf(257,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ? [C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
& ( ( plus_plus_nat @ A @ C )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_627_less__imp__add__positive) ).
thf(1397,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ? [C: nat] :
( ( ord_less_nat @ zero_zero_nat @ C )
& ( ( plus_plus_nat @ A @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(99,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_order__less__asym_H) ).
thf(742,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(59,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_634_Suc__le__mono) ).
thf(578,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(115,axiom,
! [A: nat,B: nat] : ( ord_less_nat @ A @ ( suc @ ( plus_plus_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_666_less__add__Suc1) ).
thf(783,plain,
! [A: nat,B: nat] : ( ord_less_nat @ A @ ( suc @ ( plus_plus_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(182,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_add__imp__eq) ).
thf(1118,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)],[182]) ).
thf(302,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_xt1_I10_J) ).
thf(1659,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(328,axiom,
! [A: produc1501160679le_alt > $o,B: produc1501160679le_alt,C: produc1501160679le_alt > $o] :
( ( member214075476le_alt @ B @ C )
=> ( ( ord_le97612146_alt_o @ C @ A )
=> ( member214075476le_alt @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_478_set__rev__mp) ).
thf(1739,plain,
! [A: produc1501160679le_alt > $o,B: produc1501160679le_alt,C: produc1501160679le_alt > $o] :
( ( member214075476le_alt @ B @ C )
=> ( ( ord_le97612146_alt_o @ C @ A )
=> ( member214075476le_alt @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(29,axiom,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_623_less__eq__nat_Osimps_I1_J) ).
thf(476,plain,
! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(353,axiom,
( member526088951_alt_o
@ ^ [A: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ A ) @ n ) @ ( arrow_55669061_mktop @ ( p @ A ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ A )
= n )
@ ( arrow_789600939_above @ ( p @ A ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ A ) @ e ) ) )
@ arrow_734252939e_Prof ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai) ).
thf(1810,plain,
( member526088951_alt_o
@ ^ [A: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ A ) @ n ) @ ( arrow_55669061_mktop @ ( p @ A ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ A )
= n )
@ ( arrow_789600939_above @ ( p @ A ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ A ) @ e ) ) )
@ arrow_734252939e_Prof ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(216,axiom,
! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_less__add__one) ).
thf(1207,plain,
! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(78,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_Suc__less__SucD) ).
thf(637,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(298,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_565_trans__le__add2) ).
thf(1584,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(50,axiom,
! [A: nat] :
~ ( ord_less_eq_nat @ ( suc @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_631_Suc__n__not__le__n) ).
thf(547,plain,
! [A: nat] :
~ ( ord_less_eq_nat @ ( suc @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(330,axiom,
c != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096c_A_126_061_Ad_096) ).
thf(1744,plain,
c != d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(176,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( B = A )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_xt1_I2_J) ).
thf(1099,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( B = A )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(192,axiom,
! [A: produc1501160679le_alt > $o] : ( ord_le97612146_alt_o @ A @ top_to1841428258_alt_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_top__greatest) ).
thf(1150,plain,
! [A: produc1501160679le_alt > $o] : ( ord_le97612146_alt_o @ A @ top_to1841428258_alt_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(252,axiom,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( produc1501160679le_alt > $o ) > $o,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
( ! [D: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member526088951_alt_o @ D @ C )
=> ( member377231867_alt_o @ ( A @ D ) @ B ) )
=> ( member616898751_alt_o @ A
@ ( pi_Arr1304755663_alt_o @ C
@ ^ [D: arrow_1429601828e_indi > produc1501160679le_alt > $o] : B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_578_funcsetI) ).
thf(1382,plain,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( produc1501160679le_alt > $o ) > $o,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
( ! [D: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member526088951_alt_o @ D @ C )
=> ( member377231867_alt_o @ ( A @ D ) @ B ) )
=> ( member616898751_alt_o @ A
@ ( pi_Arr1304755663_alt_o @ C
@ ^ [D: arrow_1429601828e_indi > produc1501160679le_alt > $o] : B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(186,axiom,
! [A: arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o,B: arrow_1429601828e_indi > produc1501160679le_alt > $o,C: arrow_1429601828e_indi > produc1501160679le_alt > $o,D: arrow_1429601828e_indi > $o] :
( ! [E: arrow_1429601828e_indi] :
( ( member2052026769e_indi @ E @ D )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( member526088951_alt_o @ B @ ( pi_Arr1929480907_alt_o @ D @ A ) )
= ( member526088951_alt_o @ C @ ( pi_Arr1929480907_alt_o @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_581_Pi__cong) ).
thf(1131,plain,
! [A: arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o,B: arrow_1429601828e_indi > produc1501160679le_alt > $o,C: arrow_1429601828e_indi > produc1501160679le_alt > $o,D: arrow_1429601828e_indi > $o] :
( ! [E: arrow_1429601828e_indi] :
( ( member2052026769e_indi @ E @ D )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( member526088951_alt_o @ B @ ( pi_Arr1929480907_alt_o @ D @ A ) )
= ( member526088951_alt_o @ C @ ( pi_Arr1929480907_alt_o @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(209,axiom,
! [A: produc1501160679le_alt > $o,B: ( produc1501160679le_alt > $o ) > $o,C: ( produc1501160679le_alt > $o ) > $o,D: ( produc1501160679le_alt > $o ) > $o > $o] :
( ( member1961363906lt_o_o @ B @ ( pi_Pro422690258lt_o_o @ C @ D ) )
=> ( ~ ( member_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member377231867_alt_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_PiE) ).
thf(1192,plain,
! [A: produc1501160679le_alt > $o,B: ( produc1501160679le_alt > $o ) > $o,C: ( produc1501160679le_alt > $o ) > $o,D: ( produc1501160679le_alt > $o ) > $o > $o] :
( ( member1961363906lt_o_o @ B @ ( pi_Pro422690258lt_o_o @ C @ D ) )
=> ( ~ ( member_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member377231867_alt_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(153,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_574_termination__basic__simps_I5_J) ).
thf(911,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(370,axiom,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: arrow_1429601828e_indi > produc1501160679le_alt > $o,C: arrow_475358991le_alt,D: arrow_475358991le_alt] :
( ( C != D )
=> ( ( member526088951_alt_o @ B @ arrow_734252939e_Prof )
=> ( ( member526088951_alt_o @ A @ arrow_734252939e_Prof )
=> ( ! [E: arrow_1429601828e_indi] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ ( B @ E ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ D @ C ) @ ( A @ E ) ) )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ ( f @ B ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ D @ C ) @ ( f @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__C3_C) ).
thf(1852,plain,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: arrow_1429601828e_indi > produc1501160679le_alt > $o,C: arrow_475358991le_alt,D: arrow_475358991le_alt] :
( ( C != D )
=> ( ( member526088951_alt_o @ B @ arrow_734252939e_Prof )
=> ( ( member526088951_alt_o @ A @ arrow_734252939e_Prof )
=> ( ! [E: arrow_1429601828e_indi] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ ( B @ E ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ D @ C ) @ ( A @ E ) ) )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ ( f @ B ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ D @ C ) @ ( f @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(380,axiom,
~ ! [A: produc1501160679le_alt > $o] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ A )
=> ~ ( member377231867_alt_o @ A @ arrow_823908191le_Lin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_) ).
thf(1874,plain,
~ ! [A: produc1501160679le_alt > $o] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ A )
=> ~ ( member377231867_alt_o @ A @ arrow_823908191le_Lin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(57,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_Suc__not__Zero) ).
thf(569,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(320,axiom,
! [A: produc1501160679le_alt > $o] :
( ( all @ A )
= ( ! [B: arrow_475358991le_alt,C: arrow_475358991le_alt] : ( A @ ( produc1347929815le_alt @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_split__paired__All) ).
thf(1720,plain,
! [A: produc1501160679le_alt > $o] :
( ( all @ A )
= ( ! [B: arrow_475358991le_alt,C: arrow_475358991le_alt] : ( A @ ( produc1347929815le_alt @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(38,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_add__is__0) ).
thf(503,plain,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( B = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(81,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_540_nat__le__linear) ).
thf(647,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)],[81]) ).
thf(343,axiom,
! [A: produc1501160679le_alt,B: produc1501160679le_alt > $o,C: produc1501160679le_alt > $o,D: produc1501160679le_alt > $o > $o] :
( ( member377231867_alt_o @ B @ ( pi_Pro1701359055_alt_o @ C @ D ) )
=> ( ( member214075476le_alt @ A @ C )
=> ( member_o @ ( B @ A ) @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_372_Pi__mem) ).
thf(1776,plain,
! [A: produc1501160679le_alt,B: produc1501160679le_alt > $o,C: produc1501160679le_alt > $o,D: produc1501160679le_alt > $o > $o] :
( ( member377231867_alt_o @ B @ ( pi_Pro1701359055_alt_o @ C @ D ) )
=> ( ( member214075476le_alt @ A @ C )
=> ( member_o @ ( B @ A ) @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(363,axiom,
! [A: produc1501160679le_alt] : ( member214075476le_alt @ A @ top_to1841428258_alt_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_iso__tuple__UNIV__I) ).
thf(1831,plain,
! [A: produc1501160679le_alt] : ( member214075476le_alt @ A @ top_to1841428258_alt_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(226,axiom,
! [A: product_unit,B: product_unit > produc1501160679le_alt > $o,C: product_unit > $o,D: product_unit > ( produc1501160679le_alt > $o ) > $o] :
( ( member1661784200_alt_o @ B @ ( pi_Pro1312660828_alt_o @ C @ D ) )
=> ( ~ ( member377231867_alt_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member_Product_unit @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_PiE) ).
thf(1231,plain,
! [A: product_unit,B: product_unit > produc1501160679le_alt > $o,C: product_unit > $o,D: product_unit > ( produc1501160679le_alt > $o ) > $o] :
( ( member1661784200_alt_o @ B @ ( pi_Pro1312660828_alt_o @ C @ D ) )
=> ( ~ ( member377231867_alt_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member_Product_unit @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(119,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_order__less__imp__le) ).
thf(792,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(162,axiom,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi > arrow_1429601828e_indi > produc1501160679le_alt > $o,C: arrow_1429601828e_indi > $o,D: arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
( ( member1234151027_alt_o @ B @ ( pi_Arr1060328391_alt_o @ C @ D ) )
=> ( ~ ( member526088951_alt_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member2052026769e_indi @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_PiE) ).
thf(938,plain,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi > arrow_1429601828e_indi > produc1501160679le_alt > $o,C: arrow_1429601828e_indi > $o,D: arrow_1429601828e_indi > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
( ( member1234151027_alt_o @ B @ ( pi_Arr1060328391_alt_o @ C @ D ) )
=> ( ~ ( member526088951_alt_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member2052026769e_indi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(314,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( C = A )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_ord__less__eq__trans) ).
thf(1695,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( C = A )
=> ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(48,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_647_Suc__less__eq) ).
thf(541,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ ( suc @ B ) )
= ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(200,axiom,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > product_unit,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,D: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > product_unit > $o] :
( ( member843528338t_unit @ B @ ( pi_Arr1963174508t_unit @ C @ D ) )
=> ( ~ ( member_Product_unit @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member526088951_alt_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_PiE) ).
thf(1170,plain,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > product_unit,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,D: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > product_unit > $o] :
( ( member843528338t_unit @ B @ ( pi_Arr1963174508t_unit @ C @ D ) )
=> ( ~ ( member_Product_unit @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member526088951_alt_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(207,axiom,
! [A: nat > arrow_1429601828e_indi,B: arrow_1429601828e_indi > nat] :
( ( inj_on978774663di_nat @ B @ top_to988227749indi_o )
=> ( ! [C: nat] :
( ( B @ ( A @ C ) )
= C )
=> ( ( hilber598459244di_nat @ top_to988227749indi_o @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_inj__imp__inv__eq) ).
thf(1187,plain,
! [A: nat > arrow_1429601828e_indi,B: arrow_1429601828e_indi > nat] :
( ( inj_on978774663di_nat @ B @ top_to988227749indi_o )
=> ( ! [C: nat] :
( ( B @ ( A @ C ) )
= C )
=> ( ( hilber598459244di_nat @ top_to988227749indi_o @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(275,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_eq_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526_add__leD2) ).
thf(1515,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_eq_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(387,axiom,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: arrow_1429601828e_indi > produc1501160679le_alt > $o,C: arrow_475358991le_alt,D: arrow_475358991le_alt,E: arrow_475358991le_alt,F: arrow_475358991le_alt] :
( ( E != F )
=> ( ( C != D )
=> ( ( E != D )
=> ( ( F != C )
=> ( ( member526088951_alt_o @ B @ arrow_734252939e_Prof )
=> ( ( member526088951_alt_o @ A @ arrow_734252939e_Prof )
=> ( ! [G: arrow_1429601828e_indi] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ E @ F ) @ ( B @ G ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ ( A @ G ) ) )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ E @ F ) @ ( f @ B ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ ( f @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__C2_C) ).
thf(1895,plain,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: arrow_1429601828e_indi > produc1501160679le_alt > $o,C: arrow_475358991le_alt,D: arrow_475358991le_alt,E: arrow_475358991le_alt,F: arrow_475358991le_alt] :
( ( E != F )
=> ( ( C != D )
=> ( ( E != D )
=> ( ( F != C )
=> ( ( member526088951_alt_o @ B @ arrow_734252939e_Prof )
=> ( ( member526088951_alt_o @ A @ arrow_734252939e_Prof )
=> ( ! [G: arrow_1429601828e_indi] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ E @ F ) @ ( B @ G ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ ( A @ G ) ) )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ E @ F ) @ ( f @ B ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ C @ D ) @ ( f @ A ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(120,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
= ( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_order__less__le) ).
thf(794,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
= ( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(91,axiom,
! [A: produc1501160679le_alt > $o,B: ( produc1501160679le_alt > $o ) > $o,C: ( produc1501160679le_alt > $o ) > $o] :
( ( ord_le1063113995lt_o_o @ B @ C )
=> ( ( member377231867_alt_o @ A @ B )
=> ( member377231867_alt_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_set__mp) ).
thf(718,plain,
! [A: produc1501160679le_alt > $o,B: ( produc1501160679le_alt > $o ) > $o,C: ( produc1501160679le_alt > $o ) > $o] :
( ( ord_le1063113995lt_o_o @ B @ C )
=> ( ( member377231867_alt_o @ A @ B )
=> ( member377231867_alt_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(158,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( B != A )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_xt1_I11_J) ).
thf(926,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( B != A )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(323,axiom,
! [A: arrow_1429601828e_indi] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( p @ A ) )
= ( ( ( ord_less_nat @ ( h @ A ) @ n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( arrow_55669061_mktop @ ( p @ A ) @ e ) ) )
& ( ~ ( ord_less_nat @ ( h @ A ) @ n )
=> ( ( ( ( h @ A )
= n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( arrow_789600939_above @ ( p @ A ) @ c @ e ) ) )
& ( ( ( h @ A )
!= n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( arrow_2054445623_mkbot @ ( p @ A ) @ e ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J) ).
thf(1727,plain,
! [A: arrow_1429601828e_indi] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( p @ A ) )
= ( ( ( ord_less_nat @ ( h @ A ) @ n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( arrow_55669061_mktop @ ( p @ A ) @ e ) ) )
& ( ~ ( ord_less_nat @ ( h @ A ) @ n )
=> ( ( ( ( h @ A )
= n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( arrow_789600939_above @ ( p @ A ) @ c @ e ) ) )
& ( ( ( h @ A )
!= n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( arrow_2054445623_mkbot @ ( p @ A ) @ e ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(15,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ C @ A )
=> ( ord_less_nat @ ( suc @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_less__trans__Suc) ).
thf(425,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ C @ A )
=> ( ord_less_nat @ ( suc @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(177,axiom,
! [A: product_unit,B: product_unit > $o] :
( ( member_Product_unit @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_mem__def) ).
thf(1103,plain,
! [A: product_unit,B: product_unit > $o] :
( ( member_Product_unit @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(221,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ( ord_less_nat @ B @ A )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_not__less__iff__gr__or__eq) ).
thf(1219,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ( ord_less_nat @ B @ A )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(331,axiom,
arrow_797024463le_IIA @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I3_J) ).
thf(1747,plain,
arrow_797024463le_IIA @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(58,axiom,
! [A: arrow_1429601828e_indi > nat,B: arrow_1429601828e_indi > nat,C: arrow_1429601828e_indi > $o] :
( ! [D: arrow_1429601828e_indi] :
( ( member2052026769e_indi @ D @ C )
=> ( ( A @ D )
= ( B @ D ) ) )
=> ( ( inj_on978774663di_nat @ A @ C )
= ( inj_on978774663di_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_594_inj__on__cong) ).
thf(573,plain,
! [A: arrow_1429601828e_indi > nat,B: arrow_1429601828e_indi > nat,C: arrow_1429601828e_indi > $o] :
( ! [D: arrow_1429601828e_indi] :
( ( member2052026769e_indi @ D @ C )
=> ( ( A @ D )
= ( B @ D ) ) )
=> ( ( inj_on978774663di_nat @ A @ C )
= ( inj_on978774663di_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(249,axiom,
! [A: arrow_1429601828e_indi] : ( member2052026769e_indi @ A @ top_to988227749indi_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_UNIV__I) ).
thf(1374,plain,
! [A: arrow_1429601828e_indi] : ( member2052026769e_indi @ A @ top_to988227749indi_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(334,axiom,
! [A: arrow_475358991le_alt,B: arrow_475358991le_alt,C: produc1501160679le_alt > $o] :
( ( member377231867_alt_o @ C @ arrow_823908191le_Lin )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ C )
=> ~ ( member214075476le_alt @ ( produc1347929815le_alt @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_Lin__irrefl) ).
thf(1754,plain,
! [A: arrow_475358991le_alt,B: arrow_475358991le_alt,C: produc1501160679le_alt > $o] :
( ( member377231867_alt_o @ C @ arrow_823908191le_Lin )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ C )
=> ~ ( member214075476le_alt @ ( produc1347929815le_alt @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(17,axiom,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_678_Zero__not__Suc) ).
thf(430,plain,
! [A: nat] :
( zero_zero_nat
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(129,axiom,
! [A: arrow_1429601828e_indi,B: nat,C: arrow_1429601828e_indi > nat] :
( ( inj_on978774663di_nat @ C @ top_to988227749indi_o )
=> ( ( ( C @ A )
= B )
=> ( ( hilber598459244di_nat @ top_to988227749indi_o @ C @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_inv__f__eq) ).
thf(819,plain,
! [A: arrow_1429601828e_indi,B: nat,C: arrow_1429601828e_indi > nat] :
( ( inj_on978774663di_nat @ C @ top_to988227749indi_o )
=> ( ( ( C @ A )
= B )
=> ( ( hilber598459244di_nat @ top_to988227749indi_o @ C @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(364,axiom,
! [A: produc1501160679le_alt,B: produc1501160679le_alt > product_unit,C: produc1501160679le_alt > $o,D: produc1501160679le_alt > product_unit > $o] :
( ( member593902749t_unit @ B @ ( pi_Pro1475896499t_unit @ C @ D ) )
=> ( ~ ( member_Product_unit @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member214075476le_alt @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_PiE) ).
thf(1833,plain,
! [A: produc1501160679le_alt,B: produc1501160679le_alt > product_unit,C: produc1501160679le_alt > $o,D: produc1501160679le_alt > product_unit > $o] :
( ( member593902749t_unit @ B @ ( pi_Pro1475896499t_unit @ C @ D ) )
=> ( ~ ( member_Product_unit @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member214075476le_alt @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(14,axiom,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,C: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ( ord_le134800455lt_o_o @ B @ C )
=> ( ( member616898751_alt_o @ A @ B )
=> ( member616898751_alt_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_set__mp) ).
thf(423,plain,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,C: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ( ord_le134800455lt_o_o @ B @ C )
=> ( ( member616898751_alt_o @ A @ B )
=> ( member616898751_alt_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(137,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_eq_nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_525_add__leD1) ).
thf(843,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_eq_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(111,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_leD) ).
thf(772,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(316,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_Suc__le__lessD) ).
thf(1701,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(277,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_order__less__irrefl) ).
thf(1520,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(11,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_Suc__lessE) ).
thf(413,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(61,axiom,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_gr0__conv__Suc) ).
thf(584,plain,
! [A: nat] :
( ( ord_less_nat @ zero_zero_nat @ A )
= ( ? [B: nat] :
( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(194,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_order__less__imp__not__eq) ).
thf(1154,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(237,axiom,
? [A: produc1501160679le_alt > $o] : ( member377231867_alt_o @ A @ arrow_823908191le_Lin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_linear__alt) ).
thf(1256,plain,
? [A: produc1501160679le_alt > $o] : ( member377231867_alt_o @ A @ arrow_823908191le_Lin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(224,axiom,
! [A: produc1501160679le_alt > $o,B: produc1501160679le_alt > $o,C: $o > $o] :
( ( member377231867_alt_o @ A
@ ( pi_Pro1701359055_alt_o @ B
@ ^ [D: produc1501160679le_alt] : C ) )
=> ( ( inj_on1911943593_alt_o @ A @ B )
=> ( ( finite_finite_o @ C )
=> ( ord_less_eq_nat @ ( finite537683861le_alt @ B ) @ ( finite_card_o @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_card__inj) ).
thf(1226,plain,
! [A: produc1501160679le_alt > $o,B: produc1501160679le_alt > $o,C: $o > $o] :
( ( member377231867_alt_o @ A
@ ( pi_Pro1701359055_alt_o @ B
@ ^ [D: produc1501160679le_alt] : C ) )
=> ( ( inj_on1911943593_alt_o @ A @ B )
=> ( ( finite_finite_o @ C )
=> ( ord_less_eq_nat @ ( finite537683861le_alt @ B ) @ ( finite_card_o @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(3,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_615_less__nat__zero__code) ).
thf(391,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(305,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
= ( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_555_nat__less__le) ).
thf(1669,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
= ( ( ord_less_eq_nat @ A @ B )
& ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(22,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ord_less_eq_nat @ ( suc @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_632_not__less__eq__eq) ).
thf(445,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ord_less_eq_nat @ ( suc @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(117,axiom,
! [A: produc1501160679le_alt > $o,B: ( produc1501160679le_alt > $o ) > $o,C: ( produc1501160679le_alt > $o ) > $o] :
( ( ord_le910298367lt_o_o @ B @ C )
=> ( ( member377231867_alt_o @ A @ B )
=> ( member377231867_alt_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_516_psubsetD) ).
thf(787,plain,
! [A: produc1501160679le_alt > $o,B: ( produc1501160679le_alt > $o ) > $o,C: ( produc1501160679le_alt > $o ) > $o] :
( ( ord_le910298367lt_o_o @ B @ C )
=> ( ( member377231867_alt_o @ A @ B )
=> ( member377231867_alt_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(375,axiom,
! [A: produc1501160679le_alt,B: produc1501160679le_alt > $o,C: produc1501160679le_alt > $o] :
( ( ord_le988258430_alt_o @ B @ C )
=> ( ( member214075476le_alt @ A @ B )
=> ( member214075476le_alt @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_519_psubsetD) ).
thf(1865,plain,
! [A: produc1501160679le_alt,B: produc1501160679le_alt > $o,C: produc1501160679le_alt > $o] :
( ( ord_le988258430_alt_o @ B @ C )
=> ( ( member214075476le_alt @ A @ B )
=> ( member214075476le_alt @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(325,axiom,
! [A: product_unit,B: product_unit > produc1501160679le_alt,C: product_unit > $o,D: product_unit > produc1501160679le_alt > $o] :
( ( member495332125le_alt @ B @ ( pi_Pro701847987le_alt @ C @ D ) )
=> ( ~ ( member214075476le_alt @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member_Product_unit @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_PiE) ).
thf(1733,plain,
! [A: product_unit,B: product_unit > produc1501160679le_alt,C: product_unit > $o,D: product_unit > produc1501160679le_alt > $o] :
( ( member495332125le_alt @ B @ ( pi_Pro701847987le_alt @ C @ D ) )
=> ( ~ ( member214075476le_alt @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member_Product_unit @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(173,axiom,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
( ! [D: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member526088951_alt_o @ D @ C )
=> ( member377231867_alt_o @ ( A @ D ) @ ( B @ D ) ) )
=> ( member616898751_alt_o @ A @ ( pi_Arr1304755663_alt_o @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_Pi__I) ).
thf(1092,plain,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
( ! [D: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member526088951_alt_o @ D @ C )
=> ( member377231867_alt_o @ ( A @ D ) @ ( B @ D ) ) )
=> ( member616898751_alt_o @ A @ ( pi_Arr1304755663_alt_o @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(238,axiom,
! [A: $o,B: $o > $o,C: $o > $o] :
( ( ord_less_eq_o_o @ B @ C )
=> ( ( member_o @ A @ B )
=> ( member_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_463_set__mp) ).
thf(1258,plain,
! [A: $o,B: $o > $o,C: $o > $o] :
( ( ord_less_eq_o_o @ B @ C )
=> ( ( member_o @ A @ B )
=> ( member_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(223,axiom,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi,C: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,D: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o] :
( ( member1452482393e_indi @ B @ ( pi_Arr338314351e_indi @ C @ D ) )
=> ( ~ ( member2052026769e_indi @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member616898751_alt_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_PiE) ).
thf(1224,plain,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi,C: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,D: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o] :
( ( member1452482393e_indi @ B @ ( pi_Arr338314351e_indi @ C @ D ) )
=> ( ~ ( member2052026769e_indi @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member616898751_alt_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(307,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( ord_less_nat @ C @ A )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_ord__eq__less__trans) ).
thf(1675,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( ord_less_nat @ C @ A )
=> ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(338,axiom,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: arrow_1429601828e_indi > produc1501160679le_alt > $o,C: arrow_475358991le_alt,D: arrow_475358991le_alt,E: arrow_475358991le_alt] :
( ( D != E )
=> ( ( E != C )
=> ( ( D != C )
=> ( ( member526088951_alt_o @ B @ arrow_734252939e_Prof )
=> ( ( member526088951_alt_o @ A @ arrow_734252939e_Prof )
=> ( ! [F: arrow_1429601828e_indi] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ D @ E ) @ ( B @ F ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ E @ C ) @ ( A @ F ) ) )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ D @ E ) @ ( f @ B ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ E @ C ) @ ( f @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__C4_C) ).
thf(1765,plain,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: arrow_1429601828e_indi > produc1501160679le_alt > $o,C: arrow_475358991le_alt,D: arrow_475358991le_alt,E: arrow_475358991le_alt] :
( ( D != E )
=> ( ( E != C )
=> ( ( D != C )
=> ( ( member526088951_alt_o @ B @ arrow_734252939e_Prof )
=> ( ( member526088951_alt_o @ A @ arrow_734252939e_Prof )
=> ( ! [F: arrow_1429601828e_indi] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ D @ E ) @ ( B @ F ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ E @ C ) @ ( A @ F ) ) )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ D @ E ) @ ( f @ B ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ E @ C ) @ ( f @ A ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(172,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_570_termination__basic__simps_I3_J) ).
thf(1090,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ B @ ( plus_plus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(108,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
= ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_661_Suc__le__eq) ).
thf(764,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
= ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(210,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_561_le__add1) ).
thf(1194,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(217,axiom,
! [A: produc1501160679le_alt > $o] :
~ ( ord_le988258430_alt_o @ top_to1841428258_alt_o @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_not__top__less) ).
thf(1209,plain,
! [A: produc1501160679le_alt > $o] :
~ ( ord_le988258430_alt_o @ top_to1841428258_alt_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(8,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_Suc__lessD) ).
thf(406,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ ( suc @ A ) @ B )
=> ( ord_less_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(133,axiom,
! [A: $o] : ( member_o @ A @ top_top_o_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_UNIV__I) ).
thf(831,plain,
! [A: $o] : ( member_o @ A @ top_top_o_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(260,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
=> ( ord_less_eq_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_422_add__le__imp__le__left) ).
thf(1408,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)],[260]) ).
thf(285,axiom,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75__096a_A_126_061_Ab_096) ).
thf(1542,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(190,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_nat__add__commute) ).
thf(1144,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(97,axiom,
! [A: arrow_1429601828e_indi] : ( member2052026769e_indi @ A @ top_to988227749indi_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_iso__tuple__UNIV__I) ).
thf(737,plain,
! [A: arrow_1429601828e_indi] : ( member2052026769e_indi @ A @ top_to988227749indi_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(183,axiom,
! [A: nat,B: arrow_1429601828e_indi,C: arrow_1429601828e_indi > nat,D: arrow_1429601828e_indi > $o] :
( ( inj_on978774663di_nat @ C @ D )
=> ( ( member2052026769e_indi @ B @ D )
=> ( ( ( C @ B )
= A )
=> ( ( hilber598459244di_nat @ D @ C @ A )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_inv__into__f__eq) ).
thf(1122,plain,
! [A: nat,B: arrow_1429601828e_indi,C: arrow_1429601828e_indi > nat,D: arrow_1429601828e_indi > $o] :
( ( inj_on978774663di_nat @ C @ D )
=> ( ( member2052026769e_indi @ B @ D )
=> ( ( ( C @ B )
= A )
=> ( ( hilber598459244di_nat @ D @ C @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(250,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_431_add__strict__mono) ).
thf(1376,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(294,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_567_add__le__mono) ).
thf(1574,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(13,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_gr__implies__not0) ).
thf(419,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(40,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ? [C: nat] :
( B
= ( suc @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_Suc__le__D) ).
thf(509,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ ( suc @ A ) @ B )
=> ? [C: nat] :
( B
= ( suc @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(82,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B )
| ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_linorder__less__linear) ).
thf(649,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
| ( A = B )
| ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(18,axiom,
( one_one_nat
= ( suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_656_One__nat__def) ).
thf(434,plain,
( one_one_nat
= ( suc @ zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(126,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ B @ ( suc @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_658_le__less__Suc__eq) ).
thf(811,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_nat @ B @ ( suc @ A ) )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(76,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_639_nat_Oinject) ).
thf(631,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(105,axiom,
! [A: produc1501160679le_alt > $o,B: ( produc1501160679le_alt > $o ) > product_unit,C: ( produc1501160679le_alt > $o ) > $o,D: ( produc1501160679le_alt > $o ) > product_unit > $o] :
( ( member221730070t_unit @ B @ ( pi_Pro1306850800t_unit @ C @ D ) )
=> ( ~ ( member_Product_unit @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member377231867_alt_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_PiE) ).
thf(758,plain,
! [A: produc1501160679le_alt > $o,B: ( produc1501160679le_alt > $o ) > product_unit,C: ( produc1501160679le_alt > $o ) > $o,D: ( produc1501160679le_alt > $o ) > product_unit > $o] :
( ( member221730070t_unit @ B @ ( pi_Pro1306850800t_unit @ C @ D ) )
=> ( ~ ( member_Product_unit @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member377231867_alt_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(144,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_order__eq__refl) ).
thf(858,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(46,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_nat @ B @ ( suc @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_645_not__less__eq) ).
thf(535,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_nat @ B @ ( suc @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(128,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_add__less__cancel__left) ).
thf(816,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(70,axiom,
! [A: arrow_1429601828e_indi > nat] :
( ! [B: arrow_1429601828e_indi,C: arrow_1429601828e_indi] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on978774663di_nat @ A @ top_to988227749indi_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_398_injI) ).
thf(609,plain,
! [A: arrow_1429601828e_indi > nat] :
( ! [B: arrow_1429601828e_indi,C: arrow_1429601828e_indi] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ( inj_on978774663di_nat @ A @ top_to988227749indi_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(374,axiom,
! [A: arrow_475358991le_alt,B: arrow_475358991le_alt,C: produc1501160679le_alt > $o,D: arrow_475358991le_alt,E: arrow_475358991le_alt] :
( ( D != E )
=> ( ( member377231867_alt_o @ C @ arrow_823908191le_Lin )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ ( arrow_2098199487_below @ C @ D @ E ) )
= ( ( A != B )
& ( ( B = D )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ A @ E ) @ C ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( member214075476le_alt @ ( produc1347929815le_alt @ E @ B ) @ C ) ) )
& ( ( A != D )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_523_in__below) ).
thf(1862,plain,
! [A: arrow_475358991le_alt,B: arrow_475358991le_alt,C: produc1501160679le_alt > $o,D: arrow_475358991le_alt,E: arrow_475358991le_alt] :
( ( D != E )
=> ( ( member377231867_alt_o @ C @ arrow_823908191le_Lin )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ ( arrow_2098199487_below @ C @ D @ E ) )
= ( ( A != B )
& ( ( B = D )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ A @ E ) @ C ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( member214075476le_alt @ ( produc1347929815le_alt @ E @ B ) @ C ) ) )
& ( ( A != D )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(170,axiom,
! [A: $o > $o,B: $o,C: $o > $o] :
( ( member_o @ B @ C )
=> ( ( ord_less_eq_o_o @ C @ A )
=> ( member_o @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_set__rev__mp) ).
thf(1022,plain,
! [A: $o > $o,B: $o,C: $o > $o] :
( ( member_o @ B @ C )
=> ( ( ord_less_eq_o_o @ C @ A )
=> ( member_o @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(203,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_linorder__linear) ).
thf(1177,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)],[203]) ).
thf(160,axiom,
! [A: produc1501160679le_alt > $o] :
( ( A != top_to1841428258_alt_o )
= ( ord_le988258430_alt_o @ A @ top_to1841428258_alt_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_less__top) ).
thf(932,plain,
! [A: produc1501160679le_alt > $o] :
( ( A != top_to1841428258_alt_o )
= ( ord_le988258430_alt_o @ A @ top_to1841428258_alt_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(139,axiom,
! [A: nat,B: nat] : ( ord_less_nat @ A @ ( suc @ ( plus_plus_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_665_less__add__Suc2) ).
thf(848,plain,
! [A: nat,B: nat] : ( ord_less_nat @ A @ ( suc @ ( plus_plus_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(44,axiom,
~ ! [A: arrow_1429601828e_indi > nat] :
( ( inj_on978774663di_nat @ A @ top_to988227749indi_o )
=> ( ( image_484224243di_nat @ A @ top_to988227749indi_o )
!= ( ord_at4362885an_nat @ zero_zero_nat @ ( finite97476818e_indi @ top_to988227749indi_o ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_698__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123) ).
thf(520,plain,
~ ! [A: arrow_1429601828e_indi > nat] :
( ( inj_on978774663di_nat @ A @ top_to988227749indi_o )
=> ( ( image_484224243di_nat @ A @ top_to988227749indi_o )
!= ( ord_at4362885an_nat @ zero_zero_nat @ ( finite97476818e_indi @ top_to988227749indi_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(291,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ ( plus_plus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_426_add__right__mono) ).
thf(1556,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ ( plus_plus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(110,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ~ ( ord_less_nat @ B @ A ) )
= ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_linorder__antisym__conv3) ).
thf(769,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ~ ( ord_less_nat @ B @ A ) )
= ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(132,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_add__left__imp__eq) ).
thf(827,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)],[132]) ).
thf(232,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_leI) ).
thf(1245,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(114,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_529_linorder__neqE__nat) ).
thf(780,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(168,axiom,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: arrow_1429601828e_indi] :
( ( arrow_1212662430ctator @ A @ B )
= ( ! [C: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member526088951_alt_o @ C @ arrow_734252939e_Prof )
=> ( ( A @ C )
= ( C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_dictator__def) ).
thf(1015,plain,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: arrow_1429601828e_indi] :
( ( arrow_1212662430ctator @ A @ B )
= ( ! [C: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member526088951_alt_o @ C @ arrow_734252939e_Prof )
=> ( ( A @ C )
= ( C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(4,axiom,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi,C: arrow_1429601828e_indi > nat,D: arrow_1429601828e_indi > $o] :
( ( inj_on978774663di_nat @ C @ D )
=> ( ( ( C @ A )
= ( C @ B ) )
=> ( ( member2052026769e_indi @ A @ D )
=> ( ( member2052026769e_indi @ B @ D )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_inj__onD) ).
thf(394,plain,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi,C: arrow_1429601828e_indi > nat,D: arrow_1429601828e_indi > $o] :
( ( inj_on978774663di_nat @ C @ D )
=> ( ( ( C @ A )
= ( C @ B ) )
=> ( ( member2052026769e_indi @ A @ D )
=> ( ( member2052026769e_indi @ B @ D )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(55,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less_nat @ ( suc @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_Suc__lessI) ).
thf(563,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( ( suc @ A )
!= B )
=> ( ord_less_nat @ ( suc @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(268,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_418_add__right__cancel) ).
thf(1496,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)],[268]) ).
thf(351,axiom,
! [A: produc1501160679le_alt,B: produc1501160679le_alt > $o,C: produc1501160679le_alt > $o] :
( ( ord_le97612146_alt_o @ B @ C )
=> ( ( member214075476le_alt @ A @ B )
=> ( member214075476le_alt @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_set__mp) ).
thf(1805,plain,
! [A: produc1501160679le_alt,B: produc1501160679le_alt > $o,C: produc1501160679le_alt > $o] :
( ( ord_le97612146_alt_o @ B @ C )
=> ( ( member214075476le_alt @ A @ B )
=> ( member214075476le_alt @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(301,axiom,
! [A: $o,B: $o > $o,C: $o > $o] :
( ( ord_less_eq_o_o @ B @ C )
=> ( ( member_o @ A @ B )
=> ( member_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_in__mono) ).
thf(1594,plain,
! [A: $o,B: $o > $o,C: $o > $o] :
( ( ord_less_eq_o_o @ B @ C )
=> ( ( member_o @ A @ B )
=> ( member_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(315,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_add__less__le__mono) ).
thf(1699,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_nat @ C @ D )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(322,axiom,
( member616898751_alt_o @ f
@ ( pi_Arr1304755663_alt_o @ arrow_734252939e_Prof
@ ^ [A: arrow_1429601828e_indi > produc1501160679le_alt > $o] : arrow_823908191le_Lin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_assms_I1_J) ).
thf(1726,plain,
( member616898751_alt_o @ f
@ ( pi_Arr1304755663_alt_o @ arrow_734252939e_Prof
@ ^ [A: arrow_1429601828e_indi > produc1501160679le_alt > $o] : arrow_823908191le_Lin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(244,axiom,
! [A: nat] :
( member526088951_alt_o
@ ^ [B: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ B ) @ A ) @ lab @ lba )
@ arrow_734252939e_Prof ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_PiProf) ).
thf(1364,plain,
! [A: nat] :
( member526088951_alt_o
@ ^ [B: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ B ) @ A ) @ lab @ lba )
@ arrow_734252939e_Prof ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(234,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_xt1_I8_J) ).
thf(1250,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(263,axiom,
! [A: $o] : ( member_o @ A @ top_top_o_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_iso__tuple__UNIV__I) ).
thf(1413,plain,
! [A: $o] : ( member_o @ A @ top_top_o_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(93,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ~ ( ord_less_nat @ A @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_linorder__antisym__conv2) ).
thf(722,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ~ ( ord_less_nat @ A @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(34,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_add__eq__self__zero) ).
thf(490,plain,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= A )
=> ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(310,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_order__le__neq__trans) ).
thf(1684,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(102,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_linorder__cases) ).
thf(749,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( A != B )
=> ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(72,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_less__SucI) ).
thf(617,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(240,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_563_nat__add__left__cancel__le) ).
thf(1340,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)],[240]) ).
thf(169,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_ord__eq__le__trans) ).
thf(1018,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( ord_less_eq_nat @ C @ A )
=> ( ord_less_eq_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(52,axiom,
! [A: nat] :
( ( suc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_640_Suc__n__not__n) ).
thf(553,plain,
! [A: nat] :
( ( suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(336,axiom,
~ ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ lba ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78__096_Ia_M_Ab_J_A_126_058_ALba_096) ).
thf(1758,plain,
~ ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ lba ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(198,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_linorder__le__less__linear) ).
thf(1166,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(214,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_nat @ C @ A )
=> ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_order__le__less__trans) ).
thf(1203,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( ord_less_nat @ C @ A )
=> ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(63,axiom,
! [A: nat] :
( A
!= ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_641_n__not__Suc__n) ).
thf(589,plain,
! [A: nat] :
( A
!= ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(205,axiom,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi > nat,C: arrow_1429601828e_indi > $o] :
( ( inj_on978774663di_nat @ B @ C )
=> ( ( member2052026769e_indi @ A @ C )
=> ( ( hilber598459244di_nat @ C @ B @ ( B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_386_inv__into__f__f) ).
thf(1181,plain,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi > nat,C: arrow_1429601828e_indi > $o] :
( ( inj_on978774663di_nat @ B @ C )
=> ( ( member2052026769e_indi @ A @ C )
=> ( ( hilber598459244di_nat @ C @ B @ ( B @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(130,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_order__less__not__sym) ).
thf(823,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ~ ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(135,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_add__right__imp__eq) ).
thf(836,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)],[135]) ).
thf(289,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_524_add__leE) ).
thf(1551,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ~ ( ( ord_less_eq_nat @ A @ C )
=> ~ ( ord_less_eq_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(45,axiom,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_694_zero__induct) ).
thf(525,plain,
! [A: nat > $o,B: nat] :
( ( A @ B )
=> ( ! [C: nat] :
( ( A @ ( suc @ C ) )
=> ( A @ C ) )
=> ( A @ zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(143,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_nat__add__left__commute) ).
thf(855,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)],[143]) ).
thf(235,axiom,
! [A: produc1501160679le_alt > $o,B: ( produc1501160679le_alt > $o ) > $o,C: ( produc1501160679le_alt > $o ) > $o] :
( ( ord_le1063113995lt_o_o @ B @ C )
=> ( ( member377231867_alt_o @ A @ B )
=> ( member377231867_alt_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_442_subsetD) ).
thf(1252,plain,
! [A: produc1501160679le_alt > $o,B: ( produc1501160679le_alt > $o ) > $o,C: ( produc1501160679le_alt > $o ) > $o] :
( ( ord_le1063113995lt_o_o @ B @ C )
=> ( ( member377231867_alt_o @ A @ B )
=> ( member377231867_alt_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(98,axiom,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
( ! [D: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member526088951_alt_o @ D @ C )
=> ( member377231867_alt_o @ ( A @ D ) @ ( B @ D ) ) )
=> ( member616898751_alt_o @ A @ ( pi_Arr1304755663_alt_o @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_585_Pi__I_H) ).
thf(739,plain,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
( ! [D: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member526088951_alt_o @ D @ C )
=> ( member377231867_alt_o @ ( A @ D ) @ ( B @ D ) ) )
=> ( member616898751_alt_o @ A @ ( pi_Arr1304755663_alt_o @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(246,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_eq_nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_add__le__imp__le__right) ).
thf(1368,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)],[246]) ).
thf(345,axiom,
! [A: arrow_475358991le_alt,B: arrow_475358991le_alt,C: produc1501160679le_alt > $o] :
( ( member377231867_alt_o @ C @ arrow_823908191le_Lin )
=> ( ( A != B )
=> ( ( ~ ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ C ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_notin__Lin__iff) ).
thf(1780,plain,
! [A: arrow_475358991le_alt,B: arrow_475358991le_alt,C: produc1501160679le_alt > $o] :
( ( member377231867_alt_o @ C @ arrow_823908191le_Lin )
=> ( ( A != B )
=> ( ( ~ ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ C ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(281,axiom,
! [A: nat,B: nat] :
( ( ( ord_less_nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq_nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_559_less__or__eq__imp__le) ).
thf(1531,plain,
! [A: nat,B: nat] :
( ( ( ord_less_nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq_nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(175,axiom,
member377231867_alt_o @ lba @ arrow_823908191le_Lin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74__096Lba_A_058_ALin_096) ).
thf(1098,plain,
member377231867_alt_o @ lba @ arrow_823908191le_Lin,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(287,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ ( plus_plus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_433_add__strict__right__mono) ).
thf(1547,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ ( plus_plus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(332,axiom,
! [A: arrow_475358991le_alt,B: arrow_475358991le_alt,C: produc1501160679le_alt > $o,D: arrow_475358991le_alt] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ ( arrow_55669061_mktop @ C @ D ) )
= ( ( A != D )
& ( ( B = D )
=> ( A != B ) )
& ( ( B != D )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_in__mktop) ).
thf(1748,plain,
! [A: arrow_475358991le_alt,B: arrow_475358991le_alt,C: produc1501160679le_alt > $o,D: arrow_475358991le_alt] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ ( arrow_55669061_mktop @ C @ D ) )
= ( ( A != D )
& ( ( B = D )
=> ( A != B ) )
& ( ( B != D )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(53,axiom,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_less__zeroE) ).
thf(557,plain,
! [A: nat] :
~ ( ord_less_nat @ A @ zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(341,axiom,
! [A: produc1501160679le_alt,B: produc1501160679le_alt > $o] :
( ( member214075476le_alt @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_mem__def) ).
thf(1770,plain,
! [A: produc1501160679le_alt,B: produc1501160679le_alt > $o] :
( ( member214075476le_alt @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(269,axiom,
! [A: product_unit,B: product_unit > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,C: product_unit > $o,D: product_unit > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ( member1536989448_alt_o @ B @ ( pi_Pro1782982558_alt_o @ C @ D ) )
=> ( ~ ( member616898751_alt_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member_Product_unit @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_PiE) ).
thf(1499,plain,
! [A: product_unit,B: product_unit > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,C: product_unit > $o,D: product_unit > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ( member1536989448_alt_o @ B @ ( pi_Pro1782982558_alt_o @ C @ D ) )
=> ( ~ ( member616898751_alt_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member_Product_unit @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(355,axiom,
! [A: arrow_475358991le_alt,B: arrow_475358991le_alt,C: arrow_475358991le_alt,D: arrow_475358991le_alt] :
( ( ( produc1347929815le_alt @ A @ B )
= ( produc1347929815le_alt @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_Pair__eq) ).
thf(1813,plain,
! [A: arrow_475358991le_alt,B: arrow_475358991le_alt,C: arrow_475358991le_alt,D: arrow_475358991le_alt] :
( ( ( produc1347929815le_alt @ A @ B )
= ( produc1347929815le_alt @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(378,axiom,
! [A: arrow_475358991le_alt,B: arrow_475358991le_alt,C: produc1501160679le_alt > $o,D: arrow_475358991le_alt,E: arrow_475358991le_alt] :
( ( D != E )
=> ( ( member377231867_alt_o @ C @ arrow_823908191le_Lin )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ ( arrow_789600939_above @ C @ D @ E ) )
= ( ( A != B )
& ( ( A = E )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ D @ B ) @ C ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( member214075476le_alt @ ( produc1347929815le_alt @ A @ D ) @ C ) ) )
& ( ( B != E )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_in__above) ).
thf(1869,plain,
! [A: arrow_475358991le_alt,B: arrow_475358991le_alt,C: produc1501160679le_alt > $o,D: arrow_475358991le_alt,E: arrow_475358991le_alt] :
( ( D != E )
=> ( ( member377231867_alt_o @ C @ arrow_823908191le_Lin )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ ( arrow_789600939_above @ C @ D @ E ) )
= ( ( A != B )
& ( ( A = E )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ D @ B ) @ C ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( member214075476le_alt @ ( produc1347929815le_alt @ A @ D ) @ C ) ) )
& ( ( B != E )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ A @ B ) @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(136,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_order__antisym) ).
thf(840,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)],[136]) ).
thf(228,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_add__le__less__mono) ).
thf(1235,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq_nat @ C @ D )
=> ( ( ord_less_nat @ A @ B )
=> ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(308,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_termination__basic__simps_I1_J) ).
thf(1679,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(327,axiom,
( member214075476le_alt @ ( produc1347929815le_alt @ c @ e )
@ ( f
@ ^ [A: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ A ) @ n ) @ ( arrow_55669061_mktop @ ( p @ A ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ A )
= n )
@ ( arrow_789600939_above @ ( p @ A ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ A ) @ e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
thf(1738,plain,
( member214075476le_alt @ ( produc1347929815le_alt @ c @ e )
@ ( f
@ ^ [A: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ A ) @ n ) @ ( arrow_55669061_mktop @ ( p @ A ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ A )
= n )
@ ( arrow_789600939_above @ ( p @ A ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ A ) @ e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(49,axiom,
! [A: nat] :
( ( ord_less_nat @ A @ ( suc @ zero_zero_nat ) )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_670_less__Suc0) ).
thf(544,plain,
! [A: nat] :
( ( ord_less_nat @ A @ ( suc @ zero_zero_nat ) )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(348,axiom,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
( ( arrow_797024463le_IIA @ A )
= ( ! [B: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member526088951_alt_o @ B @ arrow_734252939e_Prof )
=> ! [C: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member526088951_alt_o @ C @ arrow_734252939e_Prof )
=> ! [D: arrow_475358991le_alt,E: arrow_475358991le_alt] :
( ! [F: arrow_1429601828e_indi] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ D @ E ) @ ( B @ F ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ D @ E ) @ ( C @ F ) ) )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ D @ E ) @ ( A @ B ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ D @ E ) @ ( A @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_IIA__def) ).
thf(1790,plain,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] :
( ( arrow_797024463le_IIA @ A )
= ( ! [B: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member526088951_alt_o @ B @ arrow_734252939e_Prof )
=> ! [C: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member526088951_alt_o @ C @ arrow_734252939e_Prof )
=> ! [D: arrow_475358991le_alt,E: arrow_475358991le_alt] :
( ! [F: arrow_1429601828e_indi] :
( ( member214075476le_alt @ ( produc1347929815le_alt @ D @ E ) @ ( B @ F ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ D @ E ) @ ( C @ F ) ) )
=> ( ( member214075476le_alt @ ( produc1347929815le_alt @ D @ E ) @ ( A @ B ) )
= ( member214075476le_alt @ ( produc1347929815le_alt @ D @ E ) @ ( A @ C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(318,axiom,
( arrow_734252939e_Prof
= ( pi_Arr1929480907_alt_o @ top_to988227749indi_o
@ ^ [A: arrow_1429601828e_indi] : arrow_823908191le_Lin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_Prof__def) ).
thf(1716,plain,
( arrow_734252939e_Prof
= ( pi_Arr1929480907_alt_o @ top_to988227749indi_o
@ ^ [A: arrow_1429601828e_indi] : arrow_823908191le_Lin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(283,axiom,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,C: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ( ord_le1859604819lt_o_o @ B @ C )
=> ( ( member616898751_alt_o @ A @ B )
=> ( member616898751_alt_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_517_psubsetD) ).
thf(1538,plain,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,C: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ( ord_le1859604819lt_o_o @ B @ C )
=> ( ( member616898751_alt_o @ A @ B )
=> ( member616898751_alt_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(125,axiom,
! [A: nat,B: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_546_not__add__less1) ).
thf(808,plain,
! [A: nat,B: nat] :
~ ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(100,axiom,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi > nat] :
( ( inj_on978774663di_nat @ B @ top_to988227749indi_o )
=> ( ( hilber598459244di_nat @ top_to988227749indi_o @ B @ ( B @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_inv__f__f) ).
thf(744,plain,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi > nat] :
( ( inj_on978774663di_nat @ B @ top_to988227749indi_o )
=> ( ( hilber598459244di_nat @ top_to988227749indi_o @ B @ ( B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(84,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ B )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_linorder__antisym__conv1) ).
thf(656,plain,
! [A: nat,B: nat] :
( ~ ( ord_less_nat @ A @ B )
=> ( ( ord_less_eq_nat @ A @ B )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(67,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_eq_nat @ A @ B )
=> ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_le__SucE) ).
thf(600,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_eq_nat @ A @ B )
=> ( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(272,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_550_trans__less__add2) ).
thf(1506,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(146,axiom,
! [A: nat] :
( ( suc @ A )
= ( plus_plus_nat @ one_one_nat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_687_Suc__eq__plus1__left) ).
thf(864,plain,
! [A: nat] :
( ( suc @ A )
= ( plus_plus_nat @ one_one_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(271,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_554_add__lessD1) ).
thf(1504,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ C )
=> ( ord_less_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(65,axiom,
! [A: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ( ord_le134800455lt_o_o
@ ^ [C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] : ( member616898751_alt_o @ C @ A )
@ ^ [C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] : ( member616898751_alt_o @ C @ B ) )
= ( ord_le134800455lt_o_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_pred__subset__eq) ).
thf(595,plain,
! [A: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,B: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ( ord_le134800455lt_o_o
@ ^ [C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] : ( member616898751_alt_o @ C @ A )
@ ^ [C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o] : ( member616898751_alt_o @ C @ B ) )
= ( ord_le134800455lt_o_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(230,axiom,
! [A: arrow_475358991le_alt,B: produc1501160679le_alt > $o] :
( ( member377231867_alt_o @ B @ arrow_823908191le_Lin )
=> ( member377231867_alt_o @ ( arrow_55669061_mktop @ B @ A ) @ arrow_823908191le_Lin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_mktop__Lin) ).
thf(1240,plain,
! [A: arrow_475358991le_alt,B: produc1501160679le_alt > $o] :
( ( member377231867_alt_o @ B @ arrow_823908191le_Lin )
=> ( member377231867_alt_o @ ( arrow_55669061_mktop @ B @ A ) @ arrow_823908191le_Lin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(388,axiom,
? [A: nat] :
( ( ord_less_nat @ A @ ( finite97476818e_indi @ top_to988227749indi_o ) )
& ! [B: nat] :
( ( ord_less_eq_nat @ B @ A )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a )
@ ( f
@ ^ [C: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ C ) @ B ) @ lab @ lba ) ) ) )
& ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b )
@ ( f
@ ^ [B: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ B ) @ ( plus_plus_nat @ A @ one_one_nat ) ) @ lab @ lba ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I) ).
thf(1898,plain,
? [A: nat] :
( ( ord_less_nat @ A @ ( finite97476818e_indi @ top_to988227749indi_o ) )
& ! [B: nat] :
( ( ord_less_eq_nat @ B @ A )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a )
@ ( f
@ ^ [C: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ C ) @ B ) @ lab @ lba ) ) ) )
& ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b )
@ ( f
@ ^ [B: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ B ) @ ( plus_plus_nat @ A @ one_one_nat ) ) @ lab @ lba ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(369,axiom,
! [A: arrow_1429601828e_indi] :
( ( ( ( ord_less_nat @ ( h @ A ) @ n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ c @ e ) @ ( arrow_55669061_mktop @ ( p @ A ) @ e ) ) )
& ( ~ ( ord_less_nat @ ( h @ A ) @ n )
=> ( ( ( ( h @ A )
= n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ c @ e ) @ ( arrow_789600939_above @ ( p @ A ) @ c @ e ) ) )
& ( ( ( h @ A )
!= n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ c @ e ) @ ( arrow_2054445623_mkbot @ ( p @ A ) @ e ) ) ) ) ) )
= ( ( ( ord_less_nat @ ( h @ A ) @ ( plus_plus_nat @ n @ one_one_nat ) )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ lab ) )
& ( ~ ( ord_less_nat @ ( h @ A ) @ ( plus_plus_nat @ n @ one_one_nat ) )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ lba ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am) ).
thf(1849,plain,
! [A: arrow_1429601828e_indi] :
( ( ( ( ord_less_nat @ ( h @ A ) @ n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ c @ e ) @ ( arrow_55669061_mktop @ ( p @ A ) @ e ) ) )
& ( ~ ( ord_less_nat @ ( h @ A ) @ n )
=> ( ( ( ( h @ A )
= n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ c @ e ) @ ( arrow_789600939_above @ ( p @ A ) @ c @ e ) ) )
& ( ( ( h @ A )
!= n )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ c @ e ) @ ( arrow_2054445623_mkbot @ ( p @ A ) @ e ) ) ) ) ) )
= ( ( ( ord_less_nat @ ( h @ A ) @ ( plus_plus_nat @ n @ one_one_nat ) )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ lab ) )
& ( ~ ( ord_less_nat @ ( h @ A ) @ ( plus_plus_nat @ n @ one_one_nat ) )
=> ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ lba ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(189,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ord_less_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_linorder__not__le) ).
thf(1141,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_eq_nat @ A @ B ) )
= ( ord_less_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(282,axiom,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,C: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,D: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o > $o] :
( ( member1823529808lt_o_o @ B @ ( pi_Arr195212324lt_o_o @ C @ D ) )
=> ( ~ ( member_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member616898751_alt_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_PiE) ).
thf(1536,plain,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,C: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,D: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o > $o] :
( ( member1823529808lt_o_o @ B @ ( pi_Arr195212324lt_o_o @ C @ D ) )
=> ( ~ ( member_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member616898751_alt_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(36,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ ( suc @ B ) )
= ( suc @ ( plus_plus_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_644_add__Suc__right) ).
thf(497,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ A @ ( suc @ B ) )
= ( suc @ ( plus_plus_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(151,axiom,
! [A: product_unit,B: product_unit > arrow_1429601828e_indi > produc1501160679le_alt > $o,C: product_unit > $o,D: product_unit > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
( ( member283501700_alt_o @ B @ ( pi_Pro1662176984_alt_o @ C @ D ) )
=> ( ~ ( member526088951_alt_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member_Product_unit @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_PiE) ).
thf(876,plain,
! [A: product_unit,B: product_unit > arrow_1429601828e_indi > produc1501160679le_alt > $o,C: product_unit > $o,D: product_unit > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
( ( member283501700_alt_o @ B @ ( pi_Pro1662176984_alt_o @ C @ D ) )
=> ( ~ ( member526088951_alt_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member_Product_unit @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(138,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_order__neq__le__trans) ).
thf(845,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(266,axiom,
! [A: nat > nat > $o,B: nat,C: nat] :
( ( ( ord_less_nat @ B @ C )
=> ( A @ C @ B ) )
=> ( ( ( B = C )
=> ( A @ C @ B ) )
=> ( ( ( ord_less_nat @ C @ B )
=> ( A @ C @ B ) )
=> ( A @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_533_nat__less__cases) ).
thf(1421,plain,
! [A: nat > nat > $o,B: nat,C: nat] :
( ( ( ord_less_nat @ B @ C )
=> ( A @ C @ B ) )
=> ( ( ( B = C )
=> ( A @ C @ B ) )
=> ( ( ( ord_less_nat @ C @ B )
=> ( A @ C @ B ) )
=> ( A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(75,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_693_nat_Oexhaust) ).
thf(627,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(24,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_646_less__Suc__eq) ).
thf(450,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(31,axiom,
! [A: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_zero__less__Suc) ).
thf(482,plain,
! [A: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(89,axiom,
! [A: $o > $o,B: $o > $o] :
( ! [C: $o] :
( ( member_o @ C @ B )
=> ( member_o @ C @ A ) )
=> ( ord_less_eq_o_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_504_subsetI) ).
thf(671,plain,
! [A: $o > $o,B: $o > $o] :
( ! [C: $o] :
( ( member_o @ C @ B )
=> ( member_o @ C @ A ) )
=> ( ord_less_eq_o_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(60,axiom,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi,C: arrow_1429601828e_indi > nat] :
( ( inj_on978774663di_nat @ C @ top_to988227749indi_o )
=> ( ( ( C @ A )
= ( C @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_inj__eq) ).
thf(581,plain,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi,C: arrow_1429601828e_indi > nat] :
( ( inj_on978774663di_nat @ C @ top_to988227749indi_o )
=> ( ( ( C @ A )
= ( C @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(276,axiom,
! [A: produc1501160679le_alt > $o] :
( ( ord_le97612146_alt_o @ top_to1841428258_alt_o @ A )
=> ( A = top_to1841428258_alt_o ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_top__le) ).
thf(1517,plain,
! [A: produc1501160679le_alt > $o] :
( ( ord_le97612146_alt_o @ top_to1841428258_alt_o @ A )
=> ( A = top_to1841428258_alt_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(184,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ ( plus_plus_nat @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_566_add__le__mono1) ).
thf(1126,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ ( plus_plus_nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(352,axiom,
! [A: produc1501160679le_alt > $o,B: produc1501160679le_alt > $o > $o,C: produc1501160679le_alt > $o] :
( ! [D: produc1501160679le_alt] :
( ( member214075476le_alt @ D @ C )
=> ( member_o @ ( A @ D ) @ ( B @ D ) ) )
=> ( member377231867_alt_o @ A @ ( pi_Pro1701359055_alt_o @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_Pi__I_H) ).
thf(1807,plain,
! [A: produc1501160679le_alt > $o,B: produc1501160679le_alt > $o > $o,C: produc1501160679le_alt > $o] :
( ! [D: produc1501160679le_alt] :
( ( member214075476le_alt @ D @ C )
=> ( member_o @ ( A @ D ) @ ( B @ D ) ) )
=> ( member377231867_alt_o @ A @ ( pi_Pro1701359055_alt_o @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(166,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_536_nat__add__assoc) ).
thf(1010,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)],[166]) ).
thf(254,axiom,
! [A: produc1501160679le_alt > $o,B: ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi,C: ( produc1501160679le_alt > $o ) > $o,D: ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o] :
( ( member304866663e_indi @ B @ ( pi_Pro468373057e_indi @ C @ D ) )
=> ( ~ ( member2052026769e_indi @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member377231867_alt_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_PiE) ).
thf(1390,plain,
! [A: produc1501160679le_alt > $o,B: ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi,C: ( produc1501160679le_alt > $o ) > $o,D: ( produc1501160679le_alt > $o ) > arrow_1429601828e_indi > $o] :
( ( member304866663e_indi @ B @ ( pi_Pro468373057e_indi @ C @ D ) )
=> ( ~ ( member2052026769e_indi @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member377231867_alt_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(300,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( C = A )
=> ( ord_less_eq_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_ord__le__eq__trans) ).
thf(1590,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( C = A )
=> ( ord_less_eq_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(253,axiom,
! [A: $o,B: $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,C: $o > $o,D: $o > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ( member1957863580_alt_o @ B @ ( pi_o_A1186128886_alt_o @ C @ D ) )
=> ( ~ ( member616898751_alt_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_PiE) ).
thf(1385,plain,
! [A: $o,B: $o > ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,C: $o > $o,D: $o > ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o] :
( ( member1957863580_alt_o @ B @ ( pi_o_A1186128886_alt_o @ C @ D ) )
=> ( ~ ( member616898751_alt_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(43,axiom,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi,C: arrow_1429601828e_indi > nat,D: arrow_1429601828e_indi > $o] :
( ( inj_on978774663di_nat @ C @ D )
=> ( ( member2052026769e_indi @ B @ D )
=> ( ( member2052026769e_indi @ A @ D )
=> ( ( ( C @ B )
= ( C @ A ) )
= ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_369_inj__on__iff) ).
thf(517,plain,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi,C: arrow_1429601828e_indi > nat,D: arrow_1429601828e_indi > $o] :
( ( inj_on978774663di_nat @ C @ D )
=> ( ( member2052026769e_indi @ B @ D )
=> ( ( member2052026769e_indi @ A @ D )
=> ( ( ( C @ B )
= ( C @ A ) )
= ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(273,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_xt1_I5_J) ).
thf(1508,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)],[273]) ).
thf(83,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( ord_less_nat @ A @ C )
=> ( ord_less_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_xt1_I1_J) ).
thf(652,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( ord_less_nat @ A @ C )
=> ( ord_less_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(1,conjecture,
member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( f @ p ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( f @ p ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(390,plain,
~ ( member214075476le_alt @ ( produc1347929815le_alt @ c @ d ) @ ( f @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(278,axiom,
! [A: nat,B: nat,C: nat > nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( ord_less_nat @ ( C @ D ) @ ( C @ E ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( C @ A ) @ ( C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_569_less__mono__imp__le__mono) ).
thf(1523,plain,
! [A: nat,B: nat,C: nat > nat] :
( ! [D: nat,E: nat] :
( ( ord_less_nat @ D @ E )
=> ( ord_less_nat @ ( C @ D ) @ ( C @ E ) ) )
=> ( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_eq_nat @ ( C @ A ) @ ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(292,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_order__le__less) ).
thf(1558,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
= ( ( ord_less_nat @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(373,axiom,
( member214075476le_alt @ ( produc1347929815le_alt @ c @ d )
@ ( f
@ ^ [A: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ A ) @ n ) @ ( arrow_55669061_mktop @ ( p @ A ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ A )
= n )
@ ( arrow_789600939_above @ ( p @ A ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ A ) @ e ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).
thf(1861,plain,
( member214075476le_alt @ ( produc1347929815le_alt @ c @ d )
@ ( f
@ ^ [A: arrow_1429601828e_indi] :
( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ A ) @ n ) @ ( arrow_55669061_mktop @ ( p @ A ) @ e )
@ ( if_Pro1561232536_alt_o
@ ( ( h @ A )
= n )
@ ( arrow_789600939_above @ ( p @ A ) @ c @ e )
@ ( arrow_2054445623_mkbot @ ( p @ A ) @ e ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(312,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_528_nat__neq__iff) ).
thf(1689,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(88,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( B = A )
=> ( ord_less_eq_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_xt1_I4_J) ).
thf(667,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( B = A )
=> ( ord_less_eq_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(159,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_420_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(929,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)],[159]) ).
thf(30,axiom,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_675_nat_Osimps_I3_J) ).
thf(478,plain,
! [A: nat] :
( ( suc @ A )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(218,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_537_nat__add__left__cancel) ).
thf(1212,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)],[218]) ).
thf(303,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_add__left__cancel) ).
thf(1661,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)],[303]) ).
thf(386,axiom,
! [A: produc1501160679le_alt,B: produc1501160679le_alt > $o,C: produc1501160679le_alt > $o,D: produc1501160679le_alt > $o > $o] :
( ( member377231867_alt_o @ B @ ( pi_Pro1701359055_alt_o @ C @ D ) )
=> ( ~ ( member_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member214075476le_alt @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_PiE) ).
thf(1893,plain,
! [A: produc1501160679le_alt,B: produc1501160679le_alt > $o,C: produc1501160679le_alt > $o,D: produc1501160679le_alt > $o > $o] :
( ( member377231867_alt_o @ B @ ( pi_Pro1701359055_alt_o @ C @ D ) )
=> ( ~ ( member_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member214075476le_alt @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(90,axiom,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_560_le__add2) ).
thf(716,plain,
! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(196,axiom,
! [A: produc1501160679le_alt] : ( top_to1841428258_alt_o @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_top1I) ).
thf(1161,plain,
! [A: produc1501160679le_alt] : ( top_to1841428258_alt_o @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(122,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_linorder__neq__iff) ).
thf(800,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less_nat @ A @ B )
| ( ord_less_nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(103,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_435_add__less__cancel__right) ).
thf(752,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
= ( ord_less_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(296,axiom,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o,C: arrow_1429601828e_indi > $o] :
( ! [D: arrow_1429601828e_indi] :
( ( member2052026769e_indi @ D @ C )
=> ( member377231867_alt_o @ ( A @ D ) @ ( B @ D ) ) )
=> ( member526088951_alt_o @ A @ ( pi_Arr1929480907_alt_o @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_390_Pi__I) ).
thf(1578,plain,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o,C: arrow_1429601828e_indi > $o] :
( ! [D: arrow_1429601828e_indi] :
( ( member2052026769e_indi @ D @ C )
=> ( member377231867_alt_o @ ( A @ D ) @ ( B @ D ) ) )
=> ( member526088951_alt_o @ A @ ( pi_Arr1929480907_alt_o @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(142,axiom,
inj_on978774663di_nat @ h @ top_to988227749indi_o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_injh) ).
thf(854,plain,
inj_on978774663di_nat @ h @ top_to988227749indi_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(147,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_539_le__refl) ).
thf(867,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(68,axiom,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_le__0__eq) ).
thf(603,plain,
! [A: nat] :
( ( ord_less_eq_nat @ A @ zero_zero_nat )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(156,axiom,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,D: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
( ! [E: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member526088951_alt_o @ E @ D )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( member616898751_alt_o @ B @ ( pi_Arr1304755663_alt_o @ D @ A ) )
= ( member616898751_alt_o @ C @ ( pi_Arr1304755663_alt_o @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_582_Pi__cong) ).
thf(918,plain,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,D: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
( ! [E: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member526088951_alt_o @ E @ D )
=> ( ( B @ E )
= ( C @ E ) ) )
=> ( ( member616898751_alt_o @ B @ ( pi_Arr1304755663_alt_o @ D @ A ) )
= ( member616898751_alt_o @ C @ ( pi_Arr1304755663_alt_o @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(356,axiom,
! [A: produc1501160679le_alt,B: produc1501160679le_alt > $o,C: produc1501160679le_alt > $o] :
( ( ord_le97612146_alt_o @ B @ C )
=> ( ( member214075476le_alt @ A @ B )
=> ( member214075476le_alt @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445_subsetD) ).
thf(1816,plain,
! [A: produc1501160679le_alt,B: produc1501160679le_alt > $o,C: produc1501160679le_alt > $o] :
( ( ord_le97612146_alt_o @ B @ C )
=> ( ( member214075476le_alt @ A @ B )
=> ( member214075476le_alt @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(39,axiom,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi,C: arrow_1429601828e_indi > nat,D: arrow_1429601828e_indi > $o] :
( ( inj_on978774663di_nat @ C @ D )
=> ( ( A != B )
=> ( ( member2052026769e_indi @ A @ D )
=> ( ( member2052026769e_indi @ B @ D )
=> ( ( C @ A )
!= ( C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_inj__on__contraD) ).
thf(506,plain,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi,C: arrow_1429601828e_indi > nat,D: arrow_1429601828e_indi > $o] :
( ( inj_on978774663di_nat @ C @ D )
=> ( ( A != B )
=> ( ( member2052026769e_indi @ A @ D )
=> ( ( member2052026769e_indi @ B @ D )
=> ( ( C @ A )
!= ( C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(293,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( A @ C )
=> ( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( ( A @ ( suc @ D ) )
=> ( A @ D ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_684_inc__induct) ).
thf(1561,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( ord_less_eq_nat @ B @ C )
=> ( ( A @ C )
=> ( ! [D: nat] :
( ( ord_less_nat @ D @ C )
=> ( ( A @ ( suc @ D ) )
=> ( A @ D ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(87,axiom,
! [A: produc1501160679le_alt > $o,B: arrow_475358991le_alt,C: arrow_475358991le_alt] :
( ( B != C )
=> ( ( member377231867_alt_o @ A @ arrow_823908191le_Lin )
=> ( member377231867_alt_o @ ( arrow_789600939_above @ A @ B @ C ) @ arrow_823908191le_Lin ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_above__Lin) ).
thf(664,plain,
! [A: produc1501160679le_alt > $o,B: arrow_475358991le_alt,C: arrow_475358991le_alt] :
( ( B != C )
=> ( ( member377231867_alt_o @ A @ arrow_823908191le_Lin )
=> ( member377231867_alt_o @ ( arrow_789600939_above @ A @ B @ C ) @ arrow_823908191le_Lin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(6,axiom,
! [A: nat,B: nat] :
( ( plus_plus_nat @ ( suc @ A ) @ B )
= ( suc @ ( plus_plus_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_add__Suc) ).
thf(400,plain,
! [A: nat,B: nat] :
( ( plus_plus_nat @ ( suc @ A ) @ B )
= ( suc @ ( plus_plus_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(385,axiom,
! [A: produc1501160679le_alt] : ( member214075476le_alt @ A @ top_to1841428258_alt_o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_UNIV__I) ).
thf(1891,plain,
! [A: produc1501160679le_alt] : ( member214075476le_alt @ A @ top_to1841428258_alt_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(92,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_nat @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_430_add__less__imp__less__right) ).
thf(720,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ B ) )
=> ( ord_less_nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(201,axiom,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > product_unit,C: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,D: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > product_unit > $o] :
( ( member1924666376t_unit @ B @ ( pi_Arr830584606t_unit @ C @ D ) )
=> ( ~ ( member_Product_unit @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member616898751_alt_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_PiE) ).
thf(1172,plain,
! [A: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,B: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > product_unit,C: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > $o,D: ( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o ) > product_unit > $o] :
( ( member1924666376t_unit @ B @ ( pi_Arr830584606t_unit @ C @ D ) )
=> ( ~ ( member_Product_unit @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member616898751_alt_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(261,axiom,
member377231867_alt_o @ lab @ arrow_823908191le_Lin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73__096Lab_A_058_ALin_096) ).
thf(1410,plain,
member377231867_alt_o @ lab @ arrow_823908191le_Lin,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(109,axiom,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,D: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o > $o] :
( ( member939334982lt_o_o @ B @ ( pi_Arr952516694lt_o_o @ C @ D ) )
=> ( ~ ( member_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member526088951_alt_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_PiE) ).
thf(767,plain,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,D: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o > $o] :
( ( member939334982lt_o_o @ B @ ( pi_Arr952516694lt_o_o @ C @ D ) )
=> ( ~ ( member_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member526088951_alt_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(95,axiom,
! [A: $o,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ C @ B )
=> A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_order__less__imp__triv) ).
thf(728,plain,
! [A: $o,B: nat,C: nat] :
( ( ord_less_nat @ B @ C )
=> ( ( ord_less_nat @ C @ B )
=> A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(27,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_less__SucE) ).
thf(464,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ ( suc @ B ) )
=> ( ~ ( ord_less_nat @ A @ B )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(362,axiom,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi > produc1501160679le_alt,C: arrow_1429601828e_indi > $o,D: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member351225838le_alt @ B @ ( pi_Arr329216900le_alt @ C @ D ) )
=> ( ~ ( member214075476le_alt @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member2052026769e_indi @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_PiE) ).
thf(1829,plain,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi > produc1501160679le_alt,C: arrow_1429601828e_indi > $o,D: arrow_1429601828e_indi > produc1501160679le_alt > $o] :
( ( member351225838le_alt @ B @ ( pi_Arr329216900le_alt @ C @ D ) )
=> ( ~ ( member214075476le_alt @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member2052026769e_indi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(361,axiom,
~ ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a ) @ lab ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79__096_Ib_M_Aa_J_A_126_058_ALab_096) ).
thf(1827,plain,
~ ( member214075476le_alt @ ( produc1347929815le_alt @ b @ a ) @ lab ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(251,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_531_less__not__refl2) ).
thf(1378,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(80,axiom,
! [A: ( produc1501160679le_alt > $o ) > $o,B: ( produc1501160679le_alt > $o ) > $o] :
( ( ord_le1063113995lt_o_o
@ ^ [C: produc1501160679le_alt > $o] : ( member377231867_alt_o @ C @ A )
@ ^ [C: produc1501160679le_alt > $o] : ( member377231867_alt_o @ C @ B ) )
= ( ord_le1063113995lt_o_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_pred__subset__eq) ).
thf(644,plain,
! [A: ( produc1501160679le_alt > $o ) > $o,B: ( produc1501160679le_alt > $o ) > $o] :
( ( ord_le1063113995lt_o_o
@ ^ [C: produc1501160679le_alt > $o] : ( member377231867_alt_o @ C @ A )
@ ^ [C: produc1501160679le_alt > $o] : ( member377231867_alt_o @ C @ B ) )
= ( ord_le1063113995lt_o_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(140,axiom,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,D: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o] :
( ( member616898751_alt_o @ B @ ( pi_Arr1304755663_alt_o @ C @ D ) )
=> ( ( member526088951_alt_o @ A @ C )
=> ( member377231867_alt_o @ ( B @ A ) @ ( D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_Pi__mem) ).
thf(850,plain,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,D: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > ( produc1501160679le_alt > $o ) > $o] :
( ( member616898751_alt_o @ B @ ( pi_Arr1304755663_alt_o @ C @ D ) )
=> ( ( member526088951_alt_o @ A @ C )
=> ( member377231867_alt_o @ ( B @ A ) @ ( D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(267,axiom,
! [A: $o,B: $o > $o,C: $o > $o] :
( ( ord_less_o_o @ B @ C )
=> ( ( member_o @ A @ B )
=> ( member_o @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_512_psubsetD) ).
thf(1431,plain,
! [A: $o,B: $o > $o,C: $o > $o] :
( ( ord_less_o_o @ B @ C )
=> ( ( member_o @ A @ B )
=> ( member_o @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(389,axiom,
( member214075476le_alt @ ( produc1347929815le_alt @ a @ b )
@ ( f
@ ^ [A: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ A ) @ ( plus_plus_nat @ n @ one_one_nat ) ) @ lab @ lba ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_n_I3_J) ).
thf(1902,plain,
( member214075476le_alt @ ( produc1347929815le_alt @ a @ b )
@ ( f
@ ^ [A: arrow_1429601828e_indi] : ( if_Pro1561232536_alt_o @ ( ord_less_nat @ ( h @ A ) @ ( plus_plus_nat @ n @ one_one_nat ) ) @ lab @ lba ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(149,axiom,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: ( produc1501160679le_alt > $o ) > $o,C: arrow_1429601828e_indi > $o] :
( ! [D: arrow_1429601828e_indi] :
( ( member2052026769e_indi @ D @ C )
=> ( member377231867_alt_o @ ( A @ D ) @ B ) )
=> ( member526088951_alt_o @ A
@ ( pi_Arr1929480907_alt_o @ C
@ ^ [D: arrow_1429601828e_indi] : B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_577_funcsetI) ).
thf(871,plain,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: ( produc1501160679le_alt > $o ) > $o,C: arrow_1429601828e_indi > $o] :
( ! [D: arrow_1429601828e_indi] :
( ( member2052026769e_indi @ D @ C )
=> ( member377231867_alt_o @ ( A @ D ) @ B ) )
=> ( member526088951_alt_o @ A
@ ( pi_Arr1929480907_alt_o @ C
@ ^ [D: arrow_1429601828e_indi] : B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(193,axiom,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi > produc1501160679le_alt > $o,C: arrow_1429601828e_indi > $o,D: arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o] :
( ( member526088951_alt_o @ B @ ( pi_Arr1929480907_alt_o @ C @ D ) )
=> ( ~ ( member377231867_alt_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member2052026769e_indi @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_PiE) ).
thf(1152,plain,
! [A: arrow_1429601828e_indi,B: arrow_1429601828e_indi > produc1501160679le_alt > $o,C: arrow_1429601828e_indi > $o,D: arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o] :
( ( member526088951_alt_o @ B @ ( pi_Arr1929480907_alt_o @ C @ D ) )
=> ( ~ ( member377231867_alt_o @ ( B @ A ) @ ( D @ A ) )
=> ~ ( member2052026769e_indi @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(16,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( suc @ zero_zero_nat ) )
= ( ( ( A
= ( suc @ zero_zero_nat ) )
& ( B = zero_zero_nat ) )
| ( ( A = zero_zero_nat )
& ( B
= ( suc @ zero_zero_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_add__is__1) ).
thf(427,plain,
! [A: nat,B: nat] :
( ( ( plus_plus_nat @ A @ B )
= ( suc @ zero_zero_nat ) )
= ( ( ( A
= ( suc @ zero_zero_nat ) )
& ( B = zero_zero_nat ) )
| ( ( A = zero_zero_nat )
& ( B
= ( suc @ zero_zero_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(383,axiom,
! [A: produc1501160679le_alt > $o,B: produc1501160679le_alt > $o] :
( ( ord_le97612146_alt_o
@ ^ [C: produc1501160679le_alt] : ( member214075476le_alt @ C @ A )
@ ^ [C: produc1501160679le_alt] : ( member214075476le_alt @ C @ B ) )
= ( ord_le97612146_alt_o @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_pred__subset__eq) ).
thf(1885,plain,
! [A: produc1501160679le_alt > $o,B: produc1501160679le_alt > $o] :
( ( ord_le97612146_alt_o
@ ^ [C: produc1501160679le_alt] : ( member214075476le_alt @ C @ A )
@ ^ [C: produc1501160679le_alt] : ( member214075476le_alt @ C @ B ) )
= ( ord_le97612146_alt_o @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(21,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
= ( ( ord_less_eq_nat @ A @ B )
| ( A
= ( suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_633_le__Suc__eq) ).
thf(442,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ ( suc @ B ) )
= ( ( ord_less_eq_nat @ A @ B )
| ( A
= ( suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(33,axiom,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_638_Suc__inject) ).
thf(486,plain,
! [A: nat,B: nat] :
( ( ( suc @ A )
= ( suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(123,axiom,
! [A: ( produc1501160679le_alt > $o ) > $o,B: ( produc1501160679le_alt > $o ) > $o] :
( ! [C: produc1501160679le_alt > $o] :
( ( member377231867_alt_o @ C @ B )
=> ( member377231867_alt_o @ C @ A ) )
=> ( ord_le1063113995lt_o_o @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508_subsetI) ).
thf(803,plain,
! [A: ( produc1501160679le_alt > $o ) > $o,B: ( produc1501160679le_alt > $o ) > $o] :
( ! [C: produc1501160679le_alt > $o] :
( ( member377231867_alt_o @ C @ B )
=> ( member377231867_alt_o @ C @ A ) )
=> ( ord_le1063113995lt_o_o @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(163,axiom,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_order__refl) ).
thf(940,plain,
! [A: nat] : ( ord_less_eq_nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(161,axiom,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_eq_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_linorder__not__less) ).
thf(935,plain,
! [A: nat,B: nat] :
( ( ~ ( ord_less_nat @ A @ B ) )
= ( ord_less_eq_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(157,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ A @ C ) )
= ( ord_less_eq_nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_add__le__cancel__left) ).
thf(923,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)],[157]) ).
thf(85,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_le__imp__less__Suc) ).
thf(659,plain,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ord_less_nat @ A @ ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(54,axiom,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_618_plus__nat_Oadd__0) ).
thf(560,plain,
! [A: nat] :
( ( plus_plus_nat @ zero_zero_nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(264,axiom,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,D: ( produc1501160679le_alt > $o ) > $o] :
( ( member616898751_alt_o @ B
@ ( pi_Arr1304755663_alt_o @ C
@ ^ [E: arrow_1429601828e_indi > produc1501160679le_alt > $o] : D ) )
=> ( ( member526088951_alt_o @ A @ C )
=> ( member377231867_alt_o @ ( B @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_funcset__mem) ).
thf(1416,plain,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > produc1501160679le_alt > $o,C: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o,D: ( produc1501160679le_alt > $o ) > $o] :
( ( member616898751_alt_o @ B
@ ( pi_Arr1304755663_alt_o @ C
@ ^ [E: arrow_1429601828e_indi > produc1501160679le_alt > $o] : D ) )
=> ( ( member526088951_alt_o @ A @ C )
=> ( member377231867_alt_o @ ( B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(79,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_lessE) ).
thf(639,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
=> ( ( B
!= ( suc @ A ) )
=> ~ ! [C: nat] :
( ( ord_less_nat @ A @ C )
=> ( B
!= ( suc @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(309,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq_nat @ A @ B )
=> ( ( ord_less_eq_nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_le__antisym) ).
thf(1681,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)],[309]) ).
thf(206,axiom,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
( ( member526088951_alt_o @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_mem__def) ).
thf(1184,plain,
! [A: arrow_1429601828e_indi > produc1501160679le_alt > $o,B: ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o] :
( ( member526088951_alt_o @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(340,axiom,
member526088951_alt_o @ p @ arrow_734252939e_Prof,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096P_A_058_AProf_096) ).
thf(1769,plain,
member526088951_alt_o @ p @ arrow_734252939e_Prof,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(104,axiom,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
= ( ? [C: nat] :
( B
= ( suc @ ( plus_plus_nat @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_664_less__iff__Suc__add) ).
thf(755,plain,
! [A: nat,B: nat] :
( ( ord_less_nat @ A @ B )
= ( ? [C: nat] :
( B
= ( suc @ ( plus_plus_nat @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(1919,plain,
$false,
inference(e,[status(thm)],[1718,1411,1237,1840,1179,777,1818,1549,1586,1501,1823,1190,1168,760,1554,1110,1855,408,1401,1205,878,1793,1158,762,614,1692,1756,550,1735,797,1872,1233,814,945,538,1222,1867,500,747,913,1095,1196,1835,1576,417,1366,1529,436,1703,1228,1254,1760,785,1511,1826,587,1323,619,1545,1800,1087,1147,1247,1013,1741,1115,1773,448,1778,606,1347,1664,789,1811,1373,1109,1858,514,806,1581,1418,623,1136,834,1843,397,734,453,774,1394,1526,1351,411,1405,1201,1242,1215,634,661,1199,1783,512,942,439,1768,1868,1730,1163,1723,862,1174,1751,1883,825,1343,1217,598,1824,1370,1837,852,1888,1687,461,1787,493,1128,1392,1106,916,467,566,484,874,725,403,1672,1540,1878,1138,593,869,1397,742,578,783,1118,1659,1739,476,1810,1207,637,1584,547,1744,1099,1150,1382,1131,1192,911,1852,1874,569,1720,503,647,1776,1831,1231,792,938,1695,541,1170,1187,1515,1895,794,718,926,1727,425,1103,1219,1747,573,1374,1754,430,819,1833,423,843,772,1701,1520,413,584,1154,1256,1226,391,1669,445,787,1865,1733,1092,1258,1224,1675,1765,1090,764,1194,1209,406,831,1408,1542,1144,737,1122,1376,1574,419,509,649,434,811,631,758,858,535,816,609,1862,1022,1177,932,848,520,1556,769,827,1245,780,1015,394,563,1496,1805,1594,1699,1726,1364,1250,1413,722,490,1684,749,617,1340,1018,553,1758,1166,1203,589,1181,823,836,1551,525,855,1252,739,1368,1780,1531,1098,1547,1748,557,1770,1499,1813,1869,840,1235,1679,1738,544,1790,1716,1538,808,744,656,600,1506,864,1504,595,1240,1898,1849,1141,1536,497,876,845,1421,627,450,482,671,581,1517,1126,1807,1010,1390,1590,1385,517,1508,652,390,1523,1558,1861,1689,667,929,478,1212,1661,1893,716,1161,800,752,1578,854,867,603,918,1816,506,1561,664,400,1891,720,1172,1410,767,728,464,1829,1827,1378,644,850,1431,1902,871,1152,427,1885,442,486,803,940,935,923,659,560,1416,639,1681,1184,1769,755]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.14 % Problem : SCT171^2 : TPTP v8.2.0. Released v5.3.0.
% 0.10/0.14 % Command : run_Leo-III %s %d THM
% 0.14/0.37 % Computer : n001.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Sat Jun 22 09:34:24 EDT 2024
% 0.14/0.37 % CPUTime :
% 1.03/0.96 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.45/1.36 % [INFO] Parsing done (403ms).
% 2.45/1.37 % [INFO] Running in sequential loop mode.
% 3.22/1.60 % [INFO] eprover registered as external prover.
% 3.22/1.61 % [INFO] Scanning for conjecture ...
% 3.58/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 703 axioms. Running axiom selection ...
% 4.14/1.85 % [INFO] Axiom selection finished. Selected 387 axioms (removed 316 axioms).
% 4.58/2.04 % [INFO] Problem is higher-order (TPTP THF).
% 4.87/2.06 % [INFO] Type checking passed.
% 4.87/2.06 % [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 ...
% 17.57/5.24 % External prover 'e' found a proof!
% 17.57/5.24 % [INFO] Killing All external provers ...
% 17.57/5.24 % Time passed: 4684ms (effective reasoning time: 3866ms)
% 17.57/5.24 % 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)>
% 17.67/5.25 % Axioms used in derivation (387): fact_523_in__below, fact_82__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_, fact_509_subsetI, fact_566_add__le__mono1, fact_673_Suc__neq__Zero, fact_679_less__eq__Suc__le__raw, fact_184_inv__f__eq, fact_395_add__less__le__mono, fact_667_one__is__add, fact_556_le__eq__less__or__eq, fact_74__096Lba_A_058_ALin_096, fact_180_pred__equals__eq2, fact_493_pred__subset__eq, fact_572_termination__basic__simps_I2_J, fact_684_inc__induct, fact_84_n_I2_J, fact_67_less__top, fact_218_PiE, fact_663_less__eq__Suc__le, fact_199_PiE, fact_616_neq0__conv, fact_111_ord__less__eq__trans, fact_95_order__less__asym, fact_626_ex__least__nat__le, fact_689_Suc__le__D, fact_544_below__Lin, fact_622_le__0__eq, fact_646_less__Suc__eq, fact_422_add__le__imp__le__left, fact_471_set__rev__mp, fact_541_eq__imp__le, fact_323_order__less__le__trans, fact_76__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096, fact_235_xt1_I5_J, fact_578_funcsetI, fact_643_add__Suc, fact_318_xt1_I11_J, fact_284_order__le__less, fact_540_nat__le__linear, fact_442_subsetD, fact_210_PiE, fact_160_order__less__irrefl, fact_156_linorder__neq__iff, fact_388_inv__into__f__eq, fact_214_PiE, fact_421_one__reorient, fact_304_linorder__antisym__conv2, fact_225_order__refl, fact_585_Pi__I_H, fact_6__C2_C, fact_405_pred__subset__eq2, fact_559_less__or__eq__imp__le, fact_528_nat__neq__iff, fact_22_Pair__eq, fact_648_not__less__less__Suc__eq, fact_624_add__gr__0, fact_664_less__iff__Suc__add, fact_551_add__less__mono1, fact_428_add__le__cancel__right, fact_0_assms_I3_J, fact_644_add__Suc__right, fact_79__096_Ib_M_Aa_J_A_126_058_ALab_096, fact_209_PiE, fact_169_mem__def, fact_420_ab__semigroup__add__class_Oadd__ac_I1_J, fact_535_nat__add__left__commute, fact_653_less__SucE, fact_470_set__mp, fact_693_nat_Oexhaust, fact_41_iso__tuple__UNIV__I, fact_512_psubsetD, fact_558_le__neq__implies__less, fact_309_order__le__imp__less__or__eq, fact_670_less__Suc0, fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, fact_3__096P_A_058_AProf_096, fact_191_PiE, fact_650_less__SucI, fact_529_linorder__neqE__nat, fact_415_add__right__imp__eq, fact_476_set__rev__mp, fact_504_subsetI, fact_666_less__add__Suc1, fact_676_Suc__not__Zero, fact_263_order__eq__iff, fact_613_gr0I, fact_416_add__imp__eq, fact_135_order__less__imp__not__eq2, fact_419_add__left__cancel, fact_189_PiE, fact_517_psubsetD, fact_40_iso__tuple__UNIV__I, help_If_2_1_If_000_062_Itc__prod_Itc__Arrow____Order____Mirabelle____lcilvlkkzv_, fact_29_top1I, fact_534_nat__add__commute, fact_287_linorder__antisym__conv1, fact_659_Suc__leI, fact_637_Suc__leD, fact_524_add__leE, fact_617_not__less0, fact_561_le__add1, fact_623_less__eq__nat_Osimps_I1_J, fact_627_less__imp__add__positive, fact_553_less__add__eq__less, fact_386_inv__into__f__f, fact_75__096a_A_126_061_Ab_096, fact_28_top1I, fact_649_less__antisym, fact_21_Pair__inject, fact_668_add__is__1, fact_542_le__trans, fact_207_PiE, fact_333_order__le__less__trans, fact_20_injh, fact_43_iso__tuple__UNIV__I, fact_594_inj__on__cong, fact_487_in__mono, fact_174_mem__def, fact_660_le__imp__less__Suc, fact_228__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_, fact_168_mem__def, fact_193_PiE, fact_508_subsetI, fact_625_ex__least__nat__less, fact_573_termination__basic__simps_I1_J, fact_232_xt1_I6_J, fact_661_Suc__le__eq, fact_372_Pi__mem, fact_208_PiE, fact_373_Pi__mem, fact_374_Pi__mem, fact_88_mkbot__Lin, fact_292_order__neq__le__trans, fact_557_less__imp__le__nat, fact_654_Suc__lessD, fact_71_assms_I1_J, fact_615_less__nat__zero__code, fact_197_PiE, fact_90_const__Lin__Prof, fact_612_le0, fact_569_less__mono__imp__le__mono, fact_598_card__bij, fact_631_Suc__n__not__le__n, fact_204_PiE, fact_391_Pi__I, fact_539_le__refl, fact_274_order__less__le, fact_582_Pi__cong, fact_527_less__not__refl, fact_563_nat__add__left__cancel__le, fact_549_trans__less__add1, fact_463_set__mp, fact_671_less__Suc__eq__0__disj, fact_433_add__strict__right__mono, fact_696_surjh, fact_662_less__Suc__eq__le, fact_23_IIA__def, fact_638_Suc__inject, fact_642_add__Suc__shift, fact_614_gr__implies__not0, fact_213_PiE, fact_188_dictatorI, fact_669_gr0__conv__Suc, fact_435_add__less__cancel__right, fact_179_in__above, fact_635_le__SucI, fact_32_UNIV__I, fact_576_funcsetI, fact_581_Pi__cong, fact_468_set__mp, fact_298_leD, fact_552_add__less__mono, fact_543_le__antisym, fact_568_mono__nat__linear__lb, fact_565_trans__le__add2, fact_219_PiE, fact_59_not__top__less, fact_247_ord__le__eq__trans, fact_127_order__less__asym_H, fact_554_add__lessD1, fact_628_lessI, fact_619_Nat_Oadd__0__right, fact_564_trans__le__add1, fact_503_Pi__mono, fact_394_less__add__one, fact_181_n_I3_J, fact_87_mktop__Lin, fact_620_add__is__0, fact_123_xt1_I9_J, fact_579_linear__alt, fact_206_PiE, fact_170_mem__def, fact_367_inj__on__contraD, fact_687_Suc__eq__plus1__left, fact_86_Lin__irrefl, fact_107_xt1_I2_J, fact_497_pred__subset__eq, fact_532_less__not__refl3, fact_390_Pi__I, fact_478_set__rev__mp, fact_640_Suc__n__not__n, fact_425_add__left__mono, fact_297_xt1_I12_J, fact_338_xt1_I8_J, fact_192_PiE, fact_173_mem__def, fact_645_not__less__eq, fact_360_top__le, fact_501_Pi__mono, fact_538_nat__add__right__cancel, fact_555_nat__less__le, fact_241_order__antisym, fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J, fact_618_plus__nat_Oadd__0, fact_380_dictator__def, fact_500_pred__subset__eq, fact_548_nat__add__left__cancel__less, fact_652_less__trans__Suc, fact_265_linorder__linear, fact_267_linorder__not__less, fact_8__C4_C, fact_4_in__mkbot, fact_429_add__less__imp__less__left, fact_227__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I, fact_2__096c_A_126_061_Ad_096, fact_195_PiE, fact_398_injI, fact_103_order__less__trans, fact_656_One__nat__def, fact_533_nat__less__cases, fact_151_less__imp__neq, fact_371_inj__onD, fact_655_Suc__less__SucD, fact_35_UNIV__I, fact_352_top__unique, fact_171_mem__def, fact_443_subsetD, fact_139_order__less__imp__not__eq, fact_205_PiE, fact_250_xt1_I3_J, fact_665_less__add__Suc2, fact_641_n__not__Suc__n, fact_314_order__le__neq__trans, fact_518_psubsetD, fact_577_funcsetI, fact_418_add__right__cancel, fact_83__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk, fact_115_xt1_I1_J, fact_382_inj__eq, fact_516_psubsetD, fact_574_termination__basic__simps_I5_J, fact_99_xt1_I10_J, fact_375_Prof__def, fact_85_notin__Lin__iff, fact_194_PiE, fact_651_Suc__lessI, fact_639_nat_Oinject, fact_678_Zero__not__Suc, fact_547_not__add__less2, fact_546_not__add__less1, fact_77__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096, fact_402_Pi__anti__mono, fact_256_order__antisym__conv, fact_677_nat_Osimps_I2_J, fact_424_add__mono, fact_575_in__rel__def, fact_621_add__eq__self__zero, fact_379_funcset__mem, fact_24_unanimity__def, fact_229_linorder__le__cases, fact_182__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am, fact_426_add__right__mono, fact_33_UNIV__I, fact_1_u, fact_155_not__less__iff__gr__or__eq, fact_9_pairwise__neutrality, fact_152_linorder__neqE, fact_14_PW, fact_698__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123, fact_629_Suc__mono, fact_467_set__mp, fact_675_nat_Osimps_I3_J, fact_695_nat__induct, fact_269_linorder__le__less__linear, fact_550_trans__less__add2, fact_692_not0__implies__Suc, fact_143_order__less__imp__not__less, fact_691_Suc__lessE, fact_560_le__add2, fact_484_in__mono, fact_253_ord__eq__le__trans, fact_475_set__rev__mp, fact_328_xt1_I7_J, fact_588_card__inj, fact_15_split__paired__All, fact_584_Pi__I_H, fact_567_add__le__mono, fact_583_Pi__I_H, fact_432_add__strict__left__mono, fact_536_nat__add__assoc, fact_633_le__Suc__eq, fact_537_nat__add__left__cancel, fact_611_less__zeroE, fact_19_n_I1_J, fact_632_not__less__eq__eq, fact_186_inv__f__f, fact_580_Pi__cong, fact_389_Pi__I, fact_485_in__mono, fact_686_gr0__implies__Suc, fact_694_zero__induct, fact_592_inj__onI, fact_7__C1_C, fact_674_Zero__neq__Suc, fact_531_less__not__refl2, fact_438_subsetD, fact_5_in__mktop, fact_630_zero__less__Suc, fact_525_add__leD1, fact_647_Suc__less__eq, fact_172_mem__def, fact_634_Suc__le__mono, fact_198_PiE, fact_430_add__less__imp__less__right, fact_445_subsetD, fact_212_PiE, fact_688_Suc__eq__plus1, fact_595_finite__indi, fact_571_termination__basic__simps_I4_J, fact_657_Suc__le__lessD, fact_434_add__less__cancel__left, fact_344_top__greatest, fact_81__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_, fact_365_inj__on__def, fact_396_add__le__less__mono, fact_119_ord__eq__less__trans, fact_480_in__mono, fact_183__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am, fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk, fact_685_less__imp__Suc__add, fact_154_linorder__less__linear, fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai, fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, fact_285_leI, fact_220_complete__Lin, fact_279_less__le__not__le, fact_73__096Lab_A_058_ALin_096, fact_526_add__leD2, fact_511_subsetI, fact_530_less__irrefl__nat, fact_196_PiE, fact_369_inj__on__iff, fact_417_add__left__imp__eq, fact_80_PiProf, fact_10__C3_C, fact_519_psubsetD, fact_200_PiE, fact_431_add__strict__mono, fact_238_order__trans, fact_91_linorder__cases, fact_427_add__le__cancel__left, fact_147_order__less__not__sym, fact_286_not__leE, fact_690_lessE, fact_303_order__less__imp__le, fact_244_xt1_I4_J, fact_190_PiE, fact_260_order__eq__refl, fact_78__096_Ia_M_Ab_J_A_126_058_ALba_096, fact_423_add__le__imp__le__right, fact_562_le__iff__add, fact_636_le__SucE, fact_393_inj__imp__inv__eq, fact_268_linorder__not__le, fact_570_termination__basic__simps_I3_J, fact_378_funcset__mem, fact_658_le__less__Suc__eq, fact_498_pred__subset__eq, fact_153_linorder__antisym__conv3, fact_384_injD, fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, fact_409_subset__UNIV, fact_131_order__less__imp__triv, fact_211_PiE, fact_89_above__Lin, fact_377_funcset__mem, fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0
% 17.67/5.25 % No. of inferences in proof: 778
% 17.67/5.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4684 ms resp. 3866 ms w/o parsing
% 18.48/5.47 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.48/5.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------